Volume 136, Issue 3, 21 January 2012

The EFhand superfamily of proteins is characterized by the presence of calcium binding helixloophelix structures. Many of these proteins undergo considerable motion responsible for a wide range of properties upon binding but the exact mechanism at the root of this motion is not fully understood. Here, we use an unbiased accelerated multiscale simulation scheme, coupled with two force fields — CHARMMEEF1 and the extended OPEP — to explore in details the closing pathway, from the unbound holo state to the closed apo state, of two EFhand proteins, the Calmodulin and Troponin C Nterminal nodules. Based on a number of closing simulations for these two sequences, we show that the EFhand βscaffold, identified as crucial by Grabarek for the EFhand opening driven by calcium binding, is also important in closing the EFhand. We also show the crucial importance of the phenylalanine situated at the end of first EFhand helix, and identify an intermediate state modulating its behavior, providing a detailed picture of the closing mechanism for these two representatives of EFhand proteins.
 ARTICLES

 Theoretical Methods and Algorithms

Effective homogeneity of the exchange–correlation and noninteracting kinetic energy functionals under density scaling
View Description Hide DescriptionCorrelated electron densities, experimental ionisation potentials, and experimental electron affinities are used to investigate the homogeneity of the exchange–correlation and noninteracting kinetic energy functionals of Kohn–Sham density functional theory under density scaling. Results are presented for atoms and small molecules, paying attention to the influence of the integer discontinuity and the choice of the electron affinity. For the exchange–correlation functional, effective homogeneities are highly systemdependent on either side of the integer discontinuity. By contrast, the average homogeneity—associated with the potential that averages over the discontinuity—is generally close to 4/3 when the discontinuity is computed using positive affinities for systems that do bind an excess electron and negative affinities for those that do not. The proximity to 4/3 becomes increasingly pronounced with increasing atomic number. Evaluating the discontinuity using a zero affinity in systems that do not bind an excess electron instead leads to effective homogeneities on the electron abundant side that are close to 4/3. For the noninteracting kinetic energy functional, the effective homogeneities are less systemdependent and the effect of the integer discontinuity is less pronounced. Average values are uniformly below 5/3. The study provides information that may aid the development of improved exchange–correlation and noninteracting kinetic energy functionals.

Improved selfconsistent and resolutionofidentity approximated Becke'05 density functional model of nondynamic electron correlation
View Description Hide DescriptionIn a recent letter [E. Proynov, Y. Shao, and J. Kong, Chem. Phys. Lett.493, 381 (2010)10.1016/j.cplett.2010.05.029], Becke's B05 model of nondynamic electron correlation in density functional theory was implemented selfconsistently with computational efficiency (the “SCFRIB05” scheme). Important modifications of the algorithm were done in order to make the selfconsistency feasible. In the present work, we give a complete account of the SCFRIB05 algorithm, including all the formulae for the analytical representation of the B05 functional and for its selfconsistent field (SCF) potential. The average performance of the SCFRIB05 method reported in the above letter was somewhat less accurate, compared to the original B05 implementation, mainly because the parameters of the original B05 model were optimized with postlocalspindensity calculations. In this work, we report improved atomization energies with SCFRIB05, based on a SCF reoptimization of its four linear parameters. The reoptimized SCFRIB05 scheme is validated also on reaction barriers, and on the subtle energetics of NO dimer, an exemplary system of strong nondynamic correlation. It yields both the binding energy and the singlettriplet splitting of the NO dimer correctly, and close to the benchmarks reported in the literature.

A new method to generate spinorbit coupled potential energy surfaces: Effective relativistic coupling by asymptotic representation
View Description Hide DescriptionA new method has been developed to generate fully coupled potential energy surfaces including derivative and spinorbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spinorbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.

Higher order alchemical derivatives from coupled perturbed selfconsistent field theory
View Description Hide DescriptionWe present an analytical approach to treat higher order derivatives of HartreeFock (HF) and KohnSham (KS) density functional theory energy in the BornOppenheimer approximation with respect to the nuclear charge distribution (socalled alchemical derivatives). Modified coupled perturbed selfconsistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of KohnSham energy and up to the third derivative of HartreeFock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the “surrounding” molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle
View Description Hide DescriptionThe eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using massaction rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.

