Volume 110, Issue 13, 01 April 1999
 COMMUNICATIONS


Crossed beams reaction of atomic carbon, with benzene, Observation of the perdeutero1,2didehydro cycloheptatrienyl radical,
View Description Hide DescriptionThe reaction of atomic carbon, with perdeutero benzene, is investigated at an average collision energy of 32.1 kJ mol^{−1} using the crossed molecular beams technique combined with a universal mass spectrometric detector. Product angular distributions and timeofflight spectra of and are recorded. Forwardconvolution fitting of our timeofflight data (TOFs) and laboratory angular distribution (LAB) together with high level electronic structure calculations on the singlet and triplet potential energy surfaces are consistent with the formation of the perdeutero1,2didehydrocycloheptatrienyl radical, No adduct is found experimentally. Our investigations indicate that the carbon atom attacks the benzene molecule face without an entrance barrier to form an initial complex. This undergoes a ring opening to give triplet cycloheptatrienylidene as a intermediate. The latter fragments without exit barrier via a C–D bond rupture to yield the perdeutero1,2didehydrocycloheptatrienyl isomer, and a D atom. This barrierless route for the destruction of benzene may be involved in the synthesis of higher cyclic hydrocarbon derivatives in the interstellar medium, in outflows of dying carbon stars, in hydrocarbonrich planetary atmospheres, as well as in oxygenpoor combustion flames.

Unraveling the mysteries of metastable
View Description Hide DescriptionA recent report from our laboratory described 1+1 resonant photoionizationspectra of an energetic, metastable species produced in a dc discharge [Bevsek et al., Faraday Discuss. 108, 131 (1998)]. Although a definitive assignment of the spectra was lacking, the longpredicted covalent forms of either cyclic or “pinwheel” were adduced as possible candidates. We here present rotationally resolved photoionizationspectra,photoelectron spectra, and ab initio calculations providing strong evidence for the identity of this species as a novel complex between a ground state molecule and one in the state, which is excited via an allowed transition to the valence state. The latter then couples to the Rydberg state, shifted in energy owing to the presence of the adjacent molecule, from which it then ionizes. The results underscore the potential importance of the fully allowed but overlooked electronic transition in in the near ultraviolet, and provide a simple interpretation of puzzling results in an earlier study of electron transfer to [H. Helm and C. W. Walter, J. Chem. Phys. 98, 5444 (1993)].

On the photoelectron spectrum of the NO dimer, and the ground state of
View Description Hide DescriptionThe vibrational structure of the photoelectron spectrum of the NO dimer is calculated by ab initio methods, and compared with the observed ZEKE (zero electron kinetic energy) spectra published by I. Fischer et al. [J. Chem. Phys. 96, 7171 (1992)] and A. Strobel et al. [J. Phys. Chem. 99, 872 (1995)]. The ground state potential of is calculated to have almost isoenergetic minima at planar cis and trans geometries, but the Franck–Condon factors from the ground state of strongly favor transitions to the cis isomer. The good agreement for the vibrational frequencies and intensities shows that the isomer reached in the photoelectron spectrum has a cisplanar structure, rather than the twisted structure proposed by Fischer et al., or the transplanar structure proposed by A. Strobel et al.
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 THEORETICAL METHODS AND ALGORITHMS


Coupledcluster methods with internal and semiinternal triply and quadruply excited clusters: and approaches
View Description Hide DescriptionExtension of the closedshell coupledcluster (CC) theory to studies of bond breaking and general quasidegenerate situations requires the inclusion of the connected triply and quadruply excited clusters, and respectively. Since the complete inclusion of these clusters is expensive, we explore the possibility of incorporating dominant and contributions by limiting them to active orbitals. We restrict and clusters to internal or internal and semiinternal components using arguments originating from the multireference formalism. A hierarchy of approximations to standard CCSDT (CC singles, doubles, and triples) and CCSDTQ (CC singles, doubles, triples, and quadruples) schemes, designated as the and approaches, is proposed and tested using the and HF molecules at displaced nuclear geometries and at the equilibrium geometry. It is demonstrated that the and methods provide an excellent description of bond breaking and nondynamic correlation effects. Unlike perturbative CCSDT and CCSDTQ approaches, the and approaches do not fail at large internuclear separations, in spite of using the restricted Hartree–Fock reference. All and approaches are essentially procedures and yet they are shown to provide reliable information about and components, whose standard evaluation requires expensive and steps.

