We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency and pract
ical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.
A theoretical study is reported of the molecular-to-atomic transition in solid hydrogen at high pressure. We use the diffusion quantum Monte Carlo method to calculate the static lattice energies of the competing phases and a density-functional-theory
-based vibrational self-consistent field method to calculate anharmonic vibrational properties. We find a small but significant contribution to the vibrational energy from anharmonicity. A transition from the molecular Cmca-12 direct to the atomic I4_1/amd phase is found at 374 GPa. The vibrational contribution lowers the transition pressure by 91 GPa. The dissociation pressure is not very sensitive to the isotopic composition. Our results suggest that quantum melting occurs at finite temperature.
We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We de
velop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules.
This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point en
ergy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semi-local Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular P$6_3$/m, C2/c, Cmca-12, and Cmca structures in the pressure range from $100<P<500$ GPa over which phases I, II and III are observed experimentally. At the static level of theory, in which proton zero-point energy is ignored, the LDA, PBE and BLYP functionals give very different structural transition and metallization pressures, with the BLYP phase diagram in better agreement with experiment. Nevertheless, all three functionals provide qualitatively the same information about the band gaps of the four structures and the phase transitions between them. Going beyond the static level, we find that the frequencies of the vibron modes observed above 3000 cm$^{-1}$ depend strongly on the choice of exchange-correlation functional, although the low-frequency part of the phonon spectrum is little affected. The largest and smallest values of the proton zero-point energy, obtained using the BLYP and LDA functionals, respectively, differ by more than 10 meV/proton. Including the proton zero-point energy calculated from the phonon spectrum within the harmonic approximation improves the agreement of the BLYP and PBE phase diagrams with experiment. Taken as a whole, our results demonstrate the inadequacy of mean-field-like density functional calculations of solid molecular hydrogen in phases I, II and III and emphasize the need for more sophisticated methods.
We apply a variational wave function capable of describing qualitatively and quantitatively the so called resonating valence bond in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this fr
amework we clearly identify the Kekule and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains only within a small resonance length of few atomic units.
We introduce a method for solving a self consistent electronic calculation within localized atomic orbitals, that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our results with the
ones obtained with a standard quantum chemistry package for the simple benzene molecule. We find perfect agreement for small basis set and show that, within our scheme, it is possible to work with a very large basis in an efficient and stable way. Therefore we can avoid to introduce any extrapolation to reach the CBS limit. In our study we have also carried out variational Monte Carlo (VMC) and lattice regularized diffusion Monte Carlo (LRDMC) with a standard many-body wave function (WF) defined by the product of a Slater determinant and a Jastrow factor. Once the Jastrow factor is optimized by keeping fixed the Slater determinant provided by our new scheme, we obtain a very good description of the atomization energy of the benzene molecule only when the basis of atomic orbitals is large enough and close to the CBS limit, yielding the lowest variational energies.
