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Development of new non-empirical DFT functionals

Final Report Summary - NEWDFTFUNCT (Development of new non-empirical DFT functionals.)

The development of new functionals in the framework of the density matrix and density functional theories (DMFT and DFT) stands among the most important challenges of modern theoretical chemistry. The accuracy and range of applicability of these theories depends critically on the construction of new functionals. This project aimed at the production of benchmark results for the harmonium atom to construct new functionals. This goal was achieved through the execution of three main tasks: (A) Characterization of few-electron harmonium atoms, (B) Development of a natural-orbital based DMFT functional and (C) the development of a non-empirical DFT functional.
During this project I have generated enough physical data for three- and four-electron harmonium atoms. In particular, the energetics, the electron density, natural orbitals and occupancies of three- and four-electron harmonium have been published. The accuracy of our results exceeds by far the accuracy of the few results available in the literature. These results have been complemented with the analysis of the electron correlation regimes in these model systems. These results can be used to choose electron correlation indicators to design new DFT and DMFT functionals.
I have also worked on the decomposition of the total angular momentum of spin, S2. An important property of this decomposition is that isolated atoms within a molecule should provide the local spin of the free atom. Interestingly, many DMFT functionals do not fulfill this property because the inherent second-order density matrix behind the functional expression does not fulfill it. I have used this property to enforce new conditions in the construction of DMFT functionals. This subproject will be fully accomplished when we achieve the construction of new DMFT functional, using the results recently obtained to construct a dynamic correlation indicator. Unfortunately, the enforcement of the early termination of this project delays the fulfillment of this task until new funds are allocated to this aim.
In addition, this project includes a new approximation to the third-order density function that uses analogous expressions to Müller's DMFT functional. The corresponding generalization of this approximation will be addressed in a near future.
Finally, I have designed a new strategy to construct new DFT functionals that was presented in the last Starting Grant call from the European Research Council (score A). The results obtained thus far are beyond the expectations of the objectives planned for this task: we have designed a new local hybrid for harmonium that improves the energy by several others of magnitude (work unpublished) and, at the same time, improves the description of electron density (no existing functional is capable of such thing). Its application in the calculation of nonlinear optical properties is an ongoing research project that has also been interrupted due to the early of the termination of this project.
All in all, most the objectives of this project have been achieved, providing the tools to develop new functionals. It is expected that these results will contribute to the improvement of DMFT and DFT, the most widespread computational method, which is of great importance for many scientific disciplines, including materials, bioinorganic, organometallic chemistry and drug design.
During this project the researcher have been granted a 75,000€ national project and a five-year tenure position in the University of the Basque Country. He has been nominated finalist of two important awards (Marcial-Moreno Mañas Lectureship and the European Young Chemistry Award) and he has been granted a Marie Curie Global Fellowship as a Coordinator. He currently leads a team consisting of a PhD student, a postdoc and a master student.