Volume 133, Issue 4, 28 July 2010

In this paper, we examine the secondharmonic generation(SHG) from spincast films of the conjugated polymer poly(2methoxy5(ethylhexyloxy)paraphenylenevinylene) (MEHPPV). We find that the SHG intensity depends strongly on the speed used to spin cast the films. Twodimensional grazing incidence xray diffraction(XRD) experiments show that the bulk crystallinity of the MEHPPV films varies in the same way with spin speed as the SHG intensity. This strongly suggests that instead of being interface specific, the secondharmonic signal from conjugated polymer films is dominated by the crystalline domains in the bulk. The nonmonotonic dependence of both the SHG intensity and the degree of MEHPPV crystallinity results from a competition between the shear forces and the solvent evaporation rate during spin coating, which produces a maximum degree of crystallinity for MEHPPV films spin cast at around 1400 rpm. We also use XRD to show that thermal annealing produces MEHPPV films with a single degree of bulk crystallinity, independent of how they were originally cast. This allows us to model the angle and thicknessdependent SHG from annealed MEHPPV films with a single polarizability tensor. We find that the SHG from MEHPPV films fits best to a bulkallowed electric quadrupole mechanism, consistent with the bulk SHG seen in other stacked aromatic molecules. Thus, rather than providing information about conjugated polymer interfaces, SHG can be used as a sensitive probe of the local degree of crystallinity in the bulk of conjugated polymer films.
 COMMUNICATIONS


Communication: Highfrequency acoustic excitations and boson peak in glasses: A study of their temperature dependence
View Description Hide DescriptionThe results of a combined experimental study of the highfrequency acoustic dynamics and of the vibrational density of states (VDOS) as a function of temperature in a glass of sorbitol are reported here. The excess in the VDOS at over the Debye, elastic continuum prediction (boson peak) is found to be clearly related to anomalies observed in the acoustic dispersion curve in the mesoscopic wavenumber range of few . The quasiharmonic temperature dependence of the acoustic dispersion curves offers a natural explanation for the observed scaling of the boson peak with the elastic medium properties.

Communication: Electric properties of the molecule
View Description Hide DescriptionTo assist the proposed search for the electric dipole moment of the electron with the thorium oxide, converged ab initiocoupled cluster calculations are performed on the interaction energy, dipole moment, anisotropic static dipole polarizability, and quadrupole moment of the molecule as functions of internuclear distance. The rovibrational energy levels and wave functions are computed to derive the spectroscopic constants and matrix elements of electric properties.Ab initio calculations provide good agreement with the measured spectroscopic constants but call for a revision of the dissociation energy estimates from massspectrometric measurements and previous calculations.
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 ARTICLES

 Theoretical Methods and Algorithms

Insights into the orbital invariance problem in statespecific multireference coupled cluster theory
View Description Hide DescriptionIn this communication we report the results of our studies on the orbital invariance properties of the statespecific multireference coupled cluster approach suggested by Mukherjee and coworkers (MkMRCC). In particular, we have gathered numerical evidence to show that even when the linear excitation manifold is modified in order to span the same space for each reference, the resulting method is not orbital invariant. In order to test this conjecture we have proposed a new truncation scheme (MkMRCCSDtq) which, in addition to full single and double excitations, contains partial triple and quadruple excitations. For a reference space generated by all possible combinations of two electrons in two orbitals, the linear excitation manifold of MkMRCCSDtq spans the same set for each reference determinant. MkMRCCSDtq is found to lack energy invariance for rotations among active molecular orbitals but it is less sensitive to orbital rotations than the conventional scheme which includes only singles and doubles (MkMRCCSD). Nevertheless, MkMRCCSDtq is a very accurate method, superior with respect to multireference configuration interaction approaches, and competitive with the activespace coupled cluster method and the MRexpT ansatz.

An efficient densityfunctionaltheory force evaluation for large molecular systems
View Description Hide DescriptionAn efficient, linearscaling implementation of Kohn–Sham densityfunctional theory for the calculation of molecular forces for systems containing hundreds of atoms is presented. The densityfitted Coulomb force contribution is calculated in linear time by combining atomic integral screening with the continuous fast multipole method. For higher efficiency and greater simplicity, the nearfield Coulomb force contribution is calculated by expanding the solidharmonic Gaussian basis functions in Hermite rather than Cartesian Gaussians. The efficiency and linear complexity of the molecularforce evaluation is demonstrated by sample calculations and applied to the geometry optimization of a few selected large systems.

