Volume 138, Issue 23, 21 June 2013
 ARTICLES

 Theoretical Methods and Algorithms

Features in chemical kinetics. I. Signatures of selfemerging dimensional reduction from a general format of the evolution law
View Description Hide DescriptionSimplification of chemical kinetics description through dimensional reduction is particularly important to achieve an accurate numerical treatment of complex reacting systems, especially when stiff kinetics are considered and a comprehensive picture of the evolving system is required. To this aim several tools have been proposed in the past decades, such as sensitivity analysis, lumping approaches, and exploitation of time scales separation. In addition, there are methods based on the existence of the socalled slow manifolds, which are hypersurfaces of lower dimension than the one of the whole phasespace and in whose neighborhood the slow evolution occurs after an initial fast transient. On the other hand, all tools contain to some extent a degree of subjectivity which seems to be irremovable. With reference to macroscopic and spatially homogeneous reacting systems under isothermal conditions, in this work we shall adopt a phenomenological approach to let selfemerge the dimensional reduction from the mathematical structure of the evolution law. By transforming the original system of polynomial differential equations, which describes the chemical evolution, into a universal quadratic format, and making a direct inspection of the highorder timederivatives of the new dynamic variables, we then formulate a conjecture which leads to the concept of an “attractiveness” region in the phasespace where a welldefined statedependent rate function ω has the simple evolution along any trajectory up to the stationary state. This constitutes, by itself, a drastic dimensional reduction from a system of Ndimensional equations (being N the number of chemical species) to a onedimensional and universal evolution law for such a characteristic rate. Stepbystep numerical inspections on model kinetic schemes are presented. In the companion paper [P. Nicolini and D. Frezzato, J. Chem. Phys.138, 234102 (Year: 2013)]10.1063/1.4809593 this outcome will be naturally related to the appearance (and hence, to the definition) of the slow manifolds.

Features in chemical kinetics. II. A selfemerging definition of slow manifolds
View Description Hide DescriptionIn the preceding paper of this series (Part I [P. Nicolini and D. Frezzato, J. Chem. Phys.138, 234101 (Year: 2013)]10.1063/1.4809592) we have unveiled some ubiquitous features encoded in the systems of polynomial differential equations normally applied in the description of homogeneous and isothermal chemical kinetics (massaction law). Here we proceed by investigating a deeply related feature: the appearance of socalled slow manifolds (SMs) which are lowdimensional hypersurfaces in the neighborhood of which the slow evolution of the reacting system occurs after an initial fast transient. Indeed a geometrical definition of SM, devoid of subjectivity, “naturally” follows in terms of a specific subdimensional domain embedded in the peculiar region of the concentrations phasespace that in Part I we termed as “attractiveness region.” Numerical inspections on simple lowdimensional model cases are presented, including the benchmark case of Davis and Skodje [J. Chem. Phys.111, 859 (Year: 1999)]10.1063/1.479372 and the preliminary analysis of a simplified model mechanism of hydrogen combustion.

On the analytical representation of free energy profiles with a Morse/longrange model: Application to the water dimer
View Description Hide DescriptionWe investigate the analytical representation of potentials of mean force (pmf) using the Morse/longrange (MLR) potential approach. The MLR method had previously been used to represent potential energy surfaces, and we assess its validity for representing freeenergies. The advantage of the approach is that the potential of mean force data only needs to be calculated in the short to medium range region of the reaction coordinate while the long range can be handled analytically. This can result in significant savings in terms of computational effort since one does not need to cover the whole range of the reaction coordinate during simulations. The water dimer with rigid monomers whose interactions are described by the commonly used TIP4P model [W. Jorgensen and J. Madura, Mol. Phys.56, 1381 (Year: 1985)]10.1080/00268978500103111 is used as a test case. We first calculate an “exact” pmf using direct Monte Carlo (MC) integration and term such a calculation as our gold standard (GS). Second, we compare this GS with several MLR fits to the GS to test the validity of the fitting procedure. We then obtain the water dimer pmf using metadynamics simulations in a limited range of the reaction coordinate and show how the MLR treatment allows the accurate generation of the full pmf. We finally calculate the transition state theory rate constant for the water dimer dissociation process using the GS, the GS MLR fits, and the metadynamics MLR fits. Our approach can yield a compact, smooth, and accurate analytical representation of pmf data with reduced computational cost.

