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Shakeup spectra and core ionization potentials for formaldehyde. The role of electron spin in shakeup
Journal of Electron Spectroscopy @
and Related Phenomena,
Elsevier Scientific Publishing Company,
Amsterdam
10 (1977) 215-225 - Printed in The Netherlands
SHAKEUP SPECTRA AND CORE IONIZATION FORMALDEHYDE. THE ROLE OF ELECTRON SPIN TN SHAKEUP
T. X. CARROLL* Department (U.S.A.)
of
POTENTIALS
FOR
and T. D. THOMAS
Chemistry
and Radiation
Center,
Oregon
State
University,
Corvallis,
Oregon
97331
(First received 11 May 1976; in final form 25 June 1976)
ABSTRACT
The carbon and oxygen 1s ionization potentials in gaseous formaldehyde are 294.47 (6) and 539.44 (6) eV, respectively. A single shakeup peak is found in oxygen, 12.40 (7) eV from the main peak with an intensity 7 % that of the main peak. In the carbon spectrum there is one major shakeup peak, 10.76 (4) eV from the main peak with an intensity of 5 y0 and two peaks at 6.9 and 19.8 eV with intensity less than 1%. The results are in approximate but not detailed agreement with predictions made by Basch and by Hillier and Kendrick. The role of electron spin coupling in determining the characteristics of the shakeup spectrum is discussed. Atomic charges calculated for the atoms in formaldehyde using a point charge model are compared with those obtained by other methods. INTRODUCTION
Small molecules consisting of first-row atoms play an important role in theories of molecular structure. These contain few enough electrons that it is possible to make reasonably sophisticated calculations but are complex enough that it is possible to test various features of the theory. Experimental measurements of the predicted quantities then provide checks of the validity of the theoretical assumptions and the accuracy of the method. Recently, calculations have been reported by Baschl and by Hillier and Kendrick’ for the energies and relative intensities of “shakeup” states produced in the core ionization of formaldehyde. A shakeup state is one having simultaneously
* Present address: E. I. du Pont de Nemours and Co., Inc. Engineering Experimental Station, Wilmington, Delaware 19898, U.S.A.
Physics Laboratory,
216 a core vacancy and a valence-shell excitation. The position and intensity of these states provide information on the molecular orbitals of the species involved in the core excitation. To provide experimental data with which to compare the theoretical predictions we have measured the spectrum of electrons ejected during core ionization of formaldehyde. In order to be certain that the peaks observed are indeed due to shakeup and not to inelastic scattering, we have also measured the energy-loss spectrum for 1-keV electrons in formaldehyde. A brief report of these results has been given previously3; a more detailed description of the method and results is given below. In addition, we have measured the oxygen and carbon 1s ionization potentials in formaldehyde; these results are also given below. EXPERIMENTAL
METHODS
AND
RESULTS
White, solid para-formaldehyde was obtained by the slow evaporation to dryness of a 40 % solution of formaldehyde in water (“formalin”) containing approximately 10-15 o/o methanol as stabilizer. The lumpy, hard polymer which results from this evaporation was pulverized to a fine powder and placed in a glass ampoule. To remove absorbed water this was then evacuated for a number of hours, first at room temperature and later at roughly 60°C. Formaldehyde was distilled from the residual solid at a temperature of 60-65 “C into the gas manifold of the spectrometer. Conditions were stable enough to run at this elevated temperature for many hours without interruption. Approximately 10 g of solid were consumed in the span of 24 h running time. While a thin, white coating of the pura-formaldehyde did slowly build up in the top of the ampoule as the powder evaporated, indicating repolymerization of the monomeric gas, we found no evidence of it having occurred in the gas cell. Spectra obtained with samples produced in this way were completely reproducible and showed no evidence of peaks due to either water or methanol. The spectra presented in this report were obtained on the Oregon State University cylindrical mirror electrostatic electron energy analyzer’, using Al Koc X-rays as the radiation source. Pressures in the gas cell were typically 50-100 p. For the purpose of accurately measuring the Is binding energies the photoelectron spectra were taken with CO, as an internal standard5 for both carbon and oxygen. These measurements were performed in duplicate. The shakeup spectra were obtained without the use of an internal standard, since the position of the main Is photoelectron line serves as a reference for the satellite positions. The shakeup spectra were run on 30-eV scans. Frequent checks of focus voltage stability were made with a Julie Research Labs differential voltmeter or a Non-Linear Systems digital voltmeter. Where feasible, i.e., with the 1s and strong shakeup peaks, peak positions were determined by least-squares fitting to Gaussian line shapes. Smaller peaks were examined graphically to estimate peak positions and intensities.
217
It is crucial for obtaining spectra like these that the background counting rate be kept as low as possible. For this purpose, a small shield is placed between the X-ray source and the spectrometer entrance slit to prevent photoelectrons being ejected from the slit edges. Without the shield there is appreciable background from surface layers of carbon and oxygen; with it the background from these sources is negligible. The chief source of interference with low-intensity shakeup spectra, other than background, is energy-loss peaks, resulting from ineleastic scattering of photoelectrons with other gas or surface molecules. The resulting spectrum would exhibit
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34
._-. I 5
RELATIVE
I 10
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I 15
ENERGY
I 2’
(eVl
Figure 1. Upper: carbon 1s shakeup spectrum for formaldehyde. Middle: oxygen 1s shakeup spectrum for formaldehyde, Lower: energy-loss spectrum for I-keV electrons on formaldehyde.
