A full‐pivoting algorithm for the Cholesky decomposition of two‐electron repulsion and spin‐orbit coupling integrals

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two‐electron spin‐orbit coupling (2e‐SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e‐SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e‐SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full‐pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that is the upper limit for the errors affecting the reconstructed 2e‐SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e‐SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.     

Efficient calculation of two‐electron integrals for high angular basis functions

The computation of electron repulsion integrals (ERIs) is the most time‐consuming process in the density functional calculation using Gaussian basis set. Many temporal ERIs are calculated, and most are stored on slower storage, such as cache or memory, because of the shortage of registers, which are the fastest storage in a central processing unit (CPU). Moreover, the heavy register usage makes it difficult to launch many concurrent threads on a graphics processing unit (GPU) to hide latency. Hence, we propose to optimize the calculation order of one‐center ERIs to minimize the number of registers used, and to calculate each ERI with three or six co‐operating threads. The performance of this method is measured on a recent CPU and a GPU. The proposed approach is found to be efficient for high angular basis functions with a GPU. When combined with a recent GPU, it accelerates the computation almost 4‐fold. © 2014 Wiley Periodicals, Inc.     

Dependence of thermodynamic properties of model systems on some dissipative particle dynamics parameters

The influence of systematic perturbation of input interaction parameters on thermodynamic equilibrium properties is studied employing dissipative particle dynamics (DPD) simulations. The values of both the excess pressure and the surface tension are found to be very sensitive to the values of the soft repulsion parameter between unlike DPD particles for high values of the coarse-graining level (number of water molecules per DPD particle). For the case in which a molecular surfactant is present at the interface we have determined the dependence of these properties on the values of the parameters that characterize the bonding force between polymer beads. No significant differences were found between linear and branched surfactants.     

Differential evolution algorithms using hybrid mutation

Differential evolution (DE) has gained a lot of attention from the global optimization research community. It has proved to be a very robust algorithm for solving non-differentiable and non-convex global optimization problems. In this paper, we propose some modifications to the original algorithm. Specifically, we use the attraction-repulsion concept of electromagnetism-like (EM) algorithm to boost the mutation operation of the original differential evolution. We carried out a numerical study using a set of 50 test problems, many of which are inspired by practical applications. Results presented show the potential of this new approach.     

双幻核100Sn的基态性质

用Skyrme—Hartree—Fock方法计算了双幻核¹⁰⁰Sn基态的一些性质.计算表明,由于库仑排斥,¹⁰⁰Sn存在一个质子皮.     

低温金属抗磁演示实验

基于电磁感应定律,设计了金属跳环抗磁演示实验装置,实验可演示铜、铝、不锈钢、塑料等材料的圆环在变化螺线管磁场中因电磁感应电流而上跳的实验现象,且结合液氮低温环境演示低温下金属环的环跳,可比对两种条件下的环跳高度,拓展了电磁感应实验内容,现象直观、明显。     

Boundedness in a four‐dimensional attraction‐repulsion chemotaxis system with logistic source

In this paper, we study the attraction‐repulsion chemotaxis system with logistic source: u_t = Δu−χ∇·(u∇v)+ξ∇·(u∇w)+f(u), 0 = Δv−βv+αu, 0 = Δw−δw+γu, subject to homogeneous Neumann boundary conditions in a bounded and smooth domain , where χ,α,ξ,γ,β, and δ are positive constants, and is a smooth function satisfying f(s) ≤ a−bs^3/2 for all s ≥ 0 with a ≥ 0 and b > 0. It is proved that when the repulsion cancels the attraction (ie, ξγ=χα), for any nonnegative initial data , the solution is globally bounded. This result corresponds to the one in the classical 2‐dimensional Keller‐Segel model with logistic source bearing quadric growth restrictions.     

The hydrogen bond under pressure

The hydrogen bonds are quite pervasive in several classes of materials. Its parameters are known to show systematic variations with hydrogen bond length, and pressure variable is thus a natural way for studying hydrogen bonded substances. In this article, we review the unifying features as obtained through several experimental and theoretical investigations. Amongst other things, it is examined whether the observed pressure-induced variations in parameters of hydrogen bonds are consistent with the co-relations known on different chemical substances at normal pressure. In particular, the controversies on variations of O–H and H- - -O pairs with pressure and symmetrization of hydrogen bond have been resolved. The effects of close packing promoted by pressure such as formation of muli-centered hydrogen bonds and steric repulsions and the way the hydrogen bonds counter these in different ways are also examined.