J. Phys. Chem. 1989, 93, 3504-351 1
3504
Vacuum-Uttraviolet Spectroscopy of Group V Oxides: P406and As406 Janna L. Rose, Thomas C. VanCott, Paul N. Schatz,* Department of Chemistry, University of Virginia, Charlottesuille. Virginia 22901
Michael E . Boyle,* Chemistry Division, Code 61 23, Naval Research Laboratory, Washington, D.C. 20375-5000
and Michael H . Palmer* Department of Chemistry, University of Edinburgh, Edinburgh, EH93JJ, Great Britain (Received: August 23, 1988)
The ultraviolet and vacuum-ultraviolet absorption and magnetic circular dichroism (MCD) spectra of P406and As406isolated in Ar matrices have been measured by using the 1-GeV synchrotron at the Synchroton Radiation Center, University of Wisconsin-Madison. The P406molecule shows strong absorptions at -200 nm (band A) with a red shoulder and at 156 nm (band B). As406shows closely analogous bands at -21 1 (A) and 170 nm (B) and, in addition, a higher energy band at 144 nm (band C). Bands A and B show negative A terms for both compounds, while band C of As406shows a large positive A term. The results are analyzed according to a simple extended Huckel (EH) model and ab initio calculations, including extensive configuration interaction for P406 Though the EH treatment cannot predict meaningful transition energies, it is able to account well for the excited-state magnetic moments (A,/a),J of bands A and qualitatively for those of bands B. The ab initio calculation places the first allowed transition (‘A, ‘T2A)about 1.7 eV too high in P406. Comparison of the ab initio and EH occupied MOs shows strong resemblances which are attributed to a topological control characteristic of cagelike structures in which all atoms of a given element are in an identical environment. It does not seem possible to account for the sign and magnitude of the magnetic moment associated with band C of As406on the basis of s and p orbitals alone.
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I. Introduction The “trioxides” of phosphorus, arsenic, and antimony are of interest as examples of inorganic cage structures and prototype solid-state systems.’ Their molecular structure and physical properties have been well characterized, and it is clear that the vapor over the solid is composed of M 4 0 6molecules.2-8 These are highly symmetric species, point group Td,and may be pictured as four M atoms tetrahedrally disposed at the corners of a cube with each 0 atom equidistant along a line from the center of the cube (Figure I ) . ’ Investigations of the electronic structure of the trioxides have been very limited.”13 Egdell, Palmer, and FindlayI2 reported photoelectron spectra (PES) on P406,As406,Sb406,and P4010, and ab initio molecular orbital (MO) calculations on P406 and P4OlO (as well as P4). All of these systems have closed-shell ground states (’A’). The ab initio calculations correlated quite well with the PES spectra of P4, P406,and P4Ol0, and the strong correlation of the P406,As406, and Sb406PES spectra suggested that the general structure and ordering of the occupied MOs of P406 carried over to the two heavier analogues.I2 Thus, a good framework exists for understanding the general features of these MOs. ( I ) Greenwood, N. N.; Earnshaw, A. Chemistry ofthe Elements; Pergamon: New York, 1984; p 577 ff. (2) Hampson, G.C.; Stosick, J. J . A m . Chem. SOC.1938, 60,1814. (3) Maxwell, L. R.; Hendricks, S. B.; Deming, L. S. J . Chem. Phys. 1937, 5,626. (4) Chapman, A . C. Spectrochim. Acta 1968, A24, 1687. (5) Beattie, I . R.; Livingston, K. M . S.; Ozin, G. A,; Reynolds, A. J. J . Chem. SOC.1970, A449. (6) Brumbach, S. B.; Rosenblatt, G. M. J . Chem. Phys. 1972, 56,3110. (7) Papatheodorou, G. N.; Solin, S. A. Phys. Reu. 1976, 8 1 3 , 1741. (8) Beagley, B.; Cruickshank, D. W. J.; Hewitt, T. G.; Jost, K. H. Trans. Faraday SOC.1969, 65,1219. (9) Diemann, E. Inorg. Chim. Acta 1977, 24, L27. (IO) Canninton, P. H.; Whitfield, H. J. J . Electron Spectrosc. Relafed Phenom. 1977, 10, 35. ( 1 1) Winner, E.; Weinberger, P.: Kosakov, A.; Leonhardt, G. Phys. Status Solidi 1978, B89, 619. (12) Egdell, R. G.; Palmer, M. H.; Findlay, R. H. Inorg. Chem. 1980, 19, 1314. (13) Walther, H. P h D Thesis, Universitat Hamburg, Hamburg, 1983, pp 6-33.
0022-3654/89/2093-3504$01.50/0
In contrast, no information appears to be available on the excited states of these systems, presumably because of the difficulties of working in the vacuum ultraviolet (vacuum-UV) where most of the absorption occurs. In this paper, we report the first vacuum-UV absorption and magnetic circular dichroism (MCD) spectra of P406and As406isolated in argon matrices. The MCD measurements permit us to determine the magnetic moments associated with the lower lying transitions, and it is possible to correlate these data with the MOs involved. 11. Experimental Section The experiments were conducted at the Synchrotron Radiation Center (SRC), University of Wisconsin-Madison, using the 1-GeV electron storage ring (“Aladdin”). A 1-m A1 Seya-Namioka monochromator, with a 1200 lines/mm MgF2 overcoated aluminum grating blazed at 1300 A, was used. The minimum spectral bandpass was -0.4 A. An apparatus designed and constructed at the University of Virginia (see Figure 2) attaches to the monochromator and allows us to simultaneously collect the single-beam absorbance and MCD spectra of a matrix-isolated ~amp1e.l~ Matrices were prepared under vacuum (-lo-’ Torr) by codepositing Ar with the molecules of interest onto a CaF2 or LiF deposition window held at -5 K in the center of the superconducting solenoid (Figure 2). A sealed sample of P406was kindly supplied by Dr. Jerry L. Mills, Texas Technical University, Lubbock, TX. It was premixed with Ar in the ratio of 1/3000 by simply allowing P406to vaporize at room temperature. As406 was vaporized from a resistively heated quartz Knudsen cell at -90 OC. Ar flow rates were -2 mmol/h. Once a matrix has been prepared, the cryostat is rotated 90° to bring the deposition window into alignment with the optical axis (Figure 2), and a spectrum is taken. If additional optical density is required, further depositions may be made by rotating the cryostat back into line with the Knudsen cell. The single-beam absorbance and simultaneous (M)CD are recorded by servoing the photomultiplier high voltage to maintain
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(14) For a more detailed description of this apparatus, see: Boyle, M . E. Ph.D. Thesis, University of Virginia, Charlottesville, 1987.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3505
Vacuum-Ultraviolet Spectroscopy of P 4 0 6 and As406 TABLE I: Experimental MCD Parameters for P40s and As40s band
48 920 63 960
Do('Al AS406
46 740 58 820 69 220
A B
C
Do('Al
&('AI Barycenter.
