Hydrogen Tunneling in an Enzyme Active Site: A Quantum Wavepacket Dynamical Perspective

Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.

Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure

The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.

Computational approaches to delivery of anticancer drugs with multidimensional nanomaterials

Functionalized nanotubes (NTs), nanosheets, nanorods, and porous organometallic scaffolds are potential in vivo carriers for cancer therapeutics. Precise delivery through these agents depends on factors like hydrophobicity, payload capacity, bulk/surface adsorption, orientation of molecules inside the host matrix, bonding, and nonbonding interactions. Herein, we summarize advances in simulation techniques, which are extremely valuable in initial geometry optimization and evaluation of the loading and unloading behavior of encapsulated drug molecules. Computational methods broadly involve the use of quantum and classical mechanics for studying the behavior of molecular properties. Combining theoretical processes with experimental techniques, such as X-ray crystallography, NMR spectroscopy, and bioassays, can provide a more comprehensive understanding of the structure and function of biological molecules. This integrated approach has led to numerous breakthroughs in drug discovery, enzyme design, and the study of complex biological processes. This short review provides an overview of results and challenges described from erstwhile investigations on the molecular interaction of anticancer drugs with nanocarriers of different aspect ratios.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.

Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H₂]_n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Mapping Quantum Chemical Dynamics Problems to Spin-Lattice Simulators

The accurate computational determination of chemical, materials, biological, and atmospheric properties has a critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of quantum mechanical methods. The complexity of quantum chemical studies arises from the steep algebraic scaling of electron correlation methods and the exponential scaling in studying nuclear dynamics and molecular flexibility. To date, efforts to apply quantum hardware to such quantum chemistry problems have focused primarily on electron correlation. Here, we provide a framework that allows for the solution of quantum chemical nuclear dynamics by mapping these to quantum spin-lattice simulators. Using the example case of a short-strong hydrogen-bonded system, we construct the Hamiltonian for the nuclear degrees of freedom on a single Born-Oppenheimer surface and show how it can be transformed to a generalized Ising model Hamiltonian. We then demonstrate a method to determine the local fields and spin-spin couplings needed to identically match the molecular and spin-lattice Hamiltonians. We describe a protocol to determine the on-site and intersite coupling parameters of this Ising Hamiltonian from the Born-Oppenheimer potential and nuclear kinetic energy operator. Our approach represents a paradigm shift in the methods used to study quantum nuclear dynamics, opening the possibility to solve both electronic structure and nuclear dynamics problems using quantum computing systems.

Shear-Induced Amyloid Aggregation in the Brain: V. Are Alzheimer's and Other Amyloid Diseases Initiated in the Lower Brain and Brainstem by Cerebrospinal Fluid Flow Stresses?

Amyloid-β (Aβ) and tau oligomers have been identified as neurotoxic agents responsible for causing Alzheimer's disease (AD). Clinical trials using Aβ and tau as targets have failed, giving rise to calls for new research approaches to combat AD. This paper provides such an approach. Most basic AD research has involved quiescent Aβ and tau solutions. However, studies involving laminar and extensional flow of proteins have demonstrated that mechanical agitation of proteins induces or accelerates protein aggregation. Recent MRI brain studies have revealed high energy, chaotic motion of cerebrospinal fluid (CSF) in lower brain and brainstem regions. These and studies showing CSF flow within the brain have shown that there are two energetic hot spots. These are within the third and fourth brain ventricles and in the neighborhood of the circle of Willis blood vessel region. These two regions are also the same locations as those of the earliest Aβ and tau AD pathology. In this paper, it is proposed that cardiac systolic pulse waves that emanate from the major brain arteries in the lower brain and brainstem regions and whose pulse waves drive CSF flows within the brain are responsible for initiating AD and possibly other amyloid diseases. It is further proposed that the triggering of these diseases comes about because of the strengthening of systolic pulses due to major artery hardening that generates intense CSF extensional flow stress. Such stress provides the activation energy needed to induce conformational changes of both Aβ and tau within the lower brain and brainstem region, producing unique neurotoxic oligomer molecule conformations that induce AD.

