The domain-based local pair-natural orbital coupled-cluster (DLPNO-CC) theory has recently emerged as an efficient and powerful quantum-chemical method for the calculation of energies of molecules comprised of several hundred atoms. It has been demonstrated that the DLPNO-CC approach attains the accuracy of a standard canonical coupled-cluster calculation to about 99.9% of the basis set correlation energy while realizing linear scaling of the computational cost with respect to system size. This is achieved by combining (a) localized occupied orbitals, (b) large virtual orbital correlation domains spanned by the projected atomic orbitals (PAOs), and (c) compaction of the virtual space through a truncated pair natural orbital (PNO) basis. In this paper, we report on the implementation of an analytic scheme for the calculation of the first derivatives of the DLPNO-CC energy for basis set independent perturbations within the singles and doubles approximation (DLPNO-CCSD) for closed-shell molecules. Perturbation-independent one-particle density matrices have been implemented in order to account for the response of the CC wave function to the external perturbation. Orbital-relaxation effects due to external perturbation are not taken into account in the current implementation. We investigate in detail the dependence of the computed first-order electrical properties (e.g., dipole moment) on the three major truncation parameters used in a DLPNO-CC calculation, namely, the natural orbital occupation number cutoff used for the construction of the PNOs, the weak electron-pair cutoff, and the domain size cutoff. No additional truncation parameter has been introduced for property calculation. We present benchmark calculations on dipole moments for a set of 10 molecules consisting of 20-40 atoms. We demonstrate that 98%-99% accuracy relative to the canonical CCSD results can be consistently achieved in these calculations. However, this comes with the price of tightening the threshold for the natural orbital occupation number cutoff by an order of magnitude compared to the DLPNO-CCSD energy calculations.

In this paper, various implementations of the analytic Hartree–Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm−1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100–200 cm−1). The effects of the choice of numerical grid for density functional exchange–correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree–Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ∼3 days using 16 Intel® Xeon® 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ∼20 times faster than the calculation without the RIJCOSX approximation.

Ribonucleotide reductases (RNRs) catalyze the conversion of ribonucleotides to deoxyribonucleotides in all organisms. In all Class Ia RNRs, initiation of nucleotide diphosphate (NDP) reduction requires a reversible oxidation over 35 Å by a tyrosyl radical (Y122•, Escherichia coli) in subunit β of a cysteine (C439) in the active site of subunit α. This radical transfer (RT) occurs by a specific pathway involving redox active tyrosines (Y122 ⇆ Y356 in β to Y731 ⇆ Y730 ⇆ C439 in α); each oxidation necessitates loss of a proton coupled to loss of an electron (PCET). To study these steps, 3-aminotyrosine was site-specifically incorporated in place of Y356-β, Y731- and Y730-α, and each protein was incubated with the appropriate second subunit β(α), CDP and effector ATP to trap an amino tyrosyl radical (NH2Y•) in the active α2β2 complex. High-frequency (263 GHz) pulse electron paramagnetic resonance (EPR) of the NH2Y•s reported the gx values with unprecedented resolution and revealed strong electrostatic effects caused by the protein environment. 2H electron–nuclear double resonance (ENDOR) spectroscopy accompanied by quantum chemical calculations provided spectroscopic evidence for hydrogen bond interactions at the radical sites, i.e., two exchangeable H bonds to NH2Y730•, one to NH2Y731• and none to NH2Y356•. Similar experiments with double mutants α-NH2Y730/C439A and α-NH2Y731/Y730F allowed assignment of the H bonding partner(s) to a pathway residue(s) providing direct evidence for colinear PCET within α. The implications of these observations for the PCET process within α and at the interface are discussed.

The accurate calculation of hyperfine-coupling tensors requires a good description of the electronic spin density, especially close to and at the nucleus. Thus, dynamic correlation as well as relativistic effects have to be included in the quantum-chemical calculation of this quantity. In this paper, orbital-optimized second-order Møller–Plesset perturbation theory (MP2) is combined with the second-order Douglas–Kroll–Hess (DKH) transformation to yield an efficient and accurate ab initio method for the calculation of hyperfine couplings for larger molecules including heavy elements. Particular attention is paid to the derivation of the hyperfine-coupling tensor in the DKH framework. In the presence of a magnetic field, the DKH-transformation is not unique. Two different versions can be found in the literature. In this paper, a detailed derivation of one-electron contributions to the hyperfine-coupling tensor as they arise in linear-response theory is given for both DKH-transformations. It turns out that one of the two variants produces divergent hyperfine-coupling constants. The possibility to remove this divergence through a physically motivated finite-nucleus model taking into account the different extent of charge and magnetization distribution is discussed. Hyperfine-coupling values obtained at the orbital-optimized MP2 level with second-order DKH corrections for the non-divergent variant are presented. The influence of a Gaussian nucleus model is studied. The method is compared to four-component, high-accuracy calculations for a number of cations and atoms. Comparison to B3LYP and B2PLYP is made for a set of transition-metal complexes of moderate size.

