Volume 119, Issue 16, 22 October 2003
 ARTICLES

 Theoretical Methods and Algorithms

Splitlocalized orbitals can yield stronger configuration interaction convergence than natural orbitals
View Description Hide DescriptionThe convergence of configuration interaction (CI) expansions depends upon the orbitals from which the configurations are formed. Since their introduction half a century ago, natural orbitals have gained an increasing popularity for generating rapidly converging CI expansions and the notion has become widespread that they always yield the fastest CI convergence. It is shown here that, in fact, certain localized orbitals often yield a better CI convergence than natural orbitals, as measured by a wave function criterion as well as by an energy criterion.

Intermolecular forces and fixednode diffusion Monte Carlo: A brute force test of accuracies for and He–LiH
View Description Hide DescriptionThe accuracy of the fixednode approximation and diffusionMonte Carlo method in computing the interaction energy of van der Waals systems was investigated. Tests were carried out by simulating the electronic structures of and He–LiH. These two systems were chosen as representative of two fundamentally different interactions, namely the weak dispersion forces in and the dipole/induced–dipole interaction in He–LiH. The results for both systems are in excellent agreement with “state of the art” calculations, thereby indicating a high accuracy for the fixednode approximation. Also, our interaction energies for He–LiH indicate that the coupled cluster single double triple method [Taylor and Hinde, J. Chem. Phys. 111, 973 (1999)] gives an accurate prediction of the interaction potential for that system.

Improved leapsize selection for accelerated stochastic simulation
View Description Hide DescriptionIn numerically simulating the time evolution of a wellstirred chemically reacting system, the recently introduced “tauleaping” procedure attempts to accelerate the exact stochastic simulation algorithm by using a special Poisson approximation to leap over sequences of noncritical reaction events. Presented here is an improved procedure for determining the maximum leap size for a specified degree of accuracy.

Tunneling dissociation from a double well via path integrals
View Description Hide DescriptionIt is shown how the semiclassical theory of path integrals can be implemented in a practical manner for the analysis of a potential that combines the twostate system of a double well potential (DWP) with decay into a continuous spectrum. This potential may correspond to a variety of physical situations in physics and chemistry. The structure of the formalism and of the results is such that it allows computation not only for analytic but also for numerically given potentials. The central theme is the determination of the energydependent Green’s function, which is shown to consist of a regular part and a part containing simple and double complex poles. These poles represent the position of the energy levels, as well as the energy widths and shifts due to the interaction with the continuous spectrum. When applied to the bound DWP without tunneling, the theory is shown to reduce in certain limits to known results from the Jeffreys–Wentzel–Kiamers–Bhrillouin approximation. If the system is taken to be prepared in the first well, the interactions with the remaining of the potential lead to two types of transition rates. One represents the transient motion toward a virtual equilibrium state of the DWP. It emerges as a positive imaginary part of the selfenergy. The other represents the decay into the continuum and emerges as a negative imaginary part of the pole. Comparison of the two mechanisms of nonstationarity is made for different magnitudes of the second barrier relative to the first one. Since the system decays to the continuum while oscillating, the theory obtains a correction to the frequency of oscillation in the DWP due to the interaction with the continuum. This phenomenon is observable in real twostate systems, if an external perturbation which affects mainly one state converts it into a resonance state.

Nonlocal dielectric functions on the nanoscale: Screened forces from unscreened potentials
View Description Hide DescriptionIn this work, we prove that an intramolecular dielectric model yields accurate results for the forces between nonoverlapping molecules, at first order in the intermolecular interaction. The analysis is valid within the Born–Oppenheimer approximation. Within any perturbed molecule, a nonlocal dielectric function describes the screening of external potentials due to the induced redistribution of electronic charge, i.e., this function acts as the integral kernel that determines the effective potential at point r (within linear response), when an external potential acts on the molecule, at other points The dielectric function depends on the nonlocal chargedensity susceptibility, which can be calculated ab initio or by density functional techniques. From quantum mechanical perturbation theory, at first order the interaction energy of two molecules is determined by the unscreened Coulomb interaction energy of the unperturbed molecular charge distributions. Yet the firstorder forces on the nuclei include dielectric screening effects, due to the redistribution of the electronic charge density of each molecule in the presence of the other. This counterintuitive result follows from a relation between the chargedensity susceptibility and the derivatives of the electronic charge density with respect to nuclear coordinates. The derivation provides a quantum mechanical validation for dielectric screening models on the nanoscale, when the dielectric function for electronic response is nonlocal.

