Volume 139, Issue 7, 21 August 2013

We introduce a simple and general approach to the problem of clustering structures from atomic trajectories of chemical reactions in solution. By considering distance metrics which are invariant under permutation of identical atoms or molecules, we demonstrate that it is possible to automatically resolve as distinct structural clusters the configurations corresponding to reactants, products, and transition states, even in presence of atomexchanges and of hundreds of solvent molecules. Our approach strongly simplifies the analysis of large trajectories and it opens the way to the construction of kinetic network models of activated processes in solution employing the available efficient schemes developed for proteins conformational ensembles.
 ARTICLES

 Theoretical Methods and Algorithms

Structural cluster analysis of chemical reactions in solution
View Description Hide DescriptionWe introduce a simple and general approach to the problem of clustering structures from atomic trajectories of chemical reactions in solution. By considering distance metrics which are invariant under permutation of identical atoms or molecules, we demonstrate that it is possible to automatically resolve as distinct structural clusters the configurations corresponding to reactants, products, and transition states, even in presence of atomexchanges and of hundreds of solvent molecules. Our approach strongly simplifies the analysis of large trajectories and it opens the way to the construction of kinetic network models of activated processes in solution employing the available efficient schemes developed for proteins conformational ensembles.

Reducing the propensity for unphysical wavefunction symmetry breaking in multireference calculations of the excited states of semiconductor clusters
View Description Hide DescriptionUnphysical spatial symmetry breaking in multiconfigurational selfconsistent field calculations can lead to undesirable artifacts in the potential energy surfaces and electronic properties of molecules. Herein, we report several examples of such symmetry breaking in calculations of the excited states of small semiconductor clusters and related molecules at the stateaveraged complete active space selfconsistent field (SACASSCF) level of theory. A multireference approach is proposed to reduce its incidence: the singly excited active space complete active space configuration interaction (SEASCASCI) method. In SEASCASCI, the orbitals are determined by variationally minimizing an energy expression that does not depend on the offdiagonal Hamiltonian matrix elements which drive symmetry breaking at the SACASSCF level of theory. By application to several highly symmetric molecules, SEASCASCI is demonstrated to reduce the propensity for unphysical spatial symmetry breaking and eliminate resulting errors in the potential energy surfaces and molecular properties relative to the SACASSCF description. The SEAS method is also found to eliminate unphysical wavefunction distortion in asymmetric molecules. Finally, SEASCASCI is demonstrated to accurately describe the biradicaloid region of the potential energy surface of ethylene.

Direct evaluation of the position dependent diffusion coefficient and persistence time from the equilibrium density profile in anisotropic fluids
View Description Hide DescriptionWe derive expressions for the transverse diffusion coefficient D(z) and the average persistence time τ(z; L) within a layer of width L, for particles of a nonhomogeneous fluid enclosed in a planar nanopore. The method allows the direct evaluation of these positiondependent dynamical quantities from the equilibrium local particle density profile. We use results for the density and persistence time profiles from the virtual layer molecular dynamics method to numerically assess the significance of the Smoluchowski approximation.

A new perturbedchain equation of state for squarewell chains in fluid and solid phases
View Description Hide DescriptionConsidering the hardchain system as reference, a perturbedchain equation of state (EOS) is developed. The secondorder thermodynamic perturbation theory EOS is applied to the reference system. Monte Carlo simulation data for average intramolecular and intermolecular segmentsegment radial distribution function of hardchain systems with a chain length of 3–10 in the range of packing fraction between 0.1 and 0.72, covering both fluid and solid phases, are reported. A disordered solid phase structure is considered in this work. These customized data are used to develop the perturbation term of squarewell (SW) attractions. The performance of perturbedchain EOS is tested against computer simulation data from the literature for compressibility factor and phase equilibrium in the systems of SW chains. Results within good accuracy are obtained for all the test cases. Global vaporliquidsolid equilibrium diagrams for SW chain systems predicted by the new EOS are reported.

