Volume 126, Issue 18, 14 May 2007
 COMMUNICATIONS


Excited state calculations on fluorenebased polymer blends: Effect of stacking orientation and solvation
View Description Hide DescriptionPolyfluorenebased polymer blends have been utilized in the development of optoelectronic devices. The constituent copolymers are chemically designed to facilitate more efficient electron/hole mobility, thereby enhancing control over exciton formation and dissociation. When appropriate pairs of these are blended together, intermolecular chargedparticle localizations are induced, leading to significant intermolecular chargetransfer character and luminescence that exhibit some sensitivity to their interfacial orientation. The authors report on a timedependent density functional theory quantum chemical investigation of the relevant excited states of the polymer blend poly[9,9dioctylfluoreneco(4butylphenyl)diphenylamine]/poly(9,9dioctylfluorenecobenzothiadiazole. They show that the calculated excited states generally agree with experimental observations although there is a consistent underestimation of the chargetransfer states. Further, they show sensitivity to lateral shifts in interfacial stacking. Finally, solvation with a low dielectric solvent greatly stabilizes the chargetransfer states.

Ab initio simulation of a gadoliniumbased magnetic resonance imaging contrast agent in aqueous solution
View Description Hide DescriptionThe first ab initiomolecular dynamics simulation of a Gd(III)based contrast agent in explicit aqueous solution at ambient conditions as used in the actual magnetic resonance imaging of human bodies is presented. The description of the structure of this chelate complex is considerably improved with respect to typical force fields and ab initio calculations in continuum solventmodels if the open shell of Gd is included explicitly. The solvationshell structure is revealed to be anionic and includes a rather short hydrogen bond donated by the hydroxypropyl arm.

Morphological change during crystallization of thin amorphous solid water films on Ru(0001)
View Description Hide DescriptionThe isothermal crystallization process of thin amorphous solid water (ASW) films on Ru(0001) has been investigated in real time by simultaneously employing helium atom scattering, infrared reflection absorption spectroscopy, and isothermal temperatureprogrammed desorption. The measurements reveal that the crystallization mechanism consists of random nucleation events in the bulk of the ASW films, followed by homogeneous growth. Morphological changes of the solid water film during crystallization expose the water monolayer just above the substrate to the vacuum during the crystallization process.
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 ARTICLES

 Theoretical Methods and Algorithms

Twoelectron reduced density matrices from the antiHermitian contracted Schrödinger equation: Enhanced energies and properties with larger basis sets
View Description Hide DescriptionTwoelectron reduced density matrices (2RDMs) have recently been directly determined from the solution of the antiHermitian contracted Schrödinger equation (ACSE) to obtain 95%–100% of the groundstatecorrelationenergy of atoms and molecules, which significantly improves upon the accuracy of the contracted Schrödinger equation (CSE) [D. A. Mazziotti, Phys. Rev. Lett.97, 143002 (2006)]. Two subsets of the CSE, the ACSE and the contraction of the CSE onto the oneparticle space, known as the 1,3CSE, have two important properties: (i) dependence upon only the 3RDM and (ii) inclusion of all secondorder terms when the 3RDM is reconstructed as only a firstorder functional of the 2RDM. The error in the 1,3CSE has an important role as a stopping criterion in solving the ACSE for the 2RDM. Using a computationally more efficient implementation of the ACSE, the author treats a variety of molecules, including , , HCN, and , in larger basis sets such as correlationconsistent polarized double and triplezeta. The groundstateenergy of neon is also calculated in a polarized quadruplezeta basis set with extrapolation to the complete basisset limit, and the equilibrium bond length and harmonic frequency of are computed with comparison to experimental values. The author observes that increasing the basis set enhances the ability of the ACSE to capture correlation effects in groundstateenergies and properties. In the triplezeta basis set, for example, the ACSE yields energies and properties that are closer in accuracy to coupled cluster with single, double, and triple excitations than to coupled cluster with single and double excitations. In all basis sets, the computed 2RDMs very closely satisfy known representability conditions.

Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution
View Description Hide DescriptionThe authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes and the effect of thermal excitation. The method automatically selects the relevant vibronic contributions to the spectrum, independently of their frequency, and it is able to provide fully converged spectra with moderate computational times, both in vacuo and in solution. By describing the electronic states in the frame of the density functional theory and its timedependent extension, they computed the room temperature absorption spectra of coumarin C153 and transstilbene in cyclohexane and the phosphorescencespectrum of porphyrazine in gas phase, showing that the method is fast and efficient. The comparison with experiment for transstilbene and coumarin C153 is very satisfactory, confirming the progress made toward a reliable method for the computation and interpretation for the optical spectra of large molecules.

