Volume 137, Issue 6, 14 August 2012

Key to efficient harvesting of sunlight in photosynthesis is the first energy conversion process in which electronic excitation establishes a transmembrane charge gradient. This conversion is accomplished by the photosynthetic reaction center (RC) that is, in case of the purple photosynthetic bacterium Rhodobacter sphaeroides studied here, surrounded by light harvesting complex 1 (LH1). The RC employs six pigment molecules to initiate the conversion: four bacteriochlorophylls and two bacteriopheophytins. The excited states of these pigments interact very strongly and are simultaneously influenced by the surrounding thermal protein environment. Likewise, LH1 employs 32 bacteriochlorophylls influenced in their excited state dynamics by strong interaction between the pigments and by interaction with the protein environment. Modeling the excited state dynamics in the RC as well as in LH1 requires theoretical methods, which account for both pigmentpigment interaction and pigmentenvironment interaction. In the present study we describe the excitation dynamics within a RC and excitation transfer between light harvesting complex 1 (LH1) and RC, employing the hierarchical equation of motion method. For this purpose a set of model parameters that reproduce RC as well as LH1 spectra and observed oscillatory excitation dynamics in the RC is suggested. We find that the environment has a significant effect on LH1RC excitation transfer and that excitation transfers incoherently between LH1 and RC.
 ARTICLES

 Theoretical Methods and Algorithms

Spinorbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation
View Description Hide DescriptionA new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys.136, 034103 (2012)]10.1063/1.3675846 that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spinorbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spinorbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a wellestablished test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how oneelectron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.

Structurebased coarsegraining in liquid slabs
View Description Hide DescriptionStructurebased coarsegraining relies on matching the pair correlation functions of a reference (atomistic) and a coarsegrained system. As such, it is designed for systems with uniform density distributions. Here, we demonstrate how it can be generalized for inhomogeneous systems by coarsegraining slabs of liquid water and methanol in vacuum, as well as a single benzene molecule at the watervacuum interface. Our conclusion is that coarsegraining performed in inhomogeneous systems improves thermodynamic properties and the structure of interfaces without significant alterations to the local structure of the bulk liquid.

Dynamical hysteresis in a selfoscillating polymer gel
View Description Hide DescriptionAn ionic polymergel may undergo rhythmical swellingdeswelling kinetics induced by chemical oscillation. We demonstrate that the gel admits of dynamical hysteresis, which is manifested in the nonvanishing area of the response function—concentration (of reaction substrate) hysteresis loop, the response function being the integrated probability of residence of the polymer in any one of the swelled or deswelled states. The loop area depends on temperature and exhibits a turnover as a function of the strength of thermal noise—a phenomenon reminiscent of stochastic resonance. The numerical simulations agree well with our proposed analytical scheme.

Crystal lattice properties fully determine shortrange interaction parameters for alkali and halide ions
View Description Hide DescriptionAccurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements of aqueous solution properties such as hydration free energies and ionwater distribution functions. This dependency limits transferability of the resulting parameters because of the variety and known limitations of water models. We present a solventindependent approach to calibrating ion parameters based exclusively on crystal latticeproperties. Our procedure relies on minimization of lattice sums to calculate lattice energies and interionic distances instead of equilibrium ensemble simulations of dense fluids. The gain in computational efficiency enables simultaneous optimization of all parameters for Li+, Na+, K+, Rb+, Cs+, F−, Cl−, Br−, and I− subject to constraints that enforce consistency with periodic table trends. We demonstrate the method by presenting latticederived parameters for the primitive model and the LennardJones model with LorentzBerthelot mixing rules. The resulting parameters successfully reproduce the lattice properties used to derive them and are free from the influence of any water model. To assess the transferability of the LennardJones parameters to aqueous systems, we used them to estimate hydration free energies and found that the results were in quantitative agreement with experimentally measured values. These latticederived parameters are applicable in simulations where coupling of ion parameters to a particular solventmodel is undesirable. The simplicity and low computational demands of the calibration procedure make it suitable for parametrization of crystallizable ions in a variety of force fields.

CO oxidation on Ir(111) surfaces under large nonGaussian noise
View Description Hide DescriptionIn this article we consider the CO oxidation on Ir(111) surfaces under large external noise with large autocorrelation imposed on the composition of the feed gas, both in experiments and in theory. We report new experimental results that show how the fluctuations force the reaction rate to jump between two well defined states. The statistics of the reaction rate depend on those of the external noise, and neither of them have a Gaussian distribution, and thus they cannot be modeled by white or colored noise. A continuoustime discretestate Markov process is proposed as a suitable model for the observed phenomena. The model captures the main features of the observed fluctuations and can be modified to accommodate other surface reactions and other systems under nonGaussian external noise.

