Volume 137, Issue 7, 21 August 2012

The conformational diversity of ATP/Mg:ATP in motor proteins was investigated using molecular dynamics and data mining. Adenosine triphosphate (ATP) conformations were found to be constrained mostly by inter cavity motifs in the motor proteins. It is demonstrated that ATP favors extended conformations in the tight pockets of motor proteins such as F1ATPase and actin whereas compact structures are favored in motor proteins such as RNA polymerase and DNA helicase. The incorporation of Mg ^{2+} leads to increased flexibility of ATP molecules. The differences in the conformational dynamics of ATP/Mg:ATP in various motor proteins was quantified by the radius of gyration. The relationship between the simulation results and those obtained by data mining of motor proteins available in the protein data bank is analyzed. The data mining analysis of motor proteins supports the conformational diversity of the phosphate group of ATP obtained computationally.
 ARTICLES

 Theoretical Methods and Algorithms

Conical intersection seams in polyenes derived from their chemical composition
View Description Hide DescriptionThe knowledge of conical intersection seams is important to predict and explain the outcome of ultrafast reactions in photochemistry and photobiology. They define the energetic lowlying reachable regions that allow for the ultrafast nonradiative transitions. In complex molecules it is not straightforward to locate them. We present a systematic approach to predict conical intersection seams in multifunctionalized polyenes and their sensitivity to substituent effects. Included are seams that facilitate the photoreaction of interest as well as seams that open competing loss channels. The method is based on the extended twoelectron twoorbital method [A. Nenov and R. de VivieRiedle, J. Chem. Phys.135, 034304 (2011)]. It allows to extract the lowlying regions for nonradiative transitions, which are then divided into small linear segments. Rules of thumb are introduced to find the support points for these segments, which are then used in a linear interpolation scheme for a first estimation of the intersection seams. Quantum chemical optimization of the linear interpolated structures yields the final energetic position. We demonstrate our method for the example of the electrocyclic isomerization of trifluoromethylpyrrolylfulgide.

Selfconsistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields
View Description Hide DescriptionA selfconsistent method is presented for the calculation of the local dielectricpermittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute/liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum proteinelectrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for onthefly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with fielddependent dielectric response.

A derivation of the master equation from path entropy maximization
View Description Hide DescriptionThe master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarsegraining assumptions. Here instead, we derive nthorder Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochastic model, an nthorder Markov process emerges as the unique maximum entropy solution to this otherwise underdetermined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from the first principles.

Formulation and implementation of a unitary group adapted state universal multireference coupled cluster (UGASUMRCC) theory: Excited and ionized state energies
View Description Hide DescriptionThe traditional state universal multireference coupled cluster (SUMRCC) theory uses the JeziorskiMonkhorst (JM) based Ansatz of the wave operator: Ω = ∑_{μ}Ω_{μ}ϕ_{μ}⟩⟨ϕ_{μ}, where Ω_{μ} = exp (T _{μ}) is the cluster representation of the component of Ω inducing virtual excitations from the model function ϕ_{μ}. In the first formulations, ϕ_{μ}s were chosen to be single determinants and T _{μ}s were defined in terms of spinorbitals. This leads to spincontamination for the nonsinglet cases. In this paper, we propose and implement an explicitly spinfree realization of the SUMRCC theory. This method uses spinfree unitary generators in defining the cluster operators, {T _{μ}}, which even at singlesdoubles truncation, generates noncommuting cluster operators. We propose the use of normalordered exponential parameterization for Ω:∑_{μ}{exp (T _{μ})}ϕ_{μ}⟩⟨ϕ_{μ}, where {} denotes the normal ordering with respect to a common closed shell vacuum which makes the “direct term” of the SUMRCC equations terminate at the quartic power. We choose our model functions {ϕ_{μ}} as unitary group adapted (UGA) Gel'fand states which is why we call our theory UGASUMRCC. In the spirit of the original SUMRCC, we choose exactly the right number of linearly independent cluster operators in {T _{μ}} such that no redundancies in the virtual functions are involved. Using example applications for electron detached/attached and hp excited states relative to a closed shell ground state we discuss how to choose the most compact and nonredundant cluster operators. Although there exists a more elaborate spinadapted JMlike ansatz of Datta and Mukherjee (known as combinatoric openshell CC (COSCC), its working equations are more complex. Results are compared with those from COSCC, equation of motion coupled cluster methods, restricted openshell HartreeFock coupled cluster, and full configuration interaction. We observe that our results are more accurate with respect to most other theories as a result of the use of the cluster expansion structure for our wave operator. Our results are comparable to those from the more involved COSCC, indicating that our theory captures the most important aspects of physics with a considerably simpler scheme.

