X-ray excited photoelectron spectra of free molecules containing oxygen

Journal of Electron Spectroscopy and Related Phenomena, Elsevier Science Publishers B.V., Amsterdam

56 (1991) 117-164

X-RAY EXCITED PHOTOELECTRON SPECTRA MOLECULES CONTAINING OXYGEN

D. NORDFORS*, A. NILSSON, N. MARTENSSON, Institute

of Physics,

University

117

OF FREE

S. SVENSSON and U. GELIUS

of Uppsala, Box 530, S-751 21 Uppsala (Sweden)

H. AGREN Institute

of Quantum

Chemistry,

University

of Uppsala, Box 518, S-751 20 Uppsala (Sweden)

(First received 21 June 1990; in final form 4 September 1990)

ABSTRACT High resolution X-ray excited photoelectron spectra (XPS) of carbonyl- and hydroxyl-containing compounds are presented and discussed in terms of electronic structure theory. The results presented comprise 01s binding energy shifts, core hole shake-up/shake-off, inner-valence and outer-valence spectra. New features are analyzed by means of computational data, and various examples are given where XPS valence spectra aid a molecular orbital analysis. Emphasis is put on similarities and differences between spectra within series of compounds containing identical, hydroxyl or carbonyl, functional groups. Characteristic structures that fingerprint these compounds have been unravelled. The spectra have been investigated in terms of a simple scheme for XPS analysis. The spectra are divided into five regions, which are described within a hierarchy of approximation levels. Following this scheme, basic similarities and differences in theoretical XPS analysis of the different energy regions are identified, e.g. the character of wave functions, the roles of relaxation and electron correlation, the dominant factors in the intensity analysis and the role of orbital interpretations. Particular emphasis has been put on the analysis of the 01s shakeup spectra of the carbonyl-containing compounds. Some of these display strong shake-up peaks due to charge-transfer excitations. Analysis of these features has been carried out by means of MCSCF calculations as well as by a simple orbital model. The energetics and character of shakeup transitions involving acceptor and donor groups are established by the model, and have been further verified by the MCSCF calculations. Except for the carbonyl spectra, a few of the spectra presented have been selected for a more detailed analysis. These are the valence spectra of carbon monoxide and benzaldehyde and the core electron shake-up spectrum of water.

CONTENTS

1. Introduction................................................................................................... 2. Experimental ................................................................................................. 3. A systematic scheme for analysis of XPS spectra ...................................... 3.1. Approximation levels for analysis of XPS spectra .............................. ‘Also at Institute of Quantum Chemistry.

0368-2048/91/$03.50

0 1991-

Elsevier Science Publishers B.V.

118 120 121 121

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3.2. Character of singly-charged molecular ions ........................................ 4. Binding energy shifts .................................................................................... 5. Shake-up ........................................................................................................ 5.1. Description of spectra ............................................................................ 5.2. General remarks ..................................................................................... 5.3. Charge transfer shake-up in carbonyls ................................................ 5.4. Assignments of carbonyl shake-up spectra .......................................... 5.4.1. Computational details .................................................................. 5.4.2. Carbon monoxide ......................................................................... 5.4.3. Formaldehyde ............................................................................... 5.4.4. Acetaldehyde ................................................................................. 5.4.5. Acetone .......................................................................................... 5.5. Oxygen core electron shake-up spectra of alcohols ............................. 6. Valence X-ray photoelectron spectra .......................................................... 6.1. Valence X-ray photoelectron spectrum of CO ..................................... 6.2. Valence XPS spectra of alcohols and aldehydes ................................. 7. Conclusions .................................................................................................... Acknowledgements ............................................................................................. References ..........................................................................................................

123 128 133 133 136 140 143 143 144 146 147 148 149 154 154 158 161 162 162

1. INTRODUCTION

Even twenty years ago, at the time of the first monograph about electron spectroscopy of free molecules [ 11,X-ray excited photoelectron spectroscopy showed great potential for extracting information on important properties of molecules. Since that time many of the early prospects of the experiment have been realized and X-ray excited photoelectron spectra have been developed, in a variety of contexts, as powerful tools for analysis of electronic and conformational structures of molecular ions as well as for studies of the dynamics of the photoionization process itself. The refinement in spectral quality and spectral analysis has been based on the experimental development that has taken

place. The signal-to-background ratio in X-ray excited photoelectron spectroscopy has been increased by at least two orders of magnitude [2] and the resolution has been improved to a few tenths of an eV, making it possible to detect vibrational states in the core photoionization process [3] as well as conjugate and double shake-up processes [ 2 J. The determination of binding energies has, at least on a relative scale, been made within a few hundredths of an eV, which has made it possible to study not only the direct binding energy shift of a core level but also secondary shifts and substituent effects [ 4,5]. Recent developments of synchrotron radiation sources have opened a large field of research on the outer- and inner-valence electron structure of molecules and in particular it has become possible to study resonance phenomena.

119

During the last few years high energy monochromators have widened the scope of applications also for studies of core levels with synchrotron radiation. The development of theoretical methods to describe the photoelectron process has been progressing in parallel with the improved quality of the experiments. Advanced methods that go beyond the independent particle model have been introduced and diversified to study many aspects of phenomena associated with XPS photoionization. Assignments of spectra in terms of spin and spatial symmetry, molecular orbital theory and local decomposition of electron densities have been carried out. Difficult problems referring to continuum resonances and multiple excitation satellites, vibronic coupling and excitations, breakdown of the molecular orbital and Born-Oppenheimer approximations, are phenomena or effects that have all been studied. To this end the development of modern computer technology has often made such studies feasible in practice, at least for a class of smaller molecules. It is interesting to notice that despite the progress made, several fundamental aspects of X-ray photoelectron spectra from molecules remain to be investigated. The multiple excitations in the photoionization process, in particular the core electron shake-up phenomenon, are still not well understood. Only recently has it become experimentally possible to prove the interaction between discrete multiply-excited ionized states and the underlying continuum states that form shake-off resonances [6,7]. While calculation of ionization potentials and other properties have become a matter of routine, the theory for a state-by-state analysis of well resolved shake-up spectra still does not provide unambiguous assignments and lags behind the experiments. A fundamental experimental quantity such as the core level chemical shift is not investigated in detail. A large number of reports have dealt with Cls and Nls core level binding energy shifts, but it is perhaps a bit surprising to notice that 01s core level binding energy data are relatively sparse in the literature. Even in ref. I it was observed that the 01s shifts did not correlate well with the shifts calculated from ground state properties of the molecule. In this paper we present high resolution X-ray photoelectron spectroscopy data - inner valence spectra, shake-up spectra and core level shifts - for a number of molecules containing oxygen as a heteroelement. We focus on the description of various structures in the spectra in terms of molecular orbital or related electronic structure theory. Emphasis is put on the study of similarities between the spectra from related compounds, and to what extent observations can be used to “fingerprint” the compounds. Simple alcohols and carbonyl species are used as illustrative examples. We use existing and new computational data in this analysis, and choose some prototype spectra for more detailed analyses. An effort to systemize analysis of XPS spectra is presented in the form of a short scheme where the spectra are divided into five different energy regions. The theoretical analysis of the regions is described at seven hierarchical approximation levels, Before analysing the spectra we present some

120

experimental details behind the present data. In the subsequent sections we summarize the analysis of each particular region with respect to the approximation levels. The analysis includes the characteristics of final state wave functions, dominant factors in the intensity analysis, the role of orbital interpretations and of orbital relaxation, the role of initial versus final state correlation and of static versus dynamic correlation, and very briefly, the conditions for calculating the spectra. The core electron shake-up spectra of some carbony1 and hydroxyl containing compounds are analyzed, and a corresponding analysis is presented for the valence spectra. For the carbonyl shake-up spectra analyses are presented both in terms of a simple orbital model and in terms of MCSCF calculations. We perform a computational analysis of the valence spectrum of benzaldehyde. The new highly resolved XPS spectra of CO {valence region) and Hz0 (core region) are scrutinized in terms of the analysis scheme presented and using computational data. Other spectra are analyzed in general terms. 2. EXPERIMENTAL

Monochromatic exciting radiation is of great importance when performing gas-phase X-ray photoelectron spectroscopy. For standard X-ray anodes the natural linewidth of suitable characteristic lines, such as Mg Ka! or Al Ka, limits the resolution to = 0.8 eV. The presence of the X-ray satellites makes the interpretation of weak structures difficult and the bremsstrahlung continuum limits the signal to background ratio. The outer valence electron region of molecules is studied with the highest precision using supersonic molecular beams and ultraviolet photoelectron spectroscopy, usually performed with He resonance lamps as excitation sources. In the inner valence region tunable synchrotron radiation is used to produce spectra of high quality where a variety of resonance phenomena can be studied. However, the use of monochromatized X-rays from a rotating aluminium anode has so far proved to be the most convenient method for obtaining high quality spectra of the inner valence region, fulfilling the sudden approximation. Since current theoretical models are often limited to this approximation, X-ray photoelectron spectroscopy is an important method in the study of the inner valence electron structure of molecules and atoms. The same applies to the study of the core shake-up phenomenon. In this case the weak shake-up structures usually have intensities ranging from a few percent of the main line down to the detection limit, which is about 0.01% of the main lines. The high signal to background ratio, > 10 000/l, obtainable with monochromatized Xray excitation, permits the detection of weak double and triple shake-up events B1. The measurements in this work were carried out on an ESCA instrument equipped with a water-cooled aluminium rotating anode. Monochromatic Al

121

Ka radiation (1487 eV) was obtained by means of Bragg reflection in the (100) planes of a-quartz crystals. A more extensive description of the instrument has been published elsewhere [91. The spectrometer resolution was 0.40.6 eV. Samples of 99% purity were obtained commercially. Effects due to inelastic scattering of the photoelectrons were checked for water, methanol, phenol and benzyl alcohol by comparing spectra corresponding to different gas cell pressures. Phenol and benzyl alcohol were also run in a mixture with Ne. Thus the inelastic spectra of these compounds could be studied in the Ne2p spectrum without interference from overlapping shake-up states, which are present in the 01s and Cls spectra. In the case of the aromatic X-Z* excitations this is crucial, since the shake-up and inelastic scattering states are of almost identical character [lo]. All tests indicated that the inelastic scattering effects are negligible at the pressures used in this investigation. 3. A SYSTEMATIC

SCHEME FOR ANALYSIS OF XPS SPECTRA

In order to put the analysis of the present XPS spectra into context, we perform a systematization of theoretical XPS analysis. We divide the XPS spectra into five main regions, I-V, and the theoretical analysis into seven approximation levels, A-G. The analysis of the spectra is conducted in terms of these approximation levels and the spectral division, using both existing and new computational data. We confine ourselves to the spectral phenomena presented in this work, namely ionization energies and intensities in the limit of high-energy excitation. Spectral fine structure and effects due to vibronic excitations and interaction, angular distributions, or lifetime, etc., are ignored. 3.1. ApproGnation

levels for analysis of XPS spectra

The theoretical description of photoionization energies and cross-sections in the X-ray region can be described by the following hierarchy of approximations: A Dipole transition in an N-electron system according to Fermi’s golden rule B Static exchange, strong orthogonality, approximation for the outgoing electron C Neglect of conjugate transitions D Neglect of photoelectron matrix elements E Neglect of initial state correlation (ISCI ) F Neglect of final state correlation (FSCI ) G No self-consistent description (orbital orthogonality ) This approximation scheme should be interpreted as follows. Each entry introduces an approximation and the corresponding approximation level con-

122

tains this approximation as well as the previous ones. Thus at approximation level F, approximations A-F are employed. This scheme is merely intended as an aid in summarizing XPS analysis, and is not exact. For atomic species there are scattering theory approaches that go beyond level A, although ofton with other simplifying assumptions. Furthermore, there are possible alternative combinations of the approximations (e.g., E and G).Another exception is absolute cross sections, which require a straight evaluation of the orbital matrix elements between the molecular orbit& and the orbital describing the outgoing photoelectron {ho It^l&>, at level D, while approximations E, F and G still can be undertaken. Nevertheless, the scheme covers the mainstream of XPS analysis. A, B and C are all excellent approximations for XPS, while B and C break down at threshold excitations. Approximation level D is commonly referred to as the sudden approximation, and approximation level G matches Koopmans approximation for energies, In terms of the approximation levels presented, we study below the main character of five energy regions in XPS spectra. We focus in particular on how the important matrix elements TM0 or GM0 (defined below) contribute to the spectral intensity, the role of final state correlation (FSCI) and initial state correlation (ISCI), the need for orbital optimization, and the character of the final state wave functions, in terms of hole-particle excitations. The different characteristics are summarized in Table 1. Five different approximation levels describe the regions: I-G, II++C,III-E, IV*F, and V-D. At level C the photoionization cross sections are expressed as I=M2=~~TMo~GMO~2

(1)

MO

where we denote TM0 as the orbital element and GM0 as the generalized overlap amplitude ( GOA) ~Mo=~~Mol&&)

(2)

GMO= (‘Y,(N-l)(&oIygs(N))

(3)

TABLE 1 Photoionization energies and cross sections IC T MO*GM0( in different regions for XPS spectra MO

Spectral region I II III IV V

Outer valence Hole-mixing Inner valence Main core hole Core shake-up

Important matrix element

TM0 &%o GMo T Mo GMO

.Ghno

Character of wave function

FSCI

ISCI

Orbital optimum

Approx. level

Ih

No Yes Yes

No Yes No

No

G C E F D

2hlp lhS2hlp lh 2hlp+3h2p+...