NonBornOppenheimer potential energy curve: Hydrogen molecular ion with highly accurate free complement method
View Description Hide DescriptionAlthough the concept of a potential energy curve (PEC) originates from the outgrowth of the BornOppenheimer (BO) approximation, we propose the application of analysis methods for the physical PEC with nonBornOppenheimer (nonBO) wave functions. A numerical examination was performed with the highly accurate nonBO vibronic wave functions of hydrogen molecular ion, which were obtained in our previous studies with the free complement method. The reduced density function integrated over the electron coordinates plays an important role in understanding nuclear motion dynamics, since it corresponds to the wave function density of the vibrational and rotational motions. The maximum positions of this density indicate the high existence probability of nuclei and can be considered as a discrete representation of the PEC. Whereas an ordinary PEC with the BO approximation is obtained as a numeric curve after multiple electronic state calculations at fixed nuclear coordinates, we propose a new analytical expression of the PEC from a nonBO wave function.

Single string based global optimizer for geometry optimization in strongly coupled finite clusters: An adaptive mutationdriven strategy
View Description Hide DescriptionWe propose and implement a simple adaptive heuristic to optimize the geometries of clusters of point charges or ions with the ability to find the global minimum energy configurations. The approach uses random mutations of a single string encoding the geometry and accepts moves that decrease the energy. Mutation probability and mutation intensity are allowed to evolve adaptively on the basis of continuous evaluation of past explorations. The resulting algorithm has been called Completely Adaptive Random Mutation Hill Climbing method. We have implemented this method to search through the complex potential energy landscapes of parabolically confined 3D classical Coulomb clusters of hundreds or thousands of charges—usually found in high frequency discharge plasmas. The energy per particle (E N /N) and its first and second differences, structural features, distribution of the oscillation frequencies of normal modes, etc., are analyzed as functions of confinement strength and the number of charges in the system. Certain magic numbers are identified. In order to test the feasibility of the algorithm in cluster geometry optimization on more complex energy landscapes, we have applied the algorithm for optimizing the geometries of MgO clusters, described by Coulomb–BornMayer potential and finding global minimum of some LennardJones clusters. The convergence behavior of the algorithm compares favorably with those of other existing global optimizers.

Wave function methods for fractional electrons
View Description Hide DescriptionDetermining accurate chemical potentials is of considerable interest in various chemical and physical contexts: from small molecular chargetransfer complexes to bandgap in bulk materials such as semiconductors. Chemical potentials are typically evaluated either by density functional theory, or, alternatively, by computationally more intensive Greens function based GW computations. To calculate chemical potentials, the ground state energy needs to be defined for fractional charges. We thus explore an extension of wave function theories to fractional charges, and investigate the ionization potential and electron affinity as the derivatives of the energy with respect to the electron number. The ultimate aim is to access the chemical potential of correlated wave function methods without the need of explicitly changing the numbers of electrons, making the approach readily applicable to bulk materials. We find that even though second order perturbation theory reduces the fractional charge error considerably compared to HartreeFock and standard density functionals, higher order perturbation theory is more accurate and coupledcluster approaches are even more robust, provided the electrons are bound at the HartreeFock level. The success of postHF approaches to improve over HF relies on two equally important aspects: the integer values are more accurate and the Coulomb correlation between the fractionally occupied orbital and all others improves the straight line behavior significantly as identified by a correction to HartreeFock. Our description of fractional electrons is also applicable to fractional spins, illustrating the ability of coupledcluster singles and doubles to deal with two degenerate fractionally occupied orbitals, but its inadequacy for three and more fractional spins, which occur, for instance, for spherical atoms and when dissociating double bonds. Our approach explores the realm of typical wave function methods that are applied mostly in molecular chemistry, but become available to the solid state community and offer the advantage of an integrated approach: fundamental gap, relative energies, and optimal geometries can be obtained at the same level.

A Lagrange multiplier approach for excited state properties through intermediate Hamiltonian formulation of Fock space multireference coupledcluster theory
View Description Hide DescriptionIn this paper, we present a formulation based on Lagrange multiplier approach for efficient evaluation of excited state energy derivatives in Fock space coupled cluster theory within the intermediate Hamiltonian framework. The formulation is applied to derive the explicit generic expressions up to second order energy derivatives for [1, 1] sector of Fock space with singles and doubles approximation. Its advantage, efficiency, and interconnection in comparison to the Lagrange multiplier approach in traditional formulation of Fock space, which is built on the concept of Bloch equation based effective Hamiltonian, has been discussed. Computational strategy for their implementation has also been discussed in some detail.

