Development of Accurate DFT Methods for Computing Redox Potentials of Transition Metal Complexes: Results for Model Complexes and Application to Cytochrome P450

Single-electron reduction half potentials of 95 octahedral fourth-row transition metal complexes binding a diverse set of ligands have been calculated at the unrestricted pseudospectral B3LYP/LACV3P level of theory in a continuum solvent. Through systematic comparison of experimental and calculated potentials, it is determined that B3LYP strongly overbinds the d-manifold when the metal coordinates strongly interacting ligands and strongly underbinds the d-manifold when the metal coordinates weakly interacting ligands. These error patterns give rise to an extension of the localized orbital correction (LOC) scheme previously developed for organic molecules and which was recently extended to the spin-splitting properties of organometallic complexes. Mean unsigned errors in B3LYP redox potentials are reduced from 0.40 ± 0.20 V (0.88 V max error) to 0.12 ± 0.09 V (0.34 V max error) using a simple seven-parameter model. Although the focus of this article is on redox properties of transition metal complexes, we have found that applying our previous spin-splitting LOC model to an independent test set of oxidized and reduced complexes that are also spin-crossover complexes correctly reverses the ordering of spin states obtained with B3LYP. Interesting connections are made between redox and spin-splitting parameters with regard to the spectrochemical series and in their combined predictive power for properly closing the thermodynamic cycle of d-electron transitions in a transition metal complex. Results obtained from our large and diverse databases of spin-splitting and redox properties suggest that, while the error introduced by single reference B3LYP for simple multireference systems, like mononuclear transition metal complexes, remains significant, at around 2–5 kcal/mol, the dominant error, at around 10–20 kcal/mol, is in B3LYP’s prediction of metal–ligand binding. Application of the LOC scheme to the rate-determining hydrogen atom transfer step in substrate hydroxylation by cytochrome P450 shows that this approach is able to correct the B3LYP barriers in comparison to recent kinetics experiments

Evaluation of the Performance of the B3LYP, PBE0, and M06 DFT Functionals, and DBLOC-Corrected Versions, in the Calculation of Redox Potentials and Spin Splittings for Transition Metal Containing Systems

We have evaluated the performance of the M06 and PBE0 functionals in their ability to calculate spin splittings and redox potentials for octahedral complexes containing a first transition metal series atom. The mean unsigned errors (MUEs) for these two functionals are similar to those obtained for B3LYP using the same data sets. We then apply our localized orbital correction approach for transition metals, DBLOC, in an effort to improve the results obtained with both functionals. The PBE0-DBLOC results are remarkably close in both MUE and parameter values to those obtained for the B3LYP-DBLOC method. The M06-DBLOC results are less accurate, but the parameter values and trends are still qualitatively very similar. These results demonstrate that DBLOC corrected methods are substantially more accurate for these systems than any of the uncorrected functionals we have tested and that the deviations between hybrid DFT methods and experiment for transition metal containing systems exhibit striking physically based regularities which are very similar for the three functionals that we have examined, despite significant differences in the details of each model

Role of Desolvation in Thermodynamics and Kinetics of Ligand Binding to a Kinase

Computer simulations are used to determine the free energy landscape for the binding of the anticancer drug Dasatinib to its src kinase receptor and show that before settling into a free energy basin the ligand must surmount a free energy barrier. An analysis based on using both the ligand-pocket separation and the pocket-water occupancy as reaction coordinates shows that the free energy barrier is a result of the free energy cost for almost complete desolvation of the binding pocket. The simulations further show that the barrier is not a result of the reorganization free energy of the binding pocket. Although a continuum solvent model gives the location of free energy minima, it is not able to reproduce the intermediate free energy barrier. Finally, it is shown that a kinetic model for the on rate constant in which the ligand diffuses up to a doorway state and then surmounts the desolvation free energy barrier is consistent with published microsecond time-scale simulations of the ligand binding kinetics for this system [Shaw, D. E. et al. J. Am. Chem. Soc. 2011, 133, 9181−9183]

Accurate p<i>K</i>_a Prediction in First-Row Hexaaqua Transition Metal Complexes Using the B3LYP-DBLOC Method

