Indira H. Shrivastava

Molecular electrostatic potentials : a topographical study

The topography of the molecular electrostatic potential (MESP) is studied for some small neutral molecules and OH− ion. Different kinds of critical points (CP’s) of rank 3 are identified and their occurrences are discussed. The correlation of these CP’s with the molecular structure is brought out. Bond ellipticities are determined in terms of curvatures of bond CP’s. These ellipticities show trends similar to those reported by Bader et al. [J. Am. Chem. Soc. 105, 5061 (1983)]. A typical example of OH− illustrates the existence of a degenerate nonisolated ring of CP’s, which is a rather unique feature of the topology of the MESP of linear molecules. Some suggestive arguments with suitable examples, regarding indeterminacy of the nonisolated degenerate CP’s, have been made.

Shapes and sizes of molecular anions via topographical analysis of electrostatic potential

The theorem proposed by Pathak and Gadre [J. Chem. Phys. 93, 1770 (1990)], that the electrostatic potential (ESP) of negative ions must exhibit a directional negative valued minimum along any arbitrary direction has been verified for some small negative molecular ions, viz., OH−, CN−, N−3, NO−3, and NH−2. Also, as predicted by Gadre and Pathak [Proc. Ind. Acad. Sci. (Chem. Sci.) 102, 18 (1989)], the molecular ESP (MESP) maps are found to be devoid of local maxima. As a consequence, these maps reveal rich topographical details in the form of several saddle points as well as point minima. From the location of these critical points, estimates of the sizes and shapes of the negatively charged molecular ions are obtained. For anions, there exists a surface on which ■V⋅dS=0 and which passes through all the negative valued critical points (∇V=0). The ionic size estimates from the location of the critical points of the MESP are found to be in good agreement with the corresponding (spherically averaged) literature...

Basis set dependence of the molecular electrostatic potential topography. A case study of substituted benzenes

The basis set dependence of the topographical structure of the molecular electrostatic potential (MESP), as well as the effect of substituents on the MESP distribution, has been investigated with substituted benzenes as test cases. The molecules are studied at HF-SCF 3i?½21G and 6i?½31G** levels, with a further MESP topographical investigation at the 3i?½21G, double-zeta, 6i?½31G*, 6i?½31G**, double-zeta polarized and triple-zeta polarized levels. The MESP critical points for a 3i?½21G optimized/6i?½31G** basis are similar to the corresponding 6i?½31G** optimized/6i?½31G** ones. More generally, the qualitative features of the MESP topography computed at the polarized level are independent of the level at which optimization is carried out. For a proper representation of oxygen lone pairs, however, optimization using a polarized basis set is required. The nature of the substituent drastically changes the MESP distribution over the phenyl ring. The values and positions of MESP minima indicate the most active site for electrophilic attack. This point is strengthened by a study of disubstituted benzenes.

Cross-entropy minimization for refinement of Gaussian basis sets

Abstract Information theoretic techniques have been applied for the refinement of Gaussian basis sets. A refined distribution has been obtained by cross-entropy minimization starting from a near Hartree-Fock quality density distribution. For this purpose, the Kullback-Leibler cross-entropy, S [ϱ¦ϱ 0 ] = ∫ϱ( r )ln[ϱ( r )/ϱ 0 ( r )] d r , has been minimized subject to exact, theoretical or experimental, second moment constraints in position and momentum spaces. Here, ϱ 0 is the starting density distribution and ϱ is the corresponding refined one. The procedure has been applied to hydrogen, helium, lithium and beryllium atoms as test cases. Nearly all moments (−2 through 4), in coordinate as well as momentum spaces have improved over the original ones at an average worsening of the total energy by a mere 0.04%.

Topography-driven electrostatic charge models for molecules

Abstract A new method has been proposed for the generation of charge models for use in molecular interaction studies. These models have been developed so as to reproduce the essential topographical features of the corresponding ab initio molecular electrostatic potential. This has been achieved via the fitting of variable parameters in the model, such as point charges and their location, as well as the charge on the diffuse “floating” Gaussian, its exponent and center. Test applications to H 2 O and NH 3 are reported.

Application of rigorous bounds for efficient evaluation of molecular electrostatic potentials

Abstract Rigorous upper bounds to electrostatic potential integrals over Gaussian basis sets have been exploited for accurate and speedy evaluation of molecular electrostatic potentials (MESP). These bounds are applied to eliminate those pairs of Gaussians which contribute insignificantly to the total MESP. An efficient algorithm for MESP mapping has been developed with the help of these bounds. Further, rigorous inequalities to the auxiliary functions F m ( t ), were derived. Some of these bounds are so tight that they are employed as a good approximation to F m ( t ). The algorithm developed by incorporation of the above aspects is tested on trans-butadiene, cyclopropane and 1,2,3,4,5,6,7-octa-heptene molecules using 4–31G and 3G basis sets. A factor of six and more in terms of CPU time is obtained for all the test cases studied over the usual straightforward computation. A parallel version of this algorithm has also been developed.

A general parallel algorithm for the generation of moleular electrostatic potential maps

Abstract Application of rigorous bounds yields an algorithm approximately linear in the number of primitive Gaussians for the computation of the molecular electrostatic potential (MESP). Careful strategies for parallelization of the algorithm have been evolved. Linear as well as superlinear speedups have been achieved by effective load balancing, viz. even distribution of the workload amongst the worker processors. The parallel algorithm was tested on C 2 H 4 , C 3 H 4 , C 3 H 6 , C 4 H 6 , C 6 H 6 , C 6 H 5 NO 2 , and C 10 H 8 molecules using 4–31G ** , 4–31G and 3G basis sets. The generation of the MESP on 100 × 100 points, for any of these molecules, using the parallel algorithm requires less than 5 min on the 32-node INMOS T800-based Parsytec computing system.

Computation of molecular electrostatic potential: An efficient algorithm and parallelization

An efficient algorithm fortified by the use of rigorous inequalities has been developed for the computation of molecular electrostatic potential maps. The algorithm has further been parallelized to obtain high computation speeds. This algorithm was tested on some hydrocarbons, azide and nitrate ions, using STO-3G and 4-31G basis-sets. The parallel version of the algorithm implemented on a 32-node machine (Parsytec) is found to give a considerable CPU time factor ranging from 60 to 200 over the HP 9050 AM series machine. The results are found to be accurate up to 6 decimal digits.

A “critical” appraisal of electrostatic charge models for molecules

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.

Use of second-moment constraints for the refinement of determinantal wave functions.

A constrained least-squares fit procedure wherein the integral F[\ensuremath{\rho}(r)-