Variational and diffusion quantum Monte Carlo calculations with the CASINO code.

We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the casino program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and weaknesses. We review a range of recent applications of casino.

Shape and energy consistent pseudopotentials for correlated electron systems.

A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li-F, Sc-Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies which they provide with all electron results, with all quantities evaluated using coupled cluster singles, doubles, and triples calculations. Errors inherent in the pseudopotentials are also compared with those arising from a number of approximations commonly used with pseudopotentials. The eCEPPs provide a significant improvement in optimised geometries and dissociation energies for small molecules, with errors for the latter being an order-of-magnitude smaller than for Hartree-Fock-based pseudopotentials available in the literature. Gaussian basis sets are optimised for use with these pseudopotentials.

Computational searches for iron oxides at high pressures.

We have used density-functional-theory methods and the ab initio random structure searching (AIRSS) approach to predict stable structures and stoichiometries of mixtures of iron and oxygen at high pressures. Searching was performed for 12 different stoichiometries at pressures of 100, 350 and 500 GPa, which involved relaxing more than 32 000 structures. We find that Fe2O3 and FeO2 are the only phases stable to decomposition at 100 GPa, while at 350 and 500 GPa several stoichiometries are found to be stable or very nearly stable. We report a new structure of Fe2O3 with P2(1)2(1)2(1)2 symmetry which is found to be more stable than the known Rh2O3(II) phase at pressures above ∼233 GPa. We also report two new structures of FeO, with Pnma and R3m symmetries, which are found to be stable within the ranges 195-285 GPa and 285-500 GPa, respectively, and two new structures of Fe3O4 with Pca21 and P21/c symmetries, which are found to be stable within the ranges 100-340 GPa and 340-500 GPa, respectively. Finally, we report two new structures of Fe4O5 with P42/n and [Formula: see text] symmetries, which are found to be stable within the ranges 100-231 GPa and 231-500 GPa, respectively. Our new structures of Fe3O4 and Fe4O5 are found to have lower enthalpies than their known structures within their respective stable pressure ranges.

Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.

Correlated electron pseudopotentials for 3d-transition metals.

A recently published correlated electron pseudopotentials (CEPPs) method has been adapted for application to the 3d-transition metals, and to include relativistic effects. New CEPPs are reported for the atoms Sc - Fe, constructed from atomic quantum chemical calculations that include an accurate description of correlated electrons. Dissociation energies, molecular geometries, and zero-point vibrational energies of small molecules are compared with all electron results, with all quantities evaluated using coupled cluster singles doubles and triples calculations. The CEPPs give better results in the correlated-electron calculations than Hartree-Fock-based pseudopotentials available in the literature.

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.

Electron-phonon coupling and the metallization of solid helium at terapascal pressures.

Solid He is studied in the pressure and temperature ranges 1-40 TPa and 0-10 000 K using first-principles methods. Anharmonic vibrational properties are calculated within a self-consistent field framework, including the internal and free energies, density-pressure relation, stress tensor, thermal expansion, and the electron-phonon coupling renormalization of the electronic band gap. We find that an accurate description of electron-phonon coupling requires us to use a nonperturbative approach. The metallization pressure of 32.9 TPa at 0 K is larger than found previously. The vibrational effects are large; for example, at P=30 TPa the band gap is increased by 2.8 eV by electron-phonon coupling and a further 0.1 eV by thermal expansion compared to the static value. The implications of the calculated metallization pressure for the cooling of white dwarfs are discussed.

Comparison of Smooth Hartree-Fock Pseudopotentials.

The accuracy of two widely used scalar relativistic Hartree-Fock pseudopotentials, the Trail-Needs-Dirac-Fock (TNDF) and the Burkatzki-Filippi-Dolg (BFD) pseudopotentials, is assessed. The performance of the pseudopotentials is tested for a chemically representative set of 34 first-row molecules. All comparisons are made at the Hartree-Fock level of theory, and both sets of pseudopotentials give good results. The all-electron equilibrium geometries, molecular dissociation energies, and zero-point vibrational energies are reproduced a little more accurately by the TNDF pseudopotentials than the BFD ones.

Pseudopotentials for correlated electron systems.

A scheme is developed for creating pseudopotentials for use in correlated-electron calculations. Pseudopotentials for the light elements H, Li, Be, B, C, N, O, and F, are reported, based on data from high-level quantum chemical calculations. Results obtained with these correlated electron pseudopotentials (CEPPs) are compared with data for atomic energy levels and the dissociation energies, molecular geometries, and zero-point vibrational energies of small molecules obtained from coupled cluster single double triple calculations with large basis sets. The CEPPs give better results in correlated-electron calculations than Hartree-Fock-based pseudopotentials available in the literature.

