- Email: [email protected]
Ab initio study of low-lying electronic states of the SiCO radical
Volume 19l, number 6
CHEMICALPHYSICSLETTERS
17 April 1992
Ab initio study of low-lying electronic states of the SiCO radical Z.-L. Cai, Y.-F. W a n g a n d H.-M. X i a o Department of Chemistry, East China Institute of Technology, Nanfing 210014, People'sRepublic of China Received 15 January 1992
The equilibrium geometries,excitation energies, force constants and vibrational frequencies for the low-lyingelectronic states X 3~-~-,a IA, A 3H and 1 tFl of the SiCO radical have been calculated at the MRSDCI level with a double-zeta plus polarization basis set. Our calculatedexcitation energyfor A 3H ~ X 3E- and vibrational frequenciesfor these two states are in good agreement with experiment. Electronictransition properties for the A aH-.X 3g- transition, and the spin properties for the X 3g- state are calculated based on the MRSDCI wavefunctions,predicting results in reasonableagreementwith availableexperimentaldata.
1. Introduction
The SiCO radical was easily generated by reaction of Si atoms with CO in laboratory conditions. In recent years, there has been an increasing interest in understanding the chemistry of SiCO since it may exist in the interstellar medium and little was known for its geometry and spectroscopy properties. In 1977, Lembke et al. [ 1 ] first reported its electron spin resonance and optical spectra at 4 K, they observed optical transitions with vibrational progressions beginning at 4156 A for the SiCO radical, some IR spectra were obtained and stretching force constants were calculated for the ground state of SiCO. They studied the ESR spectrum of SiCO, and measured some hyperfine coupling data of the 13C and 29Si atoms. In 1987, van Zee et al. [2] also studied the ESR spectrum of the SiCO radical, and obtained the hyperfine splitting constant of the ~70 atom. In the literature, there are no reported experimental data for the geometries of the ground and excited states of the SiCO radical. However, there are some theoretical studies of the ground state X 3~- of SiCO [1,3]. In 1977, Lembke et al. [1] calculated the equilibrium geometry of the X 3y~- state using CNDO method. In 1988, DeKock et al. [ 3 ] calculated the equilibrium geometry of the X 3y.- state of SiCO at the HF, CASSCF and CISD levels with the D Z + P and T Z + 2P basis sets, the optimized values for the
bond lengths vary from 1.835 to 1.886/~ for R ( S i C) and 1.115 to 1.157 A for R ( C - O ) . We have studied four low-lying electronic states of the SiCO radical, X 3Z-, a 1A, A 3H and 1 q-I, by means of multireference single and double excitation configuration interaction calculations (MRSDCI) with a DZ + P basis set. In this paper, we report the optimized equilibrium geometries, calculated excitation energies, force constants, vibrational frequencies for these electronic states, we will also report electronic transition properties for the A 3H--,X 3Ztransition and the hyperfine coupling constants for the ground state X 3E-. These calculated results will be compared with available experimental data.
2. Calculations
The basis set used in our calculations consists of the (9s, 5p) Cartesian Gaussian function for C and O in the [4s, 2p] contraction, (1 ls, 7p) Cartesian Gaussian function for Si in the [6s, 4p l, given by Dunning [4,5 ], augmented by uncontracted d functions with exponent 0.75 for carbon, 0.80 for nitrogen and 0.5 for silicon [6 ], yielding a total of 56 contracted basis functions. The MRSDCI calculations were performed using the program package MELDF [7] on a VAX 8350 computer. Before CI, the SCF ( R O H F ) virtual orbitals were
000%2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
533
Volume 191, number 6
CHEMICALPHYSICSLETTERS
transformed into K orbitals [8], which have been shown to mimic frozen natural orbitals of the system, thus improving the convergence of CI. In the MRSDCI calculations, al! the single excitations from the (multi-)reference configurations were included, as well as the most important double excitations, as selected by second-order perturbation theory [9] with a selection threshold T = 15.8 Ixhartree. The reference space in our MRSDCI calculations for the selected states consisted of 5-8 configurations, generated from 5-6 selected space-orbital products. The sum of the square of coefficients in multi-reference space in our MRSDCI wavefunctions at the corresponding optimized geometries for four low-lying electronic states is no less than 0.90. The total numbers of configurations included in the MRSDCI calculations are ~ 18000 for the X 3)--, and A 31-1states, 10000 for the a ~A and 1 1FI states. In our MRSDCI calculations, the energy values are denoted by E and E(full-CI) corresponding to the MRSD-CI energy at the configuration selection threshold T and energy estimated for the entire basis (full-CI) according to the Davidson formula [ 7 ]. In our study, we assume that the SiCO molecule has a linear geometry in each of the four electronic states. Therefore, only two bond lengths, R ( S i - C ) and R ( C - O ) , were considered in searching the optimized geometries by a simple fitting procedure. The force constants and vibrational frequencies were obtained by using finite difference methods. All calculations were carried out in the C2v subgroup of C~v, whereby Z + corresponds to the A~ irreducible representation, Z - to A2, FI to Bt +B2, and A to A~ +A2. -
