58th Annual Report on Research 2013 Under Sponsorship of the ACS Petroleum Research Fund

The objective of the present research is to develop electron-hole exchange-correlation functional for accurate treatment of electronically excited states. Over the previous funding period, we have completed two developmental goals that are important for successful completion of the project. A brief description is presented below.

[1].Software development and testing:

The computation of integrals involving explicitly correlated electron-hole basis functions is one of principle component of the project. As a first step, we have developed and implemented all the necessary explicitly correlated integrals involving both electron and hole quasiparticles. The integral code was used for performing self-consistent field (SCF) calculations for electron-hole system. The developed code was used for investigating quantum confined Stark effect in GaAs quantum dots. The GaAs quantum dots have been subject of intense research and provide an ideal test case for benchmarking and testing of the developed method. Exciton binding energies were computed using explicitly correlated full configuration interaction (XCFCI) method at different field strengths. The computed results were found to be in good agreement with previously reported experimental and computational studies. One of the key results from this investigation was that the exciton binding energy scales quadratically with respect to the field strength. The method also introduces field-dependent transformation of the quasiparticle coordinates, which was found to be important for including effect of external electrostatic potential in the correlated electron-hole calculation. The developed method and the results from this study were recently published in the Journal of Chemical Physics.

[2]. Construction of electron-hole adiabatic connection curve:

The adiabatic connection curve has played a critical role in development of exchange-correlation functional in electronic structure theory. In the present work, we have constructed the adiabatic connection curve for the electron-hole system. The construction of the adiabatic connection curve is computationally demanding because it requires density constrained minimization at each point of the curve. This problem is exacerbated for the electron-hole system because of the presence of both electron and hole quasiparticles. We have developed a Lagrangian-based method that allows for efficient implementation of the density-constrained minimization process. By combining this approach with the explicitly correlated full configuration interaction (XCFCI) method described above, we have been able to construct accurate electron-hole adiabatic connection curve. The functional form of the exchange-correlation potential (Uxc) for the electron-hole system as a function of the coupling parameter was obtained from the adiabatic connection curve. This is one of the key results from the adiabatic connection curve calculation and will be used in the next step for construction of electron-hole exchange-correlation functional.