Relative efficacy of vibrational vs. translational excitation in promoting atomdiatom reactivity: Rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model
View Description Hide DescriptionTo provide a systematic and rigorous reexamination of the wellknown Polanyi's rules, excitation functions of several A + BC(v = 0, 1) reactions are determined using the Chebyshev real wave packet method on accurate potential energy surfaces. Reactions with early (F + H2 and F + HCl), late (Cl + H2), and central (H/D/Mu + H2, where Mu is a shortlived light isotope of H) barriers are represented. Although Polanyi's rules are in general consistent with the quantum dynamical results, their predictions are strictly valid only in certain energy ranges divided by a crossover point. In particular, vibrational excitation of the diatomic reactant typically enhances reactivity more effectively than translational excitation at high energies, while reverse is true at low energies. This feature persists irrespective of the barrier location. A sudden vector projection model is proposed as an alternative to Polanyi's rules. It is found to give similar, but more quantitative, predictions about mode selectivity in these reactions, and has the advantage to be extendible to reactions involving polyatomic molecules.

Multiscale modeling with smoothed dissipative particle dynamics
View Description Hide DescriptionIn this work, we consider two issues related to the use of Smoothed Dissipative Particle Dynamics (SDPD) as an intermediate mesoscale model in a multiscale scheme for solution of flow problems when there are local parts of a macroscopic domain that require molecular resolution. The first is to demonstrate that SDPD with different levels of resolution can accurately represent the fluid properties from the continuum scale all the way to the molecular scale. Specifically, while the thermodynamic quantities such as temperature, pressure, and average density remain scaleinvariant, we demonstrate that the dynamic properties are quantitatively consistent with an allatom LennardJones reference system when the SDPD resolution approaches the atomistic scale. This supports the idea that SDPD can serve as a natural bridge between molecular and continuum descriptions. In the second part, a simple multiscale methodology is proposed within the SDPD framework that allows several levels of resolution within a single domain. Each particle is characterized by a unique physical length scale called the smoothing length, which is inversely related to the local number density and can change onthefly. This multiscale methodology is shown to accurately reproduce fluid properties for the simple problem of steady and transient shear flow.

Grand canonical Monte Carlo simulations of vaporliquid equilibria using a bias potential from an analytic equation of state
View Description Hide DescriptionThis article introduces an efficient technique for the calculation of vaporliquid equilibria of fluids. Umbrella Sampling Monte Carlo simulations in the grand canonical ensemble were conducted for various types of molecules. In Umbrella Sampling, a weight function is used for allowing the simulation to reach unlikely states in the phase space. In the present case this weight function, that allows the system to overcome the energetic barrier between a vapor and liquid phase, was determined by a trivialized Density Functional Theory (DFT) using the PCSAFT equation of state. The implementation presented here makes use of a multicanonical ensemble approach to divide the space of fluctuating particle number N into various subsystems. The a priori estimate of the weight function from the analytic DFT allows the parallelization of the calculation, which significantly reduces the computation time. In addition, it is shown that the analytic equation of state can be used to substitute sampling the dense liquid phase, where the sampling of insertion and deletion moves become demanding.

Predicting the thermodynamics by using statedependent interactions
View Description Hide DescriptionWe reconsider the structurebased route to coarse graining in which the coarsegrained model is defined in such a way to reproduce some distribution functions of the original system as accurately as possible. We consider standard expressions for pressure and chemical potential applied to this family of coarsegrained models with densitydependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the lowdensity regime and polymer solutions under goodsolvent conditions. Moreover, we show that the statedependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical statedependent potentials to predict phase lines, which is typically performed in other ensembles.