218 peaks on the low kinetic energy side of the main photopeak; these would be indistinguishable from peaks due to shakeup. In order to eliminate as much uncertainty in this regard as possible, the energy-loss spectrum for lOOO-eV primary electrons was measured. This energy was chosen since C 1s and 0 1s photoelectrons have kinetic energies of - 1200 and -900 eV, respectively. The spectrometer resolution for both the energy loss and photoelectron spectra was about 1 eV. Because energy-loss peak intensities are sensitive to scattering angle and since this was the first time such spectra had been obtained with our spectrometer, an energy-loss spectrum of N, as a check, using 500-eV electrons was run. The results compared favorably with those of Lassettre and Krasnow6. The formaldehyde shakeup and energy-loss spectra obtained are shown in Fig. 1. The oxygen shakeup spectrum represents one single, continuous run, whereas the carbon spectrum is a point-by-point summation of two spectra. The abscissa represents the relative energy of the electrons with the primary lines (C fs, 0 IS, and elastic) at zero energy. The structure at higher relative energy (lower kinetic energy) is quite obvious; the intensity of the main satellite peak is about 10% that of the ground-state peak. For the C 1s spectrum the shakeup region exhibits one main peak at 10.76 eV and two minor peaks at 6.9 and 19.8 eV. The 0 1s spectrum, on the other hand, shows only one discernible peak, at 12.40 eV. The fact that the two strong peaks do not come at the same relative energies is a clear indication that they are indeed true shakeup lines, since if they were energy-loss lines their positions would coincide. The energy-loss spectrum has quite distinctive peaks lo-25 eV from the elastic line. Comparison of all three spectra clearly shows that the shakeup and energy-loss spectra do not match, and we feel this is further evidence that the observed C 1s and 0 1s lines are true shakeup peaks. The vertical lines numbered l-5 under the loss peaks correspond to the first five ionization potentials as reported by Turner et al.‘. We might expect the maxima in the energy-loss spectrum to appear at or below the values of the ionization energies due to overlap of the many Rydberg transitions taking place. An electron impact energy-loss spectrum of formaldehyde has been reported by Weiss et aL8. The resolution of that particular study was 0.03 eV, whereas ours is of the order of 1 eV. They observe a strong set of transitions between 7 and 11 eV and assign them to excitations of the 2bz nonbonding (lone pair) orbital to Rydberg states. Inspection of their spectrum shows that under our resolution we would expect a maximum near 9 eV, which we see. They also observe broad peaks near 13 and 15 eV, as we do. However, both of these are reasoned to originate in the same (5a,)- l Rydberg series, converging at 15.8 eV, the third ionization potential. Weiss et al. do not observe the n = 3 members of the (lb,)-’ series (7~- excitations} and conclude that those lines converging to the second ionization potential are of insignificant intensity. For this reason, the crude correlation of energy-loss peaks measured by us under poor resolution with ionization energies may be in error. Table 1 lists the observed relative energies and intensities for C 1s and 0 1s
219 TABLE 1 ENERGIES SPECTRA Peak
Carbon la 2 3 4 Oxygen 1* 2
AND
INTENSITIES
Energy
(eV)
lZ.76
OF OBSERVED
PEAKS
IN THE FORMALDEHYDE
Is
htensity
0.051 1.00 (4)
6.9 19.8
0 12.40 (7)
(4) < 0.01 c 0.01
1.00 0.068 (9)
* Main 1s photopeak. C 1s = 294.47 (6) eV; 0 1s = 539.44 (6) eV.
shakeup lines in formaldehyde, and the absolute 1s binding energies, CO2 was used as the internal standard for the absolute binding energy measurements; the binding energy shifts relative to CO, are -3.24 (2) eV for C 1s and - 1.88 (2) for 0 1s. The values used for the absolute ionization potentials in CO2 are those given by Shaw and Thorna?. DISCUSSION
Shakeup-the role of electron spin The theory of the so-called shakeup process has been reviewed a number of times’ ’ 93 lo. By use of configuration interaction for both the initial and final states it is possible to obtain quantitative agreement between theory and experiment. Although such good agreement is indeed satisfying, certain simple physical features are obscured in these detailed treatments. In particular, one tends to lose sight of the role of electron spin in determining the energies of the shakeup states and the intensity with which they are populated. We consider this question in more depth below. We present first some qualitative conclusions; the detailed justification will follow. We restrict our considerations to systems that initially have all closed shells. The primay photoemission leaves a core orbital with one vacancy; the shakeup results in one vacancy in a valence orbital and a single electron in another valence orbital. We are, therefore, concerned with the coupling of three spin-l/2 particles, and, as is well known, there will result two doublet states and one quartet state. Because of the monopole selection rule, there is no intensity populating the quarfet state. If the exchange integrals between the core orbital and the partially filled valence orbitals are much smaller than that between the two valence orbitals, then the valence orbitals can be regarded as coupled to either a singlet or a triplet state,
220 which is in turn coupled with the core to give the two doublets and the quartet. The splitting between the two doublets should be approximately (though not exactly) the same as the singlet-triplet splitting in the appropriate neutral species. In this case, however, the monopole selection rule forbids transitions not only to the quartet state but also to the doublet that results from coupling the triplet with the core hole. There would be only one shakeup peak due to this kind of excitation. The exchange integrals between the core orbitals and the valence orbitals are, however, not always small, and those between valence orbitals are not always large. We may expect therefore that there will be considerable mixing of the valence triplet and valence singlet configurations, with comparable intensities populating both doublets. In this case, however, the energy splitting between the doublets will depend on the exchange integrals between the valence and core orbitals and may well be quite different from the singlet-triplet splitting of the appropriate neutral species. We consider next the quantitative aspect of the foregoing remarks. We assume that each energy level can be described without configuration interaction. We use the symbols A, B, and C to represent the spatial wave functions of a core orbital (A), a valence orbita that is occupied in the original molecule (I?), and an excited orbital not occupied in the original molecule (C). Primes will denote wave functions appropriate to the original molecule; the absence of primes will denote those for the final ion. We then write the following determinantal wave functions
ti
KT
$0 $I $2 ti3
=
= = = =
A’B’B’ C(CL j? ABBaolP (ABC clolp - ABC CIPa)/,/2 (ABC aa j? + ABC a @a)/,+/6 - ABC j3acx J2/3 (ABC aa p + ABC a j&x -I- ABC @a)/,/3
Each of the first four represents the MS = l/2 component of a doublet and the last the MS = l/2 component of a quartet. The Koopman’s-theorem state is represented by $xT and the ground state of the ion with a core hole by tiO_ The remaining functions represent excited states of the ion obtained by promoting an electron from orbital B to orbital C. Function $ 1 describes a state in which the valence electrons are coupled to a singlet; 11/zdescribes one in which they are coupled to a triplet. The Hamiltonian coupling the three electrons is
ET = l/r,,
+ l/r,,
+ l/rz3
There are no off-diagonal terms between ti3 and the other wave functions; we will ignore those between $J~ and either $1 or ti2. The overlap integral <@xT 1 t,b3>, which determines the intensity to the quartet state, is identically zero. We do not need to consider the quartet state further.