A generalized any particle propagator theory: Assessment of nuclear quantum effects on electron propagator calculations
View Description Hide DescriptionIn this work we propose an extended propagator theory for electrons and other types of quantum particles. This new approach has been implemented in the LOWDIN package and applied to sample calculations of atomic and small molecular systems to determine its accuracy and performance. As a first application of the method we have studied the nuclear quantum effects on electron ionization energies. We have observed that ionization energies of atoms are similar to those obtained with the electron propagator approach. However, for molecular systems containing hydrogen atoms there are improvements in the quality of the results with the inclusion of nuclear quantum effects. An energy term analysis has allowed us to conclude that nuclear quantum effects are important for zero order energies whereas propagator results correct the electron and electronnuclear correlation terms. Results presented for a series of nalkanes have revealed the potential of this method for the accurate calculation of ionization energies of a wide variety of molecular systems containing hydrogen nuclei. The proposed methodology will also be applicable to exotic molecular systems containing positrons or muons.

Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses
View Description Hide DescriptionIn the first paper of this series [S. Torquato, J. Chem. Phys.136, 054106 (2012)10.1063/1.3679861], analytical results concerning the continuum percolation of overlapping hyperparticles in ddimensional Euclidean space were obtained, including lower bounds on the percolation threshold. In the present investigation, we provide additional analytical results for certain cluster statistics, such as the concentration of kmers and related quantities, and obtain an upper bound on the percolation threshold η_{ c }. We utilize the tightest lower bound obtained in the first paper to formulate an efficient simulation method, called the rescaledparticle algorithm, to estimate continuum percolation properties across many space dimensions with heretofore unattained accuracy. This simulation procedure is applied to compute the threshold η_{ c } and associated mean number of overlaps per particle for both overlapping hyperspheres and oriented hypercubes for 3 ⩽ d ⩽ 11. These simulations results are compared to corresponding upper and lower bounds on these percolation properties. We find that the bounds converge to one another as the space dimension increases, but the lower bound provides an excellent estimate of η_{ c } and , even for relatively low dimensions. We confirm a prediction of the first paper in this series that lowdimensional percolation properties encode highdimensional information. We also show that the concentration of monomers dominate over concentration values for higher order clusters (dimers, trimers, etc.) as the space dimension becomes large. Finally, we provide accurate analytical estimates of the pair connectedness function and blocking function at their contact values for any d as a function of density.

Particle dynamics simulations of Turing patterns
View Description Hide DescriptionThe direct simulation Monte Carlo method is used to reproduce Turing patterns at the microscopic level in reactiondiffusion systems. In order to satisfy the basic condition for the development of such a spatial structure, we propose a model involving a solvent, which allows for disparate diffusivities of individual reactive species. Onedimensional structures are simulated in systems of various lengths. Simulation results agree with the macroscopic predictions obtained by integration of the reactiondiffusion equations. Additional effects due to internal fluctuations are observed, such as temporal transitions between structures of different wavelengths in a confined system. For a structure developing behind a propagating wave front, the fluctuations suppress the induction period and accelerate the formation of the Turing pattern. These results support the ability of reactiondiffusion models to robustly reproduce axial segmentation including the formation of early vertebrae or somites in noisy biological environments.

