We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in twodimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of monolayer phosphorene. We investigate the fixed-node errors in diffusion Monte Carlo gaps evaluated with Slater-Jastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excited-state wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excited-state energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excited-state energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixed-node errors in calculations on solids the inclusion of backflow correlations is sometimes necessary.PACS numbers: 31.15. A-, 31.15.vj, 31.50.Df, 71.15.Qe, 71.35.-y arXiv:1806.04750v4 [cond-mat.mtrl-sci]

We present a new modeling scheme for ion self-diffusion coefficient, which broadens the applicable scope of ab initio approach. The essential concepts of the scheme are 'domain division' and 'coarse graining' of the diffusion network based on the barrier energies predicted by the ab initio calculation. The scheme was applied to evaluate Cu ion self-diffusion coefficient in ε-Cu 3 Sn phase of Cu-Sn alloy, which is a typical system having long-range periodicity. The model constructed with the scheme successfully reproduces the experimental values in a wide temperature range.

Density functional theory (DFT) is a valuable tool for calculating adsorption energies toward designing materials for hydrogen storage. However, dispersion forces being absent from the local/semi-local theory, it remains unclear as to how the consideration of van der Waals (vdW) interactions affects such calculations. For the first time, we applied diffusion Monte Carlo (DMC) to evaluate the adsorption characteristics of a hydrogen molecule on a (5,5) armchair silicon-carbide nanotube (H2-SiCNT). Within the DFT framework, we benchmarked various exchange-correlation functionals, including those recently developed for treating dispersion or vdW interactions. We found that the vdW-corrected DFT methods agree well with DMC, whereas the local (semilocal) functional significantly over (under)-binds. Furthermore, we fully optimized the H2-SiCNT geometry within the DFT framework and investigated the correlation between the structure and charge density. The vdW contribution to the adsorption was found to be non-negligible at ∼1 kcal/mol per hydrogen molecule, which amounts to 9–29% of the ideal adsorption energy required for hydrogen storage applications.

A common approach for studying a solid solution or disordered system within a periodic ab initio framework is to create a supercell in which certain amounts of target elements are substituted with other elements. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from many substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. Our developed Python software package, which is called Shry (Suite for High-throughput generation of models with atomic substitutions implemented by Python), allows the selection of only symmetry-inequivalent structures from the vast number of candidates based on the canonical augmentation algorithm. Shry is implemented in Python 3 and uses the CIF format as the standard for both reading and writing the reference and generated sets of substituted structures. Shry can be integrated into another Python program as a module or can be used as a stand-alone program. The implementation was verified through a comparison with other codes with the same functionality, based on the total numbers of symmetry-inequivalent structures, and also on the equivalencies of the output structures themselves. The provided crystal structure data used for the verification are expected to be useful for benchmarking other codes and also developing new algorithms in the future.

Numerous reports have elucidated the classification of a large amount of data using various clustering techniques. However, an increase in data size hinders the applicability of these methods. Here, it is investigated how to deal with the exploding number of possibilities to be sorted into irreducible classes by using a clustering technique when its input capacity cannot accommodate the total number of possibilities. This can be exemplified by atomic substitutions in the supercell modeling of alloys. The number of possibilities is sometimes equal to trillions, which is extremely large to be accommodated in a cluster. Thus, it is not practically feasible to identify directly how many irreducible classes exist even though several techniques are available to perform the clustering. In this regard, a stochastic framework is developed to avoid the shortage limitations, providing a method to estimate the total number of irreducible classes (the order of classes), as a statistical estimate. The main conclusion is that the statistical variation of the number of classes, at each sampling trial, can serve as a promising measure to estimate the total number of irreducible classes. Characteristics of this approach is also discussed by comparing with the conventional one based on Polya's theorem.