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The structure of the thioformyl radical, HCS
\~olurne 102, number 2,3
18 November 1983
CHEMICAL PHYSICS LETTERS
THE STRUCTURE
OF THE THIOFORMYL RADICAL, HCS
Keceivcd 7 September
1963
Doubfe-zeta plus polarization (UZ f- P) SCF and Cl caicufations have been carried out to predict the equilibrium geometries of the lowest ‘A’ and ‘A” (*II) electronic states of the experimentally uncharacterized thioformyt radical, HCS. Pre= 1.556 A. r&H)= 1.066 A, B,(HCS) = 180”; dicted equiiibrhtm structures from the CI calculations are: *A” (*I’!): r&S) ‘A’: r,(G) = 12570 A,re(CH) = 1.086 A. e,(HCS) = 132.8”.
1. Introduction
2. Theoreticat
approach
The spectroscopy and photophysics of thioformaldehydc have been studied both experimentally [ 1] and theoretically (e.g. refs. [2-41) in recent years. In light of such activity. it is interesting that no reports of experiments on the thioformyf radical, HCS. have appeared (although its generation has been attempted [S]) dnd only d brief mention [6] of an ab initio study on this species has been published. The present letter reports double-zeta plus polarization (DZ + P) basis set SCF and CISD calculations for the equilibriunl geometries of the lowest ?A’ and zA” (‘Ii) electronic ;lates of the thioformyl radical. Comparable calculations were carried out on carbon monosulfide, CS, IO provide contact with experiment for a closely related moiectk The harmonic vibrational frequencies for HCS have been determined at the SCF level and then scded to predict experimentai frequencies in the manner of recent work on thioformaldehyde [4] _ The present results on the thioformyl radical should aid in its experimental detection and characterization either in the laboratory [S] or possibly in the interstellar medium [7] where such molecules as HCS* [ 1S] and HzCS 191 have been observed.
Calculations were performed using the MONSTERGAUSS * ab initio program system [IO]. A doublezeta plus polarization (DZ + P) gaussian basis set was used, namely S (I ls7p~d~6s4pld) [12], C (9s5pld/ 4s2pfd) [13] and H (4slp/2slp) (141. Six Cartesian d-polarization functions with exponents a(C) = 0.75 and a(S)= 0.55 were employed. The hydrogen p-function exponent was 1.00 and the hydrogen s functions were scaled by (l-2)2. All SCF calculations were carried out within the restricted Hartree-Fock formalism [ 14]_ Quadratic force constants were calculated in Cartesian coordinates by numerically differencing the analytic SCF forces and then analyzed to yield the harmonic vibrational frequencies. The direct CI calculations [ 151 on HCS froze 6 core orbitals (approximately the Cls and Sls2sZpX2pY2p= AO) and deleted the 6 highest-energy virtual orbitals (the core complements). Thus, there were 6 doubly and 1 singly active occupied and 25 active virtual molecular orbitals. All Hartree-Fock interacting [16] single and double excitations were generated relative to the appropriate SCF reference con~guration (CISD) and included in the CI expansions. C, symmetry was employed and thus there * This prosam incorporates the GAUSSIAN 80 [ 1 l] integral
* Address to which correspondence
224
should be sent.
and analytic energy gradient routines.
0 009-2614/83/0~0-~~/$03,00
0 1983 Noah-Homed
Volume 102, number 2,3 were 7479
2A’ or 7035 2A” configurations in the respective CI expansions for the two states. The values of Co, the weights of the SCF reference configurations
ported. The DZ + P SCF and CISD values for re in carbon monosulfide are both in good agreement with experiment. Similar small differences may be anticipated between-the calculated and experimental CS bond lengths in the thioformyl radical. The predicted equilibrium geometries and rotational constants for the 2A’, and 2A” (211) electronic states of HCS at both the SCF and CISD levels are reported in table 2. The qualitative effects of CISD on the bond lengths for both states are as usually observed with both the CS and CH distances increasing relative to their values. The HCS angle in the 2A’ state decreases by 2” upon including CI and a similar change has been calculated for the HCO angle in the formyl radical upon adding correlation [20] _ The 2A’ state of HCS is distinctly bent with an equilibrium bond angle of 132.8” and a barrier to relaxed linear inversion (i.e. the 211 - 2A’ CISD energy difference) of 9.5 kcal/mole or 3330 cm- 1 _With the use of Davidson’s formula [ 193 to approximately correct for quadruple excitations, this energy difference increase to 3490 cm-l. The CS distances of 1.570 A (2A’) and 1.556 A CA”) in the thioformyl radical are closer to the experimental CS triple bond distance in carbon monosulfide (1.535 A) [ 171 than the experimental CS double bond length of 1.611 A in thioformaldehyde [21]_ Thus, the CS bond order in the thioformyl radical is predicted to be greater than 2.5. If the CISD CS distances in HCS are reduced by 0.8% as would be necessary to bring the CISD CS distance in carbon monosulfide into agreement with experiment, then estimates of the experimental r,(CS) are 2A’ 1.557 A and 2A” (211) 1.544 A_ At the DZ + P SCF optimized geometry for the 2A’ ground state of HCS, vertical excitation energies up to the 2A” electronic state were determined at several
in the CI expansions, were 0.94501 2A’ and O-94652 2A’ at the optimum CISD geometries.
