A numerical test on the equivalence of intramolecular potential expansions in normal and valence displacement coordinates for water

Abstract

The present study presents a numerical test on the equivalence of potential expansions in normal and valence displacement coordinate space by calculating the lower vibrational states in a variational procedure. The calculations are performed for HjO and they indicate that a fourth-order Taylor series expansion in valence coordinates is not well represented by an expansion in normal codrdinates which is truncated at fourth order.

Ab initio effective rotational Hamiltonians: A comparative study

“…The convergence of the first vibrational levels that are well‐determined experimentally, with the expansion order of the NRT methane PES33 in terms of normal coordinates along with the effect of the μ‐tensor expansion order in the ( J = 0)‐Watson Hamiltonian are displayed in Tables AI and AII of Appendix. Similar studies have been conducted in the past on different molecules and/or PES16, 54, 66–70, and the results obtained in this work essentially confirm previous findings. For the rest of the study, we have chosen a PES re‐expansion of 10th order in normal coordinates and a μ‐tensor second order expansion in H 0 (see Appendix for more details).…”

Alternative perturbation method for the molecular vibration–rotation problem

“…The coordinate transformation being a nonlinear one, we studied the effect of re‐expanding the original quartic potential to different orders as Maessen and Wolfsberg did for water 73. These authors used a numerical re‐expansion method; however, our analytic results perfectly parallel their findings.…”

High-Resolution Near Infrared Spectroscopy and Vibrational Dynamics of Dideuteromethane (CH2D2)

“…The vibrational spectroscopy and vibrational dynamics of polyatomic molecules on multidimensional Born−Oppenheimer potential hypersurfaces has been a long standing problem of molecular spectroscopy and molecular physics. − The traditional approach to relate spectra and properties of potential hypersurfaces has been to start out from the harmonic approximation and to derive anharmonic potential constants in a Taylor series expansion by means of fitting effective Hamiltonians derived from perturbation theory to experimental rovibrational spectra. − However, it was recognized some time ago that for an accurate description of the relation between spectra, vibrational dynamics, and potential hypersurfaces vibrational (and rovibrational) variational calculations are necessary. Max Wolfsberg and his colleagues have been among the pioneers in this field with early calculations on H 2 O and CH 2 O − about a quarter century ago. Over the years numerous calculations of increasing accuracy have been reported for these two semirigid molecules, and we quote here as examples (from a very large literature on the topic) only a few (see ref − and references cited therein).…”

“…[4][5][6][7][8][9][10][11][12] However, it was recognized some time ago that for an accurate description of the relation between spectra, vibrational dynamics, and potential hypersurfaces vibrational (and rovibrational) variational calculations are necessary. Max Wolfsberg and his colleagues have been among the pioneers in this field with early calculations on H 2 O and CH 2 O [13][14][15][16] about a quarter century ago. Over the years numerous calculations of increasing accuracy have been reported for these two semirigid molecules, and we quote here as examples (from a very large literature on the topic) only a few (see ref [17][18][19][20][21][22] and references cited therein).…”