.wDob
Bo/Bo: lo4 cm-'
-0.90 f 10% -0.85 f 20%
-0.91 f 15% -2.91 20%
99a.b cm-l
A B
p4°6
-
--
-
'T,*)/B,('A,
-1.26 f 10% -1.08 f 15% 2.1 f 30% 1T2A)/Bo('A, 'T2A)/Bo(1A,
--
*
'T2B)= 0.82 -1.93 f 10% -1.85 f 20% -1.9 f 30%
-- --- --
assignt and predom exc 'A, IT2; 5t2 3e 'A, IT2; 2t, 3e
,Al 'A, 'A,
IT2; 5t2 IT2; 2t, IT2; ?
3e 3e
'T2B) = 0.91
'T2') = 0.61
Determined by moment analysis using (1)-(4).
absorption moment obtained by numerical integration of the experimental data in accord withi6
7
"3, o>
c2
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I
Figure 1. Geometry of M 4 0 6compounds and coordinate system used. The M atoms are represented by solid circles and three of the 0 atoms by open circles. Oxygen atoms 3, 4, and 6 are along -x, -y, and -z, respectively. In P406,the nearest-neighbor P-0 distance is 1.65 8, and the P-0-P bond angle is 127.5O; in As406the corresponding values are 1.80 8, and 126°.2
a constant dc current which is passed to a preamplifier. An ac signal, which is the MCD, rides atop the constant dc signal and is detected with a lock-in amplifier. A signal proportional to the high voltage is passed to a logarithmic operational amplifier which in turn outputs a signal proportional to the absorbance. The linearity of this system is excellent if the sample optical density does not exceed 1.0. The absorption base line before deposition and the zero-field CD base line after deposition were subtracted from the absorption and MCD signals, respectively, and the resulting spectra were calibrated by using the 290-nm band of a standard solution of d-10-camphorsulfonic acid (CSA).15 Depolarization of the circularly polarized light was checked by comparing the CSA CD signal with and without the sample in the light path and was negligible for the M 4 0 6 samples. 111. Results The MCD and absorption spectra of P406and As406isolated in argon matrices at -5 K are shown respectively in Figures 3 and 4. The P406spectrum shows intense absorptions at -48 900 (band A) and 63 900 cm-' (band B), and corresponding transitions in As406 occur at -46,700 and 58,800 cm-'. Band A in both compounds shows a definite low-energy shoulder. In addition, a higher energy transition (band C) is observed in As406 at -69 200 cm-I. Since bands A-C are of comparable intensity and occur in the region of the expected optical transitions,12 we assign these bands to fully allowed 'A, 'T2 electronic transitions, the only ones that occur in point group Td. T h e band parameters are summarized in T a b l e I and were obtained by moment analysis:
-
(1)
where M , is the nth MCD moment and A , is the nth zero-field (15) Chen, G. C.; Yang, J. T. Anal. Left. 1977, 10, 1195.
= l ( A A / G ) ( G - 8), dG
(3)
A,
J ( A / & ) ( G - 8)"d&
(4)
AA = Al' - AR' is the MCD in optical density units per tesla. A is the zero-field absorbance, G = hv is the photon energy, and 8 is the band barycenter defined by A , = 0. We note that A,/a), is large and negative for bands A and B in both compounds but is even larger and positiue for band C of As406.
Y
Mo/Ao = 0.467(80 + @ , / k T ) / a ) o
M,
IV. Molecular Orbital Models The experimental data consist of two (P406)or three (As406) strong optical bands, and we interpret these in the framework of molecular orbital (MO) theory. We present ab initio treatments and compare and contrast these with the results of a vastly simpler extended Huckel (EH) model. A . Ab Initio Treatments of P406and As406. P406was run using the average of two electron diffraction structure^^,^ as in earlier work.I2 A total of 160 Gaussian-type orbitals were used whereby the P / O (12s9pld/9s5p) set was contracted to [7s4pld/4s2p] by using the Dunning c o n t r a ~ t i o n ' of ~ ~the ' ~ earlier Huzinaga bases.I9 As406 was run using the electron diffraction structure of Hampson et aL2 The 0-atom basis was [4s2p], as in P406,while the As basis, As[6s4pld], is a new contraction of the As(l4sl lp5d) one of Huzinaga,20 where the s-type functions are grouped 4,4,2,2,1,1 and p-type 6,3,1,1. In the case of P406, the G A M E S S ~ S~ C . ~F~program was used to generate input for the DIRECT-CIZ3program for the calculation of excited-state energies. In this latter procedure, the core and inner valence orbitals (36 pairs in total) were frozen and the virtual orbitals from 115 to 160 were discarded, leaving an active space of 36 electrons in 78 MOs. The principal results of the S C F and CI calculations are shown in Table I1 and Figure 5. The programs were mounted on the Rutherford Laboratory Cray-XMP148. 1. P406. The present basis set generated a rapidly increasing number of open-shell configurations so that some truncation of the valence orbital set of MOs became necessary. The final choice was (for the ground state) 18 doubly occupied MOs, with all single and double excitations into a virtual space of 60 MOs. Thus, the active space is ltl-7tl, 3t2-15t2, 2e-7e, 3al-8al. The 4-index transformation took about 1400 s, the single reference ground (16) Piepho, S . B.; Schatz, P. N. Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism; Wiley: New York, 1983;
Chapter 7 and Appendix A. (17) Dunning, T. H. Chem. Phys. Lett. 1970, 7,423. (18) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (19) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293. Huzinaga, S.; Arnau, C . J . Chem. Phys. 1970, 52, 2224. (20) Huzinaga, S . J . Chem. Phys. 1977, 66, 4245; personal cornrnunication. (21) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCC QCOl NRCC Software Catalog, VoI: 1. (22) Guest, M. F.; Kendrick, J.; Pope,S. A. GAM= Users Manual; SERC Daresbury Laboratory, DL/SCI, TMOOOT, 1986. (23) Saunders, V. R.; van Lenthe, J. H. Mol. Phys. 1983, 48, 923. ~
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Rose et al.
