146
S. Rashev and D.C. Moule
Table 8.1 (Continued)
Assign.
Observed [6]
Ab initio
Refined
Our calc.
Ref. [24]
Our calc.
Ref. [24]
2ν 4 + ν 5 + ν 6
6401.2
6394.49
6395.01
6414.91
6399.83
ν 1 + ν 3 + 2ν 4
6562.7
6560.57
6561.59
6544.88
6565.39
ν 2 + 2ν 4 + 2ν 6
6578.8
6570.28
6570.97
6572.47
6575.74
3ν 2 + ν 3
6652.2
6648.93
6649.83
6641.00
6653.34
3ν 3 + 2ν 4
6815.2
6808.70
6809.16
6791.27
6816.11
ν 1 + ν 2 + 2ν 4
6825.5
6821.30
6821.88
6838.86
6823.88
6ν 4
6909.0
6902.46
6903.18
6915.02
6910.15
ν 2 + 2ν 3 + 2ν 6
7137.4
7127.24
7139.51
7135.45
7140.25
fields [24], that are compared to the results from the respective calculations by the
authors themselves. Given are also the experimentally measured frequencies [6] and
assignments. This Table essentially corresponds to Table III from Ref. [24], but we
have changed most of the assignments in accord with Ref. [6] and excluded several
states, that do not have the correct A 1 symmetry. From a comparison of columns 3
and 4 in Table 8.1 it is seen that the results of our calculations using the parameters, corresponding to the ab initio field, are close to those of the authors [24], but
consistently somewhat lower, the difference starting from ∼0.1 cm −1 for the lowest levels and ranging up to ∼1 cm −1 or even more, for the highest excited levels
in the Table. This slight mismatch between the two sets of calculated data might
be attributed to the program suite TROVE [34], used by the authors [24] that involves a truncation of both the kinetic as well as the potential energy operators and
a limitation P max = 14 for the highest polyad number accessed in the calculation,
which limits the active space to about 21000 basis states. On the other hand, our
variational vibrational code is based on the exact expressions for both the kinetic
and the potential energy operators and a search/selection procedure, that selects as
many basis states (of almost unlimited high excitation) as needed for the calculation
at hand, the AS dimensions ranging up to 50000 or much more, when necessary. As
a result, our calculated results are converged to ∼0.01 cm −1 . Anyway, the overall
results show, that the ab initio computed PES in [24] presents an improvement over
the MLT quartic field [22].
Next, our calculations using the parameter set corresponding to the refined PES
in [24] are displayed in column 5 of Table 8.1 and the calculated results of the
authors [24] are given in the last column 6. It is obvious from a comparison of
columns 5 and 6, that both sets of results are substantially different. Our calculated
results are substantially different both from the calculated results by the authors [24]
and from the experimentally measured frequencies in column 2, of Table 8.1, as
well. In fact, according to our calculations, the so called refined field is not an improvement over the ab initio field but a deterioration. Similar is the situation with
the other sets of calculated vibrational energy levels (of symmetries A 2 , B 1 and B 2 ),
displayed in Tables IV, V and VI of Ref. [24]. Our guess could be, that either there
S. Rashev and D.C. Moule
Table 8.1 (Continued)
Assign.
Observed [6]
Ab initio
Refined
Our calc.
Ref. [24]
Our calc.
Ref. [24]
2ν 4 + ν 5 + ν 6
6401.2
6394.49
6395.01
6414.91
6399.83
ν 1 + ν 3 + 2ν 4
6562.7
6560.57
6561.59
6544.88
6565.39
ν 2 + 2ν 4 + 2ν 6
6578.8
6570.28
6570.97
6572.47
6575.74
3ν 2 + ν 3
6652.2
6648.93
6649.83
6641.00
6653.34
3ν 3 + 2ν 4
6815.2
6808.70
6809.16
6791.27
6816.11
ν 1 + ν 2 + 2ν 4
6825.5
6821.30
6821.88
6838.86
6823.88
6ν 4
6909.0
6902.46
6903.18
6915.02
6910.15
ν 2 + 2ν 3 + 2ν 6
7137.4
7127.24
7139.51
7135.45
7140.25
fields [24], that are compared to the results from the respective calculations by the
authors themselves. Given are also the experimentally measured frequencies [6] and
assignments. This Table essentially corresponds to Table III from Ref. [24], but we
have changed most of the assignments in accord with Ref. [6] and excluded several
states, that do not have the correct A 1 symmetry. From a comparison of columns 3
and 4 in Table 8.1 it is seen that the results of our calculations using the parameters, corresponding to the ab initio field, are close to those of the authors [24], but
consistently somewhat lower, the difference starting from ∼0.1 cm −1 for the lowest levels and ranging up to ∼1 cm −1 or even more, for the highest excited levels
in the Table. This slight mismatch between the two sets of calculated data might
be attributed to the program suite TROVE [34], used by the authors [24] that involves a truncation of both the kinetic as well as the potential energy operators and
a limitation P max = 14 for the highest polyad number accessed in the calculation,
which limits the active space to about 21000 basis states. On the other hand, our
variational vibrational code is based on the exact expressions for both the kinetic
and the potential energy operators and a search/selection procedure, that selects as
many basis states (of almost unlimited high excitation) as needed for the calculation
at hand, the AS dimensions ranging up to 50000 or much more, when necessary. As
a result, our calculated results are converged to ∼0.01 cm −1 . Anyway, the overall
results show, that the ab initio computed PES in [24] presents an improvement over
the MLT quartic field [22].
Next, our calculations using the parameter set corresponding to the refined PES
in [24] are displayed in column 5 of Table 8.1 and the calculated results of the
authors [24] are given in the last column 6. It is obvious from a comparison of
columns 5 and 6, that both sets of results are substantially different. Our calculated
results are substantially different both from the calculated results by the authors [24]
and from the experimentally measured frequencies in column 2, of Table 8.1, as
well. In fact, according to our calculations, the so called refined field is not an improvement over the ab initio field but a deterioration. Similar is the situation with
the other sets of calculated vibrational energy levels (of symmetries A 2 , B 1 and B 2 ),
displayed in Tables IV, V and VI of Ref. [24]. Our guess could be, that either there