3. Results and discussion
3.1. Moleczdar sfructures and energies To connect
with experiment,
the DZ + P SCF and
ClSD bond lengths for ground-state carbon monosulfide were determined and are reported in table 1. The calculated re of 1.522 A at the SCF level is 0.016 A or
1.7% shorter than the experimental bond length [ 17]_ A nearly equivalent SCF calculation on CS but with a S d exponent of 0.60 rather than 0.55 as used in this work has recently been published [ 181 and predicts an re of 1.520 A with a total energy 3 X 10m4 hartree lower than the present result. The DZ + P CISD result for re in CS is 1.541 A and thus 0.006 A or 0.8% greater than experiment. For convenience, the values of the rotational constants, B,, in MHz are also reTable 1 Comparisons between theory and experiment for the ground state of carbon monosulfide
DZ+PSCF DZ + P CISD experiment a)
18 November 1983
CHEMICAL PHYSICS LETTERS
Total energy (hartree)
re (A)
Be (hlHz)
-435.30676 -436.65721
1.522 1.541 1.535
24999 24392 24584.35
a) Ref. [ 171.
Table 2 Predicted equilibrium geometries for the 2A’ and 2A” CD) electronic states of the thioformyl square brackets have been corrected for quadruple escitations using Davidson’s formula ] 191 Level of calculation state
DZ -t P SCF ‘A” CD) 2A’ DZ + P CISD ‘A” c2D>
radical, HCS. The CI energies in
Total energy (hartree)
re(CS) (A)
r&H)
Be(HCS)
Ae
(A)
(deg)
(MHz)
(MHz)
435.86330 -435.87812
1.546 1.559
1.061 1.080
180 134.8
1022900
19781 20347
19781 19951
436.11122
1.556
1.066
180
19527
19527
1.570
1.086
132.8
20155
19733
Be
Ce (MHz)
[ 436.13704] 2A’
436.12638 [ 436.15295
942310
]
225
CHIsSiiCAL
PwYs1cs
tiz-ERS
18
November 1983
Acknowiedgement The author had several discussions regarding the thioformyl radical with Drs. D-J. Clouthier and P.A. Feldman of the Merzberg Institute for Astrophysics_
References 111 D.J. Clouthier and D.A. Ramsay. Ann. Rev_ Phys. Chem.
