Adiabatic Reaction Wave function

The vibrationally adiabatic proton wave functions provide the most useful description for PCET reactions. For typical single proton transfer reactions, the lowest adiabatic vibrational state is a double well along Zp, as shown in Figure 2a. In gen-... 

The electronic wave function has now been removed from the first two terms while the curly bracket contains tenns which couple different electronic states. The first two of these are the first- and second-order non-adiabatic coupling elements, respectively, vhile the last is the mass polarization. The non-adiabatic coupling elements are important for systems involving more than one electronic surface, such as photochemical reactions. 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

The theory of the multi-vibrational electron transitions based on the adiabatic representation for the wave functions of the initial and final states is the subject of this chapter. Then, the matrix element for radiationless multi-vibrational electron transition is the product of the electron matrix element and the nuclear element. The presented theory is devoted to the calculation of the nuclear component of the transition probability. The different calculation methods developed in the pioneer works of S.I. Pekar, Huang Kun and A. Rhys, M. Lax, R. Kubo and Y. Toyozawa will be described including the operator method, the method of the moments, and density matrix method. In the description of the high-temperature limit of the general formula for the rate constant, specifically Marcus s formula, the concept of reorganization energy is introduced. The application of the theory to electron transfer reactions in polar media is described. Finally, the adiabatic transitions are discussed. 

The consideration of the reactions of the electron tunneling transfer was until now based on Born-Oppenheimer s adiabatic approach (see Section 2 of Chapter 2) that was used for the description of the wave functions of the initial and final states. The electron tunneling interaction V results in the non-adiabatic transition between these states, if the matrix element Vtf... 

So far, we have considered various theoretical treatments of time-dependent wave packets controlled by laser pulses to produce a desired product in a chemical reaction. Another type of problem, based on adiabatic behavior of wave functions, is the transfer of population from one state to another. 

By performing the above procedures, the solvent effect is taken into account at the VBSCF level, whereby the orbitals and structural coefficients are optimized till self-consistency is achieved. Like VBSCF, the VBPCM method is suitable for diabatic states, which are calculated with the same solvent field as the one for the adiabatic state. Thus, it has the ability to compute the energy profile of the full state as well as that of individual VB structures throughout the course of a reaction, and in so doing to reveal the individual effects of solvent on the different constituents of the wave function. In this spirit, it has been used to perform a quantitative VBSCD analysis of a reaction that exhibits a marked solvent effect, the Sn2 reaction Cl- + CH3CI —> CH3CI + Cl- (55). 

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