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Theoretical study of the HCCS radical
Volume 81, number 3
CHEMICALPHYSICSLETTERS
1 August 1981
THEORETICAL STUDY OF THE HCCS RADICAL David L. COOPER Physical Chemistry Laboratory, Oxford University, Oxford OX1 3QZ, UK Received 29 April 1981
We report a preliminary ab initio study of the ground state of the HCCSradical. The results are discussed in relation to a tiansient absorption spectrum observed in the flash photolysis of thiophene.
1. Introduction
It has been suggested [1] that the carrier of the bands observed in the region 3770-4170 )k during the flash photolysis of ordinary and deuterated thiophene might be the HCCS free radical. The rotational analysis, and comparison with the isoelectronic species NCS, suggests either a r I - I I transition of a linear molecule or a AKa = 0 transition between linear and slightly non-linear states. In this Work, we present self-consistent-field (SCF) c~culations on the ground state of the HCCS radical. The spin-orbit coupling is also considered.
2. Computational details
SCF molecular orbital calculations were carried out for this radical using the ATMOL3 programs [2]. The minimal basis set, with Slater exponents taken from atomic values [3] (see table 1), consisted of Slater-type orbitals which have been expanded, according to the least-squares criterion, in three cartesian gaussians. The computations were repeated at a number of different geometries so as to obtain an estimate of the equilibrium structure parameters. It ought to be emphasised that these calculations used a rather small basis set and took no account of electron correlation effects; however, this type of method has been widely used for the study of geometries and its accuracy is well documented.
Table 1 Slater exponents for the gaussian-type orbital basis set
ls 2s 2p 3s 3p
H
C
S
1.24
5.70 1.625 1.625
15.50 5.325 5.325 2.125 2.125
The form of the spin-orbit coupling operator, and methods for calculating spin-orbit coupling integrals, have been discussed in detail elsewhere [4]. The one-electron contribution is particularly sensitive to the quality of the wavefunction in the region near the nucleus, where gaussian-type orbitals are suspect. The spin-orbit coupling calculations were performed at the geometry suggested by the minimal basis set studies, using the Slater-type orbital basis set [3] given in table 2. Restricted Hartree-Fock wavefunctions, in which Table 2 Exponents for the Slater-type orbital basis set H is
2s 2p 3s 3p 3d
C
1.24 7.52232,5.12306 1.83068,1.15282 2.73045,1.25656
0 009-2614/81/0000-0000/$ 02.50 © North-Holland Publishing Company
S
17.07720, 12.69440 6.72875, 5.24284 9.51251, 5.12050 2.66221, 1.68771 2.33793, 1.33331 0.5
479
Volume 81, number 3
CHEMICALPHYSICSLETTERS
the radial wavefunctions of two electrons differing only in spin are identical, lead to discrepancies between experimental and calculated spin-orbit coupling constants for molecules containing second-row atoms. This phenomenon, which is known as core polarisation, may be empirically treated using a correction taken from atomic values [5].
3. Results The calculations were started at the geometry suggested by Krishnamachari and Ramsay [1] and the ground-state configuration was found to be (1-5)a217r4(6-9)a227r43rr 3. Energies were computed for a range of linear geometries; attempts to decrease the H - C - C bond angle to 178 ° resulted in a poorer energy. The finally adopted bond lengths are r(C-H) = 1.089 A, r(C-C) = 1.215 A and r(C--S) = 1.715 A which lead to a value for the rotation constant B e = 0.1833 c m - t . The spin--orbit coupling constant for this state is ~ - 3 6 0 cm -1. The orbital energies for the configuration ...27r43¢r3 suggest that the first excited state will be ...27r33zr4. Since both these configurations lead to 21-[i states, and since the variation principle only applies to the lowest state of a given symmetry, it was decided not to attempt to perform calculations on the excited state. Using the wavefunction for the ground state, the spin-orbit coupling constant for the excited state was estimated to be of the order o f - 2 5 cm -1 but it must be stressed that this value is very approximate indeed.