Local expansion of Nrepresentable oneparticle density matrices yielding a prescribed electron density
View Description Hide DescriptionMultiresolution (or wavelet) analysis offers a strictly local basis set for a systematic introduction of new details into Hilbert space operators. Using this tool we have previously developed an expansion method for density matrices. The set of density operators providing a given electron density plays an essential role in density functional theory, in the minimization of energy expectation values with the constraint that the electron density is fixed. In this contribution, using multiresolution analysis, we present an excellent quality density matrix expansion yielding a prescribed electron density, and compare it to other known methods. Due to the strictly local nature of the applied basis functions, our construction has the specific advantage that the resulting density matrix is correlated and Nrepresentable in the infinite resolution limit. As a further consequence of this scheme we can conclude that the deviation of the exact kinetic energy functional from the Weizsäcker term is not a necessary consequence of the particle statistics.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

and states of GeC and GeSi: The problematic dissociation energy of GeC
View Description Hide DescriptionThe and states for the GeC and GeSi diatomics have been investigated at the highly correlated coupledcluster levels of theory. Large basis sets [including TZ3P(2d,2f)+2diff, ccpVQZ, and augccpVQZ] were employed in order to predict reliable values for the experimentally unknown spectroscopic properties. The ground states were confirmed to be the state for GeC and the state for GeSi. Advanced theoretical treatments such as inclusion of corevalence correlation, scalar relativity, and complete basis set extrapolations have been performed to determine accurate energetic properties. The dissociation energies of 91.4 kcal/mol and 72.9 kcal/mol have been predicted for the state of GeC and state of GeSi, respectively. It is observed that the theoretical value of 72.9 kcal/mol for GeSi is in very good agreement with the experimental value of 71±5 kcal/mol. However, the predicted dissociation energy for the state of GeC is found to be 18 kcal/mol smaller than the mass spectrometric measurements. Both the and state potential energy surfaces for GeC have been examined by the full valence configuration interaction technique to search for a possible transition state that might explain this discrepancy. However, it has been found that both states smoothly dissociate to the ground states of carbon and germanium without any transition state. Several theoretical and experimental aspects related to the determination of the dissociation energy of GeC have been discussed. It is concluded that the theoretically determined value of 91.4 kcal/mol should be more reliable than the reported experimental values.

Quantum and classical structures for clusters with the impurity
View Description Hide DescriptionThe structural properties and the energetics of some of the smaller clusters, with n varying from 2 to 14, are examined both with classical and quantum treatments, making also a comparison with the corresponding neutral systems The results of the calculations, the physical reliability of the employed interaction modeling, and the comparison with previous results are discussed. The emerging picture shows that for clusters of this size the dopant ion always locates itself outside the moiety.

Modecorrelated product pairs in the reaction
View Description Hide DescriptionThe title reaction was investigated at three different collision energies in a pulsed, crossedbeam apparatus. The REMPI spectra of the products revealed, in addition to the anticipated vibronic bands, a hitherto unobserved feature. The new feature was shown and assigned to the band. A timesliced ion velocity imaging technique was applied to map out the coincident DF attributes of the two product states and whose energy levels lie nearly degenerate. Remarkably similar results were found for the two states in every aspect at all three collision energies. A simple model of Fermicoupled states was proposed to rationalize this, at first sight, surprising finding. Implications to collisional processes which involve mixed molecular basis states in general are outlined. Possible quantum interference phenomenon is suggested.

Theoretical predictions of the decomposition mechanism of 1,3,3trinitroazetidine (TNAZ)
View Description Hide DescriptionA theoretical study of the decomposition pathways of 1,3,3trinitroazetidine (TNAZ) is described. Possible decomposition transitionstates, intermediates, and products are identified and structures, energies, and vibrational frequencies are determined at the level for these species. Four major pathways are apparent. Two pathways are initiated by the fission of the and bonds to yield radical intermediates, while the other two pathways involve the molecular elimination of HONO. Energy profiles for the pathways and possible routes to some of the experimentally observed species of TNAZ decomposition are presented. The energy required to initiate the bond fission pathways are 4–8 kcal/mol lower than the HONO elimination pathways. In the gas phase, the elimination pathways will be the dominant routes for TNAZ decomposition. In the condensed phase, however, this trend may be reversed.

Structural properties of and clusters: A density functional study
View Description Hide DescriptionWe determine the equilibrium structures of and clusters within the framework of density functional theory and a planewave approach. Our calculations go beyond qualitative structural assignments proposed to interpret photoelectron spectroscopy measurements. We found that the lowest energy structures for are based on units, isomers containing ozonide units being higher in energy. A different situation is observed in the case of where several isomers with one motif lie at lower energy than those made of units only. Ozonide units appear crucial to ensure the stability of clusters. This is achieved by a larger hybridization between like and like states, which persists when the ozonide unit transforms into an chain.

