Volume 130, Issue 4, 28 January 2009
 ARTICLES

 Theoretical Methods and Algorithms

Coarsegrained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment
View Description Hide DescriptionThe prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, and short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained models, where either the whole molecule (carbon dioxide, benzene, and methane) or a group of a few successive groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard–Jones (LJ) potentials such that the vaporliquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupolequadrupole interaction is included. These models are shown to provide a satisfactory description of the liquidvapor phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz–Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modeled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modeling of polar mixtures at low computational cost. In many cases Monte Carlo simulations of such models (employing the grandcanonical ensemble together with reweighting techniques, successive umbrella sampling, and finite size scaling) yield accurate results in very good agreement with experimental data. Simulation results are quantitatively compared to an analytical approximation for the equation of state of the same model, which is computationally much more efficient, and some systematic discrepancies are discussed. These very simple coarsegrained models of small molecules developed here should be useful, e.g., for simulations of polymer solutions with such molecules as solvent.

An arbitrary order Douglas–Kroll method with polynomial cost
View Description Hide DescriptionA new Douglas–Kroll transformation scheme up to arbitrary order is presented to study the convergence behavior of the Douglas–Kroll series and the influence of different choices of parametrization for the unitary transformation. The standard approach for evaluating the Douglas–Kroll Hamiltonian suffers from computational difficulties due to the huge number of matrix multiplications, which increase exponentially with respect to the order of truncation. This makes it prohibitively expensive to obtain results for very high order Douglas–Kroll Hamiltonians. The highest order previously presented is 14th order, but it is not enough to obtain accurate results for systems containing heavy elements, where the Douglas–Kroll series converges very slowly. In contrast, our approach dramatically reduces the number of matrix multiplications, which only increase with a polynomial scaling. With the new method, orders greater than 100 and machine accuracy are possible. This fast method is achieved by employing a special transformation to all Douglas–Kroll operators and our algorithm is very simple. We demonstrate the performance of our implementation with calculations on oneelectron systems and manyelectron atoms. All results show very good convergence behavior of the Douglas–Kroll series. Very small differences are found between the different parametrizations, and therefore the exponential form, which is the simplest and fastest, is recommended.

Double spinflip approach within equationofmotion coupled cluster and configuration interaction formalisms: Theory, implementation, and examples
View Description Hide DescriptionThe spinflip (SF) approach is extended to excitations that flip the spin of two electrons to describe multiconfigurational wave functions via high spin quintet references. Equations and implementation of the double SF (2SF) approach within equationofmotion coupledcluster (EOMCC) and configuration interaction (CI) formalisms are presented. The numerical performance of the resulting EOM2SFCC and 2SFCI models is demonstrated by calculations of symmetric dissociation of O–H bonds in water, electronic states of linear , double CC bondbreaking in ethylene, and lowlying states of trimethylenemethyl diradical and 2,4didehydrometaxylylene tetraradical. The results of activespace variants of 2SF are very close to the more computationally expensive fullspace counterparts. An efficient implementation of the activespace approximation of the 2SFconfiguration interaction doubles (CID) model termed 2SFconfiguration interaction singles (CIS) is also reported. The scaling of 2SFCIS is only , which allows applications to relatively large molecules.

Effect of an external electric field on the dissociation energy and the electron density properties: The case of the hydrogen bonded dimer ^{a)}
View Description Hide DescriptionThe effect of a homogeneous external electric field parallel to the hydrogen bond in the dimer has been studied by theoretical methods. The quantum theory of atoms in molecules methodology has been used for analyzing the electron distribution of the dimer, calculated with different hydrogen bond distances and external field magnitudes. It is shown that an electric field in the opposite direction to the dipole moment of the system strengthens the interaction due to a larger mutual polarization between both molecules and increases the covalent character of the hydrogen bond, while an external field in the opposite direction has the inverse effect. The properties of the complex at its equilibrium geometry with applied field have been calculated, showing that dependencies between hydrogen bond distance, dissociation energy, and properties derived from the topological analysis of the electron distribution are analogous to those observed in families of complexes. The application of an external field appears as a useful tool for studying the effect of the atomic environment on the hydrogen bond interaction. In the case of , both the kinetic energy density and the curvature of the electron density along the hydrogen bond at the bond critical point present a surprisingly good linear dependence on the dissociation energy. The interaction energy can be modeled by the sum of two exponential terms that depend on both the hydrogen bond distance and the applied electric field. Moreover, as indicated by the resulting interaction energy observed upon application of different external fields, the equilibrium distance varies linearly with the external field, and the dependence of the dissociation energy on either the hydrogen bond distance or the external electric field is demonstrated to be exponential.