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
1
1
4-----PEM C H A M B E R
Jll
I
MAGNET/ CRYOSTAT
I
MAGNET
COILS
-
I
ruwr ATE
TO M O N O C:HROM P
BOX 5
TO
PUMP
spray on
inches
I I
Figure 2. Schematic depiction of matrix isolation magnetic circular dichroism apparatus attached to the 1 -m aluminum Seya-Namioka, monochromator. The figure inset details the cryostat orientation during deposition (a) and data collection (b).
AA
a
-0 A
140
160
180
200
220
240
A hm Figure 3. Absorption spectrum (lower curve, A = absorbance) and MCD spectrum (upper curve, AA = A,' - AR' per tesla) of P4O6/Arat - 5 K.
The inset shows the higher lying occupied and lower lying virtual MOs according to the ab initio calculation. quence (Table 11). In addition, although the LUMO (3e) is maintained, there is an exchange of order in the next two virtual orbitals, 6t2 and 3t,. As with the earlier calculations,12oxygen is electron attracting (Mulliken population 8.62e) relative to P( 1 4 . 0 7 e ) s e e Table 11. The internal dipoles on P-0 are less by about O.le in the new calculation. A comparison of the 9012 and 160 basis SCF Mulliken 01 total populations (Table 11) shows relatively little difference. In both bases, the 3d populations are small (-0.5e). 130 150 170 190 210 230 Xlnrr The SCF single configuration has a density of 84.4% of the final CI wave function and is thus an excellent representation of the Figure 4. Absorption spectrum (lower curve, A = absorbance) and MCD spectrum (upper curve, AA = A,,' - AR' per tesla) of As,06/Ar at - 5 true ground state. No other configuration had a density 20.1%; K. Due to high background scatter, the MCD could not be recorded the remaining 15.6% of the density was widely spread over the beyond 138 nm. The MCD was extrapolated (dashed curve) to zero active space. The highest occupation number of the virtual set at the wavelength at which the absorption returned to zero. was the LUMO (3e) with a population of 0.019e, matching the largest depletion from 2.0e in the SCF occupied set which occurred in the H O M O (5t2, 1.972e). states about 78 s, and the open-shell states varied up to about 1500 It was apparent from the separation of 5t2(HOMO) from a depending upon the number of reference functions. rather closely placed group of 2t,, 3a,, and 2e orbitals that the Although the total energy for P,06 is markedly lowered relative lowest singlet state would be dominated by 5t2 3e processes. to the previous value (-1808.909 91 au for the (spd,90) minimal A series of single reference CI studies clearly showed that basis12), the occupied orbitals show only a single change of se-
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Vacuum-Ultraviolet Spectroscopy of P406and As406
,
ab initio
EH r
1 6 ~ . 6 6 1 lrPd.90)
4 '6 '
l02,1601
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3507 from the three reference configuration sets 5t23e, 3a16t2,and 2e6t2. Experimentally (Figure 3), 1T2Aoccurs at 200 nm (=6.198 eV); later we attribute the shoulder at -216 nm (=5.74 eV) to 'TIA. Thus the calculated values, which are limiting with this basis set, are about 1.7 eV too high. Rough calculations of the next pair of levels, lTZBand 'TIB,using much less extensive CI, gave the energies 9.272 and 9.721 eV, respectively. The former arises primarily from the excitation 5tz 6tz and the latter from 2t1 3e. Experimentally, 'TZBoccurs at 156.3 nm (=7.929 eV) with some suggestion of a shoulder at 163 nm (=7.8 eV). Again the calculated value(s) is (are) substantially high (-1.3 eV). There are several possible reasons for the discrepancy between the theoretical and observed transition energies. The structure Ghosen for the molecule comes from a very early pair of electron diffraction s t ~ d i e s . ~Modern ,~ techniques frequently lead to significant corrections to bond lengths (-0.03 A), and this may be a factor. However, the virial theorem (V/T = -2.00035) for the CI ground state is close to the theoretical limit (-2.0), which suggests that both the geometry and basis set are satisfactory. The lowest exponents used in P/O are s, 0.125; p, 0.084; d, 0.43/s, 0.284; and p, 0.214, respectively. These are distinctly valence as opposed to Rydberg in type (the latter are typically 0.02 or lower). Thus, a small amount of Rydberg character could have a significant effect upon the excited states while having little impact on the ground state. A further feature of the basis is that 'TIA and 1T2A are dominated by 5t2 3e processes and yet, even with 160 basis functions there are few e-type orbitals. The lowest singlet was computed with the set of reference configurations 5t2ne (n = 3-9, and these orbitals are widely separated in energy and mix poorly. A small multiconfiguration SCF calculation could possibly assist the CI. Unfortunately, it was not feasible to calculate angular momentum matrix elements in the ab initio treatment for comparison with the experimental .A1/Bo. Note Added in Proof. Several additional ab initio calculations have now been performed on P406to see if a larger valence basis and/or a geometry optimization would improve agreement with the experimental transition energies. The equilibrium structure was sought with several bases from STO-3G (66 basis) to triple {valence polarization (228 basis). The results were consistent, and values quite close to the early electron diffraction results were obtained. For example, the STO-3G basis gave R(P-0) = 1.6699 A, angle P-0-P = 127.23', angle 0-P-0 = 99.307' while the 220 basis gave 1.6454 A, 128.67', and 98.39', respective1 , compared to the electron diffraction values2 of 1.65 f 0.02 127.5 f l o , and 99 f 1'. The 'A, lTIAtransition energy obtained with the 220 basis [7s4p2d/4s2pld] S C F wave functions is 7.436 eV, which is quite close to the value 7.549 eV obtained with the 160 basis set. It thus seems that neither a significant error in the electron diffraction structure nor the use of an inadequate valence basis is the explanation for the discrepancy between the theoretical and observed transition energies. It does seem possible that inclusion of some Rydberg character in the low-lying excited states would make a significant difference, and this point is under investigation. 