221 The energies of the two excited doublets are equal to the sum of the Coulomb integrals Jet, + Jac + Jbc plus the eigenvalues of the matrix
4&b
-c&b - KacY2J3
+ K3, - 2Kbc)P
-w,, -
@L
~,,)/2J3
+ L
-
2%,)/2
where the K’s represent exchange integrals between the various pairs of orbitals. If the exchange integrals between the core hole and the valence orbitals (Ka,, and Kac) are very small, then these eigenvalues are just + Kbc and - Kbc. The splitting between the two states is then 2K,,, exactly the same as for the singlettriplet splitting in the appropriate neutral species. The functions 1+5 1 and $12 as written are the eigenfunctions. The overlap integrals determining the intensity are <&T
1 $I}
=
$
(&,'aSb'bSb'e
<&
[ +z>
=
(&‘&‘aSb’b
-
Sa'bSb'aSb'c)
and -
&bSb’aSb’c)
where the S’s represent overlap integrals, S,., =. Because of the near orthogonality of a and a’ to b or c and b’ to a or c, we expect both terms in the second of these expressions to be quite small. There is, therefore, likely to be negligible intensity to the state resulting from coupling the valence triplet with the core hole. This conclusion has been noted by Basch in his discussion of the formaldehyde satellites’. For the other state, we may ignore the second term and approximately equate the integrals S,,, and St,,, to 1. The intensity to this state then is approximately equal to 2S,2,=, the factor of 2 arising ultimately because there are two electrons initially in orbital B’. In the limit of weak coupling between the core hole and the valence electrons, we expect to find only one strong peak, due to the valence singlet coupled to the core hole. For many systems, however, it is not valid to assume that the exchange integrals between the core and valence orbitals are small. For instance, for the elements neon through argon the 13-2s and ls-2p exchange integrals are much larger than the 2s3s, 2p-3p, 1~38, or ls3p integrals l1 _ In the limiting case that one of the core-valence exchange integrals (Kab, for example) is much larger than the other exchange integrals the matrix becomes -
&,I2
-
K,b/@
-
&b12J3 &,I2
and - KaJ,/3. The corresponding eigenvectors are (0.97, with eigenvalues + K,,/J3 About 7 % of the intensity populates the lower of the two 0.26) and (0.26, -0.97). doublet states. It is possible, therefore, to obtain two shakeup peaks of roughly
222 comparable intensities. The splitting between the two will, however, be only indirectly related to the singlet-triplet splitting for the neutral species. Examples of these phenomena are found in the shakeup spectrum for HF calculated by Martin et al.“. The first two shakeup states correspond to an excitation from the 3a to the 417 orbital. The configuration of the valence electrons in the state at lower energy is over 80% triplet; that in the state at higher energy is over 90% singlet. The calculated intensities and experimental results show the upper state to be the more strongly populated by a factor of 20. For the In to 2~ transition the situation is different; the two states contain about equal contributions from the singlet and triplet valence configurations. Correspondingly the calculated intensities and experimental results show these states to be about equally populated.
Shakeup-comparison
between experiment and theory jbr formaldehyde
Theoretical calculations for the shakeup spectrum have been reported by Baschl and Hillier and Kendrick’. Basch has performed a multiconfiguration-selfconsistent-field (MCSCF) calculation to determine the wave functions for the ground state of formaldehyde and for the lowest lying states that have a carbon 1s or oxygen 1s hole. He has then obtained the energies and wave functions for the excited states by a configuration interaction calculation. Hillier and Kendrick have also used a configuration interaction calculation to give wave functions and energies for the excited states; they do not describe their initial-state calculations. A schematic comparison of the experimental results is given in Fig. 2, where
Oxygen
1 Expt.
IO 5 IL_II
0
IO
1
20
Energy Relative to
I
0 Main
I
I
IO Peok
,
I
I
20 eV
Figure 2. Schematic representation of experimental and theoretical shakeup spectra for formaldehyde. Data denoted by asterisks represent upper limits. The notation H and K refers to Hillier and Kendrick, ref. 2; B refers to Basch, ref. 1.
223 we have plotted intensity of the satellite peaks versus energy; both intensity and energy are given relative to that of the main peak. We consider first the results for oxygen. Experiment and theory agree that there should be a major satellite at about 12 eV. According to both sets of theoretical calculations, this feature arises from a 7~-P n* excitation. Those of Hillier and Kendrick indicate that this satellite should consist of two peaks of about equal intensity, whereas those of Basch indicate one major and one minor peak. In the experimental spectrum there is evidence that the satellite peak is somewhat broader than the main peak. This extra breadth may be due to a closely spaced doublet, in agreement with the calculations of Hillier and Kendrick. On the other hand, it may arise from a single peak that is broadened by transitions to a wide range of vibrational levels in the final state. The calculations predict a total intensity of 15 % (Basch) and 20 % (Hillier and Kendrick), substantially greater than the experimental value of 7 %_ For the carbon spectrum, both calculations predict a major peak at 11-14 eV due, as in the oxygen case, to a 7c + n* excitation. The experimental spectrum, showing a major peak at 11 eV is in reasonable agreement with these predictions, both as to energy and intensity. The two sets of calculations both indicate other peaks should be found in the carbon spectrum. There is evidence for additional satelhtes but it is possible to set only an upper limit on their intensity. In general, the theoretical calculations provide a reasonably good overall prediction of the satellite spectrum. There is, in detail, disagreement between experiment and calculation on the exact position of the peaks, on whether there will be one or two observable peaks resulting from a rc + n * transition, and on the intensity of the peaks. It is clear that the prediction of these satellite structures presents a very demanding test to the theoretical calculation. Core
ionization
potentials
There is some confusion in the literature concerning the oxygen and carbon 1s binding energies of formaldehyde. There is one reportr3 of the C shift relative to CH, as 3.3 eV, listing the original source as ref. 14. Examination reveals, however, that nowhere is there an experimental shift reported there for formaldehyde. Schwartz et al.’ 5 list + 3.2 eV but give no reference, and Jolly and Ferry16 list + 3.3 eV, also giving (14) as a reference. To add to the confusion, an oxygen shift (relative to 0,) is reported by Schwartz et al.15 as being -5.5 eV, unreferenced. Nowhere is there reported an experimental value for the oxygen shift. In any event, our values are in disagreement with the reported values, ours being + 3.51 eV (C 1s - CH.) and -4.25 eV (0 Is - 0,). One instructive and often used method of interpreting the shifts is the pointcharge analysis. Its use gives an approximate charge distribution for the molecules of interest and the results are convenient for comparison with charges derived from quantum-mechanical calculations. Assuming that the electron density of a molecule
224 TABLE 2 CALCULATED
ATOMIC Eqn. (1)
qc 40 9H s b c d
0.33 -0.37 +0.02
CHARGES
FOR FORMALDEHYDE
Ed?.= 0.12 -0.21 0.045
CNDO/2b 0.21 -0.19 -0.01
r4wc 0.02 -0.31 0.15
[532/21jd 0.26 -0.44 0.09
Ekctronegativity equalization, ref. 16. Theoretical value, ref. 19. Theoretical value, ref. 20. Theoretical value, ref. 21.