3. Results and discussion 3.1. T h e X s X - a n d a IA states
The ground molecular orbital configuration of the linear molecule SiCO, 1~22023t~24a25a 21 n46t~27c28a22n49~237t2 results in three very low-lying electronic states 3•-, IA and lZ+. The ground state 3Z- (X 3Z- ) was already theoretically investigated [ 1,3 ], but the prediction of the equilibrium geometry and description of the bond 534
17 April 1992
nature of this state seemed rather difficult. In 1988, DeKock et al. [ 3 ] reported a careful ab initio study for this state, based on their HF, CISD and CASSCF calculations, and the values for each of the two bond lengths optimized at these levels were all significantly different (no experimental geometric parameters available). Our optimized geometric parameters for the X 3Z- state are shown in table 1, together with the HF, CISD and CASSCF results copied from ref. [ 3 ]. These four sets of parameters were obtained using the same basis set (DZ + P ). As shown in table 1, our MRSDCI value for the Si-C bond length is the same as the CISD value, and the C - O bond is only 0.01 A bigger than the previous CISD value [ 3 ]. Our calculated geometric parameters at the MRSDCI level are close to previous CISD values. From table 1, we can see there is large discrepancy between our calculated geometric parameters and CASSCF values of ref. [ 3 ]. The CI energy value at our optimized geometry is -401.99399 au, which is ~, 0.0590 au lower than the previous CISD energy value [ 3 ], at the corresponding optimized geometry listed in table I. We believe that our optimized geometry is more accurate than previous CISD results although there are no experimental data to compare with. MRSDCI calculations treat electron correlation effects better than CISD ones, and there is inclusion of ~ 80% more configurations in our MRSDCI expansions than the previous CISD ones, effective K orbital technique incorporated in our calculations using the program package MELDF. The calculated force constants and vibrational frequencies for the X 3y- state are shown in table 2. Considering the calculation error of ~ 200 c m - ~, the calculated vibrational frequencies for the X 3Z- state are in agreement with experimental data. The spin properties of the triplet state X 3Z- of the SiCO radical have been calculated based on the MRSDCI wavefunction at the optimized geometry using the same program package MELDF. The calculated isotropic (a) and anisotropic (A) hyperfine coupling constants for the three atoms (assuming Si=29Si, C--13C, O = 170) are given in table 3. The calculated A± values are in reasonable agreement with the experimental values [ 1,2 ]. For the other coupling constants, there are no available experimental data. In the MRSDCI calculations, the a 'A state was
Volume 191, number 6
CHEMICAL PHYSICS LETTERS
17 April 1992
Table 1 Optimized geometric parameters (in A ) and excitation energies (in eV) for the four electronic states of the SiCO radical State
R (Si-C)
R(C-O)
R(Si-C) +R(C-O)
Te
X3Z HF a) CISD a) CASSCF ,1 a~A A 3H
1.835 1.876 1.835 1.886 1.828 1.704
1.167 1.127 1.157 1.145 1.170 1.179
3.002 3.003 2.992 3.031 2.988 2.883
0.0
l lH
1.664
1.192
2.856
0.676 (0.670)b) 3.215 (3.114) b) exp. 2.983 c) 4.896 (4.507)b)
a) Ref. [3 ]. b) Valuesin parentheses were evaluated from the estimated full-CI energies. ¢) Ref. [ 1]. Table 2 Calculated force constants (in mdyn//~) and vibrational frequencies (in cm -~ ) for the X 357- and A 31-1states of the SiCO radical
ksic kco ksic.co vl v3
X 3Z-
A 3H
3.79154 17.84063 0.30948 873 exp. 800 a) 2105 exp. 1899 a)
2.58458 17.54143 0.72985 721 exp. 750(10) a) 2086 exp. 1857(10) a)
a) Ref. [1]. Table 3 Calculated isotropic (a) and anisotropic (A) coupling constants (in MHz) for the atoms (Si = 295i, C = 13C, O = 17O ) in the X 3Z-. state of the SiCO radical
a All Al
si
c
0
9.0 75.4 80.1 exp. 86.9 a)
27.9 34.8 35.6 exp. 14 a)
9.6 8.4 26.3 exp. 29.4 b)
almost unchanged. The calculated excitation energies for X 3Z---,a IA is 0.676 eV. We failed to reach the b ~Z+ state in our M R S D C I calculations. It had been treated as the lowest single state of the A~ irreducible representation, b u t we obtained the same optimized geometry and energy value as the a 1A state, which indicates that we had reached the other component of the degenerate state a ~A. This failure implies that the energy level of the b ~Z+ state must be higher than that of the a ~A state. Based on this inference and our energy results for the X 3Zand a ~A states, we can write the energy ordering for the three electronic states emerging from the ground molecular orbital configuration as 3Z- < IA < IZ+ , which is in agreement with some rules for diatomic molecules [ 10].