2. As406. The results for As406are also summarized in Table 11. The Mulliken analysis shows very similar trends except that As is a stronger donor to 0 than P, and hence, As has a high positive charge, which is consistent with its more metallic character. Most of the positive charge is attributable to the loss of 4p rather than 4s electrons. B. Extended Hiickel (EH) Treatment of P406and As406. In this section we use a very simple model, the extended Hiickel (EH) to calculate eigenvalues and eigenvectors for P406and As406. Clearly, an a b initio treatment is preferable. However, such treatments are expensive and are severely limited by the number of electrons that can be considered and thus by the complexity of the molecule under consideration. It is therefore of considerable practical interest to determine how well a very simple model can guide the interpretation of the absorption and
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Figure 5. Plot of P406molecular orbital energies for extended Hiickel
(EH), the ab initio bases (sp,66), (spd,9O),l2 and the present work (DZ,160). The UV-PES spectrurnl2is plotted to the right.
TABLE 11: Results of ab Initio Calculations PIOn (160 Basis)
SCF total energy," au virial theorem (V/T) lal -41.30 4t2 -16.14 3ed +2.31
CI -1812.81758 -2.000 35
-1812.381 95
Orbital Energies, eV: Occupied Valence Orbitals It2 le 2t2 2a1 Itl 3t2 -39.02 -37.64 -25.47 -20.79 -20.57 -18.69 2tIb 5t2c 2e 3aIb -15.31 -15.18 -15.03 -11.46 Orbital Energies, eV: Virtual Orbitals 6t2 3t, 7t2 4al +3.81 +4.90 +5.97 +6.96 AS406
SCF total energy," au
CI
-9378.920 25
Orbital Energies, eV: Occupied Valence Orbitals It2 le 2t2 2al Itl 3tz 3al -39.69 -37.85 -36.77 -24.16 -19.78 -18.78 -17.52 -15.51 2t1 2e 5t2c 4t2 -15.40 -14.80 -14.75 -11.46 lal
Orbital Energies, eV: Virtual Orbitals 3ed 6t2 4al 3t, 7t2 +1.44 +2.94 +4.03 +4.73 +6.27 Mulliken Population Analyses p406
S
P d
total total (90 basis)
P 5.4849 8.0635 0.5206 14.0690 14.2113
AS406
0 3.8166 4.8041
8.6207 8.5258
As 7.6700 13.6398 9.9956 31.3053
0 3.9348 5.1950
9.1298
bSequence change relative to ref 12. a 1 au = 2626 kJ mo1-l. HOMO. LUMO. HOMO-LUMO excitations (resulting in TI and T2excited states) were in the 7.6-7.9-eV region and that no other excitations occurred below 9.2 eV. In all cases studied, the leading configuration was a single electron S C F excitation with density of about 0.85. When the reference states were expanded to three, the total configuration-state functions (CSF) rose to lo6, but the energy of the lowest TIand T2states was remarkably, and disappointingly, stable; the lowest state, 'TIA(7.549 eV), was obtained with the reference set 5t2 ne (n = 3-5) and a total of 982 828 CSF. The corresponding IT2*state (7.864 eV) was obtained (349 505 CSF)
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-
-
-
+
-
(24) Hoffmann,
R.J . Chem. Phys. 1963, 39, 1397.
1,
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The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
MCD spectra of molecules of increasing complexity and how closely and in what respects it resembles an ab initio calculation. We obtain our eigenvalues and eigenfunctions by solving the secular determinant IFI,
- Sl,4 = 0
(5)
with the approximation Fl,
= Sl,(F,l + F,,)
(6)
where F,,and F, are appropriate valence orbital ionization energies with negative signs (VOIE; Table VI), and i and j reference the symmetry-adapted linear combinations of atomic orbitals (SALCs) in Table IV. (Table IV lists the minimum set of symmetryadapted basis functions for P406and As406.) We only consider overlap between nearest-neighbor atoms and omit the oxygen atom 2s orbitals altogether in view of their much larger VOIE. The entire treatment then depends only on the numerical values of three atomic overlap integrals: S1 (3sp12puo),S2 (3p,P12puo), and S3 I (3pTp12pTo)in the case of P406and SI’= (4sAs12pu0),S i = (4puA”12puo),and S3/ = (4pzA”12pTo)in the case of As406. For P406,SI,S2,and S3 were calculated from the formulas of Mulliken et a1.2s Eigenvalues and eigenvectors of ( 5 ) were then calculated by using a standard NAG algorithm,26and relevant results are summarized in Table VII. To check these results (and thus Table VI), we compared our eigenvalues with those obtained using the program 1 ~ 0 ~ 8(which ~ ’ makes no use of group theory) with non-nearest-neighbor overlaps deleted. All eigenvalues were in quantitative agreement. We then used ICON8 to calculate the corresponding As406overlap integrals SI’,Si, and S3/. The results for As406 are summarized in Table VIII. Comparing Table VI1 with Table I1 and Figure 5 , we note several interesting features. First, the ascending order of the occupied P406MOs agrees with the ab initio calculations except for the interchange of 2t, and 3al. The energies often agree within 1 eV and almost always within 2 eV. Even for the virtual orbitals the EH calculation matches the order of the ab initio calculation, except for the interchange of 7t2 and 4al. On the other hand, the energies of the orbitals cannot be expected to be accurate, particularly for the unoccupied (virtual) MOs. For example, the HOMO-LUMO gap (5t2 3e) is only a small fraction of the energy of the first observed optical transition of -6 eV. Similar remarks apply for As406 (compare Table VI11 with Table 11).