sI .3 t c
11(.-S scaled
cYIlc_
scaled
156’4
3201
I Z6J SSJ
1131 764
2670 1114 662
1390 1087 593
3x1 i279 9?7
2990 iis 674
2371 1253 741
2212 11’1 663
i-:tk_
.-_.-
.._.---
___.__ ___
‘_;i” . i-2Ilf L’1 1.2 “3
z_q* u1 “2 “3 -_.__I_
DCS
(19831, to be published. f2f P-J_ Bruna. S-D. Peyerimhoff, R-J_ Buenker and P_ Rosmus. Chem. Phys. 3 (i974) 35; P.G. Burton. S.D. Peyerimhoff and R-J. Buenker. Chem. Phys. 73 (1982) 83. 131 J.D. Goddard. Can. J. Chem. 59 (1981) 3200. 14) J.D. Goddard and D-J. Clouthier. J. Chem. Phys. 76 (19S2) 5039. [S j D.J. Ciouthier, private conimunication_ 161 P.J. Bruna. R.J. Buenker and S-D. Peyerimhoff, unpublished results, quoted hy P.J. Bruna. in: Progress in thcorctical organic chemistry Vol. 2, ed. LG. Csizmadia (Elsevier. Amsterdam. 1977) p. 101. [ 71 P.A. Feldman, private communication. 18) I’. Thaddcus, M_ Guelin and R-A. Linke, Astrophys. J. 246 (19811 I-41. [ 91 M.\Y. Sinclair, N. Fourkin, J.C. R&es, B.J. Robinson, R.D. Brown and P.D. Godfrey. Australian J. Phys. 26 (1973) 85; L.11. Doherty, J-M. McLeod and T. Oka, Astrophys. J. 192 (1974) L157. IlO] M.R. Peterson and R.A. Poiricr. MONSTERGAUSS, Department of Chemistry, University of Toronto. Toronto, Ontario, Canada (1981). [ 11f J.S. BinkEey. R-A. Whiteside. R. Krishnan, R. Seeger, D.J. Del%ees. H.B. Schle~el, S. Topiol. L.R. Kahn and J-.4. Pople, GAUSSIAN 80. Department of Chemistry, Carne$e-Mellon University, Pittsburgh (1981). [ 12 j Y.H. Dunning and P-3. Hay, in: Modern theoretical chemistry. Vol. 3. ed. H.f--. Schaefer 111 (Plenum Press, New York: 1977) pp_ l-27. f 131 S. Huzinaga. J. Chem. Phys. 42 (196.5) 1293; T.H. Dunning. J. Chem. Phys. 53 (1970) 2823. I141 C.C.J. Roothaan, Rev. hfod. Phys. 32 (1960) 179. iisj N.C. Handy. J.D. Goddard and H-F. Schaefer III, J. Chem. Phys. 71 (1979) 426. 1161 A. Bunge. J. Chem. Phys. 53 (1970) 20. If71 K-P_ Huber and G. Herzberg, Constants of diitomic molecules (Van Nostrand, Princeton, 1979). flSl G.P. Raine, H.F. Schaefer HI and R.D. Haddon,J. Am. Chem. Sot. 105 (1983) 194. 1191 E.R. Davidson, in: The world of quantum chemistry, eds. R. Daudel and B. P&man (Reidel, Dordrecht, 1974). [201 T-H. Dunning, J- Chem- Phys. 73 (1980) 2304. 1211 P-H. Turner, L. Halonen and IM. Mis, J. Mol. Spectry.
88 (1981) 402.
18 November 1983
CHEMICAL PHYSICS LETTERS
THE STRUCTURE
OF THE THIOFORMYL RADICAL, HCS
Keceivcd 7 September
1963
Doubfe-zeta plus polarization (UZ f- P) SCF and Cl caicufations have been carried out to predict the equilibrium geometries of the lowest ‘A’ and ‘A” (*II) electronic states of the experimentally uncharacterized thioformyt radical, HCS. Pre= 1.556 A. r&H)= 1.066 A, B,(HCS) = 180”; dicted equiiibrhtm structures from the CI calculations are: *A” (*I’!): r&S) ‘A’: r,(G) = 12570 A,re(CH) = 1.086 A. e,(HCS) = 132.8”.
1. Introduction
2. Theoreticat
approach
The spectroscopy and photophysics of thioformaldehydc have been studied both experimentally [ 1] and theoretically (e.g. refs. [2-41) in recent years. In light of such activity. it is interesting that no reports of experiments on the thioformyf radical, HCS. have appeared (although its generation has been attempted [S]) dnd only d brief mention [6] of an ab initio study on this species has been published. The present letter reports double-zeta plus polarization (DZ + P) basis set SCF and CISD calculations for the equilibriunl geometries of the lowest ?A’ and zA” (‘Ii) electronic ;lates of the thioformyl radical. Comparable calculations were carried out on carbon monosulfide, CS, IO provide contact with experiment for a closely related moiectk The harmonic vibrational frequencies for HCS have been determined at the SCF level and then scded to predict experimentai frequencies in the manner of recent work on thioformaldehyde [4] _ The present results on the thioformyl radical should aid in its experimental detection and characterization either in the laboratory [S] or possibly in the interstellar medium [7] where such molecules as HCS* [ 1S] and HzCS 191 have been observed.
