Volume 140, Issue 6, 14 February 2014

How do lipid molecules in membranes perform a flipflop? The flipflops of lipid molecules play a crucial role in the formation and flexibility of membranes. However, little has been determined about the behavior of flipflops, either experimentally, or in molecular dynamics simulations. Here, we provide numerical results of the flipflops of model lipid molecules in a model membrane and investigate the statistical properties, using millisecondorder coarsegrained molecular simulations (dissipative particle dynamics). We find that there are three different ways of flipflops, which can be clearly characterized by their paths on the free energy surface. Furthermore, we found that the probability of the number of the flipflops is well fitted by the Poisson distribution, and the probability density function for the interoccurrence times of flipflops coincides with that of the forward recurrence times. These results indicate that the occurrence of flipflops is a Poisson process, which will play an important role in the flexibilities of membranes.
 ARTICLES

 Theoretical Methods and Algorithms

Unveiling the hidden structure of complex stochastic biochemical networks
View Description Hide DescriptionComplex Markov models are widely used and powerful predictive tools to analyze stochastic biochemical processes. However, when the network of states is unknown, it is necessary to extract information from the data to partially build the network and estimate the values of the rates. The shorttime behavior of the firstpassage time distributions between two states in linear chains has been shown recently to behave as a power of time with an exponent equal to the number of intermediate states. For a general Markov model we derive the complete Taylor expansion of the firstpassage time distribution between two arbitrary states. By combining algebraic methods and graph theory approaches it is shown that the first term of the Taylor expansion is determined by the shortest path from the initial state to the final state. When this path is unique, we prove that the coefficient of the first term can be written in terms of the product of the transition rates along the path. It is argued that the application of our results to firstreturn times may be used to estimate the dependence of rates on external parameters in experimentally measured time distributions.

Two worlds collide: Image analysis methods for quantifying structural variation in cluster molecular dynamics
View Description Hide DescriptionInspired by methods of remote sensing image analysis, we analyze structural variation in cluster molecular dynamics (MD) simulations through a unique application of the principal component analysis (PCA) and Pearson Correlation Coefficient (PCC). The PCA analysis characterizes the geometric shape of the cluster structure at each time step, yielding a detailed and quantitative measure of structural stability and variation at finite temperature. Our PCC analysis captures bond structure variation in MD, which can be used to both supplement the PCA analysis as well as compare bond patterns between different cluster sizes. Relying only on atomic position data, without requirement for a priori structural input, PCA and PCC can be used to analyze both classical and ab initio MD simulations for any cluster composition or electronic configuration. Taken together, these statistical tools represent powerful new techniques for quantitative structural characterization and isomer identification in cluster MD.

Kinetically constrained ringpolymer molecular dynamics for nonadiabatic chemical reactions
View Description Hide DescriptionWe extend ringpolymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically nonadiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginarytime pathintegral representation in the set of nuclear coordinates and electronic states to provide continuous equations of motion that describe the quantized, electronically nonadiabatic dynamics of the system. KCRPMD preserves the favorable properties of the usual RPMD formulation in the position representation, including rigorous detailed balance, timereversal symmetry, and invariance of reaction rate calculations to the choice of dividing surface. However, the new method overcomes significant shortcomings of positionrepresentation RPMD by enabling the description of nonadiabatic transitions between states associated with general, manyelectron wavefunctions and by accurately describing deeptunneling processes across asymmetric barriers. We demonstrate that KCRPMD yields excellent numerical results for a range of model systems, including a simple avoidedcrossing reaction and condensedphase electrontransfer reactions across multiple regimes for the electronic coupling and thermodynamic driving force.

Combining pathbreaking with bidirectional nonequilibrium simulations to improve efficiency in free energy calculations
View Description Hide DescriptionAn important limitation of unidirectional nonequilibrium simulations is the amount of realizations of the process necessary to reach suitable convergence of free energy estimates via Jarzynski's relationship [C. Jarzynski, Phys. Rev. Lett.78, 2690 (1997)]. To this regard, an improvement of the method has been achieved by means of pathbreaking schemes [R. Chelli et al. , J. Chem. Phys.138, 214109 (2013)] based on stopping highly dissipative trajectories before their normal end, under the founded assumption that such trajectories contribute marginally to the work exponential averages. Here, we combine the pathbreaking scheme, called probability threshold scheme, to bidirectional nonequilibrium methods for free energy calculations [G. E. Crooks, Phys. Rev. E61, 2361 (2000); R. Chelli and P. Procacci, Phys. Chem. Chem. Phys.11, 1152 (2009)]. The method is illustrated and tested on a benchmark system, i.e., the helixcoil transition of decaalanine. By using pathbreaking in our test system, the computer time needed to carry out a series of nonequilibrium trajectories can be reduced up to a factor 4, with marginal loss of accuracy in free energy estimates.

