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On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation.

We present an efficient path integral approach for evaluating thermal rate constants within the quantum instanton (QI) approximation that was recently introduced to overcome the quantitative deficiencies of the earlier semiclassical instanton approach [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)]. Since the QI rate constant is determined solely by properties of the (quantum) Boltzmann operator (specifically, by the zero time properties of the flux-flux and delta-delta correlation functions), it can be evaluated by well-established techniques of imaginary time path integrals even for quite complex chemical reactions. Here we present a series of statistical estimators for relevant quantities which can be evaluated straightforwardly with any nonlinear reaction coordinates and general Hamiltonians in Cartesian space. To facilitate the search for the optimal dividing surfaces required by the QI approximation, we introduce a two-dimensional quantum free energy surface associated with the delta-delta correlation function and describe how an adaptive umbrella sampling can be used effectively to construct such a free energy surface. The overall computational procedure is illustrated by the application to a hydrogen exchange reaction in gas phase, which shows excellent agreement of the QI rates with those obtained from quantum scattering calculations.

Journal Article↗

Potentials and pitfalls of fluorescent quantum dots for biological imaging.

Fluorescent semiconductor nanocrystals, known as quantum dots (QDs), have several unique optical and chemical features. These features make them desirable fluorescent tags for cell and developmental biological applications that require long-term, multi-target and highly sensitive imaging. The improved synthesis of water-stable QDs, the development of approaches to label cells efficiently with QDs, and improvements in conjugating QDs to specific biomolecules have triggered the recent explosion in their use in biological imaging. Although there have been many successes in using QDs for biological applications, limitations remain that must be overcome before these powerful tools can be used routinely by biologists.

Biophysics↗

Quantum dot-based protein imaging and functional significance of two mitochondrial chaperones in cellular senescence and carcinogenesis.

Mortalin/mtHSP70 and HSP60 are heat-shock proteins that reside in multiple subcellular compartments, mitochondria being the dominant compartment. We present here biochemical evidence for their in vivo and in vitro interactions. By the use of quantum dots (powerful tools used for simultaneous imaging of multiple proteins), we visualized minute differences in the subcellular niche of these two proteins in normal and cancer cells. Knockdown of either of these two by shRNA expression plasmids caused growth arrest of osteosarcoma cells. However, interestingly, whereas an overexpression of mortalin extended in vitro life span of normal fibroblasts (TIG-1), overexpression of HSP60 was neutral. We demonstrate the minute differences in subcellular distribution of mortalin and HSP60, their involvement in tumorigenesis, and functional distinction in pathways involved in senescence.

Cell Culture Techniques↗

Quantum hydrodynamics: application to N-dimensional reactive scattering.

The quantum hydrodynamic equations associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a new methodology which gives an accurate, unitary, and stable propagation of a time dependent quantum wave packet [B. K. Kendrick, J. Chem. Phys. 119, 5805 (2003)]. The methodology is applied to an N-dimensional model chemical reaction with an activation barrier. A parallel version of the methodology is presented which is designed to run on massively parallel supercomputers. The computational scaling properties of the parallel code are investigated both as a function of the number of processors and the dimension N. A decoupling scheme is introduced which decouples the multidimensional quantum hydrodynamic equations into a set of uncoupled one-dimensional problems. The decoupling scheme dramatically reduces the computation time and is highly parallelizable. Furthermore, the computation time is shown to scale linearly with respect to the dimension N=2,...,100.

Journal Article↗

Femtosecond studies of charge-transfer mediated proton transfer in 2-butylamino-6-methyl-4-nitropyridine N-oxide.

We have unraveled the effects of an amino substituent in the ortho position on the excited-state dynamics of 4-nitropyridine N-oxide by studying the picosecond fluorescence kinetics and femtosecond transient absorption of a newly synthesized compound, 2-butylamino-6-methyl-4-nitropyridine N-oxide, and by quantum chemical calculations. Similar to the parent compound, the S(1) state of the target molecule has significant charge-transfer character and shows a large (approximately 8000 cm(-1)) static Stokes shift in acetonitrile. Analysis of the experimental and the theoretical results leads, however, to a new scenario in which this intramolecular charge transfer triggers in polar, aprotic solvents an ultrafast (around 100 fs) intramolecular proton transfer between the amino and the N-O group. The electronically excited N-OH tautomer is subsequently subject to solvent relaxation and decays with a lifetime of approximately 150 ps to the ground state.