4. Discussion In valence bond (VB) terms, the structure of the HCCS radical can be thought of as being intermediate between H-C=C=S and H-C=--C-S. A minimal basis set SCF study of the ground state of the HCCS radical suggests a linear ...27r431r3 configuration with rotation constant B e = 0.1833 cm-1 and spin-orbit
480
1 August 1981
coupling ~--360 cm-1; this fits better with the second of the VB structures above. It seems likely that the first excited state of HCCS arises from a configuration ...2zr33rr4 with a B e value close to that for the ground state and spinorbit coupling ~ - 2 5 cm-1; this fits better with the first of the VB structures above, so that a slight departure from linearity is reasonable. The theoretical results support the identification of the new transient species, produced during the flash photolysis of thiophene, as the HCCS radical. The calculated B value for the ground state is in good agreement with the experimental value B" --0.18841(6) cm -1 (5648 MHz). There is still much work to be done before the carrier of the transient spectrum can be unambiguously identified as HCCS. It is worth noting that the HCCS radical is a potential interstellar molecule and that its rotation constant is similar to that for other molecules already detected by radioastronomers.
Acknowledgement The author wishes to thank Dr. R.F. Barrow for his comments on this manuscript. The computational work was supported by the Science Research
Council (UK). References [ 1] S.L.N.G. Krishnamachari and D.A. Ramsay, Discussions Faraday Soc. (1981), to be published. [21 M.F. Guest and V.R. Saunders, ATMOL3User Manuals, Rutherford Laboratory, Science Research Council (1976). [3] E. Clementi and C. Roetfi, At. Data Nucl. Data Tables 14 (1974) 177. [4] W.G. Richards, H.P. Trivedi and D.L. Cooper, Spin-orbit coupling in molecules (Oxford Univ. Press, London, 1981). [5] H. Lef~bvie-Bfion,J. Wajsbaum and N. Bessis, La structure hyperf'medes atomes et des molecules (Centre National de la Recherche Scientifique, Paris, 1967).
CHEMICALPHYSICSLETTERS
1 August 1981
THEORETICAL STUDY OF THE HCCS RADICAL David L. COOPER Physical Chemistry Laboratory, Oxford University, Oxford OX1 3QZ, UK Received 29 April 1981
We report a preliminary ab initio study of the ground state of the HCCSradical. The results are discussed in relation to a tiansient absorption spectrum observed in the flash photolysis of thiophene.
1. Introduction
It has been suggested [1] that the carrier of the bands observed in the region 3770-4170 )k during the flash photolysis of ordinary and deuterated thiophene might be the HCCS free radical. The rotational analysis, and comparison with the isoelectronic species NCS, suggests either a r I - I I transition of a linear molecule or a AKa = 0 transition between linear and slightly non-linear states. In this Work, we present self-consistent-field (SCF) c~culations on the ground state of the HCCS radical. The spin-orbit coupling is also considered.
2. Computational details
SCF molecular orbital calculations were carried out for this radical using the ATMOL3 programs [2]. The minimal basis set, with Slater exponents taken from atomic values [3] (see table 1), consisted of Slater-type orbitals which have been expanded, according to the least-squares criterion, in three cartesian gaussians. The computations were repeated at a number of different geometries so as to obtain an estimate of the equilibrium structure parameters. It ought to be emphasised that these calculations used a rather small basis set and took no account of electron correlation effects; however, this type of method has been widely used for the study of geometries and its accuracy is well documented.
