Volume 118, Issue 11, 15 March 2003
 COMMUNICATIONS


Natural transition orbitals
View Description Hide DescriptionA means of finding a compact orbital representation for the electronic transition density matrix is described. The technique utilizes the corresponding orbital transformation of Amos and Hall and allows a dramatic simplification in the qualitative description of an electronic transition.

On the determination of molecular orientation from polarized imaging in secondharmonic microscopy
View Description Hide DescriptionThe polarized imaging of a monolayer film in secondharmonic microscopy in oblique incidence geometry has been analyzed theoretically. It has been demonstrated that both azimuthal and tilt angles of molecules in the film can be determined from measurements of relative second harmonic intensities at different orientations of a polarizer or an analyzer.

Comments on the quantum Monte Carlo method and the density matrix theory
View Description Hide DescriptionDensity matrix theory is implemented in a variational quantum Monte Carlo computation of electronic properties of atoms and molecules. Differences between electronic densities from conventional and density matrix methods are detected. However, calculated properties present similar behavior and partial antisymmetry can be ignored in the cases studied.
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 ARTICLES

 Theoretical Methods and Algorithms

An arbitrary Lagrangian–Eulerian approach to solving the quantum hydrodynamic equations of motion: Equidistribution with “smart” springs
View Description Hide DescriptionRecently, the quantum trajectory method (QTM) has been utilized in solving several quantum mechanical wave packet scattering problems including barrier transmission and electronic nonadiabatic dynamics. By propagating the realvalued action and amplitude functions in the Lagrangian frame, only a fraction of the grid points needed for Eulerian fixedgrid methods are used while still obtaining accurate solutions. Difficulties arise, however, near wave functionnodes and in regions of sharp oscillatory features, and because of this many quantum mechanical problems have not yet been amenable to solution with the QTM. This study proposes a hybrid of both the Lagrangian and Eulerian techniques in what is termed the arbitrary Lagrangian–Eulerian method (ALE). In the ALE method, an additional equation of motion governing the momentum of the grid points is coupled into the quantum hydrodynamicequations. These new “quasi” Bohmian trajectories can be dynamically adapted to the emergent features of the time evolving hydrodynamic fields and are nonLagrangian. In this study it is shown that the ALE method applied to an uphill ramp potential that was previously unsolvable by the current Lagrangian QTM not only yields stable transmission probabilities with accuracies comparable to that of a high resolution Eulerian method, but does so with a small number of grid points and for extremely long propagation times. To determine the grid point positions at each new time, an equidistribution method is used that is constructed similar to the stiffness matrix of a classical spring system in equilibrium. Each “smart” spring is dependent on a local function called the monitor function which can sense gradients or curvatures of the fields surrounding its position. To constrain grid points from having zero separation and possible overlap, a new system of equations is derived that includes a minimum separation parameter which prevents this from occurring.

An initial value representation semiclassical approach for the study of molecular systems with geometric constraints
View Description Hide DescriptionWe present an approach for the inclusion of geometric constraints in quantum dynamics calculations based on the semiclassical initial value representation. An important feature of the method is that a Cartesian coordinate system is used throughout, resulting in a general approach that does not require the definition of new coordinates. The Herman–Kluk [M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984)] coherent state formulation is used. The required (constrained) classical trajectories are calculated using the standard techniques of molecular dynamics and initial conditions are sampled from a distribution that obeys the constraints. An approximate form of the Herman–Kluk prefactor is used and its evaluation requires the construction of a projected Hessian matrix. In its present form, the approach allows the calculation of energy levels from the Fourier transform of the autocorrelation function. The approach is tested on a model problem consisting of two particles in a harmonic trap and constrained to remain at a fixed distance from one another. The approach yields exact results for this simplified case when compared to the exact quantum mechanical formulation. The method is then applied to a real molecular system consisting of a water molecule with fixed OH bonds and yields accurate results when compared to exact quantum mechanical results. The accuracy of the method is comparable to that of the usual semiclassical implementation where the problem is written in a new set of coordinates. The approach can be extended to more complex cases in a straightforward manner.

The spin–flip approach within timedependent density functional theory: Theory and applications to diradicals
View Description Hide DescriptionAn extension of density functional theory to situations with significant nondynamical correlation is presented. The method is based on the spin–flip (SF) approach which is capable of describing multireference wave functions within a single reference formalism as spin–flipping, e.g., α→β, excitations from a highspin triplet reference state. An implementation of the spin–flip approach within the Tamm–Dancoff approximation to timedependent density functional theory (TDDFT) is presented. The new method, SFTDDFT/TDA or simply SFDFT, describes target states (i.e., closed and openshell singlets, as well as lowspin triplets) by linear response from a reference highspin triplet Kohn–Sham state. Contrary to traditional TDDFT, the SFDFT response equations are solved in a subspace of spin–flipping operators. The method is applied to bondbreaking (ethylene torsional potential), and equilibrium properties of eight diradicals. The results demonstrate significant improvement over traditional Kohn–Sham DFT, particularly for 50/50 hybrid functional.

