Distinguishing and quantifying the torquoselectivity in competitive ring‐opening reactions using the stress tensor and QTAIM

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring‐opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring‐opening reactions of 3‐(trifluoromethyl)cyclobut‐1‐ene and 1‐cyano‐1‐methylcyclobutene. We find the metallicity ξ( r _b) of the ring‐opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector‐based stress tensor response β_σ was used to distinguish the effect of the CN, CH₃, and CF₃ groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H( r_b ) and the stress tensor stiffness S_σ. We determine the directional properties of the TSIC and TSOC ring‐opening reactions by constructing a stress tensor space with trajectories (s) with length l in real space, longer l correlated with the lowest density functional theory‐evaluated total energy barrier and hence will be more thermodynamically favored. © 2016 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.     

A multipolar approach to the interatomic covalent interaction energy

Interatomic exchange‐correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp ) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities and , we examine in this work the mp approach to approximate the interatomic exchange‐correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1–2 pairs) albeit it works reasonably well most times for 1– n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole‐monopole xc mp term and the inter‐atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 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.     

Calculation of photoionization differential cross sections using complex Gauss‐type orbitals

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss‐type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so‐called two‐potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth‐order final continuum state and the first‐order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss‐type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular‐frame photoelectron angular distributions of and . In the calculations of , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc.     

Ab initio potential energy surface and vibration–rotation energy levels of germanium dicarbide,GeC2

The accurate ground‐state potential energy surface of germanium dicarbide, GeC₂, has been determined from ab initio calculations using the coupled‐cluster approach. The core–electron correlation, higher‐order valence‐electron correlation, and scalar relativistic effects were taken into account. The potential energy surface of GeC₂ was shown to be extraordinarily flat near the T‐shaped equilibrium configuration. The potential energy barrier to the linear CCGe configuration was predicted to be 1218 cm⁻¹. The vibration–rotation energy levels of some GeC₂ isotopologues were calculated using a variational method. The vibrational bending mode ν₃ was found to be highly anharmonic, with the fundamental wavenumber being only 58 cm⁻¹. Vibrational progressions due to this mode were predicted for the , , and states of GeC₂. © 2018 Wiley Periodicals, Inc.     

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band‐gap energies of the , Pc, and structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path‐integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero‐point energy and temperature‐induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band‐gaps substantially, leading to metallization of the and Pc phases via band overlap; the effect on the band‐gap of the structure is less pronounced. Our combined DMC‐PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band‐gap energy and vibron modes. This strong coupling induces a band‐gap reduction of more than 2.46 eV in high‐pressure solid molecular hydrogen. Comparing our DMC‐PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.     

Quantum supercharger library: Hyper‐parallel integral derivatives algorithms for ab initio QM/MM dynamics

This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two‐electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one‐ and two‐electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree–Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS‐UK, which uses the efficient Schlegel method for ‐ and ‐orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6‐31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.     

The solvent effect on two competing reaction mechanisms involving hypervalent iodine reagents (λ3‐iodanes): Facing the limit of the stationary quantum chemical approach

Trifluoromethylation of acetonitrile with 3,3‐dimethyl‐1‐(trifluoromethyl)?1λ³,2‐ benziodoxol is assumed to occur via reductive elimination (RE) of the electrophilic CF₃‐ligand and MeCN bound to the hypervalent iodine. Computations in gas phase showed that the reaction might also occur via an S_N2 mechanism. There is a substantial solvent effect present for both reaction mechanisms, and their energies of activation are very sensitive toward the solvent model used (implicit, microsolvation, and cluster‐continuum). With polarizable continuum model‐based methods, the S_N2 mechanism becomes less favorable. Applying the cluster‐continuum model, using a shell of solvent molecules derived from ab initio molecular dynamics (AIMD) simulations, the gap between the two activation barriers ( ) is lowered to a few kcal mol^?1 and also shows that the activation entropies ( ) and volumes ( ) for the two mechanisms differ substantially. A quantitative assessment of will therefore only be possible using AIMD. A natural bond orbital‐analysis gives further insight into the activation of the CF₃‐reagent by protonation. © 2014 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.     

Development of spin‐orbit coupling for stochastic configuration interaction techniques

To perform spin‐orbit coupling calculations on atoms and molecules, good zeroth‐order wavefunctions are necessary. Here, we present the software development of the Monte Carlo Configuration Interaction (MCCI) method, to enable calculation of such properties, where MCCI iteratively constructs a multireference wavefunction using a stochastic procedure. In this initial work, we aim to establish the efficacy of this technique in predicting the splitting of otherwise degenerate energy levels on a range of atoms and small diatomic molecules. It is hoped that this work will subsequently act as a gateway toward using this method to investigate singlet‐triplet interactions in larger multireference molecules. We show that MCCI can generate very good results using highly compact wavefunctions compared to other techniques, with no prior knowledge of important orbitals. Higher‐order relativistic effects are neglected and spin‐orbit coupling effects are incorporated using first‐order degenerate perturbation theory with the Breit‐Pauli Hamiltonian and effective nuclear charges in the one‐electron operator. Results are obtained and presented for B, C, O, F, Si, S, and Cl atoms and OH, CN, NO, and C₂ diatomic radicals including spin‐orbit coupling constants and the relative splitting of the lowest energy degenerate state for each species. Convergence of MCCI to the full configuration interaction result is demonstrated on the multireference problem of stretched OH. We also present results from the singlet‐triplet interaction between the and both the and states of the O₂ molecule. © 2017 Wiley Periodicals, Inc.     

