Force field approach, consistent

Folding energy and catalysis, 227 Force field approach, consistent 113 Free energy, 43,47 of activation, 87-90, 92-93, 93, 138 of charging processes, 82 convergence of calculations of, 81 in proteins, SCAAS model for, 126 of reaction, 90... 

Chymotrypsin, 170,171, 172, 173 Classical partition functions, 42,44,77 Classical trajectories, 78, 81 Cobalt, as cofactor for carboxypeptidase A, 204-205. See also Enzyme cofactors Condensed-phase reactions, 42-46, 215 Configuration interaction treatment, 14,30 Conformational analysis, 111-117,209 Conjugated gradient methods, 115-116. See also Energy minimization methods Consistent force field approach, 113 Coulomb integrals, 16, 27 Coulomb interactions, in macromolecules, 109, 123-126... 

Nonbonded interactions consist of van der Waals (VDW) and electrostatic potentials. Examples of the valence force field approach include UFF or DREIDING [54], MM2/MMP2 [55], AMBER [56], and CHARMM [57]. The parameters of the potentials can be determined from either experiments or ab initio quantum chemical methods [58]. 

Many such model force fields have been discussed in the literature. [For general discussions, see Herzberg (1945), Wilson et al. (1955), Woodward (1972), and Califano (1976). For discussions of the Urey-Bradley force field, see the review by Duncan (1975). For discussions of the entirely different consistent force field approach, see Lifson and Warshel (1968), Warshel et al. (1970), and Burkert and Allinger (1982).] We have chosen to use a simplified general valence force field (SGVFF), which has been defined as one which contains the minimum possible number of interaction constants compatible with a good fit of the spectra (Califano, 1976). Such a force field has been demonstrated to be very effective for hydrocarbons (Schachtschneider and Snyder, 1963). For this form the potential energy of Eq. (63) is written explicitly as... 

Diatomic molecules The distribution function of the center of mass of Oxygen molecules in micro-structures of glassy PVC of ca. 40 A has been evaluated [58] assuming separability between the translational and rotational degrees of freedom of the O2 molecules [see Eq. (32)]. Two different diatomic force IMds for the O2 molecule have been used. In both cases, the same three modes of solute motion have been found and computed transport coefficients were consistent with experimental data. Nevertheless, we fed that tte use of tte explidt diatomic approach is impractical today In view of the inaccuracy which intrinsically pertains to the force-field approach, one can always conveniently optimize the parameters of a united- tom force-field to properly reproduce experimental transport coeffidents oS tte diatomic molecules in dense polymers. 

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

Vibrational spectroscopy has played a very important role in the development of potential functions for molecular mechanics studies of proteins. Force constants which appear in the energy expressions are heavily parameterized from infrared and Raman studies of small model compounds. One approach to the interpretation of vibrational spectra for biopolymers has been a harmonic analysis whereby spectra are fit by geometry and/or force constant changes. There are a number of reasons for developing other approaches. The consistent force field (CFF) type potentials used in computer simulations are meant to model the motions of the atoms over a large ranee of conformations and, implicitly temperatures, without reparameterization. It is also desirable to develop a formalism for interpreting vibrational spectra which takes into account the variation in the conformations of the chromophore and surroundings which occur due to thermal motions. 

Many force fields use a Lennard-Jones 6-12 potential71 to reproduce nonbonded interactions, see Equation 7. As two atoms approach one another, the steepness or hardness of the energy curve is proportional to r 12. The use of an exponential term instead of the r12 term in force field equations better reproduces experimental data for organic structures, and it is more consistent with quantum chemical calculations. 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

In a different approach to this problem, Brenner and Garrison used molecular dynamics to examine the chemical mechanisms which lead to reordering of the atom-pairing reconstruction during atom deposition . This simulation incorporated a dissociative valence-force field potentiaF and consisted essentially of a high-temperature anneal of monolayers of silicon atoms which had been deposited on a silicon (001) reconstructed surface. 

Cui et al. performed similar analyses to fhose of Dupuis and co-workers. The side chain-side chain radial disfribufion functions (RDFs) reported by Cui et al. show remarkable qualitative deviation from fhose in Zhou et al. i It is of note that the united atom approach used by Cui and co-workers ignored electrostatic interactions between CP2 groups of the polymeric backbone. This can lead to a poor description of fhe hydrated structure in the regions close to the polymeric backbones, unlike the all-atom force field used in Zhou et al. ° For the sake of limited computational resources, Cui et al. used a relatively short representation of Nation ionomer chains consisting of three monomers as compared to the ten monomers used by Vishnyakov and Neimark or Urata et al. It can be expected that structural correlations will strongly depend on this choice. 

Continuum models are the most efficient way to include condensed-phase effects into quantum-mechanical calculations, and this is typically accomplished by using the self-consistent reaction field (SCRF) approach for the electrostatic component. Therefore it is very common to replace the quantal problem by a classical one in which the electronic energy plus the coulombic interactions of the nuclei, taken together, are modeled by a classical force field—this approach usually called molecular mechanics (MM) (Cramer and Truhlar, 1996). 

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