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Volume 120, Issue 16, 22 April 2004
 COMMUNICATIONS


Collision complexes in dissociative single electron transfer between and
View Description Hide DescriptionExperiments involving the coincident detection of the two monocationic products and from the dissociativeelectron transferreaction between and at 7.8 eV collision energy allow the nascent velocity vectors of the ionic and neutral (N) products to be determined. Examination of the correlations between these vectors shows that one pathway to the products involves the dissociation of a transitory collision complex

Inelastic tunneling spectroscopy using scanning tunneling microscopy on trans2butene molecule: Spectroscopy and mapping of vibrational feature
View Description Hide DescriptionInelastic tunnelingspectroscopy (IETS) measurement using scanning tunneling microscopy(STM) with a commercially available STM set up is presented. The STM–IETS spectrummeasured on an isolated trans2butene molecule on the Pd(110) shows a clear vibrational feature in at the bias voltage of 360 mV and −363 mV, which corresponds to the ν(CH) mode In addition, we have obtained an image by mapping the vibrational feature of ν(CH) in The image is obtained by scanning the tip on the surface with the feedback loop activated while the modulation voltage is superimposed on the sample voltage. With the method that is readily performable with conventional software, we have clearly differentiated the molecules of trans2butene and butadiene through the mapping of the vibrational feature, demonstrating its capability of chemical identification in atomic scale.

 ARTICLES

 Theoretical Methods and Algorithms

Densityfunctional generalizedgradient and hybrid calculations of electromagnetic properties using Slater basis sets
View Description Hide DescriptionIn this paper we extend our densityfunctional theory calculations, with generalized gradient approximation and hybrid functionals, using Slatertype orbitals (STOs), to the determination of secondorder molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electronrepulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin–spin coupling constants. In all cases the oneelectron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gaugeincluding atomic orbitals. The presence of twoelectron integrals on the righthand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussiantype orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater’s rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict secondorder molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.

An empirical charge transfer potential with correct dissociation limits
View Description Hide DescriptionThe empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262 (1970)] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for largescale simulations. A twostate model is explored. The main features of the model are: (1) explicit decomposition of the total system electron density is invoked; (2) the charge is defined through the density decomposition into constituent contributions; (3) the charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) a referencestate approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of “knowable” quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gasphase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.

Assessment and validation of a screened Coulomb hybrid density functional
View Description Hide DescriptionThis paper presents a revised and improved version of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional. The performance of this functional is assessed on a variety of molecules for the prediction of enthalpies of formation, geometries, and vibrational frequencies, yielding results as good as or better than the successful PBE0 hybrid functional. Results for ionization potentials and electron affinities are of slightly lower quality but are still acceptable. The comprehensive test results presented here validate our assumption that the screened, shortrange Hartree–Fock (HF) exchange exhibits all physically relevant properties of the full HF exchange. Thus, hybrids can be constructed which neglect the computationally demanding longrange part of HF exchange while still retaining the superior accuracy of hybrid functionals, compared to pure density functionals.

Dynamically weighted multiconfiguration selfconsistent field: Multistate calculations for reaction paths
View Description Hide DescriptionA novel method of dynamically adjusted weighting factors in stateaveraged multiconfiguration selfconsistentfield calculations (SA–MCSCF) is described that is applicable to systems of arbitrary dimensionality. The proposed dynamically weighted approach automatically weights the relevant electronic states in each region of the potential energy surface, smoothly adjusting between these regions with an energy dependent functional. This method is tested on the reaction, which otherwise proves challenging to describe with traditional SA–MCSCF methods due to (i) different asymptotic degeneracies of reactant (threefold) and product (twofold) channels, and (ii) presence of lowlying charge transfer configurations near the transition state region. The smoothly varying wave functions obtained by dynamically weighted multiconfigurational selfconsistent field represent excellent reference states for highlevel multireference configuration interaction calculations and offer an ideal starting point for construction of multiple state potential energy surfaces.