Excitonic versus electronic couplings in molecular assemblies: The importance of nonnearest neighbor interactions
View Description Hide DescriptionWe demonstrate that for a range of phenylene and thiophenebased conjugated polymers of practical relevance for optoelectronic applications, exciton couplings in onedimensional stacks deviate significantly from the nearest neighbor approximation. Instead, longrange interactions with nonnearest neighbors have to be included, which become increasingly important with growing oligomer size. While the exciton coupling vanishes for infinitely long ideal polymer chains and provides a sensitive measure of the actual conjugation length, the electronic coupling mediating chargetransport shows rapid convergence with molecular size. Similar results have been obtained for very different molecular backbones, thus highlighting the general character of these findings.

Analytic expressions for electrical energy and electrical force of two spheres
View Description Hide DescriptionAnalytical expressions for the electrical force and the electrical energy of two spheres immersed in a symmetric electrolytesolution are derived under conditions of constant surface potential and constant surface charge. Previous analysis under Debye–Huckel condition (linear case) is extended to the corresponding nonlinear case; because the level of the surface potential is arbitrary the results obtained have much wider applications. In general, the performance of the analytical formulas derived is satisfactory, and better than that of the available results in literature. For the case of constant surface potential, the analytic formulas obtained are most accurate for large particles, and for the case of constant surface charge, they are most accurate for small particles.

A systematic understanding of orbital energy shift in polar solvent
View Description Hide DescriptionThe orbital energy of molecule is significantly shifted upon going from gas phase to solution phase. Based on Koopmans’ theorem, the shift should be related to the change of ionization potential. However, the computed shift looks usually random and clear understanding has not been attained yet. Furthermore it is obtained only after solving complicated equations. In this study, we report a systematic framework for understanding the orbital energy shift by solvation effect and simple approximate formulae are presented.

Double excitations in finite systems
View Description Hide DescriptionTimedependent densityfunctional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double and higherexcitation characters, which are particularly important in molecules with an openshell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchangecorrelation (xc) kernel, the calculated excitation energies have a strict singleexcitation character and are fewer than the real ones. A frequencydependent xc kernel could create extra poles in the response function, which would describe states with a multipleexcitation character. We introduce a frequencydependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe–Salpeter equation with a dynamically screened Coulomb interaction , which can describe these excitations, and from this we obtain the xc kernel. Using a twoelectron model system, we show that the frequency dependence of does indeed introduce the double excitations that are instead absent in any static approximation of the electronhole screening.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Enthalpy of formation and anharmonic force field of diacetylene
View Description Hide DescriptionThe enthalpy of formation of diacetylene is pinpointed using stateoftheart theoretical methods, accounting for highorder electron correlation, relativistic effects, nonBorn–Oppenheimer corrections, and vibrational anharmonicity. Molecular energies are determined from coupled cluster theory with single and double excitations (CCSD), perturbative triples [CCSD(T)], full triples (CCSDT), and perturbative quadruples [CCSDT(Q)], in concert with correlationconsistentbasis sets (, , T, Q, 5, 6) that facilitate extrapolations to the complete basis set limit. The first full quartic force field of diacetylene is determined at the highly accurate allelectron CCSD(T) level with a ccpCVQZ basis, which includes tight functions for core correlation. Application of secondorder vibrational perturbation theory to our anharmonic force field yields fundamental frequencies with a mean absolute difference of only relative to the experimental band origins, without the use of any empirical scale factors. By a focal point approach, we converge on an enthalpy change for the isogyric reaction of (, ) at (0, 298.15) K. With the precisely established of acetylene, we thus obtain at (0, 298.15) K. Previous estimates of the diacetylene enthalpy of formation range from 102 to .

