Calculation of molecular electrostatic potentials

Etchebest, C., R. Lavery, and A. Pullman. 1982. The Calculations of Molecular Electrostatic Potential from a Multipole Expansion Based on Localized Orbitals and Developed at Their Centroids Accuracy and Applicability for Macromolecular Computations. Theor. Chim. Acta 62, 17. 

G. P. Ford and B. Wang, J. Comput. Chem., 14, 1101 (1993). New Approach to the Rapid Semiempirical Calculation of Molecular Electrostatic Potential Based on the AMI Wave Function Comparison with Ab Initio HF/6-31G Results. 

The marching-cube algorithm has been used also by Kolle and Jug (1995) to define the tesserae of isodensity surfaces. The procedure is implemented in the semiempirical SINDOl program (INDO with Slater-type orbitals, Li et al., 1992). To compute AS charges the asymptotic density model ADM (Koster et al., 1993) is used. This is an approximation to the calculation of molecular electrostatic potentials based on the cumulative atomic multipole moment procedure (CAMM, Sokalski et al., 1992). 

Accurate calculation of molecular electrostatic potentials in an algorithm which scales at most with the cube of molecule size has long remained a challenge. The established method for molecules is to fit the molecular density calculated from the orbital densities with multipolar functions attached to the atoms [39]. This method leads to a term which scales like the cube of the molecule size. It requires the introduction of an auxiliary basis set for the multipolar functions. The choice of such a basis set requires expertise and can easily lead to uncertain results. 

More recent approaches to measuring the bulk of j os[diines and other ligands have included analysis of data in the Cambridge Structural Database (K. A. Bunten, L. Chen, A. L. Fernandez, A. J. Poe, Coord. Cherru Rev., 2002, 233-234, 41) and calculations of molecular electrostatic potentials (C. H. Suresh, Inorg. Cherru, 2006,45, 4982). 

Population analysis in semiempirical methods fall into two categories. Methods including overlap in the Fock equations use the Mulliken population analysis. The majority of semiempirical methods uses the ZDO approximation, and the net charges are interpreted on the basis of symmetrically orthog-onalized AOs. It is pointed out that this interpretation is not exactly valid, because of truncation and empirical adjustment. But the corresponding nonsymmetrical orthogonalization is not uniquely defined. Charge models based on semiempirical wave functions play an important role in the calculation of molecular electrostatic potentials for reactivity. 

Rabinowitz, J. R., K. Namboodiri, and H. Weinstein. 1986. A Finite Expansion Method for the Calculation and Interpretation of Molecular Electrostatic Potentials. Int. J. Quant. Chem. 29,1697. 

A speculative proposal was made thirty years ago by Schmid and Krenmayr77, namely that a nitrosyl ion solvated, but not covalently bonded, by a water molecule may be involved in these systems. This hypothesis was investigated theoretically in 1984 by Nguyen and Hegarty78 who carried out ab initio SCF calculations of structure and properties employing the minimal STO-3G basis set, a split-valence basis set plus polarization functions. Optimized geometries of six planar and two nonplanar forms were studied for the nitrosoacidium ion. The lowest minimum of molecular electrostatic potential... 

More recently, electrostatic theory has been revived due to the concept of molecular electrostatic potentials. The potential of the solute molecule or ion was used successfully to discuss preferred orientations of solvent molecules or solvation sites 50—54). Electrostatic potentials can be calculated without further difficulty provided the nuclear geometry (Rk) and the electron density function q(R) or the molecular wave function W rxc, [Pg.14]

The use of molecular electrostatic potentials calculated from the wave function of ligands, as has been recently suggested 50—54) seems to present a less ambiguous alternative to the more empirical approach described above. This potential can either be calculated exactly for each point of interest according to Eq. (3), or it is approximated by a suitable distribution of point charges choosen either by intuitive guess or by a less arbitrary method like the one of Hall 182>. 

From a wave function, one can also calculate the molecular electrostatic potential (MEP), which is an energy of attraction or repulsion experienced by a hypothetical unit charge as it moves in the vicinity of a molecule (54). The MEP gives clues to how one molecule looks to another as they approach. Hence, MEPs can be studied to reveal how two reactants might approach each other. 

In this work the use of molecular electrostatic potential (MEP) maps for similarity studies is reviewed in light of the latest results. First, methods of obtaining MEP maps is overviewed. The methodology, reliability and the efficiency of calculations based on semi-empirical as well as ab initio methods are discussed in detail. Point-charge models and multipole expansion methods which provide MEP maps of satisfactory quality are evaluated critically. Later on, similarity indices of various kinds are analyzed, compared and examples of their use are shown. Finally, the last section lists and summarizes software packages capable of calculating MEP map based similarity indices. 

