Volume 138, Issue 24, 28 June 2013
 COMMUNICATIONS


Communication: Singularityfree hybrid functional with a Gaussianattenuating exact exchange in a planewave basis
View Description Hide DescriptionIntegrable singularity in the exact exchange calculations in hybrid functionals is an old and wellknown problem in planewave basis. Recently, we developed a hybrid functional named Gaussianattenuating PerdewBurkeErnzerhof (GauPBE), which uses a Gaussian function as a modified Coulomb potential for the exact exchange. We found that the modified Coulomb potential of Gaussian function enables the exact exchange calculation in planewave basis to be singularityfree and, as a result, the GauPBE functional shows faster energy convergence on k and q grids for the exact exchange calculations. Also, a tight comparison (same k and q meshes) between GauPBE and two other hybrid functionals, i.e., PBE0 and HSE06, indicates GauPBE functional as the least computational time consuming. The GauPBE functional employed in conjunction with a plane wave basis provides bandgaps with higher accuracy than the PBE0 and HSE06 in agreement with bandgaps previously calculated using Gaussiantypeorbitals.
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 ARTICLES

 Theoretical Methods and Algorithms

Excitedstate free energy surfaces in solution: Timedependent density functional theory/reference interaction site model selfconsistent field method
View Description Hide DescriptionConstructing free energy surfaces for electronically excited states is a first step toward the understanding of photochemical processes in solution. For that purpose, the analytic free energy gradient is derived and implemented for the linearresponse timedependent density functional theory combined with the reference interaction site model selfconsistent field method. The proposed method is applied to study (1) the fluorescence spectra of aqueous acetone and (2) the excitedstate intramolecular proton transfer reaction of orthohydroxybenzaldehyde in an acetonitrile solution.

Effect of molecularorbital rotations on groundstate energies in the parametric twoelectron reduced density matrix method
View Description Hide DescriptionDifferent sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric twoelectron reduced density matrix (2RDM) methods [D. A. Mazziotti, Phys. Rev. Lett.101, 253002 (Year: 2008)]10.1103/PhysRevLett.101.253002, also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the groundstate energies from the parametric 2RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and nonequilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2RDM. Furthermore, while the 2RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical HartreeFock calculations.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations
View Description Hide DescriptionHybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by gridbased density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 103–105 molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the longrange electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM selfconsistency iteration. The longrange parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Shortrange overpolarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMMMD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.

A simplified TammDancoff density functional approach for the electronic excitation spectra of very large molecules
View Description Hide DescriptionTwo approximations in the TammDancoff density functional theory approach (TDADFT) to electronically excited states are proposed which allow routine computations for electronic ultraviolet (UV) or circular dichroism (CD) spectra of molecules with 500–1000 atoms. Speedups compared to conventional timedependent DFT (TDDFT) treatments of about two to three orders of magnitude in the excited state part at only minor loss of accuracy are obtained. The method termed sTDA (“s” for simplified) employs atomcentered Löwdinmonopole based twoelectron repulsion integrals with the asymptotically correct 1/R behavior and perturbative single excitation configuration selection. It is formulated generally for any standard global hybrid density functional with given Fockexchange mixing parameter a x . The method performs well for two standard benchmark sets of vertical singletsinglet excitations for values of a x in the range 0.2–0.6. The mean absolute deviations from reference data are only 0.2–0.3 eV and similar to those from standard TDDFT. In three cases (two dyes and one polypeptide), good mutual agreement between the electronic spectra (up to 10–11 eV excitation energy) from the sTDA method and those from TD(A)DFT is obtained. The computed UV and CDspectra of a few typical systems (e.g., C60, two transition metal complexes, [7]helicene, polyalanine, a supramolecular aggregate with 483 atoms and about 7000 basis functions) compare well with corresponding experimental data. The method is proposed together with mediumsized double or triplezeta type atomicorbital basis sets as a quantum chemical tool to investigate the spectra of huge molecular systems at a reliable DFT level.

Kinetics of receptor occupancy during morphogen gradient formation
View Description Hide DescriptionDuring embryogenesis, sheets of cells are patterned by concentration profiles of morphogens, molecules that act as dosedependent regulators of gene expression and cell differentiation. Concentration profiles of morphogens can be formed by a sourcesink mechanism, whereby an extracellular protein is secreted from a localized source, diffuses through the tissue and binds to cell surface receptors. A morphogen molecule bound to its receptor can either dissociate or be internalized by the cell. The effects of morphogens on cells depend on the occupancy of surface receptors, which in turn depends on morphogen concentration. In the simplest case, the local concentrations of the morphogen and morphogenreceptor complexes monotonically increase with time from zero to their steadystate values. Here, we derive analytical expressions for the time scales which characterize the formation of the steadystate concentrations of both the diffusible morphogen molecules and morphogenreceptor complexes at a given point in the patterned tissue.

