David C. Chatfield

The nature and role of quantized transition states in the accurate quantum dynamics of the reaction O+H2→OH+H

Accurate quantum mechanical dynamics calculations are reported for the reaction probabilities of O(3P)+H2→OH+H with zero total angular momentum on a single potential energy surface. The results show that the reactive flux is gated by quantized transition states up to the highest energy studied, which corresponds to a total energy of 1.90 eV. The quantized transition states are assigned and compared to vibrationally adiabatic barrier maxima; their widths and transmission coefficients are determined; and they are classified as variational, supernumerary of the first kind, and supernumerary of the second kind. Their effects on state‐selected and state‐to‐state reactivity are discussed in detail.

HIV-1 protease cleavage mechanism: A theoretical investigation based on classical MD simulation and reaction path calculations using a hybrid QM/MM potential

Abstract The cleavage mechanism of HIV-1 protease (HIV-PR) is investigated with classical molecular dynamics (MD) simulation and with methods incorporating a hybrid quantum mechanical and molecular mechanical (QM/MM) potential function. An X-ray structure of an HIV-PR/inhibitor complex was used to generate model HIV-PR/substrate and HIV-PR/intermediate complexes. Analysis of the feasibility of reaction is based on three hypothetical reaction mechanisms and a variety of possible starting conditions. The classical MD simulations were analyzed for conformations consistent with reaction initiation, as reported previously. It was concluded that Asp125 is the general acid in the first reaction step and transfers a proton to the carbonyl oxygen. Simulations suggest that water 301 stabilizes productive reactant and intermediate conformations but does not participate directly in the reaction. A lytic water, when present, is held very tightly in a position propitious for nucleophilic attack at the scissile carbon. For mechanisms consistent with the classical simulations, reaction barriers were calculated using a QM/MM potential. The QM/MM potential and a restrained energy minimization method for calculating reaction paths and barriers are described. Preliminary results identify reasonable barrier heights and transition state conformations and predict that the first reaction step follows a predominantly stepwise rather than concerted pathway.

Quantized dynamical bottlenecks and transition state control of the reaction of D with H2: Effect of varying the total angular momentum

Accurate quantum mechanical scattering calculations for the reaction of D with H2 are analyzed for evidence that quantized transition states control the reaction dynamics over a wide range of total angular momenta. We find that quantized transition states control the chemical reactivity up to high energy and for values of the total angular momentum (J) up to at least nine. We show that the average transmission coefficient for individual dynamical bottlenecks up to 1.6 eV is greater than 90% for all four of the values of J considered (J=0,3,6,9). We assign energies, widths, level-specific transmission coefficients, and quantum numbers to eleven transition state levels for J=0 and two for J=1, and we show how a separable rotation approximation (SRA) based on these data predicts thermal rate constants for temperatures between 500 and 1500 K that are within 0.3%–5.0% of the values obtained from accurate quantal scattering calculations up to high J. This implementation of the SRA enables us to quantify the con...

Quantum-dynamical characterization of reactive transition states

It is shown that the accurate quantum-mechanical probability of the reaction of H with H2, with either zero or one unit of total angular momentum, increases with energy by increments of resolvable ‘quanta’ of reactive flux. These are analysed in terms of quantized transition states. Bend and stretch quantum numbers are assigned for total angular momentum J equal to zero and for both parities for J= 1 based on an analysis of the density of reactive states. A more detailed description of the reactive scattering process has been obtained by examining the state-selected densities of reactive states, and the initial H + H2 channels that contribute to the reactive flux passing through specific transition states have been determined.

Iterative methods for solving the non-sparse equations of quantum mechanical reactive scattering

Several iterative techniques are applied to solve the non-sparse, indefinite algebraic variational equations of the L2 quantum mechanical description of three-dimensional atom-diatom scattering. We do not assume a symmetric matrix although we employ a symmetric test problem that allows comparison to the standard conjugate gradient algorithm. Convergence of general minimal residual and Lanczos algorithms is shown to be rapid, enabling large savings of computer time as compared to direct methods for large-scale calculations of selected elements or columns of the reactance matrix. As the number M of basis functions varies from 100 to 504, minimal residual calculations based on the Arnoldi basis show very smooth and stable convergence, with computer time scaling as M1.8, and a Lanczos recursive algorithm is found to scale as M1.5 (for off-diagonal matrix elements).

Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations

A complex GMRes (generalized minimum residual) algorithm is presented and used to solve dense systems of linear equations arising in variational basis‐set approaches to quantum‐mechanical reactive scattering. The examples presented correspond to physical solutions of the Schrodinger equation for the reactions O+HD→OH+D, D+H2→HD+H, and H+H2→H2+H. It is shown that the computational effort for solution with GMRes depends upon both the dimension of the linear system and the total energy of the reaction. In several cases with dimensions in the range 1110–5632, GMRes outperforms the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23. In other cases, the iterative algorithm does not converge within a reasonable time. These convergence differences can be correlated with ‘‘indices of diagonal dominance,’’ which we define in detail and which are relatively easy to compute. Furthermore, we find that for a given energy, the computational effort for GMRes can vary with dime...

