Calculations of One-Electron Redox Potentials of Oxoiron(IV) Porphyrin Complexes

Density functional theory calculations have been performed to calculate the one-electron redox potential for a series of oxoiron­(IV) porphyrin complexes of the form [(TMP)­Fe^IV(O)­(L)] (TMP = 5,10,15,20-tetramesitylporphyrinate). Different axial ligands were chosen (L = none, Im, ClO₄^–, CH₃CO₂^–, Cl^–, F^–, SCH₃^–) in order to compare the results with recent electrochemical experiments. The redox potentials were calculated with a Born–Haber cycle and the use of an internal reference, i.e. the absolute redox potential of ferrocene. Diverse methodologies were tested and show that the computed redox potentials depend strongly on the functional, the basis set, and the continuum models used to compute the solvation energies. Globally, BP86 gives better results for the geometries of the complexes than B3LYP and M06-L as well as more consistent values for the redox potentials. Although the results fit the experimental data for L = Im and L = ClO₄^–, the addition of the other anionic axial ligands to the oxoiron­(IV) porphyrin complex strongly lowers the redox potential, which is in disagreement with experimental observations. This important discrepancy is discussed

Modeling Molecular Crystals by QM/MM: Self-Consistent Electrostatic Embedding for Geometry Optimizations and Molecular Property Calculations in the Solid

We present an approach to model molecular crystals using an adaptive quantum mechanics/molecular mechanics (QM/MM) based protocol. The molecule of interest (or a larger cluster thereof) is described at an appropriate QM level and is embedded in a large array of MM atoms built up from crystal structure information. The nonbonded MM force field consists of atom-centered point charges and Lennard-Jones potentials using van der Waals parameters from the UFF force field. The point charges are initially derived from a single molecule DFT calculation and are then updated self-consistently in the field of point charges. Additional charges are fitted around the MM cluster to correct for missing long-range electrostatic effects. The geometry of the central complex can then be relaxed by quantum chemical calculations in the surrounding MM reaction field, hence capturing solid-state effects on the geometry. We demonstrate the accuracy of this approach for geometry optimization by successful modeling of the huge gas-to-solid bond contraction of HCN-BF₃, the ability to reproduce periodic-DFT quality local geometries of solid VOCl₃, and the geometry of [Ru(η⁵-Cp*)(η³-CH₂CHCHC₆H₅)(NCCH₃)₂]²⁺, a difficult ruthenium allyl complex in the solid state. We further show that this protocol is well suited for subsequent molecular property calculations in the solid state (where accurate relaxed geometries are often required) as exemplified by transition metal NMR and EFG calculations of VOCl₃ and a vanadium catechol complex in the solid state

Infrared Dynamics of Iron Carbonyl Diene Complexes

The temperature dependence of the low-frequency C–O bands in the IR spectrum of [(η⁴-norbornadiene)­Fe­(CO)₃], reminiscent of signal coalescence in dynamic NMR, was interpreted by Grevels (in 1987) as chemical exchange due to very fast rotation of the diene group. Since then, there has been both support and objection to this interpretation. We discuss these various claims involving both one- and two-dimensional IR and, largely on the basis of new density functional theory calculations, furnish support for Grevels’ original interpretation

Water versus Acetonitrile Coordination to Uranyl. Density Functional Study of Cooperative Polarization Effects in Solution

International audienc

On the Origin of ^35/37Cl Isotope Effects on ¹⁹⁵Pt NMR Chemical Shifts. A Density Functional Study

Zero-point vibrationally averaged (<i>r</i>_g⁰) structures were computed at the PBE0/SDD/6-31G* level for [Pt³⁵Cl₆]^2– and [Pt³⁷Cl₆]^2–, for the [Pt³⁵Cl_<i>n</i>³⁷Cl_5–<i>n</i>(H₂O)]⁻ (<i>n</i> = 0–5), <i>cis</i>-Pt³⁵Cl_<i>n</i>³⁷Cl_{(4–<i>n</i>)}(H₂O)₂ (<i>n</i> = 0–4), and <i>fac</i>-[Pt³⁵Cl_<i>n</i>³⁷Cl_{(3–<i>n</i>)}(H₂O)₃]⁺ (<i>n</i> = 0–3) isotopologues and isotopomers. Magnetic ¹⁹⁵Pt shielding constants, computed at the ZORA-SO/PW91/QZ4P/TZ2P level, were used to evaluate the corresponding ^35/37Cl isotope shifts in the experimental ¹⁹⁵Pt NMR spectra. While the observed effects are reproduced reasonably well computationally in terms of qualitative trends and the overall order of magnitude (ca. 1 ppm), quantitative agreement with experiment is not yet achieved. Only small changes in Pt–Cl and Pt–O bond lengths upon isotopic substitution, on the order of femtometers, are necessary to produce the observed isotope shifts