Correlation potentials for molecular bond dissociation within the selfconsistent random phase approximation
View Description Hide DescriptionSelfconsistent correlation potentials for H_{2} and LiH for various interatomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exactexchange functional. The latter finding explains the improved total energy in the dissociation limit.

Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach
View Description Hide DescriptionWe develop a new general code to automatically derive exact analytical kinetic energy operators in terms of polyspherical coordinates. Computer procedures based on symbolic calculations are implemented. Sets of orthogonal or nonorthogonal vectors are used to parametrize the molecular systems in space. For each set of vectors, and whatever the size of the system, the exact analytical kinetic energy operator (including the overall rotation and the Coriolis coupling) can be derived by the program. The correctness of the implementation is tested for different sets of vectors and for several systems of various sizes.

Coupling between internal dynamics and rotational diffusion in the presence of exchange between discrete molecular conformations
View Description Hide DescriptionWe present a general formalism for the computation of orientation correlation functions involving a molecular system undergoing rotational diffusion in the presence of transitions between discrete conformational states. In this formalism, there are no proscriptions on the time scales of conformational rearrangement relative to that for rotational diffusion, and the rotational diffusiontensors of the different states can be completely arbitrary. Although closedform results are limited to the frequency domain, this is generally useful for many spectroscopic observables as the result allows the computation of the spectral density function. We specialize the results for the computation of the frequencydomain correlation function associated with the NMR relaxation.

Atomic volumes and polarizabilities in densityfunctional theory
View Description Hide DescriptionBecke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys.124, 014204 (2006)] in order to obtain atominmolecule polarizabilities from freeatom polarizabilities in their nonempirical exchangehole dipole momentmodel of dispersion interactions. Here we explore the dependence of BeckeJohnson atomic volumes on basis sets and densityfunctional approximations and provide reference data for all atoms H–Lr. A persuasive theoretical foundation for the BeckeJohnson definition is also provided.

Nuclear dynamics for a threestate Jahn–Teller model system
View Description Hide DescriptionWe report wavepacket dynamics on a model system with a threestate conical intersection. Quantum wavepacket dynamics using the multiconfigurational timedependent Hartree method have been carried out for the T ⊗ (e + t _{2}) Jahn–Teller problem, using a Jahn–Teller vibronic model Hamiltonian. The effects of the magnitude of the coupling parameters and of the initial position of the wavepacket on the dynamics around the threestate conical intersection have been considered. It was found that the effect of the coupling strength is not dramatic for the population transfer in most cases, but the details of the dynamics and the involvement of the different modes are affected by it.

A block variational procedure for the iterative diagonalization of nonHermitian randomphase approximation matrices
View Description Hide DescriptionWe present a technique for the iterative diagonalization of randomphase approximation (RPA) matrices, which are encountered in the framework of timedependent densityfunctional theory (TDDFT) and the BetheSalpeter equation. The nonHermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na_{2} and Na_{4}) and then used to compute multiple lowlying TDDFT excitation energies of the benzene molecule.

Strongly correlated barriers to rotation from parametric twoelectron reduceddensitymatrix methods in application to the isomerization of diazene
View Description Hide DescriptionRecently, parameterization of the twoelectron reduced density matrix (2RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electronpair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett.101, 253002 (2008)]. We examine the method's performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N_{2}H_{2}) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the antiHermitian contracted Schrödinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.

Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and nonadiabatic quantum dynamics
View Description Hide DescriptionWe present a new approach to calculate realtime quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into “core” and “reservoir” modes with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spinboson problem using the noninteracting blip approximation to treat the system and core, and Ehrenfest dynamics to treat the reservoir. The resulting hybrid methodology is accurate for both fast and slow baths, since it naturally reduces to its composite methods in their respective regimes of validity. In addition, our combined method is shown to yield good results in intermediate regimes where neither approximation alone is accurate and to perform equally well for both strong and weak systembath coupling. Our approach therefore provides an accurate and efficient methodology for calculating quantum dynamics in complex systems.

