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The 1A1 electronic excited states of H2CS: an ab initio MRD CI study
30 August I99 1
CHEMICAL PHYSICS LETTERS
Volume 183, number 3,4
The ‘Al electronic excited states of H,CS: an ab initio MRD CI study M. Hachey, F. Grein Department
of Chemistry,
University ofNew Brunswick,
BagService No. 452.22, Fredericton. New Brunswick, Canada E3B 6E2
and
R.P. Steer Department
of Chemistry,
University ofSaskatchewan.
Saskatoon,
Saskatchewan,
Canada S7N OWO
Received 20 March 199I ; in final form 2 I June I99 1
Ab initio CI studies have been performed to determine the energies of the lowest five ‘A, states of thioformaldehyde, H&S, as a function of C-S distance in Cz. symmetry. In addition to the well-known Rydberg and (n, ‘ II*) states, a doubly excited state of no, I[*’ configuration has been found which, at ground-state equilibrium geometry, lies very close to the R, rr* state. The chemical and spectroscopic implications of this state are discussed.
1. Introduction Thioformaldehyde, H&S, thiophosgene, Cl&S, and other small thiocarbonyl-containing molecules have been the subject of numerous spectroscopic, photophysical and theoretical studies in recent years #I [ 3- 111. The lowest triplet ( ‘A2 or 3A” ) and the lowest excited singlet ( ‘AZ or ‘A” ) states of these molecules are accessible by one-photon excitation in the visible and, with a few notable exceptions, have been we11characterized. However, the spectroscopy, photophysics and unusual photochemistry of the higher electronic states of these and larger thiocarbonyls are much less well understood and continue to present interesting challenges to both experimentalists and theoreticians. Thioformaldehyde is the prototypical thiocarbony]. It exhibits four strong absorption systems in the 180-230 nm region which have been assigned [ 571 to transitions from the ‘A, ground state to the ‘A,, ’ (IT, IT*), valence-shell state and to the lowest ’ BZ, RL For a review of the literature to 1980 and H&S see refs. [ I ,2 1, respectively.
204
‘Ai and ‘Bi Rydberg states. Other aliphatic thioketones and thioaldehydes exhibit similar UV band systems [ 12,131. Thiophosgene exhibits a very complex near-UV absorption spectrum which has been assigned to the electric dipole-allowed, valence-shell transition to its lowest ‘A, excited state [ 14,151. Not only is this spectrum broad and cluttered with vibrational hot bands owing to the large distortion of the molecule in the upper state, but its analysis is made more difficult by the presence of both chlorine isotope bands and extensive excited-state vibrational coupling [ 14,15 1. There is also an unexplained difference between the location of the origin of this system determined by direct one-photon excitation [ 14,15 1, and its apparent location when the upper state is reached by two-photon excitation via the lowest excited singlet state of ‘AZ symmetry [ 161. Moreover, analysis of the optical-optical double-resonance spectrum [ 161 yields a set of upper-state vibrational frequencies which differ from those obtained on onephoton excitation [ 14,15 1. Interestingly, the second (?) excited singlet, rr, n* state of Cl&S is also populated in an unusual electronic-energy pooling pro-
0009-2614/91/S 03.50 0 199 I Elsevier Science Publishers B.V. All rights reserved.
Volume 183, number 3,4
30 August I99 1
CHEMICAL PHYSICS LETTERS
cess involving the bimolecular annihilation of two ‘AZstates, the detailed mechanism of which has yet to be elucidated [ 171. The nature of the short-lived intermediates which are responsible for the intermolecular photochemical reactions of adamantanethione and other “model” alicyclic thiones when they are excited to their second (?) excited singlet states has also been the subject of some controversy. De Mayo and Law [ 18,191 assumed that the photochemically reactive state in these systems is the ‘A,, I ( TC,n*) state. However, Falk and Steer [ 201 subsequently showed that the excited state which carries the oscillator strength of the UV transition in these molecules is very short-lived, and that the photochemically active species must be nonfluorescent and derived from the initially populated state by a subpicosecond intramolecular process. The above information prompted us to explore the possibility that a “dark”, electronically excited state of approximately the same energy as the ‘A,, ’ (x, n*) state might be present in molecules containing the thiocarbonyl group. We have, therefore, initiated a computational-theoretical study to locate other lowlying electronic states in HzCS. We have paid particular attention to determining the location of ‘A, states of nominal rt2nox*2 orbital occupancy since these could lie at approximately the same energy as the ’ (K, x* ) states of the same symmetry. Such “doubly excited” states have not been specifically considered in previous theoretical studies of H2CS [ 81.
