Highly excited vibrational levels of ‘‘floppy’’ triatomic molecules: A discrete variable representation—Distributed Gaussian basis approach

1986 ◽  
Vol 85 (8) ◽  
pp. 4594-4604 ◽  
Author(s):  
Z. Bac̆ić ◽  
J. C. Light
Keyword(s):  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Triatomic Molecules ◽  
Vibrational Levels ◽  
Variable Representation

A finite basis‐discrete variable representation calculation of vibrational levels of planar acetylene

1992 ◽  
Vol 97 (6) ◽  
pp. 4255-4263 ◽  
Author(s):  
Joseph A. Bentley ◽  
Robert E. Wyatt ◽  
Michel Menou ◽  
Claude Leforestier
Keyword(s):  
Finite Basis ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Vibrational Levels ◽  
Variable Representation

Vibration–rotation calculations for using a Morse-based discrete variable representation

1994 ◽  
Vol 72 (5-6) ◽  
pp. 238-249 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Hamiltonian Operator ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Least Squares Fit ◽  
Vibrational Levels ◽  
Internuclear Distances ◽  
Complete Set ◽  
Vibration Rotation ◽  
Set Up ◽  
Variable Representation

The Hamiltonian operator for the X3 symmetric triatomic molecule, using Eckart axes with the three internuclear distances as internal coordinates, is derived and applied to numerical calculations of the vibration–rotation spectrum of [Formula: see text]. A C2ν-symmetrized discrete variable representation based on Morse functions is employed for the J = 0 vibrational problem. The unphysical points with ri < 0 or ri + rj < rk are avoided by giving them a large potential energy (106 cm−1). This procedure is not exact, but is adequate for vibrational levels well below the barrier to linearity. The matrices of the complete Hamiltonian in a D3h-symmetrized basis of products of the lowest 50 vibrational eigenvectors with the complete set of rotational functions for each J are set up and diagonalized, and the eigenvectors are used to calculate line strengths. Initially, the well-known potential surface of Meyer et al. (1986) was employed. Subsequently, 7 of the 30 coefficients in this potential were adjusted to give a least-squares fit to the published observed lines of [Formula: see text].

Vibration spectrum calculations of isotopic species of hydrogen sulfide using the discrete variable representation (DVR) method

2013 ◽  
Vol 91 (10) ◽  
pp. 815-821 ◽  
Author(s):  
Ang-yang Yu
Keyword(s):  
Hydrogen Sulfide ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Vibration Energy ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Triatomic Molecules ◽  
Isotopic Species ◽  
Variable Representation

In this work, a modified three-dimensional discrete variable representation (MDVR3D) program, which could be used to calculate the bound state vibration spectrum of some triatomic molecules is developed. The sine basis functions are chosen to define the DVR for the radial coordinates for this new program. Both the three-dimensional discrete variable representation (DVR3D) program and the MDVR3D program are used to calculate the vibration energy levels of the isotopic species of hydrogen sulfide (H232S, H233S, H234S, D232S, D233S, D234S, T232S, T233S, T234S). The calculated vibration energy levels from the MDVR3D program are consistent with the counterparts from the DVR3D program, which means that they are good procedures for calculating the bound state energy levels of the triatomic molecules and testing the quality of the potential energy surface (PES). The comparison of the experimental and theoretical vibration energy levels for the nine isotopic species of hydrogen sulfide molecule is made and shows good consistency. This work forms the basis for dealing with the rotational spectrum calculations and presents the first theoretical results for D233S, T232S, T233S, and T234S. Future spectrum observations are needed to compare with these new results.

Erratum: Vibration–rotation calculations for using a Morse-based discrete variable representation

1994 ◽  
Vol 72 (9-10) ◽  
pp. 702-713 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Hamiltonian Operator ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Least Squares Fit ◽  
Vibrational Levels ◽  
Internuclear Distances ◽  
Complete Set ◽  
Vibration Rotation ◽  
Set Up ◽  
Variable Representation

The Hamiltonian operator for the X3 symmetric triatomic molecule, using Eckart axes with the three internuclear distances as internal coordinates, is derived and applied to numerical calculations of the vibration–rotation spectrum of [Formula: see text]. A C2v-symmetrized discrete variable representation based on Morse functions is employed for the J = 0 vibrational problem. The unphysical points with ri < 0 or ri + rj < rk are avoided by giving them a large potential energy (106 cm−1). This procedure is not exact, but is adequate for vibrational levels well below the barrier to linearity. The matrices of the complete Hamiltonian in a D3h-symmetrized basis of products of the lowest 50 vibrational eigenvectors with the complete set of rotational functions for each J are set up and diagonalized, and the eigenvectors are used to calculate line strengths. Initially, the well-known potential surface of Meyer et al. (1986) was employed. Subsequently, 7 of the 30 coefficients in this potential were adjusted to give a least-squares fit to the published observed lines of [Formula: see text].

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