Volume 117, Issue 17, 01 November 2002
 ARTICLES

 Theoretical Methods and Algorithms

The Fourier transform Coulomb method: Efficient and accurate calculation of the Coulomb operator in a Gaussian basis
View Description Hide DescriptionWe describe a method for calculating the matrix elements of the Coulomb operator for Gaussian basis sets using an intermediate discrete Fourier transform of the density. Our goals are the same as those of the Gaussian and augmentedplanewave method of Parrinello and coworkers [M. Krack and M. Parrinello, Phys. Chem. Chem. Phys. 2, 2105 (2000)], but our techniques are quite different. In particular, we aim at much higher numerical accuracy than typical programs using plane wave expansions. Our method is free of the effects of periodic images and yields full precision. Other lowscaling methods for the Coulomb operator are compared to the Fourier transform method with regard to numerical precision, asymptotic scaling with molecular size, asymptotic scaling with basis set size, onset point (the size of the calculation where the method outperforms traditional Gaussian integral techniques by a factor of 2), and the ability to calculate the Hartree–Fock exchange operator. The Fourier transform method is superior to alternatives by most criteria. In particular, for typical molecular applications it has an earlier onset point than fast multipole methods.

Calculation of nuclear magnetic shieldings. XV. Ab initio zerothorder regular approximation method
View Description Hide DescriptionAn ab initio zerothorder regular approximation (ZORA) theory for relativistic calculation of the nuclear magnetic shieldingtensors is presented at the Hartree–Fock level. The nuclear magnetic shieldingstensors of hydrogen halides, HX Cl, Br, and I), are calculated, and the results are compared to experimental values and other calculated results obtained using the Douglas–Kroll–Hess (DKH) transformation, the fourcomponent random phase approximation (RPA), and the Dirac–Fock (DF) approaches. It is shown that the ZORA method underestimates the relativistic effects on the magnetic shieldings as compared to the fourcomponent RPA results. However, as to the protonchemical shifts, the ZORA results are closer to the experimental proton shifts than those of the DKH and 4RPA approaches.

Calculation of van der Waals coefficients in hydrodynamic approach to timedependent density functional theory
View Description Hide DescriptionIn this paper we employ hydrodynamic formulation of timedependent densityfunctional theory to obtain coefficient of the longrange part of the van der Waals interaction between alkalimetal clusters of large sizes. Such a calculation becomes computationally very demanding in the orbitalbased Kohn–Sham formalism, but is quite simple in the hydrodynamic approach. This is because in hydrodynamic formulation, electron density and current density, rather than the orbitals, are employed as basic variables. We show that for intercations between the clusters of same sizes, scales as the sixth power of the cluster radius and approaches the classically predicted value for large size clusters.

Emergence of quantumclassical dynamics in an open quantum environment
View Description Hide DescriptionThe conditions under which an open quantummechanical system may be described by mixed quantumclassical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two coupled systems, and interacting with a harmonic bath with Ohmic and superOhmic spectral densities. Subsystem is directly coupled to subsystem while is coupled directly to the bath. Calculations are presented for a model where subsystem is taken to be a twolevel system which is bilinearly coupled to a single harmonic oscillator subsystem. The loss of quantum coherence in each subsystem is discussed in the extreme nonadiabatic regime where the intrinsic dynamics of subsystem is essentially frozen. Subsystem is shown to lose its coherence rapidly, while subsystem maintains coherence for longer time periods since modulates the influence of the bath on Thus, one may identify situations where the coupled system evolution effectively obeys mixed quantumclassical dynamics.

Diffusionlimited reaction in the presence of random fields and transition rates
View Description Hide DescriptionThe diffusionlimited reaction was studied on a onedimensional lattice in the presence of random fields and transition rates using Monte Carlo simulations. In the case of transition rates the hopping probabilities at a site are distributed according to the power law with and The density of the reactants decays according to a powerlaw, for and annihilation reactions. The exponent depends on the disorder exponent ν. For we found For we observed at and α decreases monotonically for In the case of the random fields the density decays according to regardless of the strength of the random fields E for and reactions, where The diffusionlimited coagulation belongs to the same universality class as the reaction under the random fields. For annihilations we observe that the density decays according to in the presence of the random fields.