lion singly and doubly excited configurations were generated, based on 59 reference configurations. With a configuration-selection threshold T of 10 p&, 14500-24000 configurations contributed to the lowest five roots. The energies were then extrapolated to T=O. Estimates of the full-C1 energy are given throughout. Potential curves were calculated for the five lowest ‘A, states in increments of 0.1 a0 over a C-S distance ranging from 2.5 to 4.0 a,. The C-H distance and the SCH angle were fixed at their ground-state experimental values of 1.0925 A (2.06455 ao) and 116.87”, respectively [ 301. These potential curves are shown in fig. 1. The ground state, ‘A,, has a minimum at Rcs = 1.64 A ( 3.10 ao), compared with an experimental value of 1.611 A [ 30,311. A number of apparent irregularities are seen in the higher states. However, most of these can be explained on the basis of avoided crossings [ 251. The ground-state configuration of HzCS is KKL 5a:6a:2b$7a:2b:3b:. If we adopt the common orbital notations “n” for 3b2, “n” for 2b,, “rc*” for 3b,,
t -436.6
2. Theoretical methods and results Multireference configuration-interaction calculations were performed on the ‘A, states of H&S, in Cpv symmetry, using the MRD-CI programming package of Buenker, Peyerimhoff and co-workers [ 2 1-24 1. Details of the basis set and parameter settings employed in these calculations will be given elsewhere [25]. In summary, contracted Gaussian basis sets were used; 6s4p for S [ 26],%4p for C [27] and 3s for H [ 271, augmented by polarization (two for S [28], one for C [29], one for H) and diffuse functions (a set of s, p, d for both S and C [ 29 ] ). The CI wavefunction was built from ‘AZ, ’ (n, rr*), MOs. With six core orbitals frozen and the corresponding six highest MOs discarded, about 2.5 mil-
f k
E
z I
I
2.60
I
*
I
I
3.20
I
’
I
3’A, 2’A,
1
I
I
3.60
i
I
I
4.0
Rc, (bohr) Fig. I. Potential energy curves for the ‘A, states of HzCS (C,,) as a function of C-S distance. The C-H distance was held at 1.0925 A (2.06455 a,,) and the HCH angle at 116.87” (see ref. [301).
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30 August I99 I
CHEMICAL PHYSICS LETTERS
etc., the ground-state configuration, for example, may be abbreviated as A*,n2 or just n2. The leading configurations of the five ‘A, states of lowest energy at 3.0 a, are shown in table 1 together with the calculated energies of the vertical excitations from the ground state. At RcS= 3.0 ao, the third ‘A, state has no, n*2 as the leading configuration and may be viewed as resulting from a two-electron, 3b$ + 3b: promotion. It lies slightly below the A,7c*(4 ‘A, ) state at3.0ao.ThesecondandfifthstatesareRydbergstates, (n, p) (3b2-t4b2) and (n,d) (3b2+5b2), respectively. The vertical excitation energies previously calculated by Burton et al. [ 8 ] and Bruna et al. [ 32 ] are also given in table 1, together with relevant experimental data [ 5 ]. The “diabatic” potential curves are shown in fig. 2. In this figure, points representing the energies of states having the same dominant configuration have been joined. Because the 1 ‘A, and 2 ‘A, states do not show the typical pattern of an avoided crossing when they switch contigurations at 3.6 a0 (vide infra), the diabatic potential curves of the n* and the II, rr* configurations have been drawn separately from the calculated points for C-S distances greater than 3.1 a,. Note the curve for the rc, rc* state. The first time the x, x1 configuration appears among the five lowest roots is at 2.9 ao. (At shorter C-S distances, the fifth root is another Rydberg state.) Between 3.0 and 3.1 ao, the TC,rr* state “crosses” the n, p and no, A*~ states. As a result, at 3.1 a, the states 2 ‘A, to 4 ‘A, show considerable mixing of configurations. At 3.2 ao, the ordering of states, listed by their leading configuration, is (n2), (x, x*), (n, p) (no, rr**) and (n, d). For larger C-S separations, the x, R* state
-0) $!
....
r,..,-.
