### Resumé

Basic functions with singularities matching those of the actual orbitals have been tested in analytical Hartree-Fock calculations. Such functions should provide the most rapidly convergent basis set expansions. Exponential singularities at r=∞, characterized by certain "asymptotic exponents," have been identified by an asymptotic analysis of the Fock equation. Basis sets of Slater functions with these exponents give atomic energies and properties comparable to the most accurate existing analytical calculations, without significantly increasing the number of basis functions. No nonlinear optimizations were required. Calculations of the orbital moments 〈r^{n}〉 show that only moments with n≤N, the number of Slater basis functions, can be evaluated with accuracy, whether or not the exponents are optimized. This effect appears to be caused by the neglect of certain irrational powers in asymptotic forms of the orbitals. The results for molecules suggest that basis functions which more adequately describe the nuclear cusp singularities are required to reproduce the accuracy of numerical Hartree-Fock calculations.

Originalsprog | Engelsk |
---|---|

Tidsskrift | The Journal of Chemical Physics |

Vol/bind | 80 |

Udgave nummer | 2 |

Sider (fra-til) | 840-855 |

Antal sider | 16 |

ISSN | 0021-9606 |

DOI | |

Status | Udgivet - 1. jan. 1984 |

### Fingeraftryk

### Citer dette

*The Journal of Chemical Physics*,

*80*(2), 840-855. https://doi.org/10.1063/1.446738

}

*The Journal of Chemical Physics*, bind 80, nr. 2, s. 840-855. https://doi.org/10.1063/1.446738

**Accurate Hartree-Fock wave functions without exponent optimization.** / Davis, C. L.; Jensen, Hans Jörgen Aa; Monkhorst, Hendrik J.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - Accurate Hartree-Fock wave functions without exponent optimization

AU - Davis, C. L.

AU - Jensen, Hans Jörgen Aa

AU - Monkhorst, Hendrik J.

PY - 1984/1/1

Y1 - 1984/1/1

N2 - Basic functions with singularities matching those of the actual orbitals have been tested in analytical Hartree-Fock calculations. Such functions should provide the most rapidly convergent basis set expansions. Exponential singularities at r=∞, characterized by certain "asymptotic exponents," have been identified by an asymptotic analysis of the Fock equation. Basis sets of Slater functions with these exponents give atomic energies and properties comparable to the most accurate existing analytical calculations, without significantly increasing the number of basis functions. No nonlinear optimizations were required. Calculations of the orbital moments 〈rn〉 show that only moments with n≤N, the number of Slater basis functions, can be evaluated with accuracy, whether or not the exponents are optimized. This effect appears to be caused by the neglect of certain irrational powers in asymptotic forms of the orbitals. The results for molecules suggest that basis functions which more adequately describe the nuclear cusp singularities are required to reproduce the accuracy of numerical Hartree-Fock calculations.

AB - Basic functions with singularities matching those of the actual orbitals have been tested in analytical Hartree-Fock calculations. Such functions should provide the most rapidly convergent basis set expansions. Exponential singularities at r=∞, characterized by certain "asymptotic exponents," have been identified by an asymptotic analysis of the Fock equation. Basis sets of Slater functions with these exponents give atomic energies and properties comparable to the most accurate existing analytical calculations, without significantly increasing the number of basis functions. No nonlinear optimizations were required. Calculations of the orbital moments 〈rn〉 show that only moments with n≤N, the number of Slater basis functions, can be evaluated with accuracy, whether or not the exponents are optimized. This effect appears to be caused by the neglect of certain irrational powers in asymptotic forms of the orbitals. The results for molecules suggest that basis functions which more adequately describe the nuclear cusp singularities are required to reproduce the accuracy of numerical Hartree-Fock calculations.

UR - http://www.scopus.com/inward/record.url?scp=0343614796&partnerID=8YFLogxK

U2 - 10.1063/1.446738

DO - 10.1063/1.446738

M3 - Journal article

VL - 80

SP - 840

EP - 855

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

SN - 0021-9606

IS - 2

ER -