Mutsumi Aoyagi, Stephen K. Gray, and Michael J. Davis, "Variational study of the excited vibrational states of formaldehyde: accurate results up to 8500 cm−1 in excitation energy," J. Opt. Soc. Am. B 7, 1859-1864 (1990)
Variational results of the vibrational states up to 8500 cm−1 for X1A1 formaldehyde at J = 0 are presented. Our results agree reasonably well with perturbation results and with experimental results. Our calculations show additional b1 and b2 states in the energy region of the 2244 level, which could not be predicted by a simple normal-mode analysis. We also found that the eigenstates in this energy regime, seen from the zero-order normal-mode picture, have variety of characters: some states appear much more mixed than others.
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State assignments are determined from the present results. These assignments corresponds to the zero-order basis functions that make more than a 10% contribution to the total wave function.
Results from Ref. 4.
Results from a sixth-order Van Vleck perturbation theory calculation by Sibert.5
Variational results using Nmax = 14; Hamiltonian matrix dimensions of each symmetry are 11628 (a1), 7812 (a2), 8232 (b1), and 11088 (b2), respectively.
Results from Ref. 1.
Theoretical label assignments of Ref. 4 are different from those of the present results. In most cases, their leading configuration corresponds to the second dominant one of our results.
Experimental assignment of this level is 3163, while the present calculation shows almost the same amount of contribution from 5162.
Experimental assignment of this level is 315161.
Table 3
Comparison of Theoretical a1 Vibrational Energy Levels in the 8000–8300-cm−1 Range
State assignments are made in the same way as in Table 2.
Results from a sixth-order Van Vleck perturbation theory calculation by Sibert.5
Not explicitly calculated by Sibert.
Table 4
Selected Vibrational Energy Levels (in Inverse Centimeters) of X1A1 Formaldehyde (J = 0)
State assignments are made in the same way as in Table 2, except the 90th state of a1 symmetry. ith root among the states of given symmetry.
Dispersion of basis states calculated from Eq. (6).
Variational results using Nmax = 14.
Results from Ref. 1.
All coefficients are less than 0.33; labels listed have coefficients larger than 0.27.
Band origin used in Ref. 2.
Table 5
Coriolis Interaction Matrix Elements in the Region of the 2244 Level Calculated in the (J = 0) Eigenstate Basisa
, where υ = 2244 eigenlevel. Only a primary Coriolis perturbation team, −ΣμaaJaΠa, was considered as H′.
Labels listed have coefficients larger than 0.20.
Energy separation relative to the 2244 level (8021.3 cm−1). f(J, Ka) = −[J(J + 1) − Ka(Ka ± 1)]1/2 for Ka′ = Ka ± 1.
State assignments are determined from the present results. These assignments corresponds to the zero-order basis functions that make more than a 10% contribution to the total wave function.
Results from Ref. 4.
Results from a sixth-order Van Vleck perturbation theory calculation by Sibert.5
Variational results using Nmax = 14; Hamiltonian matrix dimensions of each symmetry are 11628 (a1), 7812 (a2), 8232 (b1), and 11088 (b2), respectively.
Results from Ref. 1.
Theoretical label assignments of Ref. 4 are different from those of the present results. In most cases, their leading configuration corresponds to the second dominant one of our results.
Experimental assignment of this level is 3163, while the present calculation shows almost the same amount of contribution from 5162.
Experimental assignment of this level is 315161.
Table 3
Comparison of Theoretical a1 Vibrational Energy Levels in the 8000–8300-cm−1 Range
State assignments are made in the same way as in Table 2.
Results from a sixth-order Van Vleck perturbation theory calculation by Sibert.5
Not explicitly calculated by Sibert.
Table 4
Selected Vibrational Energy Levels (in Inverse Centimeters) of X1A1 Formaldehyde (J = 0)
State assignments are made in the same way as in Table 2, except the 90th state of a1 symmetry. ith root among the states of given symmetry.
Dispersion of basis states calculated from Eq. (6).
Variational results using Nmax = 14.
Results from Ref. 1.
All coefficients are less than 0.33; labels listed have coefficients larger than 0.27.
Band origin used in Ref. 2.
Table 5
Coriolis Interaction Matrix Elements in the Region of the 2244 Level Calculated in the (J = 0) Eigenstate Basisa
, where υ = 2244 eigenlevel. Only a primary Coriolis perturbation team, −ΣμaaJaΠa, was considered as H′.
Labels listed have coefficients larger than 0.20.
Energy separation relative to the 2244 level (8021.3 cm−1). f(J, Ka) = −[J(J + 1) − Ka(Ka ± 1)]1/2 for Ka′ = Ka ± 1.
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