Computer Simulation↗

Fully adaptive propagation of the quantum-classical Liouville equation.

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Journal Article↗

The use of quantum molecular calculations to guide a genetic algorithm: a way to search for new chemistry.

The process of gene-based molecular evolution has been simulated in silico by using massively parallel density functional theory quantum calculations, coupled with a genetic algorithm, to test for fitness with respect to a target chemical reaction in populations of genetically encoded molecules. The goal of this study was the identification of transition-metal complexes capable of mediating a known reaction, namely the cleavage of N(2) to give the metal nitride. Each complex within the search space was uniquely specified by a nanogene consisting of an eight-digit number. Propagation of an individual nanogene into successive generations was determined by the fitness of its phenotypic molecule to perform the target reaction and new generations were created by recombination and mutation of surviving nanogenes. In its simplest implementation, the quantum-directed genetic algorithm (QDGA) quickly located a local minimum on the evolutionary fitness hypersurface, but proved incapable of progressing towards the global minimum. A strategy for progressing beyond local minima consistent with the Darwinian paradigm by the use of environmental variations coupled with mass extinctions was therefore developed. This allowed for the identification of nitriding complexes that are very closely related to known examples from the chemical literature. Examples of mutations that appear to be beneficial at the genetic level but prove to be harmful at the phenotypic level are described. As well as revealing fundamental aspects of molecular evolution, QDGA appears to be a powerful tool for the identification of lead compounds capable of carrying out a target chemical reaction.

Algorithms↗

Materials by numbers: computations as tools of discovery.

Current issues pertaining to theoretical simulations of materials, with a focus on systems of nanometer-scale dimensions, are discussed. The use of atomistic simulations as high-resolution numerical experiments, enabling and guiding formulation and testing of analytic theoretical descriptions, is demonstrated through studies of the generation and breakup of nanojets, which have led to the derivation of a stochastic hydrodynamic description. Subsequently, I illustrate the use of computations and simulations as tools of discovery, with examples that include the self-organized formation of nanowires, the surprising nanocatalytic activity of small aggregates of gold that, in the bulk form, is notorious for being chemically inert, and the emergence of rotating electron molecules in two-dimensional quantum dots. I conclude with a brief discussion of some key challenges in nanomaterials simulations.

Biomedical Engineering↗

A semiclassical study of wave packet dynamics in anharmonic potentials.

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.

Journal Article↗

Photoisomerization of disperse red 1 studied with transient absorption spectroscopy and quantum chemical calculations.

The photoisomerization of the push-pull substituted azo dye Disperse Red 1 is studied using femtosecond time-resolved absorption spectroscopy and other spectroscopic and computational techniques. In comparison with azobenzene, the pipi* state is more stabilized by the effects of push-pull substitution than the npi* state, but the latter is probably still the lowest in energy. This conclusion is based on the kinetics, anisotropy of the excited state absorption spectrum, the spectra of the ground states, and quantum chemical calculations. The S(1)(npi*) state is formed from the initially excited pipi* state in <0.2 ps, and decays to the ground state with time constants of 0.9 ps in toluene, 0.5 ps in acetonitrile, and 1.4 ps in ethylene glycol. Thermal isomerization transforms the Z isomer produced to the more stable E isomer with time constants of 29 s (toluene), 28 ms (acetonitrile), and 2.7 ms (ethylene glycol). The pathway of photoisomerization is likely to be rotation about the N=N bond. Quantum chemical calculations indicate that along the inversion pathway ground and excited state energy surfaces remain well separated, whereas rotation leads to a region where conical intersections can occur. For the ground-state Z to E isomerization, conclusive evidence is lacking, but inversion is more probably the favored pathway in the push-pull substituted systems than in the parent azobenzene.

Azo Compounds↗

Propagation with distributed Gaussians as a sparse, adaptive basis for higher-dimensional quantum dynamics.