Nuclear quantum effects in enzymatic reactions: simulation of the kinetic isotope effect of phenylethylamine oxidation catalyzed by monoamine oxidase A

By using computational techniques for quantizing nuclear motion one can accurately reproduce kinetic isotope effect of enzymatic reactions, as demonstrated for phenylethylamine oxidation catalyzed by the monoamine oxidase A enzyme.

Challenges in constructing accurate methods for hydrogen transfer reactions in large biological assemblies: rare events sampling for mechanistic discovery and tensor networks for quantum nuclear effects

We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites.

Shear-Induced Amyloid Formation in the Brain: III. The Roles of Shear Energy and Seeding in a Proposed Shear Model

If cerebrospinal and interstitial fluids move through very narrow brain flow channels, these restrictive surroundings generate varying levels of fluid shear and different shear rates, and dissolved amyloid monomers absorb different shear energies. It is proposed that dissolved amyloid-β protein (Aβ) and other amyloid monomers undergo shear-induced conformational changes that ultimately lead to amyloid monomer aggregation even at very low brain flow and shear rates. Soluble Aβ oligomers taken from diseased brains initiate in vivo amyloid formation in non-diseased brains. The brain environment is apparently responsible for this result. A mechanism involving extensional shear is proposed for the formation of a seed Aβ monomer molecule that ultimately promotes templated conformational change of other Aβ molecules. Under non-quiescent, non-equilibrium conditions, gentle extensional shear within the brain parenchyma, and perhaps even during laboratory preparation of Aβ samples, may be sufficient to cause subtle conformational changes in these monomers. These result from brain processes that significantly lower the high activation energy predicted for the quiescent Aβ dimerization process. It is further suggested that changes in brain location and changes brought about by aging expose Aβ molecules to different shear rates, total shear, and types of shear, resulting in different conformational changes in these molecules. The consequences of such changes caused by variable shear energy are proposed to underlie formation of amyloid strains causing different amyloid diseases. Amyloid researchers are urged to undertake studies with amyloids, anti-amyloid drugs, and antibodies while all of these are under shear conditions similar to those in the brain.

A qualitative quantum rate model for hydrogen transfer in soybean lipoxygenase

The hydrogen transfer reaction catalysed by soybean lipoxygenase (SLO) has been the focus of intense study following observations of a high kinetic isotope effect (KIE). Today high KIEs are generally thought to indicate departure from classical rate theory and are seen as a strong signature of tunnelling of the transferring particle, hydrogen or one of its isotopes, through the reaction energy barrier. In this paper, we build a qualitative quantum rate model with few free parameters that describes the dynamics of the transferring particle when it is exposed to energetic potentials exerted by the donor and the acceptor. The enzyme's impact on the dynamics is modelled by an additional energetic term, an oscillatory contribution known as "gating." By varying two key parameters, the gating frequency and the mean donor-acceptor separation, the model is able to reproduce well the KIE data for SLO wild-type and a variety of SLO mutants over the experimentally accessible temperature range. While SLO-specific constants have been considered here, it is possible to adapt these for other enzymes.

Active Site Dynamical Effects in the Hydrogen Transfer Rate-limiting Step in the Catalysis of Linoleic Acid by Soybean Lipoxygenase-1 (SLO-1): Primary and Secondary Isotope Contributions

