Potential energy surfaces structural analysis

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

In agreement with a simple Walsh-type analysis for a AH3 system with six valence electrons, the planar Dsh structure, 35, is a minimum on the potential energy surface for EH3 cations of all group 14 elements. However, a second Cs symmetric minimum, 36, exists for all cations but the methylium ion... 

The calculated MCSCF-MI potential energy surface is shown in Figure 6. Analysis of the data shows that the ionic structure again is less stable than the covalent one and than the free monomers. 

The first high-level theoretical evidence for the existence of dihydrogen bonds between CH4 and [NH4]+ came in 1996 [5]. In the sense of bonding geometry, this complex is not linear (Structure 6.5), has Csv symmetry, and exhibits three relatively short H- -H contacts with distances of 2.237, 2.357, and 2.226 A calculated at the RHF/6-31G, RHF/6-311++G, and MP2/6-31G lev-els, respectively. According to the frequency analysis at the RHF/6-31G level, the complex occupies a minimum on the potential energy surface of this system. The BSSE-corrected interaction energies have been calculated as —2.46,... 

The reaction between ammonia and methyl halides has been studied by using ab initio quantum-chemical methods.90 An examination of the stationary points in the reaction potential surface leads to a possible new interpretation of the detailed mechanism of this reaction in different media, hr the gas phase, the product is predicted to be a strongly hydrogen-bonded complex of alkylammonium and halide ions, in contrast to the observed formation of the free ions from reaction hr a polar solvent. Another research group has also studied the reaction between ammonia and methyl chloride.91 A quantitative analysis was made of the changes induced on the potential-energy surface by solvation and static uniform electric fields, with the help of different indexes. The indexes reveal that external perturbations yield transition states which are both electronically and structurally advanced as compared to the transition state in the gas phase. 

Other theoretical studies discussed above include investigations of the potential energy profiles of 18 gas-phase identity S 2 reactions of methyl substrates using G2 quantum-chemical calculations," the transition structures, and secondary a-deuterium and solvent KIEs for the S 2 reaction between microsolvated fluoride ion and methyl halides,66 the S 2 reaction between ethylene oxide and guanine,37 the complexes formed between BF3 and MeOH, HOAc, dimethyl ether, diethyl ether, and ethylene oxide,38 the testing of a new nucleophilicity scale,98 the potential energy surfaces for the Sn2 reactions at carbon, silicon, and phosphorus,74 and a natural bond orbital-based CI/MP through-space/bond interaction analysis of the S 2 reaction between allyl bromide and ammonia.17... 

Before getting into a deeper analysis of the concept of resonance, we must define precisely what we understand by chemical structure . One of the most basic concepts in molecular quantum mechanics is the one of potential energy surface (PES). It allows us to define a molecular structure as an arrangement of nuclear positions in space. The definition of molecular structure depends on the validity of the Bom-Oppenheimer approximation for a given state. Actually, its validity is limited to selected portions of the entire Bom-Oppenheimer PES. When a state is described by one PES, we call it an adiabatic state. It is clear that the concept of chemical structure , depends on the existence of a previously defined molecular structure . Only adiabatic states have a molecular structure . From now on, we will always be dealing with adiabatic states. 

The potential energy surface is the central quantity in the discussion and analysis of the dynamics of a reaction. Its determination requires the solution of the many-body electronic Schrodinger equation. While in the early days of theoretical surface science quantum chemical methods had a significant impact, nowadays electronic structure calculations using density functional theory (DFT) [20, 21] are predominantly used. DFT is based on the fact that the exact ground state density and energy can be determined by the minimisation of the energy functional E[n ... 

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