A General Approach for Calculating Strongly Anharmonic Vibronic Spectra with a High Density of States: The X̃²B₁ ← X̃¹A₁ Photoelectron Spectrum of Difluoromethane

Due to a low-lying fragmentation channel, the X̃²B₁ ← X̃¹A₁ photoelectron spectrum of difluoromethane is dominated by strong anharmonicity effects. We have used a time-independent eigenstate-free Raman wave function approach (RWF) to calculate the entire spectrum. Vibronic transitions with the most significant Franck–Condon factors were determined by employing our recently developed residual-based algorithm for the calculation of eigenpairs (RACE). An analysis of the factors controlling the accuracy of the predicted band shape is provided. The calculated spectrum is in very close agreement with experimental results

Key Hydride Vibrational Modes in [NiFe] Hydrogenase Model Compounds Studied by Resonance Raman Spectroscopy and Density Functional Calculations

Hydrogenase proteins catalyze the reversible conversion of molecular hydrogen to protons and electrons. While many enzymatic states of the [NiFe] hydrogenase have been studied extensively, there are multiple catalytically relevant EPR-silent states that remain poorly characterized. Analysis of model compounds using new spectroscopic techniques can provide a framework for the study of these elusive states within the protein. We obtained optical absorption and resonance Raman (RR) spectra of (dppe)­Ni­(μ-pdt)­Fe­(CO)₃ and [(dppe)­Ni­(μ-pdt)­(μ-H)­Fe­(CO)₃]­[BF₄], which are structural and functional model compounds for the EPR-silent Ni–SI and Ni–R states of the [NiFe] hydrogenase active site. The studies presented here use RR spectroscopy to probe vibrational modes of the active site, including metal–hydride stretching vibrations along with bridging ligand–metal and Fe–CO bending vibrations, with isotopic substitution used to identify key metal–hydride modes. The metal–hydride vibrations are essentially uncoupled and represent isolated, localized stretching modes; the iron–hydride vibration occurs at 1530 cm^–1, while the nickel–hydride vibration is observed at 945 cm^–1. The significant discrepancy between the metal–hydride vibrational frequencies reflects the slight asymmetry in the metal–hydride bond lengths. Additionally, time-dependent density functional theory (TD-DFT) calculations were carried out to obtain theoretical RR spectra of these compounds. On the basis of the detailed comparison of theory and experiment, the dominant electronic transitions and significant normal modes probed in the RR experiments were assigned; the primary transitions in the visible wavelengths represent metal-to-metal and metal-to-ligand charge transfer bands. Inherent properties of metal–hydride vibrational modes in resonance Raman spectra and DFT calculations are discussed together with the prospects of observing such vibrational modes in metal–hydride-containing proteins. Such a combined theoretical and experimental approach may be valuable for characterization of analogous redox states in the [NiFe] hydrogenases

Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

<p>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.</p

A Step beyond the Feltham–Enemark Notation: Spectroscopic and Correlated <i>ab Initio</i> Computational Support for an Antiferromagnetically Coupled M(II)–(NO)⁻ Description of Tp*M(NO) (M = Co, Ni)

Multiple spectroscopic and computational methods were used to characterize the ground-state electronic structure of the novel {CoNO}⁹ species Tp*Co(NO) (Tp* = hydro-tris(3,5-Me₂-pyrazolyl)borate). The metric parameters about the metal center and the pre-edge region of the Co K-edge X-ray absorption spectrum were reproduced by density functional theory (DFT), providing a qualitative description of the Co–NO bonding interaction as a Co(II) (<i>S</i>_Co = ³/₂) metal center, antiferromagnetically coupled to a triplet NO^– anion (<i>S</i>_NO = 1), an interpretation of the electronic structure that was validated by <i>ab initio</i> multireference methods (CASSCF/MRCI). Electron paramagnetic resonance (EPR) spectroscopy revealed significant <i>g</i>-anisotropy in the <i>S</i> = ¹/₂ ground state, but the linear-response DFT performed poorly at calculating the <i>g</i>-values. Instead, CASSCF/MRCI computational studies in conjunction with quasi-degenerate perturbation theory with respect to spin–orbit coupling were required for obtaining accurate modeling of the molecular <i>g</i>-tensor. The computational portion of this work was extended to the diamagnetic Ni analogue of the Co complex, Tp*Ni(NO), which was found to consist of a Ni(II) (<i>S</i>_Ni = 1) metal center antiferromagnetically coupled to an <i>S</i>_NO = 1 NO^–. The similarity between the Co and Ni complexes contrasts with the previously studied Cu analogues, for which a Cu(I) bound to NO⁰ formulation has been described. This discrepancy will be discussed along with a comparison of the DFT and <i>ab initio</i> computational methods for their ability to predict various spectroscopic and molecular features

A Step beyond the Feltham–Enemark Notation: Spectroscopic and Correlated <i>ab Initio</i> Computational Support for an Antiferromagnetically Coupled M(II)–(NO)⁻ Description of Tp*M(NO) (M = Co, Ni)

Multiple spectroscopic and computational methods were used to characterize the ground-state electronic structure of the novel {CoNO}⁹ species Tp*Co(NO) (Tp* = hydro-tris(3,5-Me₂-pyrazolyl)borate). The metric parameters about the metal center and the pre-edge region of the Co K-edge X-ray absorption spectrum were reproduced by density functional theory (DFT), providing a qualitative description of the Co–NO bonding interaction as a Co(II) (<i>S</i>_Co = ³/₂) metal center, antiferromagnetically coupled to a triplet NO^– anion (<i>S</i>_NO = 1), an interpretation of the electronic structure that was validated by <i>ab initio</i> multireference methods (CASSCF/MRCI). Electron paramagnetic resonance (EPR) spectroscopy revealed significant <i>g</i>-anisotropy in the <i>S</i> = ¹/₂ ground state, but the linear-response DFT performed poorly at calculating the <i>g</i>-values. Instead, CASSCF/MRCI computational studies in conjunction with quasi-degenerate perturbation theory with respect to spin–orbit coupling were required for obtaining accurate modeling of the molecular <i>g</i>-tensor. The computational portion of this work was extended to the diamagnetic Ni analogue of the Co complex, Tp*Ni(NO), which was found to consist of a Ni(II) (<i>S</i>_Ni = 1) metal center antiferromagnetically coupled to an <i>S</i>_NO = 1 NO^–. The similarity between the Co and Ni complexes contrasts with the previously studied Cu analogues, for which a Cu(I) bound to NO⁰ formulation has been described. This discrepancy will be discussed along with a comparison of the DFT and <i>ab initio</i> computational methods for their ability to predict various spectroscopic and molecular features