Spinrestricted coupledcluster theory with triple excitations
View Description Hide DescriptionWorking equations for a spinrestricted coupledcluster (SRCC) ansatz with full inclusion of triple excitations are presented. The equations have been derived using a new formulation of the SRCC theory that is equivalent to the original one but much easier processed and also provides a new interpretation of the underlying concepts of the SRCC approach. Test calculations with a preliminary SRCC singles, doubles, triples (SRCCSDT) implementation indicate that spinrestriction has a rather small effect on the computed energies and that the effects are—as expected—less pronounced than in the case of the CC singles, doubles approximation. The corresponding partially spinadapted scheme turns out less accurate and is shown in CCSDT calculations to be incorrect in the untruncated limit.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electronic structure and chemical bonding of divanadiumoxide clusters from anion photoelectron spectroscopy
View Description Hide DescriptionWe report a photoelectron spectroscopic investigation of a series of divanadiumoxide clusters Wellresolved spectra were obtained at three photonenergies (355, 266, and 193 nm), revealing the structural and electronic evolution as the number of oxygen atoms increases in the cluster series. A behavior of sequential oxidation was observed in for x up to 5: low binding energy features with primarily V characters were disappearing in numbers and simultaneously shifting to higher binding energies with increasing oxygen content as a result of charge transfers. Finally, for and the photoelectron spectra exhibit veryhighbindingenergy features characteristic of O characters. Vibrationally resolved spectra were obtained for the groundstate features of and with a spacing of 1090 cm^{−1} and 800 cm^{−1} which are assigned to V–O stretching vibrations. Electron affinities are reported for to and those of 5.61 eV for and 5.38 eV for are among the highest electronic affinities ever reported. The data are compared with previous theoretical calculations.

Hatom highn Rydberg timeofflight spectroscopy of C–H bond fission in acrolein dissociated at 193 nm
View Description Hide DescriptionThe experiments presented in this work use Hatom highnRydbergtimeofflight spectroscopy to measure the Hatom velocity distribution from one and multiplephoton dissociation processes in acrolein following excitation at 193 nm. The onephoton Hatom signal is dominated by primary C–H bond fission in acrolein. We compare some of the qualitative features of the recoil translational energy distribution for the observed H atoms with what would be expected based on theoretical results for aldehydic C–H bond fission on the ground and lowest singlet and triplet excited states and conclude that the dissociation cannot proceed through either of these paths. A possible dissociation mechanism is proposed to account for the observed that is consistent with the observation of an isotropic dissociation. Finally, we report results on methyl vinyl ketone photodissociation which provide evidence that the primary C–H bond fission process in acrolein is fission of the aldehydic bond.

Orbitally dependent kinetic exchange in a heterobimetallic pair: Ferromagnetic spin alignment and magnetic anisotropy in the cyanobridged Cr(III)Fe(II) dimer
View Description Hide DescriptionThe problem of the kinetic exchange interaction in the cyanidebridged heterobinuclear dimers involving orbitally degenerate transition metal ions is considered. The developed approach is based on the concept of the effective Hamiltonian of the orbitally dependent kinetic exchange. We deduce this manyelectron Hamiltonian on the microscopic background so that all relevant biorbital transfer processes are taken into account as well as the properties of the manyelectron states. The bioctahedral cyanidebridged Cr(III)Fe(II) dimer is considered in detail as an example distinctly exhibiting new quantitative and qualitative features of the orbitally dependent exchange and as a structural unit of threedimensional ferromagnetic crystals The proposed mechanism of the kinetic exchange involves the electron transfer from the double occupied orbitals of Fe(II) [ground state to the half occupied orbitals of Cr(III) [ground state resulting in the charge transfer state and the transfer between the halfoccupied orbitals of the metal ions resulting in the charge transfer state The effective Hamiltonian of the orbitally dependent exchange for the Cr(III)Fe(II) pair deduced within this theoretical framework describes competitive ferro and antiferromagnetic contributions arising from these two charge transfer states. This Hamiltonian leads to a complex energy pattern, consisting of two interpenetrating Heisenberglike schemes, one exhibiting ferromagnetic and another one antiferromagnetic splitting. The condition for the ferromagnetic spin alignment in the ground state is deduced. The orbitally dependent terms of the Hamiltonian are shown to give rise to a strong magnetic anisotropy of the system, this result as well as the condition for the spin alignment in the ground term are shown to be out of the scope of the Goodenough–Kanamori rules. Along with the full spin S the energy levels are labeled by the orbital quantum numbers providing thus the direct information about the magnetic anisotropy of the system. Under a reasonable estimation of the excitation energies based on the optical absorption data we conclude that the kinetic exchange in the cyanidebridged Cr(III)Fe(II) pair leads to the ferromagnetic spin alignment exhibiting at the same time strong axial magnetic anisotropy with easy axis of magnetization.

