### Abstract

We address the problem of expressing, in terms of an equation involving the one-particle density matrix, the boundary conditions that should be satisfied for a variationally consistent construction of three-dimensional partitions where a regional energy can be defined and the virial theorem satisfied. These conditions have been previously found in terms of a nonhermitian matrix P(1,1') (1 being a single particle index) which made its interpretation very difficult. We have found a simple expression connecting the one-matrix γ(1,1') and P(1,1') in terms of the virial operator. We have also found a closed expression for the gradient fields based on the matrix P(1,1') and the one-particle density ρ(1), which, in general, has very different structure. As an extension of our previous investigations for atoms and simple diatomic molecules, we have applied these results to carry out a comparison between the ρ- and P-based schemes for one-electron diatomic species using three variationally related trial wavefunctions. For quasi- atomic fragments constructed in both schemes, we express our results in terms of the fragment boundary shift as a function of a parameter, which is related to the ratio of nuclear charges of the two nuclei. For our trial wavefunction, we obtain an explicit relationship for the boundary shift in both schemes. We also performed a sensitivity analysis regarding the quality of the wavefunction and found that the P-scheme is more robust than the ρ- based one for defining quasi-atoms. (C) 2000 Elsevier Science B.V.

Original language | English (US) |
---|---|

Pages (from-to) | 115-123 |

Number of pages | 9 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 501-502 |

DOIs | |

State | Published - Apr 28 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Generalized virial partitions
- One-particle density matrix
- P(1,1'); ρ(1)

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Computational Theory and Mathematics
- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Molecular Structure: THEOCHEM*,

*501-502*, 115-123. https://doi.org/10.1016/S0166-1280(99)00420-0

**Generalized virial partitions and the one-particle density matrix.** / Mujica, Vladimiro; Squitieri, E.; Nieto, P.

Research output: Contribution to journal › Article

*Journal of Molecular Structure: THEOCHEM*, vol. 501-502, pp. 115-123. https://doi.org/10.1016/S0166-1280(99)00420-0

}

TY - JOUR

T1 - Generalized virial partitions and the one-particle density matrix

AU - Mujica, Vladimiro

AU - Squitieri, E.

AU - Nieto, P.

PY - 2000/4/28

Y1 - 2000/4/28

N2 - We address the problem of expressing, in terms of an equation involving the one-particle density matrix, the boundary conditions that should be satisfied for a variationally consistent construction of three-dimensional partitions where a regional energy can be defined and the virial theorem satisfied. These conditions have been previously found in terms of a nonhermitian matrix P(1,1') (1 being a single particle index) which made its interpretation very difficult. We have found a simple expression connecting the one-matrix γ(1,1') and P(1,1') in terms of the virial operator. We have also found a closed expression for the gradient fields based on the matrix P(1,1') and the one-particle density ρ(1), which, in general, has very different structure. As an extension of our previous investigations for atoms and simple diatomic molecules, we have applied these results to carry out a comparison between the ρ- and P-based schemes for one-electron diatomic species using three variationally related trial wavefunctions. For quasi- atomic fragments constructed in both schemes, we express our results in terms of the fragment boundary shift as a function of a parameter, which is related to the ratio of nuclear charges of the two nuclei. For our trial wavefunction, we obtain an explicit relationship for the boundary shift in both schemes. We also performed a sensitivity analysis regarding the quality of the wavefunction and found that the P-scheme is more robust than the ρ- based one for defining quasi-atoms. (C) 2000 Elsevier Science B.V.

AB - We address the problem of expressing, in terms of an equation involving the one-particle density matrix, the boundary conditions that should be satisfied for a variationally consistent construction of three-dimensional partitions where a regional energy can be defined and the virial theorem satisfied. These conditions have been previously found in terms of a nonhermitian matrix P(1,1') (1 being a single particle index) which made its interpretation very difficult. We have found a simple expression connecting the one-matrix γ(1,1') and P(1,1') in terms of the virial operator. We have also found a closed expression for the gradient fields based on the matrix P(1,1') and the one-particle density ρ(1), which, in general, has very different structure. As an extension of our previous investigations for atoms and simple diatomic molecules, we have applied these results to carry out a comparison between the ρ- and P-based schemes for one-electron diatomic species using three variationally related trial wavefunctions. For quasi- atomic fragments constructed in both schemes, we express our results in terms of the fragment boundary shift as a function of a parameter, which is related to the ratio of nuclear charges of the two nuclei. For our trial wavefunction, we obtain an explicit relationship for the boundary shift in both schemes. We also performed a sensitivity analysis regarding the quality of the wavefunction and found that the P-scheme is more robust than the ρ- based one for defining quasi-atoms. (C) 2000 Elsevier Science B.V.

KW - Generalized virial partitions

KW - One-particle density matrix

KW - P(1,1'); ρ(1)

UR - http://www.scopus.com/inward/record.url?scp=18844476027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18844476027&partnerID=8YFLogxK

U2 - 10.1016/S0166-1280(99)00420-0

DO - 10.1016/S0166-1280(99)00420-0

M3 - Article

VL - 501-502

SP - 115

EP - 123

JO - Computational and Theoretical Chemistry

JF - Computational and Theoretical Chemistry

SN - 2210-271X

ER -