“All possible steps” approach to the accelerated use of Gillespie’s algorithm
View Description Hide DescriptionMany physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by Gillespie about three decades ago [J. Phys. Chem.81, 2340 (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study the author presents a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data the author demonstrates high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.

Density functionals and transitionmetal atoms
View Description Hide DescriptionDensityfunctional calculations on transitionmetal atoms are problematic due to the numerous possible ways, having inequivalent densities, of occupying the orbitals. The problem is compounded by the issue of real orbitals versus complex orbitals. In this work we systematize the application of densityfunctional theories to transitionmetal atoms using a currentdensitydependent functional. For all the singledeterminantal angular momentum eigenstates of groundstate terms, we obtain near degeneracy for the energies as we should. Also, we find a simple rule for occupying the real orbitals that reproduces the energies of the (complex) angular momentum eigenstate results. Thus the longstanding confusion over how to compute transitionmetal atom reference energies is resolved.

Quantum effect of intramolecular highfrequency vibrational modes on diffusioncontrolled electron transfer rate: From the weak to the strong electronic coupling regions
View Description Hide DescriptionThe SumiMarcus theory is extended by introducing two approaches to investigate electron transferreactions from weaktostrong electronic coupling regime. One of these approaches is the quantum matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reactiondiffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the matrix approach is much smaller than that from the LandauZener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solventrelaxation time on the rates are also explored.

Timedependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities
View Description Hide DescriptionThe authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequencydependent Sternheimer equation, within the formalism of timedependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a realspace (basissetfree) code and applied it to benchmark molecules, namely, CO, , and paranitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.

New mixed quantum∕semiclassical propagation method
View Description Hide DescriptionThe authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use lowdimensional systems, in which comparison to exact quantum dynamics is feasible.

Interpolating moving leastsquares methods for fitting potential energy surfaces: Computing highdensity potential energy surface data from lowdensity ab initio data points
View Description Hide DescriptionA highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolatingmovingleastsquares (IMLS)based method is developed using lowdensity ab initio Hessian values to compute highdensity PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modifiedShepardbased methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in highorder IMLSbased methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which highorder IMLS is used with lowdensity ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even highorder IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modifiedShepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for onedimensional model potentials as well as for threedimensional (HCN) and sixdimensional (HOOH) molecular PESs.

Phasespace approach to dynamical density functional theory
View Description Hide DescriptionThe authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing timedependent equation for the onebody density. They show that, after suitable truncations of the BogoliubovBornGreenKirkwoodYvon hierarchy, and a multiple time scale analysis, they obtain a selfconsistent equation involving only the onebody density. This study extends to arbitrary dimensions previous work on a onedimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.

Enveloping distribution sampling: A method to calculate free energy differences from a single simulation
View Description Hide DescriptionThe authors present a method to calculate free energy differences between two states and “on the fly” from a single molecular dynamics simulation of a reference state . No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state which is designed such that the subset of phase space important to it is the union of the parts of phase space important to and . Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interactionperturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replicaexchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to and , respectively. This can be explained by the total absence of phase space overlap of and in these two cases.

Molecular dynamics simulation with stochastically constrained pressure
View Description Hide DescriptionThe authors propose a new algorithm for molecular dynamics simulation. The method includes a Monte Carlo scheme for incrementing the dilation rate in the equations of motion. The new algorithm needs no extra computation and the dynamics of the system preserves its continuity. Application of this approach is very advantageous for models where the derivation and the computation of the pressure is time consuming. The authors present results of model calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Experimental and theoretical studies of the electronic structure and the ionization and dissociation processes of trifluoromethyl peroxynitrate
View Description Hide DescriptionIn this work, we present a complete study of the ionization and dissociation processes for trifluoromethyl peroxynitrate . was generated by UV photolysis of a mixture of , , and . The product was detected and characterized by the photoelectron spectroscopy (PES) and photoionization mass spectroscopy (PIMS). The geometric and electronic structures of were investigated by the combination of experiments and the density functional and ab initio calculations. It is worthwhile mentioning that drastic changes occur in the geometry of after ionization. Due to the removal of one electron from the O–N bond, the COON dihedral angle changes to 180° and as a result, the nonplanar structure becomes planar. And the O–N single bond length increases remarkably, with the positive charge most localized on the moiety. The experimental first vertical ionization potential is . Based on the calculated bonddissociation energies, the dissociation pathway was predicted. The calculated results explain the ion intensities observed in the photoionization mass spectrum. The dissociation of O–N single bond is found to be the most favored of the possible dissociation paths for .