Exploring possible reaction pathways for the o‐atom transfer reactions to unsaturated substrates catalyzed by a [Ni‐NO2] ↔ [Ni‐NO] redox couple using DFT methods

The (nitro)(N‐methyldithiocarbamato)(trimethylphospane)nickel(II), [Ni(NO₂)(S₂CNHMe)(PMe₃)] complex catalyses efficiently the O‐atom transfer reactions to CO and acetylene. Energetically feasible sequence of elementary steps involved in the catalytic cycle of the air oxidation of CO and acetylene are proposed promoted by the Ni(NO₂)(S₂CNHMe)(PMe₃)] ↔ Ni(NO₂)(S₂CNHMe)(PMe₃) redox couple using DFT methods both in vacuum and dichloromethane solutions. The catalytic air oxidation of HC≡CH involves formation of a five‐member metallacycle intermediate, via a [3 + 2] cyclo‐addition reaction of HC≡CH to the Ni‐N = O moiety of the Ni(NO₂)(S₂CNHMe)(PMe₃)] complex, followed by a β H‐atom migration toward the C_α carbon atom of the coordinated acetylene and release of the oxidation product (ketene). The geometric and energetic reaction profile for the reversible [Ni( ‐NO₂)(S₂CNHMe)(PMe₃)] [Ni( ‐ONO)(S₂CNHMe)(PMe₃)] linkage isomerization has also been modeled by DFT calculations. © 2017 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.     

Quantum chemical study of the autoxidation of ascorbate

Reactions involved in the autoxidation of ascorbate have been investigated with quantum chemical first‐principles and ab initio methods. Reaction energies and Gibbs energies of the reactions were calculated at the density functional theory level applying the gradient‐corrected BP86 and the hybrid B3LYP functionals together with def2‐TZVP basis sets. Results of single‐point CC2, CCSD, and CCSD(T) calculations were used for calibration of the density functional theory data and show excellent agreement with the B3LYP values. Based on the Gibbs energy ascorbic acid AscH₂ is found to be the energetically lowest species in aqueous solution, whereas the monoanion ascorbate AscH is the most abundant one near pH = 7. Asc was found to be the preferred reducing agent for autoxidation and oxidation processes. The results also support a metal‐catalyzed synthesis of the reactive oxygen species H₂O₂ according to a redox cycling mechanism proposed in literature. © 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.     

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.     

Synthesizing quantum probability by a single chaotic complex‐valued trajectory

The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability . Instead of the Bohm's ensemble‐trajectory interpretation, the present paper gives a single‐trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex‐valued trajectory is enough to synthesize the quantum probability. A chaotic complex‐valued trajectory manifests both space‐filling (ergodic) and ensemble features. The space‐filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex‐valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex‐valued and real‐valued Bohmian trajectories shows that without the participation of its imaginary part, a single real‐valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real‐valued Bohmian trajectories to recover the quantum probability . © 2015 Wiley Periodicals, Inc.     

Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method

In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum‐classical correspondence in terms of mean displacement, mean‐squared displacement, and the corresponding variance in the first‐order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth‐order energy of quantum mechanics . This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to , while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function‐based vibrational second‐order perturbation theory, for the whole frequency range from ～4400 cm^?1 (H₂) to ～160 cm^?1 (Na₂). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero‐point energy effects are significant. © 2013 Wiley Periodicals, Inc.     

Stochastic structure determination for conformationally flexible heterogenous molecular clusters: Application to ionic liquids

We present a novel method that enables accurate and efficient computational determination of conformationally flexible clusters, “Kick³” This method uses stochastically generated structures in combination with fast quantum mechanical methods. We demonstrate the power of this method by elucidating the structure of ionic liquid (IL) ([xMIM⁺][ clusters (x = E, B, D, n = 1–10,15). Dispersion‐corrected, third‐order self‐consistent‐charge density‐functional tight‐binding (DFTB3) is shown to be a computationally efficient, yet reliable approximation to density functional theory for predicting and understanding IL structure and stability. The presented approach, therefore, enables the accurate and efficient screening of ILs with high potential toward practical applications, without recourse to more expensive quantum chemical methods. © 2013 Wiley Periodicals, Inc.