Coupled‐cluster frozen‐density embedding using resolution of the identity methods

Frozen‐density embedding (FDE) is combined with resolution of the identity (RI) Hartree–Fock and a RI‐variant of a second‐order approximate coupled‐cluster singles and doubles (RI‐CC2) to determine solvatochromic shifts for the lowest excitation energy of acetone and pyridazine, respectively, each solvated in different environments with total system sizes of about 2.5 nm diameter. The combination of FDE and RI‐CC2 increases efficiency and enables the calculation of numerous snapshots with 100 to 300 molecules, also allowing for larger basis sets as well as diffuse functions needed for an accurate treatment of properties. The maximum errors in the solvatochromic shifts amount up to 0.2 eV, which are similar to other approximated studies in the literature. © 2014 Wiley Periodicals, Inc.     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

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.     

Ab initio investigation of ground‐state properties of group‐12 fluorides

The performance of wavefunction‐based correlation methods in theoretical solid‐state chemistry depends on reliable Hartree–Fock (HF) results for infinitly extended systems. Therefore, we optimized basis sets of valence‐triple‐ζ quality based on HF calculations for the periodic system of group‐12‐metal difluorides. Scalar‐relativistic effects were included in the case of the metal‐ions by applying small‐core pseudopotentials. To assess the quality of the proposed basis sets, the structural parameters, bulk moduli as well as cohesive and lattice energies of the systems were evaluated at the HF and the density functional theory levels. In addition to these two mean‐field approaches and to assess further employment of our basis sets to wavefunction‐based correlation methods we performed periodic local MP2 computations. Finally, the possibilities of pressure induced structural phase transitions occurring in the ZnF₂, CdF₂, and HgF₂ were investigated. © 2014 Wiley Periodicals, Inc.     

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian‐type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange‐correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn–Sham matrix formation. © 2016 Wiley Periodicals, Inc.     

Auxiliary basis sets for density‐fitting second‐order Møller–Plesset perturbation theory: Weighted core‐valence correlation consistent basis sets for the 4d elements Y–Pd

Auxiliary basis sets (ABS) specifically matched to the cc‐pwCVnZ‐PP and aug‐cc‐pwCVnZ‐PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y‐Pd at the second‐order Møller‐Plesset perturbation theory level. Calculation of the core‐valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution‐of‐the‐identity component of explicitly correlated calculations is also investigated, where it is shown that i‐type functions are important to produce well‐controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double‐ζ calculations produce results close to conventional quadruple‐ζ, and triple‐ζ is within chemical accuracy of the complete basis set limit. © 2013 Wiley Periodicals, Inc.     

W4‐17: A diverse and high‐confidence dataset of atomization energies for benchmarking high‐level electronic structure methods

Atomization reactions are among the most challenging tests for electronic structure methods. We use the first‐principles Weizmann‐4 (W4) computational thermochemistry protocol to generate the W4‐17 dataset of 200 total atomization energies (TAEs) with 3σ confidence intervals of 1 kJ mol⁻¹. W4‐17 is an extension of the earlier W4‐11 dataset; it includes first‐ and second‐row molecules and radicals with up to eight non‐hydrogen atoms. These cover a broad spectrum of bonding situations and multireference character, and as such are an excellent benchmark for the parameterization and validation of highly accurate ab initio methods (e.g., CCSD(T) composite procedures) and double‐hybrid density functional theory (DHDFT) methods. The W4‐17 dataset contains two subsets (i) a non‐multireference subset of 183 systems characterized by dynamical or moderate nondynamical correlation effects (denoted W4‐17‐nonMR) and (ii) a highly multireference subset of 17 systems (W4‐17‐MR). We use these databases to evaluate the performance of a wide range of CCSD(T) composite procedures (e.g., G4, G4(MP2), G4(MP2)‐6X, ROG4(MP2)‐6X, CBS‐QB3, ROCBS‐QB3, CBS‐APNO, ccCA‐PS3, W1, W2, W1‐F12, W2‐F12, W1X‐1, and W2X) and DHDFT methods (e.g., B2‐PLYP, B2GP‐PLYP, B2K‐PLYP, DSD‐BLYP, DSD‐PBEP86, PWPB95, ωB97X‐2(LP), and ωB97X‐2(TQZ)). © 2017 Wiley Periodicals, Inc.     

Spectroscopic constants and molecular properties of rare‐gas diatomic molecule in Lennard‐Jones potential: Ab initio and density functional study

Ab initio and density functional theory (DFT) are applied to study the spectroscopic constants, molecular properties, and nature of force between two rare gas atoms of the weakly bound diatomic molecules He₂, Ne₂, Ar₂, HeNe, and HeAr in the Lennard‐Jones potential. A simple method is developed to calculate the spectroscopic constants of these molecules. The calculated spectroscopic constants and molecular properties agree very well with the experimental and theoretical results wherever available. Most of the spectroscopic constants and molecular properties are reported for the first time. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Ionic dissociations of chlorosulfonic acid in microsolvated clusters: A density functional theory and ab initio MO study

Ionic dissociation of chlorosulfonic acid (HSO3Cl) in the molecular clusters HSO3Cl-(H2O)n (n = 1-4) and HSO3Cl-NH3-(H2O)n (n = 0-3) was investigated by density functional theory and ab initio molecular orbital theory. The equilibrium structures, binding energies, and thermodynamic properties, such as relative enthalpy and relative Gibbs free energy, and were calculated using the hybrid density func- tional (B3LYP) method and the second order M?ller-Plesset approximation (MP2) method with the 6-311 G** basis set. Chlorosulfonic acid was found to require a minimum of three water molecules for ionization to occur and at least one water molecule to protonate ammonia. The corresponding clusters with fewer water molecules were found to be strongly hydrogen-bonded. The related properties and acid strength of chlorosulfonic acid were discussed and compared to the acid strengths of perchloric acid and sulfuric acid in the context of clusters with ammonia and water. The relative stabilities of these clusters were also investigated.     

