Heather J. Kulik

Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach.

Transition-metal centers are the active sites for a broad variety of biological and inorganic chemical reactions. Notwithstanding this central importance, density-functional theory calculations based on generalized-gradient approximations often fail to describe energetics, multiplet structures, reaction barriers, and geometries around the active sites. We suggest here an alternative approach, derived from the Hubbard U correction to solid-state problems, that provides an excellent agreement with correlated-electron quantum chemistry calculations in test cases that range from the ground state of Fe2 and Fe2- to the addition elimination of molecular hydrogen on FeO+. The Hubbard U is determined with a novel self-consistent procedure based on a linear-response approach.

Mechanically triggered heterolytic unzipping of a low-ceiling-temperature polymer

Biological systems rely on recyclable materials resources such as amino acids, carbohydrates and nucleic acids. When biomaterials are damaged as a result of aging or stress, tissues undergo repair by a depolymerization–repolymerization sequence of remodelling. Integration of this concept into synthetic materials systems may lead to devices with extended lifetimes. Here, we show that a metastable polymer, end-capped poly(o-phthalaldehyde), undergoes mechanically initiated depolymerization to revert the material to monomers. Trapping experiments and steered molecular dynamics simulations are consistent with a heterolytic scission mechanism. The obtained monomer was repolymerized by a chemical initiator, effectively completing a depolymerization–repolymerization cycle. By emulating remodelling of biomaterials, this model system suggests the possibility of smart materials where aging or mechanical damage triggers depolymerization, and orthogonal conditions regenerate the polymer when and where necessary. Strong acoustic fields applied to solutions of linear polymers typically result in mid-chain scission, yielding products half the molecular weight of the original. Now it has been shown that poly(o-phthalaldehyde), a polymer with a ceiling temperature below room temperature, undergoes chain scission and subsequent depolymerization to monomers. Introduction of an appropriate initiator to the monomer regenerates poly(o-phthaladehyde) macromolecules.

Systematic study of first-row transition-metal diatomic molecules: A self-consistent DFT+U approach

We present a systematic first-principles study of the equilibrium bond lengths, harmonic frequencies, dissociation energies, ground state symmetries, and spin state splittings of 22 diatomic molecules comprised of a first-row 3d transition-metal and a main-group element (H, C, N, O, or F). Diatomic molecules are building blocks of the key molecular bonding motifs in biological and inorganic catalytic systems, but, at the same time, their small size permits a thorough study by even the most computationally expensive quantum chemistry approaches. The results of several density-functional theory (DFT) approaches including hybrid, generalized-gradient, and generalized-gradient augmented with Hubbard U exchange-correlation functionals are presented. We compare these efficiently calculated DFT results with the highly accurate but computationally expensive post-Hartree-Fock approaches multireference configuration interaction (MRCI) and coupled cluster [CCSD(T)] as well as experimental values, where available. We show that by employing a Hubbard U approach, we systematically reduce average errors in state splittings and dissociation energies by a factor of 3. We are also able to reassign the ground state of four molecules improperly identified by hybrid or generalized-gradient approaches and provide correct assignment of all ground state symmetries as compared against experimental assignment and MRCI reference. By providing accuracy comparable to more expensive quantum chemistry approaches with the robust scaling of the generalized-gradient approximation, our DFT+U approach permits the study of very large scale systems with vastly improved results.

A self-consistent Hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on bare FeO(+)

We present a detailed analysis of the addition-elimination reaction pathways for the gas-phase conversion of molecular hydrogen and methane on FeO(+) to water and methanol, respectively, using first-principles calculations. These two reactions represent paradigmatic, challenging test cases for electronic structure approaches to transition-metal catalysis. We compare here density-functional approaches against state-of-the-art coupled-cluster and multireference quantum chemistry approaches. The quantum chemical approaches are found to be in close agreement between themselves as well as with the available experimental evidence. For the density-functional calculations, we employ a recently introduced ab initio, self-consistent Hubbard-like correction, coupled here with a generalized-gradient approximation (GGA) for the exchange-correlation functional. We find that our formulation provides a remarkable improvement in the description of the electronic structure, hybridization, and multiplet splittings for all calculated stationary points along these reaction pathways. The Hubbard term, which is not a fitting parameter and, in principle, can augment any exchange-correlation functional, brings the density-functional theory results in close agreement with the reference calculations. In particular, thermochemical errors as large as 1.4 eV in the exit channels with the GGA functional are reduced by an order of magnitude, to less than 0.1 eV on average; additionally, close agreement with the correlated-electron reference calculations and experiments are achieved for intermediate spin splittings and structures, reaction exothermicity, and spin crossovers. The role that the Hubbard U term plays in improving both quantitative and qualitative descriptions of transition-metal chemistry is examined, and its strengths as well as possible weaknesses are discussed in detail.