Acid dissociation constants are computed with density functional theory (DFT) for a series of ten first-row octahedral hexaaqua transition metal complexes at the B3LYP/LACV3P** level of theory. These results are then scaled, primarily to correct for basis set effects (as in previous work on predicting p<i>K</i>_a’s in organic systems−). Finally, localized orbital corrections (LOCs), developed by fitting properties such as ionization potentials, electron affinities, and ligand removal energies in prior publications,,,, are applied without any further parameter adjustment. The combination of a single scale factor with the DBLOC (localized orbital corrections for first row transition metals) corrections (and thus a single adjustable parameter in all) improves the mean unsigned error from 5.7 p<i>K</i>_a units (with no parameters) to 0.9 p<i>K</i>_a units (maximum error 2.2 p<i>K</i>_a units), which is close to chemical accuracy for this type of system. These results provide further encouragement with regard to the ability of the B3LYP-DBLOC model to provide accurate and robust results for DFT calculations on transition metal containing species

Covalent O–H Bonds as Electron Traps in Proton-Rich Rutile TiO₂ Nanoparticles

The cation in the electrolyte of the dye-sensitized solar cell (DSSC) has a profound effect on electron trapping and transport behavior in TiO₂ nanocrystalline film; this is one of the important factors that determines the overall efficiency of DSSCs. Here, we present a quantum mechanical investigation on the structures and energetics of proton-induced electron trap states and the thermodynamical barrier heights for the ambipolar diffusion of proton/electron pair using a large cluster model for the computations. Our calculations indicate that protons react with TiO₂ to form covalent O–H bonds. This is in contrast to the reaction of Li⁺ with TiO₂, in which case the alkali metal is more accurately described as a simple coordinating cation. The covalent O–H bonding leads both to deeper electron trap states and to significantly higher barriers for the diffusion of carriers. These results are qualitatively consistent with experimental observations, and they extend our understanding of the cation effect in DSSCs at an atomic level of detail

Conformational Dynamics of the Partially Disordered Yeast Transcription Factor GCN4

Molecular dynamics (MD) simulations have been employed to study the conformational dynamics of the partially disordered DNA binding basic leucine zipper domain of the yeast transcription factor GCN4. We demonstrate that back-calculated NMR chemical shifts and spin-relaxation data provide complementary probes of the structure and dynamics of disordered protein states and enable comparisons of the accuracy of multiple MD trajectories. In particular, back-calculated chemical shifts provide a sensitive probe of the populations of residual secondary structure elements and helix capping interactions, while spin-relaxation calculations are sensitive to a combination of dynamic and structural factors. Back-calculated chemical shift and spin-relaxation data can be used to evaluate the populations of specific interactions in disordered states and identify regions of the phase space that are inconsistent with experimental measurements. The structural interactions that favor and disfavor helical conformations in the disordered basic region of the GCN4 bZip domain were analyzed in order to assess the implications of the structure and dynamics of the apo form for the DNA binding mechanism. The structural couplings observed in these experimentally validated simulations are consistent with a mechanism where the binding of a preformed helical interface would induce folding in the remainder of the protein, supporting a hybrid conformational selection/induced folding binding mechanism

Realistic Cluster Modeling of Electron Transport and Trapping in Solvated TiO₂ Nanoparticles

We have developed a cluster model of a TiO₂ nanoparticle in the dye-sensitized solar cell and used first-principles quantum chemistry, coupled with a continuum solvation model, to compute structures and energetics of key electronic and structural intermediates and transition states. Our results suggest the existence of shallow surface trapping states induced by small cations and continuum solvent effect as well as the possibility of the existence of a surface band which is 0.3–0.5 eV below the conduction band edge. The results are in uniformly good agreement with experiment and establish the plausibility of an ambipolar model of electron diffusion in which small cations, such as Li⁺, diffuse alongside the current carrying electrons in the device, stabilizing shallowing trapping states, facilitating diffusion from one of these states to another, in a fashion that is essential to the functioning of the cell