Molecular vibrations and the adiabatic wavefunctions
View Description Hide DescriptionThe well known existence of vibrational spectra in molecules implies simplicity of the corresponding molecular wavefunctions. This simplicity suggests the existence of quasiparticles with an approximate harmonic oscillator Hamiltonian. The conventional adiabatic approximation is known to reproduce the energy differences of the observed vibrational states. In spite of this it is shown that the adiabatic wavefunctions do not have the simplicity of approximate harmonic oscillator states. In particular, in the adiabatic wave functions the relative distances between the nuclear coordinates are selected to be dynamical variables. This article shows that with such a choice the conjugate momenta density functions could be far from the harmonic oscillator predictions. It is thus concluded that the spacing of the observed molecular vibrational states cannot be used to predict the probability distributions of relative nuclear coordinates or momenta.

What can be stated by the Glansdorff–Prigogine criterion concerning the stability of massaction kinetic systems?
View Description Hide DescriptionWe investigate which general results concerning the local stability of steady states of arbitrary chemical reaction networks can be deduced with the Glansdorff–Prigogine stability criterion. Especially, it is proven that the presence of an autocatalytic reaction is not a necessary condition for a violation of the thermodynamic stability condition. It turns out that every reaction with at least one variable reactant at each side of the reaction equation can potentially destabilize the steady states. An explicit example of a simple reaction system without autocatalytic reactions where the stability of the steady state changes via a supercritical Hopf bifurcation is discussed. Furthermore, in expanding the original concept for proving local stability to global stability analyses, a general way for constructing different Lyapunov functions is given.

The He isoelectronic series and the Hooke’s law model: Correlation measures and modifications of Collins’ conjecture
View Description Hide DescriptionThe recently developed concept of a correlation entropy,S, as a quantitative measure of the correlation strength present in a correlated quantum manybody state is applied to the ground states of the He isoelectronic series with varying nuclear charge Z and of the Hooke’s law model HLM(ω) with varying oscillator frequency ω. S is constructed from the natural orbital occupation numbers. It vanishes for weak correlation (large coupling constants Z or ω), and increases monotonically with decreasing Z or ω (strengthening correlation). A reduced correlation energy per particle and a dimensionless ratio are introduced which vanish asymptotically in the weak correlation limit in contrast to and These two intensive quantities, and ε, are compared with For both model systems, and (which modifies Collins’ conjecture that ).

Pathintegral diffusion Monte Carlo: Calculation of observables of manybody systems in the ground state
View Description Hide DescriptionWe propose a new method to calculate ground state position dependent observables in quantum manybody systems. The method, which we call the pathintegral diffusionMonte Carlo (PIDMC) method, is essentially a combination of pathintegral Monte Carlo (PIMC) and diffusionMonte Carlo (DMC) methods. The distribution resulting from a DMC simulation is further propagated in imaginary time by PIMC sampling. Tests of the new method for simple cases such as the harmonic oscillator, a double well, and a set of ten coupled harmonic oscillators show that the results for several observables converge rapidly to the exact result.

On the question of empirical corrections in ab initio model chemistries
View Description Hide DescriptionModel chemistries that employ additivity schemes have become increasingly popular within the chemical community. These approaches are predicated upon the assumption that less rigorous (and, therefore, less expensive) calculations may be combined to approximate a more accurate (and otherwise intractable) level of theory. Most of these models make some use of an empirical correction, the desirability of which is at best questionable. The present paper critically examines the importance of one such correction (the “higherlevel correction”) to the most widely used additivity method (the Gaussian model). An alternative approach, which does not depend upon any sort of ad hoc empiricism, is also outlined. The current model is found to offer accuracy comparable to that of the Gaussian model.

Toward reliable density functional methods without adjustable parameters: The PBE0 model
View Description Hide DescriptionWe present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

A sizeconsistent statespecific multireference coupled cluster theory: Formal developments and molecular applications
View Description Hide DescriptionIn this paper we present a comprehensive account of a manifestly sizeconsistent coupled cluster formalism for a specific state, which is based on a reference function composed of determinants spanning a complete active space (CAS). The method treats all the reference determinants on the same footing and is hence expected to provide uniform description over a wide range of molecular geometry. The combining coefficients are determined by diagonalizing an effective operator in the CAS and are thus completely flexible, not constrained to preassigned values. A separate exponentialtype excitation operator is invoked to induce excitations to all the virtual functions from each reference determinant. The linear dependence inherent in this choice of cluster operators is eliminated by invoking suitable sufficiency conditions, which in a transparent manner leads to manifest size extensivity. The use of a CAS also guarantees size consistency. We also discuss the relation of our method with the extant statespecific formalisms. Illustrative applications are presented for systems such as in rectangular and trapezoidal geometries, the insertion reaction path, the potential energy surface of and and certain states of and molecules with pronounced multireference character. The results indicate the efficacy of the method for obviating the intruders and of providing accuracy.

