Computational Assessment of MLCT versus MC Stabilities in First-to-Third-Row d6 Pseudo-Octahedral Transition Metal Complexes

An accurate modeling of metal-to-ligand-charge-transfer (MLCT) and metal-centered (MC) excited state energies is key to predict the photoinduced response in transition metal complexes (TMCs). Herein, the importance of the ground state and excited state reference geometries is addressed for three-prototype d⁶ pseudo-octahedral TMCs, each displaying a different potential energy landscape of MLCT versus MC relative stabilities. Several functionals are used within the time-dependent density functional theory (TDDFT), as well as multireference wave-function theory (MS-CASPT2), applied to [Mn(im)(CO)₃(phen)]⁺, [Ru(im)₂(bpy)₂]²⁺, and [Re(im)(CO)₃(phen)]⁺, (im: imidazole, bpy: bypiridine, phen: phenantroline). The results revel that TDDFT is robust except when using B3LYP functional for first-row d⁶ TMCs. In contrast, MS-CASPT2 calculations are strongly biased in those cases with competitive MLCT/MC states. The results reinforce the reliability of B3LYP to describe the excited states in d⁶ TMCs, but question the validity of assessing the density functional theory (DFT)/TDDFT performance via direct comparison with MS-CASPT2 performed at the same DFT reference geometry as a standard strategy. © 2019 Wiley Periodicals, Inc.     

Redox transitions of chromium, manganese, iron, cobalt and nickel protoporphyrins in aqueous solution

The electrochemical redox behavior of immobilized chromium, manganese, iron, cobalt, and nickel protoporphyrins IX has been investigated over the pH 0-14 range. In the investigated potential domain the metalloporphyrins were observed in four different oxidation states (M(I), M(II), M(III) and M(IV)). The metalloporphyrins differ in the potentials at which the redox transitions occur, but the observed pH dependence of the redox transitions was similar for the different metalloporphyrins and revealed that the M(II)/M(III) and M(III)/M(IV) transitions were accompanied by a hydroxide transfer at high pH. The fact that the metalloporphyrins are immobilized on graphite does not seem to have a large influence on their redox behavior, as can be deduced from the comparable behavior of immobilized metalloporphyrins on gold and of watersoluble metalloporphyrins in solution. We also performed density functional theory (DFT) calculations on the metalloporphyrins in different oxidation states. The geometries and spin states predicted by these calculations agree well with experimentally determined values; the calculations were also able to predict the electrochemical potentials of the [M(II)]/[M(III)-OH] redox transition to within about 300 mV.     

Density functional theory and CCSD(T) evaluation of ionization potentials,redox potentials,and bond energies related to zirconocene polymerization catalysts

Quantum-mechanical-based computational design of molecular catalysts requires accurate and fast electronic structure calculations to determine and predict properties of transition-metal complexes. For Zr-based molecular complexes related to polyethylene catalysis, previous evaluation of density functional theory (DFT) and wavefunction methods only examined oxides and halides or select reaction barrier heights. In this work, we evaluate the performance of DFT against experimental redox potentials and bond dissociation enthalpies (BDEs) for zirconocene complexes directly relevant to ethylene polymerization catalysis. We also examined the ability of DFT to compute the fourth atomic ionization potential of zirconium and the effect the basis set selection has on the ionization potential computed with CCSD(T). Generally, the atomic ionization potential and redox potentials are very well reproduced by DFT, but we discovered relatively large deviations of DFT-calculated BDEs compared to experiment. However, evaluation of BDEs with CCSD(T) suggests that experimental values should be revisited, and our CCSD(T) values should be taken as most accurate.     

Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

The enzyme nitrogenase contains a complicated MoFe₇CS₉ cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R² = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.     

One-electron reduction potential for oxygen- and sulfur-centered organic radicals in protic and aprotic solvents

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.     

Charged states of Sc3N@C68: an in situ spectroelectrochemical study of the radical cation and radical anion of a non-IPR fullerene

The redox behavior of Sc 3N@C 68 is studied systematically by means of electrochemistry, in situ ESR/Vis-NIR spectroelectrochemistry, and detailed theoretical treatment. Formation of the negatively and positively charged paramagnetic species for the same trimetallic nitride endohedral fullerene is demonstrated for the first time. The electrochemical study of Sc 3N@C 68 exhibits two electrochemically irreversible but chemically reversible reduction steps and two reversible oxidation steps. A double-square reaction scheme is proposed to explain the observed redox reaction at cathodic potentials involving the reversible dimerisation of the Sc 3N@C 68 monoanion. The spin state of the radical cation and the radical anion is probed by ESR spectroscopy, indicating that in both states, the large part of the unpaired spin is delocalized on the fullerene cage. The charged states of the non-isolated pentagon rule fullerene are characterized furthermore by in situ absorption spectroscopy. The interpretation of experimental data is supported by the density functional theory (DFT) calculations of the spin distribution in the anion and cation radicals of Sc 3N@C 68 and time-dependent DFT calculations of the absorption spectra of the charged species.     

