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The momentum distributions and binding energies of the valence orbitals of phosphine by electron momentum spectroscopy: Quantitative comparisons using near Hartree-Fock limit and correlated wavefunctions
Chemical Physics 136 ( 1989) 55-66 North-Holland, Amsterdam
THE MOMENTUM DISTRIBUTIONS AND BINDING ENERGIES OF THE VALENCE ORBITALS OF PHOSPHINE BY ELECTRON MOMENTUM SPECTROSCOPY: QUANTITATIVE COMPARISONS USING NEAR HARTREE-FOCK LIMIT AND CORRELATED WAVEFUNCTIONS S.A.C. CLARK, C.E. BRION Department of Chemistry, The University ofBritish Columbia, 2036 Main Mall, Vancouver, B.C. Canada, V6T 1 Y6
E.R. DAVIDSON
and
C. BOYLE
Department of Chemistry, Indiana University, Bloomington, IN 47405, USA Received
12 April 1989
The binding energies and electron momentum distributions for the three valence orbitals of PH3 have been measured by high resolution electron momentum spectroscopy. The measured binding energy spectrum, which shows extensive structure in the inner valence region, is compared with CI and many-body Green function calculations. The momentum distributions are compared on a quantitative basis with a range of SCF wavefunctions up to near the Hartree-Fock limit in quality and also with full ion-neutral overlap calculations carried out using correlated wavefunctions by the method of configuration interaction. Inclusion of electron correlation is found to have minimal effect on the calculated momentum distributions.
1. Introduction
the XMP can be predicted by sufficiently accurate ab initio theory as it is related in a simply way to the ion-molecule overlap [ 1,2 1. (See eqs. ( 1) and (2 ) below.) A further simplification, often found to be quite accurate, is the target Hartree-Fock approximation [ 1,2 1, in which ionization is viewed as a single electron being ejected from a doubly occupied, canonical Hartree-Fock orbital with well defined energy. In this case, the XMP can be equated with the spherical average of the amplitude of the momentum space wavefunction of that orbital (that is, the momentum distribution or MD). Hence the XMP can be used for the evaluation and refinement of Hartree-Fock molecular orbital calculations of the momentum distribution [ 3-71. Calculations of the ionmolecule overlap distribution (OVD) go beyond the Hartree-Fock limit by using CI wavefunctions in order to include electron correlation and relaxation and can also be tested against the experimental results [ 3-
Electron momentum spectroscopy (EMS) in the symmetric non-coplanar geometry is a sensitive probe of the valence electronic structure of atoms and molecules [ 1,2 1. The complete binding energy spectrum can be measured throughout the outer and inner valence regions at low energy resolution (typically 1.7 eV fwhm). Further, by selecting electrons with particular binding energies and measuring the intensity distribution as a function of the angle between the scattered and ejected electrons, the experimental momentum profile (XMP) of target electrons removed in a given ionization process may be obtained. The shape of the XMP yields direct information about the symmetry of the electronic states involved in the ionization process and is therefore particularly useful in assigning the origin of the many-body (satellite) structure which frequently arises in the inner valence region of the binding energy spectrum. In this respect, the XMP is more easily and directly interpreted than the angular distribution parameter (/I) involved in photoelectron spectroscopy. In addition 0301-0104/89/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
71. EMS is now well established as a discriminating test of high level molecular orbital calculations [ 3-71. As part of a continuing experimental and theoretical B.V.
56
S.A.C. Clark et al. /Electron
momentum
study of the hydrides of the second [ 3,561 and third [ 4,7] row we now present new measurements of the valence shell binding energy spectrum as well as the XMPs of the valence orbitals of phosphine (PH,). The XMPs are compared with calculations up to the Hartree-Fock limit and beyond. In all of our most recent papers in this series [ 3-71 as well as in corresponding studies of HF and HCl [8,9] and noble gases [ 8,101 the XMPs have been measured with higher momentum resolution (equal to or better than 0.15 au hwhm) than in most previous work, thus allowing for a much more accurate comparison of theory with experiment. Most of these more recent studies [ 3-81 have also involved comparisons with SCF calculations of momentum distributions (MDs) using a range of wavefunctions essentially up to the Hartree-Fock limit as well as with ion-molecule overlap distributions (OVDs) calculated using configuration interaction (CI) wavefunctions for the ion and molecule. Basis set saturation, including very diffuse functions, has been achieved in obtaining very large and flexible basis sets for both the Hartree-Fock limit and CI wavefunctions [ 6,111. The configuration interaction calculations recover more of the correlation energy (for example, as much as 86% in Hz0 [ 6 ] ) than any previously published CI calculations of which we are aware. A low impact energy (400 eV), low momentum resolution (ApcO.4 au hwhm) study of PH3 has already been reported [ 12 1. The earlier results [ I2 ] showed strong splitting of the 4a, inner ionization strength due to many-body effects. This earlier study for PHj suggested that even quite modest SCF wavefunctions provided a fairly good description of the shape of the measured XMPs for the three valence orbitals. This behaviour was in very sharp contrast to the situation for NH3 [ 13 1, where very little splitting of the inner valence (2a,) ionization strength occurred and large discrepancies existed between SCF calculations and experiment for the outermost (3a, ) orbital at low momentum. Recent high impact energy ( 1200 eV), high momentum resolution EMS studies of NH3 [ 5 ] indicate that the momentum distributions are quite well described on a quantitative basis if CI calculations of the OVD are employed. The XMPs of PHx measured earlier also showed some evidence of distortion above 1 au due to the low impact energies used (400 eV). It is therefore of inter-
spectroscopy
ofphosphine
est to remeasure the XMPs of the valence orbitals of PH3 using the higher impact energy ( 1200 eV) and much improved momentum resolution (0.15 au hwhm ) now available on our spectrometer [ 10 ] and also to place the XMPs on the same relative intensity scale [ 61 to provide a more stringent quantitative comparison with calculations than was possible with the individual height normalizations used for each orbital in the earlier study [ 121. In particular it is of importance to check the apparently already quite good (shape) agreement between XMPs and MDs calculated using modest SCF wavefunctions [ 12 ] and also to compare quantitatively with the results obtained using near Hartree-Fock limit and CI wavefunctions. Earlier studies of the third-row, group VI hydride H2S [ 71 have shown that addition of correlation and relaxation to the wavefunctions (i.e. the full OVD) produces little or no further change from the MDs predicted using Hartree-Fock limit wavefunctions with saturated basis sets. The behaviour for HIS [ 71 is in sharp contrast to the second-row analogue Hz0 where inclusion of correlation and relaxation was essential to obtaining good agreement between calculation and the XMPs [ 6 1. Since addition of correlation and relaxation has also been found to produce no further change from the Hartree-Fock limit MDs for the group IV, row 2 and 3 hydrides CH, [ 31 and SiH4 [4] respectively, it is of interest to determine the situation for PH3 (group V) and compare with the results for NH3 [ 5 1. In particular the present work compares the measured XMPs of PH3 with a calculation quite close to the Hartree-Fock limit and also with an ion-molecule overlap (OVD) calculation using wavefunctions from a multireference singly and doubly excited configuration interaction calculation. In addition the binding energy spectrum of PH3 is compared to many-body Green function calculations from the literature [ 141.
2. Experimental method The high momentum resolution EMS spectrometer used in the present study has been described previously [ lo]. Briefly, a high energy electron beam ionizes a gas sample and the scattered and ejected electrons are detected in coincidence. The spectrometer selects only those events in which the scattered
S.A.C. Clark et al. /Electron momentum spectroscopy o$phosphine
and ejected electron have equal energy and that are scattered at 19=45 o with respect to the electron beam. The relative azimuthal angle (@) between the two detectors is varied by rotating one of the electron analyzers about the incident electron beam axis. Two modes of operation are possible. If the angle @ is fixed and the impact energy (E,= 1200 eV+binding energy) is varied, a binding energy spectrum is obtained. This measures vertical ionization potentials where final ion states are resolved or alternatively the spectral envelope where many closely spaced states exist due to many-body effects which commonly occur in the inner valence region. If the impact energy is fixed at 1200 eV+ the vertical IP of a given orbital, then the momentum distribution (i.e. the XMP) of that orbital can be measured by varying the angle @,since @is directly related to the momentum of the ionized electron prior to knock-out [ 15 1. Within the plane wave impulse approximation and the Born-Oppenheimer approximation, the cross section OTbcs for an EMS experiment in the symmetric non-coplanar geometry is proportional to the spherical average of the square of the ion-molecule overlap [ 1,2,15 1, ~TDCS
a
I dQlIq%l’J’,Y,)12,
(1)
where q is the momentum of the initially bound electron. If the cross section is assumed to be proportional to a canonical Hartree-Fock molecular orbital (the target Hat-tree-Fock approximation) then the cross section reduces to nTDCS
as:”
s
dQ
I@j(P)
I2 >
(2)
where g,,(p) is the momentum space wavefunction for the canonical Hartree-Fock orbital from which the electron was removed. The spectroscopic factor Sjf) is the probability that the final state ion has a hole in the inital state molecular orbital @,.Within the target Hartree-Fock approximation, the spectroscopic sum rule applies: ,YfS,(‘) = 1, where If is a sum over all final states, though in practice only states within the same symmetry manifold i will contribute. Application of the sum rule allows relative cross sections from different orbitals to be compared on the same intensity scale provided the results are summed over all final states for each initial state orbital. A common intensity scale is achieved by normalizing the XMPs
51
to the relative peak areas in the binding energy spectrum (see refs. [ 5,6] for details). The spectrometer was calibrated with Ar both before and after the study of PHJ to determine the energy resolution and momentum resolution. These were found to be 1.7 eV fwhm and 0.15 au hwhm respectively. The C.P. grade phosphine ( > 99.5% purity) was supplied by Matheson and used without further purification.