A unifying model for nonadiabatic coupling at metallic surfaces beyond the local harmonic approximation: From vibrational relaxation to scanning tunneling microscopy
View Description Hide DescriptionA model for treating excitation and relaxation of adsorbates at metallic surfaces induced by nonadiabatic coupling is developed. The derivation is based on the concept of resonant electron transfer, where the adsorbate serves as a molecular bridge for the inelastic transition between an electron source and a sink. In this picture, energy relaxation and scanning tunneling microscopy (STM) at metallic surfaces are treated on an equal footing as a quasithermal process. The model goes beyond the local harmonic approximation and allows for an unbiased description of floppy systems with multiple potential wells. Further, the limitation of the product ansatz for the vibronic wave function to include the positiondependence of the nonadiabatic couplings is avoided by explicitly enforcing detailed balance. The theory is applied to the excitation of hydrogen on palladium, which has multiple local potential minima connected by low energy barriers. The main aspects investigated are the lifetimes of adsorbate vibrations in different adsorption sites, as well as the dependence of the excitation, response, and transfer rates on an applied potential bias. The excitation and relaxation simulations reveal intricate population dynamics that depart significantly from the simplistic tunneling model in a truncated harmonic potential. In particular, the population decay from an initially occupied local minimum induced by the contact with an STM tip is found to be better described by a double exponential. The two rates are interpreted as a response to the system perturbation and a transfer rate following the perturbation. The transfer rate is found to obey a power law, as was the case in previous experimental and theoretical work.

Effective electrodiffusion equation for nonuniform nanochannels
View Description Hide DescriptionWe derive a onedimensional formulation of the PlanckNernstPoisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the FickJacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a nontrivial fashion. We consider two kinds of nonuniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and threedimensional solutions of the electrokinetic equations.

Functional derivatives of metageneralized gradient approximation (metaGGA) type exchangecorrelation density functionals
View Description Hide DescriptionMetageneralized gradient approximation (metaGGA) exchangecorrelation density functionals depend on the KohnSham (KS) orbitals through the kinetic energy density. The KS orbitals in turn depend functionally on the electron density. However, the functional dependence of the KS orbitals is indirect, i.e., not given by an explicit expression, and the computation of analytic functional derivatives of metaGGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of metaGGA density functionals for groundstate calculations is abstracted and generalized to a class of density functionals that is broader than metaGGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for metaGGA density functionals are presented here for the first time, together with the technical details of their computer implementation. The analysis presented here also uncovers the implicit assumptions in the practical solution to computing functional derivatives of metaGGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the nonuniqueness with respect to the KS orbitals, and the nonlocality of the resultant potential is also discussed.

Identification of twostep chemical mechanisms and determination of thermokinetic parameters using frequency responses to small temperature oscillations
View Description Hide DescriptionIncreased focus on kinetic signatures in biology, coupled with the lack of simple tools for chemical dynamics characterization, lead us to develop an efficient method for mechanism identification. A small thermal modulation is used to reveal chemical dynamics, which makes the technique compatible with in cellulo imaging. Then, the detection of concentration oscillations in an appropriate frequency range followed by a judicious analytical treatment of the data is sufficient to determine the number of chemical characteristic times, the reaction mechanism, and the full set of associated rate constants and enthalpies of reaction. To illustrate the scope of the method, dimeric protein folding is chosen as a biologically relevant example of nonlinear mechanism with one or two characteristic times.

Tuning of barrier crossing time of a particle by time dependent magnetic field
View Description Hide DescriptionWe have studied the effect of time dependent magnetic field on the barrier crossing dynamics of a charged particle. An interplay of the magnetic field induced electric field and the applied field reveals several interesting features. For slowly oscillating field the barrier crossing rate increases remarkably particularly at large amplitude of the field. For appreciably large frequency a generically distinct phenomenon appears by virtue of parametric resonance manifested in multiple peaks appearing in the variation of the mean first passage time as a function of the amplitude. The parametric resonance is more robust against the variation of amplitude of the oscillating field compared to the case of variation of frequency. The barrier crossing time of a particle can be tuned parametrically by appropriate choice of amplitude and frequency of the oscillating magnetic field.