-436.6
2.6
2.6
3.0
R,,
3.2
3.4
3.6
3.6
4.8
(bohr)
Fig. 2. Diabatic potential curves corresponding to the ‘A, states of H,CS, as a function of C-S distance. For details see fig. 1. ( l ) nZ; ( 0 ) n, p Rydberg and n, d Rydberg; ( A) no, I*‘; ( q ) n, rr’: (x ) crossing points.
drops even lower, and at 3.6 ao, n2 and rt, x* have equal contributions in the first root. At Rcs> 3.6 ao, the n, rr* configuration becomes the dominant configuration of the ground state. Two ‘A,-‘A, absorptions of H2CS have been observed experimentally in the quartz ultraviolet region of the spectrum. The lowest ‘A, Rydberg state appears as a sharp feature at 188 nm (AE= 6.60 eV) [ 51. The energy of this band corresponds closely to the vertical n+p transition energy. The data presented in table 1 show that there is reasonable agree-
Table I Vertical excitation energies AS (in eV) of the ‘A, states of H,CS, at R,=
3 a, ( 1.59A)
State
Contig.
This work
Ref. [8]
Ref. [32]
Expt. ”
ce (%) c’
total c* (96) d1
I ‘A, 2 ‘A, 3 ‘A, 4 ‘A, 5 ‘A,
(x2, n2) (n, p)Ryd. (no,11~’ (X,L’) (n, d)Ryd.
0.00 6.57 6.92 7.18 7.60
0.00 6.80
0.00 6.62
0.00(X) 6.60(b)
7.02
7.92
5.60 b’(fi)
67.3 71.3 64.1 45.7 65.5
91.5 90.8 90.9 90.4 90.7
a) Ref. [S]. b, For the 0: band. See text for details. c1c* of leading configuration. d, Total c* of all reference configurations.
206
Volume 183, number 3,4
CHEMICAL PHYSICS LETTERS
ment among all the calculated A& for this transition and that the value calculated in the present work (M~6.57 eV) is in good agreement with experiment. The other observed ‘A,-‘A, band system has been assigned to a strong, electric dipole-allowed, X+X* transition. This absorption band has an origin near 221 nm (5.60 eV), a maximum near 200 nm (6.2 eV), and exhibits a long progression of bands assigned to the excited-state C-S stretching vibration [ $71. The present calculations are completely consistent with the assignment of this strong, broad UV absorption system of H&S to a transition to an excited state which is primarily of ’ (K, x*) character. The existence of a shallow minimum at greatly extended C-S distances suggests that the spectrum should be broad, the C-S stretching vibration should be Franck-Condon active, and the origin should carry only a small fraction of the oscillator strength, all of which are observed in both HzCS and Cl&S. The calculated vertical transition energy to the ’ (x, x*) state of H$S at RcS= 3.0 a, cannot be readily compared with experiment. However, one can estimate the energy of the origin band of the broad UV band system from the difference between the minimum energies of the 1 ‘A, and 2 ‘A, states (cf. fig. 1). The energy of the pure electronic transition calculated in this way is 5.85 eV, and this is to be compared with the observed value of 5.60 eV [5]. The no, X*~state has been neither calculated nor directly observed previously. Nevertheless indirect spectroscopic and photochemical evidence for a “dark” state such as this has been obtained for both Cl,CS and several alicyclic thiones [ 15,201. Although a one-photon transition from the ground state to the ‘A, no, R**excited state would be formally allowed, the oscillator strength of such a transition should be low because of the two electron promotion involved. The no, xs2 state would therefore meet the requirement that it be “dark”. However, such states, if present in these molecules, would also need to exhibit energies near those of the origins of their strong, K-+X*transitions. In H,CS, the energy of the no, x*2 state calculated at the ground state geometry lies z 1.2 eV higher than that of the x+x* origin, This could indicate that the no, Keystate is not the “dark” state involved. However, calculations on H2CS with full excited-state geometry optimization, or on mol-
30 August 1991
ecules other than HzCS, will be required to establish this point with certainty. Finally, we note that an excited state with an no, Key configuration was predicted for H&O some time ago by the theoretical studies of Buenker and Peyerimhoff [ 331 and Langhoff and Davidson [ 341. These authors quote vertical n2+x *2excitation energies of 12.79 and 11.33 eV, compared with L+ IC* vertical excitation energies of 12.13 and 10.62 eV respectively.