Probing Isotope Shifts in ¹⁰³Rh and ¹⁹⁵Pt NMR Spectra with Density Functional Theory

Zero-point vibrationally averaged (<i>r</i>_g⁰) structures were computed at the PBE0/SDD/6-31G* level for the [Pt³⁵Cl_<i>n</i>³⁷Cl_5–<i>n</i>(H₂¹⁸O)]⁻ (<i>n</i> = 0–5), <i>cis</i>-Pt³⁵Cl_<i>n</i>³⁷Cl_4–<i>n</i>(H₂¹⁸O)­(H₂¹⁶O) (<i>n</i> = 0–4), <i>fac</i>-[Pt³⁵Cl_<i>n</i>³⁷Cl_3–<i>n</i>(H₂¹⁸O)­(H₂¹⁶O)₂]⁺ (<i>n</i> = 0–3), [Pt³⁵Cl_<i>n</i>³⁷Cl_5–<i>n</i>(^16/18OH)]^2– (<i>n</i> = 0–5), <i>cis</i>-[Pt³⁵Cl_<i>n</i>³⁷Cl_4–<i>n</i>(^16/18OH)₂]^2– (<i>n</i> = 0–4), <i>fac</i>-[Pt³⁵Cl_<i>n</i>³⁷Cl_3–<i>n</i>(^16/18OH)₃]^2– (<i>n</i> = 0–3), <i>cis-</i>[Pt³⁵Cl_<i>n</i>³⁷Cl_2–<i>n</i>(^16/18OH)₄]^2– (<i>n</i> = 0–2), [Pt³⁵Cl_<i>n</i>³⁷Cl_1–<i>n</i>(^16/18OH)₅]^2– (<i>n</i> = 0–1), [Rh³⁵Cl_<i>n</i>³⁷Cl_5–<i>n</i>(H₂O)]^2– (<i>n</i> = 0–5), <i>cis</i>-[Rh³⁵Cl_<i>n</i>³⁷Cl_4–<i>n</i>(H₂O)₂]⁻ (<i>n</i> = 0–4), and <i>fac</i>-Rh³⁵Cl_<i>n</i>³⁷Cl_3–<i>n</i>(H₂O)₃ (<i>n</i> = 0–3) isotopologues and isotopomers. Magnetic shielding constants, computed at the ZORA-SO/PW91/QZ4P/TZ2P level, were used to evaluate the corresponding ^35/37Cl isotope shifts on the ¹⁹⁵Pt and ¹⁰³Rh NMR spectra, which are known experimentally. While the observed effects are reproduced reasonably well computationally in terms of qualitative trends and the overall order of magnitude (ca. 1 ppm), quantitative agreement with experiment is not yet achieved. Only small changes in M–Cl and M–O bonds upon isotopic substitution, on the order of femtometers, are necessary to produce the observed isotope shifts