No

No

Yes

Yes

Yea

Yes

Here v,(N) and ?P#Y- I) are the ground state and the final ionic state wave functions, respectively, &o the annihilation operator, and t the one-electron dipole operator. The continuum orbital describing the photoelectron is denoted Qleand Q,Mo is a molecular orbital of the initial state. The above expression follows from the Fermi golden rule in the dipole approximation, with a strong orthogonality condition for the outgoing photoelectron (4)

%(N)=%(N--l)@QI, The pho~lectron is thus described which are assumed not to correlate approximation (B ) ). Furthermore, strong o~hogon~ity condition, are can be found in refs. l&l2 and 13. 3.2. Ckmzcter

by the lentil of the IV-- 1 electrons, with the photoelectron {static exchange conjugate transitions, introduced by the ignored ~approximation C ). Derivations

ofsingly-charged moZecuhr ions

A photoelectron spectrum can be divided into five regions labelled by the character of the singly-charged states (the approximate ioni~tion energies for first row elements are indicated): I

II III

IV V

Koopmans states ( KSs ) Hole-mixing states States where the orbital picture breaks down Main core hole states Core electron shake-up states

10-20 eV 20-35 eV 35-45 eV 200
The energy limits shown for the spectral regions are relevant for most first row molecules, diatomics and triatomics, For larger molecules, or for high 2 elements, the limits are shied somewhat, but the overall charac~rs of the states still remain, Spectra in all regions grow ~creasingly more complex with the size of the molecules, especially when any element of symmetry is lacking, To mention one exception, counter-examples to the classification of region I as free of satellites have very recently been given by Wardermann and von Niessen [ 14 1. Even so, many spectral similarities may be found in the spectra for series of analogous molecules. Examples of this are the 01s shake-up spectra of hydroxyl and carbonyl compounds presented in this work. I This region contains fairly intense and well-resolve st~ct~es mainly described by ionization of 2~-carting outer-valence orb&a&. They are referred to as Koopmans states (KSs) and are dominated by l-hole f lh ) conjurations (Koopmans con~~ations (KCs) ). They are described by an independent particle and molecular orbital picture, with a one-to-one correspondence between peaks and molecular orbit&. Thus their description follows ordinary Region

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molecular orbital theory. The outer valence region is well treated at level G by Koopmans theorem. Intensity evaluation can be obtained by M2, where M is truncated to one orbital index M=M,,

=

TMO

*(ho

The second element, the GOA, is close to one, since the final wave function is dominated by a single hole configuration. One can therefore set GMo= cMo9 where cMo is the coefficient for the leading (l-hole) configuration in the final state wave function [ 111. The modulation of this GOA, due to dynamical correlation effects, is weak and not significantly different for different Koopmans states. The relaxation effects are rather uniform but of opposite sign compared to the correlation energy, i.e., the F and G approximations counteract, which is a reason for the success of Koopmans theorem (the correlation contribution is negative since one valence electron is missing in the final state). For these reasons the intensity follows TMo9the orbital element, rather than GM*. For XPS the relative cross sections ( MS0 ) can be simplified as regards both &, e.g., using the plane-wave approximation, and ho, by means of atomic or LCAO decompositions [ 2 1. The usefulness of the LCAO decomposition is demonstrated below for benzaldehyde, where it is used to evaluate the XPS intensities. The absolute value of the orbital element might require more sophisticated calculations (e.g., variational ones) due to the rapidly oscillating nature of high energy photoelectron waves. Region II The wave functions of the states corresponding to the structures in the second region are dominated by hole-particle excitation components in their wave functions. Only weak mixing occurs with the main hole-configurations (KCs ) , which dominate the states in the first region. The states are often referred to as “correlation state satellites”, or “hole-mixing states” [ 15,161 as we also call them here. A complex excitation energy dependence, also for high excitation energies, is present due to the mixing of main hole configurations. The holemixing region is difficult to analyze, since the peaks do not correspond to molecular orbitals in the same simple way as in the case of the outer valence region. The wave function has a dominating two-hole one-particle (2hlp) character with only small mixings, cMo, of the main Koopmans configuration. In order to describe the 2hlp components the final state wave function has to include correlation, i.e., one has to apply approximation level E. At that level G = CM0as above (strictly only for frozen orbitals) , the only difference is thz cMo has a small value close to 0 rather than close to 1. However, the initial ground state should also include correlation, for the same reasons as for the core electron shake-up phenomenon (see below). This is due to the fact that

125

Thus the calculation of the generalized overlap amplitude for these states resembles that for core electron shake-up states. There is one simplification with respect to core electron shake-up, however. The set of orbitals does not have to be self-consistently optimized, since the small relaxation energy can be picked up by a larger configurational expansion, leading to simpler evaluations and interpretations of the GOA. On the other hand, there is also one complication with respect to core electron shake-up in the sense that more than one KC mix in the final state wave function [ 15,161. This implies that several GMos (GOAs), and also several TMos for different orbital indices have to be evaluated. Thus approximation level C has to be applied, not because the TMos are varying with energy, but simply because there are more than one KC. In practical calculations this demands more than discrete state calculations, since the continuum orbital for the photoelectron has to be optimized to obtain the TMos. One partial solution of the problem is simply to approximate TMo -

to JIi/GMo, where I’ is the intensity of the ith Koopmans state, and GMo is the corresponding GOA (which can even be set equal to 1 by virtue of the similar GMos of the KSs). However, the problem of the phases of the TMos remains. Due to the mixing of several KCs in the wave function, intensities of these hole-mixing states do not covary with any of the Koopmans states in region I. Because of different amplitudes and phases for the TMos there may also be a complex excitation energy dependence for the intensities, something which, at least in principle, can be used to figure out their orbital character and symmetry. Again, if there is only one KC, the photoelectron intensity reduces to cMo9the configuration coefficient for the KC (equal to the pole strength of the Greens function in the Tamm-Dancoff approximation) [ 111. In that case the intensities covary with the respective Koopmans state in region I. Such covariance may thus reveal both symmetry and orbital character for the states. Region III The complex inner valence region retains the dominance of a main hole configuration (KC), but now with 2s holes. However, the same hole-configuration is distributed over more than one electronic state of the ion. Thus there is no one-to-one correspondence between orbitals and ionization peaks, hence, the concept of breakdown of the molecular orbital model [ 17-201. There is a considerable enhancement of intensity in XPS with respect to the previous hole-mixing region, with the intensity being comparable to that in the outer valence region. Often the high intensity reflects the 2s character of the states. A strong domination of the Koopmans one-hole (2s-hole ) configuration (KC ) is present. As for the outer valence, the relative intensities are guided by the overlap amplitude GMO,and are well approximated by the coefficient for the leading KC, cMO.Thus approximation level E applies. The difference in comparison to the outer valence is that the KC is distributed over several states

126

(breakdown of the MO picture). The breakdown can be understood from the fact that the inner hole is resonant with double excitations, where one negative excitation fills the hole while a positive excitation promotes another electron to an empty level. As a result of the strong coupling (so-called semi-internal configuration interaction) many eigenstates with non-negligible intermixing with the KC will gather in a relatively small energy interval. In the hole-mixing region the 2hlp configurations are energetically possible, but they are still not degenerate with the inner valence KCs. Due to the large KC intermixing, approximation level E is acceptable for relative intensities in the inner valence region, i.e., neglect of initial state correlation. As a rule, initial and final states should be treated on an equal footing. This is the case when the dynamic correlation dominates, as in the hole-mixing region or the core electron shake-up region. However, when there is strong static correlation in one state (the final state), as is the case in the inner valence region or, for example, in the case of Auger emission in molecules, one can adopt a separate treatment of the initial and final states. The splitting of the states in the inner valence region is sensitive to the nature of lh-2hlp interactions. In some cases, as in water, one state dominates. Since static correlation, just like relaxation, always gives rise to a positive error (in contrast to the dynamical error which is negative ) , Koopmans theorem fails badly also in these cases. The inner valence region (III) thus appears to be simpler than the hole-mixing region (II) but more complex than the outer valence region (I). There are, however, two more hidden complexities. One is that the onsets of double ionization thresholds and continua blur structure towards higher energies and may introduce couplings between discrete states and continuum states. The other complexity is the occurrence of vibronic coupling [21]. Although such coupling appears in the outer valence region, for example between the B and C states in the COz photoelectron spectrum in Fig. 15, they are more important in the inner valence region due to the high density of states. In fact, the conditions for breakdown of the MO picture and the BO (Born-Oppenheimer) pictures go hand in hand. For exampIe, it was shown in ref. 22 that a diabatic representation of the inner valence states of acetylene gave better results than the usual adibatic one. Region IV The main core hole peaks are well separated from other states, and fit well with a l-hole configuration and an orbital description. Analysis of the main core hole region resembles that of the outer valence, albeit with some differences. The major one is the role of relaxation, which contributes lo-30 eV in energy [23]. Here approximation level F applies. The character of the corehoIe state wave function is even more dominated by the l-hole (i.e., the corehole) KC than the outer valence states. In fact, the character is similar to that of a ground state wave function, having only small contributions from single

127

excitations in the CI-expansion. Due to this resemblance and also due to the fact that the valence electron structure essentially remains intact upon core ionization, the role of correlation is small. “Contraction” correlation and corevalence correlation, which give the dominating contributions to the ionization energy, cancel to a large extent. Furthermore, the correlation contribution increases little with the size of the system, and does not at all introduce the strong “size dependence” or size-consistency problem which is present for the total correlation energy. This explains the success of the LISCF approximation, which thus applies well also for larger molecules [ 241, Neglect of relativistic effects gives a positive contribution to the error, < 1 eV for first row molecules, but can be estimated [ 251. Actually, ground state vibronic corrections dominate the error in the dSCF approximation [ 261. Core ionization energies of chemically-shifted elements can of course be evaluated by means of simplified models, as the one described in section 4. Concerning intensities, TM0 is the important matrix element for comparing main core hole states of different elements. When comparing chemically-shifted states of a specific element, the dominating part is (probably) GMo. Due to the effect of relaxation (and the associated nonorthogonality) one cannot put GMo=cMo, although it still applies approximately. Region V The shake-up region consists of a complex satellite structure following the main core hole peak. This region is characterized by a high density of states and by multiple hole-particle character of the wave functions. The core electron shake-up region has several similarities with the hole-mixing region (II), which at times is also denoted shake-up. There are also differences, namely that the shake-up state is well described by just one core orbital index, i.e., no mixing between different core holes (due to perfect orthogonality between a core orbital and any other orbital). Knowledge of the matrix element containing the photoelectron and the molecular orbitals, ( q&-,lt(&c), is at a first approximation not needed. Even so, the analysis of this phenomenon is complex, due to several contributing dynamic and intrinsic effects. However, difficulties arise even in a state-specific description of the intrinsic correlation effects, and tend to increase for the more excited shake-up states, We ascribe this complexity to two facts, firstly that the presence of a core hole introduces an extended region of excitations with a high density of states. From energetic reasons alone, the role of multiple excitations (e.g., 3h2p states) is important in comparison with “ordinary” excitation spectra of neutral molecules. A description of states dominated by multiple excitations is difficult to obtain by either variational or perturbational approaches, since such states call for correlation schemes with excitation patterns of high, perhaps unknown, orders. The other fact is that the orbital description of the initial and final states differs due to the substantial relaxation. This introduces problems con-

