Quantum chemical equations potential energy surfaces

Separation of the movement of the nuclei and electrons. This is possible because the electrons move much more rapidly (smaller mass) than the nuclei. The position of the nuclei is fixed for the calculation of the electronic Schrodinger equation (in MO calculations the nuclear positions are then parameters, not quantum chemical variables). Born-Oppenheimer surfaces are energy vs. nuclear structure plots which are (n + 1)-dimensional, where n is 3N- 6 with N atoms (see potential energy surface). 

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 ... 

The only type of chemical reaction we are likely to ever be able to solve rigorously in a quantum mechanical way is a three-body reaction of the type A+BC - AB+C. (See Fig. 5.) The input information to the dynamicist is the potential energy surface computed by the quantum structure chemist. Given this potential surface, we treat the nuclear collision dynamics using Schrodinger s equation to model the chemical reaction process. 

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. 

A straightforward approach toward the problem of calculating reaction rates is to divide the process into three distinct parts. First, the multidimensional potential energy surface reflecting the energy of interaction between all atoms must be determined. The many complexities involved in such a determination have already been discussed it is sufficient to say here that an exact surface is not yet known for any chemical reaction. However, given a potential energy surface, the second part of the problem is to solve the quantum-mechanical or classical equations of motion as a function of all initial states... 

The potential energy surface, i.e., the variation of the energy of a system as a function of the positions of all its constituent atoms, is fundamental to the quantitative description of chemical structures and reaction processes. The quantum mechanical evaluation of potential surfaces is based on the use of the Born-Oppenheimer approximation (e g., see Hehre et al. 1986 Lasaga and Gibbs 1990). In the Bom-Oppenheimer approximation, the positions of the nuclei in the system, R, are fixed and the wave equation is solved for the wavefunction of the electrons. The energy, E, will then be a function of the atomic positions E R), i.e., the solutions will produce a potential surface. If we know E R) accurately, we can predict the detailed atomic forces and the chemical behavior of the entire system. 

To deal with photoinduced chemical processes involving several potential surfaces, we need to incorporate the interaction between the molecule and the incident light pulses into the quantum mechanical description. In the semiclassical dipole approximation, the time-dependent Schrodinger equation for two potential energy surfaces Vi and V2 coupled by the laser field reads as ... 

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