The variational method for the calculation of RO-vibrational energy levels

Carter, S.; Handy, Nicholas C.

doi:10.1016/0167-7977(86)90006-7

Cited by 278 publications

(118 citation statements)

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“…Normal mode analyses are performed for Pd-Ng and Pd-Ng 2 by numerical differentiations of the counterpoise-corrected interaction energy V int,X for the most probable isotopic species ͑ 106 Pd, 40 Ar, 84 Kr, and 132 Xe͒. For triatomic compounds, Pd-Ng 2 ͑Ng= Ar, Kr, Xe͒ and Xe-Pd-Ng ͑Ng= He, Ne, Ar, Kr͒, we also carried out variational calculations to determine fundamental frequencies and low-lying vibrational energy levels using the RVIB3 code 29,30 in terms of three-dimensional interaction potential energy surfaces. To determine the potential energy surface, we calculated CCSD͑T͒ counterpoise-corrected energies at 196 points around the equilibrium structure and then fitted those energies to the fourth-order polynomials as…”

Section: Computational Detailsmentioning

confidence: 99%

“…To help the spectroa͒ scopic search of these new species, fundamental frequencies, overtones, and combination bands are evaluated for triatomic compounds by the variational method using the RVIB3 program developed by Carter and Handy. 29,30 Similar vibrational-rotational analysis is also performed for platinum-noble-gas triatomic molecules.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical prediction of noble-gas compounds: Ng–Pd–Ng and Ng–Pt–Ng

Taketsugu

Noro

2006

The Journal of Chemical Physics

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Following our recent study on Ng-Pt-Ng ͑Ng= Ar, Kr, Xe͒ ͓J. Chem. Phys. 123, 204321 ͑2005͔͒, the binding of noble-gas atoms with Pd atom has been investigated by the ab initio coupled cluster CCSD͑T͒ method with counterpoise corrections, including relativistic effects. It is shown that two Ng atoms bind with Pd atom in linear geometry due to the s-d hybridization in Pd where the second Ng atom attaches with much larger binding energy than the first. The binding energies are evaluated as 4.0, 10.2, and 21.5 kcal/ mol for Ar-Pd-Ar, Kr-Pd-Kr, and Xe-Pd-Xe, respectively, relative to the dissociation limit, Pd ͑ 1 S͒ + 2Ng. In the hybrid Ng complexes, the binding energies for XePd and Ng ͑=Ar, Kr͒ are evaluated as 4.0 and 6.9 kcal/ mol for XePd-Ar and XePd-Kr, respectively. The fundamental frequencies and low-lying vibrational-rotational energy levels are determined for each compound by the variational method, based on the three-dimensional near-equilibrium potential energy surface. Results of vibrational-rotational analyses for Ng-Pt-Ng ͑Ng= Ar, Kr, Xe͒ and XePt-Ng ͑Ng= He, Ne, Ar, Kr͒ compounds are also given.

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Section: Computational Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical prediction of noble-gas compounds: Ng–Pd–Ng and Ng–Pt–Ng

Taketsugu

Noro

2006

The Journal of Chemical Physics

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“…To solve the Schrödinger equation numerically in order to compute a vibrational or ro-vibrational spectrum, one often expands the wavefunctions of interest as linear combinations of known basis functions [1,2,3,4]. The expansion coefficients are typically obtained as components of eigenvectors of the basis representation of the Hamiltonian operator.…”

Section: Mathematical Methods For High-dimensional Problemsmentioning

confidence: 99%

Mathematical Methods in Quantum Molecular Dynamics

2016

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“…Many authors have implemented basis pruning strategies [16,18,19,53,62,63,[70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]. Although pruning has the obvious advantage that it decreases the size of the vectors one must store and the spectral range of the Hamiltonian matrix, if one uses an iterative method, it complicates the evaluation of MVPs.…”

Section: Using Pruning To Reduce Both Basis and Grid Sizementioning

confidence: 99%

Iterative Methods for Computing Vibrational Spectra

Carrington

2018

Mathematics

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I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate (F) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

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The variational method for the calculation of RO-vibrational energy levels

Cited by 278 publications

References 115 publications

Theoretical prediction of noble-gas compounds: Ng–Pd–Ng and Ng–Pt–Ng

Theoretical prediction of noble-gas compounds: Ng–Pd–Ng and Ng–Pt–Ng

Mathematical Methods in Quantum Molecular Dynamics

Iterative Methods for Computing Vibrational Spectra

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