128

cerning the interpretation, basically because the final state simulates another chemical species (equivalent core approximation) and standard MO arguments may not apply. Traditionally, the relaxation and the non-orthogonality also introduced a severe obstacle for calculations of the overlap amplitudes &os. The latter problem has, however, been solved for a large class of wave functions [27,28]. The computational problem of core electron shake-up lies at present not in the calculation of 7’Mo or GMo, but simply in finding sufficiently accurate final state wave functions. Similar to the hole-mixing region (II), initial state correlation is needed for GMo. For a state-by-state analysis of core electron shake-up, initial state correlation is important [291. An explanation is given by a simple hole-particle expansion of the wave functions IW

= ct

I@ g } + C&X

1Q-f” > +

i,j

higher order excitations

(7)

where X= gs, (ground state), Is (main hole state} or ss (shake-up state). The following obvious coefficient relations apply: cr >> c$@, cp >> c$l’, and cf << $*. Using frozen orbitals and the Slater-Condon rules, the sudden approximation intensity I=IG1,,J2=)(

Y*=“,=la,,] !P)(’

(8)

simplifies to I(gs-x)=(c~*c;,+Cc~“*c~12 Lj

(9)

Considering the relations of the coefficients given above one finds that for X= 1s (main core electron ionization) the intensity is well guided by Ic$”~$1 2. However, for the shake-up states (x= ss) at least one coefficient product in the second sum is of the same order as cr * cg. Initial state correlation is thus decisive for state-specific intensities, but also for total shake cross sections. Although the evaluation of the sudden approximation also has to involve the effect of orbital relaxation and non-orthogonality, the above simple line of thought holds for any system, atom or molecule. For unsaturated species, in particular K electron systems, the initial state correlation effect is, however, even more accentuated. Thus while low-lying shake-up states of atoms and small molecules are appropriately described by singly excited configurations in the final state, shake-up states of unsaturated species are to a large extent governed by double excitations. This is due to the fact that those excitations become energetically possible also between valence-like levels, e.g., x,x* levels, in the presence of a core hole, Since the corresponding excitations dominate over the single excitation from the ground state Hartree-Fock determinant (the singly excited determinants are non-interacting with ( c&,> (Brillouin

129

theorem) ), there is a substantial contribution from a2-x*2 excited configurations to the final intensities, c{k@*c@ , i&=x, j,l= z*. This has been verified for compounds like double-substituted benzenes, [ 30,311 but also for smaller compounds like CO, C&H, and N, [ 32,331, and is further verified by the analysis of the carbonyl shake spectra in the present work. 4. BINDING ENERGY SHIFTS

As already pointed out in the previous discussion, the core electron states may be described using the approximation level F. Furthermore, if one makes a restriction to the binding energy shifts of a particular core electron state in different chemical environments, further simplifications can be made. Therefore, the core level chemical shifts have found widespread applications in different branches of chemistry and surface physics. Although the core electron binding energy shifts have been studied for more than thirty years [ 341 the details and systematics of the shifts have still to be further investigated. For isolated core electron lines in monochromatic X-ray photoelectron spectra an absolute energy determination can be made to within a few hundredths of an eV. In order to describe the shifts on this level rather extensive ab initio dSCF calculations have to be made with relaxation of all orbitals [ 24 1. For series of related compounds it is often possible to use much less elaborate methods. Some of these are based on very simple empirical chemical arguments such as electronegativity 1341 and linear free energy relationships [ 51. The interpretations and computer simulations of XPS chemical shifts have to a great extent been carried out in terms of so-called potential models [ 11. These models relate the shift and the charge distribution in the compound to each other, often in terms of effective charges belonging to the various atomic sites, e.g., Mulliken populations. The charge distributions may be produced by inexpensive computations, for example semi-empirical methods. Thus an implicit dependence on the molecular geometry is present. A drawback of the potential model is the ambiguity concerning the charge distribution, which can correspond to either the initial neutral state or to the final ionized state, or to a mixture of both. An illustrative example of this was given in ref. 4, where the C 1s binding energy shifts were studied for the linear alkanes. Using a potential model and ground state effective atomic charges, obtained from CNDO/2 calculationsj the experimental and calculated binding energy shifts correlated, but with a negative slope of the regression line. When the final state properties were accounted for, by using a transition operator [35] in the calculations, a positive linear correlation bet een experimental and chemical shifts was obtamed, however, with a slope o%;,approximately one half. Recently, Gasteiger and Hutehings have developed an empirical model [36,37], adopting a picture of the chemical shift as a sum of the ground state

130

charge distribution and a polarization of the final state, screening the core hole. While the initial state’effective charges were determined by an iterative procedure, the final state relaxation energy was found to be directly proportional to the effective polarizability, the sum of the atomic polarizabilities weighted by the number of bonds between each atomic site and the core hole. Thus the final state effects are explicitly related to the molecular geometry. In the same work they presented a so-called connectivity number, N,, which may be computed directly from the structural formula in a manner similar to the effective polarizability. The number was shown to be linearly proportional to the proton affinity for a number of aliphatic amines NC = Cb,(0.5y

(10)

n

In the original context, the formula does not take different atomic types into consideration, only the number of bonds b, in the coordination spheresweighted by their orders n. In the present work we redefine b, as the number of sp3 hybridizedcarbon atoms. Thus N, = 0 for water. For methanol one carbon atom is adjacent to the ionized oxygen atom and N,= 1. In the case of ethanol N,= 1+0.5= 1.5, where we assume that the effect of the second atom is half that of the first. For propanol N, --1+0.5+ (0.5)2=1.75 where theterm (0.5)2 describes the effect of the third carbon atom. It is easy to see that an infinite chain would have N, = 2. It is immediately seen from Fig. 1 (data from Table 2) that N, is sufficient to describe the 01s chemical shift within this series of related alcohol compounds. In this figure also the binding energy of the outermost lone pair orbital is plotted against the connectivity number. The ionization energy depends mostly on the polarization properties of the molecule and is therefore also seen to correlate well with the connectivity number. The connectivity number also correlates well for the 01s and 02~ lone pair for the carbonyls, as is shown in Fig. 2. In a parallel work [38] the model is used for predicting the Cls ionization energies of the linear alkanes, The experimental centroids are reproduced with an accuracy of + 0.03 eV. Furthermore,the model is extended in order to include compounds containing many different elements. 5. SHAKE-UP

5.1.

Description of spectra

Oxygen core electron shake-up spectra of aliphatic and aromatic alcohols are displayed in Figs. 3 and 4,those of carbonyls in Fig. 5, while Fig. 6 shows the spectrum of CO. Except for the smaller molecules, which exhibit specific, well-resolved, structures, there are many common features that can be discerned in these spectra. Below we give a short overview of these common features. Energies and intensities for all the shake-up spectra presented are col-

131

Alcohols

512

541 510-

538 < '3-

01s

!

I .

12

OZp lone pair

11h

2 3

10

5 e'

I

I0

I1 _

I

40

I

t

I.0

CONNECTIVITY

1

I

2.0

NUMCR

I

I

31)

NC

Fig. 1.01s and 02~ lone pair binding energies for aliphatic alcohols and ethers as a function of the connectivity number NC. The numbers correspond to compounds listed in Table 2.

02p lone pair

0.0

CONNECTGTY

NW&?

N,

Fig. 2.01s and 02~ lone pair binding energies for aliphatic carbonyls as a function of the connectivity number N’,. The numbers correspond to compounds listed in Table 2.

132 TABLE 2 01s ionization energies (CO,-calibrated), valence ionization potentials [ 751 and connectivity numbers IV, for the molecules studied (all energies are in eV) No.

Compound

11 12 13

Alcohols Water Methanol Ethanol n-Propanol n-Butanol n-Octanol i-Propanol Di-methyl ether Methyl ethyl ether t-Butanol Di-ethyl ether Phenol Benzyl alcohol

14 15 16 17 18 19 20

Carbonyh (not CO) Formaldehyde Acetaldehyde Propionaldehyde n-Butyraldehyde Acetone Methyl ethyl ketone Benzaldehyde

21 22

Others Carbon monoxide Carbon dioxide

1

2 3 4 5 6 7 8 9 10

Formula

01s

I.P.

N,

H2O

539.91 539.06

12.62 10.94 10.64 10.49 10.37

0.000 1.000

CH,OH CsHSOH n-C,H,OH n-CIHsOH ri&!sH,,OH i-C&H,OH (CH,),O (CHB)O(C,H,) t-C,H,OH (C,H&O &H,OH C,H,CH,OH

CH,O CsH40 C,H,O n-CIHsO

(CH,)zCO (CI-6)CCGH,)

538.81 538.72 538.63 538.56 538.58” 538.39 538.09” 539.28 533.68

539.48 538.64’ 538.50b 537.94

&H&HO

co (302

10.36 10.04 9.86 9.61 8.+‘0

10.88 10.26 9.85 9.83 9.70 9.56 9.52”

1.500 1.750 1.875 1.992 2.000 2.660 2.500 2.500 3.000

1.000 1.500 1.750 1.875 2.000 2.250

542.57 541.28

“l&f. 76. bBef. 29. ‘Ref. 77.

lected in Tables 3 and 4. The numbering of peaks in these tables corresponds to the markings in the figures. The two main characteristic featuresfor all aliphatic alcohol spectra are the sharp structures at 17eV, with an approximate maximum intensity distribution of 0.015 eV_’ relative to the main peak total intensity, and a broad distribution at 25 eV, with an intensity distribution of w 0.02 eV- l. The aromatic alcohols, phenol and benzyl alcohol, also exhibit these featureswith the differences that the feature at 17 eV is suppressed or lacking and that typical aromatic x-ring shake-up peaks are included in the spectra. The carbonyls also have common characteristics such as the sharp and intense peak at 13 eV. The total intensity of this structure is of the order of 15% of the main peak (Table 5). For the larger carbonyl compounds, acetaldehyde and acetone, an extra

133

charge transfer shake-up peak appears at 8 eV with ~6% of the main peak intensity. Analogously to the alcohols, the addition of an aromatic group will give rise to aromatic a-ring charge transfer shake-up transitions close to the main line, as can be seen in the benzaldehyde spectrum. Between 17 and 37 eV there is a broad and flat region containing many smaller peaks with a maximum intensity distribution of typically 0.015 eV-‘. The carbonyl II shake-up dominated region is followed by a less intense region between 15 and 35 eV, which also involves shake up to o- or Rydberg-like orbitals. In formaldehyde some peaks in this region are resolved, but as the molecular size increases the structure is smeared out, as is the case for the alcohols. The intensity distribution in this region is comparable to that of the alcohols, as can be observed in Fig. 7. Also other features are similar for alcohols and carbonyls. At 30-35

water

methanol

1

50

40

30

20

10

0

50

REL. BINDING ENERGY [ev]

40

30

20

10

0

REL. BINDING ENERGY [ev]

n-propanol

ethanol .

01s

50

40

30

20

10

REL. BINDING ENERGY [ev]

Fig. 3.

