New observations and analysis of the infrared vibration–rotation spectrum of H3+

1994 ◽  
Vol 72 (11-12) ◽  
pp. 1016-1027 ◽  
Author(s):  
W. A. Majewski ◽  
A. R. W. McKellar ◽  
D. Sadovskii ◽  
J. K. G. Watson
Keyword(s):  
High Pressure ◽  
Electrical Discharge ◽  
Electronic Transitions ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Vibration Rotation ◽  
The Many ◽  
Discharge Cell ◽  
Variable Representation ◽  
Rotation Spectrum

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.

The infrared vibration–rotation spectrum of the molecular ion: extension to higher vibrational and rotational quantum numbers

1994 ◽  
Vol 72 (11-12) ◽  
pp. 1007-1015 ◽  
Author(s):  
T. Amano ◽  
M.-C. Chan ◽  
S. Civis ◽  
A. R. W. McKellar ◽  
W. A. Majewski ◽  
...  
Keyword(s):  
Amplitude Modulation ◽  
Hollow Cathode ◽  
Discrete Variable Representation ◽  
Molecular Ion ◽  
Overtone Band ◽  
Quantum Numbers ◽  
Vibration Rotation ◽  
Deuterium Gas ◽  
Variable Representation ◽  
Rotation Spectrum

The assigned infrared spectrum of the [Formula: see text] molecular ion is extended from 84 to 529 lines by three types of spectroscopic measurements on hollow-cathode electrical discharges through deuterium gas: (i) emission from a small hollow cathode, in which the [Formula: see text] lines were distinguished from the electronic transitions of D2 by the pressure dependence of their intensities; (ii) absorption in the same hollow cathode with discharge amplitude modulation; and (iii) absorption in a larger hollow cathode cell with discharge amplitude modulation. The observed lines belong mainly to the [Formula: see text] fundamental and its hot bands [Formula: see text], [Formula: see text] and [Formula: see text] in the 1330–2530 cm−1 region in experiments (i) and (ii), and to the first overtone band [Formula: see text] in the 3160–4000 cm−1 region in experiment (iii). The lines were assigned by means of calculations with a large vibration–rotation basis, using a Morse-based discrete variable representation for the vibrations. This method overcomes the convergence problems for the centrifugal terms in the effective Hamiltonian approach. Six coefficients in the Meyer–Botschwina–Burton ab initio potential were adjusted in order to fit these data with a standard deviation of 0.059 cm−1.

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].

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].

Rovibrational spectroscopic constants of the interaction between ammonia and metallo-phthalocyanines: a theoretical protocol for ammonia sensor design

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
Keyword(s):  
Dft Calculations ◽  
Theoretical Approach ◽  
Schrodinger Equation ◽  
Spectroscopic Constants ◽  
Sensor Design ◽  
Discrete Variable ◽  
Ammonia Sensor ◽  
Discrete Variable Representation ◽  
Representation Method ◽  
Variable Representation

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.

Imaginary-Time Time-Dependent Density Functional Calculation of Excited States of Atoms Using CWDVR Approach

2021 ◽  
Vol 323 ◽  
pp. 14-20
Author(s):  
Naranchimeg Dagviikhorol ◽  
Munkhsaikhan Gonchigsuren ◽  
Lochin Khenmedekh ◽  
Namsrai Tsogbadrakh ◽  
Ochir Sukh
Keyword(s):  
Excited States ◽  
Density Functional ◽  
Time Dependent ◽  
Discrete Variable ◽  
Coulomb Wave Function ◽  
Discrete Variable Representation ◽  
Density Functional Calculation ◽  
Imaginary Time ◽  
Sham Equation ◽  
Variable Representation

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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