Coarsegrained Monte Carlo simulations of nonequilibrium systems
View Description Hide DescriptionWe extend the scope of a recent method for generating coarsegrained lattice Metropolis Monte Carlo simulations[X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E86, 026708 (Year: 2012)10.1103/PhysRevE.86.026708;X. Liu, W. D. Seider, and T. Sinno, J. Chem. Phys.138, 114104 (Year: 2013)10.1063/1.4794686] from continuous interaction potentials to nonequilibrium situations. The original method has been shown to satisfy detailed balance at the coarse scale and to provide a good representation of various equilibrium properties in both atomic and molecular systems. However, we show here that the original method is inconsistent with nonequilibrium trajectories generated by fullresolution Monte Carlo simulations, which, under certain conditions, have been shown to correspond to Langevin dynamics. The modified coarsegrained method is generated by simultaneously biasing the forward and backward transition probability for every possible move, thereby preserving the detailed balance of the original method. The resulting coarsegrained Monte Carlo simulations are shown to provide trajectories that are consistent with overdamped Langevin (Smoluchowski) dynamics using a sequence of simple nonequilibrium examples. We first consider the purely diffusional spreading of a Gaussian pulse of idealgas particles and then include an external potential to study the influence of drift. Finally, we validate the method using a more general situation in which the particles interact via a LennardJones interparticle potential.

Building a kinetic Monte Carlo model with a chosen accuracy
View Description Hide DescriptionThe kinetic Monte Carlo (KMC) method is a popular modeling approach for reaching large materials length and time scales. The KMC dynamics is erroneous when atomic processes that are relevant to the dynamics are missing from the KMC model. Recently, we had developed for the first time an error measure for KMC in Bhute and Chatterjee [J. Chem. Phys.138, 084103 (Year: 2013)10.1063/1.4792439]. The error measure, which is given in terms of the probability that a missing process will be selected in the correct dynamics, requires estimation of the missing rate. In this work, we present an improved procedure for estimating the missing rate. The estimate found using the new procedure is within an order of magnitude of the correct missing rate, unlike our previous approach where the estimate was larger by orders of magnitude. This enables one to find the error in the KMC model more accurately. In addition, we find the time for which the KMC model can be used before a maximum error in the dynamics has been reached.

Enhanced exchange algorithm without detailed balance condition for replica exchange method
View Description Hide DescriptionThe replica exchange method (REM) is a powerful tool for the conformational sampling of biomolecules. In this study, we propose an enhanced exchange algorithm for REM not meeting the detailed balance condition (DBC), but satisfying the balance condition in all considered exchanges between two replicas. Breaking the DBC can minimize the rejection rate and make an exchange process rejectionfree as the number of replicas increases. To enhance the efficiency of REM, all possible pairs—not only the nearest neighbor—were considered in the exchange process. The test simulations of the alanine dipeptide confirmed the correctness of our method. The average traveling distance of each replica in the temperature distribution was also increased in proportion to an increase in the exchange rate. Furthermore, we applied our algorithm to the conformational sampling of the 10residue miniprotein, chignolin, with an implicit solvent model. The results showed a faster convergence in the calculation of its free energy landscape, compared to that achieved using the normal exchange method of adjacent pairs. This algorithm can also be applied to the conventional near neighbor method and is expected to reduce the required number of replicas.

On the derivation of semiclassical expressions for quantum reaction rate constants in multidimensional systems
View Description Hide DescriptionExpressions for reaction rate constants in multidimensional chemical systems are derived by applying semiclassical approximation to the quantum path integrals of the ImF formulation of reaction rate theory. First, the transverse degrees of freedom orthogonal to the reaction coordinate are treated within the steepest descent approximation, after which the semiclassical approximation is applied to the remaining reaction coordinate. Thus derived, the semiclassical expressions account for the multidimensional nature of quantum effects and accurately incorporate nuclear quantum effects such as multidimensional tunneling and zero point energies. The obtained expressions are applicable in the broad temperature range from the deep tunneling to hightemperature regimes. The present paper provides derivation of the semiclassical instanton expressions proposed by Kryvohuz [J. Chem. Phys.134, 114103 (Year: 2011)]10.1063/1.3565425.

Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and coresoftened potential models
View Description Hide DescriptionThe first four perturbation coefficients in the expansion of the Helmholtz free energy in power series of the inverse of the reduced temperature for a number of potential models with hardsphere cores plus coresoftened and discontinuous tails are obtained from Monte Carlo simulations. The potential models considered include squarewell, double squarewell, and squareshoulder plus squarewell, with different potential parameters. These simulation data are used to evaluate the performance of a traditional macroscopic compressibility approximation (MCA) for the second order coefficient and a recent coupling parameter series expansion (CPSE) for the first four coefficients. Comprehensive comparison indicates the incapability of the MCA for the second order coefficient in most nonstringent situations, and significance of the CPSE in accurately calculating these four coefficients.
 Advanced Experimental Techniques

Inline interferometric femtosecond stimulated Raman scattering spectroscopy
View Description Hide DescriptionWe present inline interferometric femtosecond stimulated Raman scattering (IIFSRS), a new method to measure the spectral Raman intensity and phase over a broad spectral range, potentially in a single shot. An analytic model is developed, that excellently reproduces the measured spectra. Additionally, the performance of IIFSRS is directly compared in experiments to two established techniques, namely femtosecond stimulated Raman scattering and femtosecond Raman induced Kerreffect spectroscopy.

