Index of content:
Volume 138, Issue 23, 21 June 2013
- Theoretical Methods and Algorithms
Features in chemical kinetics. I. Signatures of self-emerging dimensional reduction from a general format of the evolution law138(2013); http://dx.doi.org/10.1063/1.4809592View Description Hide Description
Simplification 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 so-called slow manifolds, which are hyper-surfaces of lower dimension than the one of the whole phase-space 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 self-emerge 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 high-order time-derivatives of the new dynamic variables, we then formulate a conjecture which leads to the concept of an “attractiveness” region in the phase-space where a well-defined state-dependent 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 N-dimensional equations (being N the number of chemical species) to a one-dimensional and universal evolution law for such a characteristic rate. Step-by-step 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.
138(2013); http://dx.doi.org/10.1063/1.4809593View Description Hide Description
In 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 (mass-action law). Here we proceed by investigating a deeply related feature: the appearance of so-called slow manifolds (SMs) which are low-dimensional hyper-surfaces 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 sub-dimensional domain embedded in the peculiar region of the concentrations phase-space that in Part I we termed as “attractiveness region.” Numerical inspections on simple low-dimensional 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/long-range model: Application to the water dimer138(2013); http://dx.doi.org/10.1063/1.4810006View Description Hide Description
We investigate the analytical representation of potentials of mean force (pmf) using the Morse/long-range (MLR) potential approach. The MLR method had previously been used to represent potential energy surfaces, and we assess its validity for representing free-energies. 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 atom-diatom reactivity: Rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model138(2013); http://dx.doi.org/10.1063/1.4810007View Description Hide Description
To provide a systematic and rigorous re-examination of the well-known 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 short-lived 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 cross-over 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.
138(2013); http://dx.doi.org/10.1063/1.4810754View Description Hide Description
In 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 scale-invariant, we demonstrate that the dynamic properties are quantitatively consistent with an all-atom Lennard-Jones 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 on-the-fly. 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 vapor-liquid equilibria using a bias potential from an analytic equation of state138(2013); http://dx.doi.org/10.1063/1.4808032View Description Hide Description
This article introduces an efficient technique for the calculation of vapor-liquid 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 PC-SAFT 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.
138(2013); http://dx.doi.org/10.1063/1.4810881View Description Hide Description
We reconsider the structure-based route to coarse graining in which the coarse-grained 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 coarse-grained models with density-dependent 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 low-density regime and polymer solutions under good-solvent conditions. Moreover, we show that the state-dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.
A gauge invariant multiscale approach to magnetic spectroscopies in condensed phase: General three-layer model, computational implementation and pilot applications138(2013); http://dx.doi.org/10.1063/1.4811113View Description Hide Description
Analytical 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 Kohn-Sham density functional theory and is extended to the Gauge-Including 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 g-tensors, and hyperfine couplings.
- Advanced Experimental Techniques
138(2013); http://dx.doi.org/10.1063/1.4805062View Description Hide Description
We 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 scalar-coupling 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 single-transition 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
138(2013); http://dx.doi.org/10.1063/1.4810864View Description Hide Description
The accurate ground-state potential energy surface of lithium monohydroxide (LiOH) has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. Results obtained with the conventional and explicitly correlated coupled-cluster methods were compared. The higher-order electron correlation, scalar relativistic, and adiabatic effects were taken into account. The vibration-rotation 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 low-frequency bending vibrational states ν23 and ν11 of dimethylsulfoxide138(2013); http://dx.doi.org/10.1063/1.4809738View Description Hide Description
We 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 high-resolution 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 (4-clusters) 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 medium-sized radicals by hybrid coupled cluster/density functional theory approaches: The case of phenyl radical138(2013); http://dx.doi.org/10.1063/1.4810863View Description Hide Description
The coupled-cluster singles doubles model with perturbative treatment of triples (CCSD(T)) coupled with extrapolation to the complete basis-set limit and additive approaches represent the “golden standard” for the structural and spectroscopic characterization of building blocks of biomolecules and nanosystems. However, when open-shell systems are considered, additional problems related to both specific computational difficulties and the need of obtaining spin-dependent 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 open-shell 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 open-shell systems has been further confirmed.
138(2013); http://dx.doi.org/10.1063/1.4810869View Description Hide Description
The structures of parent anion, M−, and deprotonated molecule, [M−H]−, anions of the highly polar p-nitroaniline (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 EOM-CCSD/Aug-cc-pVTZ 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 dipole-bound states, one at ∼110 meV and an excited state at 2 meV. No dipole-bound states are observed in the photodetachment experiments due the pronounced mixing between states with dipole-bound and valence character similar to what has been observed in other nitro systems. For the same reason, dipole-bound 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.
138(2013); http://dx.doi.org/10.1063/1.4810871View Description Hide Description
Following 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 1s-to-σ* core excitation in CF4, with high-resolution resonant Auger spectroscopy. We are able to characterize final states of both the molecular ion and the fragment. We use two-dimensional (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.
138(2013); http://dx.doi.org/10.1063/1.4809748View Description Hide Description
The 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 low-lying ν6 vibrational fundamental of the FSO3 radical by the linear vibronic coupling approach138(2013); http://dx.doi.org/10.1063/1.4810800View Description Hide Description
The 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 KDC-LVC 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 pseudo-Jahn-Teller and Jahn-Teller 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.
138(2013); http://dx.doi.org/10.1063/1.4810009View Description Hide Description
Vibrational decoherence of a “breathing sphere” oscillator in a thermal Lennard-Jones 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 Caldeira-Leggett model in this realistic system.
Dissociative electron attachment to hexafluoroacetylacetone and its bidentate metal complexes M(hfac)2; M = Cu, Pd138(2013); http://dx.doi.org/10.1063/1.4810877View Description Hide Description
Beta-diketones 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 non-dissociative electron attachment (NDEA) to hexafluoroacetylacetone (HFAc) and its bidentate metal complexes: bis-hexafluoroacetylacetonate copper(II), Cu(hfac)2 and bis-hexafluoroacetylacetonate 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.
138(2013); http://dx.doi.org/10.1063/1.4810870View Description Hide Description
Carbon 1s photoelectron spectra for 2-butyne (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 EXAFS-type scattering from the substituent chlorine atoms. In 2-butyne, however, there is no high-Z 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 density-functional model with B-spline atom-centered functions to represent the continuum electrons and a multiple-scattering model using muffin-tin potentials to represent the scattering centers. Both methods give a reasonable description of the energy dependence of the intensity ratios.
138(2013); http://dx.doi.org/10.1063/1.4811218View Description Hide Description
We report elastic integral and differential cross sections for electron scattering from the aza-derivatives 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 high-lying σ* shape resonance in each system. A sharp low-energy σ* resonance was also identified in isothiazole and thiazole. Pyrazole and imidazole presented yet a broad low-lying 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.