Volume 120, Issue 22, 08 June 2004
 ARTICLES

 Theoretical Methods and Algorithms

Basis set effects on frontier molecular orbital energies and energy gaps: A comparative study between plane waves and localized basis functions in molecular systems
View Description Hide DescriptionIn order to study the Kohn–Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximationexchangecorrelation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the planewaves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the planewave expansion have been appropriately calibrated.

Size versus volume extensivity of a new class of density matrix functionals
View Description Hide DescriptionDespite being sizeextensive, the “secondgeneration” 1matrix functionals for the electron–electron repulsion energy yield vanishing correlation energy for the homogeneous electron gas. This failure is directly related to the idempotency condition imposed upon an auxiliary matrix that enters the expression for In particular, the recently proposed Kollmar–Hess functional is not volumeextensive and thus is incapable of properly describing any delocalized system at its thermodynamic limit.

Atomic dipole moments calculated using analytical molecular secondmoment gradients
View Description Hide DescriptionWe have implemented analytical secondmoment gradients for Hartree–Fock and multiconfigurational selfconsistentfield wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basisset convergence toward a welldefined basisset limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.

An exact reformulation of the diagonalization step in electronic structure calculations as a set of second order nonlinear equations
View Description Hide DescriptionA new formulation of the diagonalization step in selfconsistentfield (SCF) electronic structure calculations is presented. It exactly replaces the diagonalization of the effective Hamiltonian with the solution of a set of second order nonlinear equations. The density matrix and/or the new set of occupied orbitals can be directly obtained from the resulting solution. This formulation may offer interesting possibilities for new approaches to efficient SCF calculations. The working equations can be derived either from energy minimization with respect to a Cayleytype parametrization of a unitary matrix, or from a similarity transformation approach.

Geminal model chemistry II. Perturbative corrections
View Description Hide DescriptionWe introduce and investigate a chemical model based on perturbative corrections to the product of singlettype strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein–Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The effect of spin–orbit coupling on fast neutral chemical reaction
View Description Hide DescriptionThe effect of nonadiabatic transitions through the spin–orbit couplings has been investigated on the fast neutral reaction, Adiabatic potential energies and the spin–orbit coupling terms have been evaluated for the four electronic states of and that correlate with the asymptote, as a function of CO distance and OCH angle under the symmetry, by ab initio electronic structure calculations using multireference internally contracted single and double excitation configuration interaction method with the basis sets. Multistate quantum reactive scattering calculations have been carried out with the use of thus obtained potential energies and spin–orbit coupling matrices, based on the generalized Rmatrix propagation method. The calculated thermal rate constants show a slight positive dependence on temperature in a range between 50 and 2000 K, supporting the previous experimental results. It is shown that the spin–orbit coupled excited states give rise to reflections over the centrifugal barrier due to the quantum interference. Classical capture calculations yield larger rate constants due to the neglect of quantum reflections. It is concluded that the effect of nonadiabatic transitions is of minor importance on the overall reactivity in this reaction.

A systematic ab initio study of the equilibrium geometry and vibrational wave numbers of bismuthine
View Description Hide DescriptionThe equilibrium structure and the harmonic and anharmonic force fields of are determined by highlevel ab initio calculations using a variety of correlation treatments, basis sets, and pseudopotentials, partly in combination with core polarization potentials. Spin–orbit effects are included by a configuration interaction treatment. This systematic study serves to establish a reliable computational protocol for such calculations and, in particular, to minimize basis set superposition errors through an improved new basis set and/or counterpoise corrections. Using the recommended procedures, the best ab initio results for the equilibrium geometry and the fundamental vibrational wave numbers are in good agreement with the available experimental data, which further supports the recent spectroscopic identification of The groundstate total atomization energy of is predicted to be 153.1 kcal/mol.

Geometry and electronic structure of complexes
View Description Hide DescriptionFirstprinciples calculations based on the generalized gradient approximation to the density functional theory are performed to explore the global geometries, groundstate spin multiplicities, relative stabilities, and energetics of neutral and anionic with complexes. The calculated results show that the complexes clearly prefer sandwich structures to riceball structures. The groundstate spin multiplicities of the complexes increased linearly with the size of the system (i.e., n). In the anionic complexes, the complex is found to be unstable against the autodetachment of the extra electron. The energy difference between adiabatic and vertical electron affinities is found to be very less, indicating negligible ionizationinduced structural changes in the groundstate geometries of complexes.

