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[Licence| Download | New Version Template] aeaj_v2_0.tar.gz(201 Kbytes)
Manuscript Title: Electron number distribution functions from molecular wavefunctions. Version 2
Authors: E. Francisco, A. Martín Pendás
Program title: edf
Catalogue identifier: AEAJ_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)2663
Programming language: Fortran 77/90.
Computer: 2.80 GHz Intel Pentium IV CPU.
Operating system: GNU/Linux.
RAM: Dynamic
Keywords: Quantum theory of atoms in molecules, Electron probability distribution, Molecular wave function, Chemical bonding theory.
Classification: 2.7.

External routines: mkl

Does the new version supersede the previous version?: Yes

Nature of problem:
Given an N-electron molecule described by a single- or multi-determinant wavefunction Ψ(1,N), and a partition of the physical space R3 into m domains Ω1, Ω2, . . ., Ωm, edf computes the probabilities p(S) of having exactly n1, n2, . . ., and nm electrons in Ω1, Ω2, . . ., and Ωm, respectively, for all possible distributions S ≡ {n1, n2, . . . , nm}, being n1, n2, . . ., and nm integer numbers.

Solution method:
Given a wavefuntion Ψ(1,N) = ΣrMcrψr(1,N), where the ψr's are Slater determinants ψr = det[Xr1, . . . ,XrN], and calling (Skrs)ij the overlap integral within the domain Ωk between Xri and Xsj, edf finds all the p(S)'s using a three-step procedure:
(1) For each (r,s) pair, solve the linear system

Σ{nσi} t1n1σ t2n2σ . . . tmnmσ prs({nσi}) = det [Σmk=1tkSkrs]

in the unknowns prs({nσi}), where σ = (α,β), {nσi} (i = 1, 2, . . . ,m) are the integer electronic populations with spin σ of the domains Ω1, Ω2, . . ., Ωm, tm = 1, and t1, . . . ,tm-1 are arbitrary real numbers,
(2) Compute the spin-resolved probabilities
p({nα;nβ}) ≡ p({ip}) = ΣMr,scrcsprs({nαi}) prs({nβi}), and
(3) obtain the p(S)'s by adding up the p({ip})'s with nαi + nβi = ni

Reasons for new version:
Dynamic memory allocation instead of static memory allocation is used throughout. Further partitions of the 3D space have been added. Thanks to the change in the algorithm used to solve the problem, the new version is 1-2 orders of magnitude faster than the previous one and can deal with molecules having a greater number of electrons. Approximate calculations as well as exact ones are possible in the new version by making use of the core-valence separability.

Summary of revisions:
Most data structures are stored in dynamic memory. The basic algorithm has been changed to ensure a much faster computation of the probabilities p(S). Algorithms to obtain the latter in an approximate manner, as well as using different partitions of the 3D space have been included.

The number of {nσi} sets in Eq. 1, i.e. the dimension of the linear system to be solved, grows very fast with m and N. This dimension is much smaller than in the previous version of edf but, even so, this restricts the applicability of the method to relatively small systems, unless some drastic approximations are used (excluding, for instance, a large part of the electrons of the system from the calculation).

Running time:
0.016 and 0.004 seconds for the test examples 1 and 2, respectively. However, running times are very variable depending on the molecule, the type of the wavefunction (single - or multi-determinant), the number of fragments (m). etc.

[1] E. Francisco, A. Martín Pendás, and M. A. Blanco. J. Chem. Phys. 126, 094102 (2007).
[2] A. Martín Pendás,, E. Francisco, and M. A. Blanco. J. Chem. Phys. 127, 144103 (2007).
[3] E. Francisco, A. Martín Pendás, and M. A. Blanco. Computer Physics Commun. 178, 621-634 (2008).
[4] A. Martín Pendás, E. Francisco, and M. A. Blanco. Faraday Discuss. 135, 423-438 (2007).
[5] A. Martín Pendás, E. Francisco, M. A. Blanco, and C. Gatti. Chemistry: A European Journal. 13, 9362-9371 (2007).
[6] A. Martín Pendás, E. Francisco, and M. A. Blanco. Phys. Chem. Chem. Phys. 9, 1087-1092 (2007).
[7] E. Francisco, A. Martín Pendás, and M. A. Blanco. J. Chem. Phys. 131, 124125 (2009).
[8] E. Francisco, A. Martín Pendás, and M. A. Blanco. Theor. Chemistry Accounts. 128, 433 (2011).
[9] E. Francisco, A. Martín Pendás, A. Costales, and M. A. García-Revilla. Comput. Theor. Chem. 975, 2-8 (2011).
[10] M. A. García-Revilla, E. Francisco, A. Martín Pendás, J. M. Recio, M. Bartolomei, M. I. Hernández, J. Campos- Martínez, E. Carmona-Novillo, and R. Hernández-Lamoneda. J. Chem. Theory Comput. 9, 2179-2188 (2013).