can be approximated
by localization of charges at points (for atoms other than the one of interest) or on a spherical shell external to the core hole (for the charge on the atom of interest), and assuming the binding energy shifts to be equal to orbital energy shifts (i.e. no differential relaxation), we can represent shifts as functions of initial-state charges, thus AEi = kiqi + e* 2 qj/Rij i+.i
(1)
The AEi are the shifts, qi the charges, Rij interatomic distances, and ki constants, dependent on the particular atom of interest. The assumptions behind the point charge model are discussed in more detail elsewhere17* ‘*. For oxygen we refer shifts to 0, and for carbon to CH,. In the past values of kc and k, that have been found to be successful are k, = 22.0, k, = 22.517* I*. The charges we calculate using these values are given in the first column of figures in Table 2. Jolly and Perry l6 have used an electronegativity equalization method to derive atomic charges for a large number of carbon- and oxygen-containing compounds. Using these charges they fit their values to equations of the form EB = kg + V + I to derive best values for k and 1. (V is the external potentia1 and I is an offset). They find that kc = 3 1.06, k, = 30.43, I, = 0.47, and lo = - 0.27. In general, the charges derived by the electronegativity equalization method are smaller than those derived by other methods. Charges computed by this method are listed in the second column of Table 2. The last three columns contain charges derived from theoretical calculations. The first is from Pople and Beveridge’sl’ CND0/2-wave functions and the second from Snyder and Basch’s near Hartree-Fock level calculations” using a contracted Gaussian basis set. The last column lists the results of accurate calculations by Neumann and Moskowitz21 using a less-restricted Gaussian basis set. Our charges (from eqn. (1)) show clearly the transfer of charge from carbon to oxygen and indicate that it is more extensive than those from all other calculations but the last. The results imply best agreement with the most accurate theoretical treatment.
225 It is noted by Neumann and Moskovitz that the charge distribution is very sensitive to the approximate nature of the basis set. One would expect the [532/21] basis set to yield more accurate charge distributions than the [42/2] basis set, and thus the closer agreement with our calculations is gratifying. We note, however, that the point-charge analysis is limited in its applicability by the choice of k’s, neglect of relaxation, and reference to the carbon shift to CH, instead of neutral carbon. ACKNOWLEDGEMENTS
This work was supported in part by the U.S. Energy Research and Development Administration.
REFERENCES 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
H. Basch, Chem, Phys., 10 (1975) 157. I. H. Hillier and J. Kendrick, J. Electron Spectrosc. Relat. Phenom., 6 (1975) 325. T. X. Carroll and T. D. Thomas, J. Electron Spectrosc. R&t. Phenom., 4 (1974) 270. P. H. Citrin, R. W. Shaw and T. D. Thomas, in D. A. Shirley (Ed.), Electron Spectroscopy, North-Holland, Amsterdam, 1972, p. 105. C (1s) in COZ = 297.71 eV and 0 (1s) = 541.32 eV. R. W. Shaw and T. D. Thomas, J. Electron Spectrosc. Relat Phenom., 5 (1974) 1081. Also see G. Johannson, J. Hedman, A. Berndtsson, M. Klasson and R. Nilsson, J. Electron Spectrosc. Relat. Phenom., 2 (1973) 295. E. N. Lassettre and M. E. Krasnow, J. Chem. Phys., 40 (1964) 1248. D. W. Turner et al., Molecular Photoelectron Spectroscopy, Wiley-Inter-science, New York, 1970. M. J. Weiss, C. E. Kuyatt and S. Mielczarek, J. Chem. Phys., 54 (1971) 4147. R. L. Martin and D. A. Shirley, J. Chem. Phys., 64 (1976) 3685. R. L. Martin and D. A. Shirley, in A. D. Baker and C. R. Brundle (Eds.), Electron Spectroscopy: Theory, Techniques and Applications, Academic Press, to be published. J. B. Mann, Atomic Structure Calculations I. Hartreo-Fock Energy Results for the Elements Hydrogen to Lawrencium, Los Alamos Scientific Laboratory Report, LA-3690, 1967. R. L. Martin, B. E. Mills and D. A. Shirley, J. Chem. Phys., 64 (1976) 3690. U. Gelius, P. F. Heden, J. H. Hedman, B. J. Lindberg, R. Manne, R. Nordberg, C. Nordling and K. Siegbahn, Phys. Ser., 2 (1970) 70. K. Siegbahn et al., ESCA Applied to Free Molecules, North-Holland, Amsterdam, 1969. M. E. Schwartz, J. D. Switalski and R. E. Stronski, in D. A. Shirley (Ed.), Electron Spectroscopy, North-Holland, Amsterdam, 1972, p. 605. W. L. Jolly and W. P. Perry, J. Am. Chem. Sot., 95 (1973) 5442. T. X. Carroll, R. W. Shaw, Jr., T. D. Thomas, C. Kindle and N. Bartlett, J. Am. Chem. Sot., 96 (1974) 1989. D. W. Davis, D. A. Shirley and T. D. Thomas, J. Am. Chem. Sot., 94 (1972) 6565. J. A. Pople and D. L. Beveridge, Approximate MoIecular Orbital Theory, McGraw-Hill, New York, 1970, p. 122. L. C. Snyder and H. Basch, Molecular Wave Functions and Properties, Wiley, New York, p. T-68. D. B. Neumann and J. W. Moskowitz, J. Chem. Phys., 50 (1969) 2216.