3.2. The A 317 and 1 111 states The molecular orbital configuration of the SiCO radical,
")Ref.[1]. b) Ref.[2].
1o 2 2 c 2 3o 2 4o 2 50 2 I n 4 60 2 70 2 80 2 2~ 4 90 1 3n 3 ,
treated as the lowest single state of the A2 irreducible representation of the C2v group, whereby the abovedescribed X 3 y - state was treated as the lowest triplet state of the same irreducible representation. The optimized b o n d lengths for the a ~A state are shown in table 1. Compared to the optimized b o n d lengths for the ground state, the S i - C b o n d is slightly shortened a n d the C - O b o n d is slightly lengthened, leaving the length of the molecule (R ( S i - C ) + R ( C - O ) )
results in the electronic states A 31-1a n d 1 q-1. In the MRSDCI calculations, the A 3I-I state was treated as the lowest triplet state of the B~ irreducible representation. The optimized b o n d lengths are shown in table 1. Compared with the optimized b o n d lengths for the ground state, the Si-C b o n d is shortened, the C - O b o n d is lengthened, a n d the length of the molecule in the A 31-I state is shorter than that in the ground state. Our predicted excitation energy for X 3y-__,A 31-I 535
Volume 19 l, number 6
CHEMICAL PHYSICS LETTERS
Table 4 Calculated values of the properties dependent upon the electronic transition dipole moment for the A 3H-X 3y.- band system Transition dipole moment Y[Rel 2 (au)
Oscillator strength f~ (au)
Radiative lifetime T (laS)
0.16906
0.00514
2.92
as the difference o f the CI energies at the corresponding o p t i m i z e d geometries o f the two states is 3.215 eV, which is in good agreement with the experimental transition energy values o f 2.983 eV [ 1 ]. We obtain an even better value (3.114 eV) for the excitation energy when we calculate it using the est i m a t e d full-CI energy values given in the output by the program package M E L D F . F o r the transition A31-I--,X 3E-, we calculated transition properties based on the CI wavefunctions, using the same p r o g r a m package. The calculated values for the square o f the electronic transition dipole m o m e n t , the oscillator strength for the absorption (taking AE = 3.215 eV ), a n d the radiative lifetime for the A 3H states are given in table 4. There are no experimental d a t a to c o m p a r e with. The force constants and vibrational frequencies for the A 3II state have also been calculated, these calculated values are shown in table 2. The calculated vibrational frequencies for this state are in agreement with experiment. The 1 trI state was treated in the M R S D C I calculations as the lowest singlet state o f the B~ irreducible representation. The o p t i m i z e d b o n d lengths are given in table 1. C o m p a r e d with the o p t i m i z e d geometry for the ground state, the S i - C b o n d is shortened and the C - O b o n d is lengthened. The calculated excitation energy for X 3y,---, 1 lI-I is 4.896 eV. It is noted that the o p t i m i z e d geometries for the A 3H a n d l ~rI state are considerably different, and the energy difference between these two states is ~ 1.7 eV.
