Potential functions nonbonded interactions

The matrix elements of the inactive electrons and the interaction between the active and inactive electrons can be approximated by expressing the corresponding potential surfaces as a quadratic expansion around the equilibrium values of the various internal coordinates, and by nonbonded potential functions for the interaction between atoms not bonded to each other or to a common atom ... 

The function Unb is used for interaction between the indicated EVB atoms while t/ b is used for nonbonded interactions between other atoms which are not bonded to each other or to a common atom. The interactions between the EVB oxygens are modeled by the corresponding 6-12 potential. 

Potential functions induced-dipole terms, 84-85 minimization, 113-116 nonbonded interactions, 84-85 Potential of mean force, 43, 144 Potential surfaces, 1,6-11, 85, 87-88, 85 for amide hydrolysis, 176-181,178,179, 217-220, 218... 

The first two terms on the right-hand side of Eq. (83) are usually assumed to be harmonic, as given for example by Eq. (6-74). The third term is often developed in a Fourier series, as given by Eq. (82). The potential function appropriate to the interaction between nonbonded atoms is taken to be of the Lennard-Jones type (Section 6.7.3). In all of these cases the necessary force constants are estimated by comparing the results obtained from a large number of similar molecules. If electrostatic interactions are to be considered, effective atomic charges must be suggested and Coulomb s law applied directly [see Eq. (6-81)]. 

The first three terms, stretch, bend and torsion, are common to most force fields although their explicit form may vary. The nonbonded terms may be further divided into contributions from Van der Waals (VdW), electrostatic and hydrogen-bond interactions. Most force fields include potential functions for the first two interaction types (Lennard-Jones type or Buckingham type functions for VdW interactions and charge-charge or dipole-dipole terms for the electrostatic interactions). Explicit hydrogen-bond functions are less common and such interactions are often modeled by the VdW expression with special parameters for the atoms which participate in the hydrogen bond (see below). 

Rigid-geometry ab initio MO calculations of 86 torsional isomers of the dimethylphosphate anion (CH30)2P02 led to the determination of parameters for the Lennard-Jones type of nonbonded interaction, two- and three-fold torsional, and electrostatic interaction potential functions (215). Extension of this approach to full relaxation ab initio and MM schemes will be extremely useful, not only for phosphorus but also for other heteroatoms. 

Conformational energies are calculated for chain segments in poly(vlnyl bromide) (PVB) homopolymer and the copolymers of vinyl bromide (VBS and ethylene (E), PEVB. Semlempirical potential functions are used to account for the nonbonded van der Waals and electrostatic Interactions. RIS models are developed for PVB and PEVB from the calculated conformational energies. Dimensions and dipole moments are calculated for PVB and PEVB using their RIS models, where the effects of stereosequence and comonomer sequence are explicitly considered. It is concluded from the calculated dimensions and dipole moments that the dipole moments are most sensitive to the microstructure of PVB homopolymers and PEVB copolymers and may provide an experimental means for their structural characterization. 

A harmonic potential is a good approximation of the bond stretching function near the energy minimum (Fig. 2.7). Therefore, most programs use this approximation (see Eq. 2.6) however the limits of the simplification have to be kept in mind, in those cases where the anharmonicity becomes important. Apart from the possibility of including cubic terms to model anharmonicity fsee the second term in Eq. 2.14), which is done in the programs MM2 and MM3[1,2,2 241, the selective inclusion of 1,3-nonbonded interactions can also be used to add anharmonicity to the total potential energy function. 

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

A method for calculating the barriers to internal rotation has recently been proposed (Scott and Scheraga, 1965). It is based on the concept that the barrier arises from two effects, exchange interactions of electrons in bonds adjacent to the bond about which internal rotation occurs, and nonbonded or van der Waals interactions. The exchange interactions are represented by a periodic function, and the nonbonded interactions either by a Buckingham 6-exp or Lennard-Jones 6-12 potential function, the parameters of which are determined semi-empirically. (The parameters of the nonbonded potential energy functions are discussed in Section VB.)... 

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