Method for calculating potential energy surfaces

P. L. Fast, M. L. Sanchez, and D. G. Truhlar, Chem. Phys. Lett., 306, 407 (1999). Multi-Coefficient Gaussian-3 Method for Calculating Potential Energy Surfaces. 

Fast PL, Sanchez ML, Truhlar DG. Multi-coefficient Gaussian-3 method for calculating potential energy surfaces. Chem Phys Lett 1999 306 407-410. 

Quantum Chemical Methods for Calculating Potential Energy Surfaces... 

Wang B, Truhlar DG (2010) Combined quantum mechanical and molecular mechanical methods for calculating potential energy surfaces tuned and balanced redistributed-charge algorithm. J Chem Theory Comput 6 359-369... 

Recent developments in ab initio methods for calculating potential energy surfaces will require new, systematic approaches for obtaining useful analytical representations. Progress has been made in this area using for example multidimensional splinespolynomial root interpolation, and many-body expansion.An important goal is to develop methods that can be systematically applied and that require a relatively small number of ab initio points. 

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

For reactions that allow the use of g—n approximation, semiempirical methods of calculating potential energy surfaces were elaborated by Basilevsky 54 55> and by Salem 56,57>. An interesting feature of the last method, which stresses the importance of interactions between the top occupied orbital of one molecule and the lowest unoccupied orbital of the other, is that, while there is no need to calculate the whole potential surface, it is possible to derive a theoretical pathway for each reaction. Salem has recently put forward a theory of asymmetric induction, enabling the difference in energy between diastereoisomeric transition states and the diastereoisomer ratio to be calculated for an achiral reagent and a model chiral substrate 58>. 

There have recently been several books and review articles on interatomic forces and potential energy surfaces1,-18 and the proceedings of a conference on the topic has been published.19 The purpose of the present chapter will be to outline and discuss the various methods available for calculating potential energy surfaces for simple chemical reactions. These methods can be subdivided into four categories ... 

The valence-bond approach plays a very important role in the qualitative discussion of chemical bonding. It provides the basis for the two most important semi-empirical methods of calculating potential energy surfaces (LEPS and DIM methods, see below), and is also the starting point for the semi-theoretical atoms-in-molecules method. This latter method attempts to use experimental atomic energies to correct for the known atomic errors in a molecular calculation. Despite its success as a qualitative theory the valence-bond method has been used only rarely in quantitative applications. The reason for this lies in the so-called non-orthogonality problem, which refers to the difficulty of calculating the Hamiltonian matrix elements between valence-bond structures. 

The calculations are CASSCF/multireference single and double excitation Cl (MRCI). The use of the MRCI method for computing potential energy surfaces is supported by full Cl studies as discussed by Bauschlicher, Langhoff, and Taylor in another article in this volume. The accuracy of this approach has also been demonstrated for reaction (2) by Walch [2], who showed that by systematically expanding the active space and basis set, the computed barrier height converged to the currently accepted value [14]. 

Shepard Interpolation Method for Generating Potential Energy Surfaces for Dynamics Calculations. 

At the present time ab initio quantum chemical calculations seem to be the best method for deriving potential energy surfaces for unimolecular reactions. One s chemical intuition can be used to formulate potential energy surfaces for model systems, and for certain real reactions such potential energy surfaces may be qualitatively correct. However, for most unimolecular reactions it will be... 

As explained above, the QM/MM-FE method requires the calculation of the MEP. The MEP for a potential energy surface is the steepest descent path that connects a first order saddle point (transition state) with two minima (reactant and product). Several methods have been recently adapted by our lab to calculate MEPs in enzymes. These methods include coordinate driving (CD) [13,19], nudged elastic band (NEB) [20-25], a second order parallel path optimizer method [25, 26], a procedure that combines these last two methods in order to improve computational efficiency [27],... 

Calculations of - reaction rates by the transition-state method and based on calculated - potential-energy surfaces refer to the potential-energy maximum at the saddle point, as this is the only point for which the requisite separability of transition-state coordinates may be assumed. The ratio of the number of assemblies of atoms that pass through to the products to the number of those that reach the saddle point from the reactants can be less than unity, and this fraction is the transmission coefficient , k. (There are also reactions, such as the gas-phase colligation of simple radicals, that do not require activation and which therefore do not involve a transition state.) See also - Gibbs energy of activation, - potential energy profile, - Poldnyi. 

A somewhat modified MO LCAO scheme, without restriction on the identity of spin orbitals (p and

unrestricted Hartree-Fock (UHF) method and is usually used to treat open-shell systems (free radicals, triplet states, etc.). Electron correlation is partially taken into account in this method, and therfore it can be expected to be more efficient than the RHF method when applied to calculate potential energy surfaces of chemical rearrangements whose intermediate or final stages may involve the formation of free- or bi-radical structures. The potentialities of the UHF method are now under active study in organic reaction calculations. Also, it is successfully coming into use in chemisorption computations (6). 

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