59th Annual Report on Research 2014

The project is in its final stage of completion; however, both the senior graduate students who were working on this project graduated in the summer of 2014. We encountered initial difficulties in numerical stability of the developed method. The identification and resolution of the numerical problems caused unexpected delay in the original schedule. These numerical issues were addressed by developing and implementing new algorithms.

To aid in construction of the electron-hole functional, we have calculated the electron-hole correlation length in CdSe clusters. The electron-hole correlation length is an important distance metric for analyzing excitonic interactions in many-electron systems. There are two novel features of this method. First, we use of explicitly correlated electron-hole wave function for construction of the 2-particle reduced density matrix. Second, we impose the exact sum-rule conditions on the cumulant for defining correlation length. The developed method was then applied to a series of CdSe clusters and the effect of size on the correlation length was analyzed. Analytical relationship between the explicitly correlated function and the electron-hole correlation length was derived and the equation was numerically inverted to obtained correlation-length dependent explicitly correlated electron-hole wave function. The quality of the correlation-length based and energy-minimized based wave functions were compared by calculating exciton binding energies. The TOC graphic shows the calculated radial cumulant as a function of electron-hole separation distance. The results from this work has been submitted as a manuscript titled “Determination of electron-hole correlation length in CdSe quantum dots using explicitly correlated two-particle cumulant” for consideration for publication in Journal of Chemical Physics.

We have also constructed the electron-hole adiabatic connection curve(eh-ACC) by performing density-constrained minimization along the coupling-constant coordinate. In the present work, the density constraint was avoided by defining an electron-hole Levy-Lieb Lagrangian (eh-LLL). For a given set of input electron and hole densities, the eh-LLL was constructed and expressed as a functional of the coupling constant dependent external potential. Unconstrained minimization of the eh-LLL was performed by varying the eh-wavefunction, external potential, and Lagrange's multipliers. An explicitly correlated ansatz was used for the eh-wavefunction and the search over the wavefunction was performed using variational Monte Carlo. The calculation was repeated for coupling constants in the range of 0 to 1 and the minimized wavefunction was used for construction of the eh-ACC. The electron-hole correlated energy was obtained by performing numerical integration of the ACC over the coupling parameter. The quality of the electron-hole adiabatic connection curve was verified by comparing the calculated eh-DFT energy with the energies obtained using wave function based methods. These results were presented in the national meeting of American Physical Society in 2013 and in Telluride Science Research Center Conference 2014. The manuscript for this work is under preparation.