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V. Interpretation of Experimental Data A . Relevant MCD Formulas. For the transition ‘Al ITz, eo= 0 in (1) (nondegenerate ground state), and the oriented and isotropic cases are equivalent so that 2,= AI,etc.28 Equations 1 and 2 require only the Franck-Condon approximation; furthermore, 23, = 0 even in the presence of Jahn-Teller effects.28 The explicit formulas for AI, So,and 210 have been given elsewhere28 and are not repeated here. Since we shall focus our attention on the experimental A terms, we require the ratio Al/B0. For IAl IT2 in point group Td, the theoretical expression is
-
A,/do = Al/fDo = (2/61/2)(TzJ11LJIT,J)
(7)
where T2Jis the electronic excited state ( J = A, B, C) and L is the many-electron orbital angular momentum operator in the many-electron reduced matrix element (T211LllT2). Equation 7 provides the fundamental connection between the experimental moments, (2), and the theoretical description of the IT2 excited states. This equation is most easily obtained by using (17.3.1) of ref 16. B. Relation of the Many-Electron Reduced Matrix Element ( T211LI(T2)to the Orbital Structure of P406and As406. Starting (25) Mulliken, R.S.;Rieke, C. A,; Orloff, D.; Orloff, H. J . Chem. Phys. 1949, 17, 1248. Note that the formula given for S(2p,,3p0), f # 0, (33), should be multiplied by -1.
(26) NAG Fortran Library Routine F02AEF. (27) Howell, J.; Rossi, A,; Wallace, D.; Haraki, K.; Hoffmann, R. QCPE 1977, 19, 344.
(28) Reference 16, section 4.5, 4.6, 7.4, 7.5.
Rose et al. TABLE 111: Reduction of (T211LIITl) to One-Electron Form’
---
MO excitation t2, t p
t2e t p t p
t16 t16
t15e t15t2
(T211U T I ) -(I /2)(t2Illlt2) -( 1/2)( t2(1)lllll t p ) - (1/2)( t2(2)lllllt2’2’) ~ ~ / ~ ~ ~ ~ l l l ~ l l t l ~ -(I /2) (tl I I ~ ItIl ) + (1 /2) (t21l1Ilt2)
’Capital and lower case letters designate many-electron and oneelectron quantities, respectively. TABLE I V Minimum Set of SALCs for PIOA(or As&) irrep and row of TA“ SALC”
“Definitions and phase conventions are those of ref 16. The atomic numbering is that of Figure 1. (Note in ref 16 that all 5’s and 6’s in Figure C.10.1, p 569, should be interchanged.)
with a closed-shell ground state (IA]), there are ten different MO excitations that can give rise to a ITZexcited state. For each of these, it is straightforward to reduce (T211LJIT2)to a sum of one-electron reduced matrix elements by using the irreducible tensor technique, explicitly (20.1.7) of ref 16. In Table 111 we summarize the results for those excitations that will be relevant in our later discussion. Each MO is an appropriate linear combination of all the SALCs belong to the same row of the same irreducible representation (irrep). For example, a t2 M O using the SALCs given in Table IV can be written 7
Int2a) = Ccint2S? i=l
(8)
where nt2 designates the nth M O of t2 symmetry, and a = (, 7, or {. Note particularly that c“‘2 is independent of component a; i.e. Citnt2
=
Ci7nt2
=
Cijllt2 I c.nt2
(9)
which is a consequence of the Wigner-Eckart theorem.29 We evaluate the one-electron reduced matrix elements of Table 111 in terms of the above coefficients as follows. Using the Wigner-Eckart theorem,29 we write (ntzlllllntd = 61’2(t~llLlt2v)
(10)
Substituting (8) into the right-hand side of (10) and using Table IV, we obtain a sum of terms of the form ( a,llzlbj), where a, and bj are AOs on centers i and j , respectively. We make the onecenter approximation, Le., (a,llzlbj) = 6,~(a,~lz~b,). Evaluation of the resulting (a,ll,lbi) is straightforward iiexplicit forms are chosen for lai) and Ibi), and this has been discussed in detail elsewhere.30 In this evaluation, we use Slater-type orbitals with Slater screening constants for P406and Clementi-Raimondi screening constants3’ (29) Reference 16, section 10.2. (30) Reference 16, section 13.4. (31) Karplus, M.; Porter, R. N. Atoms and Molecules; Benjamin: New York, 1970; p 230.
