Local Density Matrix Functional Theory (LDMFT)

• Applicant: Dr. Daniel Rohr
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2009 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 122142523

• Final Report Year: 2011

Final Report Abstract

The main objective of the project local density matrix functional theory (LDMFT) was to develop a theory that combines the successes of density functional theory (DFT) and density matrix functional theory (DMFT). Originally it was believed that this combination could be achieved by the optimized effective potential (OEP) method. However, a thorough investigation of the OEP method lead to the conclusion that OEP is not adequate to make this link. The direction of the research was adjusted to use the range-separation scheme to make the link between DFT and DMFT. During the project a new theory called srDFT+lrDMFT was developed using the range separation scheme. A particular approximation, srPBE+lrBB, to srDFT+lrDMFT was investigated. It turned out that this approximation does meet the objectives of the project. The most important objective of the project was to develop a method that shows excellent performance for the bond cleavage of covalent bonds. It was shown that srPBE+lrBB accurately reproduces the dissociation curve for a few small test systems. Another objective was the efficiency of the method. This was indeed achieved. Without any further approximations, which are conceivable, srPBE+lrBB scales N4, where N is the number of basis functions. In addition, an efficient algorithm to find the electronic ground state of srPBE+lrBB is available. It replaces the time consuming two-step optimization procedure used for approximations in DMFT. A part of the project was dedicated to the development of open-shell DMFT. The new theory was formulated and a number of exact conditions on the exact functional were proven. The new theory helped to investigate short-comings of present day approximations to DMFT and of srPBE+lrBB. It was found that srPBE +lrBB benefits from a partial cancellation of errors. In the future work on srDFT+lrDMFT will be continued. In particular, it will be investigated how newly found exact conditions on the exact functional can be exploited to develop new approximations.

Publications

• Journal of Molecular Structure, 934 (2010), 90
  D.R. Rohr, A. Savin
  
• Physical Review A, 82 (2010), 052502
  D.R. Rohr, J. Toulouse, K. Pernal