Using ab initio molecular dynamics (AIMD) simulations that facilitate the treatment of rare events, we probe the active site participation in the rate-determining hydrogen transfer step in the catalytic oxidation of linoleic acid by soybean lipoxygenase-1 (SLO-1). The role of two different active site components is probed. (a) On the hydrogen atom acceptor side of the active site, the hydrogen bonding propensity between the acceptor side hydroxyl group, which is bound to the iron cofactor, and the backbone carboxyl group of isoleucine (residue number 839) is studied toward its role in promoting the hydrogen transfer event. Primary and secondary (H/D) isotope effects are also probed and a definite correlation with subtle secondary H/D isotope effects is found. With increasing average nuclear kinetic energy, the increase in transfer probability is enhanced due to the presence of the hydrogen bond between the backbone carbonyl of I839 and the acceptor oxygen. Further increase in average nuclear kinetic energy reduces the strength of this secondary hydrogen bond which leads to a deterioration in hydrogen transfer rates and finally embrances an Arrhenius-like behavior. (b) On the hydrogen atom donor side, the coupling between vibrational modes predominantly localized on the donor-side linoleic acid group and the reactive mode is probed. There appears to be a qualitative difference in the coupling between modes that belong to linoleic acid and the hydrogen transfer mode, for hydrogen and deuterium transfer. For example, the donor side secondary hydrogen atom is much more labile (by nearly a factor of 5) during deuterium transfer as compared to the case for hydrogen transfer. This appears to indicate a greater coupling between the modes belonging to the linoleic acid scaffold and the deuterium transfer mode and also provides a new rationalization for the abnormal (nonclassical) secondary isotope effect results obtained by Knapp, Rickert, and Klinman in J. Am. Chem. Soc. , 2002 , 124 , 3865 . To substantiate our findings noted in point a above, we have suggested an I839 → A839 or I839 → V839 mutation. This will modify the bulkiness of hydrogen the bonding residue, allowing greater flexibility in the secondary hydrogen bond formation highlighted above and adversely affecting the reaction rate.

Applications of density functional theory to iron-containing molecules of bioinorganic interest

The past decades have seen an explosive growth in the application of density functional theory (DFT) methods to molecular systems that are of interest in a variety of scientific fields. Owing to its balanced accuracy and efficiency, DFT plays particularly useful roles in the theoretical investigation of large molecules. Even for biological molecules such as proteins, DFT finds application in the form of, e.g., hybrid quantum mechanics and molecular mechanics (QM/MM), in which DFT may be used as a QM method to describe a higher prioritized region in the system, while a MM force field may be used to describe remaining atoms. Iron-containing molecules are particularly important targets of DFT calculations. From the viewpoint of chemistry, this is mainly because iron is abundant on earth, iron plays powerful (and often enigmatic) roles in enzyme catalysis, and iron thus has the great potential for biomimetic catalysis of chemically difficult transformations. In this paper, we present a brief overview of several recent applications of DFT to iron-containing non-heme synthetic complexes, heme-type cytochrome P450 enzymes, and non-heme iron enzymes, all of which are of particular interest in the field of bioinorganic chemistry. Emphasis will be placed on our own work.

Quantum mechanical modeling: a tool for the understanding of enzyme reactions

Most enzyme reactions involve formation and cleavage of covalent bonds, while electrostatic effects, as well as dynamics of the active site and surrounding protein regions, may also be crucial. Accordingly, special computational methods are needed to provide an adequate description, which combine quantum mechanics for the reactive region with molecular mechanics and molecular dynamics describing the environment and dynamic effects, respectively. In this review we intend to give an overview to non-specialists on various enzyme models as well as established computational methods and describe applications to some specific cases. For the treatment of various enzyme mechanisms, special approaches are often needed to obtain results, which adequately refer to experimental data. As a result of the spectacular progress in the last two decades, most enzyme reactions can be quite precisely treated by various computational methods.

Importance of protein dynamics during enzymatic C-H bond cleavage catalysis

Quantum tunneling and protein dynamics have emerged as important components of enzyme function. This review focuses on soybean lipoxygenase-1, to illustrate how the properties of enzymatic C-H bond activation link protein motions to the fundamental bond making-breaking processes.

