Density-matrix-renormalization-group study of a one-dimensional diatomic molecule beyond the Born-Oppenheimer approximation

Abstract

We study one dimensional models of diatomic molecules where both the electrons and nuclei are treated as quantum particles, going beyond the usual Born-Oppenheimer approximation. The continuous system is approximated by a grid which computationally resembles a ladder, with the electrons living on one leg and the nuclei on the other. To simulate DMRG efficiently with this system, a three-site algorithm has been implemented. We also use a compression method to treat the long-range interactions between charged particles. We find that 1D diatomic molecules with spin-1/2 nuclei in the spin triplet state will unbind when the mass of the nuclei reduces to only a few times larger than the electron mass, while the molecule with nuclei in the singlet state always binds.The Born-Oppenheimer (BO) approximation [1] has been the starting point of solid state physics and quantum chemistry since it was first introduced in 1927. Treating the degrees of freedom of the nuclei adiabatically turns out to be a satisfactory approximation because the mass of the nucleus is more than 10 3 times of the electron mass even for the lightest atom -hydrogen.However, the BO approximation is no longer valid for exotic systems such as the positronium molecule[2-4] which consists of two positrons and two electrons, and the emergent biexciton molecule[5] which consists of two holes and two electrons in semiconductors, because their masses are equal or nearly so. In high precision spectroscopy experiments or in systems where energy levels cross, non-adiabatic effects involving the motions of the nuclei require a theoretical treatment beyond the BO approximation [6]. Such systems are difficult to treat analytically. Various numerical approaches, such as the stochastic variational method (SVM)[7-9], quantum Monte Carlo (QMC) methods [10,11], and Exact Factorization [6,12,13] combined with Density Functional Theory (DFT), have been applied to explore the spectrum of the systems in two or three dimensions and have correctly predicted the bound ground state [3] and possible bound excited states [8,9] later proved by experiments [4].The hydrogen molecule (H 2 ) and the positronium molecule (Ps 2 ) are in nearly opposite limits of mass ratios between the nuclei and electrons, 1836:1 vs 1:1, corresponding to adiabatic and non-adiabatic limits, respectively. Unlike H 2 , for which the BO approximation can be used to simplify the numerical treatments [14], the nonadiabatic features of Ps 2 requires a complete four-body treatment. The electrons in H 2 can be in either a bonding or anti-bonding state, corresponding to a spin singlet or triplet respectively, and the anti-bonding state is unstable against dissociation into two atoms. There are also two types of nuclear spin states, called spin isomers, with the singlet known as para-hydrogen and the * mingruy@uci.edu triplet known as ortho-hydrogen. In Ps 2 , if both the electrons and positrons are in spin singlet states, the molecule is bound, while the triplet-triplet excited state is unbound [7-9, 15, 16]. Sim...

Quantum Simulation of 2D Quantum Chemistry in Optical Lattices

“…One approach is to use another (classical) computational technique that is exact in some restricted conditions, but can deal with large systems where exact calculations were not possible. The most prominent example is DMRG [9] which, despite the fact that it operates in 1D lattice systems, offers an ideal platform to benchmark DFT methods [10][11][12][13]. In more general scenarios, the field of quantum computing [14][15][16][17][18][19] can play a key role to overcome numerical limitations in the long-term, offering an excellent setup to benchmark quantum chemistry computational methods.…”