Table 1 Slater exponents for the gaussian-type orbital basis set
ls 2s 2p 3s 3p
H
C
S
1.24
5.70 1.625 1.625
15.50 5.325 5.325 2.125 2.125
The form of the spin-orbit coupling operator, and methods for calculating spin-orbit coupling integrals, have been discussed in detail elsewhere [4]. The one-electron contribution is particularly sensitive to the quality of the wavefunction in the region near the nucleus, where gaussian-type orbitals are suspect. The spin-orbit coupling calculations were performed at the geometry suggested by the minimal basis set studies, using the Slater-type orbital basis set [3] given in table 2. Restricted Hartree-Fock wavefunctions, in which Table 2 Exponents for the Slater-type orbital basis set H is
2s 2p 3s 3p 3d
C
1.24 7.52232,5.12306 1.83068,1.15282 2.73045,1.25656
0 009-2614/81/0000-0000/$ 02.50 © North-Holland Publishing Company
S
17.07720, 12.69440 6.72875, 5.24284 9.51251, 5.12050 2.66221, 1.68771 2.33793, 1.33331 0.5
479
Volume 81, number 3
CHEMICALPHYSICSLETTERS
the radial wavefunctions of two electrons differing only in spin are identical, lead to discrepancies between experimental and calculated spin-orbit coupling constants for molecules containing second-row atoms. This phenomenon, which is known as core polarisation, may be empirically treated using a correction taken from atomic values [5].
3. Results The calculations were started at the geometry suggested by Krishnamachari and Ramsay [1] and the ground-state configuration was found to be (1-5)a217r4(6-9)a227r43rr 3. Energies were computed for a range of linear geometries; attempts to decrease the H - C - C bond angle to 178 ° resulted in a poorer energy. The finally adopted bond lengths are r(C-H) = 1.089 A, r(C-C) = 1.215 A and r(C--S) = 1.715 A which lead to a value for the rotation constant B e = 0.1833 c m - t . The spin--orbit coupling constant for this state is ~ - 3 6 0 cm -1. The orbital energies for the configuration ...27r43¢r3 suggest that the first excited state will be ...27r33zr4. Since both these configurations lead to 21-[i states, and since the variation principle only applies to the lowest state of a given symmetry, it was decided not to attempt to perform calculations on the excited state. Using the wavefunction for the ground state, the spin-orbit coupling constant for the excited state was estimated to be of the order o f - 2 5 cm -1 but it must be stressed that this value is very approximate indeed.
4. Discussion In valence bond (VB) terms, the structure of the HCCS radical can be thought of as being intermediate between H-C=C=S and H-C=--C-S. A minimal basis set SCF study of the ground state of the HCCS radical suggests a linear ...27r431r3 configuration with rotation constant B e = 0.1833 cm-1 and spin-orbit
480
1 August 1981
coupling ~--360 cm-1; this fits better with the second of the VB structures above. It seems likely that the first excited state of HCCS arises from a configuration ...2zr33rr4 with a B e value close to that for the ground state and spinorbit coupling ~ - 2 5 cm-1; this fits better with the first of the VB structures above, so that a slight departure from linearity is reasonable. The theoretical results support the identification of the new transient species, produced during the flash photolysis of thiophene, as the HCCS radical. The calculated B value for the ground state is in good agreement with the experimental value B" --0.18841(6) cm -1 (5648 MHz). There is still much work to be done before the carrier of the transient spectrum can be unambiguously identified as HCCS. It is worth noting that the HCCS radical is a potential interstellar molecule and that its rotation constant is similar to that for other molecules already detected by radioastronomers.
Acknowledgement The author wishes to thank Dr. R.F. Barrow for his comments on this manuscript. The computational work was supported by the Science Research
Council (UK). References [ 1] S.L.N.G. Krishnamachari and D.A. Ramsay, Discussions Faraday Soc. (1981), to be published. [21 M.F. Guest and V.R. Saunders, ATMOL3User Manuals, Rutherford Laboratory, Science Research Council (1976). [3] E. Clementi and C. Roetfi, At. Data Nucl. Data Tables 14 (1974) 177. [4] W.G. Richards, H.P. Trivedi and D.L. Cooper, Spin-orbit coupling in molecules (Oxford Univ. Press, London, 1981). [5] H. Lef~bvie-Bfion,J. Wajsbaum and N. Bessis, La structure hyperf'medes atomes et des molecules (Centre National de la Recherche Scientifique, Paris, 1967).