Diffusion quantum Monte Carlo for equilibrium structures and harmonic frequencies of ethane and ozone molecules
View Description Hide DescriptionApplication of the Ornstein–Uhlenbeck diffusionquantum Monte Carlo method in combination with a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals to studies on the equilibrium structures and harmonic frequencies of ethane and ozone is presented. These Monte Carlo computed results are compared with those of experiments as well as the coupled cluster methods with the correlation consistent basis sets for the two molecules. For ozone, we also compare the Monte Carlo results with the results from multireference calculations.

Nearinfrared spectra and rovibrational dynamics on a fourdimensional ab initio potential energy surface of
View Description Hide DescriptionSupersonic jet investigations of the dimer have been carried out using a tunable diode laser spectrometer to provide accurate data for comparison with results from a fourdimensional (4D) ab initiopotential energy surface (PES). The nearinfrared and bands of and isotopomers have been recorded in the range 2500–2600 cm^{−1} using a CW slit jet expansion with an upgraded nearinfrared diode laser spectrometer. The 4D PES has been calculated for using secondorder Møller–Plesset perturbation theory with an augmented and polarized 6311G basis set. The potential is characterized by a global minimum occurring at the H bond structure with the distance between the center of masses (CM) of the monomer being with angles and a well depth of 692.2 cm^{−1}, is the angle the HBr bond of monomerA makes with the vector from the CM of A to the CM of B, and is the corresponding angle monomerB makes with the same CM–CM vector. The barrier for the H interchange occurs at the closed structure for which and the barrier height is 73.9 cm^{−1}. The PES was fitted using a linearleast squares method and the rovibrational energy levels of the complex were calculated by a split pseudospectral method. The spectroscopic data provide accurate molecular parameters for the dimer that are then compared with the results predicted on the basis of the 4D ab initio PES.

Fractional revivals in the rovibrational motion of
View Description Hide DescriptionMotivated by pump–probe experiments of in a roomtemperature sample, the detection of fractional revivals is investigated using fulldimensional quantum wave packet calculations. It is shown that the structures observed in the pump–probe signal depend sensitively on the probe parameters employed and that the observed signal reflects a particular phase effect between fractional revivals.

Electric dipole polarizabilities of copper clusters
View Description Hide DescriptionThe static electric dipole polarizabilities of have been measured via a molecular beam deflection method. The clusters display peratom polarizabilities that decrease monotonically with size, from ∼16 Å^{3} per atom to ∼5 Å^{3} Absent are any discernible discontinuities or odd–even alternations due to electronic shell filling or electron pairing effects. For the smallest clusters, the experimental polarizabilities are ∼3 times larger than those predicted classically for conducting ellipsoids, and approach the classical values only for clusters containing more than ∼45 atoms.

Postnucleation droplet growth in supersaturated gas with arbitrary vapor concentration
View Description Hide DescriptionThis work concerns the reexamination and extension of the current theory of phase transition dynamics for liquiddroplets growing on solubleaerosols from a supersaturated gas mixture for the general case of arbitrary value of vapor concentration. We found that the inconsistency in the common treatment of the vapor diffusion, due to an implicit assumption of the constancy of gas density in the vicinity of a droplet by neglecting its dependency on temperature and vapor concentration, leads to the obvious discrepancy in the Maxwell expression for the growth rate regarding droplets of near critical size. Restoring the correct treatment of the vapor diffusion in terms of the mass concentration of water vapor and taking into the consideration variations of gas density in the vicinity of a droplet in compliance with the equation of state of moist air, we have obtained a new expression for the droplet growth rate valid for an arbitrary value of vapor concentration. The limitations imposed by the molecular kinetic fluxes to postnucleation diffusional growth of small droplets with a large Knudsen number are also reevaluated to include previously neglected physical effects. In particular, the essential contribution of the vapor molecular energy flux into the total kinetic molecular heat flux as well as the temperature variations of mean thermal velocities of air and vapor molecules in the vicinity of the dropletinterface have been taken into consideration. Surprisingly significant differences have been found in new expressions derived for the droplet growth rate and droplet temperature, even in the limit of small vapor concentration, if comparing with commonly used results. These findings could help with better interpretation of experimental measurements to infer more reliable data for the mass and thermal accommodations coefficients.