A quasicontinuum hydrodynamic model for slit shaped nanochannel flow
View Description Hide DescriptionWe propose a quasicontinuum hydrodynamic model for isothermal transport of LennardJones fluid confined in slit shaped nanochannels. In this work, we compute slip and viscous contributions independently and superimpose them to obtain the total velocity profile. Layering of fluid near the interface plays an important role in viscous contribution to the flow, by apparent viscosity change along the confining dimension. This relationship necessitates computing density profiles, which is done using the recently proposed empiricalpotential based quasicontinuum theory [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys.127, 174701 (Year: 2007)]10.1063/1.2793070. Existing correlations for density dependent viscosity provided by Woodcock [AIChE J.52, 438 (Year: 2006)]10.1002/aic.10676 are used to compute viscosity profile in the nanopores. A Dirichlet type slip boundary condition based on a static Langevin friction model describing centerofmass motion of fluid particles is used, the parameters of which are dependent on the fluctuations of total wallfluid force from an equilibrium molecular dynamics simulation. Different types of corrugated surfaces are considered to study wallfluid friction effects on boundary conditions. Proposed hydrodynamic model yields good agreement of velocity profiles obtained from nonequilibrium molecular dynamics simulations for gravity driven flow.

A density functional for strong correlation in atoms
View Description Hide DescriptionIn this work, a strongcorrelation model is developed for use with the BeckeRoussel exchange and dynamical correlation functionals. The model is free of empirical parameters and is exact for the hydrogen atom. It significantly improves on results from conventional functionals for the relative energies of spinpolarized and spinaveraged atoms through the first three rows of the periodic table, giving a mean absolute error of only 4 kcal/mol. The dissociation curve for the H2 molecule is also considered.

Nuclear dynamics of decaying states: A semiclassical approach
View Description Hide DescriptionA semiclassical method is proposed for carrying out molecular fragmentation simulations following electronic decay processes. The nuclear motion is treated classically during and after the electronic decay while a quantum mechanical description is used for the electron dynamics. The method is compared with full quantum results for benchmark examples. Good agreement is achieved. Such a method should be very useful for studying large systems for which a quantum description is not feasible.

Efficient construction of exchange and correlation potentials by inverting the Kohn–Sham equations
View Description Hide DescriptionGiven a set of canonical Kohn–Sham orbitals, orbital energies, and an external potential for a manyelectron system, one can invert the Kohn–Sham equations in a single step to obtain the corresponding exchangecorrelation potential, . For orbitals and orbital energies that are solutions of the Kohn–Sham equations with a multiplicative this procedure recovers (in the basis set limit), but for eigenfunctions of a nonmultiplicative oneelectron operator it produces an orbitalaveraged potential. In particular, substitution of Hartree–Fock orbitals and eigenvalues into the Kohn–Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbitalaveraged exchange and correlation potentials for hybrid and kineticenergydensitydependent functionals. We also show how the Kohn–Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbitaldependent functionals.

Lossless compression of wave function information using matrix factorization: A “gzip” for quantum chemistry
View Description Hide DescriptionWe propose the use of the singular value decomposition to decrease the storage required for wave function information. The specific case considered is determinantal full configuration interaction, but the same technique is readily applicable to truncated configuration interaction and coupledcluster calculations of various types; as we discuss this is a reformulation of approximate methods that have been in use for some time, but our approach eliminates those approximations. Numerical examples support the contention that considerable compression of the wave function is possible without significant loss of accuracy: as expected a considerable amount of the information contained in the full CI wave function is redundant.

