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Franck-Condon factors and r-centroids for the (D1Π−X1Σ+) transition of SiS molecule using R-K-R-V potential
Volume 63A, number 2
PHYSICS LETTERS
FRANCK-CONDON
THE (D
31 October 1977
FACTORS AND r-CENTROIDS FOR
l I l - X 1 ]~+) T R A N S I T I O N O F SiS M O L E C U L E U S I N G R - K - R - V P O T E N T I A L V.M. MUMMIGATTI and B.G. JYOTI Radiation Laboratory.H, Department of Physics, Karnatak University, Dharwar-580003, India Received 2 June 1977
Turning points of the vibrating SiS molecule in the D 11-iand X 1Z+ electronic states are evaluated using R-K-R-V method. Franck-Condon (FC) factors and r-centroids are computed for the (D IlI-X 1E+) transition of the molecule using wavefunctions appropriate to R-K-R-Vpotential energy curves. The results of the FC-factors vary in accordance with the estimated intensities and also satisfy the vibrational sum rule. The sequence difference Ar remains approximately constant in the computed r-centroids. In recent years, considerable attention is focused on the use of the precise expression for the potential energy of the diatomic molecules as a function of the internuclear distance. The accuracy of the parameters such as dissociation energy, FC-factors and r-centroids depends upon the appropriateness of the potential energy expression used to evaluate them. Thus there is a need to select a more realistic potential energy function for the accurate evaluation of the parameters. It has been stressed by many workers that the R-K-R potential as modified by Vanderslice et al. [ 1] is more realistic than other potentials. Very recently it has been shown
by Mummigatti and Jyoti [2] that the use of R-K-R-V potential yields more accurate results in the case of ( A 2 E + - X 2 E +) transition of A10 molecule for higher vibrational quantum numbers. Therefore, the purpose of the present note is to report the potential energy curves, FC-factors and r-centroids for the ( D - X ) transition of the SiS molecule using the R-K-R-V potential. Potential energy curves for D i l l and X 1E+ electronic states of SiS molecule are constructed using R-K-R-V method. Turning points obtained for all the experimentally observed energy levels are given in table 1. For the determination of the vibrational wavefunc-
Table 1 R-K-R-V potential energy curves for the ground state X 1E÷ and excited state D 111 of the SiS molecule. X 1Z+ state
0 1 2 3 4 5 6 7 8 9 10 11 12 13 88
D 1~r state Ue (cm -1 )
rmin (A)
rmax (A)
Ue+ Te (cm -1)
rmin (A)
rmax (A)
372.896 1118.078 1859.770 2594.636 3323.907 4045.250 4763.980 5477.550 6185.560 6889.210 7587.300 8280.230 8968.000 9650.610
1.876 1.840 1.817 1.798 1.783 1.770 1.758 1.747 1.737 1.728 1.720 1.712 1.706 1.698
1.986 2.031 2.064 2.092 2.117 2.140 2.161 2.182 2.202 2.220 2.239 2.257 2.274 2.292
35164.467 35671.727 36173.127 36668.667 37158.347 37642.166 38120.126 38592.226 39058.466 39518.847
1.996 1.954 1.928 1.907 1.891 1.877 1.863 1.852 1.842 1.832
2.129 2.186 2.228 2.264 2.298 2.328 2.356 2.385 2.412 2.439
Volume 63A, number 2
PHYSICS LETTERS
31 October 1977
Table 2 R-K-R-V FC-factors and r-centroids of the (D 1r I - X 1 y÷) transition of the SiS molecule. o' o"
FC-factors a
r-centroids (h)
wavelength (A)
o' o"
FC-factor s a
r-centroids (A)
wavelength (h)
0, 0 0, 1 0, 2 0, 3 0, 4 0, 5
8.131-2(8) 2.034-1 (10) 2.566-1 (10) 2.159-1 (9) 1.356-1 (8) 6.742-2(5)
