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arXiv:1803.04855 · Physical review. B./Physical review. B

Atomization of correlated molecular-hydrogen chain: A fully microscopic variational Monte Carlo solution

Andrzej Biborski, Andrzej Piotr Kądzielawa, Józef Spałek

Published Aug 7, 2018• 12 citations
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Abstract

We discuss electronic properties and their evolution for the linear chain of ${H}_{2}$ molecules in the presence of a uniform external force $f$ 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 $f$, 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 $f$ 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.

DOI
10.1103/physrevb.98.085112

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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.
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U ) were determined for an infinite atomic chain.In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb-Wu exact solution, the Gutzwiller-wave-function approximation, and the Gutzwiller--ansatz case.The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the exact diagonalization combined with an ab initio adjustment of the single-particle wave functions in the correlated state (exact diagonalization combined with an ab initio method).For the sake of completeness, we briefly characterize also each of the solutions.Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controlable parameter -the interatomic distance.
In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called ``modern theory of polarization'' and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.
Variational quantum Monte Carlo (VMC) method applied to interacting electron systems has played a pivotal role for the studies of electronic states of atoms, molecules and condensed matters. First, the many-body wave functions optimized by the VMC method provide good guiding functions in more accurate, diffusion quantum Monte Carlo (DMC) calculations for identical systems. Second, the VMC calculations themselves can give a good upper bound for the exact ground-state energy of many-electron systems when an appropriate form for the variational wave function is employed. In addition to a conventional form for the variational wave function that is expressed by the product of the Jastrow factor and the single Slater determinant, recent investigations have found that the expression in terms of many Slater determinants can provide a very accurate description of electronic states, especially for intrinsically multi-reference systems, which corresponds to the configuration interaction (CI) expansion method in conventional quantum chemistry. Although the CI method needs an extremely large number of expansion coefficients as variational parameters, the number of parameters can be reduced efficiently by using an idea of (molecular) orbital pair correlations. The purpose of the present paper is to examine the feasibility and usefulness of this idea within the framework of VMC method with the Jastrow–Slater wave function, where the ground state of a water molecule is investigated as a test case. In this study we rely on a variational wave function composed of a product of the Jastrow and Slater parts as 1⁄4 J S; ð1Þ
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adjustment of the single-particle wave functions in the correlated state (EDABI method). For the sake of completeness, we briefly characterize also each of the solutions. Our approach completes the Lieb-Wu solution, as it provides the system electronic properties evolution as a function of physically controllable parameter - the interatomic distance.
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.
One-dimensional atomic chain with a variable-range hopping is described within the extended Hubbard model.The Gutzwiller-ansatz approximation is used to determine the optimized single-particle (Wannier) wave functions in the correlated state.Hopping integral up to the third neighbors is taken into account and the results are compared with those for the infinite hopping range.Ground state energy of the system is compared with that making use of the rigorous Lieb-Wu solution with the optimized wave functions.The evolution of the properties as a function of interatomic distance is discussed.