Molecular energy calculations

The structure of A-type starch crystals was derived through the joint use of electron diffraction of single crystals, x-ray powder patterns decomposed into individual peaks, x-ray fiber diffraction data and extensive molecular modeling32 (Figure 5.5). The density calculated for the crystalline region (d = 1.48) is reasonably close to the observed density, and indicates that there are 12 glucosyl units and 4 water molecules in the unit cell. Intra- and inter-molecular energy calculations showed that... 

Molecular energies calculated by - computational chemistry methods are fundamental descriptors commonly used in QSAR models moreover, energies are used as cutoff values for the selection of the most important conformation(s). Besides the... 

Abstract Some previous results of the present author are combined in order to develop a Hermitian version of the Chemical Hamiltonian Approach. In this framework the second quantized Bom-Oppenheimer Hamiltonian is decomposed into one- and two-center components, if some finite basis corrections are omitted. (No changes are introduced into the one- and two-center integrals, while projective expansions are used for the three- and four-center ones, which become exact only in the limit of complete basis sets.) The total molecular energy calculated with this Hamiltonian can then presented as a sum of the intraatomic and diatomic energy terms which were introduced in our previous chemical energy component analysis scheme. The corresponding modified Hartree-Fock-Roothaan equations are also derived they do not contain any three- and four-center integrals, while the non-empirical character of the theory is conserved. This scheme may be useful also as a layer in approaches like ONIOM. 

The relative acidities in the gas phase can be detennined from ab initio or molecular orbital calculations while differences in the free energies of hydration of the acids and the cations are obtained from FEP sunulations in which FIA and A are mutated into FIB and B A respectively. 

Reynolds C, King P M and Richards W G 1992 Free energy calculations in molecular biophysics Mol. Phys. 76 251... 

The summation of pair-wise potentials is a good approximation for molecular dynamics calculations for simple classical many-body problems [27], It has been widely used to simulate hyperthennal energy (>1 eV) atom-surface scattering ... 

Payne M C, Teter M P, Allan D C, Arias T A and Joanopoulos J D 1992 Iterative minimization techniques for ab /M/o total energy calculations molecular dynamics and conjugate gradient Rev. Mod. Phys. 64 1045... 

Bernhard R. Brooks, Robert E. Bruccoleri, Barry D. Olafson, David J. States, S. Swaminathan, and Martin Karplus. CHARMM A program for macro-molecular energy, minimization, and dynamics calculations. J. Comp. Chem., 4(2) 187-217, 1983. 

S. Miyamoto and P. A. Kollman. Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches. Proteins, 16 226-245, 1993. 

Molecular transformation calculations can be used for computing differ-enr.es in binding free, energy for two ligands by a well-established scheme... 

Hermans, J., Yun, R. H., Anderson, A. G. Precision of free-energies calculated by molecular dynamics simulations of peptides in solution. J. Comp. Chem. 13 (1992) 429-442... 

Beutler, T. C., Mark, A. E., van Schaik, R. C., Gerber, P. R., van Gunsteren, W. F. Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations. Chem. Phys. Letters 222 (1994) 529-539... 

I. Pettersson, T. Liljefors, Molecular mechanics calculated conformational energies of organic molecules a comparison of force fields, in Reviews in Computational Chemistry, Vbl. 9,... 

MP2 correlation energy calculations may increase the computational lime because a tw o-electron integral Iran sfonnalion from atomic orbitals (.40 s) to molecular orbitals (MO s) is ret]uired. HyperClicrn rnayalso need additional main memory arul/orcxtra disk space to store the two-eleetron integrals of the MO s. 

For a molecular mechanics calculation the en ergy and the gradient are essen tially the on ly quantities available from a single pom t cal-cii lation. An analysis of the com ponen ts of th is molecular mechanics energy is placed in the log file for further detail. In the case of MM-h a much more com pleie description of the ind ividual... 

Tie hydrogen molecule is such a small problem that all of the integrals can be written out in uU. This is rarely the case in molecular orbital calculations. Nevertheless, the same irinciples are used to determine the energy of a polyelectronic molecular system. For an ([-electron system, the Hamiltonian takes the following general form ... 

Fig. 11.38 Lag ejfects in ab initio molecular dynamics. (Figure redrawn from Payne MC, M P Teter, D C Allan, R A Arias and D ] Joannopoidos 1992. Iterative Minimisaticm Techniques for Ab Initio Total-Energy Calculations Molecular Dynamics and Conjugate Gradients. Reviews of Modern Physics 64 1045-1097.)...

Buetler T C, A E Mark, R C van Schaik, P R Gerber and W F van Gunsteren 1994. Avoiding Singularities and Numerical Instabilities in Free Energy Calculations Based on Molecular Simulations. Chemical Physics Letters 222 529-539. 

Burger M T, A Armstrong, F Guamieri, D Q McDonald and W C Still 1994. Free Energy Calculations in Molecular Design Predictions by Theory and Reality by Experiment with Enantioselective Podand lonophores. Journal of the American Chemical Society 116 3593-3594. 

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