Rotationally resolved structures in the fifth and sixth torsional states of acetaldehyde: Internal rotation above the torsional barrier
View Description Hide DescriptionThe fluorescence excitation spectrum of acetaldehyde in its transition is analyzed for torsional states above the barrier. States with torsional vibrational quantum numbers and at term energies 660–927 cm^{−1} are assigned. This region is 100–370 cm^{−1} above the torsional barrier. These states lie between the limits of torsional vibrational motion and free internal rotor motion, so that the closelying and states mix for and K states in the E sublevel are widely split. From an analysis of calculated eigenfunctions, the composition of sublevels reaches nearly equal proportions of odd and even torsional wave functions when levels exceed the top of the torsional barrier, whereas the eigenfunctions of lying near consists of mostly even functions. Avoided crossings with and mod 3 selection rules are observed between E sublevels of and and between E sublevels of and The K energylevel structure of deviates significantly from the expected parabolic shape. The K structures and the K state at the lowest energy differ appreciably for the two inversion doublets and

The vibrational frequency of the vinyl radical: Conflict between theory and experiment
View Description Hide DescriptionA balanced theoretical treatment of the state of the vinyl radical is performed via application of equationofmotion coupled cluster theory for ionized states from the anion. Good agreement with experiment is generally found. The only exception is the vibrational mode, which seems to have been misassigned experimentally.

Electronic structure and chemical bonding of and by photoelectron spectroscopy and ab initio calculations
View Description Hide DescriptionThe electronic structure and chemical bonding of and were investigated using anion photoelectron spectroscopy and ab initio calculations. Vibrationally resolved photoelectron spectra were obtained for and were compared to theoretical calculations performed at various levels of theory. Extensive searches were carried out for the global minimum of which was found to have a planar structure with a closedshell ground state Excellent agreement was observed between ab initio detachment energies and the experimental spectra, firmly establishing the groundstate structures for both and The chemical bonding in was investigated and compared to that in While both and have a similar planar structure, their πbonding orbitals are different. In a πbonding orbital was previously observed to delocalize over only the three central atoms in the groundstate structure, whereas a similar π orbital was found to completely delocalize over all five atoms in the This π bonding in makes it more rigid towards butterfly outofplane distortions relative to

Nuclearexcited Feshbach resonance in the Penning ionization reaction under orientation and velocity specified collisions
View Description Hide DescriptionThe collisionenergy and orientationangleresolved Penning ionization cross section was determined for the reaction by using an oriented beam and a timeofflightmeasurement. A remarkable resonancetype structure in the Penning ionization cross section is recognized in the collision energy dependence at fixed molecular orientations, which is very similar to the one we previously observed in the reaction. This resonancetype structure could be interpreted as a new type nuclearexcited Feshbach resonance where the branching to competitive neutral dissociation channel is enhanced due to the formation of vibrationally excited Rydberg states.

Timeresolved resonance Raman spectroscopy and density functional theory investigation of the isomer and molecular complex products produced from ultraviolet photolysis of in the solution phase: Comparison of the structure and chemical reactivity of polyhalomethane isomers and polyhalomethane–halogen atom molecular complexes
View Description Hide DescriptionTimeresolved resonance Raman spectra are reported for different concentrations of in cyclohexane solution. The species is observed at low concentrations and it decays on the order of tens of nanoseconds to almost no signal at 100 ns and no other signal is observed up to 15 microseconds. Two species are observed at high concentrations. The first species spectra and lifetime are about the same as that found at low concentration of parent molecule and the second species is a molecular complex observed on the nanosecond to microsecond time scale and formed from bimolecular reaction of iodine atoms with molecules. The chemical reactivity of the species and the molecular complex towards carbon double bonds were investigated using density functional theory calculations. The structure and properties of the species and the molecular complex and their reaction towards ethylene were compared. The species and the both have weak I–I bonds that are the chromophores responsible for similar intense transient absorption bands. However, the geometry of the I–I bond relative to the C–I bond is noticeably different for these two species and this leads to distinctly different chemical reactivity toward carbon double bonds. The isomer readily reacts with ethylene to produce a cyclopropane product and leaving group via a single step and low barrier to reaction while the molecular complex reacts with ethylene to form an ethylene/I intermediate and a leaving group. Probable ramifications for other related molecule–halogen atom complexes are briefly discussed.

Fully relativistic calculation of nuclear magnetic shieldings and indirect nuclear spinspin couplings in group15 and 16 hydrides
View Description Hide DescriptionFully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin–spin couplings and and nuclear magnetic shieldings and for the group15 and 16 hydrides are presented. Relativistic calculations were performed with Dirac–Fock wave functions and the random phase approximation method. Results are compared to its nonrelativistic counterpart. Paramagnetic and diamagnetic contributions to the nuclear magnetic shielding constants are also reported. We found very large relativistic corrections to both properties in the sixthrow hydrides and Our calculations of the relativistic corrections to the isotropic part of σ at the heavy nucleus X show that it is roughly proportional to in both series of molecules. Paramagnetic term is more sensitive to the effects of relativity than the diamagnetic one even though both have a behavior proportional to third power of the nuclear charge Z.