We attempt here to describe those results which concern the quality of molecular electrostatic potential maps, methods of their calculation and their use in molecular similarity studies. 

Finally the most sensitive scheme to differentiate between the shapes of closely related conformers is by comparison of the total overlap energy [148]. It extends the calculation of electrostatic overlap energy (5.8.1) over all pairs of atoms in the molecule. This procedure mimics the calculation of molecular quantum potential even more closely than MM and eliminates the scaling of different types of steric energy. 

A model obtained by applying the GIPF approach General Interaction Properties Function approach) proposed by Politzer and co-workers [Brinck et al., 1993 Murray et al, 1993 Murray et al., 1994] as a general method to estimate physico-chemical properties in terms of -> molecular electrostatic potential (MEP) properties calculated at the -> molecular surface. 

The Z-axis forms an angle of 17° with the Zn-Ow bond shown in Figure 1. The position of Zn in the plane below [i.e., (0.0, 0.0, 0.0)] is indicated by dotted lines. The molecular wavefunctions were calculated with an ab-initio LCAO-SCF method using minimal STO-4G atom optimized basis sets. The basis set for Zn was augmented by additional diffused 3d and 4p functions obtained from an STO-4G expansion of Slater orbitals with exponents of 1.6575 and 1.45, respectively. The method used for the calculation of the electrostatic potentials is described in Ref. 65. Units are Kcal/mol. 

Figure 6. Comparison of molecular electrostatic potentials of 5-HT (a) and D-LSD (b) in a parallel plane 1.5 A above their indole portions (units are heal/ mol). The electrostatic potentials were calculated (65) from molecular wave-functions obtained as described in the legend to Figure 5.

One of the early applications of molecular electrostatic potentials was in relation to hydrogen bonding. The Fm n (most negative potentials) were found to be effective in identifying sites at which hydrogen bonds would be accepted [16,89-91]. Furthermore, Kollman et al. [89] showed that the calculated energy of the interaction between hydrogen fluoride and a series of acceptors correlates well with the value of V(r) at a fixed distance from the latter. 

Rabinowitz JR, Namboodiri K, Weinstein H. A finite expansion method for the calculation and interpretation of molecular electrostatic potentials. Int J Quantum Chem 1986 29 1697-1704. 

P. Nagy, K. Novak, and G. Szasz,/. Mol. Struct. (THEOCHEM), 201,257 (1989). Theoretical Calculations on the Basicity of Amines. Part 1. The Use of Molecular Electrostatic Potential for pKj Prediction. 

A Finite Expansion Method for the Calculation and Interpretation of Molecular Electrostatic Potentials. 

Challacombe and Schwegler used the QCTC method to do an ab initio SCF MO calculation on the 698-atom monomer of the P53 protein at a fixed geometry (obtained from a protein data bank) using the 3-21G basis set (3836 basis functions). TTiey then calculated the molecular electrostatic potential (Section 15.8) of the P53... 

The quantum-chemical tree code (QCTC) [M. Challacombe and E. Schwegler, J. Chem. Phys., 106, 5526 (1997)] is a modification of the classical tree-code method. The QCTC method allows calculation of the matrix elements of the Coulomb matrix J for large molecules in a time that is proportional to the number of basis functions b this calculation is 0 b), and one says that the calculation exhibits linear scaling with size of the molecule. Challacombe and Schwegler used the QCTC method to do an ab initio SCE MO calculation on the 698-atom monomer of the P53 protein at a fixed geometry (obtained from a protein data bank) using the 3-21G basis set (3836 basis functions). They then calculated the molecular electrostatic potential (Section 15.7) of the P53 monomer. (The P53 protein is a tetramer and acts as a tumor suppressor. Mutations in the gene for this protein are found in half of human cancers.)... 

Computational chemistry analysis appears to be helpful as an additional tool to explain the lack of separation between different forms of cobalamins. Recent theoretical studies of the group deal with the electronic and vibrational spectra of some corrins, obtained using density functional theory (DFT) calculations (Andriuniow et al. 2005). The results indicated that, for all the structures used in the calculations, the same electrostatic potential on the molecule was obtained, which supports the observed simultaneous detection of cobalamins, irrespective of the axial ligand (cyano, adenosyl and methyl group). The lack of separation between different forms of cobalamins can be explained by analysis of molecular electrostatic potential (Andriuniow et al. 2005 Lebiedzihska et al. 2007). 

J. R. Rabinowitz and S. B. Little, Int. J. Quantum. Chem., Quantum. Biol. Symp., 13, 9 (1986). Multipole Expansion Techniques for the Calculation and Characterization of Molecular Electrostatic Potentials. 

---