and Related Phenomena,
Elsevier Scientific Publishing Company,
Amsterdam
10 (1977) 215-225 - Printed in The Netherlands
SHAKEUP SPECTRA AND CORE IONIZATION FORMALDEHYDE. THE ROLE OF ELECTRON SPIN TN SHAKEUP
T. X. CARROLL* Department (U.S.A.)
of
POTENTIALS
FOR
and T. D. THOMAS
Chemistry
and Radiation
Center,
Oregon
State
University,
Corvallis,
Oregon
97331
(First received 11 May 1976; in final form 25 June 1976)
ABSTRACT
The carbon and oxygen 1s ionization potentials in gaseous formaldehyde are 294.47 (6) and 539.44 (6) eV, respectively. A single shakeup peak is found in oxygen, 12.40 (7) eV from the main peak with an intensity 7 % that of the main peak. In the carbon spectrum there is one major shakeup peak, 10.76 (4) eV from the main peak with an intensity of 5 y0 and two peaks at 6.9 and 19.8 eV with intensity less than 1%. The results are in approximate but not detailed agreement with predictions made by Basch and by Hillier and Kendrick. The role of electron spin coupling in determining the characteristics of the shakeup spectrum is discussed. Atomic charges calculated for the atoms in formaldehyde using a point charge model are compared with those obtained by other methods. INTRODUCTION
Small molecules consisting of first-row atoms play an important role in theories of molecular structure. These contain few enough electrons that it is possible to make reasonably sophisticated calculations but are complex enough that it is possible to test various features of the theory. Experimental measurements of the predicted quantities then provide checks of the validity of the theoretical assumptions and the accuracy of the method. Recently, calculations have been reported by Baschl and by Hillier and Kendrick’ for the energies and relative intensities of “shakeup” states produced in the core ionization of formaldehyde. A shakeup state is one having simultaneously
* Present address: E. I. du Pont de Nemours and Co., Inc. Engineering Experimental Station, Wilmington, Delaware 19898, U.S.A.
Physics Laboratory,
216 a core vacancy and a valence-shell excitation. The position and intensity of these states provide information on the molecular orbitals of the species involved in the core excitation. To provide experimental data with which to compare the theoretical predictions we have measured the spectrum of electrons ejected during core ionization of formaldehyde. In order to be certain that the peaks observed are indeed due to shakeup and not to inelastic scattering, we have also measured the energy-loss spectrum for 1-keV electrons in formaldehyde. A brief report of these results has been given previously3; a more detailed description of the method and results is given below. In addition, we have measured the oxygen and carbon 1s ionization potentials in formaldehyde; these results are also given below. EXPERIMENTAL
METHODS
AND
RESULTS
White, solid para-formaldehyde was obtained by the slow evaporation to dryness of a 40 % solution of formaldehyde in water (“formalin”) containing approximately 10-15 o/o methanol as stabilizer. The lumpy, hard polymer which results from this evaporation was pulverized to a fine powder and placed in a glass ampoule. To remove absorbed water this was then evacuated for a number of hours, first at room temperature and later at roughly 60°C. Formaldehyde was distilled from the residual solid at a temperature of 60-65 “C into the gas manifold of the spectrometer. Conditions were stable enough to run at this elevated temperature for many hours without interruption. Approximately 10 g of solid were consumed in the span of 24 h running time. While a thin, white coating of the pura-formaldehyde did slowly build up in the top of the ampoule as the powder evaporated, indicating repolymerization of the monomeric gas, we found no evidence of it having occurred in the gas cell. Spectra obtained with samples produced in this way were completely reproducible and showed no evidence of peaks due to either water or methanol. The spectra presented in this report were obtained on the Oregon State University cylindrical mirror electrostatic electron energy analyzer’, using Al Koc X-rays as the radiation source. Pressures in the gas cell were typically 50-100 p. For the purpose of accurately measuring the Is binding energies the photoelectron spectra were taken with CO, as an internal standard5 for both carbon and oxygen. These measurements were performed in duplicate. The shakeup spectra were obtained without the use of an internal standard, since the position of the main Is photoelectron line serves as a reference for the satellite positions. The shakeup spectra were run on 30-eV scans. Frequent checks of focus voltage stability were made with a Julie Research Labs differential voltmeter or a Non-Linear Systems digital voltmeter. Where feasible, i.e., with the 1s and strong shakeup peaks, peak positions were determined by least-squares fitting to Gaussian line shapes. Smaller peaks were examined graphically to estimate peak positions and intensities.
217
It is crucial for obtaining spectra like these that the background counting rate be kept as low as possible. For this purpose, a small shield is placed between the X-ray source and the spectrometer entrance slit to prevent photoelectrons being ejected from the slit edges. Without the shield there is appreciable background from surface layers of carbon and oxygen; with it the background from these sources is negligible. The chief source of interference with low-intensity shakeup spectra, other than background, is energy-loss peaks, resulting from ineleastic scattering of photoelectrons with other gas or surface molecules. The resulting spectrum would exhibit
E ’ l. . E
l
.-.
IOO-
.
.-xig.. . I .
750-
‘.
e
.
I
‘.h.-.,
.
-0
:*-#Y
..*\y _
-. _. .-.
I
I
I
.’ _ a;
Energy Loss
. 500-
I
I
.
. .
I I 1 I I I I I
.*-
. . . . ..a. . . ‘.
.
.
, I
.
. .
50-.’
0
;-
l.
3
8
.
.
I I
;
l
G.... _
.
.-
y&f
.
.*+,,
l
.s.
.
.* 250-
l
.
l
. ..x $ . OF
I
I
0
c
!
2
5
34
._-. I 5
RELATIVE
I 10
I 20
I 15
ENERGY
I 2’
(eVl
Figure 1. Upper: carbon 1s shakeup spectrum for formaldehyde. Middle: oxygen 1s shakeup spectrum for formaldehyde, Lower: energy-loss spectrum for I-keV electrons on formaldehyde.
