Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.     

Low‐energy structures of benzene clusters with a novel accurate potential surface

The benzene‐benzene (Bz‐Bz) interaction is present in several chemical systems and it is known to be crucial in understanding the specificity of important biological phenomena. In this work, we propose a novel Bz‐Bz analytical potential energy surface which is fine‐tuned on accurate ab initio calculations in order to improve its reliability. Once the Bz‐Bz interaction is modeled, an analytical function for the energy of the clusters may be obtained by summing up over all pair potentials. We apply an evolutionary algorithm (EA) to discover the lowest‐energy structures of clusters (for ), and the results are compared with previous global optimization studies where different potential functions were employed. Besides the global minimum, the EA also gives the structures of other low‐lying isomers ranked by the corresponding energy. Additional ab initio calculations are carried out for the low‐lying isomers of and clusters, and the global minimum is confirmed as the most stable structure for both sizes. Finally, a detailed analysis of the low‐energy isomers of the n = 13 and 19 magic‐number clusters is performed. The two lowest‐energy isomers show S₆ and C₃ symmetry, respectively, which is compatible with the experimental results available in the literature. The structures reported here are all non‐symmetric, showing two central Bz molecules surrounded by 12 nearest‐neighbor monomers in the case of the five lowest‐energy structures. © 2015 Wiley Periodicals, Inc.     

Accurate double many‐body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single‐sheeted double many‐body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the and dissociation channels involving nitrogen in the ground and first excited states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner–Teller degeneracy of the and states of . Such a work can both be recommended for dynamics studies of the reaction and as building blocks for constructing the double many‐body expansion potential energy surface of larger nitrogen/hydrogen‐containing systems. In turn, a test theoretical study of the reaction has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result. © 2013 Wiley Periodicals, Inc.     

Quantum Monte Carlo with very large multideterminant wavefunctions

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman–Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin‐specific determinants: for typical configuration interaction‐type wavefunctions the number of unique spin‐specific determinants ( ) with a non‐negligible weight in the expansion is of order . We show that a careful implementation of the calculation of the N_det ‐dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin‐specific determinants, , over a wide range of total number of determinants (here, N_det up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all‐electron fixed‐node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ～400 compared to a single‐determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.     

Bonding analysis of planar hypercoordinate atoms via the generalized BLW‐LOL

The multicenter bonding pattern of the intriguing hexa‐, hepta‐, and octacoordinate boron wheel series (e.g., , , , and SiB₈ as well as the experimentally detected isomer) is revised using the block‐localized wave function analyzed by the localized orbital locator (BLW‐LOL). The more general implementation of BLW combined with the LOL scalar field is not restricted to the analysis of the out‐of‐plane π‐system but can also provide an intuitive picture of the σ‐radial delocalization and of the role of the central atom. The results confirm the presence of a π‐ring current pattern similar to that of benzene. In addition, the LOL_π isosurfaces along with the maximum intensity in the  ΔLOL profiles located above and below the ring suggest that the central atom plays a minor role in the π‐delocalized bonding pattern. Finally, the analysis of the σ‐framework in these boron wheels is in line with a moderated inner cyclic rather than disk‐type delocalization. © 2013 Wiley Periodicals, Inc.     

FEREBUS: Highly parallelized engine for kriging training

FFLUX is a novel force field based on quantum topological atoms, combining multipolar electrostatics with IQA intraatomic and interatomic energy terms. The program FEREBUS calculates the hyperparameters of models produced by the machine learning method kriging. Calculation of kriging hyperparameters ( θ and p ) requires the optimization of the concentrated log‐likelihood . FEREBUS uses Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms to find the maximum of . PSO and DE are two heuristic algorithms that each use a set of particles or vectors to explore the space in which is defined, searching for the maximum. The log‐likelihood is a computationally expensive function, which needs to be calculated several times during each optimization iteration. The cost scales quickly with the problem dimension and speed becomes critical in model generation. We present the strategy used to parallelize FEREBUS, and the optimization of through PSO and DE. The code is parallelized in two ways. MPI parallelization distributes the particles or vectors among the different processes, whereas the OpenMP implementation takes care of the calculation of , which involves the calculation and inversion of a particular matrix, whose size increases quickly with the dimension of the problem. The run time shows a speed‐up of 61 times going from single core to 90 cores with a saving, in one case, of ～98% of the single core time. In fact, the parallelization scheme presented reduces computational time from 2871 s for a single core calculation, to 41 s for 90 cores calculation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Horizontal vectorization of electron repulsion integrals