Gauge invariance of the nuclear spin/electron orbit interaction and NMR spectral parameters
View Description Hide DescriptionA gauge transformation of the vector potential , associated to the magnetic dipole m _{ I } of nucleus I in a molecule, has been studied. The conditions for gauge invariance of nuclear magnetic shielding, nuclear spin/electron orbit contribution to spinspin coupling between two nuclei, I and J, and electronic current density induced by m _{ I }, have been expressed via quantum mechanical sum rules that are identically satisfied for exact and optimal variational wavefunctions. It is shown that separate diamagnetic and paramagnetic contributions to the properties transform into one another in the gauge transformation, whereas their sum is invariant. Therefore, only total response properties have a physical meaning. In particular, the disjoint diamagnetic and paramagnetic components of nuclear spin/electron orbit contributions to coupling constants are not uniquely defined. The diamagnetic contribution to the nuclear spinspin coupling tensor, evaluated as an expectation value in the Ramsey theory, can alternatively be expressed as a sumoverstates formula, by rewriting the secondorder Hamiltonian in commutator form à la Geertsen, as previously reported by Sauer. Other sumoverstates formulae are obtained via a gauge transformation, by a procedure formally allowing for a continuous translation of the origin of the m _{ I }induced current density, analogous to those previously proposed for magnetizabilities and nuclear magnetic shielding.

Thermodynamics and kinetics of bubble nucleation: Simulation methodology
View Description Hide DescriptionThe simulation of homogeneous liquid to vapor nucleation is investigated using three rareevent algorithms, boxed molecular dynamics, hybrid umbrella sampling Monte Carlo, and forward flux sampling. Using novel implementations of these methods for efficient use in the isothermalisobaric ensemble, the free energy barrier to nucleation and the kinetic rate are obtained for a LennardJones fluid at stretched and at superheated conditions. From the free energy surface mapped as a function of two order parameters, the global density and largest bubble volume, we find that the free energy barrier height is larger when projected over bubble volume. Using a regression analysis of forward flux sampling results, we show that bubble volume is a more ideal reaction coordinate than global density to quantify the progression of the metastable liquid toward the stable vapor phase and the intervening free energy barrier. Contrary to the assumptions of theoretical approaches, we find that the bubble takes on cohesive nonspherical shapes with irregular and (sometimes highly) undulating surfaces. Overall, the resulting free energy barriers and rates agree well between the methods, providing a set of complementary algorithms useful for studies of different types of nucleation events.

Electron transfer through a single barrier inside a molecule: From strong to weak coupling
View Description Hide DescriptionIn all theoretical treatments of electron transport through single molecules between two metal electrodes, a clear distinction has to be made between a coherent transport regime with a strong coupling throughout the junction and a Coulomb blockade regime in which the molecule is only weakly coupled to both leads. The former case where the tunnelling barrier is considered to be delocalized across the system can be well described with common meanfield techniques based on density functional theory(DFT), while the latter case with its two distinct barriers localized at the interfaces usually requires a multideterminant description. There is a third scenario with just one barrier localized inside the molecule, which we investigate here using a variety of quantumchemical methods by studying partial charge shifts in biphenyl radical ions induced by an electric field at different angles to modulate the coupling and thereby the barrier within the πsystem. We find steps rounded off at the edges in the charge versus field curves for weak and intermediate coupling, whose accurate description requires a correct treatment of both exchange and dynamical correlation effects is essential. We establish that DFT standard functionals fail to reproduce this feature, while a long range corrected hybrid functional fares much better, which makes it a reasonable choice for a proper DFTbased transport description of such single barrier systems.

