Range-Separated Hybrid Functionals with Variational Fitted Exact Exchange

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• Density functional theory (DFT) is a powerful quantum mechanical modeling method.
• Range-separated hybrid (RSH) functionals offer improved accuracy for certain chemical properties.
• Efficient computation of RSH functionals, especially the exact exchange part, remains a challenge.

Purpose of the Study:

• To develop a computationally efficient algorithm for calculating range-separated hybrid density functionals.
• To implement a variationally fitted long-range exact exchange (LREx) method within the linear combination of Gaussian type orbitals (LCGTO) approximation.
• To analyze the accuracy and performance of RSH functionals computed with the new LREx algorithm.

Main Methods:

• Development of a variationally fitted long-range exact exchange algorithm.
• Derivation of LCGTO energy and gradient expressions free of four-center integrals.
• Utilization of modified three-center integral recurrence relations for computational optimization.
• Parallel implementation of the algorithm for enhanced performance.

Main Results:

• The proposed algorithm successfully computes range-separated hybrid density functionals.
• LCGTO energy and gradient expressions are optimized by avoiding four-center integrals.
• The accuracy and performance of selected RSH functionals are evaluated.
• Benchmarking of a parallel implementation demonstrates computational efficiency.

Conclusions:

• The developed variationally fitted LREx algorithm provides an efficient route for computing RSH functionals.
• The method offers significant computational advantages by eliminating expensive four-center integrals.
• This approach enables more accurate and feasible calculations of electronic properties using RSH functionals.