Extending molecular simulation time scales: Parallel in time integrations for highlevel quantum chemistry and complex force representations
View Description Hide DescriptionParallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f (e.g., Verlet algorithm), is available to propagate the system from time t i (trajectory positions and velocities x i = (r i , v i )) to time t i + 1 (x i + 1) by x i + 1 = f i (x i ), the dynamics problem spanning an interval from t 0…t M can be transformed into a root finding problem, F(X) = [x i − f(x (i − 1)] i = 1, M = 0, for the trajectory variables. The root finding problem is solved using a variety of root finding techniques, including quasiNewton and preconditioned quasiNewton schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each timestep entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed, and the effectiveness of various approaches to solving the root finding problem is tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening timesteps provide preconditioners for the root finding problem. However, for MD and AIMD simulations, such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using StillingerWeber potentials, and a HCl + 4H2O AIMD simulation at the MP2 level. The maximum speedup ( ) obtained by parallelizing the StillingerWeber MD simulation was nearly 3.0. For the AIMD MP2 simulations, the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow transmission control protocol/Internet protocol networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl + 4H2O at the MP2/631G* level. Implemented in this way these algorithms can be used for long time highlevel AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. Using these algorithms, we are able to reduce the cost of a MP2/6311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 s/time step to 6.9 s/time step.

Informationtheoretic tools for parametrized coarsegraining of nonequilibrium extended systems
View Description Hide DescriptionIn this paper, we focus on the development of new methods suitable for efficient and reliable coarsegraining of nonequilibrium molecular systems. In this context, we propose error estimation and controlledfidelity model reduction methods based on PathSpace Information Theory, combined with statistical parametric estimation of rates for nonequilibrium stationary processes. The approach we propose extends the applicability of existing informationbased methods for deriving parametrized coarsegrained models to NonEquilibrium systems with Stationary States. In the context of coarsegraining it allows for constructing optimal parametrized Markovian coarsegrained dynamics within a parametric family, by minimizing information loss (due to coarsegraining) on the path space. Furthermore, we propose an asymptotically equivalent method—related to maximum likelihood estimators for stochastic processes—where the coarsegraining is obtained by optimizing the information content in path space of the coarse variables, with respect to the projected computational data from a finescale simulation. Finally, the associated pathspace Fisher Information Matrix can provide confidence intervals for the corresponding parameter estimators. We demonstrate the proposed coarsegraining method in (a) nonequilibrium systems with diffusing interacting particles, driven by outofequilibrium boundary conditions, as well as (b) multiscale diffusions and the corresponding stochastic averaging limits, comparing them to our proposed methodologies.
 Advanced Experimental Techniques

Generation of strong electric fields in an ice film capacitor
View Description Hide DescriptionWe present a capacitortype device that can generate strong electrostatic field in condensed phase. The device comprises an ice film grown on a cold metal substrate in vacuum, and the film is charged by trapping Cs+ ions on the ice surface with thermodynamic surface energy. Electric field within the charged film was monitored through measuring the film voltage using a Kelvin work function probe and the vibrational Stark effect of acetonitrile using IR spectroscopy. These measurements show that the electric field can be increased to ∼4 × 108 V m−1, higher than that achievable by conventional metal plate capacitors. In addition, the present device may provide several advantages in studying the effects of electric field on molecules in condensed phase, such as the ability to control the sample composition and structure at molecular scale and the spectroscopic monitoring of the sample under electric field.

Highlighting shortlived excited electronic states with pumpdegeneratefourwavemixing
View Description Hide DescriptionDetection of shortlived transient species is a major challenge in femtosecond spectroscopy, especially when thirdorder techniques like transient absorption are used. Higher order methods employ additional interactions between light and matter to highlight such transient species. In this work we address numerically and experimentally the detection of ultrafast species with pumpDegenerate Four Wave Mixing (pumpDFWM). In this respect, conclusive identification of ultrafast species requires the proper determination of timezero between all four laser pulses (pump pulse and the DFWM sequence). This is addressed here under the light of experimental parameters as well as molecular properties: The role of pulse durations, amount of pulse chirp as well as excited state life time is investigated by measuring a row of natural pigments differing mainly in the number of conjugated double bonds (N = 9 to 13). A comparison of the different signals reveals a strikingly unusual behavior of spheroidene (N = 10). Complete analysis of the pumpDFWM signal illustrates the power of the method and clearly assigns the uniqueness of spheroidene to a mixing of the initially excited state with a dark excited electronic state.