Ab initio statistical mechanics of surface adsorption and desorption. II. Nuclear quantum effects
View Description Hide DescriptionWe show how the pathintegral formulation of quantum statistical mechanics can be used to construct practical ab initio techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule and generalize the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalizedgradient exchangecorrelation functional for the case of on the MgO (001) surface at low coverage. We note that the very high vibrational frequencies of the molecule would normally require very large numbers of time slices (beads) in pathintegral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our pathintegral calculations on the system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments.

Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model
View Description Hide DescriptionWe report on the results of testing the reference interaction site model (RISM) for the estimation of the hydration free energy of druglike molecules. The optimum model was selected after testing of different RISM free energy expressions combined with different quantum mechanics and empirical forcefield methods of structureoptimization and atomic partial charge calculation. The final model gave a systematic error with a standard deviation of 2.6 kcal/mol for a test set of 31 molecules selected from the SAMPL1 blind challenge set [J. P. Guthrie, J. Phys. Chem. B113, 4501 (2009)]. After parametrization of this model to include terms for the excluded volume and the number of atoms of different types in the molecule, the root mean squared error for a test set of 19 molecules was less than 1.2 kcal/mol.

A multistage ab initio quantum wavepacket dynamics formalism for electronic structure and dynamics in open systems
View Description Hide DescriptionWe propose a multistage quantum wavepacket dynamical treatment for the study of delocalized electronic systems as well as electron transport through donorbridgeacceptor systems such as those found in molecularwire/electrode networks. The full donorbridgeacceptor system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. These facilitate a computationally efficient and potentially accurate treatment of the longrange coupling interactions between the bridge and donor/acceptor systems and the associated open system boundary conditions. Timeindependent forms of the associated, partitioned equations are also derived. In the timeindependent form corresponding to the bridge system, coupling to donor and acceptor, that is longrange interactions, is completely accounted. For the timedependent study, the quantum dynamics of the electronic flux through the bridgedonor/acceptor interface is constructed using an accurate and efficient representation of the discretized quantummechanical freepropagator. A model for an electrodemolecular wireelectrode system is used to test the accuracy of the scheme proposed. Transmission probability is obtained directly from the probability density of the electronic flux in the acceptor region. Conductivity through the molecular wire is computed using a wavepacket flux correlation function.

Determination of spin Hamiltonians from projected single reference configuration interaction calculations. I. Spin 1/2 systems
View Description Hide DescriptionThe most reliable wavefunction based treatments of magnetic systems usually start from a complete active space selfconsistent field calculation of the magnetic electrons in the magnetic orbitals, followed by extensive and expensive configuration interaction (CI) calculations. This second step, which introduces crucial spin polarization and dynamic correlation effects, is necessary to reach reliable values of the magnetic coupling constants. The computational cost of these approaches increases exponentially with the number of unpaired electrons. The singledeterminantal unrestricted density functional Kohn–Sham calculations are computationally much simpler, and may provide reasonable estimates of these quantities, but their results are strongly dependent on the chosen exchangecorrelation potential. The present work, which may be seen as an ab initio transcription of the unrestricted density functional theory technique, returns to the perturbative definition of the Heisenberg Hamiltonian as an effective Hamiltonian, and proposes a direct estimate of its diagonal energies through single reference CI calculations. The differences between these diagonal terms actually determine the entire Heisenberg Hamiltonian. The reference determinants must be vectors of the model space and the components on the other vectors of the model space are cancelled along the iterative process. The method is successfully tested on a series of bicentric and multicentric spin systems. The projected single reference difference dedicated CI treatment is both accurate and of moderate cost. It opens the way to parameterfree calculations of large spin assemblies.

Embedding theory for excited states
View Description Hide DescriptionUsing the technique of Perdew and Levy [Phys. Rev. B31, 6264 (1985)], it is shown that both the density functiontheory (DFT)inDFT and wave functiontheory (WFT)inDFT embedding approaches are formally correct in studying not only the ground state but also a subset of the excited states of the total system. Without further approximations, the DFTinDFT embedding approach results in a pair of coupled Euler–Lagrange equations. In contrast to DFTinDFT, the WFTinDFT approach is shown to ensure a systematic description of excited states if such states are mainly related to excitations within the embedded subsystem. Possible ways for the practical realization of the WFTinDFT approach for studying excited states are briefly discussed.