Phaseless Auxiliary-Field Quantum Monte Carlo on Graphical Processing Units

We present an implementation of phaseless Auxiliary-Field Quantum Monte Carlo (ph-AFQMC) utilizing graphical processing units (GPUs). The AFQMC method is recast in terms of matrix operations which are spread across thousands of processing cores and are executed in batches using custom Compute Unified Device Architecture kernels and the GPU-optimized cuBLAS matrix library. Algorithmic advances include a batched Sherman-Morrison-Woodbury algorithm to quickly update matrix determinants and inverses, density-fitting of the two-electron integrals, an energy algorithm involving a high-dimensional precomputed tensor, and the use of single-precision floating point arithmetic. These strategies accelerate ph-AFQMC calculations with both single- and multideterminant trial wave functions, though particularly dramatic wall-time reductions are achieved for the latter. For typical calculations we find speed-ups of roughly 2 orders of magnitude using just a single GPU card compared to a single modern CPU core. Furthermore, we achieve near-unity parallel efficiency using 8 GPU cards on a single node and can reach moderate system sizes via a local memory-slicing approach. We illustrate the robustness of our implementation on hydrogen chains of increasing length and through the calculation of all-electron ionization potentials of the first-row transition metal atoms. We compare long imaginary-time calculations utilizing a population control algorithm with our previously published correlated sampling approach and show that the latter improves not only the efficiency but also the accuracy of the computed ionization potentials. Taken together, the GPU implementation combined with correlated sampling provides a compelling computational method that will broaden the application of ph-AFQMC to the description of realistic correlated electronic systems

Docking and Free Energy Perturbation Studies of Ligand Binding in the Kappa Opioid Receptor

The kappa opioid receptor (KOR) is an important target for pain and depression therapeutics that lack harmful and addictive qualities of existing medications. We present a model for the binding of morphinan ligands and JDTic to the JDTic/KOR crystal structure based on an atomic level description of the water structure within its active site. The model contains two key interaction motifs that are supported by experimental evidence. The first is the formation of a salt bridge between the ligand and Asp 138^3.32 in transmembrane domain (TM) 3. The second is the stabilization by the ligand of two high energy, isolated, and ice-like waters near TM5 and TM6. This model is incorporated via energetic terms into a new empirical scoring function, WScore, designed to assess interactions between ligands and localized water in a binding site. Pairing WScore with the docking program Glide discriminates known active KOR ligands from large sets of decoy molecules much better than Glide’s older generation scoring functions, SP and XP. We also use rigorous free energy perturbation calculations to provide evidence for the proposed mechanism of interaction between ligands and KOR. The molecular description of ligand binding in KOR should provide a good starting point for future drug discovery efforts for this receptor

Multicolor Live-Cell Chemical Imaging by Isotopically Edited Alkyne Vibrational Palette

Vibrational imaging such as Raman microscopy is a powerful technique for visualizing a variety of molecules in live cells and tissues with chemical contrast. Going beyond the conventional label-free modality, recent advance of coupling alkyne vibrational tags with stimulated Raman scattering microscopy paves the way for imaging a wide spectrum of alkyne-labeled small biomolecules with superb sensitivity, specificity, resolution, biocompatibility, and minimal perturbation. Unfortunately, the currently available alkyne tag only processes a single vibrational “color”, which prohibits multiplex chemical imaging of small molecules in a way that is being routinely practiced in fluorescence microscopy. Herein we develop a three-color vibrational palette of alkyne tags using a ¹³C-based isotopic editing strategy. We first synthesized ¹³C isotopologues of EdU, a DNA metabolic reporter, by using the newly developed alkyne cross-metathesis reaction. Consistent with theoretical predictions, the mono-¹³C (¹³C¹²C) and bis-¹³C (¹³C¹³C) labeled alkyne isotopologues display Raman peaks that are red-shifted and spectrally resolved from the originally unlabeled (¹²C¹²C) alkynyl probe. We further demonstrated three-color chemical imaging of nascent DNA, RNA, and newly uptaken fatty-acid in live mammalian cells with a simultaneous treatment of three different isotopically edited alkynyl metabolic reporters. The alkyne vibrational palette presented here thus opens up multicolor imaging of small biomolecules, enlightening a new dimension of chemical imaging