3. Calculations Within the target Hat-tree-Fock approximation, the experimental momentum profiles can be compared to the spherical average of the square of the momentum space wavefunction (eq. (2) ). In addition to a minimum basis set calculation, a near-Hartree-Focklimit calculation was also performed using a 136-GTO basis set described below. Calculation of the ionmolecule overlap (eq. ( 1) ) was also performed using CI wavefunctions for the ion and molecule with which it is believed that more than 80% of the valence shell correlation energy is recovered. This 136-G(C1) configuration interaction wavefunction is also described below. Details of the wavefunctions and basis sets are given below and in table 1. The computations for PH3 were performed at the equilibrium geometry with rpn= 1.420 au and the PHP angle = 93.3 ’ [ 161. The CI calculations include only valence shell correlation and neglect core correlation and relativistic effects. MBS+3d basis set. This calculation of Boyd and Lipscomb [ 17 ] used a minimum basis set of Slater orbitals supplemented with a 3d orbital on the phosphorus. The exponents were: P 1s 14.7, P 2s and 2p 5.425, P 3s and 3p 1.6, P 3d 1.4 and H 1s 1.2. 136-GTO basis set. The extended basis set for PH3 consists of an even-tempered (2 1s, 14p,4d,2f/ 1OS, 3p,2d) primitive set contracted to a [ 12s 1Op,4d, 2f/ 6s,3p, Id] Gaussian type (GTO) basis. The s components of the Cartesian d functions and the p components of the f functions were removed to avoid linear dependence, forming the final 136-GTO basis. The basis set was taken from a calculation on PH, using energy optimized exponents [ 18,191 and employing an even-tempered restriction on the expo-
S.A.c. Clark et al. /Electron momentum spectroscopy ofphosphine
58 Table 1 Properties
of restricted
Hartree-Fock
and configuration
Type of calculation
Wavefunction label
Phosphorus
RHF RHF MR SDCI ” exp.
MBS+3d 136-CT0 136-G(CI)
Slater: 3s,2p,ld (21s,14p,4d,2f)/[ (21s,14p,4d,2f)/[
interaction
basis
wavefunctions Hydrogen
for PH3
basis
Total energy (au)
12s,lOp,4d,2f] 12s,lOp,4d,2f]
Slater: 1s (lOs,3p,2d)/[Ss,3p,ld] (lOs,3p,2d)/[Ss,3p,ld]
-341.3094 -342.4934 -342.6833 - 343.42
Dipole moment
Ref. (D)
1171
0.86 0.665 0.624
this work this work
0.578
[23,241
i') In comparing
with experimental quantities it should be noted that the calculations are for a non-vibrating molecule (equilibrium geometry) and do not include relativistic effects. In the Cl calculation only valence shell correlation is included. The core correlation and relativistic effects are expected to be slightly larger for PHJ than H2S (see discussion in ref. [7] ).
nents. The f exponents are taken from an analogous calculation on H$ by Feller et al. [ 111. The basis set was designed to saturate the diffuse basis function limit and to give improved representation of the (r-space) tail of the orbitals. It should be noted that due to the very large number of functions which have been used, the wavefunction is expected to be fairly insensitive to the exact choice of exponents. 136-G(CI) ion-molecule overlap. The CI wavefunctions for the neutral and ion species are built using the 136-GTO basis. The methods applied were Hartree-Fock singly and doubly excited configuration interaction (HF SDCI ) and multireference singly and doubly excited configuration interaction (MR SDCI ) . The valence electron CI convergence has been shown to be improved (i.e. more correlation energy was recovered with fewer configurations) when the Hartree-Fock virtual orbitals are transformed into K orbitals [ 20-221 and hence K orbitals were used. The singly and doubly excited configurations used in the MR SDCI were energy selected based on second-order Rayleigh-SchrGdinger perturbation theory and the reference space was selected based upon the coefficient contribution in the HF SDCI. This selection was necessary due to the large number of configurations associated with the extended basis set exceeding our current variational capacity. The calculations on PH: were done with neutral PH3 ground state molecular orbitals. The neutral molecule HF SDCI calculation selected 10366 spin-adapted Hartree-Fock singly and doubly excited configurations, keeping all the singly excited and using second-order perturbation theory on the doubly excited, with the neglected configura-
tions having a total contribution of less than one millihartree to the CI energy. The MR SDCI space was chosen from the HF SDCI’s largest coefficients, as discussed above; a coefficient threshold of at least 0.030 was systematically maintained for the 5a; ’ and 2e- ’ ion states, but a higher one was needed for the calculation of multiple roots of ‘A, symmetry (the 5a;’ and 4a;’ included) as discussed later. The dimension of the neutral MR SDCI was 22589 out of the total of 2495566 possible singly and doubly excited configurations. This MR SDCI energy is - 342.6833 au, with the core electrons of phosphorous uncorrelated. Some calculated properties of the neutral molecule are listed in table 1 along with experimental values [ 23,241. The calculations for the ion states of phosphine were performed using molecular orbitals for the neutral molecule. The OVDs computed from the CI wavefunctions for the ion states then have the same form as an MO expanded in the neutral basis. The calculation of the ion states involved a similar process to that of the neutral with the exception that no RHF calculations were done. HF SDCI and MR SDCI were done for the 5a; ’ and 2e-’ states. The coefficients for the MR SDCI were chosen based upon the coefficient contribution using a threshold of 0.030 for 5ar’ and 2e-‘. The ionization potentials for these two cation states are listed in table 2. The IP values are seen to be in good agreement with the experimental values. The ‘A, multiroot calculations employed a modified reference space selection. The calculation was done in C, symmetry but used a symmetrically closed set of configurations containing the largest coefficient contributions for the first 15 states from a cal-
19.45
22.61
25.46
19.4 20.6
23.2
25.6 27.2
da,
13.50(5)
10.58(l)
13.6(l)
10.59(2)
19.0
13.6
10.60
ref. [27]
19.5(2) 20.5(2)
-
-
25.6 26.5 27.8 29.1
19.4 20.6 21.7 23.2 24.1
-
-
23.23
14.17
10.58
31.60 (0.02) 33.96 (0.01)
(0.13) (0.03) (0.03) (0.03) (0.02) (0.02) (0.13)
30.05 31.18 31.54 32.90
(0.009) (0.008) (0.004) (0.007)
26.49 (0.031) 26.53 (0.083)
19.28 (0.342) 20.98 (0.100) 22.32 (0.058) 22.79 (0.231) 24.97 (0.005) 25.98 (0.003)
19.37 (0.53)
22.39 23.20 23.46 25.22 26.78 27.73 28.04
13.59 21.30 26.88 28.52 30.11 31.88 31.95
(0.904) (0.006) (0.003) (0.006) (0.004) (0.003) (0.004)
10.25 (0.911) 19.28 (0.004) 24.97 (0.006) 26.49 (0.004) 28.16 (0.015) 30.05 (0.007)
13.23 (0.93)
9.95 (0.92) 30.44 (0.02)
RHF Green function (pole strength) 136-CT0 simplified ref. [ 141 synchrotron this work Zph-TDA radiation [ 291 ADC(4) [31]
Calculation
22.01 (0.1180) 22.77 (0.0444) 23.15 (0.0056) 24.67 (0.0468) 25.41 (0.0185) 26.20 (0.0093) 27.61(0.1184) 28.14(0.0398)
19.70 (0.4373)
13.62 (0.8399)
10.44 (0.8626)
136-G(C1) (spectroscopic factor) this work
a1 These represent observed peaks for the 5a, and 2e states, but are the centres of the gaussians in the deconvolution for the inner valence (4ai ) region (see fig. I ). The deconvolution was based largely on the PES work of Cauletti et al. [29] (see text for details).
29.1 31.8 36.0
13.44
13.6
2e
10.59
10.6
ref. [26]
photoelectron spectroscopy
ref. [ 121 ref. [25]
Sal
thisworka’
EMS
State Experimental vertical IP
Table 2 Measured and calculated binding energies and calculated pole strengths and spectroscopic factors for the valence shell of PH3
S.A.C. Clark et al. /Electron momentum spectroscop.v ofphosphine
60
culation in which all the single excitations from all valence hole states were kept. The IP values and spectroscopic factors for the roots of the CI calculation are compared with Green function results [ 141 in table 2 and fig. 2 (see discussion in section 4 ).
4. Results and discussion
i
4.1. Binding energy spectra The phosphine molecule has Csv symmetry [ 161. The electronic configuration of PH3 can be written (la,)‘(2a,)‘(
le)4(3al)‘(4a,)2(2e)4(5a,)2
cure orbitals
‘A,.
valence orbitals
The EMS binding energy spectra of PH, from 838 eV, shown in figs. la and lb, were obtained at an impact energy of 1200 eV (plus the binding energy) and at relative azimuthal angles $ of 0” and 6” respectively. The two binding energy spectra are on a common (relative) intensity scale. The energy scale was calibrated with respect to the 5a, vertical ionization potential measured by high resolution photoelectron spectroscopy [25-281. Measured and calculated binding energies are summarized in table 2. Peaks due to the 5a;’ and 2e-’ ionization processes are found at vertical ionization potentials of 10.6 and 13.6 eV consistent with the results of photoelectron spectroscopy [ 25-28 1. The inner valence region shows a multipeaked spectrum consistent with previous EMS work [ 121. The main features of the inner valence part of the experimental binding energy spectrum at both @= 0’ and 6’ are seen (fig. 1) to be three large peaks at approximately 20.0, 23.2 and 25.6 eV, with the heights of the peaks in the ratio of approximately 3 : 1 : 2. The earlier low momentum resolution measurements of the binding energy spectra and the XMPs of the three principal inner valence satellite peaks of PH3 [ 12 ] lead to the conclusion that the intensity above 17 eV is predominantly due to the 4a; ’ ionization process. This assignment was subsequently supported by Green function calculations using several different basis sets [ 14 1. Until the recent studies of Cauletti et al-. [ 291 using synchrotron radiation, no comprehensive PES measurements of the inner valence region of the PH1
I
10
20
30
BINDING ENERGY
(eV)
Fig. I. Binding energy spectra for the valence shell of PH, at azimuthal angles @=O” and 6”. The solid line is a sum of Gaussian functions centred on peak locations using experimental widths and convoluted with the instrumental energy resolution.