A computational study of ultrafast acid dissociation and acidbase neutralization reactions. I. The model
View Description Hide DescriptionUltrafast, timeresolved investigations of acidbase neutralization reactions have recently been performed using systems containing the photoacid 8hydroxypyrene1,3,6trisulfonic acid trisodium salt (HPTS) and various Brønsted bases. Two conflicting neutralization mechanisms have been formulated by Mohammed et al. [Science310, 83 (2005)] and Siwick et al. [J. Am. Chem. Soc.129, 13412 (2007)] for the same acidbase system. Herein an ab initiomolecular dynamics based computational model is formulated, which is able to investigate the validity of the proposed mechanisms in the general context of groundstate acidbase neutralization reactions. Our approach consists of using 2,4,6tricyanophenol (exp. ) as a model for excitedstate and carboxylate ions for the accepting base. We employ our recently proposed dipolefield/quantum mechanics (QM) treatment [P. Maurer and R. Iftimie, J. Chem. Phys.132, 074112 (2010)] of the proton donor and acceptor molecules. This approach allows one to tune the free energy of neutralization to any desired value as well as model initial nonequilibrium hydration effects caused by a sudden increase in acidity, making it possible to achieve a more realistic comparison with experimental data than could be obtained via a fullQM treatment of the entire system. It is demonstrated that the dipolefield/QM model reproduces correctly key properties of the 2,4,6tricyanophenol acid molecule including gasphase proton dissociation energies and dipole moments, and condensedphase hydration structure and pKa values.

Analyzing molecular static linear response properties with perturbed localized orbitals
View Description Hide DescriptionPerturbed localized molecular orbitals (LMOs), correct to first order in an applied static perturbation and consistent with a chosen localization functional, are calculated using analytic derivative techniques. The formalism is outlined for a general static perturbation and variational localization functionals. Iterative and (formally) singlestep approaches are compared. The implementation employs an iterative sequence of orbital rotations. The procedure is verified by calculations of molecular electricfield perturbations. Boys LMO contributions to the electronic static polarizability and the electricfield perturbation of the expectation value are calculated and analyzed for ethene, ethyne, and fluoroethene . For ethene, a comparison is made with results from a Pipek–Mezey localization. The calculations show that a chemically intuitive decomposition of the calculated properties is possible with the help of the LMO contributions and that the polarizability contributions in similar molecules are approximately transferable.

Solidliquid surface free energy of LennardJones liquid on smooth and rough surfaces computed by molecular dynamics using the phantomwall method
View Description Hide DescriptionDifferent model LennardJones solidliquidinterfaces have been considered. In the systems, either the interaction strength between solid and liquid was varied, or the topography of the solid surface was modified. In all situations, the solidliquid interfacial free energy variations with respect to a reference solidliquidinterface were quantified by means of a thermodynamic integration method [F. Leroy et al., Macromol. Rapid Commun.30, 864 (2009)], referred to as the phantomwall method. Additionally, the liquidvapor surfacefree energy was determined. This result was combined with Young’s equation for contact angle calculations of cylindrical liquiddroplets. It allowed us to show that the change in contact angle of a droplet placed on smooth solid surfaces with respect to solidliquid interaction strength could be obtained by neglecting the solidvapor surfacefree energy contribution when the solidliquid interaction was weak. We also showed that the implementation of roughness by means of parallel grooves whose the density was varied could yield either higher or lower solidliquidsurfacefree energy, depending on the solidliquidsurfacefree energy of the smooth interface. Roughness led to lower surfacefree energy when the smooth surface had favorable interaction with the liquid, while it led to a higher surfacefree energy when the smooth surface had loose interactions with the liquid, though the effect was found to be weak. The consistency of the whole set of results, as well as agreement with the existing results on similar systems, shows the ability of the thermodynamic integration method employed here to capture the variation of interfacial thermodynamic quantities when modifying either the chemical nature or the topography of a solid surface in contact with a given liquid phase.

MultiJastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo
View Description Hide DescriptionA new type of electronic trial wavefunction suitable for quantum Monte Carlo calculations of molecular systems is presented. In contrast with the standard Jastrow–Slater form built with a unique global Jastrow term, it is proposed to introduce individual Jastrow factors attached to molecular orbitals. Such a form is expected to be more physical since it allows to describe differently the local electronic correlations associated with various molecular environments (core orbitals, magnetic orbitals, localized twocenter orbitals, delocalized orbitals, atomic lone pairs, etc.). In contrast with the standard form, introducing different Jastrow terms allows us to change the nodal structure of the wavefunction, a point which is important in the context of building better nodes for more accurate fixednode diffusion Monte Carlo (FNDMC) calculations. Another important aspect resulting from the use of local Jastrow terms is the possibility of defining and preoptimizing local and transferable correlated units for building complex trial wavefunctions from simple parts. The practical aspects associated with the computation of the intricate derivatives of the multiJastrow trial function are presented in detail. Some first illustrative applications for atoms of increasing size (O, S, and Cu) and for the potential energy curve and spectroscopic constants of the FH molecule are presented. In the case of the copper atom, the use of the multiJastrow form at the variational Monte Carlo level has allowed us to improve significantly the value of the total groundstate energy (about 75% of the correlation energy with only one determinant and three atomic orbital Jastrow factors). In the case of the FH molecule (fluorine hydride), it has been found that the multiJastrow nodes lead to an almost exact FNDMC value of the dissociation energy [ instead of the estimated nonrelativistic Born–Oppenheimer exact value of −141.1], which is not the case with standard nodes, .

Fluctuating dynamics of nematic liquid crystals using the stochastic method of lines
View Description Hide DescriptionWe construct Langevin equations describing the fluctuations of the tensor order parameter in nematic liquid crystals by adding noise terms to timedependent variational equations that follow from the Ginzburg–Landau–de Gennes free energy. The noise is required to preserve the symmetry and tracelessness of the tensor order parameter and must satisfy a fluctuationdissipation relation at thermal equilibrium. We construct a noise with these properties in a basis of symmetric traceless matrices and show that the Langevin equations can be solved numerically in this basis using a stochastic version of the method of lines. The numerical method is validated by comparing equilibrium probability distributions, structure factors, and dynamic correlations obtained from these numerical solutions with analytic predictions. We demonstrate excellent agreement between numerics and theory. This methodology can be applied to the study of phenomena where fluctuations in both the magnitude and direction of nematic order are important, as for instance, in the nematic swarms which produce enhanced opalescence near the isotropicnematic transition or the problem of nucleation of the nematic from the isotropic phase.

Electronic excitation energy calculation by the fragment molecular orbital method with threebody effects
View Description Hide DescriptionA scheme for full quantum electronic excited state calculation is proposed that is based on the fragment molecular orbital (FMO) method with threebody effects. The accuracy and efficiency of this scheme is checked by calculating the excitation energy of hydrated formaldehyde and hydrated phenol. In all cases, threebody effects improved the excitation energy by the one and twobody FMO methods with small computational cost, and the excitation energy approached more closely the full calculation value. The results also show that the threebody effects were relatively large and cannot be neglected.

Free energy calculation using molecular dynamics simulation combined with the three dimensional reference interaction site model theory. I. Free energy perturbation and thermodynamic integration along a coupling parameter
View Description Hide DescriptionThis article proposes a free energy calculation method based on the molecular dynamics simulation combined with the three dimensional reference interaction site modeltheory. This study employs the free energy perturbation (FEP) and the thermodynamic integration (TDI) along the coupling parameters to control the interaction potential. To illustrate the method, we applied it to a complex formation process in aqueous solutions between a crown ether molecule 18Crown6 (18C6) and a potassium ion as one of the simplest model systems. Two coupling parameters were introduced to switch the LennardJones potential and the Coulomb potential separately. We tested two coupling procedures: one is a “sequentialcoupling” to couple the LennardJones interaction followed by the Coulomb coupling, and the other is a “mixedcoupling” to couple both the LennardJones and the Coulomb interactions together as much as possible. The sequentialcoupling both for FEP and TDI turned out to be accurate and easily handled since it was numerically wellbehaved. Furthermore, it was found that the sequentialcoupling had relatively small statistical errors. TDI along the mixedcoupling integral path was to be carried out carefully, paying attention to a numerical behavior of the integrand. The present model system exhibited a nonmonotonic behavior in the integrands for TDI along the mixedcoupling integral path and also showed a relatively large statistical error. A coincidence within a statistical error was obtained among the results of the free energy differences evaluated by FEP, TDI with the sequentialcoupling, and TDI with the mixedcoupling. The last one is most attractive in terms of the computer power and is accurate enough if one uses a proper set of windows, taking the numerical behavior of the integrands into account. TDI along the sequentialcoupling integral path would be the most convenient among the methods we tested, since it seemed to be wellbalanced between the computational load and the accuracy. The numerical results reported in this article qualitatively agree with the experimental data for the potassium ion recognition by the 18C6 in aqueous solution.