3. Conclusions Recent spectroscopic, photochemical and photophysical studies of C12CS[ 14- 161 and larger thiones [ 18,191 have provided circumstantial evidence that a “dark” state may be present in thiocarbonyl-containing compounds at an energy near that of the wellknown ’ (K, IC*) state. The present theoretical studies have identified a previously unknown doubly excited state of no, rt**configuration in the model compound, thioformaldehyde, H2CS. Its vertical excitation energy is close to that of the calculatedwrtical n~lc* transition energy, and it has the required symmetry ( ‘A, ). These facts suggest that calculations involving full excited-state geometry optimization would be worthwhile. Such calculations are underway.
Acknowledgement The authors wish to thank the Natural Sciences and Engineering Research Council of Canada for financial support.
References [ 1] R.P. Steer, Rev. Chem. Intermed. 4 ( 198I ) I. [2 ] D.J. Clouthier and D.A. Ramsay, Ann. Rev. Phys. Chem. 34 (1983) 31. [3] B. Simard, P.A. Hackett and R.P. Steer, J. Mol. Spectry. 126 ( 1987) 307. [4] B. Simard, R.P. Steer, R.H. Judge and DC. Moule, Can. J. Chem. 66 (1988) 359. [S]C.R. Drury and DC. Moule, J. Mol. Spectry. 92 (1982) 469.
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(61 W. Goetz, D.C. Mottle and D.A. Ramsay, Can. J. Phys. 59 (1981) 1635. [ 71 CR. Drury, J.Y.K. Lai and DC. Moule, Chem. Phys. Letters 87 (1982) 520. [S] P.G. Burton, SD. Peyerimhoff and R.J. Buenker, Chem. Phys. 73 (1982) 83. [ 91 SF. Karna and F. Grein, Mol. Phys. 57 ( I986 ) 939. [ IO] M. Kawasaki, K. Kasatani and H. Sato, Chem. Phys. 94 (1985) 179. [ I I ] B. Simard, A.E. Bruno, P.G. Mezey and R.P. Steer, Chem. Phys. 103 (1986) 75. 121S. Paone, DC. Mottle, A.E. Bruno and R.P. Steer, J. Mol. Spectry. 107 (1984) I. 131K.J. Falk and R.P. Steer, Can. J. Chem. 66 (1988) 575. 141R.J. Judge and DC. Moule, J. Mol. Spectry. 80 ( 1980) 363, and references therein. 151M. Ludwiczak, D. Latimer and R.P. Steer, J. Mol. Spectry., submitted for publication. [ 161R.N. Dixon and C.M. Western, J. Mol. Spectry. I I5 ( 1986) 74. [ 171 D.J. Clouthier, A.R. Knight, R.P. Steer and P.A. Hackett, J. Chem. Phys. 72 ( 1980) 1560. [ 181P. de Mayo, Accounts Chem. Res. 9 (1976) 52. [ 191KY. Law and P. de Mayo, 1. Am. Chem. Sot. IO1 (1979) 3251. [ 201 K.J. Falk and R.P. Steer, J. Am. Chem. Sot. I 11 ( 1989) 6518. (2 I ] R.J. Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33; 39 (1975) 217.
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30 August 1991
[ 221 R.J. Buenker, SD. Peyerimhoff and W. Butacher, Mol. Phys. 35 (1978) 771. [ 231 R.J. Buenker and R.J. Phillips, J. Mol. Struct. THEOCHEM 123 (1985) 291. [ 24) R.J. Buenker, in: Proceedings of the Workshop on Molecular Physics and Quantum Chemistry into the 80’s, ed. P.B. Burton (University of Wollongong, Wollongong, I980 ): in: Studies in physical and theoretical chemistry, Vol. 2 I, ed. R. Carbo (Elsevier, Amsterdam, 1982). [25] M. Hachey and F. Grein, to be published. [ 261 A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [27] T.H. Dunning Jr., J. Chem. Phys. 55 (1971) 716. [28] B. Roes and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 199; S. Shih, SD. Peyerimhoff and R.J. Buenker, Chem. Phys. I7 (1976) 391. [29]T.H. Dunning Jr. and P.J. Hay, in: Modem theoretical chemistry, Vol. 3. Methods of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1976). [30] D.R. Johnson, F.X. Powell and W.H. Kirchhoff, J. Mol. Spectry. 39 ( 1971) 136. [ 311 P.H. Turner, L. Halonen and I.M. Mills, J. Mol. Spectry. 88 (1981) 402. [ 321 P.J. Bruna, SD. Peyerimhoff, R.J. Buenkerand P. Rosmus, Chem. Phys. 3 (1974) 35. [33] R.J. Buenker and S.D. Peyerimhoff, J. Chem. Phys. 53 (1970) 1368. [ 341 S.R. Langhoffand E.R. Davidson, J. Chem. Phys. 64 (1976) 4699.