Molecular integrals over the gaugeincluding atomic orbitals
View Description Hide DescriptionEach general formula can be derived by the use of the solid harmonic gradient operator [K. Ishida, Recent Res. Dev. Quantum Chem. 2, 147 (2001)] for each of the ten kinds of molecular integral over the gaugeincluding atomic orbitals (GIAOs). Each is obtained with the accompanying coordinate expansion (ACE) formula. These ten kinds are the overlap, the kinetic energy, the nuclear attraction, the electron repulsion, the angular momentum, the quadrupole moment, the field, the first kind field gradient, the second kind field gradient, and the “dipolefield” integrals. Except for the overlap and angular momentum integrals, we derive the general formula of these eight molecular integrals at the first level. These ACE formulas will be useful, for example, for a calculation of a molecule in a uniform magnetic field, for a relativistic calculation, and so on, using GIAO as a basis function.

Cumulant approach to the direct calculation of reduced density matrices: A critical analysis
View Description Hide DescriptionIn this paper we address a number of topics regarding the contracted Schrödinger equation (CSE): (i) The cumulant expansion of reduced density matrices (RDMs), and the reduction of the CSE to a connected form. (ii) The comparison of the resulting formalism to coupled clustertheory. (iii) The direct calculation of the twoparticle RDM in terms of the cumulants, without explicitly imposing any Nrepresentability conditions. We explore a number of approximations, the most elaborate of which is the 3,5CSE in which the cumulant expansion is carried out to the threeparticle level, and the only approximation made is to equate the four and fiveparticle cumulants to zero. Overall the numerical results we present for selected small model systems are found to be disappointing and we provide a critical analysis of the perceived shortcomings of our cumulant approach to the CSE.

G3RAD and G3XRAD: Modified Gaussian3 (G3) and Gaussian3X (G3X) procedures for radical thermochemistry
View Description Hide DescriptionThe G3RAD, G3XRAD, G3(MP2)RAD, and G3X(MP2)RAD, procedures, designed particularly for the prediction of reliable thermochemistry for free radicals, are formulated and their performance assessed using the G2/97 test set. The principal features of the RAD procedures include (a) the use of B3LYP geometries and vibrational frequencies (in place of UHF and UMP2), including the scaling of vibrational frequencies so as to reproduce ZPVEs, (b) the use of URCCSD(T) [in place of UQCISD(T)] as the highestlevel correlation procedure, and (c) the use of RMP (in place of UMP) to approximate basissetextension effects. G3RAD and G3XRAD are found to perform well overall with mean absolute deviations (MADs) from experiment of 3.96 and respectively, compared with 4.26 and for standard G3 and G3X. G3RAD and G3XRAD successfully predict heats of formation with MADs of 3.68 and respectively (compared with 3.93 and for standard G3 and G3X), and perform particularly well for radicals with MADs of 2.59 and respectively (compared with 3.51 and for standard G3 and G3X). The G3(MP2)RAD and G3X(MP2)RAD procedures give acceptable overall performance with mean absolute deviations from experiment of 5.17 and respectively, compared with 5.44 and for standard G3(MP2) and G3X(MP2). G3(MP2)RAD and G3X(MP2)RAD give improved performance over their standard counterparts for heats of formation (MADs=4.73 and respectively, versus 4.94 and G3(MP2)RAD shows similar performance to G3(MP2) for radical heats of formation (MAD=5.10 versus while G3X(MP2)RAD performs significantly better than G3X(MP2) (MAD=4.67 versus