Dimensional scaling treatment with relativistic corrections for stable multiply charged atomic ions in highfrequency superintense laser fields
View Description Hide DescriptionWe present a theoretical framework which describes multiply charged atomic ions, their stability within superintense laser fields, and also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H^{−}, H^{2 −}, He, He^{−}, He^{2 −}, He^{3 −} within superintense laser fields were completed. Also completed were threedimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind “additional” electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimize the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess electrons into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more costeffective method than the supporting D = 3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in superintense laser fields.

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems
View Description Hide DescriptionCharacterizing the sensitivity to infinitesimally small perturbations in parameters is a powerful tool for the analysis, modeling, and design of chemical reaction networks. Sensitivity analysis of networks modeled using stochastic chemical kinetics, in which a probabilistic description is used to characterize the inherent randomness of the system, is commonly performed using Monte Carlo methods.Monte Carlo methods require large numbers of stochastic simulations in order to generate accurate statistics, which is usually computationally demanding or in some cases altogether impractical due to the overwhelming computational cost. In this work, we address this problem by presenting the regularized pathwise derivative method for efficient sensitivity analysis. By considering a regularized sensitivity problem and using the random time change description for Markov processes, we are able to construct a sensitivity estimator based on pathwise differentiation (also known as infinitesimal perturbationanalysis) that is valid for many problems in stochastic chemical kinetics. The theoretical justification for the method is discussed, and a numerical algorithm is provided to permit straightforward implementation of the method. We show using numerical examples that the new regularized pathwise derivative method (1) is able to accurately estimate the sensitivities for many realistic problems and path functionals, and (2) in many cases outperforms alternative sensitivity methods, including the Girsanov likelihood ratio estimator and common reaction path finite difference method. In fact, we observe that the variance reduction using the regularized pathwise derivative method can be as large as ten orders of magnitude in certain cases, permitting much more efficient sensitivity analysis than is possible using other methods.

Exploring quantum nonlocality with de BroglieBohm trajectories
View Description Hide DescriptionHere in this paper, it is shown how the quantum nonlocality reshapes probability distributions of quantum trajectories in configuration space. By variationally minimizing the ground state energy of helium atom, we show that there exists an optimal nonlocal quantum correlation length which also minimizes the mean integrated square error of the smooth trajectory ensemble with respect to the exact manybody wave function. The nonlocal quantum correlation length can be used for studies of both static and driven manybody quantum systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Reaction dynamics of Mo + O_{2} → MoO + O studied by a crossedbeam velocity map imaging technique
View Description Hide DescriptionThe oxidation reaction dynamics of gasphase molybdenum atoms by oxygen molecules was studied under a crossedbeam condition. The product MoO was detected by a timeofflight mass spectrometer combined with laser multiphoton ionization. An acceleration lens system designed for the ionvelocity mapping condition, a twodimensional (2D) detector, and a timeslicing technique were used to obtain the velocity and angular distributions of the products at three collision energies: 10.0, 17.8, and 50.0 kJ/mol. The angular distributions showed forward and backward peaks, whose relative intensities changed by the collision energy. While two peaks had similar intensities at low collision energies, the forward peak became dominant at the highest collision energy, 50 kJ/mol. The product kinetic energy distributions showed a good correlation with the initial collision energies, i.e., almost the same energy as the collision energy appeared as the product kinetic energy. These results suggested that the reaction proceeds via an intermediate complex, and the lifetime of the complex becomes shorter than its rotational period at high collision energy.

Statetostate photodissociation dynamics of triatomic molecules: H_{2}O in the B band
View Description Hide DescriptionStatetostate photodissociationdynamics of H_{2}O in its B band has been investigated quantum mechanically on a new set of nonadiabatically coupled potential energy surfaces for the lowest two ^{1} A′ states of H_{2}O, which are developed at the internally contracted multireference configuration interaction level with the augccpVQZ basis set. Quantum dynamical calculations carried out using the Chebyshev propagator yield absorption spectra, product state distributions, branching ratios, and differential cross sections, which are in reasonably good agreement with the latest experimental results. Particular focus is placed here on the dependence of various dynamical observables on the photon energy. Detailed analyses of the dynamics have assigned the diffuse structure in absorptionspectrum to shorttime recurring dynamics near the HOH conical intersection. The nonadiabaticdissociation to the ground state OH product via the HOH conical intersection is facile, direct, fast, and produces rotationally hot OH() products. On the other hand, the adiabatic channel on the excited state leading to the OH() product is dominated by longlived resonances, which depend sensitively on the potential energy surfaces.