Synthesis and characterization of near-infrared absorbing benzannulated aza-BODIPY dyes

A series of novel aza‐diisoindolmethine dyes 9 with six different aryl and heteroaryl groups at the indole moiety have been synthesized by the addition of aryl Grignard compounds to phthalodinitrile and subsequent reaction with formamide. A plausible reaction mechanism, through a Leuckart–Wallach‐type reduction has been confirmed by means of DFT calculations of the related transition and intermediate states. The corresponding boron difluoride complexes ( 10) of 9 were prepared in a subsequent reaction step and the spectroscopic and electrochemical properties of 9 and 10 have been investigated both experimentally and theoretically. The aza‐diisoindolmethines 9 exhibit an absorption maximum in the range from 615 to 720 nm, whereas the complexes 10 show a bathochromically shifted absorption maximum between 681 and 793 nm. Measurements of 9 and 10 by cyclic voltammetry display fully reversible redox waves for the reduction and oxidation with higher potentials for 10 . From the measured redox potentials, the HOMO and LUMO energy levels were calculated for 9 and 10 . The frontier orbital energies, the energies of the absorption bands, as well as the orbitals involved in the absorption process were calculated with DFT and compared to the measured results of 9 and 10 . The absorption maximum can be related to an intense HOMO–LUMO transition and the more‐pronounced stabilization of the LUMO upon complexation is the origin of the bathochromic shift of the absorption. Additionally, single‐crystal structures for two species, 10 d and 10 f , are reported.     

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn–Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097 .     

Theoretical Study of One-electron Redox Potentials of Some NADH Model Compounds

Several 1‐benzyl‐1,4‐dihydronicotinamide derivatives, which are important NADH model compounds were studied theoretically in acetonitrile. The performances of various DFT methods including B3LYP, B1B95, B3PW91, MPW1B95, MPWKCIS, and M06 were tested to calculate the redox potentials. The first theoretical protocol to predict the redox potentials of these derivatives is B1B95, whose reliability has been tested against almost all the available experimental data. Strikingly, the mean absolute derivations (MAD) and root mean square (RMS) error of the current theoretical model equal 0.015 and 0.017, respectively. By using this method, the important thermodynamic properties of BNAHs were investigated and the mechanisms of hydride transfer progress were explained. Besides, para‐substituents that have a big effect on these redox potentials of BNAH were systematically studied and carefully demonstrated.     

Anharmonic vibrational spectroscopy calculations with electronic structure potentials: comparison of MP2 and DFT for organic molecules

Density functional theory (DFT) technique is the most commonly used approach when it comes to computation of vibrational spectra of molecular species. In this study, we compare anharmonic spectra of several organic molecules such as allene, propyne, glycine, and imidazole, computed from ab initio MP2 potentials and DFT potentials based on commonly used BLYP and B3LYP functionals. Anharmonic spectra are obtained using the direct vibrational self-consistent field (VSCF) method and its correlation-corrected extension (CC-VSCF). The results of computations are compared with available experimental data. It is shown that the most accurate vibrational frequencies are obtained with the MP2 method, followed by the DFT/B3LYP method, while DFT/BLYP results are often unsatisfactory. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Assessment of density functional theory methods for the computation of heats of formation and ionization potentials of systems containing third row transition metals

The performance of several different density functional theory (DFT) methods, including GGA, hybrid-GGA, meta-GGA, and hybrid-meta-GGA methods, have been assessed in terms of their ability to accurately compute both heats of formation and ionization potentials of systems containing third row transition metals. Two different basis sets were used in this study: 6-31G** and TZVP. It is found that the triple-zeta quality TZVP basis set generally produces the best results for both heats of formation and ionization potentials. One important observation made in this study is that the inclusion of exact exchange terms in DFT methods generally results in more consistently accurate results for both heats of formation and ionization potentials of transition metal systems. In general, DFT methods do not yield good ionization potential results for systems containing titanium or zinc. For heats of formation, it is found that the hybrid-meta-GGA functional, TPSS1KCIS, yields the best overall results when combined with the TZVP basis set, while PBE1PBE (hybrid-GGA) gives the best results for the 6-31G** basis. The hybrid-GGA functional, B3LYP, is found to produce the lowest overall errors for ionization potentials when combined with both 6-31G** and TZVP.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

Application of the stabilization method to temporary anion states of CH3CN, CH3NC, CH3SCN, and CH3NCS in density functional theory with asymptotically corrected potentials

In this paper, density functional theory (DFT) with asymptotically corrected potentials is used to investigate CH(3)CN, CH(3)NC, CH(3)SCN, and CH(3)NCS molecules. For the energies of σ* and π* temporary anion states, the stabilized Koopmans' theorem (S-KT) using long-range correction functional and stabilized Koopmans-based (S-KB) approximation using local functional, are adopted. The stabilization procedure is accomplished by varying the exponents of appropriate diffuse functions. Results indicate that the calculations based on asymptotically corrected density functionals can yield better energy results of temporary anion states over conventional DFT methods.     