4. Conclusion The equilibrium geometries, excitation energies,
536
17 April 1992
force constants a n d vibrational frequencies for four electronic states, X 3E-, a 1A, A 3H and 1 qq, o f the SiCO radical have been studied at the M R S D C I level with a D Z + P basis set. The o p t i m a l geometries and excitation energies for these four states are presented in table I, force constants a n d vibrational frequencies for the X 3E- a n d A 3H states are presented in table 2. F o r the S i - C b o n d length, the o p t i m i z e d values in the a ~A, A 31"1and 1 1I-I states are shorter than that in the X 3E- state. F o r the C - O b o n d length, the o p t i m i z e d values in the a IA, A 3H a n d 1 IH states are bigger than that in the X 3E- state. The M R S D C I calculations indicate the following energy ordering for these four states: X3E-
t A < A 3 H < 1 lI-[.
The energy level o f the b rE+ state, which emerges from the same molecular orbital configuration as the X 3E- and a ~A states, is inferred to be higher than that o f the a ~A state. The predicted excitation energies for X 3E- - , A 3rI are in good agreement with experiment, the calculated vibrational frequencies o f the X 3y,- and A 31-I states a n d spin properties o f the X 3E- state are in reasonable agreement with available experimental data.
References [ 1] R.R. Lembke, R.F. Ferrante and W. Weltner Jr., J. Am. Chem. Soc. 99 (1977) 416. [ 2 ] R.J. van Zee, R.F. Ferrante and W. Weltner Jr., Chem. Phys. Letters 139 (1987) 426. [3] R.L. DeKock, R.G. Grev and H.F. Schaefer III, J. Chem. Phys. 89 (1988) 3016. [4 ] T.H. Dunning Jr., J. Chem. Phys. 53 ( 1970 ) 2823. [5] T.H. Dunning Jr. and P.J. Hay, in: Modern theoretical chemistry, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 1. [6] T.H. Dunning Jr., J. Chem. Phys. 55 ( 1971 ) 3958. [7]E.R. Davidson et al., MELDF, QECP580, Indiana University, Bloomington, Indiana, USA ( 1988 ). [8] D. Feller and E.R. Davidson, J. Chem. Phys. 74 (1981) 3977. [9] K. Tanaka and E.R. Davidson, J. Chem. Phys. 70 (1979) 2904. [ 10 ] G. Herzberg, Molecular spectra and molecular structure, Vol. 1 (Van Nostrand, Princeton, 1950 ).
CHEMICALPHYSICSLETTERS
17 April 1992
Ab initio study of low-lying electronic states of the SiCO radical Z.-L. Cai, Y.-F. W a n g a n d H.-M. X i a o Department of Chemistry, East China Institute of Technology, Nanfing 210014, People'sRepublic of China Received 15 January 1992
The equilibrium geometries,excitation energies, force constants and vibrational frequencies for the low-lyingelectronic states X 3~-~-,a IA, A 3H and 1 tFl of the SiCO radical have been calculated at the MRSDCI level with a double-zeta plus polarization basis set. Our calculatedexcitation energyfor A 3H ~ X 3E- and vibrational frequenciesfor these two states are in good agreement with experiment. Electronictransition properties for the A aH-.X 3g- transition, and the spin properties for the X 3g- state are calculated based on the MRSDCI wavefunctions,predicting results in reasonableagreementwith availableexperimentaldata.
1. Introduction
The SiCO radical was easily generated by reaction of Si atoms with CO in laboratory conditions. In recent years, there has been an increasing interest in understanding the chemistry of SiCO since it may exist in the interstellar medium and little was known for its geometry and spectroscopy properties. In 1977, Lembke et al. [ 1 ] first reported its electron spin resonance and optical spectra at 4 K, they observed optical transitions with vibrational progressions beginning at 4156 A for the SiCO radical, some IR spectra were obtained and stretching force constants were calculated for the ground state of SiCO. They studied the ESR spectrum of SiCO, and measured some hyperfine coupling data of the 13C and 29Si atoms. In 1987, van Zee et al. [2] also studied the ESR spectrum of the SiCO radical, and obtained the hyperfine splitting constant of the ~70 atom. In the literature, there are no reported experimental data for the geometries of the ground and excited states of the SiCO radical. However, there are some theoretical studies of the ground state X 3~- of SiCO [1,3]. In 1977, Lembke et al. [1] calculated the equilibrium geometry of the X 3y~- state using CNDO method. In 1988, DeKock et al. [ 3 ] calculated the equilibrium geometry of the X 3y.- state of SiCO at the HF, CASSCF and CISD levels with the D Z + P and T Z + 2P basis sets, the optimized values for the
bond lengths vary from 1.835 to 1.886/~ for R ( S i C) and 1.115 to 1.157 A for R ( C - O ) . We have studied four low-lying electronic states of the SiCO radical, X 3Z-, a 1A, A 3H and 1 q-I, by means of multireference single and double excitation configuration interaction calculations (MRSDCI) with a DZ + P basis set. In this paper, we report the optimized equilibrium geometries, calculated excitation energies, force constants, vibrational frequencies for these electronic states, we will also report electronic transition properties for the A 3H--,X 3Ztransition and the hyperfine coupling constants for the ground state X 3E-. These calculated results will be compared with available experimental data.