0

50

b

40

30

20

IO

REL. BINDING ENERGY [ev]

0

n-octanol

i-propanol

1

31

50

40

30

20

10

0

REL. BINDiNG ENERGY [ev]

t-butanol

i : itw> , 50

40 30 20 10 0 REL. BINDING ENERGY [ev]

Fig. 3 (continued). 01s shake-up spectra for aliphatic alcohols. The intensity distribution is normalized to an 01s main peakintensity of 1.00. Energies of indicated peaks are displayed in Table 3.

eV a continuum distribution starts, with a maximum of about 0.01 eV-I, which decreases towards higher energies. An almost 10 eV broad feature is situated in the continuum region at approximately 40 eV, with a maximum intensity distribution less than 0.015 eV_l. Benzaldehyde displays a flat plateau at an intensity distribution of 0.018 eV-‘. All aldehydes and acetones have a dip at 35 eV preceding the 02s shake up at 40 eV. Any feature due to multiple shakeup in the high energy continuum is, contrary to the alcohols, not visible in the aldehyde spectra. The general profile towards higher energies is preserved in all spectra; however, the carbonyl spectra contain somewhat fewer features than the alcohol spectra.

135

phenol

benzyl alcohol 1’

50

40

30

20

10

REL. BINDING ENERGY [Ed

01s

0

7

50

40

30

20

10

0

REL. BINDING ENERGY [ev]

Fig. 4.01s shake-up spectra for aromatic alcohols: phenol and benzyl alcohol. The intensity distribution is normalized to an 01s main peak intensity of 1.00. Eneigies of indicated peaks are displayed in Table 3.

5.2. General remarks

As for other types of electronic spectra, shake-up spectra of molecules with low symmetry become increasingly more complex as the size of the molecul& grows larger. Without effective selection rules the number of particle-hole excitations and the density of final states soon become high enough for’the spectrum to exhibit band-like features, rather than resolved structures which can be interpreted in a state-by-state fashion. From the theoretical point of view, the high density of states leads to a breakdown of both the molecular orbital picture and the separability of electronic and nuclear motions. Thus the interpretation of these broad and unresolved features in terms of conventional electronic or nuclear structure models may become obscure. It is, nevertheless, quite clear from the alcohol and carbonyl shake-up spectra presented that these carry some “fingerprints” of the functional group to which the ionized oxygen atom is attached. Similar to other types of electronic spectroscopies, a distinction can be made between photoelectron shake-up spectra of saturated and unsaturated species, i.e., when the core ionized species binds with single or multiple bonds, respectively. There is a relation between the appearance of a strong shake-up structure and the appearance of correlation type satellites in the inner valence region, with the existence of low-lying excited states and of resonances in the electron-molecule scattering cross section [ 391. Core electron absorption cross sections of small hydrocarbons show a smooth attenuating behaviour represented by Rydberg-like series. First row multiply-bonded diatomics show strongly resonant features [ 401.

acetaldehyde

formaldehyde =-----q’;;j

I

50

40

30

I

20

10

0

50

40

30

20

10

REL. BINDING ENERGY [ev]

REL. BINDING ENERGY [eVj

acetone

benzaldehyde

0

01s 3

I ;.1

: I .. :

50

40

30

20

10

REL. BINDING ENERGY [ev]

0

50

40 30 20 10 0 REL. BINDING ENERGY [eVJ

Fig. 5.01s shake-up spectra for some carhonyls. The intensity distribution is normalized to an 01s main peak intensity of 1.00. Energies of indicated peaks are displayed in Table 4.

There are several other examples of this kind of distinction. Comparing Figs. 12 and 14, one observes that the carbonyls display extra features in the 02s inner valence regions, presumably due to correlation type satellites, which are absent in the alcohol spectra at the present resolution. A comparison of the oxygen shake-up spectra of alcohols and carbonyls in Figs. 3,6 and 7 shows, for the alcohols, a regular structure which varies rather smoothly as the hydroxyl group is attached to successively larger carbon chains (Fig. 3, Figs. 911), while the spectra of the smaller carbonyls show structure which is very specific for the particular molecule. This structure is most pronounced for diatomics or triatomics, which contain few vibrational degrees of freedom, while

137

carbon monoxide

50

40

30

20

10

0

REL. BINDING ENERGY [ev]

Fig. 6.01s shake-up spectra of carbon monoxide. The structure helow 12 eV, peaks 1-2, is due to inelastic scattering. The intensity distribution is normalized to an 01s main peak intensity of 1.00.Energies of indicated peaks are displayed in Table 4.

for the larger members fine structure is obscured. The underlying physical reason is given by the pile-up of electronic density in the multiple bonds, which implies strong electron correlation. Shake-up transitions involving the multiple bonds leave the molecule in a state that often can be characterized by static electron correlation (sometimes of near-degenerate type), and by many-electron excitations in’a configuration picture. These features are often accentuated in a n-electron system, where, in a molecular orbital picture, we characterize the z* orbital as valence-like. In the presence of an open core hole it may become local, or even “collapse” into the core. This has consequences for a state-specific analysis of molecular shake-up spectra. Electron correlation will be comparatively important, also for the initial ground state, and there may be a number of close-lying final shake-up states that often cannot be described as originating from single electron excitations between molecular orbit&. The integrated strength of the shake transitions relates to the relaxation ene& of core electron ionization [ 411. Often one refers to relaxation as a radial charge contraction around the core hole, and a flow of charge to the site of the core hole from neighbouring atoms. An aromatic groqp or a a bond often conducts the charge flow better than a cr bond. A strong, core-hole-induced, charge transfer leads to a strong low-energy shake-up feature [ 30,31]. We find that the larger compounds have larger relaxation energies. (Figs. 1 and 2) and, in general, more intense shake spectra. The bonding in the final state ion can be represented qualitatively by the resonance valence structure of the equivalent core ion. However, the analysis of the shake-up features, in terms of elec-

138 TABLE 3 Energies (E) and intensities Water Peak no.

Methanol

Ethanol

E (eW

Z (eV-‘)

Peak no.

E

Z

(eV)

(eV-‘)

16.7 20.3 23.2 24.7 26.9 29.0 34.9 38.1 52.5

0.005 0.012 0.030 0.028 0.013 0.010 0.009 0.010 0.008

1 2 3 4 5 6 7 8 9’ 10

10.4 14.4 16.9 20.6 22.4 24.5 34.4 38.0 42.1 50.9

0.003 0.007 0.015 0.016 0.018 0.021 0.010 0.011 0.010 0.008

n-0ctanol

nBropanol Peak no.

E

Z

(eV)

(eV_‘)

1 2 3 4 5 6 7 8

10.7

0.006

16.5 19.6 23.4 25.8 34.1 38.5 49.6

0.014 0.015 0.020 0.017 0.010 0.011 0.008

t-Butanol Peak no.

distribution values (I) for peaks in the alcohol 01s shake-up spectra

E

Z

(eV)

(eV_‘)

1 2 3 4 5

11.0 16.9 23.0 38.0 50.6

0.005 0.015 0.021 0.011 0.008

Peak no.

E

I

(@V)

(eV-‘)

1 2 3 4 5 6 7

11.8 16.5 22.5 25.3 34.4 38.8 51.9

0.009 0.015 0.021 0.018 0.011 0.011 0.008

i-Propanol

Peak no.

E

I

W)

(eV-‘)

1 2 3 4

11.8 16.4 23.4 38.5

0.009 0.015 0.023 0.013

Phenol

E

Peak no.

Benzyl alcohol

Peak no.

E

(eV)

Z (eV-‘)

12.8 15.7 21.6 24.8 38.3

0.012 0.014 0.020 0.018 0.011

1 2 3 4 5 6 7 8

E

Z

WI

Z (eV-‘)

Eo?

W)

(eV_‘)

7.3 10.8 13.3 14.4 17.8 20.3 23.8 41.5

0.027 0.011 0.010 0.010 0.013 0.018 0.020 0.012

1 2 3 4 5 6 7 8

5.2 6.9 10.0 17.3 23.5 35.0 40.0 51.9

0.012 0.015 0.007 0.013 0.020 0.013 0.013 0.009

tronic structure and bonding, requires detailed calculations. As exemplified by the oxygen shake-up spectra of the carbonyls (Figs. 5 and 6) there may be several resolved shake-up states within a small energy interval. Although much of the theory for the shake-up phenomenon is established, the implementation

E (eV)

8.5 11.5 16.0 17.5 18.3 20.2 21.6 23.6 26.4 27.8 30.7 35.7 47.4

Peak no.

1 2 3 4 5 6 7 8 9 10 11 12 13

0.005 0.904 0.065 0.031 0.032 0.014 0.006 0.014 0.011 0.012 0.011 0.012 0.008

:eV-‘1

Carbon monoxide

Peak no. 10.0 12.2 14.8 17.4 20.2 23.7 29.1 39.6

E (eV)

Formaldehyde

0.014 0.052 0.009 0.016 0.013 0.018 0.014 0.011

I (eV-‘) 1 2 3 4 5 6 7 8

Peak no. 7.6 10.5 12.9 17.5 19.6 24.2 30.4 39.0

E (eV)

Acetaldehyde

0.027 0.014 0.055 0.017 0.016 0.016 0.015 0.012

:eV-‘1 1 2 3 4 5 6 7 8

Peak no.

Acetone

8.5 11.3 13.5 19.4 21.9 25.8 31.4 39.9

E (eV)

Energies (E) and intensities distribution values (I) for peaks in the carbonyl 01s shake-up spectra

TABLE 4

0.035 0.013 0.045 0.013 0.016 0.014 0.013 0.010

:eV-‘) 1 2 3 4 5 6 7 8

Peak no.

2.3 3.9 5.4 11.1 13.4 24.4 30.1 42.1

E (eV)

Benzaldehyde

0.051 0.177 0.052 0.029 0.049 0.020 0.018 0.015

I (eV-‘)

140 TABLE 5 Charge transfer (CT), n-w* (CO) and aromatic 01s shake-up energies and intensities for the aldehydes and acetone (all energies in eV and intensities in % of the total 01s main peak) Compound

R-fl aromatic

E Formaldehyde Acetaldehyde Acetone Benzaldehyde

1

3.81 5.25

R-R*

E

I

E

I

7.50 8.39

5&l 6?1

12.11 12.78 13.31 13.37

15+2 16?3 13-t4 1726

2223 6+2

/I

01 s shake-up

eIhanol

40

CT

20

0

REL. BINDING ENERGY [eV]

Fig. 7. Comparison of ethanol and acetaldehyde 01s spectra. The intensity distribution is normalized to an 0 1s main peak intensity of 1.00. Both spectra have been smoothed by convolution with an 0.6 eV gaussian.

of this theory lags behind experiment also for high-energy excitation when compared with well-resolved spectra like those presented in Figs. 4-7. 5.3. Charge transfer shake-up in carbonyls In this section we analyze qualitatively the prominent features of the shakeup spectra of the carbonyl-containing compounds shown in Figs. 5 and 6. In

141

coming subsections we analyze these features in some detail using computational results. Starting with CO, we note that its spectrum is dominated by an unscreened Z-X* shake-up as high as 16 eV in the spectrum. This shake-up transition is retained with approximately constant energy ( N 13 eV) and intensity ( - 15% ) in the spectra of the remaining carbonyl compounds. With the addition of more groups, another band appears closer to the main peak, at about 8 eV for acetaldehyde and acetone, and even closer, ca. 4 eV, but split, in the benzaldehyde spectrum. We find these observations to be compatible with observations in some core electron spectra of both free and adsorbed molecules. In fact, a similar observation is made for benzyl alcohol and phenol in Fig. 4, where an extra, very strong, peak energies at about 6 eV above the main peak. Analysis of such features in shake-up spectra has been conducted in a series of papers, especially focusing on substituted or disubstituted benzenes characterized by donor and acceptor groups and high mobility of screening electrons. For these compounds the close-lying shake-up peak may even be of comparable strength to the main peak. Interpretations of these features have been given in terms of charge transfer shake-up and peak intensities have been related to the effect of screening and to the donor and acceptor strengths of the substituent groups [ 30,31,42-47 ] . Moreover, other carbonyl compounds, such as chromium hexacarbonyl [48], show similar features, as well as CO adsorbed on metal surfaces [49,50]. The molecular systems mentioned here can be regarded as molecular analogues of the core-hole screening process in metal surface-adsorbate systems, and have been analyzed by ab initio calculations [30,31,44,45], model hamiltonians [491 or simplifying orbital models [ 31,44,46]. These latter adopt much of the classical analysis for charge transfer UV absorption spectra, e.g., by Nakagura and Tanake [ 511 and by Longuett-Higgins and Murell [ 52 1. In the present series of compounds the charge transfer shake-up is dominated by a single excitation from a donor orbital (II) localized on the group (s ) pendant to an acceptor orbital {A) (here n*) associated with the carbonyl group. In a single excitation picture we assign the two charge transfer (CT) shake states, singlet and triplet parent coupled, as

