Table 4 \(J=1\) rovibrational energy levels of H\({}_{2}\)16O in Radau bisector embedding with different generalized centrifugal sudden approximations (GCSA) referring to each of the three choices of \({\hat{c}}\) axis along which \(K\) is projected. The results are provided in cm\({}^{-1}\) and given relative to the vibrational parent state. Vibrational [vib, \(({v}_{1}\ {v}_{2}\ {v}_{3})\)] and rotational (rot, \({J}_{{K}_{a}{K}_{c}}\)) quantum numbers are assigned for each state. The differences of the eigenvalues compared to the diagonal \({{\bf{G}}}_{{\rm{R}}}\) approximation (DGRA) [\(\Delta \)(GCSA)] are also provided.
\({ {\hat{H}} }_{{\rm{V}}{\rm{R}}}\) | DGRA | GCSA | \(\Delta \)(GCSA) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
# | level | vib | rot | ref. | CS\({}_{{\bf{x}}}\) | CS\({}_{{\bf{z}}}\) | CS\({}_{{\bf{y}}}\) | CS\({}_{{\bf{x}}}\) | CS\({}_{{\bf{z}}}\) | CS\({}_{{\bf{y}}}\) |
1 | 23.8 | (0 0 0) | \({1}_{01}\) | 23.8 | 23.8 | 30.5 | 33.1 | 0.0 | 6.7 | 9.3 |
2 | 37.1 | (0 0 0) | \({1}_{11}\) | 37.2 | 39.8 | 30.5 | 37.2 | 2.6 | \(-6.7\) | 0.0 |
3 | 42.4 | (0 0 0) | \({1}_{10}\) | 42.4 | 39.8 | 42.4 | 33.1 | \(-2.6\) | 0.0 | \(-9.3\) |
4 | 23.8 | (0 1 0) | \({1}_{01}\) | 23.9 | 23.9 | 32.3 | 34.9 | 0.0 | 8.3 | 10.9 |
5 | 40.2 | (0 1 0) | \({1}_{11}\) | 40.3 | 43.1 | 32.3 | 40.3 | 2.7 | \(-8.1\) | 0.0 |
6 | 45.8 | (0 1 0) | \({1}_{10}\) | 45.8 | 43.1 | 45.8 | 34.9 | \(-2.7\) | 0.0 | \(-10.9\) |
7 | 23.8 | (0 2 0) | \({1}_{01}\) | 24.0 | 24.0 | 34.6 | 37.2 | 0.0 | 10.6 | 13.2 |
8 | 44.5 | (0 2 0) | \({1}_{11}\) | 44.7 | 47.5 | 34.6 | 44.7 | 2.8 | \(-10.1\) | 0.0 |
9 | 50.3 | (0 2 0) | \({1}_{10}\) | 50.3 | 47.5 | 50.3 | 37.2 | \(-2.8\) | 0.0 | \(-13.1\) |
10 | 23.4 | (1 0 0) | \({1}_{01}\) | 23.4 | 23.4 | 29.8 | 32.4 | 0.0 | 6.4 | 9.0 |
11 | 36.2 | (1 0 0) | \({1}_{11}\) | 36.3 | 38.9 | 29.8 | 36.3 | 2.6 | \(-6.4\) | 0.0 |
12 | 41.4 | (1 0 0) | \({1}_{10}\) | 41.4 | 38.9 | 41.4 | 32.4 | \(-2.6\) | 0.0 | \(-9.0\) |
13 | 23.6 | (0 0 1) | \({1}_{01}\) | 23.6 | 23.6 | 29.5 | 32.3 | 0.0 | 6.0 | 8.8 |
14 | 35.8 | (0 0 1) | \({1}_{11}\) | 35.8 | 38.4 | 29.5 | 35.8 | 2.6 | \(-6.2\) | 0.0 |
15 | 41.1 | (0 0 1) | \({1}_{10}\) | 41.1 | 38.4 | 41.1 | 32.3 | \(-2.6\) | 0.0 | \(-8.7\) |
16 | 23.8 | (0 3 0) | \({1}_{01}\) | 24.1 | 24.1 | 38.0 | 40.5 | 0.0 | 13.9 | 16.4 |