2. Calculations
The basis set used in our calculations consists of the (9s, 5p) Cartesian Gaussian function for C and O in the [4s, 2p] contraction, (1 ls, 7p) Cartesian Gaussian function for Si in the [6s, 4p l, given by Dunning [4,5 ], augmented by uncontracted d functions with exponent 0.75 for carbon, 0.80 for nitrogen and 0.5 for silicon [6 ], yielding a total of 56 contracted basis functions. The MRSDCI calculations were performed using the program package MELDF [7] on a VAX 8350 computer. Before CI, the SCF ( R O H F ) virtual orbitals were
000%2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
533
Volume 191, number 6
CHEMICALPHYSICSLETTERS
transformed into K orbitals [8], which have been shown to mimic frozen natural orbitals of the system, thus improving the convergence of CI. In the MRSDCI calculations, al! the single excitations from the (multi-)reference configurations were included, as well as the most important double excitations, as selected by second-order perturbation theory [9] with a selection threshold T = 15.8 Ixhartree. The reference space in our MRSDCI calculations for the selected states consisted of 5-8 configurations, generated from 5-6 selected space-orbital products. The sum of the square of coefficients in multi-reference space in our MRSDCI wavefunctions at the corresponding optimized geometries for four low-lying electronic states is no less than 0.90. The total numbers of configurations included in the MRSDCI calculations are ~ 18000 for the X 3)--, and A 31-1states, 10000 for the a ~A and 1 1FI states. In our MRSDCI calculations, the energy values are denoted by E and E(full-CI) corresponding to the MRSD-CI energy at the configuration selection threshold T and energy estimated for the entire basis (full-CI) according to the Davidson formula [ 7 ]. In our study, we assume that the SiCO molecule has a linear geometry in each of the four electronic states. Therefore, only two bond lengths, R ( S i - C ) and R ( C - O ) , were considered in searching the optimized geometries by a simple fitting procedure. The force constants and vibrational frequencies were obtained by using finite difference methods. All calculations were carried out in the C2v subgroup of C~v, whereby Z + corresponds to the A~ irreducible representation, Z - to A2, FI to Bt +B2, and A to A~ +A2. -
3. Results and discussion 3.1. T h e X s X - a n d a IA states
The ground molecular orbital configuration of the linear molecule SiCO, 1~22023t~24a25a 21 n46t~27c28a22n49~237t2 results in three very low-lying electronic states 3•-, IA and lZ+. The ground state 3Z- (X 3Z- ) was already theoretically investigated [ 1,3 ], but the prediction of the equilibrium geometry and description of the bond 534
17 April 1992
nature of this state seemed rather difficult. In 1988, DeKock et al. [ 3 ] reported a careful ab initio study for this state, based on their HF, CISD and CASSCF calculations, and the values for each of the two bond lengths optimized at these levels were all significantly different (no experimental geometric parameters available). Our optimized geometric parameters for the X 3Z- state are shown in table 1, together with the HF, CISD and CASSCF results copied from ref. [ 3 ]. These four sets of parameters were obtained using the same basis set (DZ + P ). As shown in table 1, our MRSDCI value for the Si-C bond length is the same as the CISD value, and the C - O bond is only 0.01 A bigger than the previous CISD value [ 3 ]. Our calculated geometric parameters at the MRSDCI level are close to previous CISD values. From table 