Three electrons in a harmonic oscillator potential: Pairs versus single particles
View Description Hide DescriptionThe threedimensional Schrödinger equation for three electrons in a parabolic confinement potential (with strength measured by the frequency ω) can be decoupled into three pair problems, provided the expectation value of the center of mass vector R is small compared with the average distance between the electrons. This should be fulfilled at the strong correlation limit (small ω), where the electron system tends to crystallize. The remaining part of the Hamiltonian, which is not included in the independent pair model, is taken into account in perturbation theory. The complementary treatment of the weak correlation limit (large ω) considers noninteracting electrons as a zerothorder approximation and includes the electron–electron interaction in perturbation theory. It turns out that both approaches match satisfactorily for intermediate ω. Our results are compared with those obtained with the Hartree–Fock, configuration interaction, multiconfigurational complete active space, and stochastic variational method approaches and the data from a Wigner crystal treatment in a harmonic approximation.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Charge transfer for the ground state ion in collisions with molecules
View Description Hide DescriptionA new theoretical result of the total charge transfer cross section in collisions of ion in the ground state with molecule is reported. The collision energy of the incident ion ranges from 1 eV/u to 10 keV/u, covering the available experimental data. States of and symmetry are included in the calculation. The stateresolved cross sections are obtained by using both the semiclassical and full quantum molecular orbital close coupling method. Based on our results, we propose a possible explanation for the large discrepancies in recent measurements among various experimental groups.

Variation with the intermolecular distance of properties dependent on the electron density in cyclic dimers with two hydrogen bonds
View Description Hide DescriptionThe variation with the intermolecular distance of geometries,energies, and other properties dependent on the electron density ρ(r) are studied in three cyclic dimers linked by two hydrogen bonds: formic acid and formamide homodimers and the heterodimer formamide/formic acid complex. Topological features, energy densities and integrated atomic properties provided by AIM theory are calculated with ρ(r) obtained at optimized geometries for a number of intermonomer distances covering large separations, equilibrium, and short distances. The variation with these distances of properties studied allows to characterize the nature of the interaction in A–H⋯B (A=N, O and B=O) hydrogen bonds. Whereas at large distances the attraction is purely electrostatic,quantum effects associated with redistributions of mainly around H and B atoms dominate the interaction in the neighborhood of equilibrium. Mutual penetration of the electron densities of these atoms leads to considerable reductions of their atomic volumes and associated polarization effects as well as energetic stabilization of atom A. Although the interaction in this range of intermonomer separations displays noncovalent features, when the dimers move at distances shorter than equilibrium, characteristics typical of covalent interactions begin to appear while the systems leave the planar structures presented until then. This work complements our previous study [O. Galvez, P. C. Gomez, and L. F. Pacios, J. Chem. Phys. 115, 11166 (2001)] of dimers with one single hydrogen bond.

Calculating energy levels of isomerizing tetraatomic molecules. I. The rovibrational bound states of
View Description Hide DescriptionA general, sixdimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wideamplitude motions and isomerizations. An application to the van der Waals trimer is presented in which the HF intramolecular stretching coordinate is separated out adiabatically and is not treated explicitly. Vibrational term values up to about 100 with absolute convergence to better than 0.1 are reported. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than hitherto. States that sample Ar–Ar–HF linear configurations and approach Ar–HF–Ar linear configurations are characterized for the first time. Results for total angular momentum and 1 provide the first accurate calculations of rotational constants for this system. The rotational constants for the HF bending states of in the ground and first vibrationally excited states of the HF monomer are in good agreement with experiment, confirming the accuracy of the potential used in this work.

Simple model potential and model wave functions for (Na, K, Rb, Cs)–H molecules
View Description Hide DescriptionA simple model potential is used to describe the interaction of a valence electron with the alkali core, which has the correct asymptotic form with the Coulomb and dipolar polarizability terms, and an effective hardcore radius adjusted to give the correct energy for the valence electron. Based on this potential, some simple wave functions are developed to describe the (Na, K, Rb, Cs)–H molecules, which incorporate some important local properties, in particular the cusp property when two charged particles are close to each other. These wave functions provide reliable values for the potential, and a simple physical perspective of their structure.

Negative ion photoelectron spectra simulation of from a density functional study
View Description Hide DescriptionA density functional study of neutral and anionic vanadium trimer monoxides is presented. The calculations were of allelectron type employing a newly developed basis set for the vanadium atom. Different isomers of and were studied in order to determine the ground state structures. For both systems a planar structure with an edgebonded oxygen atom was found as the ground state. Equilibrium structure parameters of ground states as well as lowlying excited states, harmonic frequencies, the adiabatic electron affinity, and Kohn–Sham orbital diagrams are reported. The experimental negative ion photoelectron spectra of was simulated by calculating multidimensional Franck–Condon factors, using the geometries and harmonic frequencies of the calculated ground states of and The good agreement between the experimental and the theoretical spectra allows the determination of the ground state structure of and This represents the first work in which a simulation of a vibrationally resolved negative ion photoelectron spectra of a transition metal oxide is presented.