binding energy spectrum had been reported (see table 2). These PES spectra [ 291 are at higher resolution (fwhm= 0.8 eV) and show more tine structure in the inner valence region than either the present or the earlier [ 12 ] EMS results. Cauletti et al. [ 29 ] suggest, on the basis of a deconvolution analysis, that at least nine peaks exist in the 17-30 eV binding energy region. It is apparent both from the present work (fig. 1) and the PES spectra [ 291 that there is probably some additional spectral intensity above 38 eV. The lower relative intensity observed at higher binding energies in the PES spectrum (see fig. 2 of ref. [ 291) compared to the EMS spectrum is not surprising since at the low photon energy used (hv= 50 eV) the partial cross sections of the higher energy satellites are expected to be relatively lower than those at lower binding energy since they are closer to threshold. PES
S.A.C. Clark et al. /Electron momentum spectroscopy ofphosphine
spectra at significantly higher photon energies are necessary in order to make any meaningful comparison with the intensities observed in EMS for a given symmetry manifold [ 301. The deconvolution of the EMS spectrum shown in fig. 1 above 17 eV is based on the deconvolution analysis of the PES spectrum reported by Cauletti et al. [ 29 ] which shows nine peaks between 17 and 30 eV. However, due to the slightly lower resolution only six peaks have been fitted in the EMS spectrum between 17 and 30 eV. Two further peaks, not identitied in the PES spectrum, are fitted to the EMS spectrum at 32 and 36 eV. Each of the eight peaks fitted in the range 17-39 eV (fig. 1) is more intense at @= 0 ’ than at @= 6” thus confirming the dominant 4a; ’ character of the inner valence spectrum above 17 eV. In particular, the peak at 20.6 eV is clearly “s-type”, i.e. it is dominantly due to the 4a, ’ process. On the basis of a relatively small decrease in the/3value compared to that for the 19.4 eV peak, Cauletti et al. [ 291 have suggested that the 20.6 eV peak is a satellite associated with an outer valence ionization process. Such an interpretation is inconsistent with the present, more direct, experimental findings. It should also be noted that the ADC(4) many-body Green function calculations [ 3 1 ] predict that the satellite structures in this region are dominantly 4a; ’ in character ( see below and table 2 ) . The sum of the binding energy spectra taken at @=O’ and @=6”, is compared in fig. 2a with the results of two Green function calculations [ 14,3 11. The Green function calculations have been folded with the experimental energy resolution and the Franck-Condon widths obtained from the high resolution photoelectron spectra [25-291 to obtain figs. 2c and 2d. The Green function calculation shown in fig. 2c is based on the two-particle-hole Tamm-Dancoff approximation ( Zph-TDA) [ 32,331 and is taken from the work of Domcke et al. [ 141. A rather small basis set, ( 12s9p2d/4s) contracted to [ 6s4p2d/2s], was used. The calculation shown in fig. 2d [ 3 1 ] used the simplified ADC( 4) approximation [ 341 and also used a rather small basis set: ( 12s9pld/4slp) contractedto [6s4pld/2slp].Alsoshown (intig.2band table 2) are the roots and spectroscopic factors from the MR SDCI calculation done in the present work (see section 3). Again the theoretical results are
61
folded with observed widths. All calculations predict significant splitting of the 4a, ’ ionization strength due to many-body effects. The calculated spectral envelope shows quite reasonable agreement in all cases with the EMS data. Although all calculations predict qualitatively similar results, the third band appears at too high an energy (x27 eV) and with too little intensity. As has been observed for other molecules, the 2ph-TDA and ADC( n) type methods are found to underestimate pole strengths at higher binding energies [ 5,7,9,35-391. The CI calculation predicts almost exact binding energies (see table 1) for the 5a; ’ and 2e-’ ionization processes, while giving similar results to the Green function calculations in the inner valence region. 4.2. Comparison of experimental and calculated momentum distributions The experimental momentum profiles (XMPs), calculated spherically averaged momentum distributions ( MDs), and ion-molecule overlaps ( OVDs) are shown in figs. 3-5 together with momentum and position space density maps calculated in selected planes for an oriented PH3 molecule using the 136-GTO wavefunction. The momentum resolution of the XMPs is clearly improved over the earlier work [ 12 1. The XMPs were placed on the same relative intensity scale by normalization on the binding energy spectra (fig. 1) as described earlier [ 6,7]. The XMPs, MDs and OVDs have been placed on a common intensity scale by a single point normalization of the OVD calculation to the 5a, orbital. All other relative normalizations for calculations and experiment have been preserved. All calculations have been folded with the experimental momentum resolution (0.15 au hwhm). For the reasons discussed in section 2, all of the inner valence satellite intensity above 17 eV (fig. 1) has been assigned to the 4ai ’ process. The 136-G( CI ) ion-molecule overlap (OVD) calculations using correlated wavefunctions and the 136GTO SCF calculation of the momentum distributions (MD) are seen (figs. 3-5) to be very similar for a given ionization process and essentially identical in the case of the 5a, orbital (fig. 3). The calculations also give an excellent fit to the shape of the experimental data for the 5a, orbital. Agreement with the data for the 2e orbital, however, is somewhat less
62
S.A.C. Clark rt al. /Electron
momentum
spectroscopy
qfphosphrnr
Fig. 2. Experimental and calculated binding energy spectra for the valence shell of PHI (see table 2 for calculated pole assignments). (a) EMS spectra (sum of o=O’ and 6’. this work, see fig. I ); (b) Cl calculation, this work, (c) and (d) many-body Green function calculations. ref. [ 141.
SPHERICALLY
AVERAGED
MOMENTUM
DENSITY
POSITION
DENSITY
;jb’n
MOMENTUM (au)
POSITION
(au)
Fig. 3. Measured and calculated spherically averaged momentum distributions for the 5a, orbital of PH?. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136-GTO calculation. The contour values represent 0.02, 0.04, 0.06, 0.08, 0.2, 0.4, 0.6, 0.8, 2, 4, 6, 8, 20, 40, 60 and 80% ofthe maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
satisfactory in that the MD and OVD calculations maximize at slightly too high a momentum and do not completely account for the intensity near p = 0 au. If this additional intensity at low momentum in the experimental data is due to an unresolved (4a, ) symmetric pole under the 2e binding energy peak, then one would expect the experimental momentum pro-
file to contain more total intensity than the calculated momentum distribution. However, the calculation shows more intensity than the data between 0.6 and 1.0 au. The small difference at low momentum could possibly be due to uncertainty in the momenturn resolution fitting procedure. The 136-CT0 MD (and 136G( CI) OVD) for the
S.A.C. Clark et al. /Electron momentum spectroscopy ofphosphine
63
-8.0 -4.0 0.0 1.0 a.0 0.51.0
MOMENTUM
(au)
POSITION (au)
Fig. 4. Measured and calculated spherically averaged momentum distributions for the 2e orbital of PH,. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136~GTO calculations. The contour values represent 0.02,0.04, 0.06, 0.08,0.2,0.4, 0.6,0.8,2,4, 6, 8,20, 40, 60 and 80% of the maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
SPHERICALLYAVERAGED YONENTUN DISTRIBUTION
MOMENTUM
POSITION
DENSITY
MOMENTUM
(au)
DENSITY
POSITION (au)
Fig. 5. Measured and calculated spherically averaged momentum distributions for the 4a, (main peak) orbital of PH,. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136~GTO calculation. The contour values represent 0.02,0.04,0.06,0.08,0.2,0.4,0.6,0.8,2,4,6,8,20,40,60 and 80% of the maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
4a, ’ process predicts significantly greater ( x 25Oh) intensity than is observed. This discrepancy may, at least in part, reflect the existence of 4ai ’ satellite intensity lying above 38 eV, which is the limit of the presently reported binding energy spectra data. It is also possible that some absorption is occurring for this more deeply bound orbital even at the impact energy of 1200 eV [ 15 1. It can be seen from the 0.74 x ( 136G( CI ) ) curve that the shape of the 4a, XMP is reproduced exactly by the 136-G(C1) and 136-GTO calculations, except in the region of about 1.2-2 au, where the difference between theory and experiment may be due to a breakdown of the plane wave approximation which is not unexpected at higher values of momentum [ 1,15,40].
In the previous (lower momentum resolution) EMS study of PH, [ 12 1, the MBS + 3d wavefunction [ 17 ] was found to model the data reasonably satisfactorily (for shape) when the XMP of each orbital was individually height normalized to the calculation. However, in the present work, with experiment and theory now on a common intensity scale for all orbitals, the MBS + 3d calculation is found to be inadequate. In order to facilitate comparison with the earlier work [ 12 1, the MBS + 3d calculation is shown (fig. 6) separately height normalized to each of the presently determined high momentum resolution XMPs so that only the shape of the theoretical and experimental curves is compared for each orbital. It can be seen that the shapes of the Sa, and 2e orbitals
64
S.A. C. Clurk et al. /Electron
(‘)
5a
Cc)
da
--‘I PH,
1
2/
6
0
IiPH,
1
t
-‘r* \. ~_Ti- ..
.
.
momentum
.