CHEMICAL PHYSICS LETTERS
Volume 183, number 3,4
The ‘Al electronic excited states of H,CS: an ab initio MRD CI study M. Hachey, F. Grein Department
of Chemistry,
University ofNew Brunswick,
BagService No. 452.22, Fredericton. New Brunswick, Canada E3B 6E2
and
R.P. Steer Department
of Chemistry,
University ofSaskatchewan.
Saskatoon,
Saskatchewan,
Canada S7N OWO
Received 20 March 199I ; in final form 2 I June I99 1
Ab initio CI studies have been performed to determine the energies of the lowest five ‘A, states of thioformaldehyde, H&S, as a function of C-S distance in Cz. symmetry. In addition to the well-known Rydberg and (n, ‘ II*) states, a doubly excited state of no, I[*’ configuration has been found which, at ground-state equilibrium geometry, lies very close to the R, rr* state. The chemical and spectroscopic implications of this state are discussed.
1. Introduction Thioformaldehyde, H&S, thiophosgene, Cl&S, and other small thiocarbonyl-containing molecules have been the subject of numerous spectroscopic, photophysical and theoretical studies in recent years #I [ 3- 111. The lowest triplet ( ‘A2 or 3A” ) and the lowest excited singlet ( ‘AZ or ‘A” ) states of these molecules are accessible by one-photon excitation in the visible and, with a few notable exceptions, have been we11characterized. However, the spectroscopy, photophysics and unusual photochemistry of the higher electronic states of these and larger thiocarbonyls are much less well understood and continue to present interesting challenges to both experimentalists and theoreticians. Thioformaldehyde is the prototypical thiocarbony]. It exhibits four strong absorption systems in the 180-230 nm region which have been assigned [ 571 to transitions from the ‘A, ground state to the ‘A,, ’ (IT, IT*), valence-shell state and to the lowest ’ BZ, RL For a review of the literature to 1980 and H&S see refs. [ I ,2 1, respectively.
204
‘Ai and ‘Bi Rydberg states. Other aliphatic thioketones and thioaldehydes exhibit similar UV band systems [ 12,131. Thiophosgene exhibits a very complex near-UV absorption spectrum which has been assigned to the electric dipole-allowed, valence-shell transition to its lowest ‘A, excited state [ 14,151. Not only is this spectrum broad and cluttered with vibrational hot bands owing to the large distortion of the molecule in the upper state, but its analysis is made more difficult by the presence of both chlorine isotope bands and extensive excited-state vibrational coupling [ 14,15 1. There is also an unexplained difference between the location of the origin of this system determined by direct one-photon excitation [ 14,15 1, and its apparent location when the upper state is reached by two-photon excitation via the lowest excited singlet state of ‘AZ symmetry [ 161. Moreover, analysis of the optical-optical double-resonance spectrum [ 161 yields a set of upper-state vibrational frequencies which differ from those obtained on onephoton excitation [ 14,15 1. Interestingly, the second (?) excited singlet, rr, n* state of Cl&S is also populated in an unusual electronic-energy pooling pro-
0009-2614/91/S 03.50 0 199 I Elsevier Science Publishers B.V. All rights reserved.
Volume 183, number 3,4
30 August I99 1
CHEMICAL PHYSICS LETTERS
cess involving the bimolecular annihilation of two ‘AZstates, the detailed mechanism of which has yet to be elucidated [ 171. The nature of the short-lived intermediates which are responsible for the intermolecular photochemical reactions of adamantanethione and other “model” alicyclic thiones when they are excited to their second (?) excited singlet states has also been the subject of some controversy. De Mayo and Law [ 18,191 assumed that the photochemically reactive state in these systems is the ‘A,, I ( TC,n*) state. However, Falk and Steer [ 201 subsequently showed that the excited state which carries the oscillator strength of the UV transition in these molecules is very short-lived, and that the photochemically active species must be nonfluorescent and derived from the initially populated state by a subpicosecond intramolecular process. The above information prompted us to explore the possibility that a “dark”, electronically excited state of approximately the same energy as the ‘A,, ’ (x, n*) state might be present in molecules containing the thiocarbonyl group. We have, therefore, initiated a computational-theoretical study to locate other lowlying electronic states in HzCS. We have paid particular attention to determining the location of ‘A, states of nominal rt2nox*2 orbital occupancy since these could lie at approximately the same energy as the ’ (K, x* ) states of the same symmetry. Such “doubly excited” states have not been specifically considered in previous theoretical studies of H2CS [ 81.