1.992 2.024 2.055 2.085 2.114 2.144
2863.66 2926.06 2990.78 3057.95 3127.67 3200.04
1,0 1, 1 1, 3 1,4 1,5 1,6 1,7 1,8
1.944-1 (9) 1.180-1 (8) 1.827-2(3) 1.179-1 (7) 1.718-1 (7) 1.661-1 (8) 1.212-1(7) 1.717-2(3)
1.970 2.002 2.064 2.093 2.122 2.152 2.180 2.212
2822.66 2883.25 3010.92 3078.83 3149.05 3221.83 3297.64 3376.29
4, 0 4, 1 4, 7 4, 9 4, 10 4, 11 4, 12 4, 13 4, 14
1.390-1 (7) 9.081-2 (6) 1.212-2(2) 1.471-2(2) 1.667-2 (3) 3.612-2 (4) 3.591-2(3) 3.666-2(4) 1.223-2(2)
1.901 1.937 2.120 2.177 2.212 2.242 2.270 2.320 2.352
2708.78 2764.66 3143.52 3289.68 3367.78 3447.36 3531.53 3618.68 3709.14
2, 0 2, 1 2, 2 2, 3 2,6 2, 7 2, 8 2, 9 2, 10
2.417-1 (9) 3.186-2(4) 4.919-2 (4) 1.263-1 (5) 1.551-2(3) 1.313-1 (5) 1.414-1 (6) 1.399-1 (5) 1.001-2(1)
1.948 1.981 2.012 2.043 2.131 2.156 2.191 2.222 2.259
2783.18 2842.18 2902.90 2966.35 3170.35 3244.16 3320.11 3399.68 3482.84
5, 0 5, 1 5,8 5, 11 5,12 5, 13 5, 14 5, 15
7.677-2(6) 1.471-1 (5) 1.013-2 (2) 1.121-2(2) 4.122-2(4) 2.012-2(3) 3.112-2(4) 2.012-2(2)
1.877 1.914 2.132 2.223 2.251 2.281 2.331 2.364
2673.78 2728.17 3166.06 3391.40 3471.79 3556.08 3644.29 3735.75
6, 0 6, 1 6, 13 6, 14 6, 15
4.812-2(4) 1.121-2(2) 1.012-2(I) 1.124-2(2) 2.998-2(3)
1.851 1.891 2.262 2.293 2.344
2640.10 2693.06 3496.72 3582.04 3670.32
3, 0 3, 1 3, 2 3, 5 3, 8 3, 9 3, 10 3, 11 3, 12
2.081-1 (8) 1.071-2 (2) 1.225-1 (4) 1.021-1 (3) 3.397-2(4) 3.409- 2 (5) 3.601-2(5) 3.123-2 (4) 1.223-2(2)
1.925 1.959 1.991 2.082 2.167 2.202 2.233 2.269 2.310
2745.28 2802.60 2862.01 3053.03 3266.53 3343.37 3423.57 3506.35 3593.67
7, 0 7, 1
1.123-2(2) 1.567-2 (3)
1.822 1.866
2667.15 2658.77
a The negative numerical in each FC-factor entry is the power of 10 by which it is multiplied and the quantity in the bracket is the estimated intensity. tions, the procedure already described by the present authors [2] is adopted. F f - f a c t o r s (qv'o") and r-centroids (ro'o") for the said transition are c o m p u t e d using the following relations: o¢
~
oo
qo,o,,=f ¢o,¢o,,dr; ~o,o,,=//f¢o,(r)~,o,,dr/f~o,~o,,dr. 0
0
0
Where ~kv, and fly" are vibrational wavefunctions for the upper and lower states b e t w e e n which the transition takes place and r, the internuclear distance. These results are given in table 2.
F r o m table 2 it is clear that the c o m p u t e d FCfactors vary in accordance with the estimated intensities [3]. The well-known vibrational sum rule viz., Ev'qv'v" = Y-'o"qv'o" -~ 1 is also satisfied for the computed FC-factors. In the case of the r-centroids the established fact that the sequence difference A r = -ro',o" - Tv'+l,o"+l remains approximately c o n s t a n t for all the sequences. Jarmain et al. [4, 5] have shown that ~0,0 is usually greater than (tel+ re2)/2 for systems whose potentials are n o t very m u c h anharmonic. In the present case T0,0 is f o u n d to be less than (tel + re2)/2. 89
Volume 63A, number 2
PHYSICS LETTERS
This clearly indicates that the potentials are very anharmonic.
References [ 1 ] J.T. Vanderslice, E.A. Mason, W.G. Maisch and E.R. Lippincott, J. Mol. Spectra. 3 (1959) 17; 5 (1960) 83.
90
31 October 1977
[2] V.M. Mummigatti and B.G. Jyoti, Curr. Sci. 46 (8) (1977) 256.
[3] B. Rosen, Tables internationales des constants selectionn6s (Pergamon Press, New York, 1970). [4] W.R. Jarmain and R.W. Nicholls, Proc. Phys. Soc. A69 (1956) 253. [5] W.R. Jarmain, R.W. NichoUs, W. Perkinson and D. Robinson, Proc. Phys. Soc. A69 (1956) 713.
