### Abstract

Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Comparison of the two methods is presented in the context of evaluation of matrix elements in a non-direct product basis. If high accuracy of all matrix elements is required then the expansion method is the best choice. If however the accuracy of high order matrix elements is not important (as in variational ro-vibrational calculations where one is typically interested only in the lowest eigenstates), then the method based on the reduced grid offers sufficient accuracy and is much quicker than the expansion method. (C) 2004 Elsevier B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 10-14 |

Number of pages | 4 |

Journal | Computer Physics Communications |

Volume | 165 |

Issue number | 165 |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- N-ATOM PROBLEM
- QUANTUM-MECHANICS
- VECTOR PARAMETRIZATION
- MOLECULES
- TRANSFORMS
- ACETYLENE

### Cite this

*Computer Physics Communications*,

*165*(165), 10-14. https://doi.org/10.1016/j.cpc.2003.12.007

**Effective computation of matrix elements between polynomial basis functions.** / Kozin, I. N.; Tennyson, J.; Law, Mark McGregor.

Research output: Contribution to journal › Article

*Computer Physics Communications*, vol. 165, no. 165, pp. 10-14. https://doi.org/10.1016/j.cpc.2003.12.007

}

TY - JOUR

T1 - Effective computation of matrix elements between polynomial basis functions

AU - Kozin, I. N.

AU - Tennyson, J.

AU - Law, Mark McGregor

PY - 2005

Y1 - 2005

N2 - Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Comparison of the two methods is presented in the context of evaluation of matrix elements in a non-direct product basis. If high accuracy of all matrix elements is required then the expansion method is the best choice. If however the accuracy of high order matrix elements is not important (as in variational ro-vibrational calculations where one is typically interested only in the lowest eigenstates), then the method based on the reduced grid offers sufficient accuracy and is much quicker than the expansion method. (C) 2004 Elsevier B.V. All rights reserved.

AB - Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Comparison of the two methods is presented in the context of evaluation of matrix elements in a non-direct product basis. If high accuracy of all matrix elements is required then the expansion method is the best choice. If however the accuracy of high order matrix elements is not important (as in variational ro-vibrational calculations where one is typically interested only in the lowest eigenstates), then the method based on the reduced grid offers sufficient accuracy and is much quicker than the expansion method. (C) 2004 Elsevier B.V. All rights reserved.

KW - N-ATOM PROBLEM

KW - QUANTUM-MECHANICS

KW - VECTOR PARAMETRIZATION

KW - MOLECULES

KW - TRANSFORMS

KW - ACETYLENE

U2 - 10.1016/j.cpc.2003.12.007

DO - 10.1016/j.cpc.2003.12.007

M3 - Article

VL - 165

SP - 10

EP - 14

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 165

ER -