Timedependent pseudo JahnTeller effect: Phononmediated longtime nonadiabatic relaxation
View Description Hide DescriptionOur system under theoretical consideration is an impurity center in a solid. We are considering the time evolution of the center in a quasidegenerate electronic state. Strict quantum mechanical treatment of nonadiabadicity of the state is used. The phonon continuum is taken into account in addition to the vibration responsible for the main vibronic interaction. To describe the dynamics of the excited state a master equation has been used. The theoretical considerations are illustrated by the calculations of the longtime evolution of vibrations of the center, influenced by the emission of phonons to the bulk.

A deterministic thermostat for controlling temperature using all degrees of freedom
View Description Hide DescriptionWe propose a new thermostat that uses all the phase space variables for controlling temperature and thus differs from the existing thermostats that control either the kinetic (e.g., Nose Hoover) or the configurational (e.g., Braga Travis) degrees of freedom. Our thermostat is a special case of the set of equations proposed by Kusnezov et al. [Ann. Phys.204, 155 (1990)] and is derived using the extended system method. We show that it generates a canonical phasespace distribution. The performance of the thermostat is compared with those of NoseHoover kinetic thermostat and BragaTravis configurational thermostat for a system (i) in thermal equilibrium, (ii) subjected to sudden temperature changes, and (iii) in steady state nonequilibrium under thermal conduction. We observe that all three thermostats perform similarly for systems in equilibrium. However, our thermostat performs the best in the thermal conduction problem by generating a consistent temperature profile across the conduction length. We expect this thermostat to be useful in other nonequilibrium scenarios as well.

Transport and dielectric properties of water and the influence of coarsegraining: Comparing BMW, SPC/E, and TIP3P models
View Description Hide DescriptionLongterm molecular dynamics simulations are used to compare the single particle dipole reorientation time, the diffusion constant, the viscosity, and the frequencydependent dielectric constant of the coarsegrained big multipole water (BMW) model to two common atomistic threepoint water models, SPC/E and TIP3P. In particular, the agreement between the calculated viscosity of BMW and the experimental viscosity of water is satisfactory. We also discuss contradictory values for the static dielectric properties reported in the literature. Employing molecular hydrodynamics, we show that the viscosity can be computed from single particle dynamics, circumventing the slow convergence of the standard approaches. Furthermore, our data indicate that the Kivelson relation connecting single particle and collective reorientation time holds true for all systems investigated. Since simulations with coarsegrained force fields often employ extremely large time steps, we also investigate the influence of time step on dynamical properties. We observe a systematic acceleration of system dynamics when increasing the time step. Carefully monitoring energy/temperature conservation is found to be a sufficient criterion for the reliable calculation of dynamical properties. By contrast, recommended criteria based on the ratio of fluctuations of total vs. kinetic energy are not sensitive enough.

A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy
View Description Hide DescriptionUsing the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ) energies, considering the CCSD state as the unperturbed reference state and the fluctuation potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner's 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multipliers. The energy corrections define the CCSD perturbation series, CCSD(T–n) and CCSD(TQ–n), which are termwise size extensive to any order in the perturbation. A detailed comparison of the CCSD(TQ–n) series and the CC(2)PT(n) series of Hirata et al. [J. Chem. Phys.114, 3919 (2001)] has been performed, revealing some deficiencies of the latter related to the target energy of the series and its lack of size extensivity.

Semiexact concentric atomic density fitting: Reduced cost and increased accuracy compared to standard density fitting
View Description Hide DescriptionA local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical “attractive electron” state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem.34, 1486 (2013)] is alleviated by including atomwise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree–Fock theory while still producing results with errors 2–5 times smaller than standard, nonlocal density fitting. Our method allows for large Hartree–Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifactfree potential energy surfaces and the possibility of relatively simple analytic gradients.

Multireference vibration correlation methods
View Description Hide DescriptionStatespecific vibration correlation methods beyond the vibrational multiconfiguration selfconsistent field (VMCSCF) approximation have been developed, which allow for the accurate calculation of state energies for systems suffering from strong anharmonic resonances. Both variational multireference configuration interaction approaches and an implementation of approximate 2nd order vibrational multireference perturbation theory are presented. The variational approach can be significantly accelerated by a configuration selection scheme, which leads to negligible deviations in the final results. Relaxation effects due to the partitioning of the correlation space and the performance of a VMCSCF modal basis in contrast to a standard modal basis obtained from vibrational selfconsistent field theory have been investigated in detail. Benchmark calculations based on highlevel potentials are provided for the propargyl cation and cisdiazene.

