Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots
Abstract
Koopmans’ theorem implies that the HartreeFock quasiparticle gap in a closedshell system is equal to its singleparticle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closedshell graphene system within the Hubbard model is equal to its tightbinding singleparticle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the longrange Coulomb interaction, and thus, both become small when only onsite Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and singleparticle gaps of the graphene systems.
 Authors:
 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai (China)
 (China)
 (Canada)
 Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167 (China)
 Publication Date:
 OSTI Identifier:
 22415816
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 77 NANOSCIENCE AND NANOTECHNOLOGY; BINDING ENERGY; CONFIGURATION INTERACTION; COULOMB FIELD; ELECTRON CORRELATION; ENERGY GAP; GRAPHENE; HARTREEFOCK METHOD; HUBBARD MODEL; QUANTUM DOTS
Citation Formats
Sheng, Weidong, Email: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, and Zhou, Aiping. Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots. United States: N. p., 2015.
Web. doi:10.1063/1.4905789.
Sheng, Weidong, Email: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, & Zhou, Aiping. Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots. United States. doi:10.1063/1.4905789.
Sheng, Weidong, Email: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, and Zhou, Aiping. 2015.
"Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots". United States.
doi:10.1063/1.4905789.
@article{osti_22415816,
title = {Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots},
author = {Sheng, Weidong, Email: shengw@fudan.edu.cn and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 and Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5 and Luo, Kaikai and Zhou, Aiping},
abstractNote = {Koopmans’ theorem implies that the HartreeFock quasiparticle gap in a closedshell system is equal to its singleparticle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closedshell graphene system within the Hubbard model is equal to its tightbinding singleparticle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the longrange Coulomb interaction, and thus, both become small when only onsite Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and singleparticle gaps of the graphene systems.},
doi = {10.1063/1.4905789},
journal = {Journal of Chemical Physics},
number = 2,
volume = 142,
place = {United States},
year = 2015,
month = 1
}

The quasiclassical method is used to find the probability of nonadiabatic transition when the point of intersection of the terms is separated by a potential barrier from the region of free motion of the atoms. It is shown that the resonance dependence of the transition probability on the collision energy, which occurs in this case, can be observed indirectly from the nonlinear dependence of the intensity of atomic fluorescence on the intensity of the exciting radiation in experiments on the optical excitation of colliding atoms.

GENERALIZED KOOPMANS' THEOREM
Koopmans' theorem states that if the wave function of a manyelectron system is approximated by a Slater determinant of HartreeFock oneelectron wave functions, with oneelectron energies defined as the difference in energy of (N + 1) and Nparticle systems, then these oneelectron energies are given by the expectation value of the HartreeFock Hamiltonian with respect to the oneelectron wave functions. Koopmans' theorem is generalized to include correlation effects by using Hubbard's expression for the total energy of a freeelectron gas. The resulting oneelectron Hamiltonian contains in firstorder screened exchange. Hubbard's lowest polarization diagram gives, in addition, part of the screenedmore »