Chloroperoxidase-Catalyzed Epoxidation of Cis-β-Methylstyrene:Distal Pocket Flexibility Tunes Catalytic Reactivity

Chloroperoxidase, the most versatile heme protein, has a hybrid active site pocket that shares structural features with peroxidases and cytochrome P450s. The simulation studies presented here show that the enzyme possesses a remarkable ability to efficiently utilize its hybrid structure, assuming structurally different peroxidase-like and P450-like distal pocket faces and thereby enhancing the inherent catalytic capability of the active center. We find that, during epoxidation of cis-β-methylstyrene (CBMS), the native peroxidase-like aspect of the distal pocket is diminished as the polar Glu183 side chain is displaced away from the active center and the distal pocket takes on a more hydrophobic, P450-like, aspect. The P450-like distal pocket provides a significant enthalpic stabilization of ∼4 kcal/mol of the 14 kcal/mol reaction barrier for gas-phase epoxidation of CMBS by an oxyferryl heme-thiolate species. This stabilization comes from breathing of the distal pocket. As until recently the active site of chloroperoxidase was postulated to be inflexible, these results suggest a new conceptual understanding of the enzymes versatility: catalytic reactivity is tuned by flexibility of the distal pocket.

Enantiospecificity of Chloroperoxidase-Catalyzed Epoxidation: Biased Molecular Dynamics Study of a Cis-β-Methylstyrene/Chloroperoxidase-Compound I Complex

Molecular dynamics simulations of an explicitly solvated cis-β-methylstyrene/chloroperoxidase-Compound I complex are performed to determine the cause of the high enantiospecificity of epoxidation. From the simulations, a two-dimensional free energy potential is calculated to distinguish binding potential wells from which reaction to 1S2R and 1R2S epoxide products may occur. Convergence of the free energy potential is accelerated with an adaptive biasing potential. Analysis of binding is followed by analysis of 1S2R and 1R2S reaction precursor structures in which the substrate, having left the binding wells, places its reactive double bond in steric proximity to the oxyferryl heme center. Structural analysis of binding and reaction precursor conformations is presented. We find that 1), a distortion of Glu(183) is important for CPO-catalyzed epoxidation as was postulated previously based on experimental results; 2), the free energy of binding does not provide significant differentiation between structures leading to the respective epoxide enantiomers; and 3), CPOs enantiospecificity toward cis-β-methylstyrene is likely to be caused by a specific group of residues which form a hydrophobic core surrounding the oxyferryl heme center.

The conformation of end-groups is one determinant of carotenoid topology suitable for high fidelity molecular recognition: A study of β- and ε-end-groups

Conformation affects a carotenoids ability to bind selectively to proteins. We calculated adiabatic energy profiles for rotating the ring end-groups around the C6C7 bond and for flexing of the ring with respect to the polyene chain. The choice of computational methods is important. A low, 4.2 kcal/mol barrier to rotation exists for a beta-ring. An 8.3 kcal/mol barrier exists for rotation of an epsilon-ring. Rotation of the epsilon-ring is sensitive to substitution at C3. In the absence of external forces neither beta- nor epsilon-rings are rotationally constrained. The nearly parallel alignment of the beta-ring to the C6C7 bond axis contrasts to the more perpendicular orientation of the epsilon-ring. Flexion of a beta-ring to the minimized epsilon-ring conformation requires approximately 23 kcal/mol; extension of the epsilon-ring to the minimized beta-ring conformation requires approximately 8 kcal/mol. Selectivity associated with beta- versus epsilon-rings is dominated by the inability of the beta-ring to flex to minimize protein/ring steric interactions and maximize van der Waals attractions with the binding site.

Preconditioned complex generalized minimal residual algorithm for dense algebraic variational equations in quantum reactive scattering

Variational basis‐set formulations of the quantum mechanical reactive scattering problem lead to large, dense sets of equations. In previous work, we showed that the generalized minimal residual (GMRes) algorithm is sometimes competitive in terms of computer time with direct methods for these dense matrices, even when complex‐valued boundary conditions are used, leading to non‐Hermitian matrices. This paper presents a preconditioning scheme to accelerate convergence and improve performance. We block the potential energy coupling into a series of distortion blocks, and we employ the outgoing wave variational principle with nonorthogonal basis functions, including both dynamically adapted Green’s functions for the distortion blocks and also square integrable functions. The coefficient matrix of the resulting linear system couples the blocks. We have found that preconditioners formed from diagonal blocks of the coefficient matrix corresponding to the distortion blocks and vibrational blocks are effective at ...