Mathematically, one can write for the intensity Iv'v'' of a molecular
band for a v'-v'' vibronic transition in emission as
where D is a constant partly depending on the geometry of the apparatus,
Nv' the population of the level v', Ev'v'' the energy quantum,
qv ' v'' the FC factors, r v' v'' the r-centroid and 
the electronic transition moment.
The square of the overlap integral 
is termed as FC factor where 
and 
are
the vibrational wave functions for the upper and lower states respectively.
The r-centroid is the unique value of internuclear separation which may be
associated with a v'-v'' band defined as
| v'' | 0 | 1 | 2 | |
| v' | ||||
| 0 | a) 0.994 | 0.008 | 0.001 | |
| b) 1.540 | 2.514 | 1.731 | ||
| 1 | a) 0.008 | 0.934 | 0.047 | |
| b) 0.722 | 1.577 | 2.135 | ||
| 2 | a) 0.000 | 0.056 | 0.751 | |
| b) 2.679 | 1.171 | 1.611 |
system of SiD
The Morse (1929) potential yields
accurate FC factors especially for vibrational transition involving low
quantum numbers (Rajamanickam 1995; Nagarajan &
Rajamanickam 1996). The computation of the FC factors is made by
Bates' (1949) method of numerical integration according to the
detailed procedure provided by Rajamanickam et al. (1994). The
molecular constants used in the present study are collected from the
compilation of Huber & Herzberg (1979) for the system 
of SiD, 
of SiF and 
of SiN. Morse wave functions are
calculated at intervals of 
for the range of r respectively from 1.29 Å to 1.91 Å, from
1.38 Å\
to 1.80 Å and from 1.41 Å to 2.25 Å for every observed
vibrational levels of , and states of SiD, SiF
and SiN molecules. Integrals appearing in the definitions of FC factors
(qv'v'') and r-centroids (rv'v'') are computed numerically and
the results are entered respectively in Tables 1 (click here), 2 (click here) and
3 (click here) for the system of SiD, of SiF and
of SiN. The wavelength (
) data (Bredohl et al.
1976) for D-A system of SiN molecule is also included in
Table 3 (click here).
| v'' | 0 | 1 | 2 | 3 | |
| v' | |||||
| 0 | a) 0.602 | 0.297 | 0.082 | 0.017 | |
| b) 1.576 | 1.523 | 1.472 | 1.420 | ||
| 1 | a) 0.314 | 0.145 | 0.316 | 0.163 | |
| b) 1.637 | 1.585 | 1.532 | 1.481 | ||
| 2 | a) 0.074 | 0.363 | 0.007 | 0.228 | |
| b) 1.679 | 1.646 | 1.597 | 1.541 | ||
| 3 | a) 0.010 | 0.160 | 0.293 | 0.016 | |
| b) 1.762 | 1.706 | 1.656 | 1.599 | ||
| 4 | a) 0.000 | 0.032 | 0.228 | 0.188 | |
| b) 1.833 | 1.771 | 1.715 | 1.665 |
system of SiF
| v | 0 | 1 | 2 | 3 | 4 | ||
| v' | |||||||
| 0 | 0.0032 | 0.0220 | 0.0700 | 0.1406 | 0.1971 | (a) (i) | |
| 0.0029 | 0.0193 | 0.0614 | 0.1241 | -- | (ii) | ||
| 1.7392 | 1.7630 | 1.7871 | 1.8119 | 1.8373 | (b) (i) | ||
| 1.7376 | 1.7604 | -- | -- | -- | (ii) | ||
| 1 | 0.0161 | 0.0733 | 0.1396 | 0.1331 | 0.0514 | (a) (i) | |
| 0.0140 | 0.0647 | 0.1283 | -- | -- | (ii) | ||
| 1.7233 | 1.7465 | 1.7699 | 1.7935 | 1.8166 | (b) (i) | ||
| 1.7226 | 1.7451 | -- | -- | -- | (ii) | ||
| 2 | 0.0418 | 0.1206 | 0.1136 | 0.0218 | 0.0135 | (a) (i) | |
| 0.0358 | 0.1093 | -- | -- | -- | (ii) | ||
| 1.7078 | 1.7304 | 1.7530 | 1.7738 | 1.8070 | (b) (i) | ||
| 1.7225 | 1.7302 | 1.7528 | -- | -- | (ii) | ||
| -- | -- | 3699 | -- | -- | (c) | ||
| 3 | 0.0758 | 0.1262 | 0.0356 | 0.0108 | 0.0804 | (a) (i) | |
| 0.0648 | -- | -- | -- | -- | (ii) | ||
