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.     

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.     

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.     

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.     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.     

Additivity in kramers pairs symmetry: Multiplets with up to four unpaired electrons

Many fermions Kramers pairs formalism is considered from the prospective of the sum of individual single fermion time‐reversal operators. The obtained many fermions “pseudo Kramers pairs operator” ( ), as well as its square ( ), have formally the same structure as the many fermion spin operators and . Nevertheless, the shape of eigenfunctions with respect to and is different. Herein all Kramers adapted eigenfunctions of for cases of up to four unpaired fermions are compiled, and their properties with respect to further advocated. It will be shown that degeneracy of the multiplets recovers the proper behavior with respect to Pascal's triangle. A projection operator for obtaining the “high spin” Kramers adapted eigenfunctions is suggested. Noncommutation of with spin and angular momentum operators and degeneracy is discussed at last. © 2016 Wiley Periodicals, Inc.     

Theoretical prediction of the optical rotation of chiral molecules in ordered media: A computational study of (Ra)‐1,3‐dimethylallene, (2R)‐2‐methyloxirane,and (2R)‐N‐methyloxaziridine

A theoretical procedure has been developed and implemented to calculate the optical rotation of chiral molecules in ordered phase via origin‐independent diagonal components , of the optical activity tensor and origin‐independent components , for , of the mixed electric dipole‐electric quadrupole polarizability. Origin independence was achieved by referring these tensors to the principal axis system of the electric dipole dynamic polarizability at the same laser frequency ω. The approach has been applied, allowing for alternative quantum mechanical methods based on different gauges, to estimate near Hartree–Fock values for three chiral molecules, (2R)‐N‐methyloxaziridine C₂NOH₅, (2R)‐2‐methyloxirane (also referred to as propylene oxide) C₃OH₆, and ( )‐1,3‐dimethylallene C₅H₈, at two frequencies. The theoretical predictions can be useful for an attempt at measuring correspondent experimental values in crystal phase. © 2015 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.     

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.     

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.     

Geometry of the canonical Van Vleck transformation

Bloch's transformation from the zeroth‐order space for a perturbation problem to the corresponding space of exact eigenvectors, was found as a geometrically defined alternative to the algebraically constructed Van Vleck transformation. Klein's theorem of uniqueness transferred some of this geometrical interpretation to its canonical form . Quite recently Kvaal has taken a large step further by writing as a product of commuting planar rotations, obtained by describing and in terms of certain principal vectors and canonical angles. Kvaal's approach is now developed further, using a new commutation relation which simplifies algebraic manipulations substantially. It allows for a simple definition of an operator for the angle between and which has Kvaal's vectors and angles as eigenvectors and eigenvalues. Klein's theorem is refined in various ways. The impact of the approach on a number of previous results is considered. © 2015 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.     

Ruthenium(II) complexes bearing pyridine‐based tridentate and bidentate ligands: catalytic activity for transfer hydrogenation of aryl ketones

Ru(II) complexes of the general formula [RuCl₂(′′)(L)] (1: ′N = N_b, L = MeOH; 2: ′N = N_b, L = CH₃CN; 3: ′N = N_d, L = CH₃CN; 4: ′N = N_p, L = CH₃CN), [Ru(p‐cymene)(_a–b)Cl]Cl (5a: N N_a = 2,2′‐bipyridine; 5b: N N_b = 4,4′‐dimethyl–2,2′‐bipyridine), [Ru(′′)(_a–b)Cl]Cl (6a: ′N = N_b, _a = 2,2′‐bipyridine; 6b: ′N = N_b, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 7a: ′N = N_d, _a = 2,2′‐bipyridine; 7b: ′N = N_d, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 8a: ′N = N_p, _a = 2,2′‐bipyridine; 8b: ′N = N_p, _b = 4,4′‐dimethyl‐2,2′‐bipyridine) and [Ru(′′)(_a)Cl]BF₄ (9a: ′N = N_b; _a = 2,2′‐bipyridine) were synthesized from the corresponding [RuCl₂(p‐cymene)]₂ dimer, ′′ and _a–b ligands. The compounds were characterized by elemental analysis, IR and NMR. Complex 9a was studied by X‐ray diffraction, confirming its cationic‐mononuclear [RuCl(_bb)(_a)]⁺ nature. The synthesized Ru(II) complexes (1–8) were employed as catalysts for the transfer hydrogenation of ketones to secondary alcohols in the presence of KOH using 2‐propanol as a hydrogen source at 82°C. The rates of the transfer hydrogenation reactions strongly depended on the type of and ancillary ligands. Copyright © 2012 John Wiley & Sons, Ltd.     