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations
View Description Hide DescriptionHydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N ^{2}) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the “block” version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing largescale Brownian dynamics simulations with hydrodynamic interactions.

Contributions of the electronic spin and orbital current to the magnetic field probed in polarised neutron diffraction experiments
View Description Hide DescriptionPolarised neutron diffractionexperiments conducted at 4.2 K on Cs_{3}CoCl_{5} crystals have been analysed by using a fourdimensional model Hilbert space made of ab initio nelectron wave functions of the molecular ion. Two spinorbit mixing coefficients and several configuration interaction coefficients have been optimized by fitting calculated magnetic structure factors to experimental ones, to obtain the best ensemble density operator that is representable in the model space. A goodness of fit, χ^{2}, less then 1 has been obtained for the first time for the two experimental data sets available. In the present article, the optimized density operators are used to calculate the magnetic field densities that are the genuine observables probed in neutron diffractionexperiments. Density maps of such observables are presented for the first time and numerical details are provided. The respective contributions of spin density and orbital current to the magnetic field density are analyzed.

Using enveloping distribution sampling to compute the free enthalpy difference between right and lefthanded helices of a βpeptide in solution
View Description Hide DescriptionRecently, the method of enveloping distribution sampling (EDS) to efficiently obtain free enthalpy differences between different molecular systems from a single simulation has been generalized to compute free enthalpy differences between different conformations of a system [Z. X. Lin, H. Y. Liu, S. Riniker, and W. F. van Gunsteren, J. Chem. Theory Comput.7, 3884 (2011)]. However, the efficiency of EDS in this case is hampered if the parts of the conformational space relevant to the two end states or conformations are far apart and the conformational diffusion from one state to the other is slow. This leads to slow convergence of the EDS parameter values and free enthalpy differences. In the present work, we apply the EDS methodology to a challenging case, i.e., to calculate the free enthalpy difference between a righthanded 2.710/12helix and a lefthanded 314helix of a hexaβpeptide in solution from a single simulation. No transition between the two helices was detected in a standard EDS parameter update simulation, thus enhanced sampling techniques had to be applied, which included adiabatic decoupling (AD) of solute and solvent motions in combination with increasing the solute temperature, and lowering the shear viscosity of the solvent. AD was found to be unsuitable to enhance the sampling of the solute conformations in the EDS parameter update simulations. Lowering the solvent shear viscosity turned out to be useful during EDS parameter update simulations, i.e., it did speed up the conformational diffusion of the solute, more transitions between the two helices were observed. This came at the cost of more CPU time spent due to the shorter time step needed for simulations with the lower solvent shear viscosity. Using an improved EDS parameter update scheme, parameter convergence was fivefold enhanced. The resulting free enthalpy difference between the two helices calculated from EDS agrees well with the result obtained through direct counting from a long MD simulation, while the EDS technique significantly enhances the sampling of both helices over nonhelical conformations.

Excitation transfer induced spectral diffusion and the influence of structural spectral diffusion
View Description Hide DescriptionThe theory of vibrational excitation transfer, which causes spectraldiffusion and is also influenced by structural spectraldiffusion, is developed and applied to systems consisting of vibrational chromophores. Excitation transfer induced spectraldiffusion is the timedependent change in vibrational frequency induced by an excitation on an initially excited molecule jumping to other molecules that have different vibrational frequencies within the inhomogeneously broadened vibrational absorption line. The excitation transfer process is modeled as Förster resonant transfer, which depends on the overlap of the homogeneous spectra of the donating and accepting vibrational chromophores. Because the absorption line is inhomogeneously broadened, two molecules in close proximity can have overlaps of their homogeneous lines that range from substantial to very little. In the absence of structural dynamics, the overlap of the homogeneous lines of the donating and accepting vibrational chromophores would be fixed. However, dynamics of the medium that contains the vibrational chromophores, e.g., a liquid solvent or a surrounding protein, produce spectraldiffusion.Spectraldiffusion causes the position of a molecule's homogeneous line within the inhomogeneous spectrum to change with time. Therefore, the overlap of donating and accepting molecules’ homogeneous lines is time dependent, which must be taken into account in the excitation transfer theory. The excitation transfer problem is solved for inhomogeneous lines with fluctuating homogeneous line frequencies. The method allows the simultaneous treatment of both excitation transfer induced spectraldiffusion and structural fluctuation induced spectraldiffusion. It is found that the excitation transfer process is enhanced by the stochastic fluctuations in frequencies. It is shown how a measurement of spectraldiffusion can be separated into the two types of spectraldiffusion, which permits the structural spectraldiffusion to be determined in the presence of excitation transfer spectraldiffusion. Various approximations and computational methodologies are explored.

