Treatment of delocalized electron transfer in periodic and embedded cluster DFT calculations: The case of Cu on ZnO (10 0)

We assess the consequences of the interface model—embedded‐cluster or periodic‐slab model—on the ability of DFT calculations to describe charge transfer (CT) in a particularly challenging case where periodic‐slab calculations indicate a delocalized charge‐transfer state. Our example is Cu atom adsorption on ZnO(10 0), and in fact the periodic slab calculations indicate three types of CT depending on the adsorption site: full CT, partial CT, and no CT. Interestingly, when full CT occurs in the periodic calculations, the calculated Cu atom adsorption energy depends on the underlying ZnO substrate supercell size, since when the electron enters the ZnO it delocalizes over as many atoms as possible. In the embedded‐cluster calculations, the electron transferred to the ZnO delocalizes over the entire cluster region, and as a result the calculated Cu atom adsorption energy does not agree with the value obtained using a large periodic supercell, but instead to the adsorption energy obtained for a periodic supercell of roughly the same size as the embedded cluster. Different density functionals (of GGA and hybrid types) and basis sets (local atom‐centered and plane‐waves) were assessed, and we show that embedded clusters can be used to model Cu adsorption on ZnO(10 0), as long as care is taken to account for the effects of CT. © 2015 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.     

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.     

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.     

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.     

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.     

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.     

A Density Functional Theory Study on Nonlinear Optical Properties of Double Cage Excess Electron Compounds: Theoretically Design M[Cu(Ag)@(NH3)n](M = Be,Mg and Ca; n = 1–3)

In this work, we investigated the nonlinear optical (NLO) properties of excess electron electride molecules of M[Cu(Ag)@(NH₃)_n](M = Be, Mg and Ca; n = 1–3) using density functional theory (DFT). This electride molecules consist of an alkaline-earth (Be, Mg and Ca) together with transition metal (Cu and Ag) doped in NH₃ cluster. The natural population analysis of charge and their highest occupied molecular orbital suggests that the M[Cu(Ag)@(NH₃)_n] compound has excess electron like alkaline-earth metal form double cage electrides molecules, which exhibit a large static first hyperpolarizability () (electron contribution part) and one of which owns a peak value of 216,938 (a.u.) for Be[Ag@(NH₃)₂] and vibrational harmonic first hyperpolarizability () (nuclear contribution part) values and the ratio of /, namely, η values from 0.02 for Be[Ag@(NH₃)] to 0.757 for Mg[Ag@(NH₃)₃]. The electron density contribution in different regions on values mainly come from alkaline-earth and transition metal atoms by first hyperpolarizability density analysis, and also explains the reason why values are positive and negative. Moreover, the frequency-dependent values β(−2ω,ω,ω) are also estimated to make a comparison with experimental measures. © 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.     

Molecules under external electric field: On the changes in the electronic structure and validity limits of the theoretical predictions

A detailed analysis of the electronic structure of the ground and first excited spin state of three diatomic molecules ( and ) under static applied electric field is performed at CCSD(T), DFT, MRCI and MRCI(Q) levels of theory. Our findings have revealed that by boosting the applied field one induces changes in the occupation numbers of molecular orbitals, giving rise to changes in the equilibrium geometry and in the HOMO–LUMO energy gap. Specifically, singlet to triplet spin transition can be induced by increasing the applied electric field beyond a critical value. Accordingly, affecting the accuracy of the widely used expression of energy expanded in Taylor series with respect to the applied electric field. © 2018 Wiley Periodicals, Inc.     

Performance of range‐separated hybrid exchange–correlation functionals for the calculation of magnetic exchange coupling constants of organic diradicals

The prediction of magnetic behavior is important for the design of new magnetic materials. Kohn–Sham density functional theory is popular for this purpose, although one should be careful about choosing the right exchange–correlation functional. Here, we perform a statistical analysis to test different range‐separated hybrid density functionals for the calculation of magnetic exchange coupling constants J of fourteen organic diradicals. Our analysis suggests that in absolute terms the MN12SX functional performs best among the series of twelve functionals studied here (including the popular B3LYP), followed by N12SX functionals along with Scuseria's HSE series of functionals. LC‐ PBE was found to be the least accurate, which is in contrast with its good performance for calculating J for transition metal complexes. The HSE family of functionals and B3LYP are the only functionals to reproduce the qualitative trends of the coupling constants correctly for the ferromagnetically coupled diradicals under study. © 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.     

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.     

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.     

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.     

Inverse Ubbelohde effect in the short hydrogen bond of photosystem II: Relation between H/D isotope effect and symmetry in potential energy profile

The short hydrogen bond between tyrosine Y_z and D1‐His190 of photosystem II (PSII) was investigated using multicomponent quantum mechanics, where the quantum fluctuation of a hydrogen nucleus was incorporated into electronic structure calculation. Our computation demonstrated that the deuteration for hydrogen in the short hydrogen bond of PSII led to the reduction of the O…N distance. It indicated an inverse Ubbelohde effect typically recognized in strong and symmetric hydrogen‐bonding clusters such as FHF^– and . We confirmed that the relation between the geometric isotope effect and the symmetry of the potential energy profile of FHF^– was reasonably agreed with that of PSII. According to this agreement, the short hydrogen bond in PSII can be regarded as a short strong hydrogen bond. © 2016 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.     

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.     

Ab initio potential energy surface and vibration‐rotation energy levels of sulfur dioxide

An accurate potential energy surface of sulfur dioxide, SO₂, in its ground electronic state has been determined from ab initio calculations using the coupled‐cluster approach in conjunction with the correlation‐consistent basis sets up to septuple‐zeta quality. The results obtained with the conventional and explicitly correlated coupled‐cluster methods are compared. The role of the core–electron correlation, higher‐order valence–electron correlation, scalar relativistic, and adiabatic effects in determining the structure and dynamics of the SO₂ molecule is discussed. The vibration‐rotation energy levels of the ³²SO₂ and ³⁴SO₂ isotopologues were predicted using a variational approach. It was shown that the inclusion of the aforementioned effects was mandatory to attain the “spectroscopic” accuracy. © 2017 Wiley Periodicals, Inc.