Photodetachment of hydrogen negative ion near inelastic surfaces: Arbitrary laser polarization direction

The photodetachment of hydrogen negative ion near different inelastic surfaces is investigated by the semiclassical closed orbit theory for arbitrary laser polarization direction . A two‐term formula of photodetachment cross section consisting of a smooth background term and an oscillatory term is derived. The oscillatory term contains an extra angular factor that describes the dependence of oscillations in total cross section on the laser polarization direction. It is observed that the amplitude of oscillations in cross section reaches maximum at when laser polarization is parallel to the z‐axis and it approaches zero as the laser polarization direction becomes perpendicular to the z‐axis. It is also observed that as the reflection coefficient , which accounts for the inelastic behavior of the surfaces, increases the amplitude of oscillation also increases. © 2015 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.     

Synthesis of gradient copolysiloxanes by simultaneous copolymerization of cyclotrisiloxanes and mechanism for kinetics inverse between anionic and cationic ring‐opening polymerization

Trifluoropropylmethylsiloxane–phenylmethylsiloxane gradient copolysiloxanes were synthesized by anionic and cationic ring‐opening polymerization (ROP) of 1,3,5‐tris(trifluoropropylmethyl)cyclotrisiloxane ( ) and phenylmethylcyclotrisiloxane ( ). The analysis of reactivity ratios revealed that the reactivity of toward anionic ROP was higher than that of ; however, exhibited lower reactivity compared with during the cationic ROP. AB and BAB type gradient copolymers were obtained because of a difference in the reactivity of the monomers. The microstructure of copolymers was characterized by ²⁹Si NMR spectroscopy, gel permeation chromatography, and differential scanning calorimetry. Furthermore, the mechanism for kinetics inverse of copolymerization was proposed based on the results of the optimized molecular configuration. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 835–843     

The “bound wavefunction” on the repulsive excited ( ) state of the HD+ molecule

The time‐independent Schrödinger equation for the HD+ molecule is solved beyond the Born–Oppenheimer (B‐O) approximation. In the adiabatic representation, the wavefunction of the ground vibrational eigenstate is found to contain two parts: One is on the ground ( ) state which is dominant, and the other is on the repulsive excited ( ) state in the range from R = 0.0 to R = 5.0 Bohr. This is because the nonadiabatic coupling between the ground ( ) and excited ( ) states is strong in that region. The influences of the nonadiabatic coupling on the vibrational eigenfunctions are discussed in detail.     

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.     

Electronic Spectroscopy of Methylcyanodiacetylene (CH3C5N)

The results of a study devoted to the electronic spectroscopy of gaseous, solid, and cryogenic matrix‐isolated methylcyanodiacetylene (CH₃C₅N) are reported. UV absorption and optical phosphorescence spectra of the compound are described here for the first time, and the corresponding vibronic assignments are proposed. UV absorption, studied directly or through the excitation of phosphorescence, revealed the ¹E‐‐ ¹A₁ system, very weak ¹A₂– ¹A₁ bands, and a strong, broad absorption feature, tentatively identified as ¹E– ¹A₁. Spectral measurements were assisted by quantum chemical calculations at the DFT and ab initio (coupled cluster) levels of theory.