We present an efficient implementation of the Obara–Saika algorithm for the computation of electron repulsion integrals that utilizes vector intrinsics to calculate several primitive integrals concurrently in a SIMD vector. Initial benchmarks display a 2–4 times speedup with AVX instructions over comparable scalar code, depending on the basis set. Speedup over scalar code is found to be sensitive to the level of contraction of the basis set, and is best for quartets when l_D = 0 or , which makes such a vectorization scheme particularly suitable for density fitting. The basic Obara–Saika algorithm, how it is vectorized, and the performance bottlenecks are analyzed and discussed. © 2016 Wiley Periodicals, Inc.     

The performance of density functional and wavefunction‐based methods for 2D and 3D structures of Au10

The transition from 2D to 3D structures in small gold clusters occurs around 10 atoms. Density functional theory predicts a planar structure for in contrast to recent second‐order Møller–Plesset perturbation theory calculations, which predict a 3D arrangement. The validity of the use of single‐reference second‐order Møller–Plesset theory for near metallic systems remains, however, questionable. On the other hand, it is less than clear how well density functional approximations perform for such clusters. We, therefore, decided to carry out quantum chemical calculations for using a variety of different density functionals as well as wavefunction‐based methods including coupled cluster theory to compare the different energetically low lying 2D and 3D cluster isomers. The results are perhaps not encouraging showing that most computational methods do not predict correctly the energetic sequence of isomers compared to coupled cluster theory. As perturbative triple corrections in the coupled cluster treatment change the order in cluster stability, the onset of 2D to 3D transition in these gold clusters remains elusive. As expected, second‐order Møller–Plesset theory is not suitable for correctly describing such systems.     

Extension of accompanying coordinate expansion and recurrence relation method for general‐contraction basis sets

An algorithm of the accompanying coordinate expansion and recurrence relation (ACE‐RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general‐contraction (GC) scheme. The present algorithm, denoted by GC‐ACE‐RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d‐ and f‐orbitals. The performance of GC‐ACE‐RR was assessed for ‐, ‐, ‐, and ‐type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE‐RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC‐ACE‐RR computations for ERIs of three‐dimensional gold clusters Au_n (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster. © 2014 Wiley Periodicals, Inc.     

Fast search algorithms for computational protein design

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state‐of‐the‐art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well‐established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of to produce conformations in increasing order of energy, we defined new strategies combining CFN lower bounds, with new side‐chain positioning‐based branching scheme. Beyond the speedups obtained in the new ‐CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms. © 2016 Wiley Periodicals, Inc.     

Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, and , using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.     

Software package SIMPRE—Revisited

This article elucidates the pitfalls identified in the software package SIMPRE recently developed by Baldoví et al. (J. Comput. Chem. 2013, 34, 1961) for modeling the spectroscopic and magnetic properties of single ion magnets as well as single‐molecule magnets. Analysis of the methodology used therein reveals that the crystal field parameters (CFPs), expressed nominally in the Stevens formalism, exhibit features characteristic for the CFPs expressed in the Wybourne notation. The resemblance of the two types of CFPs introduces a serious confusion that may lead to wrong comparisons of the CFPs taken from various sources. To clarify this confusion, the properties of the CFPs ( , ) associated with the Stevens operators ( X = S , J , or L ), which belong to the class of the tesseral‐tensor operators, are contrasted with those of the CFPs B_kq associated with the Wybourne operators , which belong to the class of the spherical‐tensor operators. Importantly, the confused properties of Stevens and Wybourne operators may bear on reliability of SIMPRE calculations. To consider this question independent calculations are carried out using the complete approach and compared with those of the restricted approach utilized earlier. It appears that the numerical results of the package SIMPRE are formally acceptable, however, the meaning of the CFPs must be properly reformulated. Several other conceptual problems arising from misinterpretations of the crucial notions and the CFP notations identified therein are also discussed and clarified. © 2014 Wiley Periodicals, Inc.     

