EDF: Computing electron number probability distribution functions in real space from molecular wave functions

Given an N  -electron molecule and an exhaustive partition of the real space (R3R3) into m   arbitrary regions Ω1,Ω2,…,ΩmΩ1,Ω2,…,Ωm (⋃i=1mΩi=R3), the edf program computes all the probabilities P(n1,n2,…,nm)P(n1,n2,…,nm) of having exactly n1n1 electrons in Ω1Ω1, n2n2 electrons in Ω2,…, and nmnm electrons (n1+n2+⋯+nm=Nn1+n2+⋯+nm=N) in ΩmΩm. Each ΩiΩi may correspond to a single basin (atomic domain) or several such basins (functional group). In the later case, each atomic domain must belong to a single ΩiΩi. The program can manage both single- and multi-determinant wave functions which are read in from an aimpac-like wave function description (.wfn) file (T.A. Keith et al., The AIMPAC95 programs, http://www.chemistry.mcmaster.ca/aimpac, 1995). For multi-determinantal wave functions a generalization of the original .wfn file has been introduced. The new format is completely backwards compatible, adding to the previous structure a description of the configuration interaction (CI) coefficients and the determinants of correlated wave functions. Besides the .wfn file, edf only needs the overlap integrals over all the atomic domains between the molecular orbitals (MO). After the P(n1,n2,…,nm)P(n1,n2,…,nm) probabilities are computed, edf obtains from them several magnitudes relevant to chemical bonding theory, such as average electronic populations and localization/delocalization indices. Regarding spin, edf may be used in two ways: with or without a splitting of the P(n1,n2,…,nm)P(n1,n2,…,nm) probabilities into α and β spin components.Program summaryProgram title: edfCatalogue identifier: AEAJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5387No. of bytes in distributed program, including test data, etc.: 52 381Distribution format: tar.gzProgramming language: Fortran 77Computer: 2.80 GHz Intel Pentium IV CPUOperating system: GNU/LinuxRAM: 55 992 KBWord size: 32 bitsClassification: 2.7External routines: NetlibNature 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})P(n1,n2,…,nm)≡P({np}) of all possible allocations of n1n1 electrons to Ω1Ω1, n2n2 electrons to Ω2,…, and nmnm electrons to Ωm,{np}Ωm,{np} being integers.Solution method: Let us assume that the N  -electron molecular wave function, Ψ(1,N)Ψ(1,N), is a linear combination of M   Slater determinants, Ψ(1,N)=∑rMCrψr(1,N). Calling SΩkrs the overlap matrix over the 3D region ΩkΩk between the (real) molecular spin-orbitals (MSO) in ψr(χ1r,…χNr) and the MSOs in ψs,(χ1s,…,χNs), edf finds all the P({np})P({np})'s by solving the linear systemequation(1)∑{np}{∏kmtknk}P({np})=∑r,sMCrCsdet[∑kmtkSΩkrs], where tm=1tm=1 and t1,…,tm−1t1,…,tm−1 are arbitrary real numbers.Restrictions:   The number of {np}{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.References:[1] A. Martín Pendás, E. Francisco, M.A. Blanco, Faraday Discuss. 135 (2007) 423–438.[2] A. Martín Pendás, E. Francisco, M.A. Blanco, J. Phys. Chem. A 111 (2007) 1084–1090.[3] A. Martín Pendás, E. Francisco, M.A. Blanco, Phys. Chem. Chem. Phys. 9 (2007) 1087–1092.[4] E. Francisco, A. Martín Pendás, M.A. Blanco, J. Chem. Phys. 126 (2007) 094102.[5] A. Martín Pendás, E. Francisco, M.A. Blanco, C. Gatti, Chemistry: A European Journal 113 (2007) 9362–9371.