On the electronic structures of gaseous transition metal halide complexes, and Fe, Co, Ni, Br), using photoelectron spectroscopy and density functional calculations
View Description Hide DescriptionWe report a photoelectron spectroscopy (PES) and theoretical study on a series of transition metal halide complexes: and Fe, Co, Ni, Br). PES spectra were obtained at two photon energies (193 and 157 nm), revealing the complicated electronic structures of these metal complexes and their variation with the ligandfield geometry and metal center substitution. Density functional calculations were carried out to obtain information about the structures, energetics, and molecular orbitals of the metal complexes and used to interpret the PES spectra. For the tetrahedrally coordinated ferric complexes the PES data directly confirm the “inverted level scheme” electronic structure, where the electrons lie below those of the ligands due to a strong spinpolarization of the levels. For the threecoordinate complexes the calculations also revealed strong spin polarizations, but the molecular orbital diagrams present a “mixed level scheme,” in which the ligand orbitals and the majority spin orbitals are spaced closely in the same energy regions. This “mixed level scheme” is due to the larger splitting of the orbitals in the stronger ligand field and the smaller spin polarizations of the divalent metal centers. The calculations show that the metal orbitals are stabilized gradually relative to the ligand orbitals from Mn to Ni in the trihalide complexes consistent with the PES spectral patterns.

Resonant twophoton ionization spectroscopy of the van der Waals complex Structure, binding energy, intermolecular vibrations, and internal rotation
View Description Hide DescriptionResonanttwophotonionization spectrum of has been recorded, which exhibits rich information about the van der Waals vibrational modes and internal rotation of An ab initio calculation shows a point group for the complex, in which the mass center of is ∼0.35 nm above the benzene ring and the molecular axis of is in the symmetry plane but tilted slightly away from the group by ∼2°. With the help of isotopic substitution, quantum mechanics calculations, and systematic comparisons, we have tentatively assigned all the observed spectral features. The van der Waals bonding is shown to have an inhibitory effect on the internal rotation of the group. Bond dissociation energies for the complex in the excited electronic state and in the ground electronic state are estimated to be 494 and 474 cm^{−1}, respectively, in good agreement with the calculated value.

Fundamental limits on twophoton absorption cross sections
View Description Hide DescriptionWe apply sum rules to calculate the maximum limit of the resonant twophoton absorption cross section. Comparison of the theory with experimental data from the literature shows that no molecule ever measured exceeds this limit. Molecules with more π electrons have larger twophoton cross sections; but, the twophoton cross sections fall further below the fundamental limit as the number of electrons increases—implying that the additional electrons are not participating efficiently. The sum rules can aid in developing structure property relationships by providing metrics that lead to a deeper understanding of the available data.

Timedependent currents through small molecules using wideband and narrowband approximations
View Description Hide DescriptionThe theory of timedependent currents through small molecules, with attached leads, is examined. The wideband and narrowband approximations are used to describe the leads and the timedependent Schrödinger is applied directly. A variety of possible boundary conditions are considered and, within the approximations of the model, exact solutions are obtained and their form discussed. Examples using twoatom chain molecules are analyzed in detail and series solutions are obtained for longer chains.

Stateresolved dissociation dynamics of glyoxal near the threshold for formation of fragment HCO
View Description Hide DescriptionFluorescence excitation spectra for transition of transglyoxal in a supersonic jet were recorded with laser excitation in a wavelength region near 395 nm. With resolution most lines in these spectra are resolved and are assigned rotationally; of six bands assigned, three have type rotational structure, and another three have types hybrid, and Fluorescence decays with quantum beats, resulting from coherent excitation of and states, are observed for most rotational levels in this region. In spectra transformed to the frequency domain for these decays, the widths are larger than those obtained at low excitation energy. The widths from nonzero frequency lines, reflecting mostly the triplet character, indicate that the triplet state is dissociating. Fluorescence spectra of fragment HCO confirm that the dissociation channel correlated to the triplet surface of glyoxal involves formation of radical products. From an abrupt decrease of lifetime of the triplet state and onset of disappearance of fluorescence of glyoxal, the threshold for formation of fragment HCO from transglyoxal is determined to be 394.4 nm. With data for heat of formation this threshold yields an exit barrier Signal of HCO for wavelengths greater than the threshold position up to 400.5 nm is observed and is assigned to arise from the surface. Rotationally stateresolved appearance rates of HCO for a vibrational state near the dissociation threshold are measured. Relative to lifetimes obtained from eigenstates in the quantumbeat data, the appearance time of product HCO reflecting the overall depletion of glyoxal is on average longer. Some observed gateway states with enhanced yields of HCO are considered to result from strong singlet–triplet interaction.

