Development of a Thermochemically Optimized Local-Hybrid Density Functional

• Applicant: Dr. Henryk Laqua
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 529879166

Highly accurate and efficient electronic structure methods are essential for the advancement of theoretical chemistry with applications covering the entirety of chemistry ranging from material science to computational drug design. In this context, Kohn-Sham density functional theory (KS-DFT) and hybrid DFT in particular provide an excellent tradeoff between accuracy and performance justifying its status as the current "workhorse" of computational chemistry. Consequently, this proposal aims to further improve hybrid DFT to provide even higher accuracy, especially for more unusual/difficult electronic structures plagued by either static correlation errors or self-interaction errors, respectively. This is planned to be achieved by extending the already very successful ωB97M-V global-hybrid density functional approximation (DFA) developed in the group of Martin Head-Gordon (the host for this project) by transforming it into a local-hybrid DFA. In a local-hybrid DFA the fraction of exact-exchange - usually the decisive factor for the accuracy of a DFA - can be adapted flexibly to the electronic structure of the molecule of interest, in this way improving the accuracy for more exotic structures. A major motivation for this project are the recent improvements in seminumerical integration techniques such as the sn LinK method developed within my Ph. D. thesis, which now enables the evaluation of local-hybrid DFAs at essentially the same computation time as global hybrid DFAs. Thus, with the issue of the high computational cost of local-hybrid DFAs being resolved, there is now a great opportunity to advance the field of theoretical chemistry by introducing more accurate local-hybrid DFAs which optimally leverage seminumerical integration - precisely the goal of this proposal. In order to achieve this goal, the project is structured in three main parts, each anticipated to require 12 months of work for a total of 36 months, of which 24 months are funded by the DFG and 12 months are funded by the University of California (UC) Berkeley. In the first 12 months we plan to perform comprehensive benchmarks of ωB97M-V variants with different fractions of exact-exchange in order to gain deep physical insights into the impact of exact-exchange on the accuracy of the ωB97M-V DFA for various systems. In the second 12 months we plan to then utilize these physical insights to formulate the precise mathematical form of the local-hybrid extension of ωB97M-V, where the main challenge is finding suitable expressions for the form of the local-mixing function (LMF) which quantifies the mixing of exact vs. semilocal exchange at each reference point. Finally, in the last 12 month we plan to test and optimize the developed density functional on molecular properties such as geometries, vibrational frequencies, and polarizabilities. In this way we can assess its utility for a wide range of applications within theoretical chemistry.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Dr. Martin Head-Gordon