Atomic and molecular intracules for excited states
View Description Hide DescriptionIntracules in position space, momentum space and phase space have been calculated for lowlying excited states of the He atom, Be atom, formaldehyde and butadiene. The phasespace intracules (Wigner intracules) provide significantly more information than the position and momentumspace intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.

Real versus artifactual symmetrybreaking effects in Hartree–Fock, densityfunctional, and coupledcluster methods
View Description Hide DescriptionWe have examined the relative abilities of Hartree–Fock, densityfunctional theory(DFT), and coupledcluster theory in describing secondorder (pseudo) Jahn–Teller (SOJT) effects, perhaps the most commonly encountered form of symmetry breaking in polyatomic molecules. As test cases, we have considered two prototypical systems: the states of BNB and for which interaction with a lowlying excited state leads to symmetry breaking of the nuclear framework. We find that the Hartree–Fock and B3LYP methods correctly reproduce the pole structure of quadratic force constants expected from exact SOJT theory, but that both methods appear to underestimate the strength of the coupling between the electronic states. Although the Tamm–Dancoff (CIS) approximation gives excitation energies with no relationship to the SOJT interaction, the randomphaseapproximation (RPA) approach to Hartree–Fock and timedependent DFTexcitation energies predicts state crossings coinciding nearly perfectly with the positions of the force constant poles. On the other hand, the RPA excitedstate energies exhibit unphysical curvature near their crossings with the ground (reference) state, a problem arising directly from the mathematical structure of the RPA equations. Coupledcluster methods appear to accurately predict the strength of the SOJT interactions between the and states, assuming that the inclusion of full triple excitations provides a suitable approximation to the exact wave function, and are the only methods examined here which predict symmetry breaking in BNB. However, coupledcluster methods are plagued by artifactual force constant poles arising from the response of the underlying reference molecular orbitals to the geometric perturbation. Furthermore, the structure of the “true” SOJT force constant poles predicted by coupledcluster methods, although correctly positioned, has the wrong structure.

Relation between different variants of the generalized Douglas–Kroll transformation through sixth order
View Description Hide DescriptionWolf et al. have recently investigated a generalized Douglas–Kroll transformation. From a general class of unitary transformations that can be used in the Douglas–Kroll transformation, they pick one which is supposed to give, at a given order, an optimal transformed Dirac Hamiltonian. Results were presented through the fifth order. However, no data were given to demonstrate to which extent the socalled “optimal” Douglas–Kroll transformation is superior to other choices. In this work, the Douglas–Kroll transformation is extended to the sixth order for the first time, using computer algebra algorithms to obtain the working equations. It is shown how, at a given order, different variants of the Douglas–Kroll Hamiltonians are related. Various choices of the generalized transformation are examined numerically for the ground states of the oneelectron atomic ions with nuclear charges 40, 60, 80, 100, and 120. It is shown that compared to the improvement obtained by including the next order, the differences between various choices for the generalized Douglas–Kroll transformation are almost negligible. Results closest to the Diraceigenvalues are not obtained with the optimal Douglas–Kroll transformation given by Wolf et al., but with the parametrization originally suggested by Douglas and Kroll.

Mixing and reaction fronts in laminar flows
View Description Hide DescriptionAutocatalytic reaction fronts between unreacted and reacted mixtures in the absence of fluid flow propagate as solitary waves. In the presence of imposed flow, the interplay between diffusion and advection enhances the mixing, leading to Taylor hydrodynamic dispersion. We present asymptotic theories in the two limits of small and large Thiele modulus (slow and fast reaction kinetics, respectively) that incorporate flow,diffusion, and reaction. For the first case, we show that the problem can be handled to leading order by the introduction of the Taylor dispersion replacing the molecular diffusion coefficient by its Taylor counterpart. In the second case, the leadingorder behavior satisfies the eikonal equation. Numerical simulations using a lattice gas model show good agreement with the theory. The Taylor model is relevant to microfluidics applications, whereas the eikonal model applies at larger length scales.