Highresolution laser spectroscopy between 0.9 and 14.3 THz in a supersonic beam: RydbergRydberg transitions of atomic Xe at intermediate n values
View Description Hide DescriptionA laserbased, pulsed, narrowband source of submillimeterwave radiation has been developed that is continuously tunable from 0.1 THz to 14.3 THz. The source is based on differencefrequency mixing in the nonlinear crystal trans4′(dimethylamino)Nmethyl4stilbazolium tosylate. By varying the pulse length, the bandwidth of the submillimeterwave radiation can be adjusted between 85 MHz and 2.8 MHz. This new radiation source has been integrated in a vacuumultraviolet–submillimeterware doubleresonance spectrometer, with which lowfrequency transitions of atoms and molecules in supersonic beams can be detected massselectively by photoionization and timeofflight mass spectrometry. The properties of the radiation source and spectrometer are demonstrated in a study of 33f ← nd RydbergRydberg transitions in Xe with n in the range 16–31. The frequency calibration of the submillimeterwave radiation was performed with an accuracy of 2.8 MHz. The narrowest lines observed experimentally have a fullwidth at halfmaximum of ∼3 MHz, which is sufficient to fully resolve the hyperfine structure of the RydbergRydberg transitions of 129Xe and 131Xe. A total of 72 transitions were measured in the range between 0.937 THz and 14.245 THz and their frequencies are compared with frequencies calculated by multichannel quantum defect theory.
 Atoms, Molecules, and Clusters

Homogeneous connectivity of potential energy network in a solidlike state of water cluster
View Description Hide DescriptionA novel route to the exponential trappingtime distribution within a solidlike state in water clusters is described. We propose a simple homogeneous network (SHN) model to investigate dynamics on the potential energy networks of water clusters. In this model, it is shown that the trappingtime distribution in a solidlike state follows the exponential distribution, whereas the trappingtime distribution in local potential minima within the solidlike state is not exponential. To confirm the exponential trappingtime distribution in a solidlike state, we investigate water clusters, (H2O)6 and (H2O)12, by molecular dynamics simulations. These clusters change dynamically from solidlike to liquidlike state and vice versa. We find that the probability density functions of trapping times in a solidlike state are described by the exponential distribution whereas those of interevent times of large fluctuations in potential energy within the solidlike state follow the Weibull distributions. The results provide a clear evidence that transition dynamics between solidlike and liquidlike states in water clusters are well described by the SHN model, suggesting that the exponential trappingtime distribution within a solidlike state originates from the homogeneous connectivity in the potential energy network.

Polarization of molecular angular momentum in the chemical reactions Li + HF and F + HD
View Description Hide DescriptionThe quantum mechanical approach to vector correlation of angular momentum orientation and alignment in chemical reactions[G. BalintKurti and O. S. Vasyutinskii, J. Phys. Chem. A113, 14281 (Year: 2009)]10.1021/jp902796v is applied to the molecular reagents and products of the Li + HF [L. GonzalezSanchez, O. S. Vasyutinskii, A. Zanchet, C. SanzSanz, and O. Roncero, Phys. Chem. Chem. Phys.13, 13656 (Year: 2011)]10.1039/c0cp02452j and F + HD [D. De Fazio, J. Lucas, V. Aquilanti, and S. Cavalli, Phys. Chem. Chem. Phys.13, 8571 (Year: 2011)]10.1039/c0cp02738creactions for which accurate scattering information has become recently available through timedependent and timeindependent approaches. Application of the theory to two important particular cases of the reactive collisions has been considered: (i) the influence of the angular momentum polarization of reactants in the entrance channel on the spatial distribution of the products in the exit channel and (ii) angular momentum polarization of the products of the reaction between unpolarized reactants. In the former case, the role of the angular momentum alignment of the reactants is shown to be large, particularly when the angular momentum is perpendicular to the reaction scattering plane. In the latter case, the orientation and alignment of the product angular momentum was found to be significant and strongly dependent on the scattering angle. The calculation also reveals significant differences between the vector correlation properties of the two reactions under study which are due to difference in the reaction mechanisms. In the case of F + HD reaction, the branching ratio between HF and DF production points out interest in the insight gained into the detailed dynamics, when information is available either from exact quantum mechanical calculations or from especially designed experiments. Also, the geometrical arrangement for the experimental determination of the product angular momentum orientation and alignment based on a compact and convenient spherical tensor expression for the intensity of the resonance enhanced multiphoton ionization (REMPI 2 + 1) signal is suggested.