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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_0
Distribution 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(n1, n2,. . .,nm) ≡ P({np}) of all possible allocations of n1 electrons to Ω1, n2 electrons to Ω2,. . ., and nm electrons to Ωm, {np} being integers.

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) = ΣMrCrψr(1, N). Calling SrsΩk the overlap matrix over the 3D region Ωk between the (real) molecular spin-orbitals (MSO) in ψr (Xr1,. . . XrN) and the MSOs in ψs, (Xs1,. . . XsN), edf finds all the P({np}'s by solving the linear system
Σ{np}mk tnkk} P({np}) = ΣMr,sCrCs det[ΣmktkSrsΩk],                 (1)
where tm = 1 and t1, . . . , tm-1 are arbitrary real numbers.

The number of {np} sets grows very fast with 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.

[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.).