A general purpose Fortran 90 electronic structure program for conjugated systems using Pariser–Parr–Pople model

Abstract

Pariser–Parr–Pople (P-P-P) model Hamiltonian has been used extensively over the years to perform calculations of electronic structure and optical properties of π-conjugated systems successfully. In spite of tremendous successes of ab initio theory of electronic structure of large systems, the P-P-P model continues to be a popular one because of a recent resurgence in interest in the physics of π-conjugated polymers, fullerenes and other carbon-based materials. In this paper, we describe a Fortran 90 computer program developed by us, which uses P-P-P model Hamiltonian to not only solve Hartree–Fock (HF) equation for closed- and open-shell systems, but also for performing correlation calculations at the level of single configuration interactions (SCI) for molecular systems. Moreover, the code is capable of computing linear optical absorption spectrum at various levels, such as, tight-binding (TB) Hückel model, HF, SCI, and also of calculating the band structure using the Hückel model. The code also allows the user to solve the HF equation in the presence of finite external electric field, thus, permitting calculations of quantities such as static polarizabilities and electro-absorption spectra. Additionally, it can perform transformation of P-P-P model Hamiltonian from the atomic orbital (AO) representation (also called site representation) to the molecular orbital (MO) one, so that the transformed matrix elements can be used for high level post-HF calculations, such as, full CI (FCI), quadruple CI (QCI), and multi-reference singles–doubles CI (MRSDCI). We demonstrate the capabilities of our code by performing calculations of various properties on conjugated systems such as trans-polyacetylene ( t-PA), poly- para-phenylene (PPP), poly- para-phenylene-vinylene (PPV), oligo-acenes, and graphene nanodisks. Program summary Program title: ppp.x Catalogue identifier: AEFW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 900 No. of bytes in distributed program, including test data, etc.: 508 285 Distribution format: tar.gz Programming language: Fortran 90. Compilers used: Program has been tested with Intel Fortran Compiler (noncommercial version 11.1) and gfortran compiler (gcc version 4.4.0) with optimization option -O Computer: PCs, workstations Operating system: Linux. Code was developed and tested on various recent versions of Fedora including Fedora 11 (kernel version 2.6.29.4-167) Classification: 7.3, 16.1 External 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 4.3.0, while for gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The problem of interest at hand is the electronic structure of π-conjugated systems. For such systems, the effective π-electron P-P-P semi-empirical model Hamiltonian proposed by Pariser, Parr, and Pople offers an attractive alternative as compared to the ab initio approaches. The present program can solve the HF equations for both open- and closed-shell systems within the P-P-P model. Moreover, it can also include electron correlation effects at the singles CI level. Along with the wave functions and energies, various properties such as linear absorption spectra can also be computed. Solution method: The single-particle HF orbitals of a π-conjugated system are expressed as linear combinations of the p z -orbitals of individual atoms (assuming that the system is in the xy-plane). Then using the hopping and Coulomb parameters prescribed for the P-P-P method, the HF integro-differential equations are transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using the iterative diagonalizing technique. The HF orbitals thus obtained can be used to perform a variety of calculations such as the SCI, linear optical absorption spectrum, polarizability, electro-absorption spectrum, etc. Running time: The examples provided each only take a few seconds to run. For a large molecule or a polymer, however, the run time may be a few minutes.