‘%T(D-A) =

bMDh 712({&rb~A >-

(11)

and 1

(12) respectively, where D denotes donor or pendant group orbital and A the acceptor orbital [ 30,53 1. The corresponding overlap amplitudes (G,os ) are, in this

142

picture, exactly zero for the triplet coupled state and equal to JcDA ($,,I&,} I2 for the singlet coupled state. However, the model qualifies only for energies. The corresponding shake excitation energies (Es) from the main core hole state are

and Es(2~~T(D-A))=Es(2Y~T(D-A))-2KDA+K~sD+K~sA where we have used ordinary notations for orbital energies and exchange (K) integrals * A

(14) (E),

Coulomb (J)

We have displayed the numerical values for these quantities from canonical Hartree-Fock orbitals (see computational section), and the corresponding predicted shake-up energies in Table 6. Both Coulomb and exchange interaction integrals are sensitively dependent on the localization properties of the donor and acceptor with respect to the site for core ionization. The Coulomb interactions dominate and the shake-up energies in this model follow, therefore, from the interplay of core-valence inTABLE 6 Orbital model for charge transfer shake-up (all values in eV; CO, carbon monoxide; FA, formaldehyde; CT, charge transfer) Model

CO

term

R-lK*

FA X-R*

Acefaldehyde CT

R-K*

CT

ll-rc*

3.8 - 13.7 14.3 19.8 10.8 0.2 0.4 2.7

3.6 - 17.5 13.4 8.5 8.5 0.3 0.02 1.3

3.6 - 13.0 13.4 19.6 10.1 0.3 0.5 2.5

J 1aA J 1.&l J DA K I8A K 1sD &A

3.3 17.4 12.1 24.7 10.5 0.6 0.2 2.2

3.2 - 14.6 14.3 22.1 11.8 0.3 0.5 3.13

3.8 - 16.6 14.3 7.9 8.0 0.2 0.07 1.0

Shake energy Model Expt.

25.2 15.9

16.8 12.11

7.07 7.50

CA

CD

-

Acetone

14.8 12.78

9.14 8.39

15.1 13.31

143

tegrals, JlsD and JISA. Localization arguments imply that JlsD << JlsA for core ionization in the acceptor, but that JlsA <
of carbonyl shake-up spectra

In this section we present our computed results for 01s shake-up carbonyls, and compare them with the experimental spectra.

in

144

5.4. I. Computational details

In the present work we have undertaken a series of MCSCF calculations on the shake-up structures in the carbonyl compounds presented in Table 5 and Figs, 5 and 6. These include carbon monoxide (CO), formaldehyde (H2CO), acetaldehyde (CH,-CO ), and acetone ( CH3- (CO)-CH, ). The calculations employ the second order MCSCF program SIRIUS [ 54,55 1. Ground, core hole and the first six shake-up states were optimized. A scheme for choosing the correlating space was used based on ground state MP2 natural orbital analysis [56]. As a rule of thumb one correlating orbital for each strongly occupied orbital was included in a complete active space. Those orbitals deviating most from 0, respectively 2, in occupation numbers were selected. The same space as for the ground state was applied for the core hole and shake-up states, but with the core orbital added to the active space with a single occupancy restriction (introducing an error of the order of only * l/10 eV [ 25,57 J ). A doublezeta (DZ) one-particle basis set was applied for all atoms except for the carbony1 atoms for which DZ plus polarizing basis sets were applied. The choice of basis set is based simply on previous experience on optimization of core hole and shake-up states, and no basis set investigations have been undertaken in the present work. The one- and N-particle basis sets so chosen generate wave functions with typically 1-3 x lo4 configuration state functions (CSFs) and 300-1300 orbital rotation parameters. As outlined in ref. 58 variational collapse in full MCSCF optimization of core hole states is avoided with a two-step procedure where in the first step the core orbitals are kept frozen. The relaxation of the core orbital gives a stabilization energy of l-2 eV, this energy varying between the states within a few tenths of an eV. The overlap amplitude (GOA) is, on the other hand, negligibly affected by core orbital relaxation, and the calculations presented here have therefore retained a frozen core orbital. The sudden approximation overlap amplitudes were evaluated according to a scheme developed in ref. 28 coded in the WESTA post program [ 28,591. This method is based on the configuration state functions and uses a GUGA (graphical unitary group) approach to evaluate the generalized overlap amplitudes (GOAs): ( @‘)(N--1)&J p(N)} where p(N)) and @“‘(N-l) denote complete active space wave functions for ground and shake-up states, respectively. Basically it performs: (i) bi-orthogonalization of orbit& according to Malmquist [ 271, bringing the overlap matrix into diagonal form; (ii ) a GUGA sorting to a common graph for initial ground and final shake-up states; and (iii) a transformation and a scaling of the sorted CI vectors to match the biorthogonal MO basis. The final evaluation of the GOA is then obtained as a simple scalar product between two CI vectors. All operations are quick, and the computational effort to obtain the GOAs is negligible in comparison with optimization of the wave functions. Correction for state overlap was achieved by a symmetric orthogonalization procedure; however, no hamiltonian corrections were carried out.

145

5.4.2. Carbon monoxide In contrast to the Cls spectrum of CO which was early investigated (CI calculations by Guest et al. [32] ), the 01s shake-up spectrum was analyzed theoretically only recently (Schirmer et al,, employing a Greens function method, ADC (4) [57 ] ). In the latter investigation reasonable intensities were obtained for the first states in the Cls spectrum. The oxygen case turned out to be more problematic. While the Cls spectrum shows some similarities with other smaller unsaturated species (cf. N, and &Hz spectra [ 33]), the 01s spectrum is predicted to have quite a different character. In the Cls case there is a weak triplet-parent coupled x-x* state and a strong singlet-parent coupled x-x* state mixed with lt2- (x*)~ and other double excitations. In the 01s case there is also a pure, but weak, triplet, while Schirmer et al. [57] find a considerable mixing of Q excitations for the second state as well as for other states in the intense region between 15 and 20 eV. The different features of the two spectra were interpreted in terms of charge transfer screening, using the atomically decomposed character of the 0 and K orbitals involved. Thus, the screening of carbon hole states takes place within the 17manifold (Z-Z*) and the screening of the oxygen core preferentially in the C (a-a”) manifold. The screening reaction leads to a low, and intense, shake-up, while the reverse is the case for the anti-screening. This type of interpretation connects to charge transfer screening commented on in the previous section. There is, however, a distinction between the Greens functions approach and the variational (MCSCF) approach employed here, in that the former starts out from ground state orbit&s, while the latter optimizes orbitals specifically for the core hole, or core hole shake-up, species. This makes the electron excitation pattern different, and therefore, sometimes, implies a different interpretation. We find from the present MCSCF calculations that for CO gn analogous picture still holds qualitatively for the state-optimized wave functions of the shake-up states. The patterns with screening (E--K*) excitations following Cls shake-up and anti-screening (cr-a*) excitations following 01s shake-up patterns are confirmed also in this approach. Qualitatively we can thus analyze the differences in carbon and oxygen shakeup from the nature of the a and x* orbitals before and after ionization. In neutral CO the n orbital is localized towards oxygen and its correlating counterpart, x*, towards the carbon end. On C ionization, one finds an NO+ resonance valence structure, where the n orbital takes on more carbon character, while x* adjusts accordingly, leading to rather balanced components for both orbitals. The x-x* interaction is stronger for Cls states than for the neutral CO, but the reverse holds for Ols, which is compatible with the screening picture 1571. Our calculations using the “thumbrule” wave function assigns the triplet coupled x-x* shake excitation at 14.0 eV with intensity 0.2% (experimentally ca. 15 eV with undetermined intensity) and the singlet coupled (with intermixed double excitations) at 19.3 eV with 11% (experimentally 15.9 eV,

146

11.2%).A somewhat higher lying D-Z* transition with intensity 8% was also found. Virtually no 0 excitations were included in the strong second transition (3% ). An enlargement of GAS522 to a CAS533 wave function gave a value of 17.5 eV (3% ). Although this space does not give a balanced correlation, the results indicate nevertheless that we cannot claim quantitative accuracy for CO with our model. 5.43. Formaldehyde The low energy shake-up spectrum of formaldehyde contains a large peak at 12 eV. It overlaps with at least two other peaks, visible as “shoulders”. The total intensity of the structure is x 12% of the main peak. Table 7 contains a summary of the computed results. The analysis of core ionization and shakeup of formaldehyde is rather similar to that of carbon monoxide. The shakeup spectrum also contains a A anti-screening transition, and the orbital characters of these excitations are similar. The shake-up state optimized orbit& also retain their localized properties, i.e., 1cis mostly an oxygen orbital and n* is mostly a carbon orbital, or even a more polarized description with respect to the ground state. This holds roughly for the other carbonyls, as well. These transitions can be seen as both 0 to C R charge transfer and bonding to antibonding excitations. It also has the effect of reducing the it to IC*exchange TABLE 7 Computed results for the shake-up spectrum of formaldehyde (all energies in eV; the shake-up intensities in % of the main peak, for which the absolute intensity is given)

State

Natural occupation numbers

Energy intensity

d

xc0

a1

a1

bz

bz

bl

Ground state

1.98 0.02

1.98 0.03

1.98 0.01

1.97 0.03

1.93 0.07

01s

1.98 0.02

1.98 0.03

1.99 0.01

1.98 0.02

1.96 0.04

Shake 1

1.97 0.02

1.98 0.03

1.97 0.01

1.99 0.03

1.14 0.86

+ 10.60 1.04%

Shake 2

1.97 0.02

1.98 0.03

1.98 0.01

1.96 0.03

0.73 1.28

+ 12.65 10.55%

Shake 3

1.98 0.01

1.93 0.04

1.84 0.00

0.27 0.01

1.98 1.93

+ 14.38 0.60%

0.00

0.621

147

splittings, which explains the small distance between the singlet and triplet parent-coupled peaks. A difference from CO is that the main IEto z* energy is somewhat lower. According to the computed results, the structure contains three peaks, with a total intensity of 12.2%. Computed intensity ratios, 10: 100:6, and energies, 10.60 eV, 12.65 eV and 14.38 eV, seem to agree well with the experimental results. The third peak is a bz to x* double excitation. The first state, which corresponds to the low energy shoulder, is the almost pure triplet parent-coupled n to n* excitation (lb1 to 2bl). The strong peak at 12 eV is the singlet parent analogue. It is interesting to note that the natural occupation number for the n orbital is 0.73 while that for x* is 1.28, reflecting the role of the double excitation for the “singlet” parent-coupled state. The corresponding ground state occupation numbers are 1.93 and 0.07, respectively (MP2 and CAS values are close). However, the leading component of the correlated ground state wave function, except for the main hole configuration, is the double Z--K*excitation. This explains qualitatively the high intensity of the singlet parent-coupled excitations in carbonyls and analogous compounds [ 331. Since the n and x* orbitals retain their bonding and anti-bonding properties in these states, the shake-up peaks are broad. Finally, the high energy shoulder represents a pure double shake-up from the b,-orbitals to C2p,. Higher excitations also contain selected o-x and o-o transitions, as expected. 5.4.4. Acetaldehyde The most remarkable feature in the acetaldehyde spectrum, with respect to that of formaldehyde, is the appearance of the peak at 7.5 eV, which can be interpreted as a charge transfer satellite. The main peak at 12.8 eV remains almost unchanged with respect to formaldehyde. The computed spectrum, containing five shake-up states, is presented in Table 8. Only two of these states have considerable intensity: one at 8.34 eV (5%) and the other at 13.60 eV (13% ). A state with 2% intensity appears at 14.4 eV. The computed spectrum agrees with the experiment in this energy range. Thus the “thumbrule” for the active space, with one correlating orbital per strongly occupied outer orbital, is quite successful for low lying valence-like shake-up transitions, as is the case for formaldehyde and, to some degree, also for carbon monoxide Jr-72*. The analysis of the acetaldehyde spectrum is straightforward. The first computed shake-up state, at 8.0 eV, is an almost pure triplet parent-coupled n-x* state, and has no intensity at all. The second peak is a @& to R&-, charge transfer. The aliphatic CHB group orbital has decreased its occupation to I.23 for this state, while the a* gains 0.72 and the zoo orbital retains an occupation very close to 2. The third shake-up transition is a triplet parent-coupled excitation from the ffon orbital, and has little intensity. The fourth state consists of xc0 to n* transitions, with almost identical energy, intensity and occupation