Isomerselective detection of microsolvated oxonium and carbenium ions of protonated phenol: Infrared spectra of clusters
View Description Hide DescriptionInfrared photodissociation (IRPD) spectra of clusters composed of protonated phenol and several ligands L are recorded in the O–H and C–H stretch ranges using a tandem mass spectrometer coupled to a clusterion source. The complexes are generated by chemical ionization of a supersonic expansion. The IRPD spectra of mass selected clusters obtained in various fragment channels display the unambiguous fingerprints of at least two different nucleation centers: the oxonium ion (5) and the carbenium ion(s) corresponding to protonation of phenol in ortho and/or para position (1/3). These two classes of isomers show very different fragmentation behavior upon IR excitation, facilitating the assignment of the observed vibrational transitions. The vibrational frequency shifts as a function of cluster size reveal that the microsolvation of 1/3 and 5 in Ar and begins with the formation of intermolecular hydrogen bond(s) to the acidic OH group(s) and proceeds by the formation of intermolecular πbonds to the respective sixmembered rings. The analysis of photofragmentation branching ratios yields estimated ligand binding energies of the intermolecular OH and πbonds for solvation of the different isomers. The effects of microsolvation on the properties of 1/3 as reactive intermediates in electrophilic aromatic substitution reactions are discussed. Comparison of clusters of protonated phenol with those of neutral phenol reveals the drastic protonationinduced changes in the topology of the intermolecular potential of aromatic molecules interacting with a nonpolar solvent. Moreover, the results show that the IRPD process can be used to selectively generate a spectroscopically clean ion beam of either 1/3 or 5 with some control over their internal energies.

Calculation of the rate constant for stateselected recombination of as a function of temperature and pressure
View Description Hide DescriptionClassical trajectory calculations using the MERCURY/VENUS code have been carried out on the reactive system using the DMBEIV potential energy surface. The vibrational quantum number and the temperature were selected over the ranges to 15, and to 10 000 K, respectively. All other variables were averaged. Rate constants were determined for the energy transfer process, for the bimolecular exchange process, and for the dissociative process, The dissociative process appears to be a mere extension of the process of transferring large amounts of energy. Statetostate rate constants are given for the exchange reaction, and they are in reasonable agreement with previous results, while the energy transfer and dissociative rate constants have never been reported previously. The lifetime distributions of the complex, calculated as a function of and temperature, were used as a basis for determining the relative contributions of various vibrational states of to the thermal rate coefficients for recombination at various pressures. This novel approach, based on the complex’s ability to survive until it collides in a secondary process with an inert gas, is used here for the first time. Complete falloff curves for the recombination of are also calculated over a wide range of temperatures and pressures. The combination of the two separate studies results in pressure and temperaturedependent rate constants for It is found that, unlike the exchange reaction, vibrational and rotational–translational energy are liabilities in promoting recombination.

Spectroscopic properties of novel aromatic metal clusters: and their cations and anions
View Description Hide DescriptionThe ground and several excited states of metal aromatic clusters, namely and clusters have been investigated by employing complete activespace selfconsistentfield followed by multireference singles and doubles configuration interaction computations that included up to 10 million configurations and other methods. The ground states of aromatic anions are found to be symmetric electronic states with ideal square pyramid geometries. While the ground state of is also predicted to be a symmetric square pyramid, the ground state of the cluster is found to have a pyramid with a rhombus base, and the ground state of possesses a pyramid with a rectangle base. In general, these structures exhibit two competing geometries, viz., an ideal structure and a distorted rhomboidal or rectangular pyramid structure All of the ground states of the cations are computed to be pyramids with rhombus bases. The equilibrium geometries, vibrational frequencies, dissociation energies, adiabatic ionization potentials, adiabatic electron affinities for the electronic states of and their ions are computed and compared with experimental results and other theoretical calculations. On the basis of our computed excited statesenergy separations, we have tentatively suggested assignments to the observed X and A states in the anion photoelectron spectra of reported by Li et al. [X. Li, A. E. Kuznetov, H. F. Zheng, A. I. Boldyrev, and L. S. Wang, Science 291, 859 (2001)]. The X state can be assigned to a rhomboidal pyramid. The A state observed in the anion spectrum is assigned to the first excited state of the neutral with the symmetry. The assignments of the excited states are consistent with the experimental excitation energies and the previous Green’s functionbased methods for the vertical transition energy separations between the X and A bands.