| 1.6927 | 1.7149 | 1.7360 | 1.7660 | 1.7854 | (b) (i) | ||
| 1.6940 | 1.7146 | 1.7380 | 1.7604 | -- | (ii) | ||
| -- | 3480 | 3608 | 3745 | -- | (c) | ||
| 4 | 0.1081 | 0.0882 | 0.0000 | 0.0641 | 0.0641 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.6780 | 1.6997 | 1.1444 | 1.7464 | 1.7670 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 3401 | 3523 | 3653 | -- | (c) | ||
| 5 | 0.1291 | 0.0370 | 0.0252 | 0.0660 | 0.0037 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.6637 | 1.6846 | 1.7098 | 1.7299 | 1.7236 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 3326 | 3443 | -- | -- | (c) | ||
| 6 | 0.1344 | 0.0046 | 0.0618 | 0.0222 | 0.0255 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.6497 | 1.6685 | 1.6941 | 1.7134 | 1.7466 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 3255 | -- | -- | -- | (c) | ||
| 7 | 0.1253 | 0.0028 | 0.0678 | 0.0000 | 0.0554 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.6359 | 1.6609 | 1.6794 | 1.8205 | 1.7237 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 3187 | -- | -- | -- | (c) | ||
| 8 | 0.1065 | 0.0237 | 0.0433 | 0.0188 | 0.0386 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.6224 | 1.6448 | 1.6651 | 1.6893 | 1.7080 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 3123 | -- | -- | -- | (c) |
(c, Å) for
bands of 
system of SiN| v | 5 | 6 | 7 | 8 | 9 | ||
| v' | |||||||
| 0 | 0.2070 | 0.1677 | 0.1071 | 0.0546 | 0.0223 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.8635 | 1.8907 | 1.9191 | 1.9489 | 1.9803 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 1 | 0.0000 | 0.0452 | 0.1288 | 0.1627 | 0.1307 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.7222 | 1.8751 | 1.9006 | 1.9285 | 1.9581 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | 4465 | 4664 | -- | -- | (c) | ||
| 2 | 0.0868 | 0.0826 | 0.0126 | 0.0159 | 0.0980 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.8276 | 1.8511 | 1.8704 | 1.9163 | 1.9391 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| -- | -- | -- | 4722 | 4939 | (c) | ||
| 3 | 0.0452 | 0.0011 | 0.0633 | 0.0792 | 0.0135 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.8068 | 1.8605 | 1.8622 | 1.8856 | 1.9044 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 4 | 0.0024 | 0.0645 | 0.0407 | 0.0019 | 0.0647 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.8071 | 1.8179 | 1.8386 | 1.8935 | 1.8969 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 3937 | -- | -- | 4439 | 4631 | (c) | ||
| 5 | 0.0522 | 0.0352 | 0.0057 | 0.0635 | 0.0244 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.7776 | 1.7972 | 1.8361 | 1.8501 | 1.8691 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 6 | 0.0482 | 0.0009 | 0.0547 | 0.0166 | 0.0196 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.7596 | 1.8081 | 1.8083 | 1.8253 | 1.8637 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 7 | 0.0054 | 0.0387 | 0.0259 | 0.0125 | 0.0510 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.7381 | 1.7701 | 1.7878 | 1.8223 | 1.8384 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) | ||
| 8 | 0.0093 | 0.0441 | 0.0010 | 0.0477 | 0.0038 | (a) (i) | |
| -- | -- | -- | -- | -- | (ii) | ||
| 1.7359 | 1.7523 | 1.7995 | 1.7991 | 1.8071 | (b) (i) | ||
| -- | -- | -- | -- | -- | (ii) |