Solvatochromic shifts of Br2 and I2 in water cages of type 512, 51262, 51263, and 51264

Despite the relatively small size of molecular bromine and iodine, the physicochemical behavior in different solvents is not yet fully understood, in particular when excited‐state properties are sought. In this work, we investigate isolated halogen molecules trapped in clathrate hydrate cages. Relativistic supermolecular calculations reveal that the environment shift to the excitation energies of the (nondegenerate) states and lie within a spread of 0.05 eV, respectively, suggesting that environment shifts can be estimated with scalar‐relativistic treatments. As even scalar‐relativistic calculations are problematic for excited‐state calculations for clathrates with growing size and basis sets, we have applied the subsystem‐based scheme frozen‐density embedding, which avoids a supermolecular treatment. This allows for the calculation of excited states for extended clusters with coupled‐cluster methods and basis sets of triple‐zeta quality with additional diffuse functions mandatory for excited‐state properties, as well as a facile treatment at scalar‐relativistic exact two‐component level of theory for the heavy atoms bromine and iodine. This simple approach yields scalar‐relativistic estimates for solvatochromic shifts introduced by the clathrate cages. © 2015 Wiley Periodicals, Inc.     

Effects of zero point vibration on the reaction dynamics of water dimer cations following ionization

Reactions of water dimer cation following ionization have been investigated by means of a direct ab initio molecular dynamics method. In particular, the effects of zero point vibration and zero point energy (ZPE) on the reaction mechanism were considered in this work. Trajectories were run on two electronic potential energy surfaces (PESs) of : ground state (²A″‐like state) and the first excited state (²A′ ‐ like state). All trajectories on the ground‐state PES lead to the proton‐transferred product: H₂O⁺(Wd)‐H₂O(Wa) → OH(Wd)‐H₃O⁺(Wa), where Wd and Wa refer to the proton donor and acceptor water molecules, respectively. Time of proton transfer (PT) varied widely from 15 to 40 fs (average time of PT = 30.9 fs). The trajectories on the excited‐state PES gave two products: an intermediate complex with a face‐to‐face structure (H₂O‐OH₂)⁺ and a PT product. However, the proton was transferred to the opposite direction, and the reverse PT was found on the excited‐state PES: H₂O(Wd)‐H₂O⁺ (Wa) → H₃O⁺(Wd)‐OH(Wa). This difference occurred because the ionizing water molecule in the dimer switched between the ground and excited states. The reaction mechanism of and the effects of ZPE are discussed on the basis of the results. © 2017 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.     

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.     

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.     

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.     

Assessment of hydrophobic interactions and their contributions through the analysis of the methane dimer

Hydrophobic Interactions (HIs) are important in many phenomena of molecular recognition in chemistry and biology. Still, the relevance of HIs is sometimes difficult to evaluate particularly in large systems and intramolecular interactions. We put forward a method to estimate the magnitude and the different contributions of a given HI of the C···C, H? C···H, and H···H type through (i) the analysis of the electron density in the intermolecular region for eleven relative orientations of the methane dimer and (ii) the subsequent decomposition of the corresponding interaction energy in physically significant contributions using Symmetry Adapted Perturbation Theory (SAPT). Strong correlations were found between the topological properties of calculated at intermolecular bond critical points and plus its different contributions with the C···C distance of the considered orientations of (CH₄)₂. These correlations were used to construct Mollier‐like diagrams of and its components as a function of the separation between two carbons and the orientation of the groups bonded to these atoms. The ethane dimer and tert‐butylcyclohexane are used as representative examples of this new approach. Overall, we anticipate that this new method might prove useful in the study of both intramolecular and intermolecular HIs particularly of those within large systems wherein SAPT or electronic structure calculations are computationally expensive or even prohibitive. © 2014 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.     

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.     

