Quantum Proton Effects from Density Matrix Renormalization Group Calculations

Abstract

We recently introduced [J. Chem. Phys. 2020, 152, 204103] the nuclear-electronic all-particle density matrix renormalization group (NEAP-DMRG) method to solve the molecular Schrodinger equation, based on a stochastically optimized orbital basis, without invoking the Born−Oppenheimer approximation. In this work, we combine the DMRG method with the nuclearelectronic Hartree−Fock (NEHF-DMRG) approach, treating nuclei and electrons on the same footing. Inter-and intraspecies correlations are described within the DMRG method without truncating the excitation degree of the full configuration interaction wave function. We extend the concept of orbital entanglement and mutual information to nuclear-electronic wave functions and demonstrate that they are reliable metrics to detect strong correlation effects. We apply the NEHF-DMRG method to the HeHHe + molecular ion, to obtain accurate proton densities, ground-state total energies, and vibrational transition frequencies by comparison with state-of-the-art data obtained with grid-based approaches and modern configuration interaction methods. For HCN, we improve on the accuracy of the latter approaches with respect to both the ground-state absolute energy and proton density, which is a major challenge for multireference nuclear-electronic state-of-the-art methods.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

“…The many-body perturbation theory , and coupled-cluster theory have been formulated and implemented within the framework of the NOMO method. The NOMO method has been developed as an extension of KS DFT, where the electron–nucleus correlation effect as well as the electronic correlation effect were captured by explicit density functionals. , Although an accurate and computationally efficient calculation of the correlation energy in the nuclear orbital method is difficult in comparison with the case of the electronic correlation energy within the BO approximation, the development of the NOMO method has caused further challenges for theoretical chemists within the nuclear orbital method. − …”

Second-Order Self-Consistent Field Algorithms: From Classical to Quantum Nuclei

“…Orbital-based nuclear-electronic methods have often been devised by extending algorithms originally designed for electronic problems to nuclear-electronic ones . This has led to the emergence of the nuclear-electronic counterparts of many wave function − and density functional theory based − electronic structure methods. These developments have revealed that some concepts cannot be straightforwardly transferred from electronic problems to nuclear-electronic ones.…”

“…These developments have revealed that some concepts cannot be straightforwardly transferred from electronic problems to nuclear-electronic ones. For instance, molecules with a weakly correlated electronic ground state may display a strongly correlated nuclear-electronic wave function. , Quantum entanglement measures extracted from nuclear-electronic density matrix renormalization group (DMRG) calculations can guide this classification, but it was shown that, in the nuclear-electronic case, it is difficult to classify a molecule unambiguously as strongly or weakly correlated. , Consequently, the efficiency of an algorithm originally ideated for electronic problems may change drastically when applied to nuclear-electronic problems.…”

Exact factorization of the many-body Green's function theory of electrons and nuclei

“…Therefore, the beyond-BO theoretical and computational methods are expected to play an important role in understanding the properties of these systems. To describe these kinds of systems, several fully quantum mechanical beyond BO approaches have been developed such as the wave function approach [2], the exact factorization [13][14][15], the density matrix renormalization group approach [16,17], the multicomponent density functional theory [18] and the many-body Green's function theory [19].…”