Multi-electron states

Martinez T J, BenNun M and Levine R D 1996 Multi-electronic-state molecular dynamics—a wavefunction approach with applications J. Phys. Chem. 100 7884... 

Two central problems remain. One is that one needs the potential which governs the motion. In many-atom systems, even if the motion is confined to the ground electronic state, this potential is a function of the spatial configuration of all the atoms. It is therefore a function of many variables, so its analytical form is far from obvious, nor do we necessarily want to know it everywhere. Indeed, we really only want it at each point along the actual trajectory of the system (so that the forces can be computed and thereby the next point to which the system will move to can be determined). Such an approach has been implemented [25] and applied to many-atom systems, and an extension to a multi-electronic state dynamics will be important... 

It can indeed be shown that this form gives rise to the Slater-Condon rules for matrix elements between multi-electron states. Further expressions for two-particle operators may be found in the literature [8,9],... 

M. Amarouche, F. X. Gadea,and J. Durup, Chem. Phys., 130,145 (1989). A Proposal for the Theoretical Treatment of Multi-Electronic-State Molecular-Dynamics—Hemiquantal Dynamics with the Whole DIM Basis (HWD)—A Test on the Evolution of Excited Ar3 Cluster Ions. 

Nakamura and Truhlar [26] have developed direct calculation techniques to obtain quasi-diabatic states. Yet, a main issue remains there is no clear quantum-mechanical interpretation as to the meaning of an electronic wave ftinction that depends parametrically on the positive charge positions [4]. The multi-electronic-state molecular dynamics approach by Martinez et al. [27] highlights the problems raised by the use of the BO scheme. The crossing points and the uncontrolled coupling of electronic states... 

The energy term diagrams, i.e., energies of multi-electron states vs. parameter G4 both in units of Racah parameter B, obtained for d°+ (d°) ions in D31, sites... 

Amarouche M, Gadea F, Dump J (1989) A proposal for the theoretical treatment of multi-electronic-state molecular dynamics hemiquantal dynamics with the whole dim basis (HWD). A test on the evolution of excited ar3- - cluster ions. Chem Phys 130 145-157... 

A final task is to calculate the transition-moments between the corresponding multi-electronic states based on the orbital-transition moments obtained. In thetris-chelate complex under consideration, a state transition can be associated with each allowed orbital-transition. The Ai corresponds to the closed-shell ground state, based on the (f2gf configuration. Both thee twofold-degenerate E state. As an example, the 6 states are written in determinantal notation as follows, where we write only the orbitals that are singly occupied ... 

Martinez TJ, Ben-Nun M, Levine RD (1996) Multi-electronic-state molecular dynamics a wave function approach with applications. J Phys Chem 100 7884... 

One has to be careful when allowing an annihilation operator to act on a multi-electron state. In the case of a two-electron state, for example, one may write ... 

The wavefunction with the required information for the electronic and vibrational aspects of a molecule would depend on the coordinate set of the electrons r to account for the multi-electronic state and those of the nuclei R to account for the vibrational state. As a shorthand, the combined picture is referred to as a vibronic state. We use the symbol to refer to states that contain information about multiple particles and write F( r,R) to mean that the state is a function of both electron and nuclear coordinates. 

Fe site. This electron is the igj, 3d-electron of Fe since it is in the high spin multi-electronic state while the state of lowest energy for Fe " is the... 

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