Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science




Viktor N. Staroverov


Hybrid density functionals have the best overall performance among standard density func-tional approximations (DFA). According to their original design, hybrid DFAs are supposedto use the exact exchange (EXX). However, when hybrid functionals were originally intro-duced, there was no simple method to compute EXX, so all of their practical implementationsstarted using the Hartree–Fock exchange (HFX), which can be computed easily and is simi-lar to but distinct from EXX. Recent development of an efficient method for computing EXXmade it possible to implement hybrid functionals in line with their original definition. Weimplemented EXX in the PBE0 functional and compared its performance with that of HFX.We found that using EXX in PBE0 improves the standard enthalpies of formation, and thisimprovement increases with the size of the basis set and the size of the system. The max-imum improvement in standard enthalpies of formation of the G3-3 test set is 0.4 kcal/molwhen using 6-311++G(3df,3pd) basis set. For a hybrid density functional, the difference in theground-state energies computed using EXX and HFX depends quadratically on the percentageof EXX in the functional. We have also developed a method to generate the exact remainderexchange-correlation potential of the generalized Kohn–Sham DFT.

Summary for Lay Audience

Quantum chemistry enables one to predict physical and chemical properties of atoms andmolecules by solving mathematical equations. Unfortunately, only approximate solutions ofthose equations can be obtained in practice and they are not always sufficiently accurate forchemical applications. Approximate Kohn–Sham density functional theory (DFT) is the mostwidely used technique for electronic structure calculations. The accuracy of a DFT calcu-lation depends on the accuracy of the approximate density functional used. Among all suchapproximations, hybrid density functionals, which combine elements of density-functional andwave-function techniques, have the best overall performance. In most quantum-chemistry soft-ware packages, hybrid density functionals are implemented using an approximation for theirkey ingredient, the so-called exact exchange (EXX), because EXX was originally thought toodifficult to compute properly. Recently, an efficient method was invented for computing EXX,which enables us to implement hybrid density functionals properly. In this thesis, we testedthe hypothesis that the use of proper EXX in hybrid density functionals improves their per-formance. We found that it does, but the improvement is modest, which means that thereis no compelling reason to abandon the existing approach. We have also demonstrated howthe method for computing EXX can be extended to an entire new class of density-functionalapproximations that go beyond hybrid DFT.