On the determination of the potential functions of H2Co, PH3, and CH4 molecules based on experimental data

Abstract

539.194 In the present work, a method of determining multidimensional potential surfaces of polyatomic molecules is suggested. The method is based on the use of high-accuracy data on the vibrational-rotational band centers and results of vibrational-rotational theory. Results of application of the method to the CH 4 , PH 3 , AsH 3 , and H 2 CO molecules are presented.Determination of the intramolecular potential function (IMPF) of a molecule is one of the basic problems in physics, since the knowledge of the potential function (the potential surface) of this or that electronic state allows both the vibrational-rotational energy spectrum and the corresponding functions of states to be determined by means of direct quantum-mechanical calculations. In turn, the knowledge of energies and functions of states is required to solve a huge number of purely academic and applied problems of physics and chemistry, astrophysics, laser technology, etc. As a consequence, over many tens of years much attention has been given to the problem of determining the intramolecular potential surfaces of molecules. Moreover, up to the 80s of the twentieth century, the semiempirical method based on the use of quantitative data on vibrational-rotational (α β λ ) and anharmonic parameters (x λμ ) was the main method of solving this problem [1]. In the last few years, in connection with considerably increased possibilities of the computer facilities, two other approaches to the determination of the IMPF of molecules have been put forward: ab initio [2-4] and variational methods [5][6][7][8]. Allowing in principle to solve the problem for any arbitrary polyatomic molecules, both approaches have a number of serious disadvantages in practical application, connected first of all with the possibilities of the computer facilities. In particular, at present ab initio calculations even for molecules with a small number of electrons yield the results whose accuracy is by many orders of magnitude lower than the accuracy of a modern experiment in the IR and visible ranges of the spectrum. As to the variational methods, they, allowing one to perform calculations with high accuracy, by virtue of their specificity are applicable only to molecules with small (three or four) number of atoms. Already for five-atomic molecules, difficulties arise in the problem solution (see, for example, [8-10]), connected primarily with the need for the introduction of special coordinate transformations for the Hamiltonian of a concrete molecule and, which is much more important, with matrices of huge dimensions (up to 10 6 × 10 7 ). In connection with the aforesaid, extremely important and actual problem is the development of alternative approaches which would ideally allow one to determine the IMPF for any arbitrary molecule with the number of atoms greater than 4-5.Such method which, possessing the advantages of the above-mentioned approaches, is free from the majority of their disadvantages, has been developed in the Laboratory of Molecular Spectroscopy of Tomsk Stat...

A new “spectroscopic” potential energy surface for formaldehyde in its ground electronic state

“…Similar fittings have been carried out by Mardis and Sibert 25 (rms deviation: 1.5 cm −1 for 139 term values) and by Bernal and Lemus 26 (rms deviation: 2.39 cm −1 for 260 states) who employed an algebraic local-mode model for the vibrational motion. Bekhtereva 27 and Ulenikov et al 28 generated empirically adjusted force constant values in global fittings to the vibrational band centers of H 2 CO, HDCO, and D 2 CO (rms deviation: 0.97 cm −1 for 254 levels).…”