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

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].

1994 ◽  
Vol 72 (5-6) ◽  
pp. 238-249 ◽  
Author(s):  
James K. G. Watson

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].


1992 ◽  
Vol 97 (6) ◽  
pp. 4255-4263 ◽  
Author(s):  
Joseph A. Bentley ◽  
Robert E. Wyatt ◽  
Michel Menou ◽  
Claude Leforestier

1994 ◽  
Vol 72 (11-12) ◽  
pp. 1016-1027 ◽  
Author(s):  
W. A. Majewski ◽  
A. R. W. McKellar ◽  
D. Sadovskii ◽  
J. K. G. Watson

The coverage of the infrared spectrum of the [Formula: see text] molecular ion is extended by further measurements of the emission from a small high-pressure hollow-cathode electrical discharge cell, using the pressure-dependence of the intensities to distinguish the lines of [Formula: see text] from the many lies due to electronic transitions of H2 in the same region. The lines were assigned by means of calculations with a large vibration–rotation basis, using a Morse-based discrete variable representation for the vibrations. Eight coefficients in the Meyer–Botschwina–Burton ab initio potential were adjusted in order to fit 621 lines of [Formula: see text] from this and previous work with a standard deviation of 0.118 cm−1.


2017 ◽  
Vol 19 (17) ◽  
pp. 10843-10853 ◽  
Author(s):  
Alan R. Baggio ◽  
Daniel F. S. Machado ◽  
Valter H. Carvalho-Silva ◽  
Leonardo G. Paterno ◽  
Heibbe Cristhian B. de Oliveira

We developed an adapted theoretical approach based on DFT calculations (B3LYP) and the nuclear Schrödinger equation using the Discrete Variable Representation method to model the interaction of ammonia with metallo-phthalocyanines.


2021 ◽  
Vol 323 ◽  
pp. 14-20
Author(s):  
Naranchimeg Dagviikhorol ◽  
Munkhsaikhan Gonchigsuren ◽  
Lochin Khenmedekh ◽  
Namsrai Tsogbadrakh ◽  
Ochir Sukh

We have calculated the energies of excited states for the He, Li, and Be atoms by the time dependent self-consistent Kohn Sham equation using the Coulomb Wave Function Discrete Variable Representation CWDVR) approach. The CWDVR approach was used the uniform and optimal spatial grid discretization to the solution of the Kohn-Sham equation for the excited states of atoms. Our results suggest that the CWDVR approach is an efficient and precise solutions of excited-state energies of atoms. We have shown that the calculated electronic energies of excited states for the He, Li, and Be atoms agree with the other researcher values.


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