Ab initio direct dynamics studies on the reactions of H atoms with and
View Description Hide DescriptionThe multiple channel reactions (1) and (2) have been studied by ab initio direct dynamics method. The potentialenergy surface information is calculated at the level of theory. Energies along the minimum energy paths are further improved by singlepoint energy calculations at the level of theory. For the two reactions, each with two reaction channels, hydrogen atom abstraction and halogen atom abstraction have been identified. The rate constants for each reaction channel are calculated by using improved canonical variational transition state theory incorporating the smallcurvature tunneling correction in the temperature range 200–3000 K. The theoretical total rate constants, which are calculated from the sum of the individual rate constants, are in good agreement with the experimental data. For reaction (1), Habstraction reaction will be preferred in the whole temperature range. For reaction (2), Brabstraction reaction is the major channel, while as the temperature increases, the contribution of the Habstraction reaction channel should be taken into account.

Mass analyzed threshold ionization spectroscopy of methylaniline, ethylaniline, and dimethylaniline cations: Influence of alkyl substitution on the ionization energy and molecular vibration
View Description Hide DescriptionWe have applied twocolor resonanttwophoton mass analyzed threshold ionization spectroscopy to investigate some ionic properties of alkylanilines. The respective adiabatic ionization energies of methylaniline (NMA), ethylaniline (NEA), and dimethylaniline (DMA) are determined to be 59 822, 59 204, and with an uncertainty of about This indicates that the longer alkyl chain gives rise to a larger redshift in the IE due to a stronger interaction between the alkyl group and the nitrogen atom in the ionic state. Because the alkyl group gives rise to an increase in the electron density around the nitrogen atom of the neutral species, the IE of DMA is lower than that of NMA. In addition, the alkyl substitution also influences the frequency of the internal motion of the cations. However, the frequency variation is dependent upon the vibrational pattern and the extent of the coupling between the alkyl group and ring vibrations.

Reaction pathway and energy disposal of the CaH product in the reaction of
View Description Hide DescriptionThe reaction pathway for has been investigated by using the pump–probe technique in combination with potential energy surface (PES) calculations. The nascent product distributions of CaH have been found with a Boltzmann rotational temperature of 988±66 and 864±75 K for the and 1 levels, respectively, and a Boltzmann vibrational temperature of 1960±80 K. The rotational and vibrational energy partitions in CaH have been estimated to be 555±22 and 995±10 cm^{−1}, respectively. According to the PES calculations, the pathway is found to favor an insertion mechanism. approaches in or symmetry and then the collision complex may undergo a series of surface transitions to the ground state surface with which the products correlate. The findings of low rotation and high vibration for CaH may be interpreted from two aspects. First, the Ca–C bond distance of the intermediate around the surface crossing region is 2.7–2.8 Å, close to the equilibrium bond distance 2.349 Å. The strong coupling of the moieties renders the energy transfer sufficient from CaH into the radical. Second, after the surface transition, the intermediate with a small excess energy may be energetically stabilized. The longlived collision complex may have enough time for energy randomization prior to flying apart.

Dominant structural motifs of complexes: Infrared spectroscopic and ab initio studies
View Description Hide DescriptionArgon predissociationspectroscopy is used together with ab initio electronic structure calculations to characterize the clusters. In all cases, the water molecules bind to the ion through single ionic H bonds. Two isomeric forms are assigned for the species that differ according to whether the H bond occurs to the N or O atom of the core ion. While the spectra of the dihydrate indicate formation of an Hbonded water dimer subcluster consistent with all four predicted isomers, their calculated vibrational spectra are too similar to establish which of these forms is created in the ion source. Three classes of isomers are predicted for the clusters, and in this case a comparison of the experimental and theoretical infrared spectra indicates the formation of a bridging arrangement in which two of the water molecules are attached to one atom and the third to the other atom of This distorted water trimer motif is intermediate between the symmetrical trimer found in the [X=Cl,Br,I] clusters and the open structure displayed by the system. The structural differences between the complexes of water with and are discussed in the context of the relative proton affinities and the electronic structures of their ground states (i.e., versus Spectra of the clusters are also presented together with a qualitative discussion of the likely morphologies at play in these higher hydrates.

Rotationally resolved electronic spectra of both conformers of the 1propoxy radical
View Description Hide DescriptionFive bands of the laser induced fluorescencespectrum of jetcooled 1propoxy radical have been recorded with a spectral resolution of The resolved rotational and fine structure of these bands has been assigned and analyzed providing rotational constants for both the and states as well as components of the electron spinrotation tensor in the state. By comparison of these constants with ones obtained from quantum chemistry calculations, two bands have been assigned to the gauche conformer of 1propoxy and 3 bands to the trans conformer. The spectrum of each conformer abruptly terminates after the excitation of a single C–O stretch.