Modespecific photoionization dynamics of a simple asymmetric target: OCS
View Description Hide DescriptionVibrationally resolved photoelectron spectra of are used to probe coupling between photoelectron motion and molecular vibration for a simple asymmetric system. Spectra are reported over the photonenergy range of . Vibrational branching ratios for all of the normal modes are determined and the results exhibit modespecific deviations from Franck–Condon behavior. Schwinger variational calculations indicate the presence of four shape resonances, two resonances and two resonances. All of the resonances play a role in the observed vibrationally resolved behavior. Two results are striking; first, the resonances are more sensitive to the C–O stretch than to the C–S stretch, particularly for photonenergies above 30 eV. This relative insensitivity of the resonance to geometry changes involving a thirdrow element is similar to other systems studied. Second, theoretical results lead to the counterintuitive conclusion that bending the molecule suppresses the high energyresonance, even though there is an enhancement in the vibrational branching ratio curve for the single quantum bending excitation. The agreement between the theoretical and experimental branching ratio curves is good. Finally, the results unambiguously demonstrate that the forbidden bending excitation is caused by photoelectronmediated vibronic coupling, i.e., the variation in the electronic transition matrix element with geometry, rather than the traditional explanation of interchannel vibronic coupling with intensity borrowing between ionic states.

New infrared spectra of the nitrous oxide trimer
View Description Hide DescriptionInfrared spectra of trimers are studied using a tunable diode laser to probe a pulsed supersonic slitjet expansion. A previous observation by Miller and Pedersen [J. Chem. Phys.108, 436 (1998)] in the combination band region showed the trimer structure to be noncyclic, with three inequivalent monomer units which could be thought of as an dimer (slipped antiparallel configuration) plus a third monomer unit lying above the dimer plane. The present observations cover the fundamental band regions and . In the region, two trimer bands are assigned with vibrational shifts and other characteristics similar to those in the region, but in the region all three possible trimer bands are observed. Relationships among the various bands are considered with reference to their rotational intensity patterns, their vibrational shifts, and the properties of the related dimer, with results that generally support the conclusions of Miller and Pedersen. Three trimer bands are also observed for the fully substituted species in the region, and these results should aid in the detection of the asyetunobserved pure rotational microwave spectrum of the trimer.

Formation of heavyRydberg ionpair states in collisions of Rydberg atoms with attaching targets
View Description Hide DescriptionThe formation of heavyRydberg ionpair states through electron transfer in collisions between Rydberg atoms and molecules that attach lowenergy electrons is investigated. The measurements show that lowcollisions with a wide variety of target species (, , , and ) can lead to formation of bound ionpair states and that, under appropriate conditions, a small fraction of these can subsequently dissociate as free ions through internaltotranslational energy transfer. Analysis of the data suggests that those ion pairs that do dissociate typically have lifetimes of , although some can have lifetimes of or longer.

The collisional depolarization of radicals by closed shell atoms: Theory and application to
View Description Hide DescriptionClassical and quantum mechanical expressions for the vector correlation (also referred to as the rotational tilt) are presented for the situation in which the initial and final relative velocity directions are unresolved. The quantum mechanical expressions are compared with previous descriptions in the literature. It is shown that in the case of radicals in collision with closed shell species, a tensoropacity formalism can be employed in quasiclassical trajectory calculations to provide classical estimates of both open shell spinrotation state and nuclear hyperfine state changing (or conserving) cross sections. Polarization parameters are also obtained from the same formalism. The method is applied to calculations on the system using a recently developed potential energy surface. The results of both the closed and open shell quasiclassical trajectory calculations are found to compare favorably with those from closecoupled closed and open shell quantum mechanical scattering calculations. The accompanying paper provides an experimental test of these calculations and of the potential energy surface they employ.

