Energy component analysis

Ihe interaction between atoms and molecules can vary from the weak attraction between a pair of closed-shell atoms (e.g. two rare gas atoms in a molecular beam) to the large energy associated with the formation of a chemical bond. Intermediate between these two extremes are interactions due to hydrogen bonding or electron donor-acceptor processes. In these intermediate cases it is often difficult to determine what factors are important in contributing to the interaction. For example, what can a hydrogen bond be ascribed to  

The electrostatic contribution equals the interaction between the unperturbed electron distributions of the two isolated species, A and B. It is identical to the classical Coulomb interaction and equals the difference 4 — Eg, where 4 is the energy associated with the product of the two individual wavefunctions, 4  

The electronic distributions of both X and Y will be changed by the presence of the other molecule. These polarisation effects cause a dipole to be induced in (say) molecule Y due to the charge distribution in molecule X and vice versa. Polarisation also affects the higher-order multipoles. To calculate the polarisation contribution we first calculate molecular wavefunctions and J b in the presence of the other molecule. The energy of the wavefunction 2 is determined as 2, where 2 is  

In determining and 2/ no electron exchange interactions are, considered. The overlap between the electron distributions of X and Y at short range causes a repulsion because to bring together electrons with the same spin into the same region of space ultimately leads to a violation of the Pauli principle. 

The charge transfer term arises from the transfer of charge (i.e. electrons) from occupied molecular orbitals on one molecule to unoccupied orbitals on the other molecule. This contribution is calculated as the difference between the energy of the supermolecule XY when this charge transfer is specifically allowed to occur, and an analogous calculation in which it is not. 

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Archontis, G. Simonson, T., Proton binding to proteins a free energy component analysis using a dielectric continuum model, Biophys. J. 2005, 88, 3888-3904... 

For the three conformers, the binding sequence is Na > K > Rb > Cs. This is supported by energy component analysis on the trajectories, as well as by Free energy perturbation (FEP) calculations. Intrinsically, Cs+ has the weakest interactions with both hosts. The largest contribution of the cation/host interaction energy comes from the ether ring rather than from the aromatic moieties. Each complex displays a clear conformational preference. Sodium is most stable in the cone conformation, whereas cesium is most stable in the 1,3-altemate conformation. 

Archontis G, Simonson T (2005) Proton binding to proteins a free energy component analysis... 

V. Daggett, F. Brown, and P. A. Kollman,/. Am. Chem. Soc., Ill, 8247 (1989). Free Energy Component Analysis A Study of Glutamic Acid 165 - Aspartic Acid 165 Mutation in Triosephosphate Isomerase. 

There are various forms of energy component analysis that can break down non-bonded contacts in terms of their fundamental... 

As discussed above, significant discrepancies were observed between quantum benchmarks and force fields for non-bonded interactions in the benzene dimer (Sherrill et al., 2009a). Analysis of the discrepancies was greatly aided by the use of energy component analysis, specifically the SAPT method. A detailed analysis of the parallel-displaced benzene dimer at a fixed vertical distance of 3.4 A is shown in Fig. 3.4. As seen from the figure, the London dispersion interaction computed by the force field through the attractive part of the Lennard-Jones potential is fairly accurate compared to the quantum SAPT results. Moreover, in this system, SAPT shows that... 

An energy component analysis like SAPT provides insight into the character of intermolecular interactions by providing a breakdown... 

Energy Component Analysis for Dilute Aqueous Solutions of Li, Na, F , and Cl" Ions. 

Abstract Some previous results of the present author are combined in order to develop a Hermitian version of the Chemical Hamiltonian Approach. In this framework the second quantized Bom-Oppenheimer Hamiltonian is decomposed into one- and two-center components, if some finite basis corrections are omitted. (No changes are introduced into the one- and two-center integrals, while projective expansions are used for the three- and four-center ones, which become exact only in the limit of complete basis sets.) The total molecular energy calculated with this Hamiltonian can then presented as a sum of the intraatomic and diatomic energy terms which were introduced in our previous chemical energy component analysis scheme. The corresponding modified Hartree-Fock-Roothaan equations are also derived they do not contain any three- and four-center integrals, while the non-empirical character of the theory is conserved. This scheme may be useful also as a layer in approaches like ONIOM. 

Energy component analysis of the energy minimization performed on the MD average triplex structures, in the presence of T1P3P water... 

Energy component analysis was earried out for the two simulations and it was observed that the quadruplex, as well as the counter ions and water appeared to reach a stable configuration after the first 100 ps of dynamics run. Average energies and their standard deviation are calculated over 100-1100 ps and are shown in Table 4. The d(G)7 quadruplex molecule, alongwith the 6 intercalated Na ions, when present, was treated as solute, while the water molecules and 24 Na ions in the surrounding medium constitute the solvent in both cases. 

The equations of free energy component analysis are derived from the statistical mechanical equations behind TI. From equation (32), substituting in a typical expression for the potential energy (equation 2), we get... 

Singh, U.C. and KoUman, P. (1983) Energy component analysis calculations on interactions involving iodine and hydrogen iodide. J. Phys. Chem., 87, 5386-5388. 

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