Lattice Density-Functional Theory for Quantum Chemistry

Abstract

We propose a lattice density-functional theory for {\it ab initio} quantum chemistry or physics as a route to an efficient approach that approximates the full configuration interaction energy and orbital occupations for molecules with strongly-correlated electrons. We build on lattice density-functional theory for the Hubbard model by deriving Kohn-Sham equations for a reduced then full quantum chemistry Hamiltonian, and demonstrate the method on the potential energy curves for the challenging problem of modelling elongating bonds in a linear chain of six hydrogen atoms. Here the accuracy of the Bethe-ansatz local-density approximation is tested for this quantum chemistry system and we find that, despite this approximate functional being designed for the Hubbard model, the shapes of the potential curves generally agree with the full configuration interaction results. Although there is a discrepancy for very stretched bonds, this is lower than when using standard density-functional theory with the local-density approximation.

7 pages, 3 figures

References in corpus (18)

• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory
• Linking entanglement and quantum phase transitions via density functional theory
• Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
• Time Dependent Density Functional Theory meets Dynamical Mean Field Theory: Real-Time Dynamics for the 3D Hubbard model
• Entanglement in spatially inhomogeneous many-fermion systems
• Density-functional theory and the v-representability problem for model strongly correlated electron systems
• Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas
• Applying Monte Carlo configuration interaction to transition metal dimers: exploring the balance between static and dynamic correlation
• Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
• Development of Monte Carlo configuration interaction: Natural orbitals and second-order perturbation theory
• Effects of nanoscale spatial inhomogeneity in strongly correlated systems
• Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
• Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study
• Uniqueness of density-to-potential mapping for fermionic lattice systems
• Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling
• Solving lattice density functionals close to the Mott regime
• Testing density-functional approximations on a lattice and the limits of the related Hohenberg-Kohn-type theorem

Cited by in corpus (10)

• Projected site-occupation embedding theory
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling
• Semidefinite relaxation of multi-marginal optimal transport for strictly correlated electrons in second quantization
• What can lattice DFT teach us about real-space DFT?
• Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain
• Deep learning nonlocal and scalable energy functionals for quantum Ising models
• Toward Density Functional Theory on Quantum Computers?
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information