### Abstract

The recent idea of extracting effective atomic Orbitals from molecular wave functions by performing independent localization transformations for each atom separately is generalized to the case of an arbitrary Hermitian bilinear localization functional. The general equations are derived and the orthogonality relationships pertinent to the localized molecular orbitals are proved. The "intraatomic components" of these localized orbitals form an effective atomic basis, which is also automatically orthogonal if some conditions are fulfilled. Several different localization functionals are considered and it is shown that for the simplest one the orbitals obtained are natural hybrids in McWeeny's sense and are conceptually close to (but not identical,with) Weinhold's "natural hybrid orbitals". In this case one obtains for each atom of a "usual" molecule as many effective AOs of appreciable importance as the number of orbitals contained in the classical "minimal basis" of that atom, forming therefore a-distorted but still orthogonal-effective minimal basis of the atom within the molecule. The similarities and differences with Weinhold's "atomic natural orbitals" are also discussed. It is pointed out that by selecting a proper localization functional, the present approach can also be used to define the effective atomic orbitals in a basis-free manner, i.e. even if no atom-centered basis was used in calculating the wave function. A possibility of generalization for correlated wave functions is also suggested.

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

Pages (from-to) | 6249-6257 |

Number of pages | 9 |

Journal | Journal of Physical Chemistry |

Volume | 100 |

Issue number | 15 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Engineering(all)

### Cite this

*Journal of Physical Chemistry*,

*100*(15), 6249-6257.

**Atomic orbitals from molecular wave functions : the effective minimal basis.** / Mayer, I.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 100, no. 15, pp. 6249-6257.

}

TY - JOUR

T1 - Atomic orbitals from molecular wave functions

T2 - the effective minimal basis

AU - Mayer, I.

PY - 1996

Y1 - 1996

N2 - The recent idea of extracting effective atomic Orbitals from molecular wave functions by performing independent localization transformations for each atom separately is generalized to the case of an arbitrary Hermitian bilinear localization functional. The general equations are derived and the orthogonality relationships pertinent to the localized molecular orbitals are proved. The "intraatomic components" of these localized orbitals form an effective atomic basis, which is also automatically orthogonal if some conditions are fulfilled. Several different localization functionals are considered and it is shown that for the simplest one the orbitals obtained are natural hybrids in McWeeny's sense and are conceptually close to (but not identical,with) Weinhold's "natural hybrid orbitals". In this case one obtains for each atom of a "usual" molecule as many effective AOs of appreciable importance as the number of orbitals contained in the classical "minimal basis" of that atom, forming therefore a-distorted but still orthogonal-effective minimal basis of the atom within the molecule. The similarities and differences with Weinhold's "atomic natural orbitals" are also discussed. It is pointed out that by selecting a proper localization functional, the present approach can also be used to define the effective atomic orbitals in a basis-free manner, i.e. even if no atom-centered basis was used in calculating the wave function. A possibility of generalization for correlated wave functions is also suggested.

AB - The recent idea of extracting effective atomic Orbitals from molecular wave functions by performing independent localization transformations for each atom separately is generalized to the case of an arbitrary Hermitian bilinear localization functional. The general equations are derived and the orthogonality relationships pertinent to the localized molecular orbitals are proved. The "intraatomic components" of these localized orbitals form an effective atomic basis, which is also automatically orthogonal if some conditions are fulfilled. Several different localization functionals are considered and it is shown that for the simplest one the orbitals obtained are natural hybrids in McWeeny's sense and are conceptually close to (but not identical,with) Weinhold's "natural hybrid orbitals". In this case one obtains for each atom of a "usual" molecule as many effective AOs of appreciable importance as the number of orbitals contained in the classical "minimal basis" of that atom, forming therefore a-distorted but still orthogonal-effective minimal basis of the atom within the molecule. The similarities and differences with Weinhold's "atomic natural orbitals" are also discussed. It is pointed out that by selecting a proper localization functional, the present approach can also be used to define the effective atomic orbitals in a basis-free manner, i.e. even if no atom-centered basis was used in calculating the wave function. A possibility of generalization for correlated wave functions is also suggested.

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UR - http://www.scopus.com/inward/citedby.url?scp=0030123546&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030123546

VL - 100

SP - 6249

EP - 6257

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 15

ER -