Discovering Quantum Phase Transitions with Fermionic Neural Networks.

Deep neural networks have been very successful as highly accurate wave function Ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such Ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists.

Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo.

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.

Equation of state of atomic solid hydrogen by stochastic many-body wave function methods.

We report a numerical study of the equation of state of crystalline body-centered-cubic (BCC) hydrogen, tackled with a variety of complementary many-body wave function methods. These include continuum stochastic techniques of fixed-node diffusion and variational quantum Monte Carlo and the Hilbert space stochastic method of full configuration-interaction quantum Monte Carlo. In addition, periodic coupled-cluster methods were also employed. Each of these methods is underpinned with different strengths and approximations, but their combination in order to perform reliable extrapolation to complete basis set and supercell size limits gives confidence in the final results. The methods were found to be in good agreement for equilibrium cell volumes for the system in the BCC phase.

On the Possibility of Helium Adsorption in Nitrogen Doped Graphitic Materials.

The potassium salt of polyheptazine imide (K-PHI) is a promising photocatalyst for various chemical reactions. From powder X-ray diffraction data an idealized structural model of K-PHI has been derived. Using atomic coordinates of this model we defined an energetically optimized K-PHI structure, in which the K ions are present in the pore and between the PHI-planes. The distance between the anion framework and K+ resembles a frustrated Lewis pair-like structure, which we denote as frustrated Coulomb pair that results in an interesting adsorption environment for otherwise non-adsorbing, non-polar gas molecules. We demonstrate that even helium (He) gas molecules, which are known to have the lowest boiling point and the lowest intermolecular interactions, can be adsorbed in this polarized environment with an adsorption energy of  - 4.6 kJ mol-1 per He atom. The interaction between He atoms and K-PHI is partially originating from charge transfer, as disclosed by our energy decomposition analysis based on absolutely localized molecular orbitals. Due to very small charge transfer interactions, He gas adsorption saturates at 8 at%, which however can be subject to further improvement by cation variation.

Nuclear quantum effects induce metallization of dense solid molecular hydrogen.

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band-gap energies of the C2/c, Pc, and P63/m structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path-integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero-point energy and temperature-induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band-gaps substantially, leading to metallization of the C2/c and Pc phases via band overlap; the effect on the band-gap of the P63/m structure is less pronounced. Our combined DMC-PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the C2/c and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band-gap energy and vibron modes. This strong coupling induces a band-gap reduction of more than 2.46 eV in high-pressure solid molecular hydrogen. Comparing our DMC-PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.

The role of van der Waals and exchange interactions in high-pressure solid hydrogen.

We investigate the van der Waals interactions in solid molecular hydrogen structures. We calculate enthalpy and the Gibbs free energy to obtain zero and finite temperature phase diagrams, respectively. We employ density functional theory (DFT) to calculate the electronic structure and density functional perturbation theory (DFPT) with van der Waals (vdW) functionals to obtain phonon spectra. We focus on the solid molecular C2/c, Cmca-12, P63/m, Cmca, and Pbcn structures within the pressure range of 200 < P < 450 GPa. We propose two structures of the C2/c and Pbcn for phase III which are stabilized within different pressure range above 200 GPa. We find that vdW functionals have a big effect on vibrations and finite-temperature phase stability, however, different vdW functionals have different effects. We conclude that, in addition to the vdW interaction, a correct treatment of the high charge gradient limit is essential. We show that the dependence of molecular bond-lengths on exchange-correlation also has a considerable influence on the calculated metallization pressure, introducing errors of up to 100 GPa.

High-pressure hydrogen sulfide by diffusion quantum Monte Carlo.

We revisit the enthalpy-pressure phase diagram of the various products from the different proposed decompositions of H2S at pressures above 150 GPa by means of accurate diffusion Monte Carlo simulations. Our results entail a revision of the ground-state enthalpy-pressure phase diagram. Specifically, we find that the C2/c HS2 structure is persistent up to 440 GPa before undergoing a phase transition into the C2/m phase. Contrary to density functional theory, our calculations suggest that the C2/m phase of HS is more stable than the I41/amd HS structure over the whole pressure range from 150 to 400 GPa. More importantly, we predict that the Im-3m phase is the most likely candidate for H3S, which is consistent with recent experimental x-ray diffraction measurements.

Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems.

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 practical 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.

Chemical accuracy from quantum Monte Carlo for the benzene dimer.

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Dissociation of high-pressure solid molecular hydrogen: a quantum Monte Carlo and anharmonic vibrational study.

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 I41/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.

Fate of the resonating valence bond in graphene.

We apply a variational wave function capable of describing qualitatively and quantitatively the so-called "resonating valence bond" (RVB) in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule and establish the corresponding RVB energy of these structures (≃0.01 eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene, providing an estimate of the RVB energy gain, and show that this picture remains only within a small "resonance length" of a few atomic units.

Resonating valence bond wave function with molecular orbitals: application to first-row molecules.

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant nondynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be(2), B(2), C(2), N(2), O(2), and F(2)) and heteronuclear (LiF and CN) dimers for which strong nondynamical correlations and/or weak van der Waals interactions are present.

When double-wall carbon nanotubes can become metallic or semiconducting.

The electronic properties of double-wall carbon nanotubes (DWCNTs) are investigated via density functional theory. The DWCNTs are separated into four categories wherein the inner-outer nanotubes are metal-metal, metal-semiconductor, semiconductor-metal and semiconductor-semiconductor single-wall nanotubes. The band structure of the DWCNTs, the local density of states of the inner and outer nanotubes, and the total density of states are calculated. We found that for the metal-metal DWCNTs, the inner and outer nanotubes remain metallic for different distances between the walls, while for the metal-semiconductor DWCNTs, decreasing the distance between the walls leads to a phase transition in which both nanotubes become metallic. In the case of semiconductor-metal DWCNTs, it is found that at some distance the inner wall becomes metallic, while the outer wall becomes a semiconductor, and if the distance is decreased, both walls become metallic. Finally, in the semiconductor-semiconductor DWCNTs, if the two walls are far from each other, then the whole DWCNT and both walls remain semiconducting. By decreasing the wall distance, first the inner, and then the outer, nanotube becomes metallic.