Accelerating convergence to the thermodynamic limit with twist angle selection applied to methods beyond many-body perturbation theory

Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass

Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to sampling, path integral discretization errors, and thermodynamic integration errors. While the statistical errors can be reduced with virial estimators and path integral discretization errors with high-order factorization of the Boltzmann operator, here we propose a method for accelerating isotope effect calculations by eliminating the integration error. We sho…

An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas

We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the non-zero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, and which yields results comparable to full twist averaging. …

磁性金属的增强扭曲平均技术：使用量子蒙特卡罗的应用

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications using Quantum Monte Carlo

提出一种改进的量子蒙特卡罗扭曲平均方案，通过重现参考磁化强度和构造性电荷中性，避免能量波动，实现磁性金属总能量和磁性的稳健收敛。

Accelerating the 3D-RISM theory of molecular solvation with treecode summation and cut-offs

The 3D reference interaction site model (3D-RISM) of molecular solvation is a powerful tool for computing the equilibrium thermodynamics and density distributions of solvents, such as water and co-ions, around solute molecules. However, 3D-RISM solutions can be expensive to calculate, especially for proteins and other large molecules where calculating the potential energy between solute and solvent requires more than half the computation time. To address this problem, we have developed and implemented treecode summation for long-range interactions and analytically corrected cut-offs for short-…

Accelerating single-crystal growth by stimulated and self-guided channeling

We report a self-guided and "stimulated" single-crystal growth acceleration effect in static super-saturated aqueous solutions, producing inorganic (KH$_2$PO$_4$) and organic (tetraphenyl-phosphonium-family) nonlinear optical single-crystals with novel morphologies. The extraordinarily fast unidirectional growth in the presence of complete lateral growth suppression defies all current impurity, defect and dislocation based crystal growth inhibition mechanisms. We propose a self-channeling-stimulated accelerated growth theory that can satisfactorily explain all experimental results. Using molec…

An efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations

We introduce a simple but efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations. By evaluating the thermodynamic grand potential instead of the ground state total energy, we greatly reduce the sampling errors caused by twist-dependent fluctuations in the particle number. We apply this method to the electron gas and to metallic lithium, aluminum, and solid atomic hydrogen. We show that, even when using a small number of twists, grand-canonical twist averaging of the grand potential produces better estimates of ground state energies than the widely used canonic…