A gauge invariant multiscale approach to magnetic spectroscopies in condensed phase: General threelayer model, computational implementation and pilot applications
View Description Hide DescriptionAnalytical equations to calculate second order electric and magnetic properties of a molecular system embedded into a polarizable environment are presented. The treatment is limited to molecules described at the self consistent field level of theory, including Hartree–Fock theory as well as KohnSham density functional theory and is extended to the GaugeIncluding Atomic Orbital method. The polarizable embedding is described by means of our already implemented polarizable quantum mechanical/molecular mechanical (MM) methodology, where the polarization in the MM layer is handled by means of the fluctuating charge (FQ) model. A further layer of description, i.e, the polarizable continuum model, can also be included. The FQ(/polarizable continuum model) contributions to the properties are derived, with reference to the calculation of the magnetic susceptibility, the nuclear magnetic resonance shielding tensor, electron spin resonance gtensors, and hyperfine couplings.
 Advanced Experimental Techniques

Parahydrogeninduced polarization at zero magnetic field
View Description Hide DescriptionWe use symmetry arguments and simple model systems to describe the conversion of the singlet state of parahydrogen into an oscillating sample magnetization at zero magnetic field. During an initial period of free evolution governed by the scalarcoupling Hamiltonian H J , the singlet state is converted into scalar spin order involving spins throughout the molecule. A short dc pulse along the z axis rotates the transverse spin components of nuclear species I and S through different angles, converting a portion of the scalar order into vector order. The development of vector order can be described analytically by means of singletransition operators, and it is found to be maximal when the transverse components of I are rotated by an angle of ±π/2 relative to those of S. A period of free evolution follows the pulse, during which the vector order evolves as a set of oscillating coherences. The imaginary parts of the coherences represent spin order that is not directly detectable, while the real parts can be identified with oscillations in the z component of the molecular spin dipole. The dipole oscillations are due to a periodic exchange between I z and S z , which have different gyromagnetic ratios. The frequency components of the resulting spectrum are imaginary, since the pulse cannot directly induce magnetization in the sample; it is only during the evolution under H J that the vector order present at the end of the pulse evolves into detectable magnetization.
 Atoms, Molecules, and Clusters

Ab initio potential energy surface and vibrationrotation energy levels of lithium monohydroxide
View Description Hide DescriptionThe accurate groundstate potential energy surface of lithium monohydroxide (LiOH) has been determined from ab initio calculations using the coupledcluster approach in conjunction with the correlationconsistent corevalence basis sets up to septuplezeta quality. Results obtained with the conventional and explicitly correlated coupledcluster methods were compared. The higherorder electron correlation, scalar relativistic, and adiabatic effects were taken into account. The vibrationrotation energy levels of the LiOH, LiOD, Li18OH, and 6LiOH isotopologues were predicted to near “spectroscopic” accuracy.

Gyroscopic destabilisation in polyatomic molecules: Rotational structure of the lowfrequency bending vibrational states ν_{23} and ν_{11} of dimethylsulfoxide
View Description Hide DescriptionWe give details of the spectroscopic observation of the gyroscopic destabilisation in the ν23 vibrational state of dimethylsulfoxide (DMSO) announced by Cuisset, Pirali, and Sadovskií [Phys. Rev. Lett.109, 094101 (Year: 2012)]10.1103/PhysRevLett.109.094101. Following the first successful highresolution spectroscopic study of the rotational structure of the “perpendicular” band of DMSO at 324 cm−1 associated with the ν23 bending vibrational mode, the rare subsystem of ν23 rotational levels consisting of a series of fourfold quasidegenerate levels (4clusters) was identified. Our complete analysis of the underlying rotational dynamics uncovered a bifurcation leading to the gyroscopic destabilisation of one of the two stable principal axes of inertia, a phenomenon known previously only in a few triatomic molecules.

Accurate structure, thermodynamics, and spectroscopy of mediumsized radicals by hybrid coupled cluster/density functional theory approaches: The case of phenyl radical
View Description Hide DescriptionThe coupledcluster singles doubles model with perturbative treatment of triples (CCSD(T)) coupled with extrapolation to the complete basisset limit and additive approaches represent the “golden standard” for the structural and spectroscopic characterization of building blocks of biomolecules and nanosystems. However, when openshell systems are considered, additional problems related to both specific computational difficulties and the need of obtaining spindependent properties appear. In this contribution, we present a comprehensive study of the molecular structure and spectroscopic (IR, Raman, EPR) properties of the phenyl radical with the aim of validating an accurate computational protocol able to deal with conjugated openshell species. We succeeded in obtaining reliable and accurate results, thus confirming and, partly, extending the available experimental data. The main issue to be pointed out is the need of going beyond the CCSD(T) level by including a full treatment of triple excitations in order to fulfil the accuracy requirements. On the other hand, the reliability of density functional theory in properly treating openshell systems has been further confirmed.

