Fortran 90 implementation of the Hartree–Fock approach within the CNDO/2 and INDO models

Despite the tremendous advances made by the ab initio theory of electronic structure of atoms and molecules, its applications are still not possible for very large systems. Therefore, semi-empirical model Hamiltonians based on the zero-differential overlap (ZDO) approach such as the Pariser–Parr–Pople, CNDO, INDO, etc. provide attractive, and computationally tractable, alternatives to the ab initio treatment of large systems. In this paper we describe a Fortran 90 computer program developed by us, that uses CNDO/2 and INDO methods to solve Hartree–Fock (HF) equation for molecular systems. The INDO method can be used for the molecules containing the first-row atoms, while the CNDO/2 method is applicable to those containing both the first-, and the second-row, atoms. We have paid particular attention to computational efficiency while developing the code, and, therefore, it allows us to perform calculations on large molecules such as C60 on small computers within a matter of seconds. Besides being able to compute the molecular orbitals and total energies, our code is also able to compute properties such as the electric dipole moment, Mulliken population analysis, and linear optical absorption spectrum of the system. We also demonstrate how the program can be used to compute the total energy per unit cell of a polymer. The applications presented in this paper include small organic and inorganic molecules, fullerene C60, and model polymeric systems, viz., chains containing alternating boron and nitrogen atoms (BN chain), and carbon atoms (C chain).Program summaryProgram title: cindo.xCatalogue identifier: AECN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECN_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.: 23 304No. of bytes in distributed program, including test data, etc.: 217 035Distribution format: tar.gzProgramming language: Fortran 90Computer: PC's/Linux, Program has been tested with Intel Fortran Compiler (noncommercial version 10.1) and gfortran compiler (gcc version 4.3.0) with optimization option -OOperating system: Linux, Code was developed and tested on various recent versions of Fedora including Fedora 9 (kernel version 2.6.25-14)Classification: 16.1External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 3.6.0, while for gfortran compiler we used the libraries supplied with the Fedora distribution.Nature of problem: A good starting description of the electronic structure of extended many-electron systems such as molecules, clusters, and polymers, can be obtained using the Hartree–Fock (HF) method. Solution of HF equations within a fully ab initio formalism for large systems, however, is computationally quite expensive. For such systems, semi-empirical methods such as CNDO and INDO proposed by Pople and collaborators are quite attractive. The present program can solve the HF equations for both open- and closed-shell systems containing first- and second-row atoms using either the INDO model or the CNDO model.Solution method: The single-particle HF orbitals are expressed as linear combinations of the Slater-type orbital (STO) basis set specified by Pople and coworkers. Then using the parameters prescribed for the CNDO/INDO methods, the HF integro-differential equations are transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using methods of computational linear algebra.Running time: Each of the examples provided takes only a few seconds to run. For a large molecule or a cluster, however, the run time may be a few minutes.