1, we can see there is large discrepancy between our calculated geometric parameters and CASSCF values of ref. [ 3 ]. The CI energy value at our optimized geometry is -401.99399 au, which is ~, 0.0590 au lower than the previous CISD energy value [ 3 ], at the corresponding optimized geometry listed in table I. We believe that our optimized geometry is more accurate than previous CISD results although there are no experimental data to compare with. MRSDCI calculations treat electron correlation effects better than CISD ones, and there is inclusion of ~ 80% more configurations in our MRSDCI expansions than the previous CISD ones, effective K orbital technique incorporated in our calculations using the program package MELDF. The calculated force constants and vibrational frequencies for the X 3y- state are shown in table 2. Considering the calculation error of ~ 200 c m - ~, the calculated vibrational frequencies for the X 3Z- state are in agreement with experimental data. The spin properties of the triplet state X 3Z- of the SiCO radical have been calculated based on the MRSDCI wavefunction at the optimized geometry using the same program package MELDF. The calculated isotropic (a) and anisotropic (A) hyperfine coupling constants for the three atoms (assuming Si=29Si, C--13C, O = 170) are given in table 3. The calculated A± values are in reasonable agreement with the experimental values [ 1,2 ]. For the other coupling constants, there are no available experimental data. In the MRSDCI calculations, the a 'A state was
Volume 191, number 6
CHEMICAL PHYSICS LETTERS
17 April 1992
Table 1 Optimized geometric parameters (in A ) and excitation energies (in eV) for the four electronic states of the SiCO radical State
R (Si-C)
R(C-O)
R(Si-C) +R(C-O)
Te
X3Z HF a) CISD a) CASSCF ,1 a~A A 3H
1.835 1.876 1.835 1.886 1.828 1.704
1.167 1.127 1.157 1.145 1.170 1.179
3.002 3.003 2.992 3.031 2.988 2.883
0.0
l lH
1.664
1.192
2.856
0.676 (0.670)b) 3.215 (3.114) b) exp. 2.983 c) 4.896 (4.507)b)
a) Ref. [3 ]. b) Valuesin parentheses were evaluated from the estimated full-CI energies. ¢) Ref. [ 1]. Table 2 Calculated force constants (in mdyn//~) and vibrational frequencies (in cm -~ ) for the X 357- and A 31-1states of the SiCO radical
ksic kco ksic.co vl v3
X 3Z-
A 3H
3.79154 17.84063 0.30948 873 exp. 800 a) 2105 exp. 1899 a)
2.58458 17.54143 0.72985 721 exp. 750(10) a) 2086 exp. 1857(10) a)
a) Ref. [1]. Table 3 Calculated isotropic (a) and anisotropic (A) coupling constants (in MHz) for the atoms (Si = 295i, C = 13C, O = 17O ) in the X 3Z-. state of the SiCO radical
a All Al
si
c
0
9.0 75.4 80.1 exp. 86.9 a)
27.9 34.8 35.6 exp. 14 a)
9.6 8.4 26.3 exp. 29.4 b)
almost unchanged. The calculated excitation energies for X 3Z---,a IA is 0.676 eV. We failed to reach the b ~Z+ state in our M R S D C I calculations. It had been treated as the lowest single state of the A~ irreducible representation, b u t we obtained the same optimized geometry and energy value as the a 1A state, which indicates that we had reached the other component of the degenerate state a ~A. This failure implies that the energy level of the b ~Z+ state must be higher than that of the a ~A state. Based on this inference and our energy results for the X 3Zand a ~A states, we can write the energy ordering for the three electronic states emerging from the ground molecular orbital configuration as 3Z- < IA < IZ+ , which is in agreement with some rules for diatomic molecules [ 10].
3.2. The A 317 and 1 111 states The molecular orbital configuration of the SiCO radical,
")Ref.[1]. b) Ref.[2].