A simple quantum wavepacket propagation algorithm is presented, designed to produce a very compact, non-direct product representation in higher-dimensional cases. Instead of moving basis functions around, localized basis functions at pre-defined centers are added to and deleted from the representation, generating an active basis function set strictly localized to the region where the moving wavepacket has significantly non-zero values. Simple one-dimensional examples prove this property, as well as the ability of the algorithm to accommodate splitting and rejoining of an arbitrary number of wavefunction pieces, and tunnelling through potential energy barriers. It is argued that future applications to higher-dimensional examples will be less expensive than with traditional direct-product bases, since making the basis adaptive has a lower scaling than the elementary steps necessary for any propagation algorithm itself.

Algorithms↗

Modeling heme proteins using atomistic simulations.

Heme proteins are found in all living organisms, and perform a wide variety of tasks ranging from electron transport, to the oxidation of organic compounds, to the sensing and transport of small molecules. In this work we review the application of classical and quantum-mechanical atomistic simulation tools to the investigation of several relevant issues in heme proteins chemistry: (i) conformational analysis, ligand migration, and solvation effects studied using classical molecular dynamics simulations; (ii) electronic structure and spin state energetics of the active sites explored using quantum-mechanics (QM) methods; (iii) the interaction of heme proteins with small ligands studied through hybrid quantum mechanics-molecular mechanics (QM-MM) techniques; (iv) and finally chemical reactivity and catalysis tackled by a combination of quantum and classical tools.

Computer Simulation↗

Structures and stabilities of diacetylene-expanded polyhedranes by quantum mechanics and molecular mechanics.

The structures, heats of formation, and strain energies of diacetylene (buta-1,3-diynediyl) expanded molecules have been computed with ab initio and molecular mechanics calculations. Expanded cubane, prismane, tetrahedrane, and expanded monocyclics and bicyclics were optimized at the HF/6-31G(d) and B3LYP/6-31G(d) levels. The heats of formation of these systems were obtained from isodesmic equations at the HF/6-31G(d) level. Heats of formation were also calculated from Benson group equivalents. The strain energies of these expanded molecules were estimated by several independent methods. An adapted MM3 molecular mechanics force field, specifically parametrized to treat conjugated acetylene units, was employed for one measure of strain energy and as an additional method for structural analysis. Expanded dodecahedrane and icosahedrane were calculated by this method. Expanded molecules were considered structurally in the context of their potential material applications.

Acetylene↗

A new force field (ECEPP-05) for peptides, proteins, and organic molecules.

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.

Algorithms↗

Dynamics of (H(-), H(2)) collisions: a time-dependent quantum mechanical investigation on a new ab initio potential energy surface.

A global analytical potential energy surface for the ground state of H(3)(-) has been constructed by fitting an analytic function to the ab initio potential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning's augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, time-dependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities (P(R)) for the exchange reaction H(-)+H(2)(v, j)-->H(2)+H(-), for different initial vibrational (v) and rotational (j) states of H(2), for total angular momentum equal to zero. With increase in v, the number of oscillations in the P(R)(E) plot increases and the oscillations become more pronounced. While P(R) increases with increase in rotational excitation from j=0 to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in P(R)(E) plots.

Journal Article↗

Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the alanine dipeptide.

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the conformational equilibrium distribution (CED) of the model dipeptide HCO-L-Ala-NH(2)without any simplifying assumption. We use ab initio quantum mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the potential energy surface that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.

Alanine↗

Effect of aromatic molecules on the aggregation of C-phycocyanin. Quantum chemical calculations on phycocyanobilin and phycoerythrobilin.

The energies of the highest occupied and lowest empty molecular orbitals were calculated for the chromophore groups of the proteins phycocyanin and phycoerythrin. These tetrapyrrole groups on the algal proteins are shown to provide them with the potential of ating as efficient electron donors and acceptors. In addition, the pi electron charges and bond orders were also computed.

Chemical Phenomena↗

Linear scaling approaches to quantum macromolecular similarity: evaluating the similarity function.

The evaluation of the electron density based similarity function scales quadratically with respect to the size of the molecules for simplified, atomic shell densities. Due to the exponential decay of the function's atom-atom terms most interatomic contributions are numerically negligible on large systems. An improved algorithm for the evaluation of the Quantum Molecular Similarity function is presented. This procedure identifies all non-negligible terms without computing unnecessary interatomic squared distances, thus effectively turning to linear scaling the similarity evaluation. Presented also is a minimalist dynamic electron density model. Approximate, single shell densities together with the proposed algorithm facilitate fast electron density based alignments on macromolecules.

Hemoglobins↗