Measurement of Soret and Fickian diffusion coefficients by orthogonal phaseshifting interferometry and its application to protein aqueous solutions
View Description Hide DescriptionWe have developed a method to measure thermodiffusion and Fickian diffusion in transparent binary solutions. The measuring instrument consists of two orthogonally aligned phaseshifting interferometers coupled with a single rotating polarizer. This highresolution interferometer, initially developed to measure isothermal diffusion coefficients in liquid systems [J. F. Torres, A. Komiya, E. Shoji, J. Okajima, and S. Maruyama, Opt. Lasers Eng. 50, 1287 (2012)], was modified to measure transient concentration profiles in binary solutions subject to a linear temperature gradient. A convectionless thermodiffusion field was created in a binary solution sample that is placed inside a Soret cell. This cell consists of a parallelepiped cavity with a horizontal crosssection area of 10 × 20 mm2, a variable height of 1–2 mm, and transparent lateral walls. The small height of the cell reduces the volume of the sample, shortens the measurement time, and increases the hydrodynamic stability of the system. An additional free diffusion experiment with the same optical apparatus provides the socalled contrast factors that relate the unwrapped phase and concentration gradients, i.e., the measurement technique is independent and robust. The Soret coefficient is determined from the concentration and temperature differences between the upper and lower boundaries measured by the interferometer and thermocouples, respectively. The Fickian diffusion coefficient is obtained by fitting a numerical solution to the experimental concentration profile. The method is validated through the measurement of thermodiffusion in the wellknown liquid pairs of ethanolwater (ethanol 39.12 wt.%) and isobutylbenzenedodecane (50.0 wt.%). The obtained coefficients agree with the literature values within 5.0%. Finally, the developed technique is applied to visualize biomolecular thermophoresis. Two protein aqueous solutions at 3 mg/ml were used as samples: aprotinin (6.5 kDa)water and lysozyme (14.3 kDa)water. It was found that the former protein molecules are thermophilic and the latter thermophobic. In contrast to previously reported methods, this technique is suitable for both short time and negative Soret coefficient measurements.

Optical preparation of H_{2} rovibrational levels with almost complete population transfer
View Description Hide DescriptionUsing stimulated Raman adiabatic passage (SARP), it is possible, in principle, to transfer all the population in a rovibrational level of an isolated diatomic molecule to an excited rovibrational level. We use an overlapping sequence of pump (532 nm) and dump (683 nm) singlemode laser pulses of unequal fluence to prepare isolated H2 molecules in a molecular beam. In a first series of experiments we were able to transfer more than half the population to an excited rovibrational level [N. Mukherjee, W. R. Dong, J. A. Harrison, and R. N. Zare, J. Chem. Phys.138(5), 051101–1051101–4 (Year: 2013)]10.1063/1.4790402. Since then, we have achieved almost complete transfer (97% ± 7%) of population from the H2 (v = 0, J = 0) ground rovibrational level to the H2 (v = 1, J = 0) excited rovibrational level. An explanation is presented of the SARP process and how these results are obtained.

Measurement of the true transverse nuclear magnetic resonance relaxation in the presence of field gradients
View Description Hide DescriptionA measure of the nuclear spin transverse relaxation time T 2, as determined using the nuclear magnetic resonance CarrPurcell MeiboomGill (CPMG) experiment, provides unique information characterizing the microstructure of porous media which are themselves ubiquitous across fields of petrophysics, biophysics, and chemical engineering. However, the CPMG measurement is sensitive to diffusion in large magnetic field gradients. Under such conditions an effective relaxation time is observed instead, described by a combination of relaxation and diffusion exponents. The relaxation exponent always varies as nt e (where n is the number, and t e is the temporal separation, of spin echoes). The diffusion exponent varies as , where 1 < k ⩽ 3, although the exact analytic form is often unknown. Here we present a general approach to separating the influence of relaxation and diffusion by utilizing a composite diffusion exponent. Any component with a power of k > 1 is removed to provide a measure of the true T 2 relaxation time distribution from CPMG data acquired in the presence of a strong background gradient. We apply the technique to discriminate between the effects of relaxation and diffusion in porous media using catalysts and rocks as examples. The method is generally applicable to any CPMG measurements conducted in the presence of a static magnetic field gradient.