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5 degrees in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1 %. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup similar to 26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup similar to 27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of similar to 24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup similar to 15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system. (C) 2011 American Institute of Physics. [doi:10.1063/1.3533441]

The performance of the orbital-optimized MP2 method (OO-MP2) and its spin-component-scaled variant is investigated for the prediction of atomic and molecular hyperfine coupling constants (hfccs). The calculated hfccs are compared to experimental as well as to CCSD(T) reference results. The OO-MP2 isotropic hfccs for a series of small radicals are almost of CCSD quality but are obtained with iterative O (N⁵) effort. The dipolar hfccs are less well predicted by the OO-MP2 methods, whereas spin-component scaling improves the description of the hyperfine structure. The spin contamination in the OO-MP2 wave function is drastically reduced compared to the standard unrestricted Hartree-Fock wave function. The applicability of the OO-MP2 to fairly large systems is demonstrated for the solvated p-benzosemiquinone radical anion, where calculations with almost 2000 basis functions have been performed.

The photochemistry of 2-iodo-3,4,5,6-tetrafluorophenyl azide (7d) has been investigated in argon and neon matrices at 4 K, and the products characterized by IR and EPR spectroscopy. The primary photochemical step is loss of a nitrogen molecule and formation of phenyl nitrene 1d. Further irradiation with UV or visible light results in mixtures of 1d with azirine 5d', ketenimine 6d', nitreno radical 2d, and azirinyl radical 9. The relative amounts of these products strongly depend on the matrix and on the irradiation conditions. Nitreno radical 2d with a quartet ground state was characterized by EPR spectroscopy. Electronic structure calculations in combination with the experimental results allow for a detailed understanding of the properties of this unusual new type of organic high-spin molecules.

Efficient energy calculations and structure optimizations employing second-order Møller-Plesset perturbation theory (MP2) are presented. The application of the RIJCOSX approximation, which involves different approximations for the formation of the Coulomb- and exchange-type matrices, to MP2 theory is demonstrated. The RIJCOSX approximation incorporates the 'resolution of the identity' approximation in terms of a Split-RI-J variant for the evaluation of the Coulomb matrices and a seminumeric exchange treatment via the 'chain-of-spheres' algorithm for the formation of the exchange-type matrices. Beside the derivation of the working equations, the RIJCOSX-MP2 method is benchmarked against the original MP2 and the already highly efficient RI-MP2 method. Energies as well as gradients are computed employing various basis sets and are compared to the conventional MP2 results concerning accuracy and total wall clock times. Speedups of typically a factor of 5-7 in comparison to MP2 can be obeserved for the largest basis set employed in our study. Total energies are reproduced with an average error of ≤0.8 kcal/mol and minimum energy geometries differ by ∼0.1 pm in bond lengths and typically ∼0.2 degrees in bond angles. The RIJCOSX-MP2 gradient parallelizes with a speedup of 8.2 on 10 processors. The algorithms are implemented into the ORCA electronic structure package.

An efficient implementation of the orbital-optimized second-order Møller-Plesset perturbation theory (OO-MP2) within the resolution of the identity (RI) approximation is reported. Both conventional MP2 and spin-component scaled (SCS-MP2) variants are considered, and an extensive numerical investigation of the accuracy of these approaches is presented. This work is closely related to earlier work of Lochan, R. C.; Head-Gordon, M. J. Chem. Phys. 2007, 126. Orbital optimization is achieved by making the Hylleraas functional together with the energy of the reference determinant stationary with respect to variations of the double excitation amplitudes and the molecular orbital rotation parameters. A simple iterative scheme is proposed that usually leads to convergence within 5-15 iterations. The applicability of the method to larger molecules (up to ∼1000-2000 basis functions) is demonstrated. The numerical results show that OO-SCS-MP2 is a major improvement in electronically complicated situations, such as represented by radicals or by transition states where spin contamination often greatly deteriorates the quality of the conventional MP2 and SCS-MP2 methods. The OO-(SCS-)MP2 approach reduces the error by a factor of 3-5 relative to the standard (SCS-)MP2. For closed-shell main group elements, no significant improvement in the accuracy relative to the already excellent SCS-MP2 method is observed. In addition, the problems of all MP2 variants with 3d transition-metal complexes are not solved by orbital optimization. The close relationship of the OO-MP2 method to the approximate second-order coupled cluster method (CC2) is pointed out. Both methods have comparable computational requirements. Thus, the OO-MP2 method emerges as a very useful tool for computational quantum chemistry.

