Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements

A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis, and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson and coworkers, which employ a small core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density-functional (GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few milli-hartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment.Comment: 10 pages, 2 figures. To be published in Journal of Chemical Physic

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2

The use of an approximate reference state wave function |Phi_r> in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |Phi_r>. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems, and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.Comment: 8 pages, 6 figures, submitted to J. Chem. Phy

Interannual Variability and Seasonal Predictability of Wind and Solar Resources

Solar and wind resources available for power generation are subject to variability due to meteorological factors. Here, we use a new global climate reanalysis product, Version 2 of the NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA-2), to quantify interannual variability of monthly-mean solar and wind resource from 1980 to 2016 at a resolution of about 0.5 degrees. We find an average coefficient of variation (CV) of 11% for monthly-mean solar radiation and 8% for wind speed. Mean CVs were about 25% greater over ocean than over land and, for land areas, were greatest at high latitude. The correlation between solar and wind anomalies was near zero in the global mean, but markedly positive or negative in some regions. Both wind and solar variability were correlated with values of climate modes such as the Southern Oscillation Index and Arctic Oscillation, with correlations in the Northern Hemisphere generally stronger during winter. We conclude that reanalysis solar and wind fields could be helpful in assessing variability in power generation due to interannual fluctuations in the solar and wind resource. Skillful prediction of these fluctuations seems to be possible, particularly for certain regions and seasons, given the persistence or predictability of climate modes with which these fluctuations are associated

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H$_2$O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).Comment: 11 pages, 5 figures. submitted to JC

Pressure-induced diamond to beta-tin transition in bulk silicon: a near-exact quantum Monte Carlo study

The pressure-induced structural phase transition from diamond to beta-tin in silicon is an excellent test for theoretical total energy methods. The transition pressure provides a sensitive measure of small relative energy changes between the two phases (one a semiconductor and the other a semimetal). Experimentally, the transition pressure is well characterized. Density-functional results have been unsatisfactory. Even the generally much more accurate diffusion Monte Carlo method has shown a noticeable fixed-node error. We use the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to calculate the relative energy differences in the two phases. In this method, all but the error due to the phaseless constraint can be controlled systematically and driven to zero. In both structural phases we were able to benchmark the error of the phaseless constraint by carrying out exact unconstrained AFQMC calculations for small supercells. Comparison between the two shows that the systematic error in the absolute total energies due to the phaseless constraint is well within 0.5 mHa/atom. Consistent with these internal benchmarks, the transition pressure obtained by the phaseless AFQMC from large supercells is in very good agreement with experiment.Comment: 9 pages, 5 figure

Non-equilibrium phase transitions in biomolecular signal transduction

We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework

Rethinking Motor Learning and Savings in Adaptation Paradigms: Model-Free Memory for Successful Actions Combines with Internal Models

SummaryAlthough motor learning is likely to involve multiple processes, phenomena observed in error-based motor learning paradigms tend to be conceptualized in terms of only a single process: adaptation, which occurs through updating an internal model. Here we argue that fundamental phenomena like movement direction biases, savings (faster relearning), and interference do not relate to adaptation but instead are attributable to two additional learning processes that can be characterized as model-free: use-dependent plasticity and operant reinforcement. Although usually “hidden” behind adaptation, we demonstrate, with modified visuomotor rotation paradigms, that these distinct model-based and model-free processes combine to learn an error-based motor task. (1) Adaptation of an internal model channels movements toward successful error reduction in visual space. (2) Repetition of the newly adapted movement induces directional biases toward the repeated movement. (3) Operant reinforcement through association of the adapted movement with successful error reduction is responsible for savings

Plant Driven Movement: Does Plant Quality Affect the Foraging Patterns of Successful Male Sage-Grouse (Centrocercus Urophasianus)?

The structural and dietary quality of plants is highly variable across the landscape and may influence energy acquisition by herbivores needed for energy dependent activities. For sage-grouse, male display efforts are energetically expensive, with successful males expending up to four times their basal metabolic rate to display. Previous work found that males who had the greatest energy expenditure during the lekking season also lost the least weight and foraged farthest from the lek. We hypothesized that the energetic benefit of foraging farther from the lek is due to higher quality food or cover compared to near lek vegetation. To initially test this hypothesis, we quantified the structural and nutritional quality of sagebrush at different distances away from the lek as well as at patches used by sage-grouse for foraging and roosting. We found no difference in density, percent cover, or height of live or dead sagebrush among different distances (edge, 100, 200, 400 or 800 m) away from leks, but there was a trend for plants near the lek edge to have higher crude protein than those farther away from leks. We found no difference in percent grass, percent forbs, volume of sagebrush, or crude protein of sagebrush among forage, roost, or near lek (100 m from edge) patches, but forage patches tended to have taller sagebrush than roost or near lek patches. The preliminary results suggest that selection for off-lek patches by male sage-grouse may not be driven by the structural or nutritional quality of plants. We propose that plant chemical components may be more indicative of off-lek habitat use by male sage-grouse during the lekking period

On the Substitution of Identicals in Counterfactual Reasoning

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized