142
S. Rashev and D.C. Moule
to calculate 729 A 1 symmetry states up to 13500 cm −1 of excess vibrational energy, based on a slightly modified version of the Burleigh et al. adjusted PES [14].
More recently, Yachmenev et al. [24] produced an ab initio PES for ground electronic state formaldehyde, that surpassed the quality of the MLT field [22] being closer to spectroscopic accuracy. The authors [24] designed an analytical expression for their field, determined by 110 parameters. Next, these authors varied the values of the parameters, aiming to obtain a PES of spectroscopic accuracy.
In our recent work we described and implemented an alternative method [26] for
the calculation of exact frequencies in S 0 formaldehyde that is based on the exact
kinetic energy expression [25], a PES expression that should be given in separable
form (as a sum of products; the quartic expression [22] and the analytical expression [24] satisfy this requirement) and the employment of a specific iterative procedure for deriving the most economic Hamiltonian matrix of the vibrational problem,
complemented by a Lanczos manipulation of the Hamiltonian matrix. The main asset of our method is the possibility to achieve arbitrarily high precision as well as
to extend the calculations to extremely high vibrational excitation energies [26–29].
We first assessed the performance of our method [26], by reproducing exactly the
vibrational energy levels of S 0 formaldehyde, corresponding to the ab initio MLT
PES, calculated earlier by Carter et al. [11] and Luckhaus [15] and next demonstrated the ability of our method to extend the calculations up to extremely high levels of vibrational excitation energy [26]. We also performed converged large scale
calculations on deuterated species D 2 CO [27] and HDCO [28, 29] and compared
the calculated frequencies to experimentally measured values. We also studied the
IVR behavior at very high vibrational excitations and compared the mode selectivity and vibrational redistribution of different formaldehyde isotopomers [26–29]. In
all these calculations the original ab initio MLT PES was used without any adjustment.
This work is organized as follows. In Sect. 8.2 we give a very brief description of our variational vibrational procedure for calculation of vibrational energy
levels, that has been described in detail in our recent work [26]. Next in Sect. 8.3
we first briefly describe our experience with the recently computed formaldehyde
PES by Yachmenev et al. [24] and then we describe our strategy employed for
adjustment of the force constants of the original MLT field to yield vibrational
frequencies of S 0 H 2 CO, possibly closest to a set of well defined experimentally
measured H 2 CO frequencies. In Sect. 8.4 we present the newly obtained set of
quartic force constants, and a selection of H 2 CO and HDCO vibrational level energies, calculated with this new set of force constants and compared to the experimentally measured frequencies. Finally in Sect. 8.5 we conclude. Our code for
computation of the obtained refined quartic PES is given in a supplement to this
work.
S. Rashev and D.C. Moule
to calculate 729 A 1 symmetry states up to 13500 cm −1 of excess vibrational energy, based on a slightly modified version of the Burleigh et al. adjusted PES [14].
More recently, Yachmenev et al. [24] produced an ab initio PES for ground electronic state formaldehyde, that surpassed the quality of the MLT field [22] being closer to spectroscopic accuracy. The authors [24] designed an analytical expression for their field, determined by 110 parameters. Next, these authors varied the values of the parameters, aiming to obtain a PES of spectroscopic accuracy.
In our recent work we described and implemented an alternative method [26] for
the calculation of exact frequencies in S 0 formaldehyde that is based on the exact
kinetic energy expression [25], a PES expression that should be given in separable
form (as a sum of products; the quartic expression [22] and the analytical expression [24] satisfy this requirement) and the employment of a specific iterative procedure for deriving the most economic Hamiltonian matrix of the vibrational problem,
complemented by a Lanczos manipulation of the Hamiltonian matrix. The main asset of our method is the possibility to achieve arbitrarily high precision as well as
to extend the calculations to extremely high vibrational excitation energies [26–29].
We first assessed the performance of our method [26], by reproducing exactly the
vibrational energy levels of S 0 formaldehyde, corresponding to the ab initio MLT
PES, calculated earlier by Carter et al. [11] and Luckhaus [15] and next demonstrated the ability of our method to extend the calculations up to extremely high levels of vibrational excitation energy [26]. We also performed converged large scale
calculations on deuterated species D 2 CO [27] and HDCO [28, 29] and compared
the calculated frequencies to experimentally measured values. We also studied the
IVR behavior at very high vibrational excitations and compared the mode selectivity and vibrational redistribution of different formaldehyde isotopomers [26–29]. In
all these calculations the original ab initio MLT PES was used without any adjustment.
This work is organized as follows. In Sect. 8.2 we give a very brief description of our variational vibrational procedure for calculation of vibrational energy
levels, that has been described in detail in our recent work [26]. Next in Sect. 8.3
we first briefly describe our experience with the recently computed formaldehyde
PES by Yachmenev et al. [24] and then we describe our strategy employed for
adjustment of the force constants of the original MLT field to yield vibrational
frequencies of S 0 H 2 CO, possibly closest to a set of well defined experimentally
measured H 2 CO frequencies. In Sect. 8.4 we present the newly obtained set of
quartic force constants, and a selection of H 2 CO and HDCO vibrational level energies, calculated with this new set of force constants and compared to the experimentally measured frequencies. Finally in Sect. 8.5 we conclude. Our code for
computation of the obtained refined quartic PES is given in a supplement to this
work.