60th Annual Report on Research 2015

The major goal of this project is to develop electron hole correlation functional for quantum mechanical treatment of multiexcitonic systems using quasiparticle density functional theory. The extension of electronic DFT for multiexcitonic systems was first proposed by Sham and coworkers in 1973. Although the concept of electron-hole density functional theory has been around for a while, development in the field of electron hole functional has been challenging because of inherent challenges associated with treating multicomponent systems. In this work, we address this challenge by developing pair density functional approach for representing the electron-hole correlation functional.

Research strategy:

We have used a pair density functional theory approach for construction of the electron-hole correlation functional. Pair density theory has been used extensively in the many-electronic systems and has been shown to be a promising approach for handling electron-electron correlation within the framework of density functional theory.

The electron-hole correlation functional was derived using the following three steps. In the first step, we started with an explicitly correlated electron hole wave function that was defined as product of an R12-correlator operator on the electron-hole multicomponent Hartee-Fock wave function. In the second step, the explicitly correlated wave function was projected onto the direct-product occupation number space for electrons and holes, and the electron hole pair density was expressed compactly using the Hugenholtz diagrammatic representation. Finally, in the third step, a subset of these diagrams was selected and an infinite order diagrammatic summation was performed to extract the electron hole correlation functional.

Major outcomes:

[1] The analytical derivation presented in this work successfully show that an infinite order diagrammatic summation of a subset of electron-hole Hugenholtz diagrams can be represented in a closed form that involves only electron and hole densities. This is a very important analytical results because it allowed us to express the electron hole correlation functional purely in terms of electron and hole 1-particle densities and the R12- correlator operator.

[2] The second outcome of this project is that we were able to show that the parameters of the R12- correlator operator can be determined during the course of the eh-DFT calculation. This alleviates the need for determination of the parameters used in the electron-hole calculation before the start of the calculation.

[3] The derivation of the electron-hole correlation functional presented in this work is general and is not restricted only to electron hole systems. Consequently, the method developed in this work, can be applied for studying many-particle correlation effects in other multicomponent systems such as electron-proton and electron-positron systems.

Professional development of students:

The project involves contribution from three graduate students whose names are Jennifer Elward, Christopher Blanton, and Michael Bayne. Out of those three graduate students, Jen and Chris have defended their PhD successfully and now in postdoctoral positions. Specifically, Jen is a staff scientist at the Army Research Laboratory in Maryland and Chris is a scientific computing consultant in the supercomputer centre in Pennsylvania State University. Mike Bayne is a fifth-year graduate student who is schedule to defend his thesis in May 2016. The main objective of his thesis is to present non-pertubative diagrammatic theory for treatment of electron-electron and electron-hole correlation in multicomponent systems.

Dissemination of results:

The result has been disseminated to the community using publications, presentations, and posters. The students and the PI have presented seminars and posters in national meeting of American Chemical Society, American Physical Society, Gordon Research Conference, and Telluride Science Research Center. Recently, one of the graduate students (Michael Bayne) was selected to give a poster and a presentation in the upcoming March 2016 ACS meeting. The results from this work has been presented in a series of four manuscripts, two are under review and two are in preparation.