Topological analysis of the electron delocalization range

The electron delocalization range function EDR( ) (Janesko et al., J. Chem. Phys. 2014, 141, 144104) quantifies the extent to which an electron at point in a calculated wavefunction delocalizes over distance d. This work shows how topological analysis distills chemically useful information out of the EDR. Local maxima (attractors) in the EDR occur in regions such as atomic cores, covalent bonds, and lone pairs where the wavefunction is dominated by a single orbital lobe. The EDR characterizes each attractor in terms of a delocalization length D and a normalization , which are qualitatively consistent with the size of the orbital lobe and the number of lobes in the orbital. Attractors identify the progressively more delocalized atomic shells in heavy atoms, the interplay of delocalization and strong (nondynamical) correlation in stretched and dissociating covalent bonds, the locations of valence and weakly bound electrons in anionic water clusters, and the chemistry of different reactive sites on metal clusters. Application to ammonia dissociation over silicon illustrates how this density‐matrix‐based analysis can give insight into realistic systems. © 2016 Wiley Periodicals, Inc.     

An anisotropic coarse‐grained model based on Gay–Berne and electric multipole potentials and its application to simulate a DMPC bilayer in an implicit solvent model

In this work, we aim at optimizing the performance of the anisotropic GBEMP model, which adopts a framework by combining a Gay–Berne (GB) anisotropic potential with an electric multipole (EMP) potential, in simulating a DMPC lipid bilayer in an implicit solvent model. First, the Gay–Berne parameters were initially obtained by fitting to atomistic profiles of van der Waals interactions between homodimers of molecular fragments while EMP parameters was directly derived from the expansion of point multipoles at predefined EMP sites. Second, the GB and EMP parameters for DMPC molecule were carefully optimized to be comparable to AMBER atomistic model in the calculations of the dipole moments of DMPC monomers adopting different conformations as well as the nonbonded interactions between two DMPC molecules adopting different conformations and separated at various distances. Finally, the GB parameters for DMPC were slightly adjusted in simulating a 72 DMPC bilayer system so that our GBEMP model would be able to reproduce a few important structural properties, namely, thickness (), area per lipid ( ) and volume per lipid ( ). Meanwhile, the atomistic and experimental results for electron density profiles and order parameters were reproduced reasonably well by the GBEMP model, demonstrating the promising feature of GBEMP model in modeling lipid systems. Finally, we have shown that current GBEMP model is more efficient by a factor of about 25 than AMBER atomistic point charge model. © 2015 Wiley Periodicals, Inc.     

GAMPMS: Genetic algorithm managed peptide mutant screening

The prominence of endogenous peptide ligands targeted to receptors makes peptides with the desired binding activity good molecular scaffolds for drug development. Minor modifications to a peptide's primary sequence can significantly alter its binding properties with a receptor, and screening collections of peptide mutants is a useful technique for probing the receptor–ligand binding domain. Unfortunately, the combinatorial growth of such collections can limit the number of mutations which can be explored using structure‐based molecular docking techniques. Genetic algorithm managed peptide mutant screening (GAMPMS) uses a genetic algorithm to conduct a heuristic search of the peptide's mutation space for peptides with optimal binding activity, significantly reducing the computational requirements of the virtual screening. The GAMPMS procedure was implemented and used to explore the binding domain of the nicotinic acetylcholine receptor (nAChR) ‐isoform with a library of 64,000 α‐conotoxin (α‐CTx) MII peptide mutants. To assess GAMPMS's performance, it was compared with a virtual screening procedure that used AutoDock to predict the binding affinity of each of the α‐CTx MII peptide mutants with the ‐nAChR. The GAMPMS implementation performed AutoDock simulations for as few as 1140 of the 64,000 α‐CTx MII peptide mutants and could consistently identify a set of 10 peptides with an aggregated binding energy that was at least 98% of the aggregated binding energy of the 10 top peptides from the exhaustive AutoDock screening. © 2015 Wiley Periodicals, Inc.     