Calculations were performed using the MONSTERGAUSS * ab initio program system [IO]. A doublezeta plus polarization (DZ + P) gaussian basis set was used, namely S (I ls7p~d~6s4pld) [12], C (9s5pld/ 4s2pfd) [13] and H (4slp/2slp) (141. Six Cartesian d-polarization functions with exponents a(C) = 0.75 and a(S)= 0.55 were employed. The hydrogen p-function exponent was 1.00 and the hydrogen s functions were scaled by (l-2)2. All SCF calculations were carried out within the restricted Hartree-Fock formalism [ 14]_ Quadratic force constants were calculated in Cartesian coordinates by numerically differencing the analytic SCF forces and then analyzed to yield the harmonic vibrational frequencies. The direct CI calculations [ 151 on HCS froze 6 core orbitals (approximately the Cls and Sls2sZpX2pY2p= AO) and deleted the 6 highest-energy virtual orbitals (the core complements). Thus, there were 6 doubly and 1 singly active occupied and 25 active virtual molecular orbitals. All Hartree-Fock interacting [16] single and double excitations were generated relative to the appropriate SCF reference con~guration (CISD) and included in the CI expansions. C, symmetry was employed and thus there * This prosam incorporates the GAUSSIAN 80 [ 1 l] integral
* Address to which correspondence
224
should be sent.
and analytic energy gradient routines.
0 009-2614/83/0~0-~~/$03,00
0 1983 Noah-Homed
Volume 102, number 2,3 were 7479
2A’ or 7035 2A” configurations in the respective CI expansions for the two states. The values of Co, the weights of the SCF reference configurations
ported. The DZ + P SCF and CISD values for re in carbon monosulfide are both in good agreement with experiment. Similar small differences may be anticipated between-the calculated and experimental CS bond lengths in the thioformyl radical. The predicted equilibrium geometries and rotational constants for the 2A’, and 2A” (211) electronic states of HCS at both the SCF and CISD levels are reported in table 2. The qualitative effects of CISD on the bond lengths for both states are as usually observed with both the CS and CH distances increasing relative to their values. The HCS angle in the 2A’ state decreases by 2” upon including CI and a similar change has been calculated for the HCO angle in the formyl radical upon adding correlation [20] _ The 2A’ state of HCS is distinctly bent with an equilibrium bond angle of 132.8” and a barrier to relaxed linear inversion (i.e. the 211 - 2A’ CISD energy difference) of 9.5 kcal/mole or 3330 cm- 1 _With the use of Davidson’s formula [ 193 to approximately correct for quadruple excitations, this energy difference increase to 3490 cm-l. The CS distances of 1.570 A (2A’) and 1.556 A CA”) in the thioformyl radical are closer to the experimental CS triple bond distance in carbon monosulfide (1.535 A) [ 171 than the experimental CS double bond length of 1.611 A in thioformaldehyde [21]_ Thus, the CS bond order in the thioformyl radical is predicted to be greater than 2.5. If the CISD CS distances in HCS are reduced by 0.8% as would be necessary to bring the CISD CS distance in carbon monosulfide into agreement with experiment, then estimates of the experimental r,(CS) are 2A’ 1.557 A and 2A” (211) 1.544 A_ At the DZ + P SCF optimized geometry for the 2A’ ground state of HCS, vertical excitation energies up to the 2A” electronic state were determined at several
in the CI expansions, were 0.94501 2A’ and O-94652 2A’ at the optimum CISD geometries.
3. Results and discussion
3.1. Moleczdar sfructures and energies To connect
with experiment,
the DZ + P SCF and
ClSD bond lengths for ground-state carbon monosulfide were determined and are reported in table 1. The calculated re of 1.522 A at the SCF level is 0.016 A or
1.7% shorter than the experimental bond length [ 17]_ A nearly equivalent SCF calculation on CS but with a S d exponent of 0.60 rather than 0.55 as used in this work has recently been published [ 181 and predicts an re of 1.520 A with a total energy 3 X 10m4 hartree lower than the present result. The DZ + P CISD result for re in CS is 1.541 A and thus 0.006 A or 0.8% greater than experiment. For convenience, the values of the rotational constants, B,, in MHz are also reTable 1 Comparisons between theory and experiment for the ground state of carbon monosulfide
DZ+PSCF DZ + P CISD experiment a)
18 November 1983
CHEMICAL PHYSICS LETTERS
Total energy (hartree)
re (A)
Be (hlHz)
-435.30676 -436.65721
1.522 1.541 1.535
24999 24392 24584.35
a) Ref. [ 171.
