XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Cluster Embedding Method with Non-Orthogonal Wave Functions: DFT Kohn-Sham Embedding Equations and Vacant States
Emma K. Shidlovskaya1,2
1Information Systems Management Institute, Riga, Latvia

2Institute of Chemical Physics, University of Latvia, Riga, Latvia
When we theoretically study processes in large or infinite electron systems we have to treat the whole quantum system as two subsystems: small fragment of the system (cluster) and the remaining part of it. Problem "cluster in the field of the rest of system" is successfully solved in the frameworks of embedded molecular cluster (EMC) model [1] with orthogonal wave functions. Unfortunately, standard realization of EMC model leads to well-pronounced boundary effects [2].

To overcome limitations of the standard EMC model, we have treated cluster embedding problem in the frameworks of one-electron approximation with non-orthogonal wave functions. Equations for the cluster are obtained varying total energy of the system expressed in terms of non-orthogonal one-electron wave functions. Using these cluster embedding equations we have developed modified cluster embedding scheme. We have demonstrated that application of this scheme may radically reduce boundary effects in EMC model [2].

Possibility to generalize our embedding approach on the case of DFT Kohn-Sham one-electron equations is studied. We demonstrate that our variation procedure is compatible with Kohn-Sham method. Cluster embedding equations remain the same [3] if instead of Fock operator we use one-electron Kohn-Sham Hamiltonian.

For further applications of our cluster embedding method we should overcome limitations of one-electron approximation. It may be done by configurations interaction (CI) or perturbation theory (PT) methods. For this purpose we need occupied and vacant cluster states of the same localization. We have established that our initial embedding equations [2] give localized in the cluster region occupied states and delocalized vacant ones [4]. To get the same localization degree for the both occupied and vacant states, modified equations are proposed [4].

Modified cluster embedding equations [4] lead to correct description of electron transitions from occupied states to vacant ones. Treatment of electron correlation effects by CI or PT and proper description of excited states both by CI or DFT become possible. As the result, our embedding scheme now may be applied for quantum-chemical simulation of various phenomena.

[1] L.N.Kantorovich, J. Phys. C: Solid State Phys. 21, 5041 (1988).
[2] E.K. Shidlovskaya, Int. J. Quantum Chem. 89, 349 (2002).
[3] E.K. Shidlovskaya, in Topics in Chemistry and Material Science, Volume 2. Theoretical Aspects of Catalysis, eds. G. Vayssilov, T. Mineva, Heron Press, Sofia, 2009, pp. 11-18.
[4] E.K. Shidlovskaya, Computer Modelling and New Technologies 10, No 4, 17 (2006).



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