Accurate potential energy surfaces with a DFT+U(R) approach

We introduce an improvement to the Hubbard U augmented density functional approach known as DFT+U that incorporates variations in the value of self-consistently calculated, linear-response U with changes in geometry. This approach overcomes the one major shortcoming of previous DFT+U studies, i.e., the use of an averaged Hubbard U when comparing energies for different points along a potential energy surface is no longer required. While DFT+U is quite successful at providing accurate descriptions of localized electrons (e.g., d or f) by correcting self-interaction errors of standard exchange correlation functionals, we show several diatomic molecule examples where this position-dependent DFT+U(R) provides a significant two- to four-fold improvement over DFT+U predictions, when compared to accurate correlated quantum chemistry and experimental references. DFT+U(R) reduces errors in binding energies, frequencies, and equilibrium bond lengths by applying the linear-response, position-dependent U(R) at each configuration considered. This extension is most relevant where variations in U are large across the points being compared, as is the case with covalent diatomic molecules such as transition-metal oxides. We thus provide a tool for deciding whether a standard DFT+U approach is sufficient by determining the strength of the dependence of U on changes in coordinates. We also apply this approach to larger systems with greater degrees of freedom and demonstrate how DFT+U(R) may be applied automatically in relaxations, transition-state finding methods, and dynamics.

Mediation of donor–acceptor distance in an enzymatic methyl transfer reaction

Significance During the past 30 years, the methyl transfer community has attempted to find the molecular origin of the methyltransferases’ catalytic power. This report describes a combination of experimental and computational studies of enzymatic methyl transfer catalyzed by catechol-O-methyltransferase and its mutants at position Tyr68. The results show structural and dynamical differences between WT and mutants, as well as a role for substrate ionization in the generation of active site compaction. For the first time, to our knowledge, we are able to show a trend in donor–acceptor distance in the ground state that can be correlated with catalytic efficiency. This work provides an important step forward and a clear new direction for understanding enzymatic methyl transfer. Enzymatic methyl transfer, catalyzed by catechol-O-methyltransferase (COMT), is investigated using binding isotope effects (BIEs), time-resolved fluorescence lifetimes, Stokes shifts, and extended graphics processing unit (GPU)-based quantum mechanics/molecular mechanics (QM/MM) approaches. The WT enzyme is compared with mutants at Tyr68, a conserved residue that is located behind the reactive sulfur of cofactor. Small (>1) BIEs are observed for an S-adenosylmethionine (AdoMet)-binary and abortive ternary complex containing 8-hydroxyquinoline, and contrast with previously reported inverse (<1) kinetic isotope effects (KIEs). Extended GPU-based computational studies of a ternary complex containing catecholate show a clear trend in ground state structures, from noncanonical bond lengths for WT toward solution values with mutants. Structural and dynamical differences that are sensitive to Tyr68 have also been detected using time-resolved Stokes shift measurements and molecular dynamics. These experimental and computational results are discussed in the context of active site compaction that requires an ionization of substrate within the enzyme ternary complex.

First-principles study of non-heme Fe(II) halogenase SyrB2 reactivity

We present here a computational study of reactions at a model complex of the SyrB2 enzyme active site. SyrB2, which chlorinates L-threonine in the syringomycin biosynthetic pathway, belongs to a recently discovered class of alpha-ketoglutarate (alphaKG), non-heme Fe(II)-dependent halogenases that share many structural and chemical similarities with hydroxylases. Namely, halogenases and hydroxylases alike decarboxylate the alphaKG co-substrate, facilitating formation of a high-energy ferryl-oxo intermediate that abstracts a hydrogen from the reactant complex. The reaction mechanisms differ at this point, and mutation of active site residues (Asp for the hydroxylase to Ala or Ala to Asp/Glu for halogenase) fails to reproduce hydroxylating activity in SyrB2 or halogenating activity in similar hydroxylases. Using a density functional theory approach with a recently implemented Hubbard U correction for accurate treatment of transition-metal chemistry, we explore probable reaction pathways and mechanisms via a model complex consisting of only the iron center and its direct ligands. We show that the first step, alphaKG decarboxylation, is barrierless and exothermic, but the subsequent hydrogen abstraction step has an energetic barrier consistent with that accessible under biological conditions. In the model complex we use, radical chlorination is barrierless and exothermic, whereas the analogous hydroxylation is found to have a small energetic barrier. The hydrogen abstraction and radical chlorination steps are strongly coupled: the barrier for the hydrogen abstraction step is reduced when carried out concomitantly with the exothermic chlorination step. Our work suggests that the lack of chlorination in mutant hydroxylases is most likely due to poor binding of chlorine in the active site, whereas mutant halogenases do not hydroxylate for energetic reasons. Although secondary shell residues undoubtedly modulate the overall reactivity and binding of relevant substrates, we show that a small model compound consisting exclusively of the direct ligands to the metal can help explain reactivity heretofore not yet understood in the halogenase SyrB2.

