Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors

Gatti, Fabien; Iung, Christophe; Menou, Michel J.; Justum, Yves; Nauts, André; Chapuisat, Xavier

doi:10.1063/1.476327

Cited by 157 publications

(112 citation statements)

References 56 publications

Supporting

Mentioning

109

Contrasting

Unclassified

Order By: Relevance

“…Most methods of deriving kinetic energy operators follow one of two routes: (1) obtain the classical kinetic energy expression and then quantize it (usually using the procedure of Podolsky [105]) or (2) use the chain rule to transform a known quantum mechanical KEO (usually the space-fixed Cartesian KEO) to derive a new KEO. Chapuisat and co-workers [99][100][101][106][107][108] have advocated the first route. Sutcliffe and Tennyson [109][110][111][112][113] and Handy [114] were early proponents of the second route.…”

Section: Representations Of the Kinetic Energy Operatormentioning

confidence: 99%

See 1 more Smart Citation

Variational quantum approaches for computing vibrational energies of polyatomic molecules

2008

View full text Add to dashboard Cite

In this article we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) are represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as sum of products. It then exploits the powerful multiconfiguration Hartree time dependent method to solve the time-dependent Schrödinger equation and extract the eigenvalue spectrum. The third approach we present uses contracted basis functions in conjunction with a Lanczos eigensolver. Matrix vector products are done without transforming to a direct-product grid. The usefulness of these methods is demonstrated for several example molecules, e.g., methane, methanol and the Zundel cation.2

show abstract

Section: Representations Of the Kinetic Energy Operatormentioning

confidence: 99%

“…The KEO in these coordinates is given in many papers. [100,102,115,116]. One convenient form [117] is,…”

Section: Representations Of the Kinetic Energy Operatormentioning

confidence: 99%

Variational quantum approaches for computing vibrational energies of polyatomic molecules

2008

View full text Add to dashboard Cite

show abstract

“…An alternative is to store an intermediate matrix [6,54]. To explain how this is done, consider a (J = 0) Hamiltonian in polyspherical coordinates [55][56][57] …”

Section: Evaluating Matrix-vector Products Without Storing a Vector Amentioning

confidence: 99%

“…The functions B i (r) and the operators T (i) b (θ) are known [55,56,58]. One constructs contracted bend functions from a Hamiltonian obtained by fixing the stretch coordinates at some reference geometry and contracted stretch functions from a Hamiltonian obtained by fixing all the bend coordinates at reference values.…”

Section: Evaluating Matrix-vector Products Without Storing a Vector Amentioning

confidence: 99%

Iterative Methods for Computing Vibrational Spectra

Carrington

2018

Mathematics

View full text Add to dashboard Cite

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.

show abstract

“…59,61 To explain how this is done, consider a (J = 0) Hamiltonian in orthogonal polyspherical coordinates, [117][118][119] …”

Section: General Pes/iterative-eigensolver/contracted-basis (G/i/cmentioning

confidence: 99%

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

Carrington

2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

In this perspective, I review methods for computing (ro-)vibrational energy levels and wavefunctions of molecules with more than four atoms. I identify three problems one confronts (1) reducing the size of the basis; (2) computing hundreds of eigenvalues and eigenvectors of a large matrix; (3) calculating matrix elements of the potential, and present ideas that mitigate them. Most modern methods use a combination of these ideas. I divide popular methods into groups based on the strategies used to deal with the three problems. Published by AIP Publishing. [http://dx

show abstract

Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors

Cited by 157 publications

References 56 publications

Variational quantum approaches for computing vibrational energies of polyatomic molecules

Variational quantum approaches for computing vibrational energies of polyatomic molecules

Iterative Methods for Computing Vibrational Spectra

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

Contact Info

Product

Resources

About