Computational methods for molecules

C and T Lengauer 2000. Computational Methods for the Structural Alignment of Molecules. nal of Computer-Aided Molecular Design 14 215-232. 

The se the orie s are inevitablj based upem analyse s of the interactions and transformations of molecular orbitals, and consequently the accurate construction and re presentation of molecular orbitals has become essential, furthermore, although the forms of molecular orbitals in diatomics and of delocalized tt orbitals in conjugated systems are familiar, a general, non-computational method for determining the qualitative nature of or and t orbitals in arbitrary molecules has been lacking. 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

Lemmen, C. and Lengauer, T. Computational methods for the structural alignment of molecules. 

Lemmen, C. and Lengauer, T. (2000) Computational methods for the structural alignment of molecules../. Comput.-Aided Mol. Design 14, 215-232. 

The Molecular Surface (MS) first introduced by Richards (19) was chosen as the 3D space where the MLP will be calculated. MS specifically refers to a molecular envelope accessible by a solvent molecule. Unlike the solvent accessible surface (20), which is defined by the center of a spherical probe as it is rolled over a molecule, the MS (19), or Connolly surface (21) is traced by the inwardfacing surface of the spherical probe (Fig. 2). The MS consists of three types of faces, namely contact, saddle, and concave reentrant, where the spherical probe touches molecule atoms at one, two, or three points, simultaneously. Calculation of molecular properties on the MS and integration of a function over the MS require a numerical representation of the MS as a manifold S(Mk, nk, dsk), where Mk, nk, dsk are, respectively, the coordinates, the normal vector, and the area of a small element of the MS. Among the published computational methods for a triangulated MS (22,23), the method proposed by Connolly (21,24) was used because it provides a numerical presentation of the MS as a collection of dot coordinates and outward normal vectors. In order to build the 3D-logP descriptor independent from the calculation parameters of the MS, the precision of the MS area computation was first estimated as a function of the point density and the probe radius parameters. When varying... 

The computational methods for the structure of a molecule are divided into the ab initio, the semi-empirical, and the molecular mechanics methods. 

J. A. Pople, in Computational Methods for Large Molecules and Localized States in Solids , ed. F. Herman, A. D. McLean, and R. K. Nesbet, Plenum Press, New York, 1973, p. 11. 

Bagus, P. S., Liu, B., McLean, A. D., Yoshimine, M. Ab initio computation of molecular structures through configuration interaction. In Computational methods for large molecules and localized states in solids. Herman, F., McLean, A. D., Nesbet, R. K. (eds.). New York Plenum Press 1973, pp. 87-115... 

Huo, W.M. and Gianturco, F.A. (1995). Computational Methods for Electron-Molecule Collisions (Plenum, New York). 

Domcke, W. (1991). Theory of resonance and threshold effects in electron-molecule collisions the projection-operator approach, Phys. Rep. 208, 97-188. [178] Huo, W.M. and Gianturco, F.A., eds. (1995). Computational Methods for Electron-Molecule Collisions (Plenum, New York). 

Gillan, C.J., Tennyson, J. and Burke, P.G. (1995). The UK molecular R-matrix scattering package a computational perspective, in Computational Methods for Electron-Molecule Collisions, eds. W.M. Huo and F.A. Gianturco (Plenum,... 

All calculations discussed here have been chosen as representative of various computational methods and no attempt at encyclopedic coverage of calculations on simple atomic and molecular systems has been made. A somewhat more comprehensive discussion of computational methods for atoms and molecules can be found in Sanders [4] while Morgan [5] also reviews recent developments in high-precision computational methods. 

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