148 TABLE 8 Computed results for the shake-up spectrum of acetaldehyde (all energies in eV; shake-up intensities in % of the main peak, for which the absolute intensity is given) State

Natural occupation numbers a‘

Ground state 01s Shake 1 Shake 2 Shake 3 Shake 4 Shake 5

Energy intensity a”

c7

r7

Q

XR

xc0

1.98 0.02 1.98 0.01 1.98 0.02 1.96 0.02 1.98 0.02 1.97 0.02 1.40 0.02

1.98

0.02 1.98 0.02 1.97 0.02 1.97 0.04 1498 0.02 1.98 0.02 1.98 0.03

1.98 0.02 1.99 0.02 1.98 0.02 1.98 0.02 1.04 0.96 1.96 0.04 1.97 0.60

1.98 0.07 1.98 0.02 1.01 0.01 1.29 0.01 1.97 0.02 1.95 0.02 1.72 0.27

1.93 O-02 1.97 0.03 2.00 1.00 1.99 0.72 1.94 0.07 0.75 1.28 1.82 0.18

0.00

0.602 + 7.98 0.00% + 8.84 5.02% + 13.60 0.02% + 13.21 12.67% + 14.42 1.74%

numbers as the corresponding state in formaldehyde. Shake state number five is a mixed transition with both strong 0-0 and z-a components. 54.5. Acetone

The acetone spectrum is similar to that of acetaldehyde in many respects. Comparing the two spectra there is a slight increase in shake transition energies, and a slight increase in the intensity ratio between the charge transfer and the R-K* shake-up peaks. The computational results in Table 9 confirm this view, although with some modification. The triplet-coupled CT excitation is predicted at 8.8 eV and again with low intensity. The singlet-coupled analogue at 10.3 eV turns up with a high intensity. The triplet-coupled x-z* excitation is found relativelyhigh up in the spectrum, and involves some electron motion between the CH, and CO groups. Finally, fit 15 eV, one finds the strong R-B* excitation. In contrast to acetaldehyde it also contains some a(&.)-~* excitation character, leading to a final charge population of the a* orbital of 1.39. Except for this feature, the whole shake spectrum takes place within the K (b, ) manifold. The a, electron structure is basically untouched. Although the computational results for acetone are comparable with those of formaldehyde and acetaldehyde,we cannot claim the same accuracy. This is connected to the increase in the number of electrons that forces us to leave quite a few valence 0 electrons uncorrelated when using the scheme for choos-

149 TABLE 9 Computed results for the shake-up spectrum of acetone (all energies in eV; shake-up intensities in % of the main peak, for which the absolute intensity is given)

State

Energy intensity

Natural occupation numbers o

KR

a1

b,

h

Ground state

1.99 0.01

1.98 0.02

1.99 0.01

1.95 0.07

1.99 0.01

01s

1.98 0.02

1.99 0.01

1.99 0.01

1.97 0.03

1.99 0.01

0.00 0.565

Shake 1

1.98 0.02

1.98 0.02

1.02 0.01

2.00 0.98

1.96 0.03

8.82 0.68%

Shake 2

1.98 0.02

1.98 0.02

1.17 0.89

1.95 0.02

1.96 0.02

10.34 10.36%

Shake 3

1.98 0.02

1.98 0.02

1.81 0.02

1.18 0.99

1.97 0.02

12.08 4.00%

Shake 4

1.83 0.02

1.16 0.02

1.39 0.02

1.96 0.02

1.60 1.39

15.17 7.72%

ing CAS spaces described above. Lack of appropriate correlation causes, in some cases, a non-negligible overlap between different shake-up states. In such cases the intensities must be taken with care, even after an orthogonalization procedure, because of possible hamiltonian interactions [ 271. There is a need for wave functions with excitation schemes restricted with respect to excitation order, but expanded with respect to orbital space and the total number of correlated electrons. A program for shake-up intensities using such restricted active space wave functions is now under development [ 601. 5.5. Oxygen core ekxtron shuke-up spectra of alcohols

Oxygen core electron shake-up spectra for a series of aliphatic and aromatic alcohols are displayed in Figs, 3 and 4, As the smallest species in this series we have also included a new high-resolution shake-up spectrum of water. This spectrum has served as a prime teat-case for various theoretical methods for the molecular shake phenomenon [ 13,61,62]. In comparison with the earlier published monochromatized spectrum, Fig. 3 shows an additional feature at 52 eV in the shake-off region. In Fig. 8 we also present the 01s shake-up spectrum

150

of DzO. It is evident that the water spectrum shows similarities with the other alcohols in the series and we will here briefly recapitulate the interpretation of this spectrum. The discrete shake-up spectrum of water contains four main features, at 16, 20,,24 and 38 eV. According to the interpretation of Arneberg et al. [ 131 and of Agren and Carravetta [ 621 these features are due to shake-up transitions involving the angle-bonding 3a1, the lone-pair lbl, the angle-anti-bonding lb, and the oxygen 2s-containing 2a1 orbitals, respectively. These transitions are split into two components, and other excitations involving higher unoccupied orbitals also intermingle in the spectrum so that the first 15 eV of the shakeup spectrum contains in all some 20 transitions with more than 0.1% intensity. A remarkable feature is the strong band at 24 eV which, according to the calculations, has a large contribution from one of the lbz components. It is found that compared to the other 2p-based shake channels the I& channel becomes “semi-resonant” by the anisotropy of the molecular field in that much of the intensity in the continuum shake-off part of this channel is absorbed into the discrete transition at 24 eV. An expected general sharpening of the structures is observed for the deuterated compound, see Fig. 8. As for the valence levels [ 63 1, most of this sharpening can probably be referred to an initial state effect where the smaller amplitudes of the zero-level vibrational motion projects out a narrower Franck-Condon region. However, some observations for the final states can be made, which are relevant for the peak assignments. In particular, the 24 eV structure now indicates at least two strong shake-up transitions. The sharpening is less pronounced for the 16 eV than for the 20 eV structure, which supports the predicted double-peak nature of the former band. According to the calculations, several shake-off edges are situated around 30 eV, which explains the extra feature in this energy region. The continuum part of the spectrum has three clearly observable bumps at 38,52 and 65 eV (Fig. 3). It is an important observation that all the studied molecules, except molecular oxygen, display a “38 eV feature” and many of them a “52 eV feature”. According to the water calculations [ 13,623 the former is due to the spin-split transitions involving the oxygen localized 2s, and its appearance is thus largely unperturbed by the chemical surroundings. The shake-off calculations of Agren and Carravetta [ 621, including all one-electron channels, predicted monotonously decaying shake-off cross sections without any trace of a shape-resonant behaviour in the continuum. This fact plus the position of the “52 eV feature”, cf. the shake spectrum of the iso-electronic neon species [ 64 1, suggests that it is due to a manifold of &electron shake-up transitions superimposed on the one-electron shake-off continuum. The shake spectrum of HZ0 is paralleled by the spectrum of neon for the 2p-np shake-up region at 35-50 eV. The 2al4a1 bump corresponds to the neon Bs-ns series at 60-80 eV and the 52 eV bump corresponds to the neon double shake-up region beginning at 85 eV. Substituting one of the hydrogens in Hz0 with an alkyl chain brings us to

151

01 s shake-up

I

I

-

D20

______H20

I

35

25

15

REL. BINDING ENERGY [eVj

Fig. 8. Comparison between 01s shake-up spectra of H,O and D20. The intensity distribution is normalized to an 01s main peak intensity of 1.00. Both spectra have been smoothed by convolution with an 0.5eV gaussian.

the alcohols. The main difference in the spectra is a build-up of intensity in the low energy shake region, 5-20 eV (Figs. 9-11). The intermediate and high energy regions still have the same general features as in the case of H20, however they are more blurred. The intermediate region is broadened mainly towards lower energies. A remarkable feature is the 17 eV peak, which remains sharp, or is even sharpened, for most of the members in the aliphatic series. It is therefore reasonable to assign it to a shake-up transition in the OH CJbond. It is notable that for the larger members of the series there is an extra feature emerging at 12 eV. In general it is difficult to provide simple explanations for the differences in the spectral features due to their complexity. The introduction of an alkyl group will enhance the possibilities of charge transfer shakeup and also perturb the local electronic structure of the OH group. The number of shake-off edges will increase and these edges will occur at lower energies. This effect is indicated in our experimental results in Fig. 3 through the smearing of the dip at 30 eV and smearing of the structures at higher energies, which increases with the increasing number of alkyl groups. Figures 9,lO and 11show how the shake-up profile develops with increasing

152

01s shake-up

J

30

25 15 REL. BINDING ENERGY [eq

5

Fig. 9. Comparison between 01s shake-up spectra of methanol, ethanol and n-propanol. The intensity distribution is normalized to an 01s main peak intensity of 1.00. All spectra have been smoothed by convolution with an 0.6 eV gaussian.

molecular size. As the molecule gets larger the intensity in the low energy region, 5-15 eV, will increase, the peak at 25 eV will shift towards lower energy and the number of shake-off thresholds will increase, causing a smearing of the structures above the first threshold. The low energy region enhancement and the 25 eV peak shift seem to follow the trend of the connectivity number NC (eqn. 10). In Fig. 9 we present the spectra of methanol (NC= l), ethanol (NC= 1.5) and n-propanol (NC= 1.75 ). Between n-propanol and n-octanol (NC= 1.99) there is only a very small difference according to Fig. 10. The systematic change in profile is different for the series of alcohols displayed in Fig. 11. Here second next neighbour alkyl groups are added to methanol giving ethanol, iso-propanol (NC= 2) and tcrt-butanol (NC= 2.5). In the low energy region intensity is built up at 12 eV, contrary to the spectra in Fig. 9, where the additional intensity is spread over the entire region. The shift of the 25 eV structure also seems to vary consistently with the size of the molecule. We have chosen to study phenol and benzyl alcohol, the spectra of which are displayed in Fig. 4. The substitution of one hydrogen atom in benzene by the hydroxyl group leads to splitting of the doubly degenerate le,, orbital into an a2 orbital and two b, orbitals that mix with the n-like bi orbital of the hydroxyl group. The a, orbital has a node while the b, orbitals have maximum electron

153

01 s shake-up

-

n-prapano’

______. n-ocaand

,

25

t5

REL. BINDING ENERGY [eV]

Fig. 10. Comparison between 01s shake-up spectra of n-propanol and n-octanol. The intensity distribution is normalized to an 01s main peak intensity of 1.00. Both spectra have been smoothed by convolution with an 0.6 eV gaussian.