lion singly and doubly excited configurations were generated, based on 59 reference configurations. With a configuration-selection threshold T of 10 p&, 14500-24000 configurations contributed to the lowest five roots. The energies were then extrapolated to T=O. Estimates of the full-C1 energy are given throughout. Potential curves were calculated for the five lowest ‘A, states in increments of 0.1 a0 over a C-S distance ranging from 2.5 to 4.0 a,. The C-H distance and the SCH angle were fixed at their ground-state experimental values of 1.0925 A (2.06455 ao) and 116.87”, respectively [ 301. These potential curves are shown in fig. 1. The ground state, ‘A,, has a minimum at Rcs = 1.64 A ( 3.10 ao), compared with an experimental value of 1.611 A [ 30,311. A number of apparent irregularities are seen in the higher states. However, most of these can be explained on the basis of avoided crossings [ 251. The ground-state configuration of HzCS is KKL 5a:6a:2b$7a:2b:3b:. If we adopt the common orbital notations “n” for 3b2, “n” for 2b,, “rc*” for 3b,,
t -436.6
2. Theoretical methods and results Multireference configuration-interaction calculations were performed on the ‘A, states of H&S, in Cpv symmetry, using the MRD-CI programming package of Buenker, Peyerimhoff and co-workers [ 2 1-24 1. Details of the basis set and parameter settings employed in these calculations will be given elsewhere [25]. In summary, contracted Gaussian basis sets were used; 6s4p for S [ 26],%4p for C [27] and 3s for H [ 271, augmented by polarization (two for S [28], one for C [29], one for H) and diffuse functions (a set of s, p, d for both S and C [ 29 ] ). The CI wavefunction was built from ‘AZ, ’ (n, rr*), MOs. With six core orbitals frozen and the corresponding six highest MOs discarded, about 2.5 mil-
f k
E
z I
I
2.60
I
*
I
I
3.20
I
’
I
3’A, 2’A,
1
I
I
3.60
i
I
I
4.0
Rc, (bohr) Fig. I. Potential energy curves for the ‘A, states of HzCS (C,,) as a function of C-S distance. The C-H distance was held at 1.0925 A (2.06455 a,,) and the HCH angle at 116.87” (see ref. [301).
205
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CHEMICAL PHYSICS LETTERS
etc., the ground-state configuration, for example, may be abbreviated as A*,n2 or just n2. The leading configurations of the five ‘A, states of lowest energy at 3.0 a, are shown in table 1 together with the calculated energies of the vertical excitations from the ground state. At RcS= 3.0 ao, the third ‘A, state has no, n*2 as the leading configuration and may be viewed as resulting from a two-electron, 3b$ + 3b: promotion. It lies slightly below the A,7c*(4 ‘A, ) state at3.0ao.ThesecondandfifthstatesareRydbergstates, (n, p) (3b2-t4b2) and (n,d) (3b2+5b2), respectively. The vertical excitation energies previously calculated by Burton et al. [ 8 ] and Bruna et al. [ 32 ] are also given in table 1, together with relevant experimental data [ 5 ]. The “diabatic” potential curves are shown in fig. 2. In this figure, points representing the energies of states having the same dominant configuration have been joined. Because the 1 ‘A, and 2 ‘A, states do not show the typical pattern of an avoided crossing when they switch contigurations at 3.6 a0 (vide infra), the diabatic potential curves of the n* and the II, rr* configurations have been drawn separately from the calculated points for C-S distances greater than 3.1 a,. Note the curve for the rc, rc* state. The first time the x, x1 configuration appears among the five lowest roots is at 2.9 ao. (At shorter C-S distances, the fifth root is another Rydberg state.) Between 3.0 and 3.1 ao, the TC,rr* state “crosses” the n, p and no, A*~ states. As a result, at 3.1 a, the states 2 ‘A, to 4 ‘A, show considerable mixing of configurations. At 3.2 ao, the ordering of states, listed by their leading configuration, is (n2), (x, x*), (n, p) (no, rr**) and (n, d). For larger C-S separations, the x, R* state
-0) $!
....
r,..,-.