Analytic evaluation of nonadiabatic coupling terms at the MRCI level. I. Formalism
View Description Hide DescriptionAn efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MRCI) level is presented. This method is based on a previously developed formalism for analytic MRCI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration selfconsistent field and MRCI levels are possible, allowing flexible selections of MRCI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MRCI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.

Analytic evaluation of nonadiabatic coupling terms at the MRCI level. II. Minima on the crossing seam: Formaldehyde and the photodimerization of ethylene
View Description Hide DescriptionThe method for the analytic calculation of the nonadiabatic coupling vector at the multireference configurationinteraction (MRCI) level and its program implementation into the COLUMBUS program system described in the preceding paper [Lischka et al., J. Chem. Phys. 120, 7322 (2004)] has been combined with automatic searches for minima on the crossing seam (MXS). Based on a perturbative description of the vicinity of a conical intersection, a Lagrange formalism for the determination of MXS has been derived. Geometry optimization by direct inversion in the iterative subspace extrapolation is used to improve the convergence properties of the corresponding NewtonRaphson procedure. Three examples have been investigated: the crossing between the valence states in formaldehyde, the crossing between the valence and Rydberg states in formaldehyde, and three crossings in the case of the photodimerization of ethylene. The methods developed allow MXS searches of significantly larger systems at the MRCI level than have been possible before and significantly more accurate calculations as compared to previous completeactive space selfconsistent field approaches.

Irreducible Brillouin conditions and contracted Schrödinger equations for electron systems. III. Systems of noninteracting electrons
View Description Hide DescriptionWe analyze the structure and the solutions of the irreducible particle Brillouin conditions and the irreducible contracted Schrödinger equations for an electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to physically realistic systems with electron interaction. The leads to a Liouville equation for the oneparticle density matrix consistent with our earlier analysis that the holds both for a pure and an ensemble state. The or the must be solved subject to the constraints imposed by the representability condition, which is particularly simple for γ. For a closedshell state γ is idempotent, i.e., all natural spin orbitals (NSO’s) have occupation numbers 0 or 1, and all cumulants with vanish. For openshell states there are NSO’s with fractional occupation number, and at the same time nonvanishing elements of which are related to spin and symmetry coupling. It is often useful to describe an openshell state by a totally symmetric ensemble state. If one wants to treat a oneparticle perturbation by means of perturbation theory, this mainly as a runup for the study of a twoparticle perturbation, one is faced with the problem that the perturbation expansion of the Liouville equation gives information only on the nondiagonal elements (in a basis of the unperturbed states) of γ. There are essentially three possibilities to construct the diagonal elements of γ: (i) to consider the perturbation expansion of the characteristicpolynomial of γ, especially the idempotency for closedshell states, (ii) to rely on the which (at variance with the also gives information on the diagonal elements, though not in a very efficient manner, and (iii) to formulate the perturbation theory in terms of a unitary transformation in Fock space. The latter is particularly powerful, especially, when one wishes to study realistic Hamiltonians with a twobody interaction.