What are the most efficient basis set strategies for correlated wave function calculations of reaction energies and barrier heights?
View Description Hide DescriptionAs electronic structure methods are being used to obtain quantitatively accurate reaction energies and barrier heights for increasingly larger systems, the choice of an efficient basis set is becoming more critical. The optimum strategy for achieving basis set convergence can depend on the way that electron correlation is treated and can take advantage of flexibility in the order in which basis functions are added. Here we study several approaches for estimating accurate reaction energies and barrier heights from postHartree–Fock electronic structure calculations. First and second, we evaluate methods of estimating the basis set limit of second order MøllerPlesset perturbation theory and of coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations by using explicitly correlated basis functions (in the F12a implementation) along with valence, polarization, and diffuse oneelectron basis functions. Third, we test the scheme of adding a higherorder correction to MP2 results (sometimes called MP2/CBS + ΔCCSD(T)). Finally, we evaluate the basis set requirements of these methods in light of comparisons to Weizmann3.2, Weizmann4, and CCSDT(2)_{Q}/CBS+CV+R results.

Timedependent partitioning theory of the control of radiationless transitions in 24mode pyrazine
View Description Hide DescriptionWe consider the control of internal conversion between the S _{2}(^{1} B _{2u }) excited electronic state of pyrazine and the S _{1}(^{1} B _{3u }) state. The study is performed both during and after the femtosecond excitation of the ground electronic state S _{0}(^{1} A _{ g }) to form the S _{2} state. The dynamics is examined using the newly developed “effective modes” technique which enables the full computation of quantum dynamics in multidimensional spaces. Using this technique, we also investigate the coherent control of population transfer from S _{0} to the S _{2} and S _{1} electronic states. We find that the use of shaped laser pulses enables a significant delay of the internal conversion. For example, after 60 fs, the S _{2} population amounts to ∼60% of the initial S _{0} population, and remains at ∼20% after 100 fs, in contrast to the S _{0} electronic state which is completely depopulated within 75 fs.

Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation
View Description Hide DescriptionA methodology for the rigorous nonperturbative derivation of magnetic pseudospin Hamiltonians of mononuclear complexes and fragments based on ab initio calculations of their electronic structure is described. It is supposed that the spinorbit coupling and other relativistic effects are already taken fully into account at the stage of quantum chemistry calculations of complexes. The methodology is based on the establishment of the correspondence between the ab initiowave functions of the chosen manifold of multielectronic states and the pseudospin eigenfunctions, which allows to define the pseudospin Hamiltonians in the unique way. Working expressions are derived for the pseudospin Zeeman and zerofield splitting Hamiltonian corresponding to arbitrary pseudospins. The proposed calculation methodology, already implemented in the SINGLE_ANISO module of the MOLCAS7.6 quantum chemistry package, is applied for a firstprinciples evaluation of pseudospin Hamiltonians of several complexes exhibiting weak, moderate, and very strong spinorbit couplingeffects.

A generalized manybody expansion and a unified view of fragmentbased methods in electronic structure theory
View Description Hide DescriptionFragmentbased quantum chemistry methods are a promising route towards massively parallel electronic structure calculations in large systems. Unfortunately, the literature on this topic consists of a bewildering array of different methods, with no clear guiding principles to choose amongst them. Here, we introduce a conceptual framework that unifies many of these ostensibly disparate approaches. The common framework is based upon an approximate supersystem energy formula for a collection of intersecting (i.e., overlapping) fragments. This formula generalizes the traditional manybody expansion to cases where the “bodies” (fragments) share some nuclei in common, and reduces to the traditional manybody expansion for nonoverlapping fragments. We illustrate how numerous fragmentbased methods fit within this framework. Preliminary applications to molecular and ionic clusters suggest that twobody methods in which dimers are constructed from intersecting fragments may be a route to achieve very high accuracy in fragmentbased calculations.

Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion
View Description Hide DescriptionWe propose a kinetic Monte Carlo method for the simulation of subdiffusive random walks on a Cartesian lattice. The random walkers are subject to viscoelastic forces which we compute from their individual trajectories via the fractional Langevin equation. At every step the walkers move by one lattice unit, which makes them differ essentially from continuous time random walks, where the subdiffusive behavior is induced by random waiting. To enable computationally inexpensive simulations with nstep memories, we use an approximation of the memory and the memory kernel functions with a complexity . Eventual discretization and approximation artifacts are compensated with numerical adjustments of the memory kernel functions. We verify with a number of analyses that this new method provides binary fractional random walks that are fully consistent with the theory of fractional Brownian motion.

Density functional theory for Yukawa fluids
View Description Hide DescriptionWe develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the meanfield approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to “dressed counterions,” interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.