Gaining insight into the chemistry of lipoxygenases: a computational investigation into the catalytic mechanism of (8R)-lipoxygenase

Lipoxygenases (LOXs) are ubiquitous in nature and catalyze a range of life-essential reactions within organisms. In particular they are critical to the formation of eicosanoids, which are critical for normal cell function. However, a number of important questions about the reactivity and mechanism of these enzymes still remain. Specifically, although the initial step in the mechanism of LOXs has been well studied, little is known of subsequent steps. Thus, with use of a quantum mechanical/molecular mechanical approach, the complete catalytic mechanism of (8R)-LOX was investigated. The results have provided a better understanding of the general chemistry of LOXs as a whole. In particular, from comparisons with soybean LOX-1, it appears that the initial proton-coupled electron transfer may be very similar among all LOXs. Furthermore, LOXs appear to undergo multistate reactivity where potential spin inversion of an electron may occur either in the attack of O(2) or in the regeneration of the active site. Lastly, it is shown that with the explicit modeling of the environment, the regeneration of the active center likely occurs via the rotation of the intermediate followed by an outer-sphere [Formula: see text] transfer as opposed to the formation of a "purple intermediate" complex.

Multiple-site concerted proton-electron transfer reactions of hydrogen-bonded phenols are nonadiabatic and well described by semiclassical Marcus theory

Photo-oxidations of hydrogen-bonded phenols using excited-state polyarenes are described to derive fundamental understanding of multiple-site concerted proton-electron transfer reactions (MS-CPET). Experiments have examined phenol bases having -CPh(2)NH(2), -Py, and -CH(2)Py groups ortho to the phenol hydroxyl group and tert-butyl groups in the 4,6-positions for stability (HOAr-NH(2), HOAr-Py, and HOAr-CH(2)Py, respectively; Py = pyridyl; Ph = phenyl). The photo-oxidations proceed by intramolecular proton transfer from the phenol to the pendent base concerted with electron transfer to the excited polyarene. For comparison, 2,4,6-(t)Bu(3)C(6)H(2)OH, a phenol without a pendent base and tert-butyl groups in the 2,4,6-positions, has also been examined. Many of these bimolecular reactions are fast, with rate constants near the diffusion limit. Combining the photochemical k(CPET) values with those from prior thermal stopped-flow kinetic studies gives data sets for the oxidations of HOAr-NH(2) and HOAr-CH(2)Py that span over 10(7) in k(CPET) and nearly 0.9 eV in driving force (ΔG(o)'). Plots of log(k(CPET)) vs ΔG(o)', including both excited-state anthracenes and ground state aminium radical cations, define a single Marcus parabola in each case. These two data sets are thus well described by semiclassical Marcus theory, providing a strong validation of the use of this theory for MS-CPET. The parabolas give λ(CPET) ≅ 1.15-1.2 eV and H(ab) ≅ 20-30 cm(-1). These experiments represent the most direct measurements of H(ab) for MS-CPET reactions to date. Although rate constants are available only up to the diffusion limit, the parabolas clearly peak well below the adiabatic limit of ca. 6 × 10(12) s(-1). Thus, this is a very clear demonstration that the reactions are nonadiabatic. The nonadiabatic character slows the reactions by a factor of ~45. Results for the oxidation of HOAr-Py, in which the phenol and base are conjugated, and for oxidation of 2,4,6-(t)Bu(3)C(6)H(2)OH, which lacks a base, show that both have substantially lower λ and larger pre-exponential terms. The implications of these results for MS-CPET reactions are discussed.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

"Pump-probe" atom-centered density matrix propagation studies to gauge anharmonicity and energy repartitioning in atmospheric reactive adducts: case study of the OH + isoprene and OH + butadiene reaction intermediates

Time-resolved "pump-probe" ab initio molecular dynamics studies are constructed to probe the stability of reaction intermediates, the mechanism of energy transfer, and energy repartitioning, for moieties involved during the interaction of volatile organic compunds with hydroxyl radical. These systems are of prime importance in the atmosphere. Specifically, the stability of reaction intermediates of hydroxyl radical adducts to isoprene and butadiene molecules is used as a case study to develop novel computational techniques involving "pump-probe" ab initio molecular dynamics. Starting with the various possible hydroxyl radical adducts to isoprene and butadiene, select vibrational modes of each of the adducts are populated with excess energy to mimic the initial conditions of an experiment. The flow of energy into the remaining modes is then probed by subjecting the excited adducts to ab initio molecular dynamics simulations. It is found that the stability of the adducts arises directly due to the anhormonically driven coupling of the modes to facilitate repartitioning of the excess vibrational energy. This kind of vibrational repartitioning has a critical influence on the energy density.