The efficiency of two approximate Hartree-Fock approaches was benchmarked. Weigend's RI-JK algorithm is compared to the recently developed RIJCOSX technique in terms of accuracy and total wall clock times. Both methods reproduce the canonical results within the chemical accuracy of similar to kcal mol(-1). RI-JK turns out to be more robust than RIJCOSX due to an overall positive error in the total energies. However, RIJCOSX outperforms RI-JK regarding speed-ups for the largest (gly)(8) chain and maintains comparable accuracy. (C) 2009 Elsevier B.V. All rights reserved.

2,3,5,6-Tetrafluorophenylnitren-4-yl (5) was synthesized in argon at 4 K via the photolysis of 2,3,5,6-tetrafluoro-4-iodo-phenyl azide (6). Electron paramagnetic resonance (EPR) spectroscopy allows us to observe triradical 5 in its quartet state with the zero-field splitting (ZFS) parameters |D/hc| = 0.285 and |E/hc| = 0.043 cm-1. The quartet ground state of 5 is in accordance with our previous infrared (IR) spectroscopic investigation, in which the high-spin quartet state, but no low-spin doublet state, of 5 was observed in solid argon at 4 K [Wenk, H. H.; Sander, W. Angew. Chem., Int. Ed. 2002, 41, 2742-2745]. Because annealing of the matrix at temperatures of >10 K results in the rapid recombination of the highly reactive species 5 with I atoms produced during the photolysis of 6, the Curie-Weiss behavior could not be investigated. However, the absence of low-spin states in the IR investigations, as well as the results of ab initio and density functional theory (DFT) calculations, strongly suggest that 5 has a robust quartet ground state that is best-described as an unprecedented sigma,sigma,pi-triradical. The ZFS of 5 has been successfully reproduced by DFT calculations, which furthermore provide qualitative insight into the origin of the observed EPR parameters.

The performance of modern density functionals for the prediction of molecular hyperfine couplings is investigated for a series of small radicals and transition metal complexes. Besides the established BP86 (GGA) and B3LYP (hybrid) functionals we have tested two prototypical members of emerging classes of density functionals, namely the TPSS meta-GGA functional (together with its hybrid version TPSSh) and the B2PLYP double-hybrid functional. The latter is the first member of a 'fifth-rung' density functional that incorporates a fraction of orbital dependent nonlocal correlation energy estimated at the level of second-order many-body perturbation theory. Since this approach is non-variational, it becomes necessary to derive and implement the so-called 'relaxed' densities in order to properly predict hyperfine couplings. The necessary formalism is described in some detail and the new method has been implemented into the ORCA electronic structure program. The results of extended test calculations reveal that TPSS is superior to BP86. The hybrid variant TPSSh is at least as accurate or better than the B3LYP functional and significantly superior to the non-hybrid TPSS variant. The B2PLYP functional also leads to accurate predictions and is a clear improvement for the difficult metal nucleus HFCs. However, it also showed a few significant outliers in the test set which points to a somewhat reduced stability in the method. The latter effect is largely attributed to the elevated fraction Hartree-Fock exchange (53%) and to some extent also to the perturbative correction.

Combined cyclic voltammetry and in situ scanning tunneling microscopy studies were employed to gain information about the interfacial structure of a chloride modified Cu(100) electrode surface exposed to an acidic electrolyte solution that contained redox-active dibenzylviologens (DBV, 1,1 '-dibenzyl-4,4 '-bipyridinium molecules). A particular focus of this contribution lies in the structural characterization of the electrode surface under nonequilibrium reactive conditions, for example, during the occurrence of an electron-transfer reaction. Typically, two pairs of clearly distinguishable current waves denoted as Pl/Pl ' and P2/P2 ' appear in the cyclic voltammogram of Cu(100) in a mixture of 10 mM HCl and 0.1 MM DBVCl2, provided the cathodic potential limit remains restricted to values of E-work > -425 mV vs reversible hydrogen electrode. Systematic variations of the DBV solution concentration and the nature of the counterion strongly suggest that PI has to be assigned to the first electron-transfer reaction reducing the dicationic DBV2+ to the radical monocationic DBV center dot+ species while P V represents the corresponding oxidation process. Not only solution but also preadsorbed viologen species are involved in this charge-transfer reaction. Triggered by the electron transfer, the more open DBVads2+ "cavitand" structure formed on top of the preadsorbed c(2 x 2)-Cl layer prior to the electron transfer transforms into a more compact polymeric (DBVads center dot+)(n) stacking phase upon reaching P1. Both the reactants and products of the electron-transfer reaction form condensed and laterally ordered 2D phases. In particular, the quite stable (DBVads center dot+)(n) stacking phase maintains its structural integrity during the ongoing electron-transfer reaction involving solution species. Passing P2 in the cyclic voltammogram, however, initiates an order-disorder transition within the organic film with defect lines or point defects in the (DBVads center dot+)(n) ads stacking phase acting as active sites for this structural transition. The driving force for this further phase transition is the starting chloride desorption through the (DBVads center dot+)(n) film. In the presence of the covering viologen film, the chloride desorption occurs at a potential that is Delta E-desorp approximate to 100 mV lower than that in the pure supporting electrolyte pointing to a significant additional activation barrier for that process. Reduced monomeric and oligomeric viologen species reveal a significantly lower lateral mobility on the metallic substrate than that on the chloride lattice. In the reverse potential sweep, chloride anions are forced to readsorb on the metallic copper substrate through the disordered viologen film resulting in a full restoration of the c(2 x 2)-Cl lattice in direct contact to the metallic copper and, in addition, in the full restoration of the ordered (DBVads center dot+)(n) stacking phase on top of the chloride lattice.

