We develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born–Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron–ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born–Oppenheimer approximation. Based on the Kubo–Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.
Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation
Current address: Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA/DRF/IRAMIS, Institut Polytechnique de Paris, F-91128 Palaiseau, France.
Note: This paper is part of the JCP Special Topic on Frontiers of Stochastic Electronic Structure Calculations.
Vitaly Gorelov, David M. Ceperley, Markus Holzmann, Carlo Pierleoni; Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation. J. Chem. Phys. 21 December 2020; 153 (23): 234117. https://doi.org/10.1063/5.0031843
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