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3509
Vacuum-Ultraviolet Spectroscopy of P406and As406 TABLE V: Correlations of OhSALCs" with
Td
SALCsb
center of the cube (Figure 1) to a P atom in atomic units. For P406,k = 1.6 and R = 3.424.2 For As406,the only change is that ( 3sPld/dz13p,P) must be replaced by (4shld/dzl4pZAS). The - 3k,]/8(ks + kp), where latter has the value (2(kskp)1'2/31/2)K[5ks K = (2ks)4(2kp)4/(k, kP)*.The integral reduces to the expression k/4(3)II2 as it should when k, = k , = k . For As, k, = 2.2360, k , = 1.8623,31and R = 3.71 1.2 Note that (t2111(lt2)and (tlllllltl) are the only two kinds of in the reduced matrix elements that can contribute to A 1 / B o absence of configuration interaction, because only the t l and t2 irrep's carry angular momentum in point group Td. (Note also that Cc? # 1 in general because Si, # 0.) C . Calculation of A l / B oUsing the EH Model. 1 . P406. We substitute the c, from Table VI1 into (1 1) and (12) and obtain:
+
- - -
"Table C.lO.l(a), ref 16. bTable C.lO.l(b), ref 16. CCorrelations [, etc. not listed are identical, Le., B 8, x x, TABLE VI: Parameters for Extended Hiickel Treatment VOIE," eV 2s0 = 32.2, 3sp = 18.8, 2p0 = 15.8, 3pp = 10.1 4sA' = 17.6, 4pAs = 9.1 A, blockb~c SZ3= -61/2VSI; S 3 4 = 61/2(UVS2 2R'DS3); S24 = 0 E blockb~c S23 = -61/2VD52 2'I2(2R'- V)R53 TI blockb*c SI2= 6Il2R'D'S2 (2R'V- V2 - l)S3/21/2; SZ3= 0 5'13 = 6'I2R'DS2 (1 + 2R'V- V2)S3/2'I2 T2 blockbSc S2, = -21/2VSI; S24 = 2 R S 1 ; s25 = 2iR51; s 3 6 = 2(VD52 - RUS,); S 3 7 = 21/2(UVS2 2R'D'S3); s4.5 = 2'/2R'D52 ( u v - 31/2)S3/21/2; s 4 7 = 2(VD53 - UR'&); s56 = -i(21/2R'D52 (3Il2 U V ) S ~ / ~ ~ Ss7 / ~ ) =; s26 = S 2 7 = Sg4= S3s = s45= S6, = 0
+
+ + +
+
+
+
(6t21)1(16t2)= -1.13
(5t2111115t2) = 2.09;
-
+
"DeKock, P. L.; Gray, H. B. Chemical Structure and Bonding; Benjamin: New York, 1980; p 227. bS,,= 1; R' = R/3ll2rO;D' = D/31/2r0;R = M-0, ro = P-0, and D = M-0 distances, respectively, with M the point at center of cube, Figure 1. U = (3II2R'- D'), V = (3IlZD'- R q , SI = (3pp12pSo), S2 (3p,p12pSo), S3 = (3prp12pro). cFor P406:2 R(P-P) = 2.95 i 0.03 A,R(P-0) = 1.65 i 0.02 A,angle P-0-P = 127.5 f 1'; R ' = 0.6340, D ' = 0.6214. SI = 0.1948, S2 = 0.2553, S, = 0.1319. For R(As-As) = 3.20 i 0.03 A, R(As-O) = 1.80 i 0.02 A,angle As-O-As = 126 i 3'; R ' = 0.6300, D' = 0.6258. SI' = 0.1873, Si = 0.2522, S,' = 0.1170. All overlaps calculated by using Slater-type orbitals with Slater screening constants for P4Q6 and Clementi-Raimondi screening constants for As406.
for As406. The results for P406are (omitting the superscripts on the ci): (t211111tz) = 61'2[0.5(~42- Ics21 c62) + 21/2(c3c4- c6c7) 2ll2c2c6R(3sPld/dz(3p,P)] (1 1)
+
(tilllllti) = - ( 6 1 / 2 / 2 ) ( ~ ~+2~2~ - 1~3'1) (12) where (3sPld/dz13p,P) = k/3(3)'I2 and R is the distance from the
(13)
-
If we assume that the first observed band (band A, Figure 3) arises LUMO excitation, 5t2 3e, then from the predicted HOMO using Table 111 and substituting (13) into (7), we obtain &,/Bo = 4 . 8 5 . While the near quantitative agreement with the observed value (-0.90; Table I) must be regarded as somewhat fortuitous, the result certainly supports our prediction that the first strong transition in P406is dominated by the 5t2 3e excitation. It then follows immediately that the A l / B ovalue is a direct probe of the angular momentum of the HOMO. The 3e LUMO cannot contribute to the angular momentum (t2 @ e €fe). If we examine the 5t2 eigenvector in Table VII, we observe that the three composite terms in ( 1 1) give the same sign. Thus we may anticipate that the calculated will not change greatly with quantitative refinement of the 5t2 MO provided that phosphorus d-orbital contributions to 5t2, which we have neglected, are not extensive and that configuration interaction (CI), which we do not consider in the EH treatment, does not play a major role. Both of these suppositions are supported by the ab initio results. With regard to the second observed band (B) at -8.0 eV ( 156 nm; Figure 3), there appear to be several possibilities for the (main) excitation, and the EH calculation cannot hope to distinguish among these. Obvious choices include 5t2 6t2, 3al 3e, 2t1 3e, and 2e 3e. Two of these, 3al 3e and 2e +
N
-
-
-+
+
+
TABLE VII: Eigenvalues" and Eigenvectors for PAOrb = -20.70
A, block
€2
s2
-0.751 0.487 0.092
s3 s4
e*
2e = -15.90
€6
s2
0.983 -0.126
2t2 = -22.17
€1
s2
-0.689 0.167 -0.334 -0.340 -0.031 0.029
s 3 s4
-is5 s6
s 7
€4
3t2 = -16.80
0.047 -0.536 0.304 -0.590 -0.303 -0.131
€5
4t2 = -16.13
0.078 0.67 1 0.586 -0.300 -0.091 0.205
= -2.31
0.342 0.827 -0.968 3e(LUMO) €10 = -9.86 0.199 0.995
0.000 0.894 -0.448
-0.374 -0.351 -0.701 T2 block
€13
0.611 0.565 0.489
E block SI
= -14.97
1.035 -0.346 -0.691
StZ(HOM0) €9 = -1 1.53
€11
6t2 = -7.20
-0.532 -0.005 0.553 0.122 0.397 -0.567
-0,146 -0.487 0.240 -0.230 0.668 0.705
€14
7t2 = -1.29
0.622 0.275 -0.4 15 -0.772 0.652 -0.443
"Numbered in ascending order, which is 2t22a,lt13t24t22e2t13a15t23e6t23t14a17t2. We retain the EFPI2 numbering, and thus some of our orbitals start with the prefix 2 because we have not included oxygen 2s orbitals. bc,: In the order of Table IV omitting oxygen 2s orbitals.