.,
_
3
0 MOMElNTUM
’ (au)
Fig. 6. Measured and calculated (MBS+ 3d) momentum distributions for the valence orbitals of PH,. Each calculation shown is separately height normalized to experiment for each orbital to facilitate direct comparison with earlier measurements [ 121.
show about the same level of agreement with experiment as was found in the earlier work. It is important to note that much poorer agreement is obtained between the MBS + 3d calculation and experiment when correct relative intensities are established for all orbitals (see figs. 3-5). This shows that independent height normalization could lead to erroneous conclusions as to the quality of the wavefunction. The very limited basis set in the MBS+ 3d wavefunction in fact discriminates against the chemically important low p parts of the wavefunction. This low p region is evidently much better modeled by the much more saturated basis set, including diffuse functions, employed in the variationally superior 136-GTO wavefunction.
spectroscopy
qfphosphine
In the momentum and position space density-maps, all coordinates are in atomic units. The phosphorus nucleus is at the origin of the position space maps, and the hydrogens located at approximately (0,2.25, - 1.46) (in the plane of the picture) and ( ? 1.95, - 1.13, - 1.46) (out of the plane of the picture). These pictures are consistent with the simplest notions of how we expect these orbitals to be built up from atomic orbitals. To a first approximation, the 4a, is composed of a phosphorus 3s orbital bonding with hydrogen 1s orbitals. The 2e orbital consists of a-phosphorus 3p orbital in the “plane” of the molecule (although the molecule is not quite planar) combined appropriately with hydrogen 1s orbitals. It is degenerate since there are two orthogonal p functions in the plane. (For the orientation of PH3 shown in the density maps, this is the xy plane.) The 5a, orbital consists of a p function perpendicular to this plane bonding with the hydrogen s functions. The 5a, orbital in PH3 shows much more phosphine 3s contribution (this is seen as the symmetric density near the origin) than the corresponding orbital in NH3 ( 3a, ) shows nitrogen 2s intensity [ 5 1. In phosphine, all three orbitals show more density near the origin of position space (despite strong contributions from the hydrogens) than the corresponding orbitals in NH3. Both from EMS and PES results it has been observed that there is much more satellite structure in the inner valence region of the binding energy spectrum of PH3 (see figs. 1, 2 and also refs. [ 12,291) than of NH3 [ 5,13,4 1,42 1. It is also noted that CI calculations of the ion-molecule overlap (OVD) of the inner valence orbitals of PH3 and NH3 vary little, if at all, from calculations based on the target HartreeFock approximation [ 5 1. In fact, this is true for all valence orbitals of PHs. Yet a significant difference is observed between the ion-molecule overlap (OVD) and the target Hartree-Fock approximation momentum distribution (MD) for the 3a, orbital of NH3 [ 5 1. This may suggest that the main factor which causes the CI calculation of the OVD to differ from the MD is the incorporation of relaxation. This will be discussed in more detail and with reference to the EMS results for all the second- and third-row hydrides in an upcoming paper [ 8 1. The present results and findings for the valence orbitals of PH3 follow closely those found for HIS [ 71
S.A.C. Clark et al. /Electron momenlum spectroscopy ofphosphine
and HCl [ 91, i.e. the XMPs of the hydrides with thirdrow heavy atoms from groups V, VI and VII are already quite well described by SCF wavefunctions near to the Hartree-Fock limit as was suggested in earlier studies of H2S [ 431. Incorporation of correlation and relaxation in PH3, H2S [ 71 and HCl [ 8,9] produces a negligible change in the description of the momentum distribution. This is in sharp contrast to the situation for the corresponding row 2 hydrides, NH3 [ 5 1, Hz0 [ 61, and HF [ 8,9 ] where incorporation of the correlation and relaxation has been found to be of crucial importance for the outermost valence orbitals since major discrepancies exist between the measured XMPs and calculated MDs even at the Hartree-Fock limit for the valence orbitals. For NH3, Hz0 and HF the outer valence orbitals have more low momentum density (i.e. a greater spatial extension) than predicted by the independent particle model. The relative spatial extensions of the PHx (5a, ) and NH3 (3a, ) orbitals has been discussed in detail in an earlier paper [ 121. The situation appears to be that at larger r, the NH3 3a, orbital has higher electron density than its PHS counterpart. This is consistent with the “lone pair” in NH3 being a better o donor than in PH3. 5. Conclusion The present EMS results show good agreement between the measured XMPs for the 5a, orbital and the corresponding 136GTO MD and somewhat less good agreement for the 2e orbital. The inclusion of correlation and relaxation ( 136-G (CI ) ) is not required to predict the momentum distribution provided a sufficiently saturated and diffuse basis set is used for the SCF calculation. A significant discrepancy in intensity but not shape between calculation and experiment for the 4a, ’ ionization process is most likely due to missing satellite intensity beyond the upper limit of the present binding energy spectra.
Acknowledgement This work received financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the National Science Foundation (USA). An NSERC postgraduate scholarship
65
(SACC) is also gratefully acknowledged. We would like to thank Professor W. von Niessen for providing us with the results of the ADC (4) calculation.
References [ I] I.E. McCarthy and E. Weigold, Rept. Progr. Phys. 5 1 ( 1988) 299, and references therein. [2] C.E. &ion, Intern. J. Quantum Chem. 29 (1986) 1397, and references therein. [3] S.A.C. Clark, T.J. Reddish, C.E. Brion, R.F. Frey and E.R. Davidson, to be published. [ 41 S.A.C. Clark, E. Weigold, C.E. Brion, E.R. Davidson, R.F. Frey, C.M. Boyle, W. von Niessen and J. Schirmer, Chem. Phys. 134 (1989) 229. [ 5] A.O. Bawagan, R. Miiller-Fiedler, C.E. Brion, E.R. Davidson and C. Boyle, Chem. Phys. 120 (1988) 335. [6] A.O. Bawagan, C.E. Brion, E.R. Davidson and D. Feller, Chem.Phys. 113 (1987) 19. [ 71 C.L. French, C.E. Brion and E.R. Davidson, Chem. Phys. 122 (1988) 247. [ 8 ] E.R. Davidson, S.A.C. Clark and C.E. Brion, to be published. [9] C.E. Brion, S.T. Hood, I.H. Suzuki, E. Weigold and G.R.J. Williams, J. Electron Spectry. 2 I ( 1980) 7 1. [ IO] K.T. Leung and C.E. Brion, Chem. Phys. 82 ( 1983) 87. [ 1I ] D. Feller, C.M. Boyle and E.R. Davidson, J. Chem. Phys. 86 (1987) 3424. [ 121 A. Hamnett, S.T. Hood and C.E. Brion, J. Electron Spectry. I1 (1977)263. [ 131 S.T. Hood, A. Hamnett and C.E. Brion, Chem. Phys. Letters 39 (1976) 252. [ 141 W. Domcke, L.S. Cederbaum, J. Schirmer, W. von Niessen and J.P. Maier, J. Electron Spectry. 14 ( 1978) 59. [ 151 I.E. McCarthy and E. Weigold, Phys. Rept. 27 (1976) 275. [ 161 J.H. Callomon, E. Hirota, K. Kuchitsu, W.J. Lafferty, A.G. Maki and C.S. Pote, in: Numerical Data and Functional Relationships in Science and Technology, New Series, Group II: Atomic and Molecular Physics, Vol. 7. Structure Data of Free Polyatomic Molecules, eds. K.-H. Hellwege and A.M. Hellwege (Spinger, Berlin, 1976). [ 171 D.B. Boyd and W.N. Lipscomb, J. Chem. Phys. 46 ( 1967) 910. [ 181 W.M. Schmidt and K. Reudenberg, J. Chem. Phys. 71 (1979) 3951. [ 191 D. Feller and K. Reudenberg, Theoret. Chim. Acta 52 (1979) 231. [20] D. Feller and E.R. Davidson, J. Chem. Phys. 74 ( 1981) 3977. [21] I.C. Cooper and C.N.M. Pounder, J. Chem. Phys. 77 ( 1982) 5045. [22] P. Fantucci and V. Bonacic-Koutecky, J. Comput. Chem. 6 (1985) 462. [ 231 R. Moccia, J. Chem. Phys. 40 ( 1964) 2 176. [24] C.A. Burrus, J. Chem. Phys. 28 (1958) 427.
66
S.A. C. Clark et al. /Electron momentum spectroscopy of phosphine
[25] J.P. Maier and D.W. Turner, J. Chem. Sot. Faraday Trans. I168 (1972)711. [26] G.R. Branton, D.C. Frost, C.A. McDowell and I.A. Stenhouse. Chem. Phys. Letters 5 (1970) 1. [27] P. Dechant, A. Schweig and W. Thiel, Angew. Chem. 85 (1973) 358. [28] A.W. Potts and W.C. Price, Proc. Roy. Sot. A 326 (1972) 181. [ 291 C. Cauletti, M.Y. Adam and M.N. Piancastelli, J. Electron Spectry. 48 (1989) 379 [ 301 C.E. Brion, A.O. Bawagan and K.H. Tan, Chem. Phys. Letters 134 ( 1987) 76, and references therein. [ 3 1 ] W. von Niessen, private communication. [ 321 L.S. Cederbaum and W. Domcke, Advan. Chem. Phys. 36 (1977) 205. [ 331 J. Schirmer and L.S. Cederbaum, J. Phys. B 11 ( 1978) 1889. [34] W. von Niessen, P. Tomasello, J. Schirmer and L.S. Cederbaum, Australian J. Phys. 39 ( 1986) 687. [ 351 A. Minchinton, I. Fuss and E. Weigold, J. Electron Spectry. 27 (1982) 1.
[ 361 K.T. Leung and C.E. Brion, Chem. Phys. 9 1 ( 1984) 43. [ 37 ] L. Frost, A.M. Grisogono, I.E. McCarthy, E. Weigold, C.E. Brion, A.O. Bawagan, P.K. Mukherjee, W. von Niessen, M. Rosi and A. Sgamellotti, Chem. Phys. 113 ( 1987) 1. [38] L. Frost, A.M. Grisogono, E. Weigold, C.E. Brion, A.O. Bawagan, P. Tomasello and W. von Niessen, Chem. Phys. 119 (1988) 253. [ 39 ] A.M. Grisogono, R. Pascual, E. We&old, A.O. Bawagan, C.E. Brion, P. Tomasello and W. von Niessen, Chem. Phys. 124 (1988) 121. [40] A. Lahmam-Bennani, A. Duguet and C. Dal Cappello, J. Electron Spectry. 40 ( 1986) 14 1. [41] MS. Banna and D.A. Shirley, J. Chem. Phys. 63 (1975) 4759. [42] D.A. Allison and R.G. Cavell, J. Chem. Phys. 68 (1978) 593. [43] J.P.D. Cook, C.E. Brion and A. Hamnett, Chem. Phys. 45 (1980) I.
