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arXiv:1506.03356 · Physical Review B

Discontinuous transition of molecular-hydrogen chain to the quasiatomic state: Combined exact diagonalization andab initioapproach

Andrzej Piotr Kądzielawa, Andrzej Biborski, Józef Spałek

Published Oct 6, 2015• 8 citations
arXivHTMLPDF

Abstract

We obtain in a direct and rigorous manner a transition from a stable molecular-hydrogen $n{\text{H}}_{2}$ single chain to the quasiatomic two-chain $2n\text{H}$ state. We devise a method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains that are possible to tackle, $n=3--6$. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio $U/W$ reflects the Mott-Hubbard transition aspect of atomization. A universal feature of the transition relation to the Mott criterion for the insulator-metal transition is also noted. The role of electron correlations is thus shown to be of fundamental significance in this case. The long-range nature of Coulomb interactions is included.

DOI
10.1103/physrevb.92.161101

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We obtain in a direct and rigorous manner a transition from a stable molecular-hydrogen nH2n{\text{H}}_{2}nH2​ single chain to the quasiatomic two-chain 2nH2n\text{H}2nH state. We devise a method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains that are possible to tackle, n=3−−6n=3--6n=3−−6. The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio U/WU/WU/W reflects the Mott-Hubbard transition aspect of atomization. A universal feature of the transition relation to the Mott criterion for the insulator-metal transition is also noted. The role of electron correlations is thus shown to be of fundamental significance in this case. The long-range nature of Coulomb interactions is included.
We discuss electronic properties and their evolution for the linear chain of H2{H}_{2}H2​ molecules in the presence of a uniform external force fff acting along the chain. The system is described by an extended Hubbard model within a fully microscopic approach. Explicitly, the microscopic parameters describing the intra- and intersite Coulomb interactions are determined together with the hopping integrals, by optimizing simultaneously the system ground state energy and the single-particle wave functions in the correlated state. The many-body wave function is taken in the Jastrow form and the variational Monte Carlo (VMC) method is used in combination with an ab initio approach to determine the energy. Both the effective Bohr radii of the renormalized single-particle wave functions and the many-body wave function parameters are determined for each fff, which is the only external parameter in the whole analysis. Hence the evolution of the system can be analyzed in detail as a function of the equilibrium intermolecular distance, which in turn is determined for each fff value. The transition to the atomic state, including the Peierls distortion stability, can thus be studied in a systematic manner, particularly near the threshold of the dissociation of the molecular into an atomic chain. We also show that interelectronic correlations enhance the Peierls distortion. The computational reliability of the VMC approach is also estimated.
Abstract We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding.
We overview the EDABI method developed recently and combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localization-delocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show, that, the statistical distribution function for electrons in a nanochain evolves from the Fermi-Dirac-like to the Luttinger-liquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresponds to the HOMO-LUMO splitting in the molecular and organic solid states. Also, the nanochains exhibit magnetic splitting (Slater-like), even without the symmetry breaking, since the spin-spin correlations extend over the whole system. Thus, the correlated nanoscopic systems exhibit unique and universal features, which differ from those of molecular and infinite systems. These features define unique properties reflecting "the Mott physics" on the nanoscale. We also employ the EDABI method to the transport properties in nanoscopic systems. For example, we show that the particle-hole symmetry is broken when the tunneling conduction through H2 molecule is calculated.
We apply our new method of approach to electronic states in correlated systems [for a brief review, Part I, see: Acta Phys. Pol. B31, 2879 (2000)] to the analysis of the states and electron localization in nanoscopic chains containing up to N = 12 atoms. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. We also define the many-particle wave function and calculate it explicitly for the hydrogen molecule. Further applications of our method are listed at the end.
The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent density functional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a density functional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.
Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation.An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model.Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantummechanical ground state.Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.