Negative ions of pnitroaniline: Photodetachment, collisions, and ab initio calculations
View Description Hide DescriptionThe structures of parent anion, M−, and deprotonated molecule, [M−H]−, anions of the highly polar pnitroaniline (p NA) molecule are studied experimentally and theoretically. Photoelectron spectroscopy (PES) of the parent anion is employed to estimate the adiabatic electron affinity (EAa = 0.75 ± 0.1 eV) and vertical detachment energy (VDE = 1.1 eV). These measured energies are in good agreement with computed values of 0.73 eV for the EAa and the range of 0.85 to 1.0 eV for the VDE at the EOMCCSD/AugccpVTZ level. Collision induced dissociation (CID) of deprotonated p NA, [p NA − H]−, with argon yielded [p NA − H − NO]− (i.e., rearrangement to give loss of NO) with a threshold energy of 2.36 eV. Calculations of the energy difference between [p NA − H]− and [p NA − H − NO]− give 1.64 eV, allowing an estimate of a 0.72 eV activation barrier for the rearrangement reaction. Direct dissociation of [p NA − H]− yielding occurs at a threshold energy of 3.80 eV, in good agreement with theory (between 3.39 eV and 4.30 eV). As a result of the exceedingly large dipole moment for p NA (6.2 Debye measured in acetone), we predict two dipolebound states, one at ∼110 meV and an excited state at 2 meV. No dipolebound states are observed in the photodetachment experiments due the pronounced mixing between states with dipolebound and valence character similar to what has been observed in other nitro systems. For the same reason, dipolebound states are expected to provide highly efficient “doorway states” for the formation of the p NA − valence anion, and these states should be observable as resonances in the reverse process, that is, in the photodetachment spectrum of p NA − near the photodetachment threshold.

Ultrafast dynamics in C 1s coreexcited CF_{4} revealed by twodimensional resonant Auger spectroscopy
View Description Hide DescriptionFollowing core excitation in an isolated molecule, ultrafast dissociation of one particular chemical bond can occur, where “ultrafast” is defined as taking place during the lifetime of the core hole, of the order of few femtoseconds. The signature of such phenomenon can be observed in resonant Auger spectra following core excitation. We present here an investigation of ultrafast dissociation following C 1stoσ* core excitation in CF4, with highresolution resonant Auger spectroscopy. We are able to characterize final states of both the molecular ion and the fragment. We use twodimensional (2D) maps to record resonant Auger spectra across the resonance as a function of photon energy and to characterize ultrafast dynamics. This method provides immediate visual evidence of one of the important characteristics of the study of spectral features related to molecular versus fragment ionic final states, and namely their dispersion law. In the 2D maps we are also able to identify the dissociation limit for one of the molecular final states.

The photoelectron angular distribution of water clusters
View Description Hide DescriptionThe angular distribution of photoelectrons emitted from water clusters has been measured by linearly polarized synchrotron radiation of 40 and 60 eV photon energy. Results are given for the three outermost valence orbitals. The emission patterns are found more isotropic than for isolated molecules. While a simple scattering model is able to explain most of the deviation from molecular behavior, some of our data also suggest an intrinsic change of the angular distribution parameter. The angular distribution function was mapped by rotating the axis of linear polarization of the synchrotron radiation.

Theoretical explanation of the lowlying ν_{6} vibrational fundamental of the FSO_{3} radical by the linear vibronic coupling approach
View Description Hide DescriptionThe first attempt for a theoretical explanation of the ν6 fundamental energy levels of the fluorosulfate radical (FSO3) electronic ground state has been made. The vibronic interaction of the two lowest electronic states of the radical ( 2 A 2 and 2 E) has been taken into consideration in the basis of the linear vibronic coupling (LVC) approximation. The strengths of the intrastate and interstate vibronic couplings have been calculated within the framework of the Köppel, Domcke, and Cederbaum (KDC) model Hamiltonian. Already this simple KDCLVC model provides the ν6 fundamental energy, which is in very good agreement with the experimental results. From the inclusion of vibronic interactions such as the pseudoJahnTeller and JahnTeller effects into the calculation of the fundamental energy of the ν6 mode, it can be said that mainly the interstate coupling with the electronic excited state E causes the unexpectedly low fundamental energy ν6 of the FSO3 radical.