Car-Parrinello simulation of the vibrational spectrum of a medium strong hydrogen bond by two-dimensional quantization of the nuclear motion: application to 2-hydroxy-5-nitrobenzamide

The nature of medium strong intra- and intermolecular hydrogen bonding in 2-hydroxy-5-nitrobenzamide in the crystal phase was examined by infrared spectroscopy and Car-Parrinello molecular dynamics simulation. The focal point of our study was the part of the infrared spectra associated with the O-H and N-H stretching modes that are very sensitive to the strength of hydrogen bonding. For spectra calculations we used an isolated dimer and the fully periodic crystal environment. We calculated the spectra by using harmonic approximation, the time course of the dipole moment function as obtained from the Car-Parrinello simulation, and the quantization of the nuclear motion of the proton for an instantaneous snapshot of the structures in one and two dimensions. Although quantitative assessment of the agreement between the computed and experimental band contour is difficult due to the fact that the experimental band is very broad, we feel that the most reasonable qualitative agreement with the experiment is obtained from snapshot structures and two-dimensional quantization of the proton motion. We have also critically examined the methods of constructing the one-dimensional proton potential. Perspectives are given for the treatment of nuclear quantum effects in biocatalysis.

Probing quantum and dynamic effects in concerted proton-electron transfer reactions of phenol-base compounds

The oxidation of three phenols, which contain an intramolecular hydrogen bond to a pendent pyridine or amine group, has been shown, in a previous experimental study, to undergo concerted proton-electron transfer (CPET). In this reaction, the electron is transferred to an outer-sphere oxidant, and the proton is transferred from the oxygen to nitrogen atom. In the present study, this reaction is studied computationally using a version of Hammes-Schiffer's multistate continuum theory where CPET is formulated as a transmission frequency between neutral and cation vibrational-electronic states. The neutral and cation proton vibrational wave functions are computed from one-dimensional potential energy surfaces (PESs) for the transferring proton in a fixed heavy atom framework. The overlap integrals for these neutral/cation wave functions, considering several initial (i.e., neutral) and final (i.e., cation) vibrational states, are used to evaluate the relative rates of oxidation. The analysis is extended to heavy atom configurations with various proton donor-acceptor (i.e., O-N) distances to assess the importance of heavy atom "gating". Such changes in d(ON) dramatically affect the nature of the proton PESs and wave functions. Surprisingly, the most reactive configurations have similar donor-acceptor distances despite the large (~0.2 Å) differences in the optimized structures. These theoretical results qualitatively reproduce the experimental faster reactivity of the reaction of the pyridyl derivative 1 versus the CH(2)-pyridyl 2, but the computed factor of 5 is smaller than the experimental 10(2). The amine derivative is calculated to react similarly to 1, which does not agree with the experiments, likely due to some of the simplifying assumptions made in applying the theory. The computed kinetic isotope effects (KIEs) and their temperature dependence are in agreement with experimental results.

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

Protein dynamics and enzyme catalysis: insights from simulations

The role of protein dynamics in enzyme catalysis is one of the most active and controversial areas in enzymology today. Some researchers claim that protein dynamics are at the heart of enzyme catalytic efficiency, while others state that dynamics make no significant contribution to catalysis. What is the biochemist - or student - to make of the ferocious arguments in this area? Protein dynamics are complex and fascinating, as molecular dynamics simulations and experiments have shown. The essential question is: do these complex motions have functional significance? In particular, how do they affect or relate to chemical reactions within enzymes, and how are chemical and conformational changes coupled together? Biomolecular simulations can analyse enzyme reactions and dynamics in atomic detail, beyond that achievable in experiments: accurate atomistic modelling has an essential part to play in clarifying these issues. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.