-436.6
2.6
2.6
3.0
R,,
3.2
3.4
3.6
3.6
4.8
(bohr)
Fig. 2. Diabatic potential curves corresponding to the ‘A, states of H,CS, as a function of C-S distance. For details see fig. 1. ( l ) nZ; ( 0 ) n, p Rydberg and n, d Rydberg; ( A) no, I*‘; ( q ) n, rr’: (x ) crossing points.
drops even lower, and at 3.6 ao, n2 and rt, x* have equal contributions in the first root. At Rcs> 3.6 ao, the n, rr* configuration becomes the dominant configuration of the ground state. Two ‘A,-‘A, absorptions of H2CS have been observed experimentally in the quartz ultraviolet region of the spectrum. The lowest ‘A, Rydberg state appears as a sharp feature at 188 nm (AE= 6.60 eV) [ 51. The energy of this band corresponds closely to the vertical n+p transition energy. The data presented in table 1 show that there is reasonable agree-
Table I Vertical excitation energies AS (in eV) of the ‘A, states of H,CS, at R,=
3 a, ( 1.59A)
State
Contig.
This work
Ref. [8]
Ref. [32]
Expt. ”
ce (%) c’
total c* (96) d1
I ‘A, 2 ‘A, 3 ‘A, 4 ‘A, 5 ‘A,
(x2, n2) (n, p)Ryd. (no,11~’ (X,L’) (n, d)Ryd.
0.00 6.57 6.92 7.18 7.60
0.00 6.80
0.00 6.62
0.00(X) 6.60(b)
7.02
7.92
5.60 b’(fi)
67.3 71.3 64.1 45.7 65.5
91.5 90.8 90.9 90.4 90.7
a) Ref. [S]. b, For the 0: band. See text for details. c1c* of leading configuration. d, Total c* of all reference configurations.
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ment among all the calculated A& for this transition and that the value calculated in the present work (M~6.57 eV) is in good agreement with experiment. The other observed ‘A,-‘A, band system has been assigned to a strong, electric dipole-allowed, X+X* transition. This absorption band has an origin near 221 nm (5.60 eV), a maximum near 200 nm (6.2 eV), and exhibits a long progression of bands assigned to the excited-state C-S stretching vibration [ $71. The present calculations are completely consistent with the assignment of this strong, broad UV absorption system of H&S to a transition to an excited state which is primarily of ’ (K, x*) character. The existence of a shallow minimum at greatly extended C-S distances suggests that the spectrum should be broad, the C-S stretching vibration should be Franck-Condon active, and the origin should carry only a small fraction of the oscillator strength, all of which are observed in both HzCS and Cl&S. The calculated vertical transition energy to the ’ (x, x*) state of H$S at RcS= 3.0 a, cannot be readily compared with experiment. However, one can estimate the energy of the origin band of the broad UV band system from the difference between the minimum energies of the 1 ‘A, and 2 ‘A, states (cf. fig. 1). The energy of the pure electronic transition calculated in this way is 5.85 eV, and this is to be compared with the observed value of 5.60 eV [5]. The no, X*~state has been neither calculated nor directly observed previously. Nevertheless indirect spectroscopic and photochemical evidence for a “dark” state such as this has been obtained for both Cl,CS and several alicyclic thiones [ 15,201. Although a one-photon transition from the ground state to the ‘A, no, R**excited state would be formally allowed, the oscillator strength of such a transition should be low because of the two electron promotion involved. The no, xs2 state would therefore meet the requirement that it be “dark”. However, such states, if present in these molecules, would also need to exhibit energies near those of the origins of their strong, K-+X*transitions. In H,CS, the energy of the no, x*2 state calculated at the ground state geometry lies z 1.2 eV higher than that of the x+x* origin, This could indicate that the no, Keystate is not the “dark” state involved. However, calculations on H2CS with full excited-state geometry optimization, or on mol-
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ecules other than HzCS, will be required to establish this point with certainty. Finally, we note that an excited state with an no, Key configuration was predicted for H&O some time ago by the theoretical studies of Buenker and Peyerimhoff [ 331 and Langhoff and Davidson [ 341. These authors quote vertical n2+x *2excitation energies of 12.79 and 11.33 eV, compared with L+ IC* vertical excitation energies of 12.13 and 10.62 eV respectively.
3. Conclusions Recent spectroscopic, photochemical and photophysical studies of C12CS[ 14- 161 and larger thiones [ 18,191 have provided circumstantial evidence that a “dark” state may be present in thiocarbonyl-containing compounds at an energy near that of the wellknown ’ (K, IC*) state. The present theoretical studies have identified a previously unknown doubly excited state of no, rt**configuration in the model compound, thioformaldehyde, H2CS. Its vertical excitation energy is close to that of the calculatedwrtical n~lc* transition energy, and it has the required symmetry ( ‘A, ). These facts suggest that calculations involving full excited-state geometry optimization would be worthwhile. Such calculations are underway.
