Non-bonded energies

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

It has already been stated that the evaluation of the non-bonded energy is by far the most time-consuming. Consider a series of calculations of linear alkanes CH3(CH2)n-2CH3. The number of individual contributions to each energy term is given in Table 2.4. 

Table 2.5 Comparing the distance behaviour of non-bonded energy contributions. (Distances are in A, energies in kcai/mol)...

Figure 2.8 Molecules A and B are chemical isomers but are composed of different atomic types (atomic typomers ). Thus, the sums of the heats of formation of their respective unstrained atom types, which serve as their zeroes of force-field energy, are different. To each zero, strain energy and non-bonded energy (the sum of which are force-field energy) are added to determine heat of formation. In this example, note that A is predicted to have a lower heat of formation than B even though it has a substantially larger strain energy (and force-field energy) this difference is more than offset by the difference in the reference zeroes...

Finally, there are a number of entirely mundane (but still very worthwhile ) steps that can be taken to reduce the total computer time required for a MD simulation. As a single example, note that any force on a particle derived from a force-field non-bonded energy term is induced by some other particle (i.e., the potential is pairwise). Newton s Third Law tells us that... 

In these models, the potential energy function is based on the molecular mechanics all-atom force field and includes the bond, angle, dihedral and non-bonded energy terms. The parameterization is based on the statistical analysis of sets of experimental structures. If a variable q describes a degree of freedom in the system (e.g., bond distances, angles, dihedrals) then, P(q), the probability distribution associated with this degree of freedom, is related to the potential of mean force, W(q), by the following equation... 

It has already been stated that the evaluation of the non-bonded energy is by far the most... 

I able 2.5 Companng the distance behaviour of non-bonded energy Contributions. (Distances ire in A, energies in kcal/mol)--------------------------------------------------- -------------------... 

Newton s second law, 2, 383 NMR shielding, 239 Non-adiabatic coupling elements, 55 Non-bonded energy, in force held methods, 18 Non-bonded list, in force held methods, 43 Non-local DFT methods, 184 Norm-extended Hessian ophmizahon method, 320... 

For the w electrons of ethylene (Fig. 29.5), there are two molecular orbitals since there are two linear combinations of the two component p orbitals. The broken line in the figure indicates the non-bonding energy level below it lies the bonding orbital, tt, and above it lies the antibonding orbital, tt. ... 

Eydw Is the van der Waals ene,rgy describing the repulsion or attraction between atoms that are not directly bonded. Together with the electrostatic term Eei (Section 2.2.6) they describe the non-bonded energy. Ey w may be interpreted as the part of the interaction which is not related to electrostatic energy due to (atomic) charges. This may for... 

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