218 peaks on the low kinetic energy side of the main photopeak; these would be indistinguishable from peaks due to shakeup. In order to eliminate as much uncertainty in this regard as possible, the energy-loss spectrum for lOOO-eV primary electrons was measured. This energy was chosen since C 1s and 0 1s photoelectrons have kinetic energies of - 1200 and -900 eV, respectively. The spectrometer resolution for both the energy loss and photoelectron spectra was about 1 eV. Because energy-loss peak intensities are sensitive to scattering angle and since this was the first time such spectra had been obtained with our spectrometer, an energy-loss spectrum of N, as a check, using 500-eV electrons was run. The results compared favorably with those of Lassettre and Krasnow6. The formaldehyde shakeup and energy-loss spectra obtained are shown in Fig. 1. The oxygen shakeup spectrum represents one single, continuous run, whereas the carbon spectrum is a point-by-point summation of two spectra. The abscissa represents the relative energy of the electrons with the primary lines (C fs, 0 IS, and elastic) at zero energy. The structure at higher relative energy (lower kinetic energy) is quite obvious; the intensity of the main satellite peak is about 10% that of the ground-state peak. For the C 1s spectrum the shakeup region exhibits one main peak at 10.76 eV and two minor peaks at 6.9 and 19.8 eV. The 0 1s spectrum, on the other hand, shows only one discernible peak, at 12.40 eV. The fact that the two strong peaks do not come at the same relative energies is a clear indication that they are indeed true shakeup lines, since if they were energy-loss lines their positions would coincide. The energy-loss spectrum has quite distinctive peaks lo-25 eV from the elastic line. Comparison of all three spectra clearly shows that the shakeup and energy-loss spectra do not match, and we feel this is further evidence that the observed C 1s and 0 1s lines are true shakeup peaks. The vertical lines numbered l-5 under the loss peaks correspond to the first five ionization potentials as reported by Turner et al.‘. We might expect the maxima in the energy-loss spectrum to appear at or below the values of the ionization energies due to overlap of the many Rydberg transitions taking place. An electron impact energy-loss spectrum of formaldehyde has been reported by Weiss et aL8. The resolution of that particular study was 0.03 eV, whereas ours is of the order of 1 eV. They observe a strong set of transitions between 7 and 11 eV and assign them to excitations of the 2bz nonbonding (lone pair) orbital to Rydberg states. Inspection of their spectrum shows that under our resolution we would expect a maximum near 9 eV, which we see. They also observe broad peaks near 13 and 15 eV, as we do. However, both of these are reasoned to originate in the same (5a,)- l Rydberg series, converging at 15.8 eV, the third ionization potential. Weiss et al. do not observe the n = 3 members of the (lb,)-’ series (7~- excitations} and conclude that those lines converging to the second ionization potential are of insignificant intensity. For this reason, the crude correlation of energy-loss peaks measured by us under poor resolution with ionization energies may be in error. Table 1 lists the observed relative energies and intensities for C 1s and 0 1s
219 TABLE 1 ENERGIES SPECTRA Peak
Carbon la 2 3 4 Oxygen 1* 2
AND
INTENSITIES
Energy
(eV)
lZ.76
OF OBSERVED
PEAKS
IN THE FORMALDEHYDE
Is
htensity
0.051 1.00 (4)
6.9 19.8
0 12.40 (7)
(4) < 0.01 c 0.01
1.00 0.068 (9)
* Main 1s photopeak. C 1s = 294.47 (6) eV; 0 1s = 539.44 (6) eV.
shakeup lines in formaldehyde, and the absolute 1s binding energies, CO2 was used as the internal standard for the absolute binding energy measurements; the binding energy shifts relative to CO, are -3.24 (2) eV for C 1s and - 1.88 (2) for 0 1s. The values used for the absolute ionization potentials in CO2 are those given by Shaw and Thorna?. DISCUSSION
Shakeup-the role of electron spin The theory of the so-called shakeup process has been reviewed a number of times’ ’ 93 lo. By use of configuration interaction for both the initial and final states it is possible to obtain quantitative agreement between theory and experiment. Although such good agreement is indeed satisfying, certain simple physical features are obscured in these detailed treatments. In particular, one tends to lose sight of the role of electron spin in determining the energies of the shakeup states and the intensity with which they are populated. We consider this question in more depth below. We present first some qualitative conclusions; the detailed justification will follow. We restrict our considerations to systems that initially have all closed shells. The primay photoemission leaves a core orbital with one vacancy; the shakeup results in one vacancy in a valence orbital and a single electron in another valence orbital. We are, therefore, concerned with the coupling of three spin-l/2 particles, and, as is well known, there will result two doublet states and one quartet state. Because of the monopole selection rule, there is no intensity populating the quarfet state. If the exchange integrals between the core orbital and the partially filled valence orbitals are much smaller than that between the two valence orbitals, then the valence orbitals can be regarded as coupled to either a singlet or a triplet state,
220 which is in turn coupled with the core to give the two doublets and the quartet. The splitting between the two doublets should be approximately (though not exactly) the same as the singlet-triplet splitting in the appropriate neutral species. In this case, however, the monopole selection rule forbids transitions not only to the quartet state but also to the doublet that results from coupling the triplet with the core hole. There would be only one shakeup peak due to this kind of excitation. The exchange integrals between the core orbitals and the valence orbitals are, however, not always small, and those between valence orbitals are not always large. We may expect therefore that there will be considerable mixing of the valence triplet and valence singlet configurations, with comparable intensities populating both doublets. In this case, however, the energy splitting between the doublets will depend on the exchange integrals between the valence and core orbitals and may well be quite different from the singlet-triplet splitting of the appropriate neutral species. We consider next the quantitative aspect of the foregoing remarks. We assume that each energy level can be described without configuration interaction. We use the symbols A, B, and C to represent the spatial wave functions of a core orbital (A), a valence orbita that is occupied in the original molecule (I?), and an excited orbital not occupied in the original molecule (C). Primes will denote wave functions appropriate to the original molecule; the absence of primes will denote those for the final ion. We then write the following determinantal wave functions
ti
KT
$0 $I $2 ti3
=
= = = =
A’B’B’ C(CL j? ABBaolP (ABC clolp - ABC CIPa)/,/2 (ABC aa j? + ABC a @a)/,+/6 - ABC j3acx J2/3 (ABC aa p + ABC a j&x -I- ABC @a)/,/3
Each of the first four represents the MS = l/2 component of a doublet and the last the MS = l/2 component of a quartet. The Koopman’s-theorem state is represented by $xT and the ground state of the ion with a core hole by tiO_ The remaining functions represent excited states of the ion obtained by promoting an electron from orbital B to orbital C. Function $ 1 describes a state in which the valence electrons are coupled to a singlet; 11/zdescribes one in which they are coupled to a triplet. The Hamiltonian coupling the three electrons is
ET = l/r,,
+ l/r,,
+ l/rz3
There are no off-diagonal terms between ti3 and the other wave functions; we will ignore those between $J~ and either $1 or ti2. The overlap integral <@xT 1 t,b3>, which determines the intensity to the quartet state, is identically zero. We do not need to consider the quartet state further.
