Electron diabatic

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. 

The treatment developed here is based on the density matrix of quantum mechanics and extends previous work using wavefunctions.(42 5) The density matrix approach treats all energetically accessible electronic states in the same fashion, and naturally leads to average effective potentials which have been shown to give accurate results for electronically diabatic collisions. 19) The approach is taken here for systems where the dynamics can be described by a Hamiltonian operator, as it is possible for isolated molecules or in models where environmental effects can be represented by terms in an effective Hamiltonian. 

Quantum reaction dynamics, electronic states (Continued) diabatization matrix, 295-300 electronically diabatic representation, 292-293... 

The components of the two vectors ( 1 i 2X when multiplied by the electronic (diabatic) basis set ( cj>i), 14b)), form the corresponding electronic adiabatic basis... 

Ethylene electronic isomerism is introduced as a new concept and examined from the perspective of the generalized electronic diabatic (GED) scheme. In chemistry isomerism is related to distributions in space of atomic nucleus in one and the same adiabatic potential energy surface. Therefore, in this case cis and trans isomers would be indistinguishable when the four hydrogen atoms are identical. Nevertheless, in this paper we show that isomerism is an electronic... 

In principle, the time evolution of a particular linear superposition on the molecular base states will reflect a chemical process via the changes shown by the amplitudes. This represents a complete quantum mechanical representation of the chemical processes in Hilbert space. The problem is that the separability cannot be achieved in a complete and exact manner. One way to introduce a model that is able to keep as much as possible of the linear superposition principle is to use generalized electronic diabatic base functions. 

Constructing a linearly independent set of factored functions solves the problem in the sense that eq. (8) is diagonal. The diabatic potential is used to define equations for the nuclear wavefrinctions leading to a product set ( )k(q)Ckm(Q) by solving for each electronic diabatic potential the corresponding equation (9) ... 

The time evolution operator propagates an arbitrary quantum state thanks to the non-zero matrix elements (Ve0ph)j m ,jm- The set ( )j(q)Qm(Q) has all electronic base states corresponding to all possible chemical species in the sense discussed above only because the generalized electronic diabatic set is complete. 

A manner to do away with the problem is to introduce appropriate algorithms in the sense that mappings from real space to Hilbert space can be defined. The generalized electronic diabatic, GED approach fulfils this constraint while the BO scheme as given by Meyer [2] does not due to an early introduction of center-of-mass coordinates and rotating frame. The standard BO takes a typical molecule as an object description. Similarly, the wave function is taken to describe the electrons and nuclei. Thus, the adiabatic picture follows. The electrons instantaneously follow the position of the nuclei. This picture requires the system to be always in the ground state. 

Once the electronic diabatic base set is obtained, the quantum state is a linear superposition where the PCB configuration enters parametrically as Ck amplitudes ... 

The GED approach is a general procedure based on the exact solutions to the n-electron system. Only one Hamiltonian is required at variance with the infinite Hamiltonian approach (defined on the parametric -space) characteristic of the BO scheme. All the base functions are expanded from a unique origin of the I-frame. The characteristics of the n-electrons diabatic base functions are independent from the positions taken by the sources of the external potential. 

The non-adiabatic character of the process under study is included in the present approach in the evaluation of the initial wavepacket in Eq.(7). In an electronic diabatic representation, the electronic wavefunctions are considered to do not depend on the nuclear coordinates, so that the coupling between different states is only given by the electronic Hamiltonian, being of potential-type character. 

D. Beksic and D. A. Micha. Electronically diabatic quantum dynamics of molecular desorption. J. Chem. Phys., 103 3795, 1995. 

Mulliken-Hush formula for the diabatic electronic coupling. We suggest that the latter approach might be rather useful to thoroughly investigate multistate effects on the electronic diabatic coupling recently pursued by Cave and co-workers [66]. 

The solution phase theory for the reaction is couched in terms of coupled electronically diabatic, or VB states, B and A. B has a bound state character, with the charge mainly localized on the ring, while A will be a dissociative state with the charge localized in the C - Cl moiety. The curves VB,A for these states and the coupling between them can be extracted from vacuum ab initio electronic structure calculations of the electronically adiabatic ground- and excited-state curves Vg e via... 

O. Tapia, Quantum linear superposition theory for chemical processes A generalized electronic diabatic approach, Adv. Quantum Chem. 56 (2009) 31-93. 

The time-dependence of the electronic (diabatic) populations of the B state in the A-B coaled state dynamics is shown in Fig. 6b. The WP is initially (t = 0) located on the B state and therefore, its population starts from 1.0. Since th e ilibrium minimum of the B state nearly coincides with the minimum ofjhe A-B CIs, the population of this state decays (nonradiatively) rapidly to the A state through the CIs, and reaches to a value of 0.05 at longer times. The initial fast decay of the population relates to a decay rate of 30 fs for the B state. 

Fig. 9 Decay of the electronic (diabatic) populations of the A (panel a) and B (panel b) electronic states in the coupled X—A—B—C states dynamics of PA +...

Another PER exists that is based on an underlying electronic diabatic perspective (although aspects of the electronic coupling are included) the PER in the electronically adiabatic ET limit for a curve-crossing picture is [40]... 

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