An efficient umbrella potential for the accurate calculation of free energies by molecular simulation
View Description Hide DescriptionUmbrella sampling has been widely used to calculate free energies in many chemical and biological applications because it can effectively bridge the systems of interest and sample in the united phase space that is essential to yield accurate results. Many algorithms have implemented the idea of umbrella sampling that greatly improves the calculation of free energies. An efficient umbrella potential not only can connect the systems of interest, but also can lower the energetic barriers and facilitate the sampling over the relevant phase spaces. Here we present such an umbrella potential that is built on the equations of the weighted histogram analysis method. The proposed umbrella potential can facilitate the sampling of the important phase spaces of the systems of interest, which ensures the accurate calculation of free energies. We test this umbrella potential using a harmonicmodel system, a water system, and a LennardJones system. We demonstrate that this umbrella potential is effective in the circumstances when the systems of interest do not exhibit overlap in their phase spaces.

Hartree–Fock perturbative corrections for total and reaction energies
View Description Hide DescriptionWe have performed an assessment of the Hartree–Fock perturbative correction (HFPC) on a large and diverse set of molecules and reactions. Errors in both absolute and reaction energies with respect to converged secondary basis Hartree–Fock results are reported for a wide spectrum of primary/secondary basis set combinations. These results show that using an adequate primary basis, HFPC can accurately reproduce secondary basis energies at a substantially reduced cost. Comparisons of HFPC with the related dual basis Hartree–Fock (DBHF) scheme are also made for several molecules and target secondary basis sets. Our results indicate that HFPC is faster and more accurate than DBHF for approaching triplebasis sets. For quadruple secondary basis sets, HFPC is capable of yielding more accurate energies at a marginally increased cost over DBHF.

Transferability of anharmonic force fields in simulations of molecular vibrations
View Description Hide DescriptionAccurate simulations of vibrational molecular spectra require precise molecular force fields, at least with cubic and quartic anharmonic corrections beyond the harmonic limits. Generation of such force field terms becomes computationally prohibitive for larger molecules. In this work, an alternate possibility is explored, where approximate anharmonic force field components are obtained from molecular fragments. Transferability properties of the cubic and incomplete quartic fields are discussed and tested on model oligoproline molecules. Automatic transfer schemes including cubic, two and three atomic quartic force constants are developed and implemented. The results indicate that the main vibrational interactions in molecules are local and the anharmonic constants are mostly well amendable to the transfer. Exact anharmonic normal mode force fields of larger molecules compared very well to those obtained from smaller molecular parts. The most important changes in vibrational spectra caused by the anharmonic interactions could be reproduced with two and three atomic force field terms. The transfer scheme thus provides molecular anharmonic force fields without a significant loss of accuracy and brings significant savings of computer time and memory needed to generate molecular vibrational energies and spectra.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociation energy of the ground state of NaH
View Description Hide DescriptionThe dissociation energy of the ground state of NaH was determined by analyzing the observed near dissociation rovibrational levels. These levels were reached by stimulated emission pumping and fluorescence depletion spectroscopy. A total of 114 rovibrational levels in the ranges and were assigned to the state of NaH. The highest vibrational level observed was only about from the dissociation limit in the ground state. One quasibound state, above the dissociation limit and confined by the centrifugal barrier, was observed. Determining the vibrational quantum number at dissociation from the highest four vibrational levels yielded the dissociation energy. Based on new observations and available data, a set of Dunham coefficients and the rotationless Rydberg–Klein–Rees curve were constructed. The effective potential curve and the quasibound states were discussed.