THE MOMENTUM DISTRIBUTIONS AND BINDING ENERGIES OF THE VALENCE ORBITALS OF PHOSPHINE BY ELECTRON MOMENTUM SPECTROSCOPY: QUANTITATIVE COMPARISONS USING NEAR HARTREE-FOCK LIMIT AND CORRELATED WAVEFUNCTIONS S.A.C. CLARK, C.E. BRION Department of Chemistry, The University ofBritish Columbia, 2036 Main Mall, Vancouver, B.C. Canada, V6T 1 Y6
E.R. DAVIDSON
and
C. BOYLE
Department of Chemistry, Indiana University, Bloomington, IN 47405, USA Received
12 April 1989
The binding energies and electron momentum distributions for the three valence orbitals of PH3 have been measured by high resolution electron momentum spectroscopy. The measured binding energy spectrum, which shows extensive structure in the inner valence region, is compared with CI and many-body Green function calculations. The momentum distributions are compared on a quantitative basis with a range of SCF wavefunctions up to near the Hartree-Fock limit in quality and also with full ion-neutral overlap calculations carried out using correlated wavefunctions by the method of configuration interaction. Inclusion of electron correlation is found to have minimal effect on the calculated momentum distributions.
1. Introduction
the XMP can be predicted by sufficiently accurate ab initio theory as it is related in a simply way to the ion-molecule overlap [ 1,2 1. (See eqs. ( 1) and (2 ) below.) A further simplification, often found to be quite accurate, is the target Hartree-Fock approximation [ 1,2 1, in which ionization is viewed as a single electron being ejected from a doubly occupied, canonical Hartree-Fock orbital with well defined energy. In this case, the XMP can be equated with the spherical average of the amplitude of the momentum space wavefunction of that orbital (that is, the momentum distribution or MD). Hence the XMP can be used for the evaluation and refinement of Hartree-Fock molecular orbital calculations of the momentum distribution [ 3-71. Calculations of the ionmolecule overlap distribution (OVD) go beyond the Hartree-Fock limit by using CI wavefunctions in order to include electron correlation and relaxation and can also be tested against the experimental results [ 3-
Electron momentum spectroscopy (EMS) in the symmetric non-coplanar geometry is a sensitive probe of the valence electronic structure of atoms and molecules [ 1,2 1. The complete binding energy spectrum can be measured throughout the outer and inner valence regions at low energy resolution (typically 1.7 eV fwhm). Further, by selecting electrons with particular binding energies and measuring the intensity distribution as a function of the angle between the scattered and ejected electrons, the experimental momentum profile (XMP) of target electrons removed in a given ionization process may be obtained. The shape of the XMP yields direct information about the symmetry of the electronic states involved in the ionization process and is therefore particularly useful in assigning the origin of the many-body (satellite) structure which frequently arises in the inner valence region of the binding energy spectrum. In this respect, the XMP is more easily and directly interpreted than the angular distribution parameter (/I) involved in photoelectron spectroscopy. In addition 0301-0104/89/$03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
71. EMS is now well established as a discriminating test of high level molecular orbital calculations [ 3-71. As part of a continuing experimental and theoretical B.V.
56
S.A.C. Clark et al. /Electron
momentum
study of the hydrides of the second [ 3,561 and third [ 4,7] row we now present new measurements of the valence shell binding energy spectrum as well as the XMPs of the valence orbitals of phosphine (PH,). The XMPs are compared with calculations up to the Hartree-Fock limit and beyond. In all of our most recent papers in this series [ 3-71 as well as in corresponding studies of HF and HCl [8,9] and noble gases [ 8,101 the XMPs have been measured with higher momentum resolution (equal to or better than 0.15 au hwhm) than in most previous work, thus allowing for a much more accurate comparison of theory with experiment. Most of these more recent studies [ 3-81 have also involved comparisons with SCF calculations of momentum distributions (MDs) using a range of wavefunctions essentially up to the Hartree-Fock limit as well as with ion-molecule overlap distributions (OVDs) calculated using configuration interaction (CI) wavefunctions for the ion and molecule. Basis set saturation, including very diffuse functions, has been achieved in obtaining very large and flexible basis sets for both the Hartree-Fock limit and CI wavefunctions [ 6,111. The configuration interaction calculations recover more of the correlation energy (for example, as much as 86% in Hz0 [ 6 ] ) than any previously published CI calculations of which we are aware. A low impact energy (400 eV), low momentum resolution (ApcO.4 au hwhm) study of PH3 has already been reported [ 12 1. The earlier results [ I2 ] showed strong splitting of the 4a, inner ionization strength due to many-body effects. This earlier study for PHj suggested that even quite modest SCF wavefunctions provided a fairly good description of the shape of the measured XMPs for the three valence orbitals. This behaviour was in very sharp contrast to the situation for NH3 [ 13 1, where very little splitting of the inner valence (2a,) ionization strength occurred and large discrepancies existed between SCF calculations and experiment for the outermost (3a, ) orbital at low momentum. Recent high impact energy ( 1200 eV), high momentum resolution EMS studies of NH3 [ 5 ] indicate that the momentum distributions are quite well described on a quantitative basis if CI calculations of the OVD are employed. The XMPs of PHx measured earlier also showed some evidence of distortion above 1 au due to the low impact energies used (400 eV). It is therefore of inter-
spectroscopy
ofphosphine
est to remeasure the XMPs of the valence orbitals of PH3 using the higher impact energy ( 1200 eV) and much improved momentum resolution (0.15 au hwhm ) now available on our spectrometer [ 10 ] and also to place the XMPs on the same relative intensity scale [ 61 to provide a more stringent quantitative comparison with calculations than was possible with the individual height normalizations used for each orbital in the earlier study [ 121. In particular it is of importance to check the apparently already quite good (shape) agreement between XMPs and MDs calculated using modest SCF wavefunctions [ 12 ] and also to compare quantitatively with the results obtained using near Hartree-Fock limit and CI wavefunctions. Earlier studies of the third-row, group VI hydride H2S [ 71 have shown that addition of correlation and relaxation to the wavefunctions (i.e. the full OVD) produces little or no further change from the MDs predicted using Hartree-Fock limit wavefunctions with saturated basis sets. The behaviour for HIS [ 71 is in sharp contrast to the second-row analogue Hz0 where inclusion of correlation and relaxation was essential to obtaining good agreement between calculation and the XMPs [ 6 1. Since addition of correlation and relaxation has also been found to produce no further change from the Hartree-Fock limit MDs for the group IV, row 2 and 3 hydrides CH, [ 31 and SiH4 [4] respectively, it is of interest to determine the situation for PH3 (group V) and compare with the results for NH3 [ 5 1. In particular the present work compares the measured XMPs of PH3 with a calculation quite close to the Hartree-Fock limit and also with an ion-molecule overlap (OVD) calculation using wavefunctions from a multireference singly and doubly excited configuration interaction calculation. In addition the binding energy spectrum of PH3 is compared to many-body Green function calculations from the literature [ 141.
2. Experimental method The high momentum resolution EMS spectrometer used in the present study has been described previously [ lo]. Briefly, a high energy electron beam ionizes a gas sample and the scattered and ejected electrons are detected in coincidence. The spectrometer selects only those events in which the scattered
S.A.C. Clark et al. /Electron momentum spectroscopy o$phosphine
and ejected electron have equal energy and that are scattered at 19=45 o with respect to the electron beam. The relative azimuthal angle (@) between the two detectors is varied by rotating one of the electron analyzers about the incident electron beam axis. Two modes of operation are possible. If the angle @ is fixed and the impact energy (E,= 1200 eV+binding energy) is varied, a binding energy spectrum is obtained. This measures vertical ionization potentials where final ion states are resolved or alternatively the spectral envelope where many closely spaced states exist due to many-body effects which commonly occur in the inner valence region. If the impact energy is fixed at 1200 eV+ the vertical IP of a given orbital, then the momentum distribution (i.e. the XMP) of that orbital can be measured by varying the angle @,since @is directly related to the momentum of the ionized electron prior to knock-out [ 15 1. Within the plane wave impulse approximation and the Born-Oppenheimer approximation, the cross section OTbcs for an EMS experiment in the symmetric non-coplanar geometry is proportional to the spherical average of the square of the ion-molecule overlap [ 1,2,15 1, ~TDCS
a
I dQlIq%l’J’,Y,)12,
(1)
where q is the momentum of the initially bound electron. If the cross section is assumed to be proportional to a canonical Hartree-Fock molecular orbital (the target Hat-tree-Fock approximation) then the cross section reduces to nTDCS
as:”
s
dQ
I@j(P)
I2 >
(2)
where g,,(p) is the momentum space wavefunction for the canonical Hartree-Fock orbital from which the electron was removed. The spectroscopic factor Sjf) is the probability that the final state ion has a hole in the inital state molecular orbital @,.Within the target Hartree-Fock approximation, the spectroscopic sum rule applies: ,YfS,(‘) = 1, where If is a sum over all final states, though in practice only states within the same symmetry manifold i will contribute. Application of the sum rule allows relative cross sections from different orbitals to be compared on the same intensity scale provided the results are summed over all final states for each initial state orbital. A common intensity scale is achieved by normalizing the XMPs
51
to the relative peak areas in the binding energy spectrum (see refs. [ 5,6] for details). The spectrometer was calibrated with Ar both before and after the study of PHJ to determine the energy resolution and momentum resolution. These were found to be 1.7 eV fwhm and 0.15 au hwhm respectively. The C.P. grade phosphine ( > 99.5% purity) was supplied by Matheson and used without further purification.