On the molecular structure of HOOO
View Description Hide DescriptionThe molecular structure of trans, planar hydridotrioxygen (HOOO) has been examined by means of isotopic spectroscopy using Fourier transform microwave as well as microwavemillimeterwave double resonance techniques, and highlevel coupled cluster quantumchemical calculations. Although this weakly bound molecule is readily observed in an electrical discharge of H_{2}O and O_{2} heavily diluted in an inert buffer gas, we find that HOOO can be produced with somewhat higher abundance using H_{2} and O_{2} as precursor gases. Using equal mixtures of normal and ^{18}O_{2}, it has been possible to detect three new isotopic species, H^{18}OOO, HO^{18}O^{18}O, and H^{18}O^{18}O^{18}O. Detection of these species and not others provides compelling evidence that the dominant route to HOOO formation in our discharge is via the reaction OH + O_{2} → HOOO. By combining derived rotational constants with those for normal HOOO and DOOO, it has been possible to determine a fully experimental (r _{0}) structure for this radical, in which all of the structural parameters (the three bond lengths and two angles) have been varied. This bestfit structure possesses a longer central O–O bond (1.684 Å), in agreement with earlier work, a markedly shorter O–H bond distance (0.913 Å), and a more acute ∠HOO angle (92.4°) when compared to equilibrium (r _{ e }) structures obtained from quantumchemical calculations. To better understand the origin of these discrepancies, vibrational corrections have been obtained from coupledcluster calculations. An empirical equilibrium () structure, derived from the experimental rotational constants and theoretical vibrational corrections, gives only somewhat better agreement with the calculated equilibrium structure and large residual inertial defects, suggesting that still higher order vibrational corrections (i.e., γ terms) are needed to properly describe largeamplitude motion in HOOO. Owing to the high abundance of this oxygenchain radical in our discharge expansion, a very wide spectral survey for other oxygenbearing species has been undertaken between 6 and 25 GHz. Only about 50% of the observed lines have been assigned to known hydrogen–oxygen molecules or complexes, suggesting that a rich, unexplored oxygen chemistry awaits detection and characterization. Somewhat surprisingly, we find no evidence in our expansion for rotational transitions of cis HOOO or from lowlying vibrationally excited states of trans HOOO under conditions which optimize its ground state lines.

Dissociative photoionization of methyl chloride studied with threshold photoelectronphotoion coincidence velocity imaging
View Description Hide DescriptionUtilizing threshold photoelectronphotoion coincidence (TPEPICO) velocity imaging, dissociation of stateselected CH_{3}Cl^{+} ions was investigated in the excitation energy range of 11.0–18.5 eV. TPEPICO timeofflight mass spectra and threedimensional timesliced velocity images of CH_{3} ^{+} dissociated from CH_{3}Cl^{+}(A^{2}A_{1} and B^{2}E) ions were recorded. CH_{3} ^{+} was kept as the most dominant fragment ion in the present energy range, while the branching ratio of CH_{2}Cl^{+} fragment was very low. For dissociation of CH_{3}Cl^{+}(A^{2}A_{1}) ions, a series of homocentric rings was clearly observed in the CH_{3} ^{+} image, which was assigned as the excitation of umbrella vibration of CH_{3} ^{+} ions. Moreover, a dependence of anisotropic parameters on the vibrational states of CH_{3} ^{+}(1^{1}A′) provided a direct experimental evidence of a shallow potential well along the C–Cl bond rupture. For CH_{3}Cl^{+}(B^{2}E) ions, total kinetic energy released distribution for CH_{3} ^{+} fragmentation showed a near MaxwellBoltzmann profile, indicating that the Clloss pathway from the B^{2}E state was statistical predissociation. With the aid of calculated Clloss potential energy curves of CH_{3}Cl^{+}, CH_{3} ^{+} formation from CH_{3}Cl^{+}(A^{2}A_{1}) ions was a rapid direct fragmentation, while CH_{3}Cl^{+}(B^{2}E) ions statistically dissociated to CH_{3} ^{+} + Cl via internal conversion to the high vibrational states of X^{2}E.