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Register a new userBenchmark Quantum Monte Carlo calculations of the ground-state kinetic, interaction, and total energy of the three-dimensional electron gas
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Added by
Idoia G. de Gurtubay
Publication date
2010
fields
Physics
and research's language is
English
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We report variational and diffusion Quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N=54, 102, 178, and 226 electrons. We remove finite-size effects by extrapolation and we find lower energies than previously reported. Using the Hellman-Feynman operator sampling method introduced in Phys. Rev. Lett. 99, 126406 (2007), we compute accurately, within the fixed-node pproximation, the separate kinetic and interaction contributions to the total ground-state energy. The difference between the interaction energies obtained from the original Slater-determinant nodes and the backflow-displaced nodes is found to be considerably larger than the difference between the corresponding kinetic energies.
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We report all-electron variational and diffusion quantum Monte Carlo (VMC and DMC) calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with Z.
The author reports on new high-fidelity simulations of charge carriers in the high-T$_c$ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in X-ray, EELS, and neutron experiments. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.
The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures.
We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo (QMC) techniques. We have performed variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP-like single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mHa, yielding a DMC energy of -76.42830(5) Ha, which is only 10 mHa above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcal/mol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) Debye and dimer dipole moments which range between 2.628(6) and 2.672(5) Debye.
Spin crossover molecules have recently emerged as a family of compounds potentially useful for implementing molecular spintronics devices. The calculations of the electronic properties of such molecules is a formidable theoretical challenge as one has to describe the spin ground state of a transition metal as the legand field changes. The problem is dominated by the interplay between strong electron correlation at the transition metal site and charge delocalization over the ligands, and thus it fits into a class of problems where density functional theory may be inadequate. Furthermore, the crossover activity is extremely sensitive to environmental conditions, which are difficult to fully characterize. Here we discuss the phase transition of a prototypical spin crossover molecule as obtained with diffusion Monte Carlo simulations. We demonstrate that the ground state changes depending on whether the molecule is in the gas or in the solid phase. As our calculation provides a solid benchmark for the theory we then assess the performances of density functional theory. We find that the low spin state is always over-stabilized, not only by the (semi-)local functionals, but even by the most commonly used hybrids (such as B3LYP and PBE0). We then propose that reliable results can be obtained by using hybrid functionals containing about 50% of exact-exchange.
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