Shridhar R. Gadre

Significant progress in predicting the crystal structures of small organic molecules – a report on the fourth blind test

We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.

Molecular tailoring approach for geometry optimization of large molecules: Energy evaluation and parallelization strategies

A linear-scaling scheme for estimating the electronic energy, gradients, and Hessian of a large molecule at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided molecular tailoring approach (CG-MTA) for ab initio geometry optimization of large molecules is implemented. The method employs energy gradients extracted from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for density-functional-theory-based geometry optimization of a variety of molecules including alpha-tocopherol, taxol, gamma-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient estimates obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large molecules.

Maximal and minimal characteristics of molecular electrostatic potentials

Existence of strict local maxima within the molecular electrostatic potential (MESP) maps has been rigorously ruled out. The proof to this effect is based solely on the classical electrostatic Poisson equation. It has been further shown that at least one‐directional negative‐valued minimum in MESP for a negative molecular ion must occur along any arbitrary direction. Under some special circumstances, an equipotential MESP surface could exist for such a species. These results properly reduce to their atomic counterparts proven by Politzer and co‐workers [Weinstein et al., Theor. Chim. Acta (Berl.) 38, 59 (1975); Sen and Politzer, J. Chem. Phys. 90, 4370 (1989)].

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...

Ab initio quality one‐electron properties of large molecules: Development and testing of molecular tailoring approach

The development of a linear‐scaling method, viz. “molecular tailoring approach” with an emphasis on accurate computation of one‐electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree–Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N3) scaling order within HF theory to an n·O(N′3) one, where n is the number of fragments and N′, the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One‐electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful.

Topography of molecular scalar fields. I. Algorithm and Poincaré–Hopf relation

A new algorithm for locating the critical points (CP’s) of a three-dimensional molecular scalar field is discussed. The algorithm is based on a ray search from the surface extrema of appropriately defined atom-centered spheres. The algorithm is tested for molecular electrostatic potentials and electron densities of a few test molecules such as tetrahedrane, cubane, anthracene, diborane, etc. Furthermore, the Poincare–Hopf relationship is examined for the set of CP’s thus obtained. A topological interpretation of the Euler characteristic of a given isosurface is employed for a stronger regional check on the number of CP’s enclosed in the isosurface.

Molecular electrostatics. A comprehensive topographical approach

Abstract An integrated approach to the study of molecular electrostatics is presented. Efficient sequential and parallel algorithms are developed for the computation of the molecular electrostatic potential (MESP) and the molecular electrostatic field (MEF) along with the MEF gradient at a given set of points. Strict bounds for MESP and MEF are used for enhancing the power of the program by virtue of rigorous elimination of numerically insignificant integrals. Recent studies have highlighted the features and utility of MESP topography (in terms of its critical points) in chemistry. An algorithm for locating the critical points (CPs) is described. Some CPs of the MESP for test molecules (viz. C 4 H 6 , ClO − 3 , P 4 S 3 and [V 10 O 28 ] 6− ) are located and characterized in terms of the eigenvalues of the respective Hessians. A rapid yet accurate characterization of the MESP topography is seen to be possible with this approach.

Enabling ab initio Hessian and frequency calculations of large molecules

A linear scaling method, termed as cardinality guided molecular tailoring approach, is applied for the estimation of the Hessian matrix and frequency calculations of spatially extended molecules. The method is put to test on a number of molecular systems largely employing the Hartree-Fock and density functional theory for a variety of basis sets. To demonstrate its ability for correlated methods, we have also performed a few test calculations at the Moller-Plesset second order perturbation theory. A comparison of central processing unit and memory requirements for medium-sized systems with those for the corresponding full ab initio computation reveals substantial gains with negligible loss of accuracy. The technique is further employed for a set of larger molecules, Hessian and frequency calculations of which are not possible on commonly available personal-computer-type hardware.

Ab initio investigation of benzene clusters: molecular tailoring approach.

An exhaustive study on the clusters of benzene (Bz)(n), n = 2-8, at MP2/6-31++G(∗∗) level of theory is reported. The relative strengths of CH-π and π-π interactions in these aggregates are examined, which eventually govern the pattern of cluster formation. A linear scaling method, viz., molecular tailoring approach (MTA), is efficiently employed for studying the energetics and growth patterns of benzene clusters consisting up to eight benzene (Bz) units. Accuracy of MTA-based calculations is appraised by performing the corresponding standard calculations wherever possible, i.e., up to tetramers. For benzene tetramers, the error introduced in energy is of the order of 0.1 mH (∼0.06 kcal/mol). Although for higher clusters the error may build up, further corrections based on many-body interaction energy analysis substantially reduce the error in the MTA-estimate. This is demonstrated for a prototypical case of benzene hexamer. A systematic way of building up a cluster of n monomers (n-mer) which employs molecular electrostatic potential of an (n-1)-mer is illustrated. The trends obtained using MTA method are essentially identical to those of the standard methods in terms of structure and energy. In summary, this study clearly brings out the possibility of effecting such large calculations, which are not possible conventionally, by the use of MTA without a significant loss of accuracy.