density at the point of substitution.The adjacent alkyl group in benzyl alcohol obviously prevents similar behaviour. Our spectra show typical aromatic Kexcitations below 10 eV for both molecules,but with strongerintensityfor phenol. The peak at 7 eV, due to a la,-2% excitation in the aromatic ring, coincides with an inelastic scattering peak [lo] which may make some contribution to the spectra, even though these are ‘recorded at low pressure. This shake-up transition originates in the polarization of the ring towards the core hole site due to electrostatic attraction and is expected to be situatedat 7 eV, regardless of the substituent, due to the a2 orbital node. The intensity will, however, diminish with increasing distance to the core hole site due to decreasingpolarization from the core hole. It can be noticed that phenol lacks the fingerprint “17 eV” structure while benzyl alcohol, except for the n-ring excitations, is rather similar to the larger aliphatic alcohols. 6. VALENCE X-RAY PHOTOELECTRON SPECTRA

Figures 12-15 display the XPS valence electron spectra corresponding to the molecules discussed in the previous sections. The smallestmember in this series, CO, shows an XPS valence spectrum that is rather typical for first row

154

01 s shake-up

1

30

25 15 REL. BINDING ENERGY [ev]

Fig. 11. Comparisonbetween01s shake-up spectra of methanol, ethanol, i-propanol and t-butanol. The intensity distribution is normalized to an 01s main peak intensity of 1.00. All spectra have been smoothed by convolution with an 0.6 eV gaussian.

diatomic molecules. It is clear from Fig. 15 that the inner valence region contains much structure at this level of resolution. There are a great number of theoretical calculations concerning outer valence spectra of the compounds considered here; however, for the inner valence part only the water [ 17,65-671 spectra have been addressed. There is to our and carbon monoxide [l&68-70] knowledge only one other work that has treated the full valence spectrum of a series of oxygen-containing compounds, namely ref. 16 where valence spectra of oxo-compounds were investigated by von Niessen et al. within the 2plh Tamm-Dancoff approximation. Water has for long been a prototype for the breakdown of the molecular orbital picture, with “semi-internal CI” type satellites broadening the main 2q peak [ 17,65-671. However, with improved resolution, the carbon monoxide spectrum presented in Fig. 15 shows more structure and serves better for a closer inspection of theoretical results and for a prototype analysis of an XPS valence spectrum, as we outline in some detail below. 6.1. Valence X-ray pho toekc tron spectrum of CO In this section we analyze the valence XPS spectrum of CO (Fig. 15), covering the spectral regions, I, II and III in the scheme given in Section 3.2.

155

30 20 BINDING ENERGY [eV]

10

Fig. 12. XPS valence spectra for some aliphatic alcohols.

Roughly, the spectrum exhibits intense, well-resolved outer-valence peaks at 14,17 and 20 eV; weak structures between 23 and 35 eV; and a broad intense band at 35-45 eV. These are appropriately described by the division of the energy regions given in Section 3 and can thus be analyzed as stated there. The first comprises Koopmans states and are easily described by an independent particle picture, with a one-to-one correspondence between peaks and molecular orbitals, here the 50, lx, and 40 orbit&. The relative intensities of these, 0.42,0.28 and 1.00 respectively, follow essentially the mixing of 2p versus (carbon) 2s orbital components, the latter having the largest XPS amplitude. Ap-

156

30 20 BINDING ENERGY [aVj

10

Fig. 14. XPS valence spectra for some carbonyls.

157

CO valence

BINDING ENERGY [ev]

Fig. 15. XPS valence spectra for carbon monoxide.

proximation levels E and G describe this region well 172 1, while a relaxation correction works rather poorIy. Regions II and III are considerably more complex. CI calculations 1721 predict some twenty states, mostly 21 states, in a 20 eV broad region starting at 24 eV. These calculations predict stronger peaks at 24.55,33.16 and 38.81 eV, and a structure with four adjacent states at 40-41 eV. The corresponding intensities are 0.002,0.099,0.024 and 1.836, relative to the @I, band at 20 eV. The three former states are dominated by 2-hole-l-particle (2hlp) configurations slightIy mixed with the main 0-l configurations (Koopmans configurations). The latter are the ones which carry intensity. The C-state observed at 23.5 eV contains 50-l la-’ 2x’ 2hlp configurations mixed with the three 3a-l, 40-l and5aP1KCs, whilethe secondandthirdstatescontain40-’ In-’ Towards the high energy end of the region 2~’ configurations mixed with 3a-‘. 3hZp excitations also appear in the wave functions. Between the first (C) state and second state there is also the D state, one of the few ‘II states in the region. For this state the intermixed Koopmans configuration (KC) is the A-’ configuration, which carries intensity for ultraviolet excitation, but not much for X-rays. Three ?I states in this region are predicted [ 691, but only one with appreciable intensity. One more 211state is predicted at 35 eV, again with low intensity. We conclude from the above section that the tentatively assigned intensity for the C state deviates rather significantly from the experimental value. The reason for this deviation lies in the occurrence of considerable holemixing. The overlap amplitudes were predicted as Gas= 0.008, GdQ= 0.040, and

158

G,,=O.OZZ [ 721. As shown in Section 3, one can approximate the absolute value of the corresponding TMo s as 0 I’ GM0 , i.e. the measured intensity and the overlap amplitudes for Koopmans states in region I corresponding to ionization in orbital i ( i = 3cr,4a and 50). Doing so, we see that the absolute values of the three products 2’Mo *GMo are of comparable magnitude. However, in order to obtain their phases (before being summed and squared) an actual calculation including the high energy continua of CO + is required. It can be pointed out that the assignments of states in the hole-mixing region is aided by an analysis of resonance Auger transitions from core excited states in the neutral molecule, as recently shown in several investigations i&73,74]. The final states are either of 1h character, ending up in region I, or of 2hlp character referring to the hole-mixing region II in the XPS spectrum. For example, two very strong lines in this spectrum correspond to the C and D states referred to above. Finally, in region III the 3oderived KC appears with considerable amplitude in 4 states at 40-42 eV. Thus there is a breakdown of the 3a orbital picture in the sense that we cannot associate only one state to ionization in the 30 orbital. Since this orbital is guided by 02s, with high XPS amplitude, the total intensity for the collected states is high. Considering the other carbonyl and alcohol spectra, we anticipate this breakdown to be a general phenomenon for compounds containing oxygen. Since the separation of states is in the order of the energy for one vibrational quantum, one can anticipate considerable vibronic coupling. However, the total distributed intensity would probably still be well described by the XPS intensity model [2 3. 6.2. Valence XPS spectra of alcohols and aldehydes As for shake-up spectra, it is clear that the valence spectra grow increasingly more complex with the size of the molecules. Furthermore, there are considerable similarities between the spectra of hydroxyl or carbonyl-containing aliphatic compounds (Figs. 12 and 14), while the aromatic analogues are different in character. Region I is apparently expanded at the expense of region II. There is some overlap between the two regions, however, and most of the holemixing states are therefore not discerned. The region containing the background, which increases towards higher energies, is probably caused by a multitude of weak hole-mixing states. Their number increases steeply with the number of valence electrons [ 161. There are some prominent characteristics which can be observed in the spectra. All of the investigated alcohols display a broad and unresolved inner valence structure due to oxygen 2s ionization, of much the same shape as that for water. In the spectra of the aldehydes the details appear differently. In particular, the formaldehyde spectrum displays an intense extra peak at 29 eV, which

159

seems to resemble the above assigned correlation state satellite in the CO spectrum at 32 eV. A prominent feature in these spectra is the build-up of a bandlike structure in the intermediate energy region. These structures can readily be associated with carbon Zs-containing molecular orbitals, which have large cross sections for X-ray photons. It is no surprise that these features are similar to the ones observed for the series of linear alkanes [4]. Spectra of such molecules with up to thirteen carbon atoms showed how the quasi-linear, onedimensional infinite solid, polyethylene, was built up in progressive steps [4]. For the 2p based outer valence region the trends are not as distinct because of mixing with orbitals of the hydroxyl (carbonyl) group and mixing of 2s and 2pcontaining orbitals, the former having comparatively large X-ray cross sections. Except for the aromatic molecules, the 02~ “lone pair” orbital is the highest occupied molecular orbital (HOMO) for all molecules included in this investigation. The notion of a “lone pair” is only approximate, since it is slightly delocalized for some of the compounds. An indication of its mainly local character is, however, given by the well-behaved correlation, similar to the one for the oxygen core ionization shifts, between ionization energy and the connectivity number N, which is shown in Figs. 1 and 2 for the aliphatic molecules. UPS measurements [ 751 have determined all the outer valence states for many of the investigated molecules. These assignments have been recapitulated in Table 10 together with the energies of the visible peaks. By means of simple MO arguments and the XPS intensity model [2] some qualitative statements can be made about the overall features of the spectra. As an example we show in Fig. 16 the earlier recorded valence spectrum of benzene [ 21 together with the valence spectrum of benzaldehyde. A theoretical spectrum of benzaldehyde from the intensity model using the atomic cross sections of ref. 2 and Koopmans ionization potentials, is given in Fig. 17. Upon adding a carbonyl group to benzene the symmetry is lowered from De,, to CZv. As a consequence, the degenerate orbitals will split into symmetrical and antisymmetrical CZ, orbitals. Since all antisymmetric orbitals have a node at the site where the carbonyl group binds to the ring, these will be unable to interact with the carbonyl orbitals. This is demonstrated in the case of the benzene 2eZgorbital where the symmetric component forms a bonding and an antibonding combination with the C2s orbital of the carbonyl group, while the antisymmetric component remains stationary. According to molecular orbital calculations, we find that also the symmetric component of 2el, will mix somewhat with carbonyl2s orbitals. However, the interaction is too small to cause any visible decomposition of the spectral peak at 23 eV. Another example is given by the spectrum of benzyl alcohol (Fig. 13 ) for which a methylene group is attached to the benzene ring. It can be argued that there is a considerable interaction between the 2e,, orbital of the phenyl group and the methylene 2s orbital since the peak at 23 eV splits in the spectrum of benzyl alcohol. On the

160 TABLE 10 Valence region ionization potentials, in eV, for the aliphatic alcohols and carbonyls. All spectra are calibratedto the first ionization potential according to UPS data [ 751 from which the assignments of the outer valence statesare also obtained Compound

E,,

Assignment

Compound

Water

32.22 27 18.63 14.88 12.62

2a,, 02s hole-mixing lb1 3a, lb,, 02p 1.p.

t-Butanol

31.25 24.38 21.79 19.62 9.83

02s c2s c2s c2s 02p 1.p.

Methanol

32.02 22.62 17.55 15.10 12.64 10.94

2a’, 02s 3a’, C2s 5a’ 6~’+ la” 7a’ 2u”) 02p 1.p.

Formaldehyde

34.18 29.29 16.14 14.60 10.88

2&l,02s 3al, hole-mixing 5a, + lbe lb, 2bz, 02p 1.p.

Acetaldehyde Ethanol

31.81 24.00 20.62 10.64

02s c2s c2s 02p 1.p.

34.03 24.35 19.41 16.42 15.40

02s c2s c2s 7a’ la”

n-Propanol

31.83 24.48 22.27 19.62 10.49

02s c2s c2s c2s 02p 1.p.

31.76 24.42 22.27 19.62 10.36

02s c2s c2s c2s 02p 1.p.

i-Propanol

Acetone

Eb

Assignment

(14.15) 13.14 10.26

9a’ 2a” lOa’, 02p 1-p.

33.06 24.35 23.00 17.91 15.63 14.11 (13.41) 12.50 9.70

02s c2s c2s c2s 15, 8% 4bz 2bl 5b,, 02~ hp.

