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Manuscript Title: EDF: Computing electron number probability distribution functions in
real space from molecular wave functions. | ||

Authors: E. Francisco, A.
Martín Pendás, M. A. Blanco | ||

Program title: edf | ||

Catalogue identifier: AEAJ_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 178(2008)621 | ||

Programming language: Fortran 77. | ||

Computer: 2.80 GHz Intel Pentium IV CPU. | ||

Operating system: GNU/Linux. | ||

RAM: 55992 KB | ||

Word size: 32 bits | ||

Keywords: Quantum theory of atoms in molecules. Electron probability
distribution. Molecular wave function. Chemical bonding theory. | ||

PACS: 31.15.-p, 31.10.+z, 31.15.Ar, 02.70.-c. | ||

Classification: 2.7. | ||

External routines: Netlib | ||

Nature of problem:Let us have an N-electron molecule and define an
exhaustive partition of the physical space into m three-dimensional
regions. The edf program computes the probabilities
P(n, _{1}n,. . .,_{2}n)
≡ _{m}P({n}) of all possible allocations of
_{p}n electrons to Ω_{1}_{1}, n
electrons to Ω_{2}_{2},. . ., and n electrons to
Ω_{m}_{m}, {n} being integers._{p} | ||

Solution method:Let us assume that the N-electron molecular
wave function, Ψ(1, N), is a linear combination of M Slater
determinants, Ψ(1, N) =
Σ^{M}_{r}Cψ_{r}_{r}(1, N). Calling S^{rs}_{Ωk}
the overlap matrix over the 3D region Ω_{k} between the (real)
molecular spin-orbitals (MSO) in ψ_{r}
(X,. . . ^{r}_{1}X) and
the MSOs in ψ^{r}_{N}_{s}, (X,. . .
^{s}_{1}X), ^{s}_{N}edf finds all the
P({n}'s by solving the linear system _{p}Σ _{{np}} {Π^{m}_{k
}t} ^{nk}_{k}P({n}) =
Σ_{p}^{M}_{r,s}C
det[Σ_{r}C_{s}^{m}_{k}t_{k}S_{Ωk}],
(1)where t = 1 and _{m}t, . . . ,
_{1}t are arbitrary real numbers._{m-1} | ||

Restrictions:The number of { n} sets grows very fast
with _{p}m and N, so that the dimension of the linear system 1 soon
becomes very large. Moreover, the computer time required to obtain the
determinants in the second member of Eq. 1 scales quadratically with M.
These two facts limit the applicability of the method to relatively small
molecules. | ||

Unusual features:Most of the real variables are of precision real*16. | ||

Running time:0.030, 2.010, and 0.620 seconds for test examples 1, 2, and 3, respectively. | ||

References: | ||

[1] | A. Martín Pendás, E. Francisco, and M. A. Blanco. Faraday Discuss.135, 423-438 (2007). | |

[2] | A. Martín Pendás, E. Francisco, and M. A. Blanco. J. Phys. Chem. A 111, 1084 1090 (2007). | |

[3] | A. Martín Pendás, E. Francisco, and M. A. Blanco. Phys. Chem. Chem. Phys. 9, 1087-1092 (2007). | |

[4] | E. Francisco, A. Martín Pendás and M. A. Blanco. J. Chem. Phys. 126, 094102 (2007). | |

[5] | A. Martín Pendás, E. Francisco, M. A. Blanco, and Carlo Gatti. Chemistry: A European Journal (in press.). |

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