PHYSICS LETTERS
FRANCK-CONDON
THE (D
31 October 1977
FACTORS AND r-CENTROIDS FOR
l I l - X 1 ]~+) T R A N S I T I O N O F SiS M O L E C U L E U S I N G R - K - R - V P O T E N T I A L V.M. MUMMIGATTI and B.G. JYOTI Radiation Laboratory.H, Department of Physics, Karnatak University, Dharwar-580003, India Received 2 June 1977
Turning points of the vibrating SiS molecule in the D 11-iand X 1Z+ electronic states are evaluated using R-K-R-V method. Franck-Condon (FC) factors and r-centroids are computed for the (D IlI-X 1E+) transition of the molecule using wavefunctions appropriate to R-K-R-Vpotential energy curves. The results of the FC-factors vary in accordance with the estimated intensities and also satisfy the vibrational sum rule. The sequence difference Ar remains approximately constant in the computed r-centroids. In recent years, considerable attention is focused on the use of the precise expression for the potential energy of the diatomic molecules as a function of the internuclear distance. The accuracy of the parameters such as dissociation energy, FC-factors and r-centroids depends upon the appropriateness of the potential energy expression used to evaluate them. Thus there is a need to select a more realistic potential energy function for the accurate evaluation of the parameters. It has been stressed by many workers that the R-K-R potential as modified by Vanderslice et al. [ 1] is more realistic than other potentials. Very recently it has been shown
by Mummigatti and Jyoti [2] that the use of R-K-R-V potential yields more accurate results in the case of ( A 2 E + - X 2 E +) transition of A10 molecule for higher vibrational quantum numbers. Therefore, the purpose of the present note is to report the potential energy curves, FC-factors and r-centroids for the ( D - X ) transition of the SiS molecule using the R-K-R-V potential. Potential energy curves for D i l l and X 1E+ electronic states of SiS molecule are constructed using R-K-R-V method. Turning points obtained for all the experimentally observed energy levels are given in table 1. For the determination of the vibrational wavefunc-
Table 1 R-K-R-V potential energy curves for the ground state X 1E÷ and excited state D 111 of the SiS molecule. X 1Z+ state
0 1 2 3 4 5 6 7 8 9 10 11 12 13 88
D 1~r state Ue (cm -1 )
rmin (A)
rmax (A)
Ue+ Te (cm -1)
rmin (A)
rmax (A)
372.896 1118.078 1859.770 2594.636 3323.907 4045.250 4763.980 5477.550 6185.560 6889.210 7587.300 8280.230 8968.000 9650.610
1.876 1.840 1.817 1.798 1.783 1.770 1.758 1.747 1.737 1.728 1.720 1.712 1.706 1.698
1.986 2.031 2.064 2.092 2.117 2.140 2.161 2.182 2.202 2.220 2.239 2.257 2.274 2.292
35164.467 35671.727 36173.127 36668.667 37158.347 37642.166 38120.126 38592.226 39058.466 39518.847
1.996 1.954 1.928 1.907 1.891 1.877 1.863 1.852 1.842 1.832
2.129 2.186 2.228 2.264 2.298 2.328 2.356 2.385 2.412 2.439
Volume 63A, number 2
PHYSICS LETTERS
31 October 1977
Table 2 R-K-R-V FC-factors and r-centroids of the (D 1r I - X 1 y÷) transition of the SiS molecule. o' o"
FC-factors a
r-centroids (h)
wavelength (A)
o' o"
FC-factor s a
r-centroids (A)
wavelength (h)
0, 0 0, 1 0, 2 0, 3 0, 4 0, 5
8.131-2(8) 2.034-1 (10) 2.566-1 (10) 2.159-1 (9) 1.356-1 (8) 6.742-2(5)
1.992 2.024 2.055 2.085 2.114 2.144
2863.66 2926.06 2990.78 3057.95 3127.67 3200.04