3. Calculations Within the target Hat-tree-Fock approximation, the experimental momentum profiles can be compared to the spherical average of the square of the momentum space wavefunction (eq. (2) ). In addition to a minimum basis set calculation, a near-Hartree-Focklimit calculation was also performed using a 136-GTO basis set described below. Calculation of the ionmolecule overlap (eq. ( 1) ) was also performed using CI wavefunctions for the ion and molecule with which it is believed that more than 80% of the valence shell correlation energy is recovered. This 136-G(C1) configuration interaction wavefunction is also described below. Details of the wavefunctions and basis sets are given below and in table 1. The computations for PH3 were performed at the equilibrium geometry with rpn= 1.420 au and the PHP angle = 93.3 ’ [ 161. The CI calculations include only valence shell correlation and neglect core correlation and relativistic effects. MBS+3d basis set. This calculation of Boyd and Lipscomb [ 17 ] used a minimum basis set of Slater orbitals supplemented with a 3d orbital on the phosphorus. The exponents were: P 1s 14.7, P 2s and 2p 5.425, P 3s and 3p 1.6, P 3d 1.4 and H 1s 1.2. 136-GTO basis set. The extended basis set for PH3 consists of an even-tempered (2 1s, 14p,4d,2f/ 1OS, 3p,2d) primitive set contracted to a [ 12s 1Op,4d, 2f/ 6s,3p, Id] Gaussian type (GTO) basis. The s components of the Cartesian d functions and the p components of the f functions were removed to avoid linear dependence, forming the final 136-GTO basis. The basis set was taken from a calculation on PH, using energy optimized exponents [ 18,191 and employing an even-tempered restriction on the expo-
S.A.c. Clark et al. /Electron momentum spectroscopy ofphosphine
58 Table 1 Properties
of restricted
Hartree-Fock
and configuration
Type of calculation
Wavefunction label
Phosphorus
RHF RHF MR SDCI ” exp.
MBS+3d 136-CT0 136-G(CI)
Slater: 3s,2p,ld (21s,14p,4d,2f)/[ (21s,14p,4d,2f)/[
interaction
basis
wavefunctions Hydrogen
for PH3
basis
Total energy (au)
12s,lOp,4d,2f] 12s,lOp,4d,2f]
Slater: 1s (lOs,3p,2d)/[Ss,3p,ld] (lOs,3p,2d)/[Ss,3p,ld]
-341.3094 -342.4934 -342.6833 - 343.42
Dipole moment
Ref. (D)
1171
0.86 0.665 0.624
this work this work
0.578
[23,241
i') In comparing
with experimental quantities it should be noted that the calculations are for a non-vibrating molecule (equilibrium geometry) and do not include relativistic effects. In the Cl calculation only valence shell correlation is included. The core correlation and relativistic effects are expected to be slightly larger for PHJ than H2S (see discussion in ref. [7] ).
nents. The f exponents are taken from an analogous calculation on H$ by Feller et al. [ 111. The basis set was designed to saturate the diffuse basis function limit and to give improved representation of the (r-space) tail of the orbitals. It should be noted that due to the very large number of functions which have been used, the wavefunction is expected to be fairly insensitive to the exact choice of exponents. 136-G(CI) ion-molecule overlap. The CI wavefunctions for the neutral and ion species are built using the 136-GTO basis. The methods applied were Hartree-Fock singly and doubly excited configuration interaction (HF SDCI ) and multireference singly and doubly excited configuration interaction (MR SDCI ) . The valence electron CI convergence has been shown to be improved (i.e. more correlation energy was recovered with fewer configurations) when the Hartree-Fock virtual orbitals are transformed into K orbitals [ 20-221 and hence K orbitals were used. The singly and doubly excited configurations used in the MR SDCI were energy selected based on second-order Rayleigh-SchrGdinger perturbation theory and the reference space was selected based upon the coefficient contribution in the HF SDCI. This selection was necessary due to the large number of configurations associated with the extended basis set exceeding our current variational capacity. The calculations on PH: were done with neutral PH3 ground state molecular orbitals. The neutral molecule HF SDCI calculation selected 10366 spin-adapted Hartree-Fock singly and doubly excited configurations, keeping all the singly excited and using second-order perturbation theory on the doubly excited, with the neglected configura-
tions having a total contribution of less than one millihartree to the CI energy. The MR SDCI space was chosen from the HF SDCI’s largest coefficients, as discussed above; a coefficient threshold of at least 0.030 was systematically maintained for the 5a; ’ and 2e- ’ ion states, but a higher one was needed for the calculation of multiple roots of ‘A, symmetry (the 5a;’ and 4a;’ included) as discussed later. The dimension of the neutral MR SDCI was 22589 out of the total of 2495566 possible singly and doubly excited configurations. This MR SDCI energy is - 342.6833 au, with the core electrons of phosphorous uncorrelated. Some calculated properties of the neutral molecule are listed in table 1 along with experimental values [ 23,241. The calculations for the ion states of phosphine were performed using molecular orbitals for the neutral molecule. The OVDs computed from the CI wavefunctions for the ion states then have the same form as an MO expanded in the neutral basis. The calculation of the ion states involved a similar process to that of the neutral with the exception that no RHF calculations were done. HF SDCI and MR SDCI were done for the 5a; ’ and 2e-’ states. The coefficients for the MR SDCI were chosen based upon the coefficient contribution using a threshold of 0.030 for 5ar’ and 2e-‘. The ionization potentials for these two cation states are listed in table 2. The IP values are seen to be in good agreement with the experimental values. The ‘A, multiroot calculations employed a modified reference space selection. The calculation was done in C, symmetry but used a symmetrically closed set of configurations containing the largest coefficient contributions for the first 15 states from a cal-
19.45
22.61
25.46
19.4 20.6
23.2
25.6 27.2
da,
13.50(5)
10.58(l)
13.6(l)
10.59(2)
19.0
13.6
10.60
ref. [27]
19.5(2) 20.5(2)
-
-
25.6 26.5 27.8 29.1
19.4 20.6 21.7 23.2 24.1
-
-
23.23
14.17
10.58
31.60 (0.02) 33.96 (0.01)
(0.13) (0.03) (0.03) (0.03) (0.02) (0.02) (0.13)
30.05 31.18 31.54 32.90
(0.009) (0.008) (0.004) (0.007)
26.49 (0.031) 26.53 (0.083)
19.28 (0.342) 20.98 (0.100) 22.32 (0.058) 22.79 (0.231) 24.97 (0.005) 25.98 (0.003)
19.37 (0.53)
22.39 23.20 23.46 25.22 26.78 27.73 28.04
13.59 21.30 26.88 28.52 30.11 31.88 31.95
(0.904) (0.006) (0.003) (0.006) (0.004) (0.003) (0.004)
10.25 (0.911) 19.28 (0.004) 24.97 (0.006) 26.49 (0.004) 28.16 (0.015) 30.05 (0.007)
13.23 (0.93)
9.95 (0.92) 30.44 (0.02)
RHF Green function (pole strength) 136-CT0 simplified ref. [ 141 synchrotron this work Zph-TDA radiation [ 291 ADC(4) [31]
Calculation
22.01 (0.1180) 22.77 (0.0444) 23.15 (0.0056) 24.67 (0.0468) 25.41 (0.0185) 26.20 (0.0093) 27.61(0.1184) 28.14(0.0398)
19.70 (0.4373)
13.62 (0.8399)
10.44 (0.8626)
136-G(C1) (spectroscopic factor) this work
a1 These represent observed peaks for the 5a, and 2e states, but are the centres of the gaussians in the deconvolution for the inner valence (4ai ) region (see fig. I ). The deconvolution was based largely on the PES work of Cauletti et al. [29] (see text for details).
29.1 31.8 36.0
13.44
13.6
2e
10.59
10.6
ref. [26]
photoelectron spectroscopy
ref. [ 121 ref. [25]
Sal
thisworka’
EMS
State Experimental vertical IP
Table 2 Measured and calculated binding energies and calculated pole strengths and spectroscopic factors for the valence shell of PH3
S.A.C. Clark et al. /Electron momentum spectroscop.v ofphosphine
60
culation in which all the single excitations from all valence hole states were kept. The IP values and spectroscopic factors for the roots of the CI calculation are compared with Green function results [ 141 in table 2 and fig. 2 (see discussion in section 4 ).
4. Results and discussion
i
4.1. Binding energy spectra The phosphine molecule has Csv symmetry [ 161. The electronic configuration of PH3 can be written (la,)‘(2a,)‘(
le)4(3al)‘(4a,)2(2e)4(5a,)2
cure orbitals
‘A,.
valence orbitals
The EMS binding energy spectra of PH, from 838 eV, shown in figs. la and lb, were obtained at an impact energy of 1200 eV (plus the binding energy) and at relative azimuthal angles $ of 0” and 6” respectively. The two binding energy spectra are on a common (relative) intensity scale. The energy scale was calibrated with respect to the 5a, vertical ionization potential measured by high resolution photoelectron spectroscopy [25-281. Measured and calculated binding energies are summarized in table 2. Peaks due to the 5a;’ and 2e-’ ionization processes are found at vertical ionization potentials of 10.6 and 13.6 eV consistent with the results of photoelectron spectroscopy [ 25-28 1. The inner valence region shows a multipeaked spectrum consistent with previous EMS work [ 121. The main features of the inner valence part of the experimental binding energy spectrum at both @= 0’ and 6’ are seen (fig. 1) to be three large peaks at approximately 20.0, 23.2 and 25.6 eV, with the heights of the peaks in the ratio of approximately 3 : 1 : 2. The earlier low momentum resolution measurements of the binding energy spectra and the XMPs of the three principal inner valence satellite peaks of PH3 [ 12 ] lead to the conclusion that the intensity above 17 eV is predominantly due to the 4a; ’ ionization process. This assignment was subsequently supported by Green function calculations using several different basis sets [ 14 1. Until the recent studies of Cauletti et al-. [ 291 using synchrotron radiation, no comprehensive PES measurements of the inner valence region of the PH1
I
10
20
30
BINDING ENERGY
(eV)
Fig. I. Binding energy spectra for the valence shell of PH, at azimuthal angles @=O” and 6”. The solid line is a sum of Gaussian functions centred on peak locations using experimental widths and convoluted with the instrumental energy resolution.
