Volume 120, Issue 17, 01 May 2004
 ARTICLES

 Theoretical Methods and Algorithms

Interelectronic angle densities of equivalent electrons in Hartree–Fock theory of atoms
View Description Hide DescriptionThe interelectronic angle density is the probability density function that the angle subtended by the vectors and of any two electrons i and j becomes For equivalent electrons in atoms, it is shown that the density in the Hartree–Fock theory is given by a simple polynomial of Detailed expressions are reported for all LS terms arising from and electron configurations. With no modifications, the present results apply as well to the interelectronic angle density in momentum space, where is the angle between two electron momenta.

Monomer basisset truncation effects in calculations of interaction energies: A model study
View Description Hide DescriptionSupermolecular interaction energies are analyzed in terms of the symmetryadapted perturbation theory and operators defining the inaccuracy of the monomerwave functions. The basis set truncation effects are shown to be of first order in the monomer inaccuracy operators. On the contrary, the usual counterpoise correction schemes are of second order in these operators. Recognition of this difference is used to suggest an approach to corrections for basisset truncation effects. Also earlier claims—that dimercentered basis sets may lead to interaction energies free of basisset superposition effects—are shown to be misleading. According to the present study the basisset truncation contributions, evaluated by means of the symmetryadapted perturbation theory with monomercentered basis sets, provide physically and mathematically justified corrections to supermolecular results for interaction energies.

A computational strategy for geometry optimization of ionic and covalent excited states, applied to butadiene and hexatriene
View Description Hide DescriptionWe propose a computational strategy that enables ionic and covalent ππ^{*}excited states to be described in a balanced way. This strategy depends upon (1) the restricted active space selfconsistent field method, in which the dynamic correlation between core σ and valence π electrons can be described by adding single σ excitations to all π configurations and (2) the use of a new conventional oneelectron basis set specifically designed for the description of valence ionic states. Together, these provide excitation energies comparable with more accurate and expensive ab initio methods—e.g., multiconfigurational secondorder perturbation theory and multireference configuration interaction. Moreover, our strategy also allows full optimization of excitedstate geometries—including conical intersections between ionic and covalent excited states—to be routinely carried out, thanks to the availability of analytical energy gradients. The prototype systems studied are the cis and trans isomers of butadiene and hexatriene, for which the ground lowerlying dark (i.e., symmetry forbidden covalent) and spectroscopic (valence ionic) states were investigated.

Body frames in the separation of collective angles in quantum Nbody problems
View Description Hide DescriptionThe application of the concept of bodyfixed reference frames, proposed by C. Eckart [Phys. Rev. 47, 552 (1935)], to the problem of the separation of three collective angles in quantum Nbody problems is analyzed based on the technique recently developed by Meremianin and Briggs [Phys. Rep. 384, 121 (2003)]. Special attention is paid to the body frame defined by the “second Eckart condition” which minimizes vibrorotational couplings near the equilibrium position. The important case of the Eckart frame for threebody systems is considered in detail. The connection of the basis vectors of the Eckart frame with Jacobi vectors is derived. All results of this work are valid for an arbitrary choice of internal (bodyframe) coordinates.

A growing string method for determining transition states: Comparison to the nudged elastic band and string methods
View Description Hide DescriptionInterpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.

Extracting atoms from molecular electron densities via integral equations
View Description Hide DescriptionThe observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclearcentered, spherically symmetric functions. The functions that are optimal in a leastsquares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The role of symmetry and optical selection rules in revealing the molecular structure of the lowest Rydberg and ionic states of the van der Waals complexes
View Description Hide DescriptionThe van der Waals complexes have been investigated using a combination of resonance enhanced multiphoton ionization (REMPI) and zero electron kinetic energy (ZEKE) spectroscopy. The additivity of the spectral shifts observed in both REMPI and ZEKE spectra, taken together with analysis of vibrational structure, suggest that in both DABCO–Ar and the argon atoms bind in equivalent equatorial (face) locations between two adjacent bridges. However, the cumulative evidence from both REMPI and ZEKE spectra, together with ab initio results, suggests that the complex does not revert to symmetry, but rather adopts a structure in which all three argon atoms bind to one side of the DABCO framework. The exceptionally low wavenumber vibrational structure observed in the REMPI spectra suggest that the van der Waals interaction in the excited state is extremely weak. However, ionization necessarily increases the strength of the interaction by virtue of the introduction of chargeinduced dipole forces, as revealed by a consistent increase in vibrational wave numbers of the modes observed in the resultant ZEKE spectra.

