Molecular systems coupling

In this review we discuss the theoretical frame which may serve as a basis for a DFT formulation of solvent effects for atoms and molecules embedded in polar liquid environments. The emphasis is focused on the calculation of solvation energies in the context of the RF model, including the derivation of an effective energy functional for the atomic and molecular systems coupled to an electrostatic external field. 

Based on the above definitions and approximations, we have the following representation of the Hamiltonian for the molecular system coupled to the two dielec-... 

Molecular dynamics methods can be used to explore the isoenergy phase space of molecular systems. Coupled Newton s equations of motion for each atom in the system are solved to generate the trajectory for each atom moving in the force field of all other atoms ... 

The vibronic coupling model has been applied to a number of molecular systems, and used to evaluate the behavior of wavepackets over coupled surfaces [191]. Recent examples are the radical cation of allene [192,193], and benzene [194] (for further examples see references cited therein). It has also been used to explain the lack of structure in the S2 band of the pyrazine absoiption spectrum [109,173,174,195], and recently to study the photoisomerization of retina] [196],... 

THE ELECTRONIC NON-ADIABATIC COUPLING TERM IN MOLECULAR SYSTEMS ... 

B. The Study of a Real Three-State Molecular System Strongly Coupled (2,3) and (3,4) Conical Intersections... 

By following Section II.B, we shall be more specific about what is meant by strong and weak interactions. It turns out that such a criterion can be assumed, based on whether two consecutive states do, or do not, form a conical intersection or a parabolical intersection (it is important to mention that only consecutive states can form these intersections). The two types of intersections are characterized by the fact that the nonadiabatic coupling terms, at the points of the intersection, become infinite (these points can be considered as the black holes in molecular systems and it is mainly through these black holes that electronic states interact with each other.). Based on what was said so far we suggest breaking up complete Hilbert space of size A into L sub-Hilbert spaces of varying sizes Np,P = 1,..., L where... 

When studying molecular systems one encounters two almost insurmountable difficulties (1) That of numerically treating the non-adiabatic coupling terms that are not only spiky—a feature that is in itself a recipe for numerical... 

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