Calculation of molecular electrostatic

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. 

Great attention has been paid to the fast, accurate calculation of molecular electrostatic properties within VAMP. The natural atomic orbital-point charge (NAO-PC) model for representing the molecular electron density as a... 

As motivation for the rest of the chapter, a few further observations can be made. Eirst, the calculation of full electrostatics is expensive. A typical molecular mechanics potential function is of the form... 

Hurley, A. C., Proc. Roy. Soc. London) A226, 170, 179, The electrostatic calculation of molecular energies. I. Methods of calculating molecular energies. II. Approximate wave functions and the electrostatic model/ ... 

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. 

St.-Amant, A., W. D. Cornell, P. Kollman, and T. A. Halgren. 1995. Calculation of Molecular Geometries, Relative Conformation Energies, Dipole Moments, and Molecular Electrostatic Potential Fitted Charges of Small Organic Molecules of Biochemical Interest by Density Functional Theory. J. Comp. Chem. 16, 1483. 

The new treatment had its origins partly in ab initio molecular orbital calculations of substituent effects and partly in extensive studies of gas-phase proton transfer reactions from about 1980 (Section V.A). Various aspects of this work essentially drew attention to the importance of substituent polarizability. In 1986 Taft, Topsom and their colleagues252 developed a scale of directional substituent polarizability parameters , oa, by ab initio calculations of directional electrostatic polarization potentials at the 3-21G//3-31G level for a large set of CH3X molecules. The oa values were shown to be useful in the correlation analysis of gas-phase acidities of several series of substrates252, and such work has subsequently been extended by Taft and Topsom151. 

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>. 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

Calculation of the electrostatic terms in this way is only an option when such a function has been coded into the molecular mechanics program. A perhaps unexpected... 

There are two other main directions for the calculation of the electrostatic interaction between the solute and a surrounding dielectric continuum for molecular-shaped cavities. Both require intensive numerical calculations and are thus slower than GB methods. The first direction is the direct numerical solution of the Poisson equation for the volume polarization P(r) at a position r of the dielectric medium ... 

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. 

St.-Amant A, Cornell WD, Kollman PA, Halgren TA (1995) Calculation of molecular geometries, relative conformational energies, dipole-moments, and molecular electrostatic potential fitted charges of small organic-molecules of biochemical interest by density-functional theory, J Comput Chem, 16 1483-1506... 

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. 

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