221 The energies of the two excited doublets are equal to the sum of the Coulomb integrals Jet, + Jac + Jbc plus the eigenvalues of the matrix
4&b
-c&b - KacY2J3
+ K3, - 2Kbc)P
-w,, -
@L
~,,)/2J3
+ L
-
2%,)/2
where the K’s represent exchange integrals between the various pairs of orbitals. If the exchange integrals between the core hole and the valence orbitals (Ka,, and Kac) are very small, then these eigenvalues are just + Kbc and - Kbc. The splitting between the two states is then 2K,,, exactly the same as for the singlettriplet splitting in the appropriate neutral species. The functions 1+5 1 and $12 as written are the eigenfunctions. The overlap integrals determining the intensity are <&T
1 $I}
=
$
(&,'aSb'bSb'e
<&
[ +z>
=
(&‘&‘aSb’b
-
Sa'bSb'aSb'c)
and -
&bSb’aSb’c)
where the S’s represent overlap integrals, S,., =
&,I2
-
K,b/@
-
&b12J3 &,I2
and - KaJ,/3. The corresponding eigenvectors are (0.97, with eigenvalues + K,,/J3 About 7 % of the intensity populates the lower of the two 0.26) and (0.26, -0.97). doublet states. It is possible, therefore, to obtain two shakeup peaks of roughly
222 comparable intensities. The splitting between the two will, however, be only indirectly related to the singlet-triplet splitting for the neutral species. Examples of these phenomena are found in the shakeup spectrum for HF calculated by Martin et al.“. The first two shakeup states correspond to an excitation from the 3a to the 417 orbital. The configuration of the valence electrons in the state at lower energy is over 80% triplet; that in the state at higher energy is over 90% singlet. The calculated intensities and experimental results show the upper state to be the more strongly populated by a factor of 20. For the In to 2~ transition the situation is different; the two states contain about equal contributions from the singlet and triplet valence configurations. Correspondingly the calculated intensities and experimental results show these states to be about equally populated.
Shakeup-comparison
between experiment and theory jbr formaldehyde
Theoretical calculations for the shakeup spectrum have been reported by Baschl and Hillier and Kendrick’. Basch has performed a multiconfiguration-selfconsistent-field (MCSCF) calculation to determine the wave functions for the ground state of formaldehyde and for the lowest lying states that have a carbon 1s or oxygen 1s hole. He has then obtained the energies and wave functions for the excited states by a configuration interaction calculation. Hillier and Kendrick have also used a configuration interaction calculation to give wave functions and energies for the excited states; they do not describe their initial-state calculations. A schematic comparison of the experimental results is given in Fig. 2, where
Oxygen
1 Expt.
IO 5 IL_II
0
IO
1
20
Energy Relative to
I
0 Main
I
I
IO Peok
,
I
I
20 eV
Figure 2. Schematic representation of experimental and theoretical shakeup spectra for formaldehyde. Data denoted by asterisks represent upper limits. The notation H and K refers to Hillier and Kendrick, ref. 2; B refers to Basch, ref. 1.
223 we have plotted intensity of the satellite peaks versus energy; both intensity and energy are given relative to that of the main peak. We consider first the results for oxygen. Experiment and theory agree that there should be a major satellite at about 12 eV. According to both sets of theoretical calculations, this feature arises from a 7~-P n* excitation. Those of Hillier and Kendrick indicate that this satellite should consist of two peaks of about equal intensity, whereas those of Basch indicate one major and one minor peak. In the experimental spectrum there is evidence that the satellite peak is somewhat broader than the main peak. This extra breadth may be due to a closely spaced doublet, in agreement with the calculations of Hillier and Kendrick. On the other hand, it may arise from a single peak that is broadened by transitions to a wide range of vibrational levels in the final state. The calculations predict a total intensity of 15 % (Basch) and 20 % (Hillier and Kendrick), substantially greater than the experimental value of 7 %_ For the carbon spectrum, both calculations predict a major peak at 11-14 eV due, as in the oxygen case, to a 7c + n* excitation. The experimental spectrum, showing a major peak at 11 eV is in reasonable agreement with these predictions, both as to energy and intensity. The two sets of calculations both indicate other peaks should be found in the carbon spectrum. There is evidence for additional satelhtes but it is possible to set only an upper limit on their intensity. In general, the theoretical calculations provide a reasonably good overall prediction of the satellite spectrum. There is, in detail, disagreement between experiment and calculation on the exact position of the peaks, on whether there will be one or two observable peaks resulting from a rc + n * transition, and on the intensity of the peaks. It is clear that the prediction of these satellite structures presents a very demanding test to the theoretical calculation. Core
ionization
potentials
There is some confusion in the literature concerning the oxygen and carbon 1s binding energies of formaldehyde. There is one reportr3 of the C shift relative to CH, as 3.3 eV, listing the original source as ref. 14. Examination reveals, however, that nowhere is there an experimental shift reported there for formaldehyde. Schwartz et al.’ 5 list + 3.2 eV but give no reference, and Jolly and Ferry16 list + 3.3 eV, also giving (14) as a reference. To add to the confusion, an oxygen shift (relative to 0,) is reported by Schwartz et al.15 as being -5.5 eV, unreferenced. Nowhere is there reported an experimental value for the oxygen shift. In any event, our values are in disagreement with the reported values, ours being + 3.51 eV (C 1s - CH.) and -4.25 eV (0 Is - 0,). One instructive and often used method of interpreting the shifts is the pointcharge analysis. Its use gives an approximate charge distribution for the molecules of interest and the results are convenient for comparison with charges derived from quantum-mechanical calculations. Assuming that the electron density of a molecule
224 TABLE 2 CALCULATED
ATOMIC Eqn. (1)
qc 40 9H s b c d
0.33 -0.37 +0.02
CHARGES
FOR FORMALDEHYDE
Ed?.= 0.12 -0.21 0.045
CNDO/2b 0.21 -0.19 -0.01
r4wc 0.02 -0.31 0.15
[532/21jd 0.26 -0.44 0.09
Ekctronegativity equalization, ref. 16. Theoretical value, ref. 19. Theoretical value, ref. 20. Theoretical value, ref. 21.