Water versus Acetonitrile Coordination to Uranyl. Effect of Chloride Ligands

Optimizations at the BLYP and B3LYP levels are reported for the mixed uranyl chloro/water/acetonitrile complexes [UO₂Cl_<i>n</i>(H₂O)_<i>x</i>(MeCN)_{5<i>–n</i>−<i>x</i>}]^2–<i>n</i> (<i>n</i> = 1–3) and [UO₂Cl_<i>n</i>(H₂O)_<i>x</i>(MeCN)_{4<i>–n</i>−<i>x</i>}]^2–<i>n</i> (<i>n</i> = 2–4), in both the gas phase and a polarizable continuum modeling acetonitrile. Car–Parrinello molecular dynamics (CPMD) simulations have been performed for [UO₂Cl₂(H₂O)­(MeCN)₂] in the gas phase and in a periodic box of liquid acetonitrile. According to population analyses and dipole moments evaluated from maximally localized Wannier function centers, uranium is less Lewis acidic in the neutral UO₂Cl₂ than in the UO₂²⁺ moiety. In the gas phase the latter binds acetonitrile ligands more strongly than water, whereas in acetonitrile solution, the trend is reversed due to cooperative polarization effects. In the polarizable continuum the chloro complexes have a slight energetic preference for water over acetonitrile ligands, but several mixed complexes are so close in free energy Δ<i>G</i> that they should exist in equilibrium, in accord with previous interpretations of EXAFS data in solution. The binding strengths of the fifth neutral ligands decrease with increasing chloride content, to the extent that the trichlorides should be formulated as four-coordinate [UO₂Cl₃L]⁻ (L = H₂O, MeCN). Limitations to their accuracy notwithstanding, density functional calculations can offer insights into the speciation of a complex uranyl system in solution, a key feature in the context of nuclear waste partitioning by complexant molecules

Liquid Methanol from DFT and DFT/MM Molecular Dynamics Simulations

We present a comparative study of computational protocols for the description of liquid methanol from <i>ab initio</i> molecular dynamics simulations, in view of further applications directed at the modeling of chemical reactivity of organic and organometallic molecules in (explicit) methanol solution. We tested density functional theory molecular dynamics (DFT-MD) in its Car–Parrinello Molecular Dynamics (CPMD) and Quickstep/Born–Oppenheimer MD (CP2K) implementations, employing six popular density functionals with and without corrections for dispersion interactions (namely BLYP, BLYP-D2, BLYP-D3, BP86, BP86-D2, and B97-D2). Selected functionals were also tested within the two QM/MM frameworks implemented in CPMD and CP2K, considering one DFT molecule in a MM environment (described by the OPLS model of methanol). The accuracy of each of these methods at describing the bulk liquid phase under ambient conditions was evaluated by analyzing their ability to reproduce (<i>i</i>) the average structure of the liquid, (<i>ii</i>) the mean squared displacement of methanol molecules, (<i>iii</i>) the average molecular dipole moments, and (<i>iv</i>) the gas-to-liquid red-shift observed in their infrared spectra. We show that it is difficult to find a DFT functional that describes these four properties equally well within full DFT-MD simulations, despite a good overall performance of B97-D2. On the other hand, DFT/MM-MD provides a satisfactory description of the solvent–solute polarization effects with all functionals and thus represents a good alternative for the modeling of methanol solutions in the context of chemical reactivity in an explicit environment

Speciation of La(III) Chloride Complexes in Water and Acetonitrile: A Density Functional Study

Car–Parrinello molecular dynamics (CMPD) simulations and static computations are reported at the BLYP level of density functional theory (DFT) for mixed [LaCl_<i>x</i>(H₂O)_<i>y</i>(MeCN)_<i>z</i>]^3–<i>x</i> complexes in aqueous and nonaqueous solution (acetonitrile). Both methodologies predict coordination numbers (i.e., <i>x</i> +<i> y</i> +<i> z</i>) that are successively lower than nine as the Cl content increases from <i>x</i> = 0 to 3. While the static DFT method with implicit solvation through a polarizable continuum model overestimates the binding strength of chloride and erroneously predicts [LaCl₂(H₂O)₅]⁺ as global free-energy minimum, constrained CPMD simulations with explicit solvent and thermodynamic integration reproduce the weak binding of chloride in water reasonably well. Special attention is called to the dipole moments of coordinated water molecules as function of coligands and solvent, evaluated through maximally localized Wannier function centers along the CPMD trajectories. Cooperative polarization of these water ligands by the metal cation and the surrounding solvent is remarkably sensitive to fluctuations of the La–O distances and, to a lesser extent, on the La-water tilt angles. The mean dipole moment of water ligands is rather insensitive to the other coligands, oscillating around 3.2 D, 3.5 D, and 3.3 D in MeCN, water, and [dmim]­Cl solution, respectively, the latter being an archetypical ionic liquid