: Molecules with simultaneous planar tetracoordinate carbon, aluminum, and silicon/germanium
View Description Hide DescriptionThe authors report the first theoretical study on the hexaatomic molecules at the , , and (single point) levels. Three lowlying isomers (within ) can be formally viewed as constructed by one interacting with the planar at the side Al–X bond (X1), side Al–Al bond (X2), and central C atom (X3). The isomers X1 and X2 both have planar structures that include the planar tetracoordinate carbon,aluminum, and silicon/germanium, while the threedimensional isomer X3 has the pentacoordinate carbon. The planarity of X1 and X2 is ascribed to the ligand fivecenter twoelectron bonding molecular orbital, similar to the orbital responsible for the planarity of . Kinetically, the two planar structures X1 and X2 can be easily interconverted to each other via the intermediate X3, indicative of their coexistence. Of particular interest, isomer X1 represents the first example that simultaneously contains three types of planar centers in a single molecule, to the best of our knowledge. The three lowlying and structurally interesting isomers X1, X2, and X3 await future experimental verification. The present results could enrich the planar chemistry.

Spinorbit relaxation of and in a gas of
View Description Hide DescriptionThe authors present quantum scattering calculations of rate coefficients for the spinorbit relaxation of atoms in a gas of molecules and atoms in a gas of and molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in agrees very well with an experimental measurement at room temperature. It is found that the spinorbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state is dominated by the nearresonant electronictorotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spinorbit relaxation in collisions with molecules increases to a great extent with the rotational excitation of the molecules. They have found that the isotope effect in the relaxation of is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in and at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.

Combined vacuum ultraviolet laser and synchrotron pulsed field ionization study of
View Description Hide DescriptionThe pulsed field ionizationphotoelectron (PFIPE) spectrum of bromochloromethane in the region of has been measured using vacuum ultraviolet laser. The vibrational structure resolved in the PFIPE spectrum was assigned based on ab initio quantum chemical calculations and FranckCondon factor predictions. At energies above the adiabatic ionizationenergy (IE) of , the Br–C–Cl bending vibration progression of is well resolved and constitutes the major structure in the PFIPE spectrum, whereas the spectrum at energies above the is found to exhibit complex vibrational features, suggesting perturbation by the low lying excited state. The assignment of the PFIPE vibrational bands gives the and the bending frequencies for . We have also examined the dissociativephotoionization process, , in the energy range of using the synchrotron based PFIPEphotoion coincidence method, yielding the threshold or appearance energy. Combining the and values obtained in this study, together with the known , we have determined the bond dissociation energies for and . We have also performed CCSD(T, full)/complete basis set (CBS) calculations with highlevel corrections for the predictions of the , , , , and . The comparison between the theoretical predictions and experimental determinations indicates that the CCSD(T, full)/CBS calculations with highlevel corrections are highly reliable with estimated error limits of .

Nuclear quadrupole moment of from highaccuracy atomic calculations
View Description Hide DescriptionThe electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment from experimental nuclear quadrupole coupling constants possible. The fourcomponent DiracCoulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fockspace coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to uncontracted Gaussians) are employed. Energy splittings of the and levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with up to , whereas the latter display significant nonlinearity even at Larger values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between values derived from and data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of is . It is lower than the muonic and agrees within error bounds with the recent value of obtained from molecular calculations.

Photoelectron studies of neutral in helium droplets
View Description Hide DescriptionPhotoelectron spectra of neutral silver trimers, grown in ultracold helium nanodroplets, are recorded after ionization with laser pulses via a strong optical resonance of this species. Varying the photon energy reveals that direct vertical twophotonionization is hindered by a rapid relaxation into the lower edge of a longliving excited state manifold. An analysis of the ionization threshold of the embedded trimer yields an ionization potential of consistent with the value found in the gas phase. The asymmetrical form of the electron energy spectrum, which is broadened toward lower kinetic energies, is attributed to the influence of the matrix on the photoionization process. The lifetime of the excited state was measured in a twocolor pumpprobe experiment to be .