A simple grand canonical approach to compute the vapor pressure of bulk and finite size systems
View Description Hide DescriptionIn this article we introduce a simple grand canonical screening (GCS) approach to accurately compute vapor pressures from molecular dynamics or Monte Carlo simulations. This procedure entails a screening of chemical potentials using a conventional grand canonical scheme, and therefore it is straightforward to implement for any kind of interface. The scheme is validated against data obtained from Gibbs ensemble simulations for water and argon. Then, it is applied to obtain the vapor pressure of the coarsegrained mW water model, and it is shown that the computed value is in excellent accord with the one formally deduced using statistical thermodynamics arguments. Finally, this methodology is used to calculate the vapor pressure of a water nanodroplet of 94 molecules. Interestingly, the result is in perfect agreement with the one predicted by the Kelvin equation for a homogeneous droplet of that size.

Translation and integration of numerical atomic orbitals in linear molecules
View Description Hide DescriptionWe present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding twodimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

Relaxed active space: Fixing tailoredCC with high order coupled cluster. II
View Description Hide DescriptionDue to the steep increase in computational cost with the inclusion of higherconnected cluster operators in coupledcluster applications, it is usually not practical to use such methods for larger systems or basis sets without an active space partitioning. This study generates an active space subject to unambiguous statistical criteria to define a space whose size permits treatment at the CCSDT level. The automated scheme makes it unnecessary for the user to judge whether a chosen active space is sufficient to correctly solve the problem. Two demanding applications are presented: twisted ethylene and the transition states for the bicyclo[1,1,0]butane isomerization. As biradicals both systems require at least a CCSDT level of theory for quantitative results, for the geometries and energies.

Electronic excitation spectra of molecules in solution calculated using the symmetryadapted clusterconfiguration interaction method in the polarizable continuum model with perturbative approach
View Description Hide DescriptionA perturbative approximation of the state specific polarizable continuum model (PCM) symmetryadapted clusterconfiguration interaction (SACCI) method is proposed for efficient calculations of the electronic excitations and absorption spectra of molecules in solutions. This firstorder PCM SACCI method considers the solvent effects on the energies of excited states up to the firstorder with using the zerothorder wavefunctions. This method can avoid the costly iterative procedure of the selfconsistent reaction field calculations. The firstorder PCM SACCI calculations well reproduce the results obtained by the iterative method for various types of excitations of molecules in polar and nonpolar solvents. The firstorder contribution is significant for the excitation energies. The results obtained by the zerothorder PCM SACCI, which considers the fixed groundstate reaction field for the excitedstate calculations, are deviated from the results by the iterative method about 0.1 eV, and the zerothorder PCM SACCI cannot predict even the direction of solvent shifts in nhexane for many cases. The firstorder PCM SACCI is applied to studying the solvatochromisms of (2,2^{′}bipyridine)tetracarbonyltungsten [W(CO)4(bpy), bpy = 2,2^{′}bipyridine] and bis(pentacarbonyltungsten)pyrazine [(OC)5W(pyz)W(CO)5, pyz = pyrazine]. The SACCI calculations reveal the detailed character of the excited states and the mechanisms of solvent shifts. The energies of metal to ligand charge transfer states are significantly sensitive to solvents. The firstorder PCM SACCI well reproduces the observed absorption spectra of the tungsten carbonyl complexes in several solvents.
 Advanced Experimental Techniques

Laserassisted electron diffraction for femtosecond molecular imaging
View Description Hide DescriptionWe report the observation of laserassisted electron diffraction (LAED) through the collision of 1 keV electrons with gasphase CCl4 molecules in a femtosecond nearinfrared laser field. In the angular distribution of the scattered electrons with the energy shifts of ±ℏω, we observed clear diffraction patterns which reflect the geometrical structure of the molecules at the moment of laser irradiation. Our results demonstrate that ultrafast nuclear dynamics of molecules can be probed by LAED with the high temporal (<10 fs) and spatial (∼0.01 Å) resolutions.
 Atoms, Molecules, and Clusters

Optically promoted bipartite atomic entanglement in hybrid metallic carbon nanotube systems
View Description Hide DescriptionWe study theoretically a pair of spatially separated extrinsic atomic type species (extrinsic atoms, ions, molecules, or semiconductor quantum dots) near a metallic carbon nanotube, that are coupled both directly via the interatomic dipoledipole interactions and indirectly by means of the virtual exchange by resonance plasmon excitations on the nanotube surface. We analyze how the optical preparation of the system by using strong laser pulses affects the formation and evolution of the bipartite atomic entanglement. Despite a large number of possible excitation regimes and evolution pathways, we find a few generic scenarios for the bipartite entanglement evolution and formulate practical recommendations on how to optimize and control the robust bipartite atomic entanglement in hybrid carbon nanotube systems.