Aqueous acidities of primary benzenesulfonamides: Quantum chemical predictions based on density functional theory and SMD

Aqueous of selected primary benzenesulfonamides are predicted in a systematic manner using density functional theory methods and the SMD solvent model together with direct and proton exchange thermodynamic cycles. Some test calculations were also performed using high‐level composite CBS‐QB3 approach. The direct scheme generally does not yield a satisfactory agreement between calculated and measured acidities due to a severe overestimation of the Gibbs free energy changes of the gas‐phase deprotonation reaction by the used exchange‐correlation functionals. The relative values calculated using proton exchange method compare to experimental data very well in both qualitative and quantitative terms, with a mean absolute error of about 0.4 units. To achieve this accuracy, we find it mandatory to perform geometry optimization of the neutral and anionic species in the gas and solution phases separately, because different conformations are stabilized in these two cases. We have attempted to evaluate the effect of the conformer‐averaged free energies in the predictions, and the general conclusion is that this procedure is highly too costly as compared with the very small improvement we have gained. © 2015 Wiley Periodicals, Inc.     

Energy decomposition analysis of cation–π, metal ion–lone pair,hydrogen bonded,charge‐assisted hydrogen bonded,and π–π interactions

This study probes the nature of noncovalent interactions, such as cation–π, metal ion–lone pair (M–LP), hydrogen bonding (HB), charge‐assisted hydrogen bonding (CAHB), and π–π interactions, using energy decomposition schemes—density functional theory (DFT)–symmetry‐adapted perturbation theory and reduced variational space. Among cation–π complexes, the polarization and electrostatic components are the major contributors to the interaction energy (IE) for metal ion–π complexes, while for onium ion–π complexes ( , , , and ) the dispersion component is prominent. For M–LP complexes, the electrostatic component contributes more to the IE except the dicationic metal ion complexes with H₂S and PH₃ where the polarization component dominates. Although electrostatic component dominates for the HB and CAHB complexes, dispersion is predominant in π–π complexes.Copyright © 2015 Wiley Periodicals, Inc.     

Fast and accurate determination of the relative binding affinities of small compounds to HIV‐1 protease using non‐equilibrium work

The fast pulling ligand (FPL) out of binding cavity using non‐equilibrium molecular dynamics (MD) simulations was demonstrated to be a rapid, accurate and low CPU demand method for the determination of the relative binding affinities of a large number of HIV‐1 protease (PR) inhibitors. In this approach, the ligand is pulled out of the binding cavity of the protein using external harmonic forces, and the work of pulling force corresponds to the relative binding affinity of HIV‐1 PR inhibitor. The correlation coefficient between the pulling work and the experimental binding free energy of shows that FPL results are in good agreement with experiment. It is thus easier to rank the binding affinities of HIV‐1 PR inhibitors, that have similar binding affinities because the mean error bar of pulling work amounts to . The nature of binding is discovered using the FPL approach. © 2016 Wiley Periodicals, Inc.     

Rapid QM/MM approach for biomolecular systems under periodic boundary conditions: Combination of the density‐functional tight‐binding theory and particle mesh Ewald method

A quantum mechanical/molecular mechanical (QM/MM) approach based on the density‐functional tight‐binding (DFTB) theory is a useful tool for analyzing chemical reaction systems in detail. In this study, an efficient QM/MM method is developed by the combination of the DFTB/MM and particle mesh Ewald (PME) methods. Because the Fock matrix, which is required in the DFTB calculation, is analytically obtained by the PME method, the Coulomb energy is accurately and rapidly computed. For assessing the performance of this method, DFTB/MM calculations and molecular dynamics simulation are conducted for a system consisting of two amyloid‐β(1‐16) peptides and a zinc ion in explicit water under periodic boundary conditions. As compared with that of the conventional Ewald summation method, the computational cost of the Coulomb energy by utilizing the present approach is drastically reduced, i.e., 166.5 times faster. Furthermore, the deviation of the electronic energy is less than . © 2016 Wiley Periodicals, Inc.     

Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system‐specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.