Selective detection of isomers with photoionization mass spectrometry for studies of hydrocarbon flame chemistry
View Description Hide DescriptionWe report the first use of synchrotron radiation, continuously tunable from 8 to 15 eV, for flamesampling photoionizationmass spectrometry (PIMS). Synchrotron radiation offers important advantages over the use of pulsed vacuum ultraviolet lasers for PIMS; these include superior signaltonoise, soft ionization, and access to photon energies outside the limited tuning ranges of current VUV laser sources. Nearthreshold photoionization efficiency measurements were used to determine the absolute concentrations of the allene and propyne isomers of in lowpressure laminar ethylene–oxygen and benzene–oxygen flames. Similar measurements of the isomeric composition of species in a fuelrich ethylene–oxygen flame revealed the presence of substantial concentrations of ethenol (vinyl alcohol) and acetaldehyde. Ethenol has not been previously detected in hydrocarbon flames. Absolute photoionization cross sections were measured for ethylene, allene, propyne, and acetaldehyde, using propene as a calibration standard. PIE curves are presented for several additional reaction intermediates prominent in hydrocarbon flames.

Reactions of phenylium ions with
View Description Hide DescriptionThe reaction of phenylium and phenylium ions with molecular deuterium has been investigated both experimentally and theoretically. Theoretical calculations have been carried out at the level of theory. The key features of the potential energy surfaces and all the relevant thermochemical parameters have been calculated. These results are in good agreement with previous theoretical studies concerning the unimolecular dissociation of benzenium ions. Theoretical calculations provide a clear insight on the reaction mechanisms for the system under study. Experimental studies have been carried out by means of a guided beam tandem mass spectrometer. We have measured the reaction cross section for four different reaction channels, as a function of the collision energy, in the range from thermal energies up to about 1 eV. The bimolecular reactivity of is dominated by the substitution of one or two hydrogen atoms by deuterium, leading to the formation of and products. The reaction cross section is nearly the same for the two reaction channels. This fact is interpreted as evidence of a statistical behavior, as expected by assuming a fast shift of hydrogen (deuterium) within the aromatic ring. Another very weak reaction channel leading to the formation of the benzene ion has been measured. The cross section for such a process is lower than about over the entire energy range explored in our experiment. A structure observed at collision energies around about 0.1 eV has been attributed to the reaction of phenylium ions in their triplet state. When the density of the gas in the scattering cell is increased, the formation of collisionally stabilized benzenium ions is observed.

Application of a VUV Fourier transform spectrometer and synchrotron radiation source to measurements of. VI. The ε(0,0) band of NO
View Description Hide DescriptionThe ε(0,0) band of NO has been recorded by using a vacuum ultraviolet Fourier transformspectrometer from Imperial College, London, with synchrotron radiation at the Photon Factory, KEK, Japan, as a continuum light source. Analysis of the ε(0,0) band provides accurate rotational line positions and term values as well as the photoabsorption cross sections. Molecular constants of the level of the state have been determined as and Accurate rotational line strengths have also been obtained and the sum of the line strengths for all rotational lines is determined as The band oscillator strength of the ε(0,0) band is determined to be

Ab initio studies of He–HCCCN interaction
View Description Hide DescriptionFive twodimensional potential energy surfaces for the interaction of He with cyanoacetylene (HCCCN) are presented, obtained from ab initio calculations using symmetryadapted perturbation theory and the supermolecular method at different levels of electron correlation. HCCCN is taken to be a rigid linear molecule with the interatomic distances fixed at the experimental geometry extracted from groundstaterotational constants. The complex was found to have a global minimum at a Tshaped configuration and a secondary minimum at the linear configuration with the He atom facing the H atom. Two saddle points were also located. There is good agreement between the positions of the stationary points on each of the five surfaces though their energies differ by up to 19%. Rovibrational bound state calculations were performed for the and complexes. Spectra (including intensities) and wave functions of obtained from these calculations are presented. The effective rotational constant of HCCCN solvated in a helium droplet was estimated by minimizing the energy of for selecting the complex as giving the largest magnitude of interaction energy per He, and shifting the resulting ring of He atoms to the position corresponding to the average geometry of the ground state of the He–HCCCN dimer. This estimate is within 4.8% of the measured value.