Irreducible Brillouin conditions and contracted Schrödinger equations for electron systems. IV. Perturbative analysis
View Description Hide DescriptionThe particle irreducible Brillouin conditions and the particle irreducible contracted Schrödinger equations for a closedshell state are analyzed in terms of a Møller–Plesset–type perturbation expansion. The zeroth order is Hartree–Fock. From the i.e., from the twoparticle IBC to first order in the perturbation parameter μ, one gets the leading correction to the twoparticle cumulant correctly. However, in order to construct the secondorder energy one also needs the secondorder diagonal correction to the oneparticle density matrix γ. This can be obtained: (i) from the idempotency of the particle density matrix, i.e., essentially from the requirement of nrepresentability; (ii) from the or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the to get which is needed in the to get which, in turn, is needed in the to get Generally the particle approximation is needed to obtain correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ignoring and by a renormalized hierarchy, in which only is ignored, and is expressed in terms of the of lower particle rank via the partial trace relation for Then the particle approximation is needed to obtain correctly. This is still poorer than coupledcluster theory, where the particle approximation yields We also study the possibility to use some simple necessary representability conditions, based on the nonnegativity of and two related matrices, in order to get estimates for in terms of In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of in terms of a localized representation. The perturbative analysis does not encourage the use of a particle hierarchy based on the (or on their reducible counterparts, the it rather favors the approach in terms of the unitary transformation, where the particle approximation yields the energy correct up to The problems that arise are related to the unavoidable appearance of exclusionprinciple violating cumulants. The good experience with perturbation theory in terms of a unitary transformation suggests that one should abandon a linearly convergent iteration scheme based on the hierarchy, in favor of a quadratically convergent one based on successive unitary transformations.

Structural properties of reciprocal form factor in neutral atoms and singly charged ions
View Description Hide DescriptionStructural characteristics of the spherically averaged internally folded density or reciprocal form factor are studied within the Hartree–Fock framework for 103 neutral atoms, 54 singly charged cations, and 43 anions in their ground state. The function is classified throughout the Periodic Table into three types: (i) monotonic decrease from the origin, (ii) maximum at and a negative minimum at and (iii) a local maximum at and a pair maximum–minimum out of the origin. A detailed study of the corresponding properties for individual subshells as well as their relative weight for the total is also carried out. For completeness, the analytical for hydrogenlike atoms in both ground and excited states is also analyzed.

A local approach to delocalized electronic systems: Semilocal evaluation of the cohesive energies of tightbinding Hamiltonians
View Description Hide DescriptionStarting from strongly localized Nelectron functions built from either pure atomic orbitals or fully localized bond molecular orbitals, it is possible to evaluate the ground state energy of a periodic lattice ruled by a tightbinding Hamiltonian without explicitly introducing the monoelectronic crystal orbitals. The method consists of a selfconsistent perturbation of the zerothorder wave function which incorporates high order effects and offers reasonable convergence properties. Along this framework, a single variable per bond type is introduced, namely the amplitude of the charge transfer. The method leads to a set of coupled equations which can be numerically solved, if not analytically. Shortrange delocalization effects under periodic conditions are explicitly taken into account and relatively accurate cohesive energies are estimated for regular homoatomic and heteroatomic onedimensional chains as well as for honeycomb lattices. In addition, good agreement with experiment for the distortion amplitude in polyacetylene is obtained. This exploratory tool may be easily extended to more sophisticated Hamiltonians, for which the solutions are not accessible. Since our approach only introduces shortrange delocalization effects, its performance questions the importance of the specifically collective delocalization effects.

Globally uniform semiclassical surfacehopping wave function for nonadiabatic scattering
View Description Hide DescriptionA globally uniform timeindependent semiclassical wave function for nonadiabaticscattering is presented. This wave function, which takes the form of a surfacehopping expansion, is motivated by the globally uniform semiclassical wave function of Kay and coworkers for the singlesurface case. The surfacehopping expansion is similar to a previously presented primitive semiclassical wave function for nonadiabatic problems. This earlier wave function has the important feature that it correctly incorporates all phase terms, allowing for an accurate treatment of quantum interferenceeffects. The globally uniform expression has important numerical advantages over the primitive formulation. The globally uniform wave function does not have caustic singularities, and the globally uniform calculation avoids a root search for trajectories obeying doubleended boundary conditions that is required by the primitive semiclassical calculation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociative recombination of and ions: Storage ring experiments and ab initio molecular dynamics
View Description Hide DescriptionThe dissociative recombination (DR) process of and molecular ions with free electrons has been studied at the heavyion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm University). The absolute cross sections for DR of and in the collision energy range 0.001–1 eV are reported, and thermal rate coefficients for the temperature interval from 10 to 2000 K are calculated from the experimental data. The absolute cross section for agrees well with earlier work and is about a factor of 2 larger than the cross section for The dissociative recombination of is dominated by the product channels and while the DR of mainly results in Ab initio direct dynamics simulations, based on the assumption that the dissociationdynamics is governed by the neutral groundstatepotential energy surface, suggest that the primary product formed in the DR process is The ejection of the H atom is direct and leaves the molecule highly vibrationally excited. A fraction of the excited ammonia molecules may subsequently undergo secondary fragmentation forming It is concluded that the model results are consistent with gross features of the experimental results, including the sensitivity of the branching ratio for the threebody channel to isotopic exchange.