Energy extrapolation schemes for adaptive multiscale molecular dynamics simulations
View Description Hide DescriptionThis paper evaluates simple schemes to extrapolate potential energy values using the set of energies and forces extracted from a molecular dynamics trajectory. In general, such a scheme affords the maximum amount of information about a molecular system at minimal computational cost. More specifically, schemes like this are very important in the field of adaptive multiscale molecular dynamics simulations. In this field, often the computation of potential energy values at certain trajectory points is not required for the simulation itself, but solely for the a posteriorianalysis of the simulation data. Extrapolating the values at these points from the available data can save considerable computational time. A set of extrapolation schemes are employed based on Taylor series and central finite difference approximations. The schemes are first tested on the trajectories of molecular systems of varying sizes, obtained at MM and QM level using velocityVerlet integration with standard simulation time steps. Remarkably good accuracy was obtained with some of the approximations, while the failure of others can be explained in terms of the distinct features of a molecular dynamics trajectory. We have found that, for a Taylor expansion of the potential energy, both a first and a second order truncation exhibit errors that grow with system size. In contrast, the second order central finite difference approximation displays an accuracy that is independent of the size of the system, while giving a very good estimate of the energy, and costing as little as a first order truncation of the Taylor series. A fourth order central finite difference approximation requires more input data, which is not always available in adaptive multiscale simulations. Furthermore, this approximation gives errors of similar magnitude or larger than its second order counterpart, at standard simulation time steps. This leads to the conclusion that a second order central finite difference approximation is the optimal choice for energy extrapolation from molecular dynamics trajectories. This finding is confirmed in a final application to the analysis of an adaptive multiscale simulation.

Multipartite quantum entanglement evolution in photosynthetic complexes
View Description Hide DescriptionWe investigate the evolution of entanglement in the FennaMatthewOlson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.

Dynamical quantumelectrodynamics embedding: Combining timedependent density functional theory and the nearfield method
View Description Hide DescriptionWe develop an approach for dynamical (ω > 0) embedding of mixed quantum mechanical (QM)/classical (or more precisely QM/electrodynamics) systems with a quantum subregion, described by timedependent density functional theory (TDDFT), within a classical subregion, modeled here by the recently proposed nearfield (NF) method. Both subsystems are propagated simultaneously and are coupled through a common Coulomb potential. As a first step we implement the method to study the plasmonic response of a metalfilm which is half jelliumlike QM and half classical. The resulting response is in good agreement with both fullscale TDDFT and the purely classical NF method. The embedding method is able to describe the optical response of the whole system while capturing quantum mechanical effects, so it is a promising approach for studying electrodynamics in hybrid moleculesmetals nanostructures.

Response theory for confined systems
View Description Hide DescriptionIn this work, we use the transient time correlation function (TTCF) method to evaluate the response of a fluid confined in a nanopore and subjected to shear. The shear is induced by the movement of the boundaries in opposite directions and is made of moving atoms. The viscous heat generated inside the pore is removed by a thermostat applied exclusively to the atomic walls, so as to leave the dynamics of the fluid purely Newtonian. To establish a link with nonlinear response theory and apply the TTCF formalism, dissipation has to be generated inside the system. This dissipation is then time correlated with a phase variable of interest (e.g., pressure) to obtain its response. Until recently, TTCF has been applied to homogeneous fluids whose equations of motion were coupled to a mechanical field and a thermostat. In our system dissipation is generated by a boundary condition rather than a mechanical field, and we show how to apply TTCF to these realistic confined systems, comparing the shear stress response so obtained with that of homogeneous systems at equivalent state points.

Incorporation of quantum effects for selected degrees of freedom into the trajectorybased dynamics using spatial domains
View Description Hide DescriptionThe approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the MadelungdeBroglieBohm formulation of timedependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the “quantum” degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for twodimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.

Rapid topography mapping of scalar fields: Large molecular clusters
View Description Hide DescriptionAn efficient and rapid algorithm for topography mapping of scalar fields, molecular electron density (MED) and molecular electrostatic potential (MESP) is presented. The highlight of the work is the use of fast function evaluation by Deformedatomsinmolecules (DAM) method. The DAM method provides very rapid as well as sufficiently accurate function and gradient evaluation. For mapping the topography of large systems, the molecular tailoring approach (MTA) is invoked. This new code is tested out for mapping the MED and MESP critical points (CP’s) of small systems. It is further applied to large molecular clusters viz. (H_{2}O)_{25}, (C_{6}H_{6})_{8} and also to a unit cell of valine crystal at MP2/631+G(d) level of theory. The completeness of the topography is checked by extensive search as well as applying the PoincaréHopf relation. The results obtained show that the DAM method in combination with MTA provides a rapid and efficient route for mapping the topography of large molecular systems.

