8 A Refined Quartic Potential Surface for S 0 Formaldehyde
151
Table 8.3 (Continued)
Assignment
Calculated this work
Calculated [12]
Calculated [14]
Experimental [6]
2 2 6 2
5986.74
5985.4
5986.2
1 1 2 1 3 1
5998.87
5997.8
5996.0
2 1 3 1 5 1
6057.55
6052.3
6051.7
2 2 3 1 4 1
6105.21
6108.1
6106.2
3 1 4 4
6119.98
6122.9
6123.6
3 1 4 3 6 1
6195.63
6189.3
6189.1
2 2 3 1 6 1
6198.55
6196.7
6194.8
1 1 4 3
6235.88
6239.9
6235.2
1 1 2 2
6252.96
6254.6
6254.7
3 1 4 2 6 2
6272.80
6264.8
6263.1
2 2 5 1
6276.04
6275.4
6276.4
on the much higher excited vibrational levels (up to ∼12500 cm −1 and higher) and
compared them to the experimentally measured and calculated frequencies from
Ref. [6], as well as with the results from calculations by Lee and Light [18], who
used essentially the PES of Burleigh et al. [14], with a slight modification for the
out-of-plane mode. Our calculated results were found to be reasonably close to the
experimentally measured frequencies as well as to the calculated frequencies by
Burleigh et al. [6, 14] and by Lee et al. [18].
In order to demonstrate that in spite of our using only vibrational levels of A 1
symmetry in the adjustment process, the levels of other symmetries were also well
approximated, we have provided the Table 8.4, containing calculated vibrational
levels using our refined PES, of A 2 , B 1 and B 2 symmetries, up to ∼5000 cm −1 ,
compared to the experimentally measured frequencies [6]. It is readily seen from the
table, that the agreement between the calculated and the experimentally measured
values is quite satisfactory.
Lee and Light [18] calculated all vibrational levels of A 1 symmetry up to
13500 cm −1 in S 0 H 2 CO and they found their exact number to be 729. In our present
calculation with the newly obtained quartic PES (Table 8.1) we have counted 727
A 1 vibrational levels in this energy range. There is a remarkable agreement between
the two calculations. This can be considered as evidence, that the two fields are of
the same quality. In addition we have found 422 A 2 levels, 501 B 1 levels, and 615
B 2 levels in the same energy range (0–13500 cm −1 ).
In order to find out whether our refined field retains the physically justified character of the ab initio computed fields, we have calculated cuts through all four types
of vibrational curvilinear coordinates in formaldehyde (1-CH and 2-CO stretches,
3-HCO in plane bend and 4- out of plane bend of the two HCO planes), in each case
holding all the remaining coordinates fixed at equilibrium. For the sake of comparison, we have also calculated the corresponding cuts for three other fields: the
original MLT field [22] and the ab initio and refined fields by Yachmenev et al. [24].
These cuts for all four fields are displayed in Figs. 8.1, 8.2, 8.3, and 8.4, for the
151
Table 8.3 (Continued)
Assignment
Calculated this work
Calculated [12]
Calculated [14]
Experimental [6]
2 2 6 2
5986.74
5985.4
5986.2
1 1 2 1 3 1
5998.87
5997.8
5996.0
2 1 3 1 5 1
6057.55
6052.3
6051.7
2 2 3 1 4 1
6105.21
6108.1
6106.2
3 1 4 4
6119.98
6122.9
6123.6
3 1 4 3 6 1
6195.63
6189.3
6189.1
2 2 3 1 6 1
6198.55
6196.7
6194.8
1 1 4 3
6235.88
6239.9
6235.2
1 1 2 2
6252.96
6254.6
6254.7
3 1 4 2 6 2
6272.80
6264.8
6263.1
2 2 5 1
6276.04
6275.4
6276.4
on the much higher excited vibrational levels (up to ∼12500 cm −1 and higher) and
compared them to the experimentally measured and calculated frequencies from
Ref. [6], as well as with the results from calculations by Lee and Light [18], who
used essentially the PES of Burleigh et al. [14], with a slight modification for the
out-of-plane mode. Our calculated results were found to be reasonably close to the
experimentally measured frequencies as well as to the calculated frequencies by
Burleigh et al. [6, 14] and by Lee et al. [18].
In order to demonstrate that in spite of our using only vibrational levels of A 1
symmetry in the adjustment process, the levels of other symmetries were also well
approximated, we have provided the Table 8.4, containing calculated vibrational
levels using our refined PES, of A 2 , B 1 and B 2 symmetries, up to ∼5000 cm −1 ,
compared to the experimentally measured frequencies [6]. It is readily seen from the
table, that the agreement between the calculated and the experimentally measured
values is quite satisfactory.
Lee and Light [18] calculated all vibrational levels of A 1 symmetry up to
13500 cm −1 in S 0 H 2 CO and they found their exact number to be 729. In our present
calculation with the newly obtained quartic PES (Table 8.1) we have counted 727
A 1 vibrational levels in this energy range. There is a remarkable agreement between
the two calculations. This can be considered as evidence, that the two fields are of
the same quality. In addition we have found 422 A 2 levels, 501 B 1 levels, and 615
B 2 levels in the same energy range (0–13500 cm −1 ).
In order to find out whether our refined field retains the physically justified character of the ab initio computed fields, we have calculated cuts through all four types
of vibrational curvilinear coordinates in formaldehyde (1-CH and 2-CO stretches,
3-HCO in plane bend and 4- out of plane bend of the two HCO planes), in each case
holding all the remaining coordinates fixed at equilibrium. For the sake of comparison, we have also calculated the corresponding cuts for three other fields: the
original MLT field [22] and the ab initio and refined fields by Yachmenev et al. [24].
These cuts for all four fields are displayed in Figs. 8.1, 8.2, 8.3, and 8.4, for the