Quantum methods using potential energy surfaces

6 Quantum methods using potential energy surfaces 

In order to incorporate quantum effects into the nuclear motions (vibrational effects and tunnelling), the time-dependent (nuclear) Schrodinger equation must be used in place of Newton s equation. 

Each time step thus involves a calculation of the effect of the Hamiltonian operator acting on the wave function. In fully quantum methods, the wave function is often represented on a grid of points, these being the equivalent of basis functions for an electronic wave function. The effect of the potential energy operator is easy to evaluate, as it just involves a multiplication of the potential at each point with the value of the wave function. The kinetic energy operator, however, involves the derivative of the wave function, and a direct evaluation would require a very dense set of grid points for an accurate representation. 

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A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

The topic of this review, reactions at metal surfaces, has been in general treated in a similar way to gas-phase reactivity. High level ab initio electronic structure methods are used to construct potential energy surfaces of catalytically important surface reactions in reduced dimensions. Once a chemically accurate potential surface is available, quantum or classical dynamics may be carried out in order to more deeply understand the microscopic nature of the reaction. 

Another attempt to perform a general mechanistic consideration of [3 + 21-cycloaddition reactions of nitronates with olefins has been made relatively recently by Prof. Denmark and coworkers (162) using modern quantum-chemical methods, which allow one to correctly calculate the potential energy surfaces for model substrates. Since these data have been summarized in the recent review (335), it is not necessary to consider them as comprehensively as the study in (337). 

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