Line broadening of confined CO gas: From moleculewall to moleculemolecule collisions with pressure
View Description Hide DescriptionThe infrared absorption in the fundamental band of CO gas confined in porous silica xerogel has been recorded at room temperature for pressures between about 5 and 920 hPa using a high resolution Fourier transform spectrometer. The widths of individual lines are determined from fits of measured spectra and compared with ab initio predictions obtained from requantized classical molecular dynamics simulations. Good agreement is obtained from the low pressure regime where the line shapes are governed by moleculewall collisions to high pressures where the influence of moleculemolecule interactions dominates. These results, together with those obtained with a simple analytical model, indicate that both mechanisms contribute in a practically additive way to the observed linewidths. They also confirm that a single collision of a molecule with a wall changes its rotational state. These results are of interest for the determination of some characteristics of the opened porosity of porous materials through optical soundings.

Electrical, thermal, and species transport properties of liquid eutectic GaIn and GaInSn from first principles
View Description Hide DescriptionUsing ab initio molecular dynamics, the atomic structure and transport properties of eutectic GaIn and GaInSn are investigated. The KuboGreenwood (KG) and the ZimanFaber (ZF) formulations and the WiedemannFranz (WF) law are used for the electrical and electronic thermal conductivity. The species diffusivity and the viscosity are also predicted using the mean square displacement and the StokesEinstein (SE) relation. Alloying Ga causes more disordered structure, i.e., broadening the atomic distance near the In and Sn atoms, which reduces the transport properties and the melting temperature. The KG treatment shows excellent agreement with the experimental results while ZF treatment formula slightly overestimates the electrical conductivity. The predicted thermal conductivity also shows good agreement with the experiments. The species diffusivity and the viscosity are slightly reduced by the alloying of Ga with In and Sn atoms. Good agreements are found with available experimental results and new predicted transportproperty results are provided.

Highresolution spectroscopy and quantumdefect model for the gerade triplet np and nf Rydberg states of He_{2}
View Description Hide DescriptionPhotoionization spectra and Rydbergstateresolved thresholdionization spectra of the gerade triplet np Rydberg states of ^{4}He2 located in the vicinity of the ionization threshold were recorded from the metastable state. An accuracy of 0.01 cm^{−1} was achieved for the experimental term values of the observed Rydberg states. The data were combined with spectroscopic data on lowlying triplet np and nf Rydberg states from the literature to derive energy and internucleardistancedependent eigenquantumdefect parameters of multichannel quantumdefect theory (MQDT). The MQDT calculations reproduce the experimental data within their experimental uncertainties and enabled the derivation of potentialenergy curves for the lowest triplet p Rydberg states (n = 2–5) of He2. The eigenquantumdefect parameters describing the p f interaction were found to be larger than 0.002 at the energies corresponding to the highn Rydberg states, so that the p f interaction plays an important role in the autoionization dynamics of np Rydberg states with v ^{+} = 0. By extrapolating the experimental term values of triplet np Rydberg states of ^{4}He2 in the range of principal quantum number n between 87 and 110, the positions of the (v ^{+} = 0, N ^{+} = 3) and (v ^{+} = 0, N ^{+} = 5) levels of the ground state of ^{4} were determined to lie 70.937(3) cm^{−1} and 198.369(6) cm^{−1}, respectively, above the (v ^{+} = 0, N ^{+} = 1) ground rotational level.

The antimonygroup 11 chemical bond: Dissociation energies of the diatomic molecules CuSb, AgSb, and AuSb
View Description Hide DescriptionThe intermetallic molecules CuSb, AgSb, and AuSb were identified in the effusive molecular beam produced at high temperature under equilibrium conditions in a doublecelllike Knudsen source. Several gaseous equilibria involving these species were studied by mass spectrometry as a function of temperature in the overall range 1349–1822 K, and the strength of the chemical bond formed between antimony and the group 11 metals was for the first time measured deriving the following thermochemical dissociation energies ( , kJ/mol): 186.7 ± 5.1 (CuSb), 156.3 ± 4.9 (AgSb), 241.3 ± 5.8 (AuSb). The three species were also investigated computationally at the coupled cluster level with single, double, and noniterative quasiperturbative triple excitations (CCSD(T)). The spectroscopic parameters were calculated from the potential energy curves and the dissociation energies were evaluated at the Complete Basis Set limit, resulting in an overall good agreement with experimental values. An approximate evaluation of the spinorbit effect was also performed. CCSD(T) calculations were further extended to the corresponding group 11 arsenide species which are here studied for the first time and the following dissociation energies ( , kJ/mol): 190 ± 10 (CuAs), 151 ± 10 (AgAs), 240 ± 15 (AuAs) are proposed. Taking advantage of the new experimental and computational information here presented, the bond energy trends along group 11 and 4th and 5th periods of the periodic table were analyzed and the bond energies of the diatomic species CuBi and AuBi, yet experimentally unobserved, were predicted on an empirical basis.