Reducing the time-step errors in diffusion Monte Carlo.

We modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error of the total energy. Furthermore, we present a reweighting scheme that has the desirable feature that it is exactly size-consistent, i.e., the energy of a system containing widely separated fragments is the same as the sum of the energies of the individual fragments. The practical utility of the latter improvement is that it reduces the time-step error of the binding energies of some weakly interacting systems.

Reliable radical stabilization energies from diffusion Monte Carlo calculations.

We assess the performance of variational (VMC) and diffusion (DMC) quantum Monte Carlo methods for calculating the radical stabilization energies of a set of 43 carbon-centered radical species. Even using simple single-determinant trial wavefunctions, both methods perform exceptionally well, with mean absolute deviations from reference values well under the chemical accuracy standard of 1 kcal/mol. In addition, the use of DMC results in a highly concentrated spread of errors, with all 43 results within chemical accuracy at the 95% confidence level. These results indicate that DMC is an extremely reliable method for calculating radical stabilization energies and could be used as a benchmark method for larger systems in future.

Density functional orbitals in quantum Monte Carlo: The importance of accurate densities.

There has been significant recent attention surrounding the accuracy of electronic densities produced by modern parameterized density functional approximations (DFAs). Here, we investigate the impact of using orbitals from density functional calculations in fixed-node Diffusion Monte Carlo (DMC) methods, which is common practice in the calculation of large systems. We find that the accuracy of the density is a strong indicator of the quality of the many-body nodal surface produced by a determinant of the corresponding Kohn-Sham orbitals. Functionals which produce the most accurate electronic densities also produce the lowest variational DMC energies, while functionals that produce poor densities lead to significantly higher energies. This result simplifies the process of choosing orbitals for DMC calculations of large systems and suggests that prioritizing accurate densities in the future development of DFAs would also contribute to the continued improvement of DMC.

Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo.

We present a method for truncating large multi-determinant expansions for use in diffusion Monte Carlo calculations. Current approaches use wavefunction-based criteria to perform the truncation. Our method is more intuitively based on the contribution each determinant makes to the total energy. We show that this approach gives consistent behaviour across systems with varying correlation character, which leads to effective error cancellation in energy differences. This is demonstrated through accurate calculations of the electron affinity of oxygen and the atomisation energy of the carbon dimer. The approach is simple and easy to implement, requiring only quantities already accessible in standard configuration interaction calculations.

Performance of quantum Monte Carlo for calculating molecular bond lengths.

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

Impact of distributions and mixtures on the charge transfer properties of graphene nanoflakes.

Many of the promising new applications of graphene nanoflakes are moderated by charge transfer reactions occurring between defects, such as edges, and the surrounding environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity and chemical hardness can be useful indicators of the efficiency of graphene nanoflakes for different reactions, and can help identify new application areas. However, as samples of graphene nanoflakes cannot necessarily be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of flakes, and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of ensembles where restrictions have been placed on the diversity of the structures. By predicting quality factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified.

Size and shape dependent deprotonation potential and proton affinity of nanodiamond.

Many important reactions in biology and medicine involve proton abstraction and transfer, and it is integral to applications such as drug delivery. Unlike electrons, which are quantum mechanically delocalized, protons are instantaneously localized on specific residues in these reactions, which can be a distinct advantage. However, the introduction of nanoparticles, such as non-toxic nanodiamonds, to this field complicates matters, as the number of possible sites increases as the inverse radius of the particle. In this paper we present > 10(4) simulations that map the size- and shape-dependence of the deprotonation potential and proton affinity of nanodiamonds in the range 1.8-2.7 nm in average diameter. We find that while the average deprotonation potential and proton affinities decrease with size, the site-specific values are inhomogeneous over the surface of the particles, exhibiting strong shape-dependence. The proton affinity is strongly facet-dependent, whereas the deprotonation potential is edge/corner-dependent, which creates a type of spatial hysteresis in the transfer of protons to and from the nanodiamond, and provides new opportunities for selective functionalization.

Ab initio electronic properties of dual phosphorus monolayers in silicon.

IN THE MIDST OF THE EPITAXIAL CIRCUITRY REVOLUTION IN SILICON TECHNOLOGY, WE LOOK AHEAD TO THE NEXT PARADIGM SHIFT: effective use of the third dimension - in particular, its combination with epitaxial technology. We perform ab initio calculations of atomically thin epitaxial bilayers in silicon, investigating the fundamental electronic properties of monolayer pairs. Quantitative band splittings and the electronic density are presented, along with effects of the layers' relative alignment and comments on disordered systems, and for the first time, the effective electronic widths of such device components are calculated.

Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon.

: The differences in energy between electronic bands due to valley splitting are of paramount importance in interpreting transport spectroscopy experiments on state-of-the-art quantum devices defined by scanning tunnelling microscope lithography. Using vasp, we develop a plane-wave density functional theory description of systems which is size limited due to computational tractability. Nonetheless, we provide valuable data for the benchmarking of empirical modelling techniques more capable of extending this discussion to confined disordered systems or actual devices. We then develop a less resource-intensive alternative via localised basis functions in siesta, retaining the physics of the plane-wave description, and extend this model beyond the capability of plane-wave methods to determine the ab initio valley splitting of well-isolated δ-layers. In obtaining an agreement between plane-wave and localised methods, we show that valley splitting has been overestimated in previous ab initio calculations by more than 50%.

Delocalized oxygen as the origin of two-level defects in Josephson junctions.

One of the key problems facing superconducting qubits and other Josephson junction devices is the decohering effects of bistable material defects. Although a variety of phenomenological models exist, the true microscopic origin of these defects remains elusive. For the first time we show that these defects may arise from delocalization of the atomic position of the oxygen in the oxide forming the Josephson junction barrier. Using a microscopic model, we compute experimentally observable parameters for phase qubits. Such defects are charge neutral but have nonzero response to both applied electric field and strain. This may explain the observed long coherence time of two-level defects in the presence of charge noise, while still coupling to the junction electric field and substrate phonons.

How Important is Orbital Choice in Single-Determinant Diffusion Quantum Monte Carlo Calculations?

The accuracy of total electronic energies obtained using the fixed-node diffusion quantum Monte Carlo (FN-DMC) method is determined by the choice of the many-body nodal surface. Here, we perform a systematic comparison of the quality of FN-DMC energies for a selection of atoms and diatomic molecules using nodal surfaces defined by single determinants of Hartree-Fock, B3LYP, and LDA orbitals. Through comparison with experimental results, we show that the use of Kohn-Sham orbitals results in significantly improved FN-DMC atomization energies over those obtained using Hartree-Fock orbitals. We also discuss the effect of spin contamination in the orbitals.

Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus.

We derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zero-variance and zero-bias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the first-row atoms Li-Ne, the Ar atom, and the diatomic molecules B(2), N(2), and F(2).

Anisotropic intracule densities and electron correlation in H2: a quantum Monte Carlo study.

We derive efficient quantum Monte Carlo estimators for the anisotropic intracule and extracule densities. These estimators are used in conjunction with an accurate explicitly correlated wave function to investigate the bond-length dependence of electron correlation effects in the ground-state H(2) molecule. It is shown that the localized increase in the magnitude of the correlation energy as the bond is stretched is accompanied by highly anisotropic correlation effects. In addition, we find a small long-range part of the Coulomb hole, which is present even at the equilibrium bond length.

An analysis of the correlation energy contribution to the interaction energy of inert gas dimers.

An accurate description of electron correlation is essential for the calculation of interaction energies in cases where dispersion energy is a major component, for example, for the rare gas atoms, physisorption on graphite, and graphene-graphene interactions. Such calculations are computationally demanding using supermolecule methods and the energies calculated lack a simple, physical interpretation. Alternatively density functional theories (DFTs) may be used to give an approximate estimate of the correlation energy. However, the physical nature of this DFT estimate of electron correlation energy is not well understood and, in fact, most current DFT methods do not describe dispersion energy at all. Hence, an analysis of the correlation energy contribution to interaction energies where dispersion energy is important is needed. In order to do this we provide an analysis of the correlation energy contribution to the potential energy curves of He(2), Ne(2), and Ar(2) in terms of the Hartree-Fock (HF) interaction term DeltaE(int) (HF), a dispersion energy term E(disp) and an electron correlation term DeltaE(int) (C). DeltaE(int) (C) includes all other correlation energy effects besides E(disp) and is shown to be repulsive, of a similar short range character to, but of smaller magnitude than DeltaE(int) (HF). This analysis was used to develop a theoretical model which gives a very good estimate of the potential energy wells for He(2), Ne(2), Ar(2), HeNe, HeAr, and NeAr.

Electron-nucleus cusp correction and forces in quantum Monte Carlo.

A simple method is presented which ensures the electron-nucleus cusp condition is satisfied by the Slater-Jastrow wavefunctions commonly employed in quantum Monte Carlo simulations. The method is applied in variational energy calculations of the neon atom and a selection of molecules using both Gaussian and Slater basis sets. In addition, we discuss the relationship between the electron-nucleus cusps and the variance of forces, and investigate the sensitivity of forces to the quality of the cusps for various diatomic molecules.