can be approximated
by localization of charges at points (for atoms other than the one of interest) or on a spherical shell external to the core hole (for the charge on the atom of interest), and assuming the binding energy shifts to be equal to orbital energy shifts (i.e. no differential relaxation), we can represent shifts as functions of initial-state charges, thus AEi = kiqi + e* 2 qj/Rij i+.i
(1)
The AEi are the shifts, qi the charges, Rij interatomic distances, and ki constants, dependent on the particular atom of interest. The assumptions behind the point charge model are discussed in more detail elsewhere17* ‘*. For oxygen we refer shifts to 0, and for carbon to CH,. In the past values of kc and k, that have been found to be successful are k, = 22.0, k, = 22.517* I*. The charges we calculate using these values are given in the first column of figures in Table 2. Jolly and Perry l6 have used an electronegativity equalization method to derive atomic charges for a large number of carbon- and oxygen-containing compounds. Using these charges they fit their values to equations of the form EB = kg + V + I to derive best values for k and 1. (V is the external potentia1 and I is an offset). They find that kc = 3 1.06, k, = 30.43, I, = 0.47, and lo = - 0.27. In general, the charges derived by the electronegativity equalization method are smaller than those derived by other methods. Charges computed by this method are listed in the second column of Table 2. The last three columns contain charges derived from theoretical calculations. The first is from Pople and Beveridge’sl’ CND0/2-wave functions and the second from Snyder and Basch’s near Hartree-Fock level calculations” using a contracted Gaussian basis set. The last column lists the results of accurate calculations by Neumann and Moskowitz21 using a less-restricted Gaussian basis set. Our charges (from eqn. (1)) show clearly the transfer of charge from carbon to oxygen and indicate that it is more extensive than those from all other calculations but the last. The results imply best agreement with the most accurate theoretical treatment.
225 It is noted by Neumann and Moskovitz that the charge distribution is very sensitive to the approximate nature of the basis set. One would expect the [532/21] basis set to yield more accurate charge distributions than the [42/2] basis set, and thus the closer agreement with our calculations is gratifying. We note, however, that the point-charge analysis is limited in its applicability by the choice of k’s, neglect of relaxation, and reference to the carbon shift to CH, instead of neutral carbon. ACKNOWLEDGEMENTS
This work was supported in part by the U.S. Energy Research and Development Administration.
REFERENCES 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
H. Basch, Chem, Phys., 10 (1975) 157. I. H. Hillier and J. Kendrick, J. Electron Spectrosc. Relat. Phenom., 6 (1975) 325. T. X. Carroll and T. D. Thomas, J. Electron Spectrosc. R&t. Phenom., 4 (1974) 270. P. H. Citrin, R. W. Shaw and T. D. Thomas, in D. A. Shirley (Ed.), Electron Spectroscopy, North-Holland, Amsterdam, 1972, p. 105. C (1s) in COZ = 297.71 eV and 0 (1s) = 541.32 eV. R. W. Shaw and T. D. Thomas, J. Electron Spectrosc. Relat Phenom., 5 (1974) 1081. Also see G. Johannson, J. Hedman, A. Berndtsson, M. Klasson and R. Nilsson, J. Electron Spectrosc. Relat. Phenom., 2 (1973) 295. E. N. Lassettre and M. E. Krasnow, J. Chem. Phys., 40 (1964) 1248. D. W. Turner et al., Molecular Photoelectron Spectroscopy, Wiley-Inter-science, New York, 1970. M. J. Weiss, C. E. Kuyatt and S. Mielczarek, J. Chem. Phys., 54 (1971) 4147. R. L. Martin and D. A. Shirley, J. Chem. Phys., 64 (1976) 3685. R. L. Martin and D. A. Shirley, in A. D. Baker and C. R. Brundle (Eds.), Electron Spectroscopy: Theory, Techniques and Applications, Academic Press, to be published. J. B. Mann, Atomic Structure Calculations I. Hartreo-Fock Energy Results for the Elements Hydrogen to Lawrencium, Los Alamos Scientific Laboratory Report, LA-3690, 1967. R. L. Martin, B. E. Mills and D. A. Shirley, J. Chem. Phys., 64 (1976) 3690. U. Gelius, P. F. Heden, J. H. Hedman, B. J. Lindberg, R. Manne, R. Nordberg, C. Nordling and K. Siegbahn, Phys. Ser., 2 (1970) 70. K. Siegbahn et al., ESCA Applied to Free Molecules, North-Holland, Amsterdam, 1969. M. E. Schwartz, J. D. Switalski and R. E. Stronski, in D. A. Shirley (Ed.), Electron Spectroscopy, North-Holland, Amsterdam, 1972, p. 605. W. L. Jolly and W. P. Perry, J. Am. Chem. Sot., 95 (1973) 5442. T. X. Carroll, R. W. Shaw, Jr., T. D. Thomas, C. Kindle and N. Bartlett, J. Am. Chem. Sot., 96 (1974) 1989. D. W. Davis, D. A. Shirley and T. D. Thomas, J. Am. Chem. Sot., 94 (1972) 6565. J. A. Pople and D. L. Beveridge, Approximate MoIecular Orbital Theory, McGraw-Hill, New York, 1970, p. 122. L. C. Snyder and H. Basch, Molecular Wave Functions and Properties, Wiley, New York, p. T-68. D. B. Neumann and J. W. Moskowitz, J. Chem. Phys., 50 (1969) 2216.