Framework for constructing generic Jastrow correlation factors.

We have developed a flexible framework for constructing Jastrow factors which allows for the introduction of terms involving arbitrary numbers of particles. The use of various three- and four-body Jastrow terms in quantum Monte Carlo calculations is investigated, including a four-body van der Waals-like term, and anisotropic terms. We have tested these Jastrow factors on one- and two-dimensional homogeneous electron gases, the Be, B, and O atoms, and the BeH, H2O, N2, and H2 molecules. Our optimized Jastrow factors retrieve more than 90% of the fixed-node diffusion Monte Carlo correlation energy in variational Monte Carlo for each system studied.

Crystal structure of ammonia dihydrate II.

We have used density-functional-theory (DFT) methods together with a structure searching algorithm to make an experimentally constrained prediction of the structure of ammonia dihydrate II (ADH-II). The DFT structure is in good agreement with neutron diffraction data and verifies the prediction. The structure consists of the same basic structural elements as ADH-I, with a modest alteration to the packing, but a considerable reduction in volume. The phase diagram of the known ADH and ammonia monohydrate + water-ice structures is calculated with the Perdew-Burke-Ernzerhof density functional, and the effects of a semi-empirical dispersion corrected functional are investigated. The results of our DFT calculations of the finite-pressure elastic constants of ADH-II are compared with the available experimental data for the elastic strain coefficients.

Quantum Monte Carlo study of a positron in an electron gas.

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects.

Predicted formation of superconducting platinum-hydride crystals under pressure in the presence of molecular hydrogen.

Noble metals adopt close-packed structures at ambient pressure and rarely undergo structural transformation at high pressures. Platinum (Pt) is normally considered to be unreactive and is therefore not expected to form hydrides under pressure. We predict that platinum hydride (PtH) has a lower enthalpy than its constituents solid Pt and molecular hydrogen at pressures above 21.5 GPa. PtH transforms to a hexagonal close-packed or face-centered cubic (fcc) structure between 70 and 80 GPa. Linear response calculations indicate that PtH is a superconductor at these pressures with a critical temperature of about 10-25 K. These findings help to shed light on recent observations of pressure-induced metallization and superconductivity in hydrogen-rich materials. We show that the formation of fcc noble metal hydrides under pressure is common and examine the possibility of superconductivity in these materials.

Predicted pressure-induced s-band ferromagnetism in alkali metals.

First-principles density-functional-theory calculations show that compression of alkali metals stabilizes open structures with localized interstitial electrons which may exhibit a Stoner-type instability towards ferromagnetism. We find ferromagnetic phases of the lithium-IV-type, simple cubic, and simple hexagonal structures in the heavier alkali metals, which may be described as s-band ferromagnets. We predict that the most stable phases of potassium at low temperatures and pressures around 20 GPa are ferromagnets.

Ab initio random structure searching.

It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as density-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.

Quantum Monte Carlo study of the first-row atoms and ions.

Quantum Monte Carlo calculations of the first-row atoms Li-Ne and their singly positively charged ions are reported. Multideterminant-Jastrow-backflow trial wave functions are used which recover more than 98% of the correlation energy at the variational Monte Carlo level and more than 99% of the correlation energy at the diffusion Monte Carlo level for both the atoms and ions. We obtain the first ionization potentials to chemical accuracy. We also report scalar relativistic corrections to the energies, mass-polarization terms, and one- and two-electron expectation values.

Aluminium at terapascal pressures.

Studying materials at terapascal (TPa) pressures will provide insights into the deep interiors of large planets and chemistry under extreme conditions. The equation of state of aluminium is of interest because it is used as a standard material in shock-wave experiments and because it is a typical sp-bonded metal. Here we use density-functional-theory methods and a random-searching approach to predict stable structures of aluminium at multiterapascal pressures, finding that the low-pressure close-packed structures transform to more open structures above 3.2 TPa (nearly ten times the pressure at the centre of the Earth), with an incommensurate host-guest structure being stable over a wide range of pressures and temperatures. We show that the high-pressure phases may be described by a two-component model consisting of positive ions and interstitial electron 'blobs', and propose that such structures are common in sp-bonded materials up to multiterapascal pressures.

Fundamental high-pressure calibration from all-electron quantum Monte Carlo calculations.

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We compute the static contribution to the free energy with the QMC method and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We compute the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy.

Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica.

Silica (SiO(2)) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger's equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense alpha-PbO(2) structure above the core-insulating D" layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules.

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.