Highly excited rovibrational states of small molecules

1990 ◽  
Vol 332 (1625) ◽  
pp. 329-341 ◽  
Keyword(s):  
First Principles ◽  
Energy Levels ◽  
Dipole Approximation ◽  
Rotational Spectrum ◽  
Discrete Variable Representation ◽  
Triatomic Molecules ◽  
Step Procedure ◽  
Variational Calculations ◽  
Rovibrational States ◽  
Variable Representation

The use of first principles variational calculations for the calculation of high-lying energy levels, wavefunctions and transition intensities for triatomic molecules is considered. Theoretical developments are considered, including the use of generalized internal coordinates, the use of a two-step procedure for rotationally excited systems and a finite element method known as the discrete variable representation. Illustrative calculations are presented including ones for H 2, LiCN and the Ar-N2 Van der Waals molecule. A first principles ‘rotational’ spectrum of H 2D+ is computed using states up to J = 30. The transition intensities in this spectrum are reproduced accurately in a frozen dipole approximation but are poorly represented by models that involve approximating the wavefunction.

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.

ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

2013 ◽  
Vol 12 (01) ◽  
pp. 1250107 ◽  
Author(s):  
BENHUI YANG ◽  
BILL POIRIER
Keyword(s):  
Quantum Dynamics ◽  
Bound States ◽  
Energy Levels ◽  
Effective Potentials ◽  
Spectral Transform ◽  
Physical Insight ◽  
Rovibrational States ◽  
Three Body ◽  
Massive Parallelization ◽  
Variable Representation

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN

1990 ◽  
Vol 332 (1625) ◽  
pp. 309-327 ◽  
Keyword(s):  
Potential Surface ◽  
Energy Levels ◽  
Energy Operator ◽  
High Energy ◽  
Exact Expression ◽  
Hamiltonian Matrix ◽  
Energy Potential ◽  
Advantages And Disadvantages ◽  
Variational Calculations ◽  
Rovibrational States

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca . 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm -1 , to about + 1 cm -1 , and the corresponding rotational constants to about +0.001 cm -1 . We use a hamiltonian expressed in internal coordinates r 1 , r 2 and 0 , using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y for the bond stretches and the interbond angle 0 . The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos 0 in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matrix is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form ; the dimensions of the final hamiltonian matrix vary from 240 x 240 to 1000 x 1000. We believe that our calculation is converged to better than 1 cm -1 at 18000 cm -1 . Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

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