binding energy spectrum had been reported (see table 2). These PES spectra [ 291 are at higher resolution (fwhm= 0.8 eV) and show more tine structure in the inner valence region than either the present or the earlier [ 12 ] EMS results. Cauletti et al. [ 29 ] suggest, on the basis of a deconvolution analysis, that at least nine peaks exist in the 17-30 eV binding energy region. It is apparent both from the present work (fig. 1) and the PES spectra [ 291 that there is probably some additional spectral intensity above 38 eV. The lower relative intensity observed at higher binding energies in the PES spectrum (see fig. 2 of ref. [ 291) compared to the EMS spectrum is not surprising since at the low photon energy used (hv= 50 eV) the partial cross sections of the higher energy satellites are expected to be relatively lower than those at lower binding energy since they are closer to threshold. PES
S.A.C. Clark et al. /Electron momentum spectroscopy ofphosphine
spectra at significantly higher photon energies are necessary in order to make any meaningful comparison with the intensities observed in EMS for a given symmetry manifold [ 301. The deconvolution of the EMS spectrum shown in fig. 1 above 17 eV is based on the deconvolution analysis of the PES spectrum reported by Cauletti et al. [ 29 ] which shows nine peaks between 17 and 30 eV. However, due to the slightly lower resolution only six peaks have been fitted in the EMS spectrum between 17 and 30 eV. Two further peaks, not identitied in the PES spectrum, are fitted to the EMS spectrum at 32 and 36 eV. Each of the eight peaks fitted in the range 17-39 eV (fig. 1) is more intense at @= 0 ’ than at @= 6” thus confirming the dominant 4a; ’ character of the inner valence spectrum above 17 eV. In particular, the peak at 20.6 eV is clearly “s-type”, i.e. it is dominantly due to the 4a, ’ process. On the basis of a relatively small decrease in the/3value compared to that for the 19.4 eV peak, Cauletti et al. [ 291 have suggested that the 20.6 eV peak is a satellite associated with an outer valence ionization process. Such an interpretation is inconsistent with the present, more direct, experimental findings. It should also be noted that the ADC(4) many-body Green function calculations [ 3 1 ] predict that the satellite structures in this region are dominantly 4a; ’ in character ( see below and table 2 ) . The sum of the binding energy spectra taken at @=O’ and @=6”, is compared in fig. 2a with the results of two Green function calculations [ 14,3 11. The Green function calculations have been folded with the experimental energy resolution and the Franck-Condon widths obtained from the high resolution photoelectron spectra [25-291 to obtain figs. 2c and 2d. The Green function calculation shown in fig. 2c is based on the two-particle-hole Tamm-Dancoff approximation ( Zph-TDA) [ 32,331 and is taken from the work of Domcke et al. [ 141. A rather small basis set, ( 12s9p2d/4s) contracted to [ 6s4p2d/2s], was used. The calculation shown in fig. 2d [ 3 1 ] used the simplified ADC( 4) approximation [ 341 and also used a rather small basis set: ( 12s9pld/4slp) contractedto [6s4pld/2slp].Alsoshown (intig.2band table 2) are the roots and spectroscopic factors from the MR SDCI calculation done in the present work (see section 3). Again the theoretical results are
61
folded with observed widths. All calculations predict significant splitting of the 4a, ’ ionization strength due to many-body effects. The calculated spectral envelope shows quite reasonable agreement in all cases with the EMS data. Although all calculations predict qualitatively similar results, the third band appears at too high an energy (x27 eV) and with too little intensity. As has been observed for other molecules, the 2ph-TDA and ADC( n) type methods are found to underestimate pole strengths at higher binding energies [ 5,7,9,35-391. The CI calculation predicts almost exact binding energies (see table 1) for the 5a; ’ and 2e-’ ionization processes, while giving similar results to the Green function calculations in the inner valence region. 4.2. Comparison of experimental and calculated momentum distributions The experimental momentum profiles (XMPs), calculated spherically averaged momentum distributions ( MDs), and ion-molecule overlaps ( OVDs) are shown in figs. 3-5 together with momentum and position space density maps calculated in selected planes for an oriented PH3 molecule using the 136-GTO wavefunction. The momentum resolution of the XMPs is clearly improved over the earlier work [ 12 1. The XMPs were placed on the same relative intensity scale by normalization on the binding energy spectra (fig. 1) as described earlier [ 6,7]. The XMPs, MDs and OVDs have been placed on a common intensity scale by a single point normalization of the OVD calculation to the 5a, orbital. All other relative normalizations for calculations and experiment have been preserved. All calculations have been folded with the experimental momentum resolution (0.15 au hwhm). For the reasons discussed in section 2, all of the inner valence satellite intensity above 17 eV (fig. 1) has been assigned to the 4ai ’ process. The 136-G( CI ) ion-molecule overlap (OVD) calculations using correlated wavefunctions and the 136GTO SCF calculation of the momentum distributions (MD) are seen (figs. 3-5) to be very similar for a given ionization process and essentially identical in the case of the 5a, orbital (fig. 3). The calculations also give an excellent fit to the shape of the experimental data for the 5a, orbital. Agreement with the data for the 2e orbital, however, is somewhat less
62
S.A.C. Clark rt al. /Electron
momentum
spectroscopy
qfphosphrnr
Fig. 2. Experimental and calculated binding energy spectra for the valence shell of PHI (see table 2 for calculated pole assignments). (a) EMS spectra (sum of o=O’ and 6’. this work, see fig. I ); (b) Cl calculation, this work, (c) and (d) many-body Green function calculations. ref. [ 141.
SPHERICALLY
AVERAGED
MOMENTUM
DENSITY
POSITION
DENSITY
;jb’n
MOMENTUM (au)
POSITION
(au)
Fig. 3. Measured and calculated spherically averaged momentum distributions for the 5a, orbital of PH?. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136-GTO calculation. The contour values represent 0.02, 0.04, 0.06, 0.08, 0.2, 0.4, 0.6, 0.8, 2, 4, 6, 8, 20, 40, 60 and 80% ofthe maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
satisfactory in that the MD and OVD calculations maximize at slightly too high a momentum and do not completely account for the intensity near p = 0 au. If this additional intensity at low momentum in the experimental data is due to an unresolved (4a, ) symmetric pole under the 2e binding energy peak, then one would expect the experimental momentum pro-
file to contain more total intensity than the calculated momentum distribution. However, the calculation shows more intensity than the data between 0.6 and 1.0 au. The small difference at low momentum could possibly be due to uncertainty in the momenturn resolution fitting procedure. The 136-CT0 MD (and 136G( CI) OVD) for the
S.A.C. Clark et al. /Electron momentum spectroscopy ofphosphine
63
-8.0 -4.0 0.0 1.0 a.0 0.51.0
MOMENTUM
(au)
POSITION (au)
Fig. 4. Measured and calculated spherically averaged momentum distributions for the 2e orbital of PH,. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136~GTO calculations. The contour values represent 0.02,0.04, 0.06, 0.08,0.2,0.4, 0.6,0.8,2,4, 6, 8,20, 40, 60 and 80% of the maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
SPHERICALLYAVERAGED YONENTUN DISTRIBUTION
MOMENTUM
POSITION
DENSITY
MOMENTUM
(au)
DENSITY
POSITION (au)
Fig. 5. Measured and calculated spherically averaged momentum distributions for the 4a, (main peak) orbital of PH,. Density contour maps in momentum and position space are also shown. The contour maps were generated with the 136~GTO calculation. The contour values represent 0.02,0.04,0.06,0.08,0.2,0.4,0.6,0.8,2,4,6,8,20,40,60 and 80% of the maximum density. The side panels (top and right side) show the density along the dashed lines (horizontal and vertical) in the density map.
4a, ’ process predicts significantly greater ( x 25Oh) intensity than is observed. This discrepancy may, at least in part, reflect the existence of 4ai ’ satellite intensity lying above 38 eV, which is the limit of the presently reported binding energy spectra data. It is also possible that some absorption is occurring for this more deeply bound orbital even at the impact energy of 1200 eV [ 15 1. It can be seen from the 0.74 x ( 136G( CI ) ) curve that the shape of the 4a, XMP is reproduced exactly by the 136-G(C1) and 136-GTO calculations, except in the region of about 1.2-2 au, where the difference between theory and experiment may be due to a breakdown of the plane wave approximation which is not unexpected at higher values of momentum [ 1,15,40].
In the previous (lower momentum resolution) EMS study of PH, [ 12 1, the MBS + 3d wavefunction [ 17 ] was found to model the data reasonably satisfactorily (for shape) when the XMP of each orbital was individually height normalized to the calculation. However, in the present work, with experiment and theory now on a common intensity scale for all orbitals, the MBS + 3d calculation is found to be inadequate. In order to facilitate comparison with the earlier work [ 12 1, the MBS + 3d calculation is shown (fig. 6) separately height normalized to each of the presently determined high momentum resolution XMPs so that only the shape of the theoretical and experimental curves is compared for each orbital. It can be seen that the shapes of the Sa, and 2e orbitals
64
S.A. C. Clurk et al. /Electron
(‘)
5a
Cc)
da
--‘I PH,
1
2/
6
0
IiPH,
1
t
-‘r* \. ~_Ti- ..
.
.
momentum
.