Two and threebody photodissociation of gas phase
View Description Hide DescriptionThe photodissociation dynamics of from 390 to 290 nm (3.18 to 4.28 eV) have been investigated using fast beam photofragment translational spectroscopy in which the products are detected and analyzed with coincidence imaging. At photon energies ⩽3.87 eV, twobody dissociation that generates and vibrationally excited is observed, while at energies ⩾3.87 eV, is the primary twobody dissociation channel. In addition, threebody dissociation yielding photofragments is seen throughout the energy range probed; this is the dominant channel at all but the lowest photon energy. Analysis of the threebody dissociation events indicates that this channel results primarily from a synchronous concerted decay mechanism.

Measurement of orientation and alignment moment relaxation by polarization spectroscopy: Theory and experiment
View Description Hide DescriptionA diagrammatic perturbation theory description of onecolor polarizationspectroscopy (PS) is developed which emphasizes the significance of orientation and alignment tensor moments of the rotational angular momentum, and their collisional evolution. The influences of Dopplermotion, velocitychanging collisions, decay of population, orientation and alignment, and nuclear hyperfine depolarization on the calculated PS signal are discussed. Illustrative simulations are presented of the evolution of the PS signal as a function of pump–probe laser delay. These are generated by a Monte Carlo integration of the derived equations for the signal electric field over typical experimental pump and probe laser temporal profiles and velocity distributions for a commonly studied system, the OH (0,0) band. These predictions are compared with a preliminary set of results obtained in an experimental apparatus designed for onecolor polarizationspectroscopy using independent pump and probe lasers. Measurements are presented using linearly polarized pump light on the transition of the OH (0,0) band with He as the collision partner. The decay of the experimental PS pump–probe signal is discussed with reference to inelastic collisional population transfer rates in the literature. It is concluded that the collisional depolarization of rotational alignment is rapid, with a rate approximately twice that of population transfer. This is consistent with previous measurements in atmospheric pressure flames. PS is shown to be a viable novel spectroscopic method for determining rotational angular momentum orientation and alignment relaxation rates, which are valuable quantities because they are sensitive probes of the forces involved in inelastic collisions.

Electronic properties of CrF and CrCl in the state: Observation of the halogen hyperfine structure by Fourier transform microwave spectroscopy
View Description Hide DescriptionThe rotational spectra of the CrF and CrCl radicals in the state were observed by employing a Fourier transformmicrowave spectrometer. The CrF and CrCl radicals were generated by the reaction of laserablated Cr with and respectively, diluted in Ar. A chromium rod made of chromiumpowder pasted with epoxy resin was ablated by a Nd:YAG laser. Rotational transitions were measured in the region between 8 and 26 GHz. Several hyperfine constants due to the halogen nuclei were determined by a leastsquares analysis. The electronic properties of CrF and CrCl were derived from their hyperfine constants and were compared with those of other transition metal monohalides: TiF, MnF, FeF, CoF, NiF, and FeCl.

Electron momentum spectroscopy of Experimental and theoretical momentum profiles for outer valence orbitals
View Description Hide DescriptionElectron momentum distributions for outer valence orbitals of have been obtained by electron momentum spectroscopy at an incident energy of energy. The experimental electron momentum profiles are compared with Hartree–Fock and density functional theory(DFT) calculations using B3LYP hybrid functional with the 631G and basis sets. Generally, the shapes of the experimental momentum profiles are well reproduced by DFT calculations using larger basis sets An attempt has been made to clarify the ordering of the outer valence orbitals, which have been in controversy, by comparing experimental results with calculations.