17 | 50.7 | (0 3 0) | \({1}_{11}\) | 51.0 | 53.9 | 38.0 | 51.0 | 2.9 | \(-13.0\) | 0.0 |
18 | 56.8 | (0 3 0) | \({1}_{10}\) | 56.8 | 53.9 | 56.8 | 40.5 | \(-2.9\) | 0.0 | \(-16.3\) |
19 | 23.4 | (1 1 0) | \({1}_{01}\) | 23.6 | 23.6 | 31.5 | 34.1 | 0.0 | 8.0 | 10.6 |
20 | 39.2 | (1 1 0) | \({1}_{11}\) | 39.3 | 42.0 | 31.5 | 39.3 | 2.7 | \(-7.8\) | 0.0 |
21 | 44.7 | (1 1 0) | \({1}_{10}\) | 44.7 | 42.0 | 44.7 | 34.1 | \(-2.7\) | 0.0 | \(-10.6\) |
22 | 23.6 | (0 1 1) | \({1}_{01}\) | 23.7 | 23.7 | 31.1 | 33.9 | 0.0 | 7.4 | 10.2 |
23 | 38.5 | (0 1 1) | \({1}_{11}\) | 38.6 | 41.3 | 31.1 | 38.6 | 2.8 | \(-7.5\) | 0.0 |
24 | 44.1 | (0 1 1) | \({1}_{10}\) | 44.1 | 41.3 | 44.1 | 33.9 | \(-2.8\) | 0.0 | \(-10.2\) |
25 | 23.7 | (0 4 0) | \({1}_{01}\) | 24.1 | 24.1 | 43.3 | 45.8 | 0.0 | 19.2 | 21.7 |
26 | 60.8 | (0 4 0) | \({1}_{11}\) | 61.2 | 64.1 | 43.3 | 61.2 | 3.0 | \(-17.8\) | 0.0 |
27 | 67.1 | (0 4 0) | \({1}_{10}\) | 67.1 | 64.1 | 67.1 | 45.8 | \(-3.0\) | 0.0 | \(-21.3\) |
28 | 23.4 | (1 2 0) | \({1}_{01}\) | 23.6 | 23.6 | 33.8 | 36.4 | 0.0 | 10.1 | 12.7 |
29 | 43.2 | (1 2 0) | \({1}_{11}\) | 43.4 | 46.2 | 33.8 | 43.4 | 2.8 | \(-9.7\) | 0.0 |
30 | 49.0 | (1 2 0) | \({1}_{10}\) | 49.0 | 46.2 | 49.0 | 36.4 | \(-2.8\) | 0.0 | \(-12.7\) |
31 | 23.6 | (0 2 1) | \({1}_{01}\) | 23.8 | 23.8 | 33.2 | 35.9 | 0.0 | 9.4 | 12.2 |
32 | 42.2 | (0 2 1) | \({1}_{11}\) | 42.3 | 45.2 | 33.2 | 42.3 | 2.9 | \(-9.2\) | 0.0 |
33 | 48.1 | (0 2 1) | \({1}_{10}\) | 48.1 | 45.2 | 48.1 | 35.9 | \(-2.9\) | 0.0 | \(-12.1\) |
34 | 23.0 | (2 0 0) | \({1}_{01}\) | 23.1 | 23.1 | 29.1 | 31.8 | 0.0 | 6.1 | 8.7 |
35 | 35.3 | (2 0 0) | \({1}_{11}\) | 35.3 | 37.9 | 29.1 | 35.3 | 2.6 | \(-6.2\) | 0.0 |
36 | 40.5 | (2 0 0) | \({1}_{10}\) | 40.5 | 37.9 | 40.5 | 31.8 | \(-2.6\) | 0.0 | \(-8.7\) |
37 | 23.2 | (1 0 1) | \({1}_{01}\) | 23.2 | 23.2 | 28.9 | 31.7 | 0.0 | 5.7 | 8.5 |
38 | 34.9 | (1 0 1) | \({1}_{11}\) | 34.9 | 37.5 | 28.9 | 34.9 | 2.6 | \(-6.0\) | 0.0 |
39 | 40.2 | (1 0 1) | \({1}_{10}\) | 40.2 | 37.5 | 40.2 | 31.7 | \(-2.6\) | 0.0 | \(-8.5\) |
40 | 23.3 | (0 0 2) | \({1}_{01}\) | 23.2 | 23.2 | 28.7 | 31.6 | 0.0 | 5.4 | 8.3 |
41 | 34.6 | (0 0 2) | \({1}_{11}\) | 34.5 | 37.2 | 28.7 | 34.5 | 2.7 | \(-5.9\) | 0.0 |
42 | 39.9 | (0 0 2) | \({1}_{10}\) | 39.9 | 37.2 | 39.9 | 31.6 | \(-2.7\) | 0.0 | \(-8.3\) |
