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.Comment: 7 pages, 7 figures, published by J. Chem. Phys (substantial changes after first submission

Timescales for dynamical relaxation to the Born rule

We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie-Bohm ontology, the box contains an objectively-existing 'pilot wave' which guides the electron trajectory, and this is represented mathematically by a Schroedinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born-rule ones and stay there; in analogy with the classical case this represents a decay to 'quantum equilibrium'. The proximity to equilibrium is characterized by the coarse-grained subquantum H-function which is found to decrease roughly exponentially towards zero over the course of time. The timescale tau for this relaxation is calculated for various values of M and the coarse-graining length epsilon. Its dependence on M is found to disagree with an earlier theoretical prediction. A power law - tau inversely proportional to M - is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of tau on epsilon is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of timescales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.Comment: 27 pages, 8 figures; Replacement with small number of changes reflecting referees' comment

Benchmarking the performance of Density Functional Theory and Point Charge Force Fields in their Description of sI Methane Hydrate against Diffusion Monte Carlo

High quality reference data from diffusion Monte Carlo calculations are presented for bulk sI methane hydrate, a complex crystal exhibiting both hydrogen-bond and dispersion dominated interactions. The performance of some commonly used exchange-correlation functionals and all-atom point charge force fields is evaluated. Our results show that none of the exchange-correlation functionals tested are sufficient to describe both the energetics and the structure of methane hydrate accurately, whilst the point charge force fields perform badly in their description of the cohesive energy but fair well for the dissociation energetics. By comparing to ice Ih, we show that a good prediction of the volume and cohesive energies for the hydrate relies primarily on an accurate description of the hydrogen bonded water framework, but that to correctly predict stability of the hydrate with respect to dissociation to ice Ih and methane gas, accuracy in the water-methane interaction is also required. Our results highlight the difficulty that density functional theory faces in describing both the hydrogen bonded water framework and the dispersion bound methane.Comment: 8 pages, 4 figures, 1 table. Minor typos corrected and clarification added in Method

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

We present a detailed study of the energetics of water clusters (H$_2$O)$_n$ with $n \le 6$, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.Comment: 34 pages, 6 figure

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces

Jastrow correlation factor for atoms, molecules, and solids

A form of Jastrow factor is introduced for use in quantum Monte Carlo simulations of finite and periodic systems. Test data are presented for atoms, molecules, and solids, including both all-electron and pseudopotential atoms. We demonstrate that our Jastrow factor is able to retrieve a large fraction of the correlation energy

Quantum Monte Carlo study of the Ne atom and the Ne+ ion

We report all-electron and pseudopotential calculations of the ground-stateenergies of the neutral Ne atom and the Ne+ ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered

Response of face-selective brain regions to trustworthiness and gender of faces

Neuropsychological and neuroimaging studies have demonstrated a role for the amygdala in processing the perceived trustworthiness of faces, but it remains uncertain whether its responses are linear (with the greatest response to the least trustworthy-looking faces), or quadratic (with increased fMRI signal for the dimension extremes). It is also unclear whether the trustworthiness of the stimuli is crucial or if the same response pattern can be found for faces varying along other dimensions. In addition, the responses to perceived trustworthiness of face-selective regions other than the amygdala are seldom reported. The present study addressed these issues using a novel set of stimuli created through computer image-manipulation both to maximise the presence of naturally occurring cues that underpin trustworthiness judgments and to allow systematic manipulation of these cues. With a block-design fMRI paradigm, we investigated neural responses to computer-manipulated trustworthiness in the amygdala and core face-selective regions in the occipital and temporal lobes. We asked whether the activation pattern is specific for differences in trustworthiness or whether it would also track variation along an orthogonal male–female gender dimension. The main findings were quadratic responses to changes in both trustworthiness and gender in all regions. These results are consistent with the idea that face-responsive brain regions are sensitive to face distinctiveness as well as the social meaning of the face features

Molecular brakes regulating mTORC1 activation in skeletal muscle following synergist ablation

The goal of the current work was to profile positive (mTORC1 activation, autocrine/paracrine growth factors) and negative [AMPK, unfolded protein response (UPR)] pathways that might regulate overload-induced mTORC1 (mTOR complex 1) activation with the hypothesis that a number of negative regulators of mTORC1 will be engaged during a supraphysiological model of hypertrophy. To achieve this, mTORC1- IRS-1/2 signaling, BiP/CHOP/IRE1, and AMPK activation were determined in rat plantaris muscle following synergist ablation (SA). SA resulted in significant increases in muscle mass of 4% per day throughout the 21 days of the experiment. The expression of the insulin-like growth factors (IGF) were high throughout the 21st day of overload. However, IGF signaling was limited, since IRS-1 and -2 were undetectable in the overloaded muscle from day 3 to day 9. The decreases in IRS-1/2 protein were paralleled by increases in GRB10 Ser501/503 and S6K1 Thr389 phosphorylation, two mTORC1 targets that can destabilize IRS proteins. PKB Ser473 phosphorylation was higher from 3– 6 days, and this was associated with increased TSC2 Thr939 phosphorylation. The phosphorylation of TSC2 Thr1345 (an AMPK site) was also elevated, whereas phosphorylation at the other PKB site, Thr1462, was unchanged at 6 days. In agreement with the phosphorylation of Thr1345, SA led to activation of AMPK1 during the initial growth phase, lasting the first 9 days before returning to baseline by day 12. The UPR markers CHOP and BiP were elevated over the first 12 days following ablation, whereas IRE1 levels decreased. These data suggest that during supraphysiological muscle loading at least three potential molecular brakes engage to downregulate mTORC1. m