Generalized electronic diabatic

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. 

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. 

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

We examine a post-Bom-Oppenheimer approach based on a generalized electronic diabatic (GED) ansatz for electronuclear dynamics in external electromagnetic belds. The model is a quantum -electron system interacting with a set of m classical positive charges located at = ( 1) m) itt laboratory space. The system s Coulomb Hamiltonian is Wc =... 

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 correlation function can be written in a basis set Ra) = R) a) chosen as the tensor product of the coordinate representation for the nuclear degrees of freedom, and a nuclear coordinate independent electronic basis. In this chapter we shall refer to this electronic representation as the diabatic basis. (We refer the interested reader to reference [40] for the development of this approach with a more general electronic representation). By inserting resolutions of the identity in this basis, one obtains... 

Non-adiabatic case. The diabatic states or the adiabatic states may be used to construct the basis set for the motion of the electrons and nuclei in the non-adiabatic approach. Such a basis function is taken as a product of the electronic (diabatic or adiabatic) wave function and of a rovibrational wave function that depends on R. In a non-adiabatic approach the total wave function is a superposition of these product-like contributions [a generalization of eq. (6.7)] ... 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

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