Atom–bond electronegativity equalization method. II. Lonepair electron model
View Description Hide DescriptionBased on the principle of electronegativity equalization and density functional theory, a lone pair electron model was developed through partitioning the molecular electron density into atomic electron densities, chemical bond electron densities, and lone pair electrons’ densities. The expressions of total molecular energy and the “effective electronegativity” of an atom or a chemical bond or a lone pair electron are obtained. Then the lone pair electron electronegativity is explicitly defined and the corresponding parameters are calibrated through regression and leastsquares optimization procedure. The atom–bond electronegativity equalization method plus lone pair electron model is then proposed for the direct calculation of the charge distribution and charge polarization in large molecules. In this paper we give the results of the charge distributions in some large molecules obtained by Through comparing the charge distributions and ab initio ones, it can be concluded that the lone pair electron model and the parameters are reasonable. In the following paper we will discuss the results of charge polarization in molecules obtained by Through comparing charge polarization and ab initio ones, it will be seen that considering lone pair electron explicitly is not only reasonable but also necessary.

Fitting classical microcanonical unimolecular rate constants to a modified RRK expression: Anharmonic and variational effects
View Description Hide DescriptionClassical RRKM (i.e., microcanonical) rate constants are often calculated for analytic potential energy surfaces (PESs) developed to represent unimolecular decomposition reactions. The values for these rate constants reflect the complete anharmonicities of the PESs. A common procedure is to fit these rate constants with the expression of RRK theory, which is the harmonic limit of classical RRKM theory. These RRK fits often give values for s significantly less than which are not meaningful, since anharmonic rate constants are represented with a harmonic model. In this work different schemes are proposed for introducing anharmonic and also variational transition state effects into the RRK expression. These modified RRK schemes allow one to fit classical anharmonic RRKM rate constants with The fits give information about the importance of anharmonicity in the unimolecular reactant’s density of states and the transition state’s sum of states.

On the origin and contribution of the diamagnetic term in fourcomponent relativistic calculations of magnetic properties
View Description Hide DescriptionThe relativistic Dirac Hamiltonian that describes the motion of electrons in a magnetic field contains only paramagnetic terms (i.e., terms linear in the vector potential A) while the corresponding nonrelativistic Schrödinger Hamiltonian also contains diamagnetic terms (i.e., those from an operator). We demonstrate that all diamagnetic terms relativistically arise from secondorder perturbation theory and that they correspond to a “redressing” of the electrons by the magnetic field. If the nonrelativistic limit is taken with a fixed nopair Hamiltonian (no redressing), the diamagnetic term is missing. The Schrödinger equation is normally obtained by taking the nonrelativistic limit of the Dirac oneelectron equation, we show why nonrelativistic use of the operator is also correct in the manyelectron case. In nonrelativistic approaches, diamagnetic terms are usually considered in firstorder perturbation theory because they can be evaluated as an expectation value over the ground state wave function. The possibility of also using an expectation value expression, instead of a secondorder expression, in the relativistic case is investigated. We also introduce and discuss the concept of “magnetically balanced” basis sets in relativistic calculations.

Towards the ab initio determination of strictly diabatic states, study for
View Description Hide DescriptionA generalization of the effective metric approach is proposed and applied both for the calculation of radial couplings and for the determination of diabatic states along a single coordinate using the formalism of variational effective Hamiltonian theory. The application to the ionic molecule shows that strictly diabatic states are obtained even for very short distances where a huge number of crossings are observed. Polarization and electronic delocalization effects are estimated. A comparison with various diabatization methods is performed. The proposed method brings a significant improvement with respect to the existing ones.