Table 2 Predicted equilibrium geometries for the 2A’ and 2A” CD) electronic states of the thioformyl square brackets have been corrected for quadruple escitations using Davidson’s formula ] 191 Level of calculation state
DZ -t P SCF ‘A” CD) 2A’ DZ + P CISD ‘A” c2D>
radical, HCS. The CI energies in
Total energy (hartree)
re(CS) (A)
r&H)
Be(HCS)
Ae
(A)
(deg)
(MHz)
(MHz)
435.86330 -435.87812
1.546 1.559
1.061 1.080
180 134.8
1022900
19781 20347
19781 19951
436.11122
1.556
1.066
180
19527
19527
1.570
1.086
132.8
20155
19733
Be
Ce (MHz)
[ 436.13704] 2A’
436.12638 [ 436.15295
942310
]
225
CHIsSiiCAL
PwYs1cs
tiz-ERS
18
November 1983
Acknowiedgement The author had several discussions regarding the thioformyl radical with Drs. D-J. Clouthier and P.A. Feldman of the Merzberg Institute for Astrophysics_
References 111 D.J. Clouthier and D.A. Ramsay. Ann. Rev_ Phys. Chem.
sI .3 t c
11(.-S scaled
cYIlc_
scaled
156’4
3201
I Z6J SSJ
1131 764
2670 1114 662
1390 1087 593
3x1 i279 9?7
2990 iis 674
2371 1253 741
2212 11’1 663
i-:tk_
.-_.-
.._.---
___.__ ___
‘_;i” . i-2Ilf L’1 1.2 “3
z_q* u1 “2 “3 -_.__I_
DCS
(19831, to be published. f2f P-J_ Bruna. S-D. Peyerimhoff, R-J_ Buenker and P_ Rosmus. Chem. Phys. 3 (i974) 35; P.G. Burton. S.D. Peyerimhoff and R-J. Buenker. Chem. Phys. 73 (1982) 83. 131 J.D. Goddard. Can. J. Chem. 59 (1981) 3200. 14) J.D. Goddard and D-J. Clouthier. J. Chem. Phys. 76 (19S2) 5039. [S j D.J. Ciouthier, private conimunication_ 161 P.J. Bruna. R.J. Buenker and S-D. Peyerimhoff, unpublished results, quoted hy P.J. Bruna. in: Progress in thcorctical organic chemistry Vol. 2, ed. LG. Csizmadia (Elsevier. Amsterdam. 1977) p. 101. [ 71 P.A. Feldman, private communication. 18) I’. Thaddcus, M_ Guelin and R-A. Linke, Astrophys. J. 246 (19811 I-41. [ 91 M.\Y. Sinclair, N. Fourkin, J.C. R&es, B.J. Robinson, R.D. Brown and P.D. Godfrey. Australian J. Phys. 26 (1973) 85; L.11. Doherty, J-M. McLeod and T. Oka, Astrophys. J. 192 (1974) L157. IlO] M.R. Peterson and R.A. Poiricr. MONSTERGAUSS, Department of Chemistry, University of Toronto. Toronto, Ontario, Canada (1981). [ 11f J.S. BinkEey. R-A. Whiteside. R. Krishnan, R. Seeger, D.J. Del%ees. H.B. Schle~el, S. Topiol. L.R. Kahn and J-.4. Pople, GAUSSIAN 80. Department of Chemistry, Carne$e-Mellon University, Pittsburgh (1981). [ 12 j Y.H. Dunning and P-3. Hay, in: Modern theoretical chemistry. Vol. 3. ed. H.f--. Schaefer 111 (Plenum Press, New York: 1977) pp_ l-27. f 131 S. Huzinaga. J. Chem. Phys. 42 (196.5) 1293; T.H. Dunning. J. Chem. Phys. 53 (1970) 2823. I141 C.C.J. Roothaan, Rev. hfod. Phys. 32 (1960) 179. iisj N.C. Handy. J.D. Goddard and H-F. Schaefer III, J. Chem. Phys. 71 (1979) 426. 1161 A. Bunge. J. Chem. Phys. 53 (1970) 20. If71 K-P_ Huber and G. Herzberg, Constants of diitomic molecules (Van Nostrand, Princeton, 1979). flSl G.P. Raine, H.F. Schaefer HI and R.D. Haddon,J. Am. Chem. Sot. 105 (1983) 194. 1191 E.R. Davidson, in: The world of quantum chemistry, eds. R. Daudel and B. P&man (Reidel, Dordrecht, 1974). [201 T-H. Dunning, J- Chem- Phys. 73 (1980) 2304. 1211 P-H. Turner, L. Halonen and IM. Mis, J. Mol. Spectry.
88 (1981) 402.