Picosecond IR–UV pump–probe spectroscopic study of the dynamics of the vibrational relaxation of jetcooled phenol. I. Intramolecular vibrational energy redistribution of the OH and CH stretching vibrations of bare phenol
View Description Hide DescriptionThe intramolecular vibrational energy redistribution (IVR) of the OH stretching vibration of jetcooled phenol and phenol in the electronic ground state has been investigated by picosecond timeresolved IR–UV pump–probe spectroscopy. The OH stretching vibration of phenol was excited with a picosecond IR laser pulse, and the subsequent temporal evolutions of the initially excited level and the redistributed ones due to the IVR were observed by multiphoton ionization detection with a picosecond UV pulse. The IVR lifetime for the OH stretch vibration of phenol was determined to be 14 ps, while that of the OH stretch for phenol was found to be 80 ps. This remarkable change of the IVR rate constant upon the dueteration of the CH groups strongly suggests that the “doorway states” for the IVR from the OH level would be the vibrational states involving the CH stretching modes. We also investigated the IVR rate of the CH stretching vibration for phenol It was found that the IVR lifetime of the CH stretch is less than 5 ps. The fast IVR is described by the strong anharmonic resonance of the CH stretch with many other combinations or overtone bands.

Picosecond IR–UV pump–probe spectroscopic study of the dynamics of the vibrational relaxation of jetcooled phenol. II. Intracluster vibrational energy redistribution of the OH stretching vibration of hydrogenbonded clusters
View Description Hide DescriptionA picosecond timeresolved IR–UV pump–probe spectroscopic study has been carried out for investigating the intracluster vibrational energy redistribution (IVR) and subsequent dissociation of hydrogenbonded clusters of phenol and partially deuterated phenol phenol with various solvent molecules. The Hbonded OH stretching vibration was pumped by a picosecond IR pulse, and the transient UV spectra from the pumped level as well as the redistributed levels were observed with a picosecond UV laser. Two types of hydrogenbonded clusters were investigated with respect to the effect of the Hbonding strength on the energy flow process: the first is of a strong “σtype Hbond” such as phenol and phenol dimer, and the second is phenol having a weak “πtype Hbond.” It was found that the population of the IRpumped OH level exhibits a singleexponential decay, whose rate increases with the Hbond strength. On the other hand, the transient UVspectrum due to the redistributed levels showed a different time evolutions at different monitoring UV frequency. From an analysis of the time profiles of the transient UV spectra, the following threestep scheme has been proposed for describing the energy flow starting from the IVR of the initially excited Hbonded OH stretching level to the dissociation of the H bond. (1) The intramolecular vibrational energy redistribution takes place within the phenolic site, preparing a hot phenol. (2) The energy flows from the hot phenol to the intermolecular vibrational modes of the cluster. (3) Finally, the hydrogen bond dissociates. Among the three steps, the rate constant of the first step was strongly dependent on the Hbond strength, while the rate constants of the other two steps were almost independent of the Hbond strength. For the dissociation of the hydrogen bond, the observed rate constants were compared with those calculated by the Rice, Ramsperger, Kassel, and Marcus model. The result suggests that dissociation of the hydrogen bond takes place much faster than complete energy randomization within the clusters.