Quantum decoherence of I_{2} in liquid xenon: A classical Wigner approach
View Description Hide DescriptionVibrational decoherence of a “breathing sphere” oscillator in a thermal LennardJones bath is examined using a classical analog approach. The equivalence between this approach and the linearized semiclassical initial value representation (IVR) is established and the method is exploited to produce a useful computational strategy that can efficiently evaluate the time dependence of the decoherence in these systems. A comparison between Harmonic and Morse “breathing sphere” models is presented and the rate of decoherence is found to depend on the choice of model, the initial state of the oscillator, the initial conditions of the bath (temperature, density), and the choice of quantity measuring the decoherence rate. The results are used to examine the utility of the CaldeiraLeggett model in this realistic system.

Dissociative electron attachment to hexafluoroacetylacetone and its bidentate metal complexes M(hfac)_{2}; M = Cu, Pd
View Description Hide DescriptionBetadiketones are a versatile class of compounds that can complex almost any metal in the periodic table of elements. Their metal complexes are found to be fairly stable and generally have sufficient vapor pressure for deposition techniques requiring volatile metal sources. Motivated by the potential role of low energy electrons in focused electron beam induced deposition, we have carried out a crossed electron/molecular beam study on the dissociative electron attachment and nondissociative electron attachment (NDEA) to hexafluoroacetylacetone (HFAc) and its bidentate metal complexes: bishexafluoroacetylacetonate copper(II), Cu(hfac)2 and bishexafluoroacetylacetonate palladium(II), Pd(hfac)2. The relative ion yield curves for the native precursor to the ligand as well as its stable, 16 valence electron Pd(II) complex and open shell, 17 valence electron Cu(II) complex, are presented and compared. For HFAc, the loss of HF leads to the dominant anion observed, and while NDEA is only weakly pronounced for Pd(hfac)2 and loss of hfac− is the main dissociation channel, [Cu(hfac)2]− formation from Cu(hfac)2 dominates. A comparison of the ion yield curves and the associated resonances gives insight into the role of the ligand in the attachment process and highlights the influence of the central metal atom.

Intensity oscillations in the carbon 1s ionization cross sections of 2butyne
View Description Hide DescriptionCarbon 1s photoelectron spectra for 2butyne (CH3C≡CCH3) measured in the photon energy range from threshold to 150 eV above threshold show oscillations in the intensity ratio C2,3/C1,4. Similar oscillations have been seen in chloroethanes, where the effect has been attributed to EXAFStype scattering from the substituent chlorine atoms. In 2butyne, however, there is no highZ atom to provide a scattering center and, hence, oscillations of the magnitude observed are surprising. The results have been analyzed in terms of two different theoretical models: a densityfunctional model with Bspline atomcentered functions to represent the continuum electrons and a multiplescattering model using muffintin potentials to represent the scattering centers. Both methods give a reasonable description of the energy dependence of the intensity ratios.

Lowenergy electron scattering from the azaderivatives of pyrrole, furan, and thiophene
View Description Hide DescriptionWe report elastic integral and differential cross sections for electron scattering from the azaderivatives of pyrrole, furan, and thiophene, namely, pyrazole, imidazole, isoxazole, oxazole, isothiazole, and thiazole. The calculations were performed within the Schwinger multichannel method with pseudopotentials, with inclusion of static, exchange, and polarization interactions, for energies up to 10 eV. We found two π* shape resonances and a highlying σ* shape resonance in each system. A sharp lowenergy σ* resonance was also identified in isothiazole and thiazole. Pyrazole and imidazole presented yet a broad lowlying σ* resonance. The positions of the resonances agree very well with existing experimental results. We discuss the similarities and differences among the resonances of these compounds.