Energy decomposition method

As mentioned above, the method of KM is the most widely used variational energy decomposition method and works well for hydrogen-bonded systems, but it is not completely foolproof. Some of the shortcomings of the KM scheme include its limitation to only the HF method the final INT obtained is not corrected for unphysical lowering of energy caused by the basis set superposition error (BSSE). Also, molecular complexes separated by short distances, for instance, the cation-jt complexes of benzene with Li+ and Mg +, exhibit numerical instabilities in POL and CT energies. Several alternative schemes have been proposed to avoid problans of the KM EDA, one among which is the RVS analysis developed by Stevens and Fink and has been successfully applied to molecular complexes with various kinds of interactions. 

Figure 3 Schematic representation of the energy decomposition method.

The reaction path of the enzyme TIM was characterized by energy minimizations using the combined AMl/CHARMM potential.28 >285 in that study, the substrate and the catalytic side chains of His-95 and Glu-165 were treated quantum mechanically, and all other molecules in a stochastic boundary system (a 16-A sphere) were treated by the empirical CHARMM potential. The entire system consisted of 1250 protein atoms and 100 water molecules. An energy decomposition method was used to locate residues important in catalysis. In addition to the large energy contributions from conserved residues, other amino acids make smaller contributions, but their cumulative effect is significant. Interestingly, a number of residues far from the active site also have sizable effects on the enzyme s catalytic ability.284... 

The cluster-cage bonding in ScsNcsCts and ScsNcsCgo was also analyzed using the energy decomposition method (Campanera et al. 2002). The authors have shown that after the... 

In a recent paper. Mo and Gao [5] used a sophisticated computational method [block-localized wave function energy decomposition (BLW-ED)] to decompose the total interaction energy between two prototypical ionic systems, acetate and meth-ylammonium ions, and water into permanent electrostatic (including Pauli exclusion), electronic polarization and charge-transfer contributions. Furthermore, the use of quantum mechanics also enabled them to account for the charge flow between the species involved in the interaction. Their calculations (Table 12.2) demonstrated that the permanent electrostatic interaction energy dominates solute-solvent interactions, as expected in the presence of ion species (76.1 and 84.6% for acetate and methylammonium ions, respectively) and showed the active involvement of solvent molecules in the interaction, even with a small but evident flow of electrons (Eig. 12.3). Evidently, by changing the solvent, different results could be obtained. 

The shared-electron number (SEN) method was used for the evaluation of hydrogen bond energies. This method was developed for the evaluation of hydrogen bonds in compounds which cannot be decomposed into two parts such that the decomposition energy can be solely attributed to the broken hydrogen bond. Details of the SEN method are described in Ref. (82). 

To express the collective solvent reaction coordinate as in equation (6), it is necessary to define the specific diabatic potential surface for the reactant and product state. This, however, is not a simple task, and there is no unique way of defining such diabatic states. What is needed is a method that allows the preservation of the formal charges of the fragments of reactant and product resonance states. At the same time, solvent effects can be incorporated into electronic structure calculations in molecular dynamics and Monte Carlo simulations. Recently, we developed a block-localized wave function (BLW) method for studying resonance stabilization, hyperconjugation effects, and interaction energy decomposition of organic molecules.20-23 The BLW method can be formulated to specify the effective VB states.14... 

The use of the direct thermal decomposition method has been fairly widespread, and the values obtained by it will be discussed in the appropriate sections of this book. The O - N bond in alkyl nitrates and nitrites, and the G N bond in nitromethane are among those whose dissociation energy has been measured by this method, but in view of the possible kinetic complexities which may be encountered, such as those already mentioned in connection with the pyrolysis of organic iodides (see Section 4.2.4) the values obtained are often at best only tentative. 

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