A hierarchy of three models for combined quantum mechanical (QM) and molecular mechanical (MM) approaches is presented. They simplify the QM description of large molecules by reducing it to the electronically important fragment which interacts with the molecular mechanically treated remainder of the molecule. In the simplest model A, the QM fragments are only mechanically embedded in their MM environment. The more refined models B and C include a quantum mechanical treatment of electrostatic interactions between the fragments and a semiclassical description of polarization. The implementation of models A-C for MNDO type wavefunctions and the MM3 force field is outlined. Selected applications in organic chemistry are discussed, addressing the ability of the proposed models to reproduce substituent effects (MM) on chemical structure and reactivity (QM). These applications include protonations, deprotonations, hydride transfer reactions, nucleophilic additions, and nucleophilic ring cleavage reactions.

Hybrid Models for Combined Quantum Mechanical and Molecular Mechanical Approaches

The electrostatic potential V(r) that is created by a system of nuclei and electrons is formulated directly from Coulomb's law and is a physical observable, which can be determined both experimentally and computationally. When V(r) is evaluated in the outer regions of a molecule, it shows how the latter is ‘seen’ by an approaching reactant, and thus is a useful guide to the molecule's reactive behavior, especially in noncovalent interactions. However, V(r) is a fundamental property of a system, the significance of which goes beyond its role in reactivity. For example, the energy of an atom or molecule can be expressed rigorously in terms of the electrostatic potentials at its nuclei. These and other features of V(r) are discussed in this overview. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 153-163 DOI: 10.1002/wcms.19

The electrostatic potential: an overview

Theoretical Methods for the Description of the Solvent Effect in Biomolecular Systems.

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.

Molecular electrostatic potentials: A topographical study

Absolute free energies of hydration have been computed for 13 diverse organic molecules using partial charges derived from ab initio 6-31G* wave functions. Both Mulliken charges and charges fit to the electrostatic potential surface (EPS) were considered in conjunction with OPLS Lennard–Jones parameters for the organic molecules and the TIP4P model of water. Monte Carlo simulations with statistical perturbation theory yielded relative free energies of hydration. These were converted to absolute quantities through perturbations to reference molecules for which absolute free energies of hydration had been obtained previously in TIP4P water. The average errors in the computed absolute free energies of hydration are 1.1 kcal/mol for the 6-31G* EPS charges and 4.0 kcal/mol for the Mulliken charges. For the EPS charges, the largest individual errors are under 2 kcal/mol except for acetamide, in which case the error is 3.7 kcal/mol. The hydrogen bonding between the organic solutes and water has also been characterized. © John Wiley & Sons, Inc.

Accuracy of free energies of hydration for organic molecules from 6-31G-derived partial charges

A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.

Comparative study of the molecular Electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

Effect of electron correlation on the electrostatic potential distribution of molecules

The H2 receptor activation mechanism model proposed by Weinstein et al. [Mol. Pharmacol. 12:738-745 (1976)] has been considered for the set of H2 agonists. The energetics of the model proton transfer processes from a proton-donor site to the heterocycle ring of the agonist molecule and from this one to a proton acceptor site have been studied by using the semiempirical AM1 and MNDO quantum mechanical methods. The STO-3G ab initio molecular electrostatic potential for each compound in its active form has also been computed. Results show the mechanistic model to be satisfactory and lead to a qualitative and quantitative explanation of the H2 activity data.

F. J. Luque

Papers

Comparative study of the molecular Electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

Effect of electron correlation on the electrostatic potential distribution of molecules

On the mechanism of histamine H2 receptor activation.