Complete basis set extrapolated potential energy, dipole, and polarizability surfaces of alkali halide ionneutral weakly avoided crossings with and without applied electric fields
View Description Hide DescriptionComplete basis set extrapolations of alkali halide (LiF, LiCl, NaF, NaCl) energy, dipole, and polarizabilitysurfaces are performed with and without applied fields along the internuclear axis using stateaveraged multireference configuration interaction. Comparison between properties (equilibrium separation, dissociation energy, crossing distance, diabatic coupling constant, dipole, and polarizability) derived from the extrapolated potential energy (or dipole) surfaces are made with those obtained from direct extrapolation from the basis set trends. The two extrapolation procedures are generally found to agree well for these systems. Crossing distances from this work are compared to those of previous work and values obtained from the Rittner potential. Complete basis set extrapolated crossing distances agree well with those derived from the Rittner potential for LiF, but were significantly larger for LiCl, NaF, and NaCl. The results presented here serve as an important set of benchmark data for the development of newgeneration manybody force fields that are able to model charge transfer.

Ground and excited states of Electron propagator and quantum defect analysis
View Description Hide DescriptionVertical excitation energies of the Rydberg radical are inferred from ab initio electron propagator calculations on the electron affinities of The adiabatic ionization energy of is evaluated with coupledcluster calculations. These predictions provide optimal parameters for the molecularadapted quantum defect orbital method, which is used to determine Einstein emission coefficients and radiative lifetimes. Comparisons with spectroscopic data and previous calculations are discussed.

Products of the addition of water molecules to clusters: Structure, bonding, and electron binding energies in and
View Description Hide DescriptionTwo stable products of reactions of water molecules with the cluster, and are studied with electronic structure calculations. There are several minima with similar energies for both anions and the corresponding molecules. Dissociative absorption of a water molecule to produce an anionic cluster with hydroxide ions is thermodynamically favored over the formation of complexes. Vertical electron detachment energies of and calculated with ab initio electron propagator methods provide a quantitative interpretation of recent anion photoelectron spectra. Contrasts and similarities in these spectra may be explained in terms of the Dyson orbitals associated with each transition energy.

Theoretical prediction of electronic structures of fully πconjugated zinc oligoporphyrins with curved surface structures
View Description Hide DescriptionA theoretical prediction of the electronic structures of fully πconjugated zinc oligoporphyrins with curved surface, ring, tube, and ballshaped structures was conducted as the objective for the future development of triply meso–meso, β–β, and β–βlinked planar zinc oligoporphyrins. The excitation energies and oscillator strengths for the optimal ring and ball structures were calculated using the timedependent density functional theory(DFT). Although there is an extremely small energy difference of <0.1 eV between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the ring structure relative to the samesized triply linked planar one, the Q and B bands of the former are smaller redshifted excitation energies and intensified oscillator strengths than those of the latter due to the structurally shortened effective πconjugated lengths for the electron transition. It is expected that the ball structure becomes an excellent electron acceptor and shows the highly redshifted band in the nearIR region relative to the monomer. The minimum value of the HOMO–LUMO energy gaps of the infinitelength ring structures was estimated using periodic boundary conditions within the DFT, resulting in the metallic characters of both the tube structures with and without the spiral triply linked porphyrin array. The relation between the diameters and strain energies of the tube and ball structures was also examined. The present fused zincporphyrins may become more colorful materials with new optelectronic properties including artificial photosynthesis than the carbon nanotubes and fullerenes when the axial coordinations of the central metal of porphyrins are functionally used.

Quantum chemical densityfunctional theory calculations of the structures of defect with four vacancies
View Description Hide DescriptionQuantum chemical densityfunctional theory(DFT) calculations have been carried out for the six isomers obtained by removing four adjacent atoms from The most stable isomer consists of twelve 5member and eighteen 6member rings, indicating that the removal of some atoms from which contains twelve 5member rings and twenty 6member rings, does not always generate larger holes. Each of the other five isomers contains at least one 4member ring and one larger ring (7, 8, 9, or 10member ring) besides the 5 and 6member rings. All isomers have similar structures for singlet and triplet spin multiplicities but with different stabilities. The ground states for two of the isomers are triplets, whereas the ground states for the other isomers are singlets. Furthermore, a comparison between the various isomers allowed one to examine the effect of the structure on the stability of fullerene cages.

