A review of rigorous bounds to electron-repulsion integrals for atoms and molecules is presented. Inequalities involving direct (classical) as well as indirect (quantal) Coulomb energies are discussed. This is followed by an account of two-electron integrals in a Hartree Fock context over Gaussian basis-sets. Novel rigorous bounds to these integrals are derived and tested for some organic molecules. Connections are established with the density-based inequalities presented earlier. The present results are expected to enhance the efficiency of a generalab initio Gaussian program and yet have a sound theoretical footing.

The conventional electrostatic charge models (PD-AC) are constructed so as to reproduce the molecular electrostatic potential (MESP) on and beyond the van der Waals’ (vdW) surface. The MESP distribution has recently [S R Gadre, S A Kulkarni and I H Shrivastava (1992)J. Chem. Phys.96 5253] been shown to exhibit rich topographical features. With this in view, a detailed topographical comparison of the MESP derived from the charge models, with the respectiveab initio (MO) ones is taken up for water, hydrogen sulphide, methane and benzene molecules as test cases. It is shown that the point charge models have a fundamental lacuna, viz. they fail to mimic the essential topographical features of MESP. A new model incorporating a small number of floating spherical Gaussians is shown to restore all the critical features of the molecules under study. A comparative study of the standard deviations of MESP derived from charge models on scaled vdW surfaces further reveals that the present model leads to a better representation ofab initio MESP.

The recognition of interaction between two molecules is analysed via the topography of their molecular electrostatic potentials (MESP). The point of recognition between two species is proposed to be the geometry at which there is a change in the nature of the set of MESP critical points of one of the molecules vis-a-vis with its MESP topography at infinite separation. These results are presented for certain model systems such as pyridine and benzene dimers, cytosine-guanine and adenine-thymine base pairs in various orientations of approach of the two species.

Molecular Tailoring Approach (MTA) is a method developed for enabling ab initio calculations on prohibitively large molecules or atomic/molecular clusters. A brief review of MTA, a linear scaling technique based on set inclusion and exclusion principle, is provided. The Molecular Electrostatic Potential (MESP) of smaller clusters is exploited for building initial geometries for the larger ones, followed by MTA geometry optimization. The applications of MTA are illustrated with a few test cases such as (CO₂)$_n$ and Li$_n$ clusters employing Density Functional theory (DFT) and a nanocluster of orthoboric acid at the Hartree-Fock (HF) level. Further, a discussion on the geometries and energetics of benzene tetramers and pentamers, treated at the Møller-Plesset second order (MP2) perturbation theory, is given. MTA model is employed for evaluating some cluster properties viz. adiabatic ionization potential, MESP, polarizability, Hessian matrix and infrared frequencies. These property evaluations are carried out on a series of test cases and are seen to offer quite good agreement with those computed by an actual calculation. These case studies highlight the advantages of MTA model calculations vis-à-vis the actual ones with reference to the CPU-time, memory requirements and accuracy.

Molecular orbitals (MO’s) within Hartree-Fock (HF) theory are of vital importance as they provide preliminary information of bonding and features such as electron localization and chemical reactivity. The contemporary literature treats the Kohn-Sham orbitals within density functional theory (DFT) equivalently to the MO's obtained within HF framework. The high scaling order of ab initio methods is the main hurdle in obtaining the MO's for large molecular systems. With this view, an attempt is made in the present work to employ molecular tailoring approach (MTA) for obtaining the complete set of MO's including occupied and virtual orbitals, for large molecules at HF and B3LYP levels of theory. The energies of highest occupied and lowest unoccupied molecular orbitals, and hence the band gaps, are accurately estimated by MTA for most of the test cases benchmarked in this study, which include 𝜋-conjugated molecules. Typically, the root mean square errors of valence MO's are in range of 0.001 to 0.010 a.u. for all the test cases examined. MTA shows a time advantage factor of 2 to 3 over the corresponding actual calculation, for many of the systems reported.