Local Effects in the X-ray Absorption Spectrum of Salt Water

Both first-principles molecular dynamics and theoretical X-ray absorption spectroscopy have been used to investigate the aqueous solvation of cations in 0.5 M MgCl(2), CaCl(2), and NaCl solutions. We focus here on the species-specific effects that Mg(2+), Ca(2+), and Na(+) have on the X-ray absorption spectrum of the respective solutions. For the divalent cations, we find that the hydrogen-bonding characteristics of the more rigid magnesium first-shell water molecules differ from those in the more flexible solvation shell surrounding calcium. In particular, the first solvation shell water molecules of calcium are able to form acceptor hydrogen bonds, and this results in an enhancement of a post-edge peak near 540 eV. The absence of acceptor hydrogen bonds for magnesium first shell water molecules provides an explanation for the experimental and theoretical observation of a lack of enhancement at the post-main-edge peak. For the sodium monovalent cation we find that the broad tilt angle distribution results in a broadening of postedge features, despite populations in donor-and-acceptor configurations consistent with calcium. We also present the reaveraged spectra of the MgCl(2), CaCl(2), and NaCl solutions and show that trends apparent with increasing concentration (0.5, 2.0, 4.0 M) are consistent with experiment. Finally, we examine more closely both the effect that cation coordination number has on the hydrogen-bonding network and the relative perturbation strength of the cations on lone pair oxygen orbitals.

Substrate Placement Influences Reactivity in Non-heme Fe(II) Halogenases and Hydroxylases

Background: SyrB2 is a non-heme Fe(II) halogenase that reacts on tethered amino acid substrates. Results: Hydroxylation and hydrogen abstraction are less sensitive to substrate positioning at the active site than halogenation. Conclusion: Observed halogenation of native l-Thr substrate by SyrB2 can be explained by positioning effects. Significance: Our work could inform how to redesign tether-dependent enzymes toward alternative products. We employ error-corrected density functional theory methods to map out the dependence of reactivity on substrate position for SyrB2, a member of a family of non-heme iron halogenases and hydroxylases that are only reactive toward amino acid substrates delivered via prosthetic phosphopantetheine arms. For the initial hydrogen abstraction step, the inherent flexibility of the phosphopantetheine molecule weakens the position dependence for both the native substrate (threonine for SyrB2) and alternative substrates. Over a 5 Å window of substrate positions, the tethered hydrogen abstraction step proceeds with nearly identical activation energies and donor-acceptor distances in the transition state. The propensity of a particular substrate toward halogenation or hydroxylation is found to depend strongly on the substrate placement following hydrogen abstraction, with deeper substrate delivery into the active (for native substrates) site favoring halogenation and shallower substrate delivery favoring hydroxylation.

Quantum Chemistry for Solvated Molecules on Graphical Processing Units Using Polarizable Continuum Models

The conductor-like polarization model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in chemical simulations. However, its application in quantum mechanical calculations of large-scale biomolecular systems can be limited by computational expense of both the gas phase electronic structure and the solvation interaction. We have previously used graphical processing units (GPUs) to accelerate the first of these steps. Here, we extend the use of GPUs to accelerate electronic structure calculations including C-PCM solvation. Implementation on the GPU leads to significant acceleration of the generation of the required integrals for C-PCM. We further propose two strategies to improve the solution of the required linear equations: a dynamic convergence threshold and a randomized block-Jacobi preconditioner. These strategies are not specific to GPUs and are expected to be beneficial for both CPU and GPU implementations. We benchmark the performance of the new implementation using over 20 small proteins in solvent environment. Using a single GPU, our method evaluates the C-PCM related integrals and their derivatives more than 10× faster than that with a conventional CPU-based implementation. Our improvements to the linear solver provide a further 3× acceleration. The overall calculations including C-PCM solvation require, typically, 20-40% more effort than that for their gas phase counterparts for a moderate basis set and molecule surface discretization level. The relative cost of the C-PCM solvation correction decreases as the basis sets and/or cavity radii increase. Therefore, description of solvation with this model should be routine. We also discuss applications to the study of the conformational landscape of an amyloid fibril.