Index of content:
Volume 138, Issue 24, 28 June 2013
- Theoretical Methods and Algorithms
Excited-state free energy surfaces in solution: Time-dependent density functional theory/reference interaction site model self-consistent field method138(2013); http://dx.doi.org/10.1063/1.4811201View Description Hide Description
Constructing 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 linear-response time-dependent density functional theory combined with the reference interaction site model self-consistent field method. The proposed method is applied to study (1) the fluorescence spectra of aqueous acetone and (2) the excited-state intramolecular proton transfer reaction of ortho-hydroxybenzaldehyde in an acetonitrile solution.
Effect of molecular-orbital rotations on ground-state energies in the parametric two-electron reduced density matrix method138(2013); http://dx.doi.org/10.1063/1.4811202View Description Hide Description
Different 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 two-electron reduced density matrix (2-RDM) 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 ground-state energies from the parametric 2-RDM 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 non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM 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 Hartree-Fock calculations.
Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations138(2013); http://dx.doi.org/10.1063/1.4811292View Description Hide Description
Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based 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 long-range 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 self-consistency iteration. The long-range 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. Short-range over-polarization 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/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.
A simplified Tamm-Dancoff density functional approach for the electronic excitation spectra of very large molecules138(2013); http://dx.doi.org/10.1063/1.4811331View Description Hide Description
Two approximations in the Tamm-Dancoff density functional theory approach (TDA-DFT) 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. Speed-ups compared to conventional time-dependent DFT (TD-DFT) 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 atom-centered Löwdin-monopole based two-electron 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 Fock-exchange mixing parameter a x . The method performs well for two standard benchmark sets of vertical singlet-singlet 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 TD-DFT. 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 CD-spectra of a few typical systems (e.g., C60, two transition metal complexes, 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 medium-sized double- or triple-zeta type atomic-orbital basis sets as a quantum chemical tool to investigate the spectra of huge molecular systems at a reliable DFT level.
138(2013); http://dx.doi.org/10.1063/1.4811654View Description Hide Description
During embryogenesis, sheets of cells are patterned by concentration profiles of morphogens, molecules that act as dose-dependent regulators of gene expression and cell differentiation. Concentration profiles of morphogens can be formed by a source-sink 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 morphogen-receptor complexes monotonically increase with time from zero to their steady-state values. Here, we derive analytical expressions for the time scales which characterize the formation of the steady-state concentrations of both the diffusible morphogen molecules and morphogen-receptor complexes at a given point in the patterned tissue.
A unifying model for non-adiabatic coupling at metallic surfaces beyond the local harmonic approximation: From vibrational relaxation to scanning tunneling microscopy138(2013); http://dx.doi.org/10.1063/1.4811150View Description Hide Description
A model for treating excitation and relaxation of adsorbates at metallic surfaces induced by non-adiabatic 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 quasi-thermal 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 position-dependence of the non-adiabatic 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.
138(2013); http://dx.doi.org/10.1063/1.4811516View Description Hide Description
We derive a one-dimensional formulation of the Planck-Nernst-Poisson 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 Fick-Jacobs 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 non-trivial fashion. We consider two kinds of non-uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one- and three-dimensional solutions of the electrokinetic equations.
Functional derivatives of meta-generalized gradient approximation (meta-GGA) type exchange-correlation density functionals138(2013); http://dx.doi.org/10.1063/1.4811270View Description Hide Description
Meta-generalized gradient approximation (meta-GGA) exchange-correlation density functionals depend on the Kohn-Sham (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 meta-GGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of meta-GGA density functionals for ground-state calculations is abstracted and generalized to a class of density functionals that is broader than meta-GGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for meta-GGA 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 meta-GGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the non-uniqueness with respect to the KS orbitals, and the non-locality of the resultant potential is also discussed.
Identification of two-step chemical mechanisms and determination of thermokinetic parameters using frequency responses to small temperature oscillations138(2013); http://dx.doi.org/10.1063/1.4811288View Description Hide Description
Increased 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.
138(2013); http://dx.doi.org/10.1063/1.4811363View Description Hide Description
We 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 para-metrically by appropriate choice of amplitude and frequency of the oscillating magnetic field.
138(2013); http://dx.doi.org/10.1063/1.4811656View Description Hide Description
We extend the scope of a recent method for generating coarse-grained 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 non-equilibrium 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 non-equilibrium trajectories generated by full-resolution Monte Carlo simulations, which, under certain conditions, have been shown to correspond to Langevin dynamics. The modified coarse-grained 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 coarse-grained Monte Carlo simulations are shown to provide trajectories that are consistent with overdamped Langevin (Smoluchowski) dynamics using a sequence of simple non-equilibrium examples. We first consider the purely diffusional spreading of a Gaussian pulse of ideal-gas 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 Lennard-Jones interparticle potential.
