XVIth International Workshop on Quantum Systems in Chemistry and Physics 

Abstract 
Cluster Embedding Method with NonOrthogonal Wave Functions: DFT KohnSham Embedding Equations and Vacant States 
Emma K. Shidlovskaya^{1,2}
^{1}Information Systems Management Institute, Riga, Latvia
^{2}Institute 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 wellpronounced boundary effects [2].
To overcome limitations of the standard EMC model, we have treated cluster embedding problem in the frameworks of oneelectron approximation with nonorthogonal wave functions. Equations for the cluster are obtained varying total energy of the system expressed in terms of nonorthogonal oneelectron 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 KohnSham oneelectron equations is studied. We demonstrate that our variation procedure is compatible with KohnSham method. Cluster embedding equations remain the same [3] if instead of Fock operator we use oneelectron KohnSham Hamiltonian.
For further applications of our cluster embedding method we should overcome limitations of oneelectron 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 quantumchemical 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. 1118.
[4] E.K. Shidlovskaya, Computer Modelling and New Technologies 10, No 4, 17 (2006).


