Nuclear-Electronic All-Particle Density Matrix Renormalization Group

Abstract

We introduce the Nuclear Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrödinger equation simultaneously for electrons and other quantum species. In contrast to already existing multicomponent approaches, in this work we construct from the outset a multi-reference trial wave function with stochastically optimized non-orthogonal Gaussian orbitals. By iterative refining of the Gaussians' positions and widths, we obtain a compact multi-reference expansion for the multicomponent wave function. We extend the DMRG algorithm to multicomponent wave functions to take into account inter- and intra-species correlation effects. The efficient parametrization of the total wave function as a matrix product state allows NEAP-DMRG to accurately approximate full configuration interaction energies of molecular systems with more than three nuclei and twelve particles in total, which is currently a major challenge for other multicomponent approaches. We present NEAP-DMRG results for two few-body systems, i.e., H${}_2$ and H${}_3^{+}$, and one larger system, namely BH${}_3$

arXiv comment37 pages, 5 figures, 2 tables

References in corpus (33)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Low-energy spectrum of iron-sulfur clusters directly from many-particle quantum mechanics
• The density matrix renormalization group for ab initio quantum chemistry
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
• Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
• Representing molecule-surface interactions with symmetry-adapted neural networks
• Finite automata for caching in matrix product algorithms
• Development of a Practical Multicomponent Density Functional for Electron-Proton Correlation to Produce Accurate Proton Densities
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Spin-adapted Matrix Product States and Operators
• Matrix Product State applications for the ALPS project
• Accurate ab initio spin densities
• An anisotropic local modification of crystal field levels in Pr-based pyrochlores: a muon-induced effect modelled using density functional theory
• Vibrational Density Matrix Renormalization Group
• Calculating vibrational spectra of molecules using tensor train decomposition
• Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations
• A novel general mapping for bosonic and fermionic operators in Fock space
• Schrödinger equation solved for the hydrogen molecule with unprecedented accuracy
• Optimization of highly excited matrix product states with an application to vibrational spectroscopy
• Generalized elimination of the global translation from explicitly correlated Gaussian functions
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
• Developing effective electronic-only coupled-cluster and Muller-Plesset perturbation theories for the muonic molecules
• Density Matrix Renormalization Group Study of a One Dimensional Diatomic Molecule beyond the Born-Oppenheimer Approximation

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• Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system
• Exact factorization of the many-body Green's function theory of electrons and nuclei
• Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Reaching precise proton affinities in non-Born-Oppenheimer calculations
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