3510 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
Rose et al.
TABLE VIII: Eigenvalues' and Eigenvectors for As4Oi 2ai AI block
€2
s 2
-0.706 0.545 0.093
s3 S4
= -19.79
tg
3a1 = -14.12
0.668 0.579 0.444 €6
s 2
0.982 -0.119
TI block
€3
3e(LUMO)
= -1 5.90
2tl €1
1tl = -17.06
€7
s 2
-0.661 0.184 -0.358 -0.364 -0.03 1 0.030
s 3
s4
-is5 s6
s 7
€4
= -8.79
2ti = -15.80
€13
0.000 -0.881 0.473
3t2
= -21.16
€10
0.210 0.997
0.327 0.389 0.724
T2 block
= -16.50
€5
-0.036 0.609 -0.270 0.590 0.249 0.113
= -3.04
0.329 0.757 -0.973
2e
E block
s3
4a1 €12
4t2 = -15.96
0.052 0.630 0.649 -0.349 -0.063 0.137
3t1 = -2.96
1.043 -0.341 -0.636
5t,(HOMO) €9 = -1 1.03
€11
6t2 = -6.76
0.586 0.093 -0.503 -0.178 -0.391 0.538
-0.143 -0.45 1 0.198 -0.182 0.663 0.729
7t2 €14
= -2.16
0.593 0.237 -0.400 -0.722 0.674 -0.459
'Numbered in ascending order, which is 2t22allt13t24t22e2t13a15t23e6t24a13t,7t2. We use the same numbering as for P406,Table VII. order of Table IV omitting oxygen 2s orbitals.
can be eliminated at once since they cannot give rise to A terms. For the other two, we again use Table I11 and substitute (13) into (7):
-,3e
A1/a)o(5t2+6t2)
= -0.39
(15)
Al/a)o(2tl-.3e)
= -0.30
(16)
The experimental value (Table I) is -0.85, which is consistent in sign with both (1 5) and (16). The ab initio calculation associates 3e. band B with the excitation 2tl 2. As406. Comparing bands A and B of As406 with the corresponding bands of P406,we note a strong resemblance in both the absorption and MCD (Figures 3 and 4 and Table I). A sharp change in the spectrum occurs with the appearance of band C of As406 with a large positive Al/Do (Table I). To the high-energy limit that we could reach ( 130 nm), we saw no counterpart of this band in P406. The similarity of bands A and B in As406and P406suggests that they originate from similar excitations, and both the ab initio and EH treatment of As406 support this supposition. Substituting the c, from Table VI11 into (11) and (12), we obtain
-
N
(5t2111ll5t2) = 2.17; (6t2(11116t2) = -0.96; (7t2111117t2) = -1.14 (2t11111)2tl) = -0.68;
(3tI111113tI) = -0.98
(17) (18)
-
in place of (13) and (14). If, as with P406,we assume that the first observed optical band arises from the St,(HOMO) 3e(LUMO) excitation, we obtain .A1/a),, = -0.88 vs an observed value of -1.26. Again the agreement with experiment is probably better than can be expected on the basis of such a simple treatment. For the second optical transition (band B), we obtain Al/a)o(5t2+6tz)
= -0.49
(19)
Al/a)o(2tl-3e)
= -0.27
(20)
-
By comparison with the ab initio calculation on P406,it would seem reasonable to associate band B with the excitation 2tl 3e; but (19) and (20) give no definitive guidance on this score.
In the
b ~ i :
It is clear from (17) and (18) and Table 111 that A1/2J0 of the sign and magnitude observed for band C of As406 cannot be achieved on the basis of s and p orbitals alone. D. The Low-Energy Shoulder on Band A . There is clearly a low-energy shoulder on band A in both P406and As406which is somewhat more apparent in the MCD, particularly for P406. Since the ab initio calculation indicates that the 5t2(HOMO) -, 3e(LUMO) excitation is well separated from the next excitation (2tl 3e), the two obvious mechanisms that could account for this shoulder are spin-orbit or vibronic coupling. Spin-orbit effects (singlet-triplet mixing) seem unlikely since the shoulder is more pronounced and is further away from the main band in P406than in As406(roughly 4000 cm-' vs 2700 cm-I). On the other hand, the ab initio calculation places ]Al -,]TIAabout 2500 cm-' to the red of IAl 'TZA(section IV.A.3) and allowed character can be introduced into the orbitally forbidden transition via vibronic borrowing from the nearby lTZAstate. We think this is the most likely explanation of the shoulder, though more complex vibronic mechanisms cannot be ruled out since both IT2 and 'TI are Jahn-Teller susceptible. We note that the Al/210value obtained for band A by the method of moments is invariant to first-order vibronic effects,I6 but by the same token sheds no light on their importance.
-
-
VI. Discussion and Conclusions The first two bands (A and B) in P406 and As406 are very similar in absorption and MCD patterns. The orbital angular momentum (.Al/210) can be reasonably well rationalized by a very simple extended Hiickel treatment (EH) which employs ns and np orbitals for M (=P, As) and 2p orbitals for oxygen. However, the highest energy band in As406,band C, cannot be understood on such a basis and very likely arises from an excited state containing significant admixtures of higher angular momentum ( I I2) orbitals. The first excitation in atomic As that involves a d orbital is 4p 4d at -63 500 cm-' ( 158 nm),32and it seems quite possible that 4d orbitals, which should be Rydberg in nat ~ r econtribute ,~~ significantly to the excited state associated with
-
N
(32) Moore, C . E.Atomic Energy Levels; Nntl. Bur. Stnnd. (US.), Circ. No. 467, Vol. I and 11; NBS: Washington, DC, 1958. (33) Robin, M. B. Higher Excited States ofPolyntomic Molecules; Academic Press: New York, 1974; Vol. 1, p 229.