1,0 1, 1 1, 3 1,4 1,5 1,6 1,7 1,8
1.944-1 (9) 1.180-1 (8) 1.827-2(3) 1.179-1 (7) 1.718-1 (7) 1.661-1 (8) 1.212-1(7) 1.717-2(3)
1.970 2.002 2.064 2.093 2.122 2.152 2.180 2.212
2822.66 2883.25 3010.92 3078.83 3149.05 3221.83 3297.64 3376.29
4, 0 4, 1 4, 7 4, 9 4, 10 4, 11 4, 12 4, 13 4, 14
1.390-1 (7) 9.081-2 (6) 1.212-2(2) 1.471-2(2) 1.667-2 (3) 3.612-2 (4) 3.591-2(3) 3.666-2(4) 1.223-2(2)
1.901 1.937 2.120 2.177 2.212 2.242 2.270 2.320 2.352
2708.78 2764.66 3143.52 3289.68 3367.78 3447.36 3531.53 3618.68 3709.14
2, 0 2, 1 2, 2 2, 3 2,6 2, 7 2, 8 2, 9 2, 10
2.417-1 (9) 3.186-2(4) 4.919-2 (4) 1.263-1 (5) 1.551-2(3) 1.313-1 (5) 1.414-1 (6) 1.399-1 (5) 1.001-2(1)
1.948 1.981 2.012 2.043 2.131 2.156 2.191 2.222 2.259
2783.18 2842.18 2902.90 2966.35 3170.35 3244.16 3320.11 3399.68 3482.84
5, 0 5, 1 5,8 5, 11 5,12 5, 13 5, 14 5, 15
7.677-2(6) 1.471-1 (5) 1.013-2 (2) 1.121-2(2) 4.122-2(4) 2.012-2(3) 3.112-2(4) 2.012-2(2)
1.877 1.914 2.132 2.223 2.251 2.281 2.331 2.364
2673.78 2728.17 3166.06 3391.40 3471.79 3556.08 3644.29 3735.75
6, 0 6, 1 6, 13 6, 14 6, 15
4.812-2(4) 1.121-2(2) 1.012-2(I) 1.124-2(2) 2.998-2(3)
1.851 1.891 2.262 2.293 2.344
2640.10 2693.06 3496.72 3582.04 3670.32
3, 0 3, 1 3, 2 3, 5 3, 8 3, 9 3, 10 3, 11 3, 12
2.081-1 (8) 1.071-2 (2) 1.225-1 (4) 1.021-1 (3) 3.397-2(4) 3.409- 2 (5) 3.601-2(5) 3.123-2 (4) 1.223-2(2)
1.925 1.959 1.991 2.082 2.167 2.202 2.233 2.269 2.310
2745.28 2802.60 2862.01 3053.03 3266.53 3343.37 3423.57 3506.35 3593.67
7, 0 7, 1
1.123-2(2) 1.567-2 (3)
1.822 1.866
2667.15 2658.77
a The negative numerical in each FC-factor entry is the power of 10 by which it is multiplied and the quantity in the bracket is the estimated intensity. tions, the procedure already described by the present authors [2] is adopted. F f - f a c t o r s (qv'o") and r-centroids (ro'o") for the said transition are c o m p u t e d using the following relations: o¢
~
oo
qo,o,,=f ¢o,¢o,,dr; ~o,o,,=//f¢o,(r)~,o,,dr/f~o,~o,,dr. 0
0
0
Where ~kv, and fly" are vibrational wavefunctions for the upper and lower states b e t w e e n which the transition takes place and r, the internuclear distance. These results are given in table 2.
F r o m table 2 it is clear that the c o m p u t e d FCfactors vary in accordance with the estimated intensities [3]. The well-known vibrational sum rule viz., Ev'qv'v" = Y-'o"qv'o" -~ 1 is also satisfied for the computed FC-factors. In the case of the r-centroids the established fact that the sequence difference A r = -ro',o" - Tv'+l,o"+l remains approximately c o n s t a n t for all the sequences. Jarmain et al. [4, 5] have shown that ~0,0 is usually greater than (tel+ re2)/2 for systems whose potentials are n o t very m u c h anharmonic. In the present case T0,0 is f o u n d to be less than (tel + re2)/2. 89
Volume 63A, number 2
PHYSICS LETTERS
This clearly indicates that the potentials are very anharmonic.
References [ 1 ] J.T. Vanderslice, E.A. Mason, W.G. Maisch and E.R. Lippincott, J. Mol. Spectra. 3 (1959) 17; 5 (1960) 83.
90
31 October 1977
[2] V.M. Mummigatti and B.G. Jyoti, Curr. Sci. 46 (8) (1977) 256.
[3] B. Rosen, Tables internationales des constants selectionn6s (Pergamon Press, New York, 1970). [4] W.R. Jarmain and R.W. Nicholls, Proc. Phys. Soc. A69 (1956) 253. [5] W.R. Jarmain, R.W. NichoUs, W. Perkinson and D. Robinson, Proc. Phys. Soc. A69 (1956) 713.