Collisional depolarization of with Ar: Experiment and theory
View Description Hide DescriptionZeemanquantum beat spectroscopy has been used to measure the 300 K rate constants for the angular momentum depolarization of in the presence of Ar. We show that the beat amplitude at short times, in the absence of collisions, is well described by previously developed line strength theory for laser induced fluorescence. The subsequent pressure dependent decay of the beat amplitude is used to extract depolarization rate constants and estimates of collisional depolarization cross sections. Depolarization accompanies both inelastic collisions, giving rise to rotational energy transfer, and elastic collisions, which change but conserve . Previous experimental studies, as well as classical theory, suggest that elastic scattering contributes around 20% to the observed total depolarization rate at low . Simulation of the experimental beat amplitudes, using theoretical calculations presented in the preceding paper, reveals that depolarization of OH(A) by Ar has a rate constant comparable to, if not larger than, that for energy transfer. This is consistent with a significant tilting or realignment of away from on collision. The experimental data are used to provide a detailed test of quantum mechanical and quasiclassical trajectory scattering calculations performed on a recently developed ab initio potential energy surface of Kłos et al. [J. Chem. Phys.129, 054301 (2008)]. The calculations and simulations account well for the observed cross sections at high , but underestimate the experimental results by between 10% and 20% at low , possibly due to remaining inaccuracies in the potential energy surface or perhaps to limitations in the dynamical approximations made, particularly the freezing of the bond.

Photodissociation of vinyl cyanide at 193 nm: Nascent product distributions of the molecular elimination channels
View Description Hide DescriptionThe photodissociation dynamics of vinyl cyanide (, acrylonitrile) and deuterated vinyl cyanide at 193 nm are examined using timeresolved Fourier transform infrared emission spectroscopy. Prior photofragment translational spectroscopy studies [D. A. Blank et al., J. Chem. Phys.108, 5784 (1998)] of the dissociation have observed the presence of four main dissociation channels; two molecular and two radical in nature. However, with the exception of quantum yield determined for the CN radical loss channel, the branching ratios of the remaining three elimination channels were not measured. The timeresolvedemission spectra, including those from the deuterated samples, revealed the presence of acetylene, hydrogen cyanide (HCN), as well as the energetically less stable isomer hydrogen isocyanide (HNC). Acetylene is found in two distinct energetic distributions, suggesting that both three and fourcentered elimination reactions are occurring significantly in the dissociation. In contrast to prior ab initio studies that have suggested the dominant nature of the threecenter elimination of molecular hydrogen and cyanovinylidene , we find this reaction channel to be of little importance as there is no evidence to support any significant presence of rovibrationally excited cyanoacetylene. Spectral modeling of the product distributions allows for the first experimental determination of the relative occurrence of the threecentered (resulting in ) versus fourcentered elimination channels as 3.34 to 1.00, in contrast to the previously calculated value of 126:1. Rice–Ramsperger–Kassel–Marcus analysis depicts that the transition state energy of the fourcentered reaction should be about lower than the threecentered reaction.

Control of photodissociation and photoionization of the NaI molecule by dynamic Stark effect
View Description Hide DescriptionThe diabatic photodissociation and photoionization processes of the NaI molecule are studied theoretically using the quantum wave packet method. A pump laser pulse is used to prepare a dissociation wave packet that propagates through both the ionic channel and the covalent channel . A Stark pulse is used to control the diabatic dissociation dynamics and a probe pulse is employed to ionize the products from the two channels. Based on the first order nonresonant nonperturbative dynamic Stark effect, the dissociation probabilities and the branching ratio of the products from the two channels can be controlled. Moreover the final photoelectron kinetic energy distribution can also be affected by the Stark pulse. The influences of the delay time, intensity, frequency, and carrierenvelope phase of the Stark pulse on the dissociation and ionization dynamics of the NaI molecule are discussed in detail.