J. Phys. Chem. 1989, 93, 3511-3514 TABLE i X Atomic Populations (%) in MOs of P40s: EH Calculatian (and spd,901*)" P 0
2P (4)
0 0 0 39
(3) (1)
(48) 33 (65) 74 (66) 81 (80)
91 (76) 47 (94) 100 (96) 35 (1)
28 (26)
" (spd,90) values in parentheses. band C of As406. The reasonable success of the E H treatment in calculating the angular momenta of the A and B bands very likely reflects an element of topological control in the nature and sequence of the MOs in P406. That is, all calculations seem to lead to a (nearly) constant orbital sequence. We have noticed this34in relation to other cagelike structures of general type M,N, where all atoms M / N have a single type of environment. Some examples are As4S4 and P4S435and even (NSF)3 and (NSF)4.36 Given the wide divergence in methodology of the ab initio and EH methods, we pursue this point a little further. While ab initio and EH MO energies show notable differences (Table I1 vs Table VII), a Mulliken population analysis of the E H calculation (Table IX) shows striking resemblances to that of the earlier ab initio studyI2 (parentheses, Table IX), particularly for the higher occupied orbitals. We also note that few MOs are mixtures of P/O in close to even proportions and few have mixed s/p character. This is an ideal circumstance for topological control of the MOs and means that the exact parameters used in the E H calculation will not be critical. Comparing the E H and ab initio MOs (Table IX), we note that 5t2(HOMO) in both cases is very similar and is largely lone-pair phosphorus in character whereas the E H 3al is significantly more delocalized (more oxygen character) than (34) Palmer, M . H. Unpublished work. (35) Palmer, M. H.; Findlay, R. H. J . Mol. Struct. (THEOCHEM) 1983, 104, 321. (36) Palmer, M. H.; Westwood, N. P. C.; Oakley, R. T. Chem. Phys., in
press.
3511
its a b initio counterpart. (Some previous studies of ab initio vs E H MOs in N-heterocycles have noted higher delocalization of lone pair nitrogen orbitals in the latter.37,38) Orbital 2al is also significantly different, being largely oxygen 2p (ab initio) versus phosphorus 3s (EH). There is also a close similarity between the ab initio and EH wave functions for As406. The occupied (and virtual) sets of MOs have similar groupings in the two calculations (compare Tables I1 and VIII) including the relative shift of 4al toward the LUMO. However, the HOMO/LUMO gap is larger for As406vs P406 in the E H calculation while the reverse is true for the ab initio one. The strong resemblances of the EH and ab initio MOs and the reasonable success of the former in accounting for the excited-state angular momentum associated with bands A and B is encouraging. It suggests at least the possibility that this very simple approach can guide the interpretation of the MCD spectra of more complex systems where ab initio calculations are not feasible. A crucial test will come in the application to cagelike structures in which the participating atoms of a given kind are in more than one environment. We expect to address this point in future work. It would also be of interest to see whether the addition of higher angular momentum orbitals can rationalize the sign and magnitude of & , / B oin band C of As406.
Acknowledgment. We are deeply indebted to Dr. Jerry L. Mills, Department of Chemistry and Biochemistry, Texas Technical University, Lubbock, TX, for his generous donation of a sample of P406. We thank the technical staff of the Synchrotron Radiation Center, Physical Sciences Laboratory, University of Wisconsin-Madison for their generous assistance, Professor Patricia A. Snyder, Florida Atlantic University, for her loan to us of several items of equipment, Dr. Jenny Green, Oxford University, for the use of her ICONBprogram and Ms. Cary Boyle and Dr. David Clark for comments on the use of the program. We thank Dr. K. P. Lawley for pointing out the direct products arising from the T d / C , mapping. P.N.S. thanks Dr. Peter Day, the Fellows of St. John's College and the Inorganic Chemistry Laboratory, Oxford University, for most generous hospitality while a portion of this work was carried out. This work was supported by the National Science Foundation under Grant CHE8700754. Registry No. P406,12440-00-5;As,O,, 12505-67-8;Ar, 7440-37-1, (37) Clementi, E. J . Chem. Phys. 1967,46, 4731; J . Chem. Phys. 1967, 46, 4737. ( 3 8 ) Hoffmann, R . J . Chem. Phys. 1964, 40, 2745.
ESR Studies of eaq- in Liquid Solution Using Photolytic Production A. S. Jeevarajan and R. W. Fessenden* Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: September 15, 1988) Continuous photolysis of solutions of sulfite ion in aqueous solution has been found to produce observable signals of eaq-in electron spin resonance (ESR)experiments. These experiments represent the first solution-phase ESR observation of this species in other than pulse radiolysis experiments. In this way, it has been possible to study the effects of solvent environment on the g factor and spin relaxation times of this species. The g factor decreases a small amount with increased temperature and is raised when D 2 0 is used as solvent. Measurements of the ESR signal which is out of phase with the fidd modulation (at 30 kHz) allowed the spin relaxation times to be measured (assuming T , = T2). The value of T I at 23 OC is 8 p s in H 2 0 and 9 p s in D,O; the relaxation time decreases with increasing temperature. A discussion of the implications of these results for the structure of eaq- is given. The chemical half-life was found, by competition experiments, to be about 100 p s . Introduction
The electron spin resonance (ESR) spectrum of the hydrated electron, e, -,in liquid aqueous solutions has only been detected in pulse radiolysis The spectrum consists of a 0022-3654/89/2093-3511$01.50/0
single narrow line at g = 2.0004. The solvated electron has also been studied in pulse experiments in methanol and ethanol4 and ( 1 ) Avery, E. C.; Remko, J. R.; Smaller, B. J . Chem. Phys. 1968, 49, 951.
0 1989 American Chemical Society
