Exploring Potential Energy Surfaces

Both molecular and quantum mechanics methods rely on the Born-Oppenheimer approximation. In quantum mechanics, the Schrodinger equation (1) gives the wave functions and energies of a molecule. 

H = (kinetic energy) + (kinetic energy+ (repulsion) + (repulsion)gg + (attraction 

Nuclei have many times more mass than electrons. During a very small period of time when the movement of heavy nuclei is negligible, electrons are moving so fast that their distribution is smooth. This leads to the approximation that the electron distribution is dependent only on the fixed positions of nuclei and not on their velocities. This approximation allows two simplifications 

Since the nuclear-nuclear repulsion is constant for a fixed configuration ofatoms, this term also drops out. The Hamiltonian isnow purely electronic. 

After solving the electronic Schrodinger equation (equation 4), to calculate a potential energy surface, you must add back nuclear-nuclear repulsions (equation 5). 

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Chemical Reactivity Exploring Potential Energy Surfaces... 

Schlegel, H. B. 2003. Exploring Potential Energy Surfaces for Chemical Reactions An Overview of Some Practical Methods , J. Comput. Chem. 124, 1514. 

Schlegel, H.B., Exploring potential energy surfaces for chemical reactions an overview of some practical methods, J. Computational Chem., 24, 1514—1527, 2003. 

Deng L, Exploring Potential Energy Surfaces using Density Functional Theory and Intrinsic Reaction Coordinate Methods, PhD Thesis (University of Calgary, Calgary, 1996)... 

Because of slow convergence, lack of size consistency, and disappointing results of CISD calculations. Cl calculations have lost their former dominance in correlation calculations, and several other correlation methods have been developed (Sections 15.18-15.20). However, multireference Cl calculations (MRCI) are widely used to explore potential-energy surfaces— for example in studying chemical reactions (Section 15.26). 

A comparative ab initio study [22] on these two alternative reaction pathways concludes that a zwitterionic structure of the type suggested by Westheimer is not a stationary point on the explored potential energy surfaces for the systems H2O + (H0)2P(0)H and H2O + (H0)3P(0). Two types of critical points were found for these model systems. The first type corresponds to transition structures for the concerted addition of water to these phosphoryl compounds (Figure 3.1). 

HyperChem combines molecular computation and visualization tools with a flexible and intuitive graphical user interface. Its computational algorithms enable users to calculate and explore potential energy surfaces for molecular systems, both simple and complex. Energy minimization and transition state search, molecular dynamics, Langevin dynamics, and Monte Carlo calculations are supported, with extensive user control and customization capabilities. This article summarizes methods used to compute potential energy surfaces in HyperChem, and provides references to the literature that describe the theoretical and computational approaches upon which HyperChem s implementation is based. More complete and current information may be obtained from Hypercube s website. 

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