NMR shielding constants in and magnetic dipole moments of and nuclei
View Description Hide DescriptionGasphase NMR spectra of , , and in are reported, and highlevel ab initio calculations of the corresponding NMR shielding constants are described. Extrapolation of the measuredresonance frequencies to the zerodensity limit ensures that the results correspond to the ab initio values for an isolated molecule. Simultaneous measurements of resonance frequencies and application of the calculated shielding constants allow us to determine improved values of the nuclear magnetic dipole moments of and . The magnetic moments of both isotopes are also determined independently by comparing with the spectral parameters (frequencies and shielding constants). The separately derived nuclear magnetic moments are in good agreement, whereas the literature moments of both and are noticeably less accurate.

Photodissociation of the propargyl and propynyl radicals at 248 and 193 nm
View Description Hide DescriptionThe photodissociation of perdeuterated propargyl and propynyl radicals was investigated using fast beam photofragment translational spectroscopy. Radicals were produced from their respective anions by photodetachment at 540 and 450 nm (below and above the electron affinity of propynyl). The radicals were then photodissociated at 248 or 193 nm. The recoiling photofragments were detected in coincidence with a time and positionsensitive detector. Three channels were observed: loss, , and . Observation of the D loss channel was incompatible with this experiment and was not attempted. Our translational energy distributions for loss peaked at nonzero translational energy, consistent with ground statedissociation over small exit barriers with respect to separated products. Translational energy distributions for the two heavy channels peaked near zero kinetic energy, indicating dissociation on the ground state in the absence of exit barriers.

Reading molecular messages from highorder harmonic spectra at different orientation angles
View Description Hide DescriptionWe investigate the orientation dependence of highorder harmonic generation (HHG) from with different internuclear distances irradiated by intense laser fields both numerically and analytically. The calculated molecular HHG spectra are found to be sensitive to the molecular axis orientation relative to incident laser field polarization and internuclear separation. In particular, our simulations demonstrate that at certain harmonic orders the envelopes of the HHG spectra taken at different orientation angles intersect. Moreover, the position of intersection is largely independent of the laser intensity while strongly dependent on the internuclear separation. This striking “intersection” phenomenon is identified as arising due to intramolecular twocenter interference in the HHG and can be used to probe the molecular instantaneous structure.

Theoretical investigation of the direct observation of anharmonic coupling in in the time domain with femtosecond stimulated Raman scattering
View Description Hide DescriptionThe femtosecond stimulated Raman scattering (FSRS) difference spectra of from the ground potential energy surface, with and without offresonance impulsive stimulated Raman pumping, taken at various delay times from the impulsive pump by Kukura et al. [Phys. Rev. Lett.96, 238303 (2006)], showed sidebands of the C–Cl bends with periodic changes in phase as well as having an inversion symmetry to the high and low frequency sides of the Stokes C–D stretch at . The semiclassical coupledwave approach and a onedimensional (1D) oscillator model for the C–D stretch whose frequency is modulated in time by the C–Cl bends could account for some features of the experimental results. Here, a quantum mechanical investigation is made of the FSRS difference spectra with a modulated 1D oscillator and threedimensional (3D) harmonic and anharmonic potentials. It is shown that (i) the sidebands are allowed, with or without anharmonic coupling between the C–D stretch and the C–Cl bends, (ii) in the 3D harmonic model the sidebands have mirror symmetry about the Stokes C–D stretch, (iii) in the 3D anharmonic model with appropriate coupling terms between the C–D stretch and the C–Cl bends, the experimental results are well accounted for in both the phase changes in the FSRS difference spectra with time delay as well as the inversion symmetry of the sidebands for the C–Cl bends about the Stokes C–D stretch, (iv) there is a correspondence between the phase changes in the FSRS difference spectra and the wavepacket motion induced by the impulsive pump pulse on the ground potential energy surface as a function of the delay time, and (v) changing the polarization of the impulsive pump pulse, say, directly affects the coordinate dependence of the linear transition dipole moment in the asymmetric mode and hence its phase in the FSRS difference spectra, but not so for the symmetric modes where the displacement of the excited statesurface governs the FSRS difference spectra more than the transition dipole moment. This work illustrates the potential of offresonance FSRS in studying polyatomic molecular dynamics.