.,
_
3
0 MOMElNTUM
’ (au)
Fig. 6. Measured and calculated (MBS+ 3d) momentum distributions for the valence orbitals of PH,. Each calculation shown is separately height normalized to experiment for each orbital to facilitate direct comparison with earlier measurements [ 121.
show about the same level of agreement with experiment as was found in the earlier work. It is important to note that much poorer agreement is obtained between the MBS + 3d calculation and experiment when correct relative intensities are established for all orbitals (see figs. 3-5). This shows that independent height normalization could lead to erroneous conclusions as to the quality of the wavefunction. The very limited basis set in the MBS+ 3d wavefunction in fact discriminates against the chemically important low p parts of the wavefunction. This low p region is evidently much better modeled by the much more saturated basis set, including diffuse functions, employed in the variationally superior 136-GTO wavefunction.
spectroscopy
qfphosphine
In the momentum and position space density-maps, all coordinates are in atomic units. The phosphorus nucleus is at the origin of the position space maps, and the hydrogens located at approximately (0,2.25, - 1.46) (in the plane of the picture) and ( ? 1.95, - 1.13, - 1.46) (out of the plane of the picture). These pictures are consistent with the simplest notions of how we expect these orbitals to be built up from atomic orbitals. To a first approximation, the 4a, is composed of a phosphorus 3s orbital bonding with hydrogen 1s orbitals. The 2e orbital consists of a-phosphorus 3p orbital in the “plane” of the molecule (although the molecule is not quite planar) combined appropriately with hydrogen 1s orbitals. It is degenerate since there are two orthogonal p functions in the plane. (For the orientation of PH3 shown in the density maps, this is the xy plane.) The 5a, orbital consists of a p function perpendicular to this plane bonding with the hydrogen s functions. The 5a, orbital in PH3 shows much more phosphine 3s contribution (this is seen as the symmetric density near the origin) than the corresponding orbital in NH3 ( 3a, ) shows nitrogen 2s intensity [ 5 1. In phosphine, all three orbitals show more density near the origin of position space (despite strong contributions from the hydrogens) than the corresponding orbitals in NH3. Both from EMS and PES results it has been observed that there is much more satellite structure in the inner valence region of the binding energy spectrum of PH3 (see figs. 1, 2 and also refs. [ 12,291) than of NH3 [ 5,13,4 1,42 1. It is also noted that CI calculations of the ion-molecule overlap (OVD) of the inner valence orbitals of PH3 and NH3 vary little, if at all, from calculations based on the target HartreeFock approximation [ 5 1. In fact, this is true for all valence orbitals of PHs. Yet a significant difference is observed between the ion-molecule overlap (OVD) and the target Hartree-Fock approximation momentum distribution (MD) for the 3a, orbital of NH3 [ 5 1. This may suggest that the main factor which causes the CI calculation of the OVD to differ from the MD is the incorporation of relaxation. This will be discussed in more detail and with reference to the EMS results for all the second- and third-row hydrides in an upcoming paper [ 8 1. The present results and findings for the valence orbitals of PH3 follow closely those found for HIS [ 71
S.A.C. Clark et al. /Electron momenlum spectroscopy ofphosphine
and HCl [ 91, i.e. the XMPs of the hydrides with thirdrow heavy atoms from groups V, VI and VII are already quite well described by SCF wavefunctions near to the Hartree-Fock limit as was suggested in earlier studies of H2S [ 431. Incorporation of correlation and relaxation in PH3, H2S [ 71 and HCl [ 8,9] produces a negligible change in the description of the momentum distribution. This is in sharp contrast to the situation for the corresponding row 2 hydrides, NH3 [ 5 1, Hz0 [ 61, and HF [ 8,9 ] where incorporation of the correlation and relaxation has been found to be of crucial importance for the outermost valence orbitals since major discrepancies exist between the measured XMPs and calculated MDs even at the Hartree-Fock limit for the valence orbitals. For NH3, Hz0 and HF the outer valence orbitals have more low momentum density (i.e. a greater spatial extension) than predicted by the independent particle model. The relative spatial extensions of the PHx (5a, ) and NH3 (3a, ) orbitals has been discussed in detail in an earlier paper [ 121. The situation appears to be that at larger r, the NH3 3a, orbital has higher electron density than its PHS counterpart. This is consistent with the “lone pair” in NH3 being a better o donor than in PH3. 5. Conclusion The present EMS results show good agreement between the measured XMPs for the 5a, orbital and the corresponding 136GTO MD and somewhat less good agreement for the 2e orbital. The inclusion of correlation and relaxation ( 136-G (CI ) ) is not required to predict the momentum distribution provided a sufficiently saturated and diffuse basis set is used for the SCF calculation. A significant discrepancy in intensity but not shape between calculation and experiment for the 4a, ’ ionization process is most likely due to missing satellite intensity beyond the upper limit of the present binding energy spectra.
Acknowledgement This work received financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the National Science Foundation (USA). An NSERC postgraduate scholarship
65
(SACC) is also gratefully acknowledged. We would like to thank Professor W. von Niessen for providing us with the results of the ADC (4) calculation.
References [ I] I.E. McCarthy and E. Weigold, Rept. Progr. Phys. 5 1 ( 1988) 299, and references therein. [2] C.E. &ion, Intern. J. Quantum Chem. 29 (1986) 1397, and references therein. [3] S.A.C. Clark, T.J. Reddish, C.E. Brion, R.F. Frey and E.R. Davidson, to be published. [ 41 S.A.C. Clark, E. Weigold, C.E. Brion, E.R. Davidson, R.F. Frey, C.M. Boyle, W. von Niessen and J. Schirmer, Chem. Phys. 134 (1989) 229. [ 5] A.O. Bawagan, R. Miiller-Fiedler, C.E. Brion, E.R. Davidson and C. Boyle, Chem. Phys. 120 (1988) 335. [6] A.O. Bawagan, C.E. Brion, E.R. Davidson and D. Feller, Chem.Phys. 113 (1987) 19. [ 71 C.L. French, C.E. Brion and E.R. Davidson, Chem. Phys. 122 (1988) 247. [ 8 ] E.R. Davidson, S.A.C. Clark and C.E. Brion, to be published. [9] C.E. Brion, S.T. Hood, I.H. Suzuki, E. Weigold and G.R.J. Williams, J. Electron Spectry. 2 I ( 1980) 7 1. [ IO] K.T. Leung and C.E. Brion, Chem. Phys. 82 ( 1983) 87. [ 1I ] D. Feller, C.M. Boyle and E.R. Davidson, J. Chem. Phys. 86 (1987) 3424. [ 121 A. Hamnett, S.T. Hood and C.E. Brion, J. Electron Spectry. I1 (1977)263. [ 131 S.T. Hood, A. Hamnett and C.E. Brion, Chem. Phys. Letters 39 (1976) 252. [ 141 W. Domcke, L.S. Cederbaum, J. Schirmer, W. von Niessen and J.P. Maier, J. Electron Spectry. 14 ( 1978) 59. [ 151 I.E. McCarthy and E. Weigold, Phys. Rept. 27 (1976) 275. [ 161 J.H. Callomon, E. Hirota, K. Kuchitsu, W.J. Lafferty, A.G. Maki and C.S. Pote, in: Numerical Data and Functional Relationships in Science and Technology, New Series, Group II: Atomic and Molecular Physics, Vol. 7. Structure Data of Free Polyatomic Molecules, eds. K.-H. Hellwege and A.M. Hellwege (Spinger, Berlin, 1976). [ 171 D.B. Boyd and W.N. Lipscomb, J. Chem. Phys. 46 ( 1967) 910. [ 181 W.M. Schmidt and K. Reudenberg, J. Chem. Phys. 71 (1979) 3951. [ 191 D. Feller and K. Reudenberg, Theoret. Chim. Acta 52 (1979) 231. [20] D. Feller and E.R. Davidson, J. Chem. Phys. 74 ( 1981) 3977. [21] I.C. Cooper and C.N.M. Pounder, J. Chem. Phys. 77 ( 1982) 5045. [22] P. Fantucci and V. Bonacic-Koutecky, J. Comput. Chem. 6 (1985) 462. [ 231 R. Moccia, J. Chem. Phys. 40 ( 1964) 2 176. [24] C.A. Burrus, J. Chem. Phys. 28 (1958) 427.
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[25] J.P. Maier and D.W. Turner, J. Chem. Sot. Faraday Trans. I168 (1972)711. [26] G.R. Branton, D.C. Frost, C.A. McDowell and I.A. Stenhouse. Chem. Phys. Letters 5 (1970) 1. [27] P. Dechant, A. Schweig and W. Thiel, Angew. Chem. 85 (1973) 358. [28] A.W. Potts and W.C. Price, Proc. Roy. Sot. A 326 (1972) 181. [ 291 C. Cauletti, M.Y. Adam and M.N. Piancastelli, J. Electron Spectry. 48 (1989) 379 [ 301 C.E. Brion, A.O. Bawagan and K.H. Tan, Chem. Phys. Letters 134 ( 1987) 76, and references therein. [ 3 1 ] W. von Niessen, private communication. [ 321 L.S. Cederbaum and W. Domcke, Advan. Chem. Phys. 36 (1977) 205. [ 331 J. Schirmer and L.S. Cederbaum, J. Phys. B 11 ( 1978) 1889. [34] W. von Niessen, P. Tomasello, J. Schirmer and L.S. Cederbaum, Australian J. Phys. 39 ( 1986) 687. [ 351 A. Minchinton, I. Fuss and E. Weigold, J. Electron Spectry. 27 (1982) 1.
[ 361 K.T. Leung and C.E. Brion, Chem. Phys. 9 1 ( 1984) 43. [ 37 ] L. Frost, A.M. Grisogono, I.E. McCarthy, E. Weigold, C.E. Brion, A.O. Bawagan, P.K. Mukherjee, W. von Niessen, M. Rosi and A. Sgamellotti, Chem. Phys. 113 ( 1987) 1. [38] L. Frost, A.M. Grisogono, E. Weigold, C.E. Brion, A.O. Bawagan, P. Tomasello and W. von Niessen, Chem. Phys. 119 (1988) 253. [ 39 ] A.M. Grisogono, R. Pascual, E. We&old, A.O. Bawagan, C.E. Brion, P. Tomasello and W. von Niessen, Chem. Phys. 124 (1988) 121. [40] A. Lahmam-Bennani, A. Duguet and C. Dal Cappello, J. Electron Spectry. 40 ( 1986) 14 1. [41] MS. Banna and D.A. Shirley, J. Chem. Phys. 63 (1975) 4759. [42] D.A. Allison and R.G. Cavell, J. Chem. Phys. 68 (1978) 593. [43] J.P.D. Cook, C.E. Brion and A. Hamnett, Chem. Phys. 45 (1980) I.