‘1.p.5 lone pair.

other hand, the appearance of the 2ezBpeak is seemingly unperturbed by the addition of a methylene group. Only the symmetric Cz, components of the benzene orbitals are able to bond to 02s. A weak, but visible, effect is the line shape of the structure at 20 eV in phenol, corresponding to the 2ezr structure in the benzene spectrum shown in Fig. 16.The structure is slightly flattened on the low energy side of the maximum, indicating contributions from more than one peak. The corresponding effect for the other aromatic compounds, benzaldehyde and benzyl alcohol, is probably weaker due to larger distances

161

Valence

BJNDING ENERGY

I

(eV)

Fig. 16. XPS valence spectra for benzene (from ref. 2) and benzaldehyde. EXPERIMENTAL

CALCULATED

30

25

20

BINDING ENERGY [ev

15

25

20

15

10

BINDING ENERGY [eq

Fig. 17. Experimental and calculated XPS valence spectra of benzaldehyde. Each computed peak is represented by a 1 eV broad gaussian simulating the experimental spectrometer and vibrational broadenings.

between the oxygen and the phenyl group, and is furthermore obscured by the much stronger C2s mixing effects. In the same vein we find that the lowering of the intensity for the mid “C2s” band for i-propanol compared to that in n-propanol is explained by the fact that the 02s participation in this orbital is effedively symmetry-forbidden in i-propanol, while 02s contributes in all three C2s-dominated molecular orbitals of n-propanol. 7.

CONCLUSIONS

High-resolution XPS spectra of molecules containing oxygen as a heteroelement have been presented. We have used electronic structure theory and-com-

162

putationalresultsto analyze different featuresof the spectra. Some of the spectra were analyzed in detail, other in more general terms. In the latter case the emphasiswas put on similaritiesand differences between spectrawithin series of compounds containing identical functional groups. Several characteristics that fingerprint the spectra were pointed out. The detailed spectral analysis contained the following: analysis of outer valence spectra by means of MO theory and local decomposition schemes for the intensities; analysis of hole-mixing and inner valence regions by methods that go beyond the independent particle approximation; analysis of main core hole spectra and the core electron chemical shifts by means of a topological model; and finally, the analysis of charge transfer shake-up of carbonyl compounds both by means of a multi-configurational self-consistent field method and a simple orbital model. In order to interrelate the characteristics of the spectra a simple scheme was devised in which the spectra are divided into five energy regions described in terms of a hierarchy of approximation levels. With this scheme similaritiesand differences in theoretical XPS analysis of the different energy regions are identified, e.g., the character of wave tinctions, the roles of relaxation and electron correlation, the dominant factors in the intensity analysis and the role of orbital interpretations.In conclusion, we find that details in XPS spectra of the kind presented here call for an advanced analysis. At the same time, however, the spectra show regularitiesthat potentially can be used for chemical identifications by means of simple models. ACKNOWLEDGEMENTS

The authors thank Hans RyGker and Jan-Olov Forsell for technical assistance. This work has been supportedby the SwedishNatural Science Research Council (NFR) and the Swedish Bureau for Technical Developments (STU) .

REFERENCES 1

2 3 4 5 6 7

K. Siegbahn, C. Nordling, G. Johansson, J. Hedman, P.F. Hedin, K. Hamrin, U. Gelius, T. Bergmark, L.O. Werme, R. Manne and Y. Baer, ESCA Applied to Free Molecules, NorthHolland, Amsterdam, 1969. U. Gelius, J. Electron Spectrosc. Relat. Phenom., 5 (1974) 985. U. Geliua, S. Svensson, H. Siegbahn, E. Basilier, A. Fax&lv and K. Siegbahn, Chem. Phys. Let&, 28 (1974) 1. J.J. Pireaux, S. Svensson, E. Basilier, P. Mahnqvist, U. Gelius, R. Caudano and K. Siegbahn, Phys. Rev. A, 14 (1976) 2133. B. Lindberg, S. Svensson, P.A. Malmquist, E. Basilier, U. Gelius and K. Siegbahn, Chem. Phys. Lett., 40(2) (1976) 175. S. Svensson, N. M&ensson and U. Gelius, Phys. Rev. L.&t., 58 (1987) 2639. V. Carravetta, J. Phys. B, 21 (1988) 1777.

163 8 9

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16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

35 36 37 38 39 40 41 42 43 44 45

S. Svensson, M. Carlsson-Gothe, L. Karlsson, A. Nilsson, N. M&tensson and U. Gelius, UppsaIa University Report, UUIP-1200,1989. U. Gelius, L. Asplund, E. Basilier, S. Hedman, K. Helenelund and K. Siegbahn, Nucl. Instrum. Methods. B, 1 (1984) 85. D. Nordfors, A. Nilsson, N. M&tensson, S. Svensson, U. Gelius and S. Lunell, J. Chem. Phys., 88 { 1988) 2630. L.S. Cederbaum and W. Domcke, Adv. Chem. Phys., 36 (1977) 205. L.S. Cederbaum, W. Domcke, J. Schirmer and W. von Niessen, Phys. Ser., 21 (1980) 481. R. Arneberg, J. Miiller and R. Marine, Chem. Phys., 64 (1982) 249. W. Wardermann and W. von Niessen, J. Electron Spectrosc. Relat. Phenom., 51 (1990) 173. A. Bradshaw, W. Eberhardt, H. Levinson, W. Domcke and L.S. Cederbaum, Chem. Phys. Lett., 70 (1980) 36. W. von Niessen, J.S.G. Bieri and L. Cederbaum, Chem. Phys., 65 (1982) 157. L.S. Cederbaum, Mol. Phys., 28 (1974) 479. J. Schirmer, L.S. Cederbaum, W. Domcke and W. von Niessen, Chem. Phys., 26 (1977) 149. L.S. Cederbaum, J. Schirmer, W. Domcke and W. von Nieseen, J. Phys. B, 10 (1977) L549. G. Wendin, Structure and Bonding, Springer, Heidelberg, 1981. L-S. Cederbaum and I-&Kappel, Chem. Phys. L&t., 87 (1982) 14. A.Flores-Riveros, H. Agren, R. Brammer andH.J.A. Jensen, J. Chem. Phys., 85 (1986) 6270. P. Bag-us, Phys. Rev., 139 (1965) 619. A. Brito, N. Correia, S. Svensson and H. Agren, J. Electron Spectrosc. Relat. Phenom., to be published. V. Carravetta, H. bigren and A. CeT, Chem. Phys. Lett., 148 (1988) 210. D. Nordfors, N. M&tensson and H. Agren, J. Electron Spectrosc. Relat. Phenom., 53 (1990) 129. P.Aa Malmquist, Int. J. Quantum. Chem., 30 (1986) 479. H. Agren and H.J.A. Jensen, Chem. Phys. Lett., 137 (1987) 431. B.E. Mills, R.L. Martin and D.A. Shirley, J. Am. Chem. Sot., 98 (1976) 2380. H.Agren, B.O. Rods, P.S. Bagus, U. Gelius, P.A. Malmquist, R. Maripuu and K. Siegbahn, Chtm. Phys., 77 (1982) 3893. H. Agren, Int. J. Quantum. Chem., 23 (1983) 577. M. Guest, W. Rogwell, T. Darko, I. Hiflier and J. Kendrick, J. Chem. Phys., 66 (1977) 5447. R. Ameberg, H. Agren, P. Malmquist and S. Svensson, Chem. Phys. Lett., 92 (1982) 125. K. Siegbahn, C. Nordhng, A. Fahlman, R. Nordberg, K. Harm-in, J. Hedman, G. Johansson, T. Bergmark, S. Karlsson, I. Lindgren and B. Lindberg, ESCA-Atomic, Molecular and Solid State Structure Studied by means of Electron Spectroscopy, North-Holland, Amsterdam, 1966. J. Howat and 0. Goscinski, Chem. Phys. L&t., 30 (1975) 87. J. Gasteiger and M.G. Hutchings, J. Am. Chem. Sot., 106 (1984) 6489. J. Gasteiger and M.5. Hutchings, J. Chem. Sot. Perkin Trans. II, (1984) 559. D. Nordfors and H. Agren, J. Electron Spectrosc. Relat. Phenom., 56 (1991) 1. L.S. Cederbaum, W. Domcke, J. Schirmer, W. von Niessen, G.H.F. Diercksen and W.P. Kraemer, J. Chem.Phys., 69 (1978) 1591. M. Tronc, G.C. Kigg and F.H. Read, J. Phys. B, 12 (1979) 137. R. Manne and T. Aberg, Chem. Phys. L&t., 7 (1970) 282. G. Distefano, M. Guerra, D. Jones and A. Modelli, Chem. Phys., 59 (1981) 169. R. Nakagaki, D. Frost and C. McDowell, J. Electron Spectrosc. Relat. Phenom., 19 (1980) 255. W. Domcke, L.S. Cederbaum, J. Schirmer and W. von Niessen, Phys. Rev. Mt., 42 (1979) 1237. W. Domcke, L.S. Cederbaum, J. Schirmer and W. von Niessen, Chem. Phys., 39 (1979) 149.

164 46 47 48 49

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

76 77

R. Bigelow, R. Weagly and H. Freund, Chem. Phys. Lett., 82 (1981) 305. H. Freund and R. Bigelow, Chem, Phys., 55 (1981) 407. A. Nilsson, N. M&ensson, S. Svensson, D. Nordfors, U. Gelius and H. &en, UppsaIa University Report, WIP-1204,199O. 0. Gunnarson and K. SchZjnhammer, Solid State Commun., 26 (1978) 147. A. Nilsson and N. MBrt.ensson, Phys. Rev. B, 40 (1989) 10249. S. Nakagura and J. Tanaka, J. Chem. Phys., 22 (1954) 236. H. Longuett-Higgins and J.N. MureII, Proc. Phys. Sot. London, Sect. A, 68 (1955) 601. R. Bigelow and H.J. FFund, J. Chem. Phys., 88 (1988) 2830. H.J.A. Jensen and H. @en, Chem. Phys. Lett., 110 (1984) 140. H.J.A. Jensen and H. Agren, Che_m.Phys., 104 (1986) 229. H.J.A. Jensen, P. Jorgensen, H. Agren and J. Olsen, J. Chem. Phys., 88 (1988) 3824. J. Schirmer, G. Angonoa, S. Svensso!, D. Nordfors and U. Gelius, J. Phys. B, 20 (1987 16031. H.J:A. Jensen, P. Jorgensen and H. Agren, J. Chem. Phys., 87 (1987) 451. H. Agren, A. Fltres-Riveros and H.J.A. Jensen, Phys. Rev. A, 34 (1986) 4606. J. Olsen and H.*en, to be published. S. SJensson, H. Agren and U.I. Wahlgren, Chem. Phys. Lett., 38 (1976) 1. H. Agren and V. Carravetta, J. Chem. Phys., 87 (1987) 370. D. Nordfors, S. Svensson and U. Gelius, J. Phys. (Paris), CoIIoq., C9 (1937) C9. S. Svensson, B. Eriksson, N. M&t.ensson, G. Wendin and U. Gelius, J. Electron Spectrosc. Relat. Phenom., 47 (1988) 327. M. Mishra and Y. ohm, Chem. Phys. I_&., 71 (1980) 549. H. Agren and H. Siegbahn, Chem. Phys. Lett., 69 (1980) 424. I. CaceIIi, V. Carravetta and R. Moccia, Chem. Phys., 71 (1982) 199. P.S. Bagus and W. Viinikka, Phys. Rev. A, 15 (1977) 1486. P.W. Langhoff, S.R. Langhoff, T.N. Rescigno, J. Schirmer, L.S. Cederbaum, W. Domcke and W. pon Niessen, Chem. Phys., 58 (1981) 71. H. Agren and R. Ameberg, Phys. SC?., 28 ( 1983 ) 80. W. Domcke, L.S. Cederbaum, J. Schirmer, W. von Niessen, C.E. Brion and K.H. Tan, Chem. PhyOs.,40 (1979) 171. H. Agren and G. KarlstriJm, J. Chem. Phys., 79 (1983) 587. W. Eberhardt, E. Plummer, C. Chen and D. Ford, Au&r. J. Phys., 39 (1986) 853. H. Freund and C. Liegener, Chem. Phys. Lett., 134 (1987) 70. K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Imata, Handbook of He1 Photoelectron Spectra of Fundamental Organic Molecules, Japan Scientific Societies Press, Tokyo, 1986. W.L. Jolly, K.D. Bomben and C.J. Eyermann, At. Data Nucl. Data Tables, 31 (1984) 433. K. Watanabe, T. Nakayama and J. Mottl, J. Quantum. Spectrosc. Radiat. Transfer, 2, (1962 ) 369.

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