Computer simulation of the role of torsional flexibility on mass and momentum transport for a series of linear alkanes
View Description Hide DescriptionWe present the results obtained from a systematic equilibrium molecular dynamics study of the effect of torsional flexibility on the diffusion and viscosity of a series of linear alkanes. To make unambiguous comparisons between molecules with torsional flexibility and those without, we use the frozen distribution sampling (FDS) method introduced by Travis et al. [J. Chem. Phys.98, 1524 (1993)10.1063/1.464317; Travis et al.J. Chem. Phys.102, 2174 (1995)]10.1063/1.468739 but modified and updated for increased efficiency. We first demonstrate comprehensively that FDS guarantees corresponding thermodynamic states. We then show that removal of torsional flexibility results in a significant lowering of the diffusion coefficient (and corresponding increase in shear viscosity) and furthermore that this effect increases with increasing chain length. The results are discussed in terms of the possible mechanism giving rise to this dynamic coupling phenomenon.

Selfinteraction correction in a realtime KohnSham scheme: Access to difficult excitations in timedependent density functional theory
View Description Hide DescriptionWe present a realtime KohnSham propagation scheme for the selfinteraction correction (SIC). The multiplicative KohnSham potential is constructed in realtime and realspace based on the generalized optimized effective potential equation. We demonstrate that this approach yields promising results for a wide range of test systems, including hydrogen terminated silicon clusters, conjugated molecular chains, and molecular chargetransfer systems. We analyze the nature of excitations by calculating transition densities from the time evolution and by evaluating the timedependent exchangecorrelation potential. A properly constructed KohnSham SIC potential shows a timedependent fieldcounteracting behavior. These favorable characteristics of the exchangecorrelation potential may be lost in approximations such as the SICSlater potential.

Variational properties of the discrete variable representation: Discrete variable representation via effective operators
View Description Hide DescriptionA variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator has been introduced. By calculating its matrix elements exactly one obtains, depending on the choice of the basis set, either a variational FBR or a variational DVR. The domain of grid points on which the FBR/DVR is variational has been shown to consist of the subsets of the set of grid points one obtains by diagonalizing commuting variational basis representations of the coordinate operators. The variational property implies that the optimal of the subsets of a fixed number of points, i.e., the subset which gives the possible highest accuracy eigenpairs, gives the DVR of the smallest trace. The symmetry properties of the variational FBR/DVR Hamiltonian operator are analyzed and methods to incorporate symmetry into FBR/DVR calculations are discussed. It is shown how the Fourierbasis FBR/DVR suitable to solving periodic systems arise within the theory presented. Numerical examples are given to illustrate the theoretical results. The use of variational effective Hamiltonian and coordinate operators has been instrumental in this study. They have been introduced in a novel way by exploiting quasiHermiticity.
 Atoms, Molecules, and Clusters

Feasibility of encoding Shor's algorithm into the motional states of an ion in the anharmonic trap
View Description Hide DescriptionWe demonstrate theoretically that it may be possible to encode states of a multiqubit system into the progression of quantized motional/vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radiofrequency fields shaped optimally for excitation of the desired statetostate transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different statetostate transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the fourqubit version of Shor's algorithm in a single step. Accuracy of the qubitstate transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the timeevolution of state populations and by spectral analysis of the optimized pulse.

Influence of velocity effects on the shape of N_{2} (and air) broadened H_{2}O lines revisited with classical molecular dynamics simulations
View Description Hide DescriptionThe modeling of the shape of H_{2}O lines perturbed by N_{2} (and air) using the KeilsonStorer (KS) kernel for collisioninduced velocity changes is revisited with classical molecular dynamics simulations (CMDS). The latter have been performed for a large number of molecules starting from intermolecularpotential surfaces. Contrary to the assumption made in a previous study [H. Tran, D. Bermejo, J.L. Domenech, P. Joubert, R. R. Gamache, and J.M. Hartmann, J. Quant. Spectrosc. Radiat. Transf.108, 126 (2007)]10.1016/j.jqsrt.2007.03.009, the results of these CMDS show that the velocityorientation and modulus changes statistically occur at the same time scale. This validates the use of a single memory parameter in the KeilsonStorer kernel to describe both the velocityorientation and modulus changes. The CMDS results also show that velocity and rotational statechanging collisions are statistically partially correlated. A partially correlated speeddependent KeilsonStorer model has thus been used to describe the lineshape. For this, the velocity changes KS kernel parameters have been directly determined from CMDS, while the speeddependent broadening and shifting coefficients have been calculated with a semiclassical approach. Comparisons between calculated spectra and measurements of several lines of H_{2}O broadened by N_{2} (and air) in the ν_{3} and 2ν_{1} + ν_{2} + ν_{3} bands for a wide range of pressure show very satisfactory agreement. The evolution of nonVoigt effects from Doppler to collisional regimes is also presented and discussed.