1o 2 2 c 2 3o 2 4o 2 50 2 I n 4 60 2 70 2 80 2 2~ 4 90 1 3n 3 ,
treated as the lowest single state of the A2 irreducible representation of the C2v group, whereby the abovedescribed X 3 y - state was treated as the lowest triplet state of the same irreducible representation. The optimized b o n d lengths for the a ~A state are shown in table 1. Compared to the optimized b o n d lengths for the ground state, the S i - C b o n d is slightly shortened a n d the C - O b o n d is slightly lengthened, leaving the length of the molecule (R ( S i - C ) + R ( C - O ) )
results in the electronic states A 31-1a n d 1 q-1. In the MRSDCI calculations, the A 3I-I state was treated as the lowest triplet state of the B~ irreducible representation. The optimized b o n d lengths are shown in table 1. Compared with the optimized b o n d lengths for the ground state, the Si-C b o n d is shortened, the C - O b o n d is lengthened, a n d the length of the molecule in the A 31-I state is shorter than that in the ground state. Our predicted excitation energy for X 3y-__,A 31-I 535
Volume 19 l, number 6
CHEMICAL PHYSICS LETTERS
Table 4 Calculated values of the properties dependent upon the electronic transition dipole moment for the A 3H-X 3y.- band system Transition dipole moment Y[Rel 2 (au)
Oscillator strength f~ (au)
Radiative lifetime T (laS)
0.16906
0.00514
2.92
as the difference o f the CI energies at the corresponding o p t i m i z e d geometries o f the two states is 3.215 eV, which is in good agreement with the experimental transition energy values o f 2.983 eV [ 1 ]. We obtain an even better value (3.114 eV) for the excitation energy when we calculate it using the est i m a t e d full-CI energy values given in the output by the program package M E L D F . F o r the transition A31-I--,X 3E-, we calculated transition properties based on the CI wavefunctions, using the same p r o g r a m package. The calculated values for the square o f the electronic transition dipole m o m e n t , the oscillator strength for the absorption (taking AE = 3.215 eV ), a n d the radiative lifetime for the A 3H states are given in table 4. There are no experimental d a t a to c o m p a r e with. The force constants and vibrational frequencies for the A 3II state have also been calculated, these calculated values are shown in table 2. The calculated vibrational frequencies for this state are in agreement with experiment. The 1 trI state was treated in the M R S D C I calculations as the lowest singlet state o f the B~ irreducible representation. The o p t i m i z e d b o n d lengths are given in table 1. C o m p a r e d with the o p t i m i z e d geometry for the ground state, the S i - C b o n d is shortened and the C - O b o n d is lengthened. The calculated excitation energy for X 3y,---, 1 lI-I is 4.896 eV. It is noted that the o p t i m i z e d geometries for the A 3H a n d l ~rI state are considerably different, and the energy difference between these two states is ~ 1.7 eV.
4. Conclusion The equilibrium geometries, excitation energies,
536
17 April 1992
force constants a n d vibrational frequencies for four electronic states, X 3E-, a 1A, A 3H and 1 qq, o f the SiCO radical have been studied at the M R S D C I level with a D Z + P basis set. The o p t i m a l geometries and excitation energies for these four states are presented in table I, force constants a n d vibrational frequencies for the X 3E- a n d A 3H states are presented in table 2. F o r the S i - C b o n d length, the o p t i m i z e d values in the a ~A, A 31"1and 1 1I-I states are shorter than that in the X 3E- state. F o r the C - O b o n d length, the o p t i m i z e d values in the a IA, A 3H a n d 1 IH states are bigger than that in the X 3E- state. The M R S D C I calculations indicate the following energy ordering for these four states: X3E-
t A < A 3 H < 1 lI-[.
The energy level o f the b rE+ state, which emerges from the same molecular orbital configuration as the X 3E- and a ~A states, is inferred to be higher than that o f the a ~A state. The predicted excitation energies for X 3E- - , A 3rI are in good agreement with experiment, the calculated vibrational frequencies o f the X 3y,- and A 31-I states a n d spin properties o f the X 3E- state are in reasonable agreement with available experimental data.
References [ 1] R.R. Lembke, R.F. Ferrante and W. Weltner Jr., J. Am. Chem. Soc. 99 (1977) 416. [ 2 ] R.J. van Zee, R.F. Ferrante and W. Weltner Jr., Chem. Phys. Letters 139 (1987) 426. [3] R.L. DeKock, R.G. Grev and H.F. Schaefer III, J. Chem. Phys. 89 (1988) 3016. [4 ] T.H. Dunning Jr., J. Chem. Phys. 53 ( 1970 ) 2823. [5] T.H. Dunning Jr. and P.J. Hay, in: Modern theoretical chemistry, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 1. [6] T.H. Dunning Jr., J. Chem. Phys. 55 ( 1971 ) 3958. [7]E.R. Davidson et al., MELDF, QECP580, Indiana University, Bloomington, Indiana, USA ( 1988 ). [8] D. Feller and E.R. Davidson, J. Chem. Phys. 74 (1981) 3977. [9] K. Tanaka and E.R. Davidson, J. Chem. Phys. 70 (1979) 2904. [ 10 ] G. Herzberg, Molecular spectra and molecular structure, Vol. 1 (Van Nostrand, Princeton, 1950 ).