Semiempirical potential energy surfaces

The characteristic ratio of atactic polylferf.-butyl vinyl ketone) is determined from light scattering and viscosimetry measurements, and at 300 K in benzene the dipole moment ratio and its temperature coefficient are measured. Calculations of Ca and Da based on a two-state RIS model, with parameters independently derived from a previously developed semiempirical potential energy surface and from epimerization equilibrium measurements for dimeric and trimeric oligomers, are in excellent agreement with the experimental results. The predicted temperature coefficient is positive but lower in magnitude than that observed. 

Since the early work mentioned above, H3 calculations have proceeded along the two lines, semiempirical or ab initio. Semiempirical potential energy surfaces have been produced by Sato, Porter and Karplus, Cashion and Herschbach, and Salomon. ... 

Rossi and Truhlar o give a novel example of the use of GAs for parameterizing semiempirical potential energy surfaces. The object is to obtain a set of semiempirical parameters that would reproduce a surface described by a small number of high level ab initio data points. An SGA is used, yielding good fits. 

In so far as Westheimer s treatment correlates isotope effects with changes in force constants and the structure of the transition state, it cannot be tested without some experimental measure of these properties, and usually it has been assumed that, within a family of related reactions, the structure of the transition state varies smoothly with the rate constants and equilibrium constants of the reactions, with reactant-like transition states associated with reactive substrates and exothermic reactions. This assumption, which derives from observations of rate-equilibrium and reactivity-selectivity correlations [2, 3, 42], as well as calculations of semiempirical potential energy surfaces [43], is generally known (not quite accurately) as Hammond s Postulate [44]. It should be noted that while the postulate probably applies more generally to proton transfers than to other reactions, recent considerations of its scope and limitations [45, 46], based on extensive experimental experience, strongly suggest that departures... 

N. J. Brown and D. M. Silver, Comparison of reactive and inelastic scattering of H2 + D2 using four semiempirical potential energy surfaces, J. Chem, Phys. 72 3869 (1980). 

Ah initio trajectory calculations have now been performed. However, these calculations require such an enormous amount of computer time that they have only been done on the simplest systems. At the present time, these calculations are too expensive to be used for computing rate constants, which require many trajectories to be computed. Semiempirical methods have been designed specifically for dynamics calculations, which have given insight into vibrational motion, but they have not been the methods of choice for computing rate constants since they are generally inferior to analytic potential energy surfaces fitted from ah initio results. 

DIM (diatomics-in-molecules) a semiempirical method used for representing potential energy surfaces... 

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... 

Before discussing the kinds of kinetic information provided by potential energy surfaces we will briefly consider methods for calculating these surfaces, without going into detail, for theoretical calculations are outside the scope of this treatment. Detailed procedures are given by Eyring et ah There are three approaches to the problem. The most basic one is purely theoretical, in the sense that it uses only fundamental physical quantities, such as electronic charge. The next level is the semiempirical approach, which introduces experimental data into the calculations in a limited way. The third approach, the empirical one, makes extensive use of experimental results. 

Potential energy surfaces calculated by means of the London equation (5-15) cannot be highly accurate, but the results have been very useful in disclosing the general shape of the surface and the reaction coordinate. The London equation also forms the basis of some semiempirical methods. 

The semiempirical methods combine experimental data with theory as a way to circumvent the calculational difficulties of pure theory. The first of these methods leads to what are called London-Eyring-Polanyi (LEP) potential energy surfaces. Consider the triatomic ABC system. For any pair of atoms the energy as a function of intermolecular distance r is represented by the Morse equation, Eq. (5-16),... 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

The semiempirical nature of the methods used to construct multidimensional potential energy surfaces makes the quantitative validity of the results questionable. Hence the present state of the theoretical calculation of activation energies is unsatisfactory. 

Semiempirical Calculations. The CeH5N potential energy surface has received less attention from theoreticians than from experimentalists. Until recently, species on the reaction pathway for ring expansion of lb had been stud-... 

Much of the early literature in this field is cited in Haddon s (1979b) semiempirical and ab initio study. Haddon concluded that there are two minima on the potential energy surface, one corresponding with the... 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

Semiempirical and ab initio calculations of the potential-energy surface for the addition of CI2 to CH2=CH2 in the presence of CP in the gas phase and in polar solvent led to the identification of the reactant [CP.Cl2-CH2=CH2] and the product [CH2C1CH2C1-CP] minima in the gas phase only the product minimum was found in the solution. Potential barriers in the two systems were compared. 

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