Imaging reactions in crossed molecular beams: Vertical versus adiabatic H abstraction dynamics
View Description Hide DescriptionWe present a crossed molecular beam study of the reaction of with alkanes, using velocity map imaging of the alkyl radical product via single photonionization at 157 nm. We obtained the differential cross sections and translational energy distributions for reaction of with cyclohexane, nbutane and isobutane at a range of welldefined collision energies from 4.7 to 14.8 kcal/mol. The product alkyl radicals are largely backscattered with respect to the alkane beam at all collision energies, but the scattering distribution is clearly broadened with increasing collision energy. This is consistent with a picture of direct rebound dynamics but inconsistent with a recent result for the vibrationally excited OH component [H. Tsurumaki et al., J. Chem Phys. 112, 8338 (2000)], and we explore the source of this inconsistency. More surprising is the large fraction of the available energy partitioned into internal degrees of freedom of the alkyl radical, showing that the simple triatomic picture of the reaction is inadequate to account for all of the observations. To explain the observed dynamics we propose a modification of the triatomic model in which the exoergicity is adjusted to reflect “vertical” rather than “adiabatic” H abstraction energetics, and this picture is supported by ab initio calculations and by detailed consideration of the translational energy release patterns.

A theoretical study of the lowlying states of the AuSi molecule: An assignment of the excited A and D states
View Description Hide DescriptionThe lowest 42 electronic states of diatomic gas phase gold silicide are calculated by complete active space selfconsistent field and secondorder multiconfigurational perturbation theory. The scalar relativistic effect is considered by the thirdorder DouglasKroll method and the spin–orbit coupling is treated perturbatively after the spinfree calculations. The ground state of AuSi is confirmed to be the state, and the spin–orbit splitting of to is estimated as 1527 cm^{−1}. From the careful analysis of the potential energy curves and the spectroscopic constants, the experimentally observed A and Dexcited states are assigned to or and or respectively.

Resonanceleaking to specific background states: A loss mechanism in molecular multiphoton transitions
View Description Hide DescriptionWe report a remarkably robust phenomenon in the HCN/HNC molecule where the population of a target state induced by a resonant multiphoton (MP) πpulse along a stronglycoupled subset of states can leak to a background state only weakly coupled to this subset. This resonance leaking of population, which may be complete, is due to the overlap of the resonant MP transition to the target state with a resonant MP transition to the background state that includes the target state as an intermediate. We also demonstrate how the population leak can be fully controlled using fields of greater complexity compared to a single πpulse, such as two overlapping, phaseadjusted Gaussian pulses. The robustness of resonance leaking in the HCN/HNC molecule suggests that the phenomenon have a significant probability of occurrence in other molecular systems as well. The implications of our findings for the viability of reduced basis set treatments in providing converged ab initio fields and the predictability of these fields in lasercontrolled molecular processes are discussed.

High resolution spectroscopy and channelcoupling treatment of the complex of NaRb
View Description Hide DescriptionThe paper presents the study of the fully mixed complex of the NaRb molecule based on highresolution subDoppler spectroscopy and intensity measurements, ab initio relativistic calculations of energies, transition moments and spin–orbit interactions, as well as an inverted channelcoupling approach (ICCA) deperturbation analysis. A twolaser type pump–probe excitation scheme was employed to obtain transition frequencies to 16 Astate vibrational levels from to with J from 8 to 23. Additionally, relative intensities in laserinduced fluorescence spectra have been recorded, including progressions with all observable transitions to the ground state vibronic levels, the latter yielding unambiguous assignment of the Astate levels observed. All experimental rovibronic term values and all measured intensity distributions were embedded in a direct simultaneous weighted nonlinear fitting in the framework of an elaborated ICCA allowing us to obtain deperturbed relativistic diabatic potentials of the interacting and states. To make this possible, ab initio structure calculations of the spin–orbit singlet–triplet coupling parameter, the spin–orbit splitting of the state, the transitiondipole moments, and the electronic energy differences for internuclear distance 3.0–7.0 Å have been performed using second order manybody multipartitioning perturbation theory. The developed ICCA is proved to be appropriate for deperturbation analysis of strongly coupled electronic states provided that accurate nonadiabatic matrix elements are known. This allows unambiguous assignment of the vibrational levels of the state, which is not directly observed.

Dissociative electron attachment study to nitromethane
View Description Hide DescriptionDissociative electron attachment (DEA) to in the gas phase was studied in the electron energy range from zero up to 10 eV with an energy resolution of 140 meV. For the most intense negative fragments estimates for the absolute partial cross sections were obtained for the first time at 0.62 eV, at 5.4 eV, at 4 eV, at 1.7 eV, and at 4 eV]. In the case of and ion formation at very low electron energies (≈0 eV) has been observed in contrast to previous studies. The formation of and at these low electron energies is explained in terms of DEA to vibrationally excited molecules. Analyzing measured partial cross sections, the standard enthalpy of formation of the (nitrosomethane) and the CNO radical has been estimated, as and respectively.