Exploring the dynamics of hydrogen atom release from the radical–radical reaction of with
View Description Hide DescriptionThe gasphase radical–radical reaction dynamics of was studied at an average collision energy of 6.4 kcal/mol in a crossed beam configuration. The groundstate atomic oxygen and allyl radicals were generated by the photolysis of and the supersonic flash pyrolysis of allyl iodide, respectively. Nascent hydrogen atom products were probed by the vacuumultraviolet–laser induced fluorescence spectroscopy in the Lymanα region centered at 121.6 nm. With the aid of the CBS–QB3 level of ab initio theory, it has been found that the barrierless addition of to forms the energyrich addition complexes on the lowest doublet potential energy surface, which are predicted to undergo a subsequent direct decomposition step leading to the reaction products The major counterpart of the probed hydrogen atom is calculated to be acrolein after taking into account the factors of barrier height, reactionenthalpy, and the number of intermediates involved along the reaction pathway. The nascent Hatom Doppler profile analysis shows that the average centerofmass translational energy of the products and the fraction of the total available energy released as the translational energy were determined to be 3.83 kcal/mol and 0.054, respectively. On the basis of comparison with statistical calculations, the reaction proceeds through the formation of shortlived addition complexes rather than statistical, longlived intermediates, and the polyatomic acrolein product is significantly internally excited at the moment of the decomposition.

Formation of doubly positively charged diatomic ions of produced by sputtering of an Mo metal surface
View Description Hide DescriptionLonglived metastable doubly positively charged diatomic ions of have been produced by bombardment of a molybdenummetal surface. These exotic molecular dications, such as for example at could be observed in positive ion mass spectra for ion flight times of ∼17 μs in a Cameca IMS3f secondary ion mass spectrometer, when the ion extraction field was adjusted for detection of ions that are formed in the gas phase several micrometers in front of the sputteredsurface. was observed at high primary current densities for projectile ions of but could not be detected under very similar bombarding conditions for projectile ions of Such a dependence of ion production by inert gas sputtering on the primary ion species [ionization energies: IP1(Ar)=15.76 eV and IP1(Xe)=12.13 eV] is unusual. It is shown that formation of dications takes place by resonant charge transfer in grazing gasphase collisions between incoming projectile ions of and sputtered molecular ions of The efficiency for such a resonant electron capture is of the order of for the bombarding conditions in our mass spectrometer and corresponds to a cross section of a few

Calculation of the transport properties of carbon dioxide. II. Thermal conductivity and thermomagnetic effects
View Description Hide DescriptionThe transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilutegas limit for thermal conductivity and thermomagnetic coefficients for temperatures ranging from 200 K to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Since thermal conductivity is influenced by vibrational degrees of freedom, not included in the rigidrotor classical trajectory calculation, a correction for vibration has also been employed. The calculations indicate that the secondorder thermal conductivity corrections due to the angular momentum polarization and velocity polarization are both small. Thermal conductivity values calculated using the potential energy hypersurface by Bukowski et al. (1999) are in good agreement with the available experimental data. They underestimate the best experimental data at room temperature by 1% and in the range up to 470 K by 1%–3%, depending on the data source. Outside this range the calculated values, we believe, may be more reliable than the currently available experimental data. Our results are consistent with measurements of the thermomagnetic effect at 300 K only when the vibrational degrees of freedom are considered fully. This excellent agreement for these properties indicates that particularly the potential surface of Bukowski et al. provides a realistic description of the anisotropy of the surface.

Positive electron affinity of fullerenes: Its effect and origin
View Description Hide DescriptionThe universal variation pattern of the total energy of various fullerenes including singlewalled carbon nanotubes with respect to their extra charge is revealed by the densityfunctionaltheory calculations. The parabolic energycharge curve with its lowest energy value corresponding to a negatively charged fullerene indicates that these carbon materials have positive electron affinity and are not in the most stable state. The positive electron affinity seems to originate from the πelectrons and is found to be related to the aggregation property of fullerenes.