Acknowledgement The authors wish to thank the Natural Sciences and Engineering Research Council of Canada for financial support.
References [ 1] R.P. Steer, Rev. Chem. Intermed. 4 ( 198I ) I. [2 ] D.J. Clouthier and D.A. Ramsay, Ann. Rev. Phys. Chem. 34 (1983) 31. [3] B. Simard, P.A. Hackett and R.P. Steer, J. Mol. Spectry. 126 ( 1987) 307. [4] B. Simard, R.P. Steer, R.H. Judge and DC. Moule, Can. J. Chem. 66 (1988) 359. [S]C.R. Drury and DC. Moule, J. Mol. Spectry. 92 (1982) 469.
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(61 W. Goetz, D.C. Mottle and D.A. Ramsay, Can. J. Phys. 59 (1981) 1635. [ 71 CR. Drury, J.Y.K. Lai and DC. Moule, Chem. Phys. Letters 87 (1982) 520. [S] P.G. Burton, SD. Peyerimhoff and R.J. Buenker, Chem. Phys. 73 (1982) 83. [ 91 SF. Karna and F. Grein, Mol. Phys. 57 ( I986 ) 939. [ IO] M. Kawasaki, K. Kasatani and H. Sato, Chem. Phys. 94 (1985) 179. [ I I ] B. Simard, A.E. Bruno, P.G. Mezey and R.P. Steer, Chem. Phys. 103 (1986) 75. 121S. Paone, DC. Mottle, A.E. Bruno and R.P. Steer, J. Mol. Spectry. 107 (1984) I. 131K.J. Falk and R.P. Steer, Can. J. Chem. 66 (1988) 575. 141R.J. Judge and DC. Moule, J. Mol. Spectry. 80 ( 1980) 363, and references therein. 151M. Ludwiczak, D. Latimer and R.P. Steer, J. Mol. Spectry., submitted for publication. [ 161R.N. Dixon and C.M. Western, J. Mol. Spectry. I I5 ( 1986) 74. [ 171 D.J. Clouthier, A.R. Knight, R.P. Steer and P.A. Hackett, J. Chem. Phys. 72 ( 1980) 1560. [ 181P. de Mayo, Accounts Chem. Res. 9 (1976) 52. [ 191KY. Law and P. de Mayo, 1. Am. Chem. Sot. IO1 (1979) 3251. [ 201 K.J. Falk and R.P. Steer, J. Am. Chem. Sot. I 11 ( 1989) 6518. (2 I ] R.J. Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33; 39 (1975) 217.
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[ 221 R.J. Buenker, SD. Peyerimhoff and W. Butacher, Mol. Phys. 35 (1978) 771. [ 231 R.J. Buenker and R.J. Phillips, J. Mol. Struct. THEOCHEM 123 (1985) 291. [ 24) R.J. Buenker, in: Proceedings of the Workshop on Molecular Physics and Quantum Chemistry into the 80’s, ed. P.B. Burton (University of Wollongong, Wollongong, I980 ): in: Studies in physical and theoretical chemistry, Vol. 2 I, ed. R. Carbo (Elsevier, Amsterdam, 1982). [25] M. Hachey and F. Grein, to be published. [ 261 A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [27] T.H. Dunning Jr., J. Chem. Phys. 55 (1971) 716. [28] B. Roes and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 199; S. Shih, SD. Peyerimhoff and R.J. Buenker, Chem. Phys. I7 (1976) 391. [29]T.H. Dunning Jr. and P.J. Hay, in: Modem theoretical chemistry, Vol. 3. Methods of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1976). [30] D.R. Johnson, F.X. Powell and W.H. Kirchhoff, J. Mol. Spectry. 39 ( 1971) 136. [ 311 P.H. Turner, L. Halonen and I.M. Mills, J. Mol. Spectry. 88 (1981) 402. [ 321 P.J. Bruna, SD. Peyerimhoff, R.J. Buenkerand P. Rosmus, Chem. Phys. 3 (1974) 35. [33] R.J. Buenker and S.D. Peyerimhoff, J. Chem. Phys. 53 (1970) 1368. [ 341 S.R. Langhoffand E.R. Davidson, J. Chem. Phys. 64 (1976) 4699.