Massanalyzed threshold ionization spectroscopy of pmethylphenol and pethylphenol cations and the alkyl substitution effect
View Description Hide DescriptionThe massanalyzed threshold ionization (MATI) spectra of pmethylphenol and pethylphenol have been recorded by ionizing via various vibronic levels. The adiabatic ionization energies (IEs) of pmethylphenol and pethylphenol are determined to be and which are less than that of phenol by 2707 and 2997 cm^{−1}, respectively. This redshift indicates that the interaction between the alkyl group and the ring of alkylphenols in the cationic state is greater than that in the neutral state. Moreover, a longer alkyl group gives rise to a greater redshift in the IE. Analysis of the MATI spectra shows that most of the active modes are related to the inplane ring vibrations of these two cations. However, the length of the alkyl group has an insignificant effect on the frequency of the observed ring vibrations. No band with frequency less than 350 cm^{−1} is observed for the pmethylphenol cation. In contrast, many lowfrequency bands resulting from the characteristic motions (e.g., the torsion and and C–OH bending vibrations) appear in the MATI spectra of pethylphenol. The present results show that the ethyl group enhances the substituentsensitive and many largeamplitude vibrations of the cation.

Broadening and line mixing in the and Q branches of carbon dioxide: Experimental results and energycorrected sudden modeling
View Description Hide DescriptionUsing both a difference frequency spectrometer and a Fourier transform spectrometer, we have measured transitions in the band of carbon dioxide at room temperature and pressures up to 19 atm. The lowpressure spectra were analyzed using a variety of standard spectral profiles, all with an asymmetric component to account for weak line mixing. For this band, we have been able to retrieve experimental line strengths and the broadening and weak mixing parameters. In this paper we also compare the suitability of the energycorrected sudden model to predict mixing in the two previously measured Q branches the and the present Q branch of pure all at room temperature.

Rotational statedependent mixings between resonance states of vibrationally highly excited DCO
View Description Hide DescriptionRotational statedependent mixings between highly excited resonance states of DCO were investigated by stimulated emission pumping spectroscopy via a series of intermediate rotational levels in the electronic state of the radical. Two examples for such interactions, between pairs of accidentally nearly degenerate vibrational states at energies of and respectively, were analyzed in detail. Deperturbations of the measured spectra provided the zerothorder vibration–rotation term energies, widths, and rotational constants of the states and the absolute values of the vibrational coupling matrix elements. The coupled states turned out to have very different Arotational constants so that their mixings switch on or off as they are tuned relative to each other as function of the rotational quantum number. The respective zerothorder states could be assigned to different interlaced vibrational polyads. Thus, when two states belonging to different polyads are accidentally nearly isoenergetic, even very weak interpolyad interactions may start to play important roles. The derived interpolyad coupling elements are small compared to the typical intrapolyad coupling terms so that their influences on the vibrational term energies are small. However, large effects on the widths (i.e., decay rates) of the states can be observed even from weak coupling terms when a narrow, longlived state is perturbed by a broad, highly dissociative state. This influence contributes to the previously observed strong statetostate fluctuations of the unimolecular decay rates of the DCO radical as function of vibrational excitation. Similar mechanisms are likely to promote the transition to “statistical” rates in many larger molecules.

Relative vibrational overtone intensity of cis–cis and trans–perp peroxynitrous acid
View Description Hide DescriptionThe vibrational overtone spectrum of HOONO is examined in the region of the and bands using action spectroscopy in conjunction with ab initio intensity calculations. The present measurements indicate that the oscillator strength associated with the higher energy trans–perp conformer of HOONO is stronger relative to the lower energy cis–cis conformer for both these vibrational overtone levels. Ab initio intensity calculations carried out at the QCISD level of theory suggest that this disparity in oscillator strength apparently arises from differences in the second derivative of the transition dipole moment function of the two isomers. The calculations indicate that the oscillator strength for the trans–perp isomer is ∼5.4 times larger than that of the cis–cis isomer for the band and ∼2 times larger for band. The band positions and intensities predicted by the calculations are used to aid in the assignment of features in the experimental action spectra associated with the OH stretching overtones of HOONO. The observed relative intensities in the experimental action spectra when normalized to the calculated oscillator strengths appears to suggest that the concentration of the higher energy trans–perp isomer is comparable to the concentration of the cis–cis isomer in these room temperature experiments.