Energy representation method

Two protein complexes were examined a complex consisting of bovine trypsin and CMTl-1 squash inhibitor (PDB ID of the complex IPPE [60]), and RNase SA in complex with barstar (PDB ID of the complex 1AY7 [61]). They consist of 252 and 185 residues, respectively. We prepare a set of decoy strucmres as described in the following, and select the right structure through free-energy calculations with the energy-representation method. 

As one can easily note, a well-defined hierarchy of successive interaction energy approximations, varying from the most expensive MP2 method to the various electrostatic energy representation (the more simplified the theory, the less computationally demanding calculation), demonstrates the utility of this decomposition scheme (Figure 8-3) ... 

The evaluation of the free energy is essential to quantitatively treat a chemical process in condensed phase. In this section, we review methods of free-energy calculation within the context of classical statistical mechanics. We start with the standard free-energy perturbation and thermodynamic integration methods. We then introduce the method of distribution functions in solution. The method of energy representation is described in its classical form in this section, and is combined with the QM/MM methodology in the next section. 

The above drawbacks of RISM and its variants are well documented since their first formulations [11,12], They are all related to the point that a molecule is treated as a collection of sites. In the method of energy representation introduced next, each of the solute and solvent molecules is taken to be a single unit as a whole, and those drawbacks vanish. 

In the currently used version of the method of energy representation [15,16,19], the solvation free energy A/x is approximately expressed in terms of distribution functions constructed from pe in the solution and pure solvent systems. In our treatments, the solution system refers to the system in which the solute molecule interacts with the solvent under the solute-solvent interaction v of interest at full coupling. In the solution, the average distribution pe of the v value is relevant in the approximate construction of Ap, and is given by... 

Secondly, the treatment of inhomogeneous system and clusters is straightforward. So far, the formulation does not assume the system homogeneity and the thermodynamic limit. The application to inhomogeneous and/or finite systems is then possible without modification. The binding of a molecule to such nanoscale structures as protein, micelle, and membrane can be viewed as a solvation in an inhomogeneous and finite, mixed solvent [57], The method of energy representation can thus be a... 

In Sections 17.2 and 17.3, we have reviewed the QM/MM approach based on the real-space grids [40,41,58,59,60,61,62] and the novel theory of solutions [14,15,16], respectively. As has been suggested, the theory of energy representation is readily applicable to a solute that is quantum chemically described. The present section is devoted to the details of the methodology, referred to as QM/MM-ER, developed by combining the QM/MM approach with the theory of energy representation [19]. The point of the method is to divide the total solvation free energy into the contributions due to the pairwise additive interaction between the solute and the solvent and the residual contribution due to the electron density fluctuation. A focus will be placed on the treatment of the many-body interaction inherent in the quantum chemical object. 

In this subsection, we presented an approximate scheme to evaluate the contribution S/u. of the electron density fluctuation to the excess chemical potential. Although we saw that this contribution is minor for a QM water molecule in ambient and supercritical water, it should emphasized that 8p, can be treated quantitatively in the method of energy representation. Actually, the treatment of the electron density fluctuation is not directly possible in the PCM and RISM-SCF methods. Furthermore, the approximate 8p, is exact to second order in the solvent density and in the electron density fluctuation. Thus, when the effect of the electron density fluctuation is weak, the calculation of 5p, is expected to be accurate. 

Figure 3 Schematic representation of the energy decomposition method.

Scheme 15.2 Schematic representation of the energy transfer method used for determination of the triplet molar absorption coefficient in the laser flash photolysis apparatus...

The Hamiltonian and the coordinates are discretized by means of the generalized pseudospectral (GPS) method in prolate spheroidal coordinates [44-47], allowing optimal and nonuniform spatial grid distribution and accurate solution of the wave functions. The time-dependent Kohn-Sham Equation 3.5 can be solved accurately and efficiently by means of the split-operator method in the energy representation with spectral expansion of the propagator matrices [44-46,48]. We employ the following split operator, second-order short-time propagation formula [40] ... 

A Quantum Chemical Approach to the Free Energy Calculations in Condensed Systems The QM/MM Method Combined with the Theory of Energy Representation. 

Figure 5.4 Pictorial representation of the surfaces that may be used to implement the energy flux method for a molecule + metal nanoparticle...

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