Theoretical Study on Gas—phase Pyrolytic Reactions of N—Ethyl,Isopropyl and N—t—Butyl Substituted 2—Aminopyrazine

Density functional theory (DFT) and ab initio methods were used to study gas‐phase pyrolytic reaction mechanisms of iV‐ethyl, N‐isopropyl and N‐t‐butyl substituted 2‐aminopyrazine at B3LYP/6–31G* and MP2/6–31G*, respectively. Single‐point energies of all optimized molecular geometries were calculated at B3LYP/6–311 + G(2d,p) level. Results show that the pyrolytic reactions were carried out through a unimolecular first‐order mechanism which were caused by the migration of atom H(17) via a six‐member ring transition state. The activation energies which were verified by vibrational analysis and correlated with zero‐point energies along the reaction channel at B3LYP/6–311 + G(2d,p) level were 252.02 kJ. mo^?1 (N‐ethyl substituted), 235.92 kJ‐mol^?1 (N‐t‐isopropyl substituted) and 234.27 kJ‐mol^?1 (N‐t‐butyl substituted), respectively. The results were in good agreement with available experimental data.     

Coupled‐cluster reaction barriers of : An application of the coupled‐cluster//Kohn–Sham density functional theory model chemistry

In this work, we report a theoretical investigation concerning the use of the popular coupled‐cluster//Kohn‐Sham density functional theory (CC//KS‐DFT) model chemistry, here applied to study the entrance channel of the reaction, namely by comparing CC//KS‐DFT calculations with KS‐DFT, MRPT2//CASSCF, and CC//CASSCF results from our previous investigations. This was done by performing single point energy calculations employing several coupled cluster methods and using KS‐DFT geometries optimized with six different functionals, while conducting a detailed analysis of the barrier heights and topological features of the curves and surfaces here obtained. The quality of this model chemistry is critically discussed in the context of the title reaction and also in a wider context. © 2013 Wiley Periodicals, Inc.     

Single‐ and double‐electron reductions of CO2 by using superalkalis: An ab initio study

CO₂, a major contributor to global warming, can be balanced by converting it into fuels. The reduction of CO₂ has been difficult due to its extremely high stability. Recently, single‐electron reduction of CO₂ by superalkalis has been proposed using quantum chemical methods. Herein, we report a systematic study on the single‐reduction of CO₂ by using typical superalkalis. Superalkalis are hypervalent species possessing lower ionization energies than alkali atoms. We have studied the interaction of CO₂ with FLi₂, OLi₃, and NLi₄ superalkalis using ab initio MP2 calculations. We notice that this interaction leads to stable superalkali‐CO₂ complexes in which the structure of CO₂ is bent due to electron transfer from superalkalis. This clearly reveals that the CO₂ can successfully be reduced to the anion. It has been also noticed that the size of superalkalis plays a crucial in the single‐electron reduction of CO₂. For instance, the binding energy of superalkali‐CO₂ complex and charge transfer to CO₂ decreases monotonically with the increase in the size of superalkali. We have also proposed that CO₂ can be further reduced to in case of the anionic complex such as (FLi₂ CO₂)‾. Thus, FLi₂ superalkali is also capable of double‐electron reduction of CO₂. These findings should provide new insights into CO₂‐activation as well as motivate further research in this direction.     

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four‐component relativistic density functional theory by calculating the static and frequency‐dependent electric dipole–dipole polarizabilities of all (ground‐state) closed‐shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape‐corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient‐regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple‐zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite‐field calculations using the coupled‐cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape‐corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare‐gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.     

Effect of surrounding point charges on the density functional calculations of NixOx clusters (x = 4-12)

Embedded Ni(x)O(x) clusters (x = 4-12) have been studied by the density-functional method using compensating point charges of variable magnitude to calculate the ionic charge, bulk modulus, and lattice binding energy. The computations were found to be strongly dependent on the value of the surrounding point charge array and an optimum value could be found by choosing the point charge to reproduce the experimentally observed Ni--O lattice parameter. This simple, empirical method yields a good match between computed and experimental data, and even small variation from the optimum point charge value produces significant deviation between computed and measured bulk physical parameters. The optimum point charge value depends on the cluster size, but in all cases is significantly less than +/-2.0, the formal oxidation state typically employed in cluster modeling of NiO bulk and surface properties. The electronic structure calculated with the optimized point charge magnitude is in general agreement with literature photoemission and XPS data and agrees with the presently accepted picture of the valence band as containing charge-transfer insulator characteristics. The orbital population near the Fermi level does not depend on the cluster size and is characterized by hybridized Ni 3d and O 2p orbitals with relative oxygen contribution of about 70%.     

Angular‐Resolved Magnetometry Beyond Triclinic Crystals: Out‐of‐Equilibrium Studies of Cp*ErCOT Single‐Molecule Magnet

Angular‐resolved single‐crystal magnetometry is a key tool to characterise lanthanide‐based materials with low symmetry, for which conjectures based on idealised geometries can be totally misleading. Unfortunately the technique is strictly successful only for triclinic structures, thus reducing significantly its application. By collecting out‐of‐equilibrium magnetisation data the technique was extended to the orthorhombic organometallic Cp*ErCOT single‐molecule magnet (SMM), thus allowing for the first time the reconstruction of the molecular anisotropy tensor notwithstanding the two molecular orientations in the crystal lattice. The results, flanked by state‐of‐the‐art ab initio calculations, confirmed the expected orientation of the molecular easy axis of magnetisation and thus validated the synthetic strategy based on organometallic complexes of a single lanthanide ion.