Direct ab initio calculation of groundstate electronic energies and densities for atoms and molecules through a timedependent single hydrodynamical equation
View Description Hide DescriptionBy using an imaginarytime evolution technique, coupled with the minimization of an expectation value, groundstate electron densities and energies have been directly calculated for six atomic and molecular systems (He, Ne, ), from a single timedependent (TD) quantum fluid dynamical equation of motion whose realtime solution yields the TD electron density. For all the systems, a local Wignertype correlation functional has been employed. For Ne, a local exchange functional is used while, for all the other systems, the exchange energy is calculated exactly. The static (groundstate) results are of beyondHartree–Fock quality for all the species.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Electron affinities of the oxides of aluminum, silicon, phosphorus, sulfur, and chlorine
View Description Hide DescriptionThe adiabatic electron affinities of five second row atoms (Al, Si, P, S, Cl) and their monoxides and dioxides were determined using six different density functional or hybrid Hartree–Fock/density functional methods. The 15 species selected form a convenient closed set for which reliable experimental electron affinities exist for 13 of the species. Zeropoint vibrational energy corrected electron affinities are also reported. Equilibrium geometries and vibrational frequencies were determined with each density functional method. The method based on the Becke exchange functional and the Lee–Yang–Parr correlation (BLYP) functional reproduced the experimental electron affinities most accurately, having an average absolute error of 0.15 eV. Using this functional, the electron affinities were predicted for SiO and molecules for which electron affinities are not known experimentally, as 0.11 eV and 2.03 eV, respectively. It is concluded that the accuracy observed for density functional theory methods applied to first row atoms and molecules extends to molecules containing second row atoms and that density functional theory continues to provide a computationally affordable means of producing electron affinities reliable to within a few tenths of an eV of definitive experimental values.

Photolysis of hydrogen chloride embedded in the first argon solvation shell: Rotational control and quantum dynamics of photofragments
View Description Hide DescriptionUnder standard conditions reaction yields are connected with terms like free energy differences and thermal distributions. However, many modern experimental techniques, such as supersonic beam expansion or matrix isolation, deal with cryogenic temperatures and isolated reactants in inert clusters or solid matrices. Under these conditions the photochemical reaction mechanism is in many cases strongly dependent on the shape of delocalized initial vibrational or rotational wave functions of the reactants which can be employed for an efficient reaction yield control. Here, we apply, using quantum molecular dynamics simulations, such a scheme to the rotational control of photolysis of the HCl molecule embedded in an icosahedral cluster. First, the HCl molecule is preexcited into a specific low lying rotational level. Depending on the rotational state, the hydrogen probability is enhanced in different directions within the cluster. In a second step, the HCl molecule is photolyzed by an UV pulse. The rapidly dissociating hydrogen atom then reaches primarily either the holes in the solvent shell or the argon atoms, depending on the rotational preexcitation. Starting either from the ground or from the first totally symmetric excited rotational states, the direct dissociation and the delayed process accompanied by a temporary trapping of the hydrogen atom have very different relative yields. As a consequence, differences up to a factor of 5 in the temporary population of the hydrogen atom inside the cluster after the first hydrogencage collision are observed. In the energy domain a significant difference in the structure of the kinetic energy distribution spectra, connected with the existence of shortlived vibrational resonances of the hydrogen atom, is predicted.

Femtosecond laser interactions with methyl iodide clusters. I. Coulomb explosion at 795 nm
View Description Hide DescriptionThe study of the interaction of femtosecond laser radiation with matter, especially clusters, has blossomed in recent years due to advances in laser technology. One aspect of this interaction is Coulomb explosion. This effect occurs when the repulsive energy of like charges, known as Coulomb repulsion, overcomes the cluster’s total cohesive energy, causing the cluster to disintegrate into charged fragments. In this study, the interactions of methyl iodide clusters, formed in a supersonic expansion using argon and helium as carrier gases, were investigated at 795 nm using a Ti:Sapphire femtosecond laser. The resulting atomic and cluster ions were analyzed in a reflection timeofflightmass spectrometer. The focus of these studies was the elucidation of the effects of carrier gas and laser wavelength on the lasercluster interactions leading to Coulomb explosion. To achieve these goals, the effects of different carrier gases, laser power, cluster distribution, and the resulting Coulomb explosion energies were examined. A secondary consideration was to examine the experimental results with regard to the Coherent Electron Motion and Ionization Ignition models.

Infrared spectroscopy of negatively charged water clusters: Evidence for a linear network
View Description Hide DescriptionWe report autodetachment spectra of the massselected, anionic water clusters, 3, 5–9, 11 in the OH stretching region (3000–4000 cm^{−1}), and interpret the spectra with the aid of ab initio calculations. For the spectra are structured and are generally dominated by an intense doublet, split by about 100 cm^{−1}, which gradually shifts toward lower energy with increasing cluster size. This behavior indicates that the clusters share a common structural motif. The strong bands appear in the frequency region usually associated with singledonor vibrations of water molecules embedded in extended networks, and theoretical calculations indicate that the observed spectra are consistent with linear “chainlike” species. We test this assignment by recording the spectral pattern of the cooled (argon solvated) isotopomer over the entire OH stretching frequency range.
