Systematic reduction of sign errors in many-body calculations of atoms and molecules

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf 79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an accurate and robust method for calculating the ground state of atoms and molecules. By direct comparison with accurate configuration interaction results for the oxygen atom we show that SHDMC converges systematically towards the ground-state wave function. We present results for the challenging N$_2$ molecule, where the binding energies obtained via both energy minimization and SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that SHDMC is robust enough to find the nodal surface for systems at least as large as C$_{20}$ starting from random coefficients. SHDMC is a linear-scaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.Comment: Final version accepted in Physical Review Letters. The review history (referees' comments and our replies) is included in the source

Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations

We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave-function with better nodal structure and (b) we argue that the noise in the fixed-node wave-function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. We propose a method to improve both single determinant and multi-determinant expansions of the trial wave-function. We test the method in a model system where benchmark configuration interaction calculations can be performed. Comparing the DMC calculations with the exact solutions, we find that the trial wave-function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave-functions orthogonal to the exact ground state. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted earlier[Phys.Rev. B {\bf 77}, 245110 (2008)]. We obtain the exact Kohn-Sham effective potential from the DMC data.Comment: Final version of the paper accepted in Physical Review B. The review reports and replies are included in the sourc

Quantum molecular dynamics simulations of uranium at high pressure and temperature

Constant-volume quantum molecular dynamics (QMD) simulations of uranium (U) have been carried out over a range of pressures and temperatures that span the experimentally observed solid orthorhombic {alpha}-U, body-centered cubic (bcc), and liquid phases, using an ab initio plane-wave pseudopotential method within the generalized gradient approximation of density functional theory. A robust U pseudopotential has been constructed for these simulations that treats the 14 valence and outer-core electrons per atom necessary to calculate accurate structural and thermodynamic properties up to 100 GPa. Its validity has been checked by comparing low-temperature results with experimental data and all-electron full-potential linear-muffin-tin-orbital calculations of several different uranium solid structures. Calculated QMD energies and pressures for the equation of state of uranium in the solid and liquid phases are given, along with results for the Grueneisen parameter and the specific heat. We also present results for the radial distribution function, bond-angle distribution function, electronic density of states, and liquid diffusion coefficient, as well as evidence for short-range order in the liquid

Dissolved Iron Supply from Asian Glaciers: Local Controls and a Regional Perspective

Ice sheets have been shown to deliver large amounts of labile iron (Fe) to aquatic ecosystems; however, the role of glaciers distinct from ice sheets in supplying labile Fe to downstream ecosystems is less well understood despite their rapid volume loss globally. Direct and continuous measurements of Fe from glaciers throughout an entire melt season are very limited to date. Here we present extensive seasonal data on 0.45-μm-filtered Fe (dFe) from three glaciers in Asia. Concentrations of dFe are negatively correlated with glacier discharge, and dFe yields are closely related to specific discharge. Based on our study and previously published dFe data, we estimate the release of dFe from Asian glaciers to be 23.8±14.1 Gg/a. We further compile a global data set of dFe from more than 12 glaciers, which, when combined with data on glacier discharge, suggest that the release of dFe from glaciers globally is on the order of 185±172 Gg/a. This finding suggests that glaciers may provide a substantial, but largely unrecognized source of potentially labile Fe, and may become increasingly important for the Fe biogeochemical cycle in a warming climate

Phase transitions and spin-state of iron in FeO at the conditions of Earth's deep interior

Iron-bearing oxides undergo a series of pressure-induced electronic, spin and structural transitions that can cause seismic anomalies and dynamic instabilities in Earth's mantle and outer core. We employ x-ray diffraction and x-ray emission spectroscopy along with state-of-the-art density functional plus dynamical mean-field theory (DFT+DMFT) to characterize the electronic structure and spin states, and crystal-structural properties of w\"ustite (Fe$_{1-x}$O) -- a basic oxide component of Earth's interior -- at high pressure-temperature conditions up to 140 GPa and 2100 K. We find that FeO exhibits complex polymorphism under pressure, with abnormal compression behavior associated with electron-spin and crystallographic phase transitions, and resulting in a substantial change of bulk modulus. Our results reveal the existence of a high-pressure phase characterized by a metallic high-spin state of iron at about the pressure-temperature conditions of Earth's core-mantle boundary. The presence of high-spin metallic iron near the base of the mantle can significantly influence the geophysical and geochemical properties of Earth's deep interior.Comment: 5 figures, with supplementary material

Quantum Monte Carlo Assessment of the Relevance of Electronic Correlations in Defects and EOS in Metals

We have developed a highly accurate computational capability to calculate the equation of state (EOS) and defect formation energies of metallic systems. We are using a newly developed algorithm that enables the study of metallic systems with quantum Monte Carlo (QMC) methods. To date, technical limitations have restricted the application of QMC methods to semiconductors, insulators and the homogeneous electron gas. Using this new 'QMC for metals' we can determine, for the first time, the significance of correlation effects in the EOS and in the formation energies of point defects, impurities, surfaces and interfaces in metallic systems. These calculations go beyond the state-of-the-art accuracy which is currently obtained with Density Functional Theory approaches. Such benchmark calculations can provide more accurate predictions for the EOS and the formation energies of vacancies and interstitials in simple metals. These are important parameters in determining the mechanical properties as well as the micro-structural evolution of metals in irradiated materials or under extreme conditions. We describe the development of our 'QMC for metals' code, which has been adapted to run efficiently on a variety of computer architectures including BG/L. We present results of the first accurate quantum Monte Carlo calculation of an EOS of a realistic metallic system that goes beyond the homogeneous electron gas

Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.Comment: 13 pages, 4 figures. To appear in Phys. Rev.