Effect of strong electron correlation on the efficiency of photosynthetic light harvesting
View Description Hide DescriptionResearch into the efficiency of photosynthetic light harvesting has focused on two factors: (1) entanglement of chromophores, and (2) environmental noise. While chromophores are conjugated πbonding molecules with strongly correlated electrons, previous models have treated this correlation implicitly without a mathematical variable to gauge correlationenhanced efficiency. Here we generalize the singleelectron/exciton models to a multielectron/exciton model that explicitly shows the effects of enhanced electron correlation within chromophores on the efficiency of energy transfer. The model provides more detailed insight into the interplay of electron correlation within chromophores and electron entanglement between chromophores. Exploiting this interplay is assisting in the design of new energyefficient materials, which are just beginning to emerge.
 Atoms, Molecules, and Clusters

Optical Zeeman spectroscopy of the (0,0) B ^{4}Γ – X ^{4}Φ band systems of titanium monohydride, TiH, and titanium monodeuteride, TiD
View Description Hide DescriptionThe Zeeman effect in the (0,0) bands of the B ^{4}Γ_{5/2} – X ^{4}Φ_{3/2} system of titanium monohydride, TiH, and titanium monodeuteride, TiD, has been recorded and analyzed. Magnetic tuning of the spectral features recorded at high resolution (full width at half maximum ≅ 35 MHz) and at a field strength of 4.5 kG is accurately modeled using an effective Zeeman Hamiltonian. The determined magnetic gfactors for the X ^{4}Φ_{3/2} (v = 0) state deviate only slightly from those expected for an isolated ^{4}Φ_{3/2} state whereas those for the B ^{4}Γ_{5/2}(v = 0) deviate significantly from those of an isolated ^{4}Γ_{5/2} state. The rotational dependence of the magnetic tuning in the B ^{4}Γ_{5/2}(v = 0) state is attributed to perturbations from a nearby ^{4}Φ state.

Direct measurement of Sbranch N_{2}H_{2} Raman linewidths using timeresolved pure rotational coherent antiStokes Raman spectroscopy
View Description Hide DescriptionSbranch N_{2}H_{2} Raman linewidths have been measured in the temperature region 294–1466 K using timeresolved dualbroadband picosecond pure rotational coherent antiStokes Raman spectroscopy (RCARS). Data are extracted by mapping the dephasing rates of the CARS signal temporal decay. The Jdependent coherence decays are detected in the time domain by following the individual spectral lines as a function of probe delay. The linewidth data set was employed in spectral fits of N_{2} RCARS spectra recorded in binary mixtures of N_{2} and H_{2} at calibrated temperature conditions up to 661 K using a standard nanosecond RCARS setup. In this region, the set shows a deviation of less than 2% in comparison with thermocouples. The results provide useful knowledge for the applicability of N_{2}CARS thermometry on the fuelside of H_{2} diffusion flames.

A combined spectroscopic and theoretical study of propofol·(H_{2}O)_{3}
View Description Hide DescriptionPropofol (2,6diisopropylphenol) is probably the most widely used general anesthetic. Previous studies focused on its complexes containing 1 and 2 water molecules. In this work, propofol clusters containing three water molecules were formed using supersonic expansions and probed by means of a number of massresolved laser spectroscopic techniques. The 2color REMPI spectrum of propofol·(H_{2}O)_{3} contains contributions from at least two conformational isomers, as demonstrated by UV/UV hole burning. Using the infrared IR/UV double resonance technique, the IR spectrum of each isomer was obtained both in ground and first excited electronic states and interpreted in the light of density functional theory (DFT) calculations at M062X/6311++G(d,p) and B3LYP/6311++G(d,p) levels. The spectral analysis reveals that in both isomers the water molecules are forming cyclic hydrogen bond networks around propofol's OH moiety. Furthermore, some evidences point to the existence of isomerization processes, due to a complicated conformational landscape and the existence of multiple paths with low energy barriers connecting the different conformers. Such processes are discussed with the aid of DFT calculations.