Hydrogen bond network between amino acid radical intermediates on the proton-coupled electron transfer pathway of E. coli α2 ribonucleotide reductase.

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 ß 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 ß 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-ß, Y731- and Y730-α, and each protein was incubated with the appropriate second subunit ß(α), CDP and effector ATP to trap an amino tyrosyl radical (NH2Y•) in the active α2ß2 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. (2)H 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.

Derivation and assessment of relativistic hyperfine-coupling tensors on the basis of orbital-optimized second-order Møller-Plesset perturbation theory and the second-order Douglas-Kroll-Hess transformation.

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.

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

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° 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 ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~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.

Correlated ab initio spin densities for larger molecules: orbital-optimized spin-component-scaled MP2 method.

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.

3,4,5,6-Tetrafluorophenylnitren-2-yl: a ground-state quartet triradical.

The photochemistry of 2-iodo-3,4,5,6-tetrafluorophenyl azide (7 d) 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 1 d. Further irradiation with UV or visible light results in mixtures of 1 d with azirine 5 d', ketenimine 6 d', nitreno radical 2 d, and azirinyl radical 9. The relative amounts of these products strongly depend on the matrix and on the irradiation conditions. Nitreno radical 2 d 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 Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method.

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.

Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics.

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.

2,3,5,6-Tetrafluorophenylnitren-4-yl: electron paramagnetic resonance spectroscopic characterization of a quartet-ground-state nitreno radical.

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.

Choline saccharinate and choline acesulfamate: ionic liquids with low toxicities.

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.

Cooperativity in ionic liquids.

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.