138(2013); http://dx.doi.org/10.1063/1.4812319View Description Hide Description
The 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.
138(2013); http://dx.doi.org/10.1063/1.4811711View Description Hide Description
The 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 rejection-free 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 10-residue 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 systems138(2013); http://dx.doi.org/10.1063/1.4811221View Description Hide Description
Expressions 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 high-temperature 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 core-softened potential models138(2013); http://dx.doi.org/10.1063/1.4811285View Description Hide Description
The 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 hard-sphere cores plus core-softened and discontinuous tails are obtained from Monte Carlo simulations. The potential models considered include square-well, double square-well, and square-shoulder plus square-well, 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 non-stringent situations, and significance of the CPSE in accurately calculating these four coefficients.
- Advanced Experimental Techniques
138(2013); http://dx.doi.org/10.1063/1.4811486View Description Hide Description
We present in-line interferometric femtosecond stimulated Raman scattering (II-FSRS), 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 II-FSRS is directly compared in experiments to two established techniques, namely femtosecond stimulated Raman scattering and femtosecond Raman induced Kerr-effect spectroscopy.
High-resolution laser spectroscopy between 0.9 and 14.3 THz in a supersonic beam: Rydberg-Rydberg transitions of atomic Xe at intermediate n values138(2013); http://dx.doi.org/10.1063/1.4809740View Description Hide Description
A laser-based, pulsed, narrow-band source of submillimeter-wave radiation has been developed that is continuously tunable from 0.1 THz to 14.3 THz. The source is based on difference-frequency mixing in the nonlinear crystal trans-4′-(dimethylamino)-N-methyl-4-stilbazolium tosylate. By varying the pulse length, the bandwidth of the submillimeter-wave radiation can be adjusted between 85 MHz and 2.8 MHz. This new radiation source has been integrated in a vacuum-ultraviolet–submillimeter-ware double-resonance spectrometer, with which low-frequency transitions of atoms and molecules in supersonic beams can be detected mass-selectively by photoionization and time-of-flight mass spectrometry. The properties of the radiation source and spectrometer are demonstrated in a study of 33f ← nd Rydberg-Rydberg transitions in Xe with n in the range 16–31. The frequency calibration of the submillimeter-wave radiation was performed with an accuracy of 2.8 MHz. The narrowest lines observed experimentally have a full-width at half-maximum of ∼3 MHz, which is sufficient to fully resolve the hyperfine structure of the Rydberg-Rydberg 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
138(2013); http://dx.doi.org/10.1063/1.4811289View Description Hide Description
A novel route to the exponential trapping-time 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 trapping-time distribution in a solidlike state follows the exponential distribution, whereas the trapping-time distribution in local potential minima within the solidlike state is not exponential. To confirm the exponential trapping-time 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 trapping-time distribution within a solidlike state originates from the homogeneous connectivity in the potential energy network.
138(2013); http://dx.doi.org/10.1063/1.4809992View Description Hide Description
The quantum mechanical approach to vector correlation of angular momentum orientation and alignment in chemical reactions[G. Balint-Kurti 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. Gonzalez-Sanchez, O. S. Vasyutinskii, A. Zanchet, C. Sanz-Sanz, 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 time-dependent and time-independent 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.
Microsolvation in superfluid helium droplets studied by the electronic spectra of six porphyrin derivatives and one chlorine compound138(2013); http://dx.doi.org/10.1063/1.4811199View Description Hide Description
After almost two decades of high resolution molecular spectroscopy in superfluid helium droplets, the understanding of microsolvation is still the subject of intense experimental and theoretical research. According to the published spectroscopic work including microwave, infrared, and electronic spectroscopy, the latter appears to be particularly promising to study microsolvation because of the appearance of pure molecular transitions and spectrally separated phonon wings. Instead of studying the very details of the influence of the helium environment for one particular dopant molecule as previously done for phthalocyanine, the present study compares electronic spectra of a series of non-polar porphyrin derivatives when doped into helium droplets consisting of 104–105 helium atoms. Thereby, we focus on the helium-induced fine structure, as revealed most clearly at the corresponding electronic origin. The interpretation and the assignment of particular features obtained in the fluorescence excitation spectra are based on additional investigations of dispersed emission spectra and of the saturation behavior. Besides many dopant-specific results, the experimental study provides strong evidence for a particular triple peak feature representing the characteristic signature of helium solvation for all seven related dopant species.