Cu催化水煤气的变换反应机理

采用密度泛函理论(DFT), 对Cu催化水煤气变换反应三种可能的微观机理进行了理论研究. 在GGA-PW91理论水平下优化了反应通道上各驻点(反应物、中间体、过渡态和产物)的几何构型, 并通过频率分析对过渡态进行了验证. 研究结果表明, 甲酸根机理的可能性最小, 羧基机理与氧化还原机理的可能性较大, 且与氧化还原机理相比, 羧基机理因在反应过程中有中间体COOH(s)生成, 且它与OH(s)发生歧化反应仅需越过3.8 kJ·mol-1的活化能垒, 所以反应更易遵循这条路径进行.     

密度泛函理论研究镥二聚体低电子能态的相对稳定性、结构以及成键性质

用密度泛函理论方法研究了镥二聚体（Lu2）低能量电子态的性质,计算了电子态相对能量、平衡键长、振动频率以及基态解离能,考察了密度泛函性质、相对论有效势种类以及Hartree—Fock交换作用大小对计算结果的影响．结果表明,无论采用何种密度泛函和相对论有效势,体系的基态都为三重态,与其他一些基于分子轨道理论的从头计算方法得到的结论是一致的．另外,与分子轨道从头计算结果以及实验结果比较发现,采用杂化密度泛函理论和Stuttgart小核有效势计算得到的结果总体吻合最好．最后,特别分析研究了B3LYP计算中Hartree—Fock交换作用大小对基态键长和基态解离能的影响,发现随着交换作用的增大,键长增长,解离能减小,这是由于5d轨道杂化导致的共价成键作用减弱造成的．     

Classical force field parameters for the heme prosthetic group of cytochrome c

Accurate force fields are essential for describing biological systems in a molecular dynamics simulation. To analyze the docking of the small redox protein cytochrome c (cyt c) requires simulation parameters for the heme in both the reduced and oxidized states. This work presents parameters for the partial charges and geometries for the heme in both redox states with ligands appropriate to cyt c. The parameters are based on both protein X-ray structures and ab initio density functional theory (DFT) geometry optimizations at the B3LYP/6-31G* level. The simulations with the new parameter set reproduce the geometries of the X-ray structures and the interaction energies between water and heme prosthetic group obtained from B3LYP/6-31G* calculations. The parameter set developed here will provide new insights into docking processes of heme containing redox proteins.     

铝原子团簇Al5、Al5-和Al5+稳定结构的密度泛函理论研究

采用密度泛函理论的四种方法:杂化密度泛函B3LYP与B3PW91、Perdew-Wang91交换与相关泛函WP91PW91、局域自旋密度近似SVWN,研究了A15、Al5-和Al5+团簇的多种可能结构,找到了它们稳定的结构与自旋态,与已有的理论结果作了比较,并计算了Al5-的绝热与垂直电子离解能、Al5的绝热与垂直电离势,同有关的实验数据比较,符合较好.同时对四种密度泛函方法的计算结果作了一些比较与讨论.     

Theoretic calculation for understanding the oxidation process of 1,4-dimethoxybenzene-based compounds as redox shuttles for overcharge protection of lithium ion batteries

The effect of substituents on the oxidation potential for the one-electron reaction of 1,4-dimethoxybenzene was understood with a theoretical calculation based on density functional theory (DFT) at the level of B3LYP/6-311+G(d). It is found that the oxidation potential for the one-electron reaction of 1,4-dimethoxybenzene is 4.13 V (vs Li/Li(+)) and can be changed from 3.8 to 5.9 V (vs Li/Li(+)) by substituting electron-donating or electron-withdrawing groups for the hydrogen atoms on the aromatic ring. These potentials are in the range of the limited potentials for the lithium ion batteries using different cathode materials, and thus the substituted compounds can be selected as the redox shuttles for the overcharge prevention of these batteries. The oxidation potential of 1,4-dimethoxybenzene decreases when the hydrogen atoms are replaced with electron-donating groups but increases when replaced with electron-withdrawing groups. The further oxidation of these substituted compounds was also analyzed on the basis of the theoretic calculation.