An open library of relativistic core electron density function for the QTAIM analysis with pseudopotentials

Based on two‐component relativistic atomic calculations, a free electron density function (EDF) library has been developed for nearly all the known ECPs of the elements Li (Z = 3) up to Ubn (Z = 120), which can be interfaced into modern quantum chemistry programs to save the .wfx wavefunction file. The applicability of this EDF library is demonstrated by the analyses of the quantum theory of atoms in molecules (QTAIM) and other real space functions on HeCuF, , OgF₄, and TlCl₃(DMSO)₂. When a large‐core ECP is used, it shows that the corrections by EDF may significantly improve the properties of some density‐derived real space functions, but they are invalid for the wavefunction‐depending real space functions. To classify different chemical bonds and especially some nonclassical interactions, a list of universal criteria has also been proposed. © 2018 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.     

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.     

Spin–orbit effects on magnetically induced current densities in the () clusters

This study reports the spin–orbit effects on the aromaticity of the , , , , , and anionic clusters via the magnetically induced current‐density method. All‐electron density functional theory (DFT) calculations were carried out using the four‐component Dirac‐Coulomb (DC) hamiltonian, including scalar and spin–orbit relativistic effects. The magnetic index of aromaticity was calculated by numerical integration over the current flow between two atoms in the pentagonal ring. These values were compared to the spin‐free values (spin–orbit coupling switched off), in order to assess the spin–orbit effect on aromaticity. It was found that in the heavy anions, and , there is a significant influence of the spin–orbit coupling. © 2018 Wiley Periodicals, Inc.     

Structure and electrochemical properties for complexes of nitrocompounds with inorganic ions: A theoretical approach

Reduction and oxidation (redox) reactions are widely used for removal of nitrocompounds from contaminated soil and water. Structures and redox properties for complexes of nitrocompounds, such as 2,4,6‐trinitrotoluene (TNT), 2,4‐dinitrotoluene (DNT), 2,4‐dinitroanisole (DNAN), and 5‐nitro‐2,4‐dihydro‐3H?1,2,4‐triazol‐3‐one (NTO), with common inorganic ions (Na⁺, Cl^?, ) were investigated at the SMD(Pauling)/PCM(Pauling)/MPWB1K/TZVP level of theory. Atoms in molecules (AIM) theory was applied to analyze the topological properties of the bond critical points involved in the interactions between the nitrocompounds and the ions. Topological analyses show that intermolecular interactions of the types O(N)…Na⁺, C‐H…Cl^?( ), and C…Cl^?( ) may be discussed as noncovalent closed‐shell interactions, while N‐H···Cl^?( ) hydrogen bonds are partially covalent in nature. Complexation causes significant decrease of redox activity of the nitrocompounds. Analysis of the reduction potentials of the complexes obtained through application of the Pourbaix diagram of an iron/water system revealed that sodium complexes of NTO might be reduced by metallic iron. © 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.     

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.     

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.     

Efficiency of perturbation‐selection and its orbital dependence in the SAC‐CI calculations for valence excitations of medium‐size molecules

The efficiency and accuracy of the perturbation‐selection used in the symmetry‐adapted cluster‐configuration interaction (SAC‐CI) calculations are investigated for several low‐lying valence excited states of 21 medium‐size molecules, including typical chromophores with heterocyclic macrocycles (free‐base porphine, coumarin, indole, and BODIPY), nucleobases, amino acids (tyrosine and tryptophan), polycyclic aromatic hydrocarbons, and organometallics (ferrocene and Re(bpy) ). Benchmark SAC‐CI calculations with up to 110 million operators are performed. The efficiency of the perturbation‐selection depends on the molecular orbitals (MOs); therefore, the canonical MO and localized MO (LMO) obtained by Pipek‐Mezey's method are examined. Except for the highly symmetric molecules, using LMOs improves the efficiency and accuracy of the perturbation‐selection. With using LMOs and perturbation‐selection, sufficiently reliable results can be obtained in less than 10% of the computational costs required for the full‐dimensional calculations. The perturbation‐selection with LMOs is suggested to be a promising method for excited states in larger molecular systems. Copyright © 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.