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Choline saccharinate and choline acesulfamate are two examples of hydrophilic ionic liquids, which can be prepared from easily available starting materials (choline chloride and a non-nutritive sweetener). The (eco)toxicity of these ionic liquids in aqueous solution is very low in comparison to other types of ionic liquids. A general method for the synthesis and purification of hydrophilic ionic liquids is presented. The method consists of a silver-free metathesis reaction, followed by purification of the ionic liquid by ion-exchange chromatography. The crystal structures show a marked difference in hydrogen bonding between the two ionic liquids, although the saccharinate and the acesulfamate anions show structural similarities. The optimized structures, the energetics, and the charge distribution of cation-anion pairs in the ionic liquids were studied by density functional theory (DFT) and second-order (Møller-Plesset) perturbation theory calculations. The occupation of the non-Lewis orbitals was considered to obtain a qualitative picture of the Lewis structures. The calculated interaction energies and the dipole moments for the ion pairs in the gas phase were discussed.

The surface redox-chemistry of adsorbed viologens is studied by means of cyclic voltammetry (CV) in combination with in situ scanning tunneling microscopy (STM). 1,1'-Dibenzyl- 4,4'-bipyridinium molecules (DBV2+) adsorb on a chloride modified Cu(100) electrode surface under formation of a laterally well ordered 2D array of supramolecular cavitand ensembles. Each cavitand consists at least of 4 individual DBV2+ sub-units which are arranged in a certain circular manner making this supramolecular cavitand chiral. Both possible enantiomeric forms are found in two mirror domains at the surface. Reducing the di-cationic DBV(ads)2+ species to the corresponding radical mono-cation DBV(ads).+ causes a phase transition from the pre-existing DBV 2+ ( ads) cavitand phase to a stripe pattern following a nucleation and growth mechanism. DBV(ads).+ species are adsorbed with their main molecular axis parallel to the surface in a side-on adsorption geometry. Enhanced intermolecular pi - pi-interactions are identified as the main driving force for the formation of 1D oligomer and polymer chains as the characteristic structural motif of the DBV(ads).+ phase. These structural motifs are generally independent of the electronic and structural substrate properties. Chloride desorption through the viologen film is discussed as the reason for an order - disorder transition within the viologen film at even more negative potentials.

Cooperativity in ionic liquids is investigated by means of static quantum chemical calculations. Larger clusters of the dimethylimidazolium cation paired with a chloride anion are calculated within density functional theory combined with gradient corrected functionals. Tests of the monomer unit show that density functional theory performs reasonably well. Linear chain and ring aggregates have been considered and geometries are found to be comparable with liquid phase structures. Cooperative effects occur when the total energy of the oligomer differs from a simple sum of monomer energies. Cooperative effects have been found in the structural motifs examined. A systematic study of linear chains of increasing length (up to nine monomer units) has shown that cooperativity plays a more important role than expected and is stronger than in water. The Cl...H distance of the chloride to the most acidic proton increases with an increasing number of monomer units. The average bond distance approaches 218.9 pm asymptotically. The dipole moment grows almost linearly and the dipole moment per monomer unit reaches the asymptotic value of 16.3 D. The charge on the chloride atoms decreases with an increasing chain length. In order to detect local hydrogen bonding in the clusters a new parametrization of the shared-electron number method is introduced. We find decreasing hydrogen bond energies with an increasing cluster size for both the first hydrogen bond to the most acidic proton and the average hydrogen bond.