Volume 117, Issue 8, 22 August 2002
 ARTICLES

 Theoretical Methods and Algorithms

Degenerate perturbation theory corrections for the vibrational selfconsistent field approximation: Method and applications
View Description Hide DescriptionA new algorithm for computing anharmonic vibrational states for polyatomic molecules is proposed. The algorithm starts with the vibrational selfconsistent field (VSCF) method and uses degenerate perturbation theory to correct for effects of correlation between different vibrational modes. The algorithm is developed in a version that computes the anharmonic vibrational spectroscopy directly from potential energy surface points calculated by using ab initio codes. The method is applied to several molecules where near degeneracies occur for excited vibrational states, including HOOH, HSSH, and HOOOH. The method yields results in very good accordance with experiments and generally provides improvements over nondegenerate perturbation corrections for VSCF.

Wavelets in curvilinear coordinate quantum calculations: electronic states
View Description Hide DescriptionMultiscale wavelets are used to solve the quantum eigenvalue equations for the hydrogen molecular ion in the Born–Oppenheimer approximation. Normally restricted to Cartesian systems, “wavelets on the interval” (a normal wavelet family augmented by special edge functions) have recently been applied to such boundary value problems as the hydrogen atom in spherical polar coordinates [J. Mackey, J. L. Kinsey, and B. R. Johnson, J. Comp. Phys. 168, 356 (2001)]. These methods are extended here to ground and excited electronic states of the simplest molecule, for which the electronic Hamiltonian is separable in confocal elliptic coordinates. The set of curvilinear coordinate quantum systems for which wavelet bases have been applied is thus enlarged.

An effective potential function with enhanced chargetransfertype interaction for hydrogenbonding liquids
View Description Hide DescriptionThe potential energy function (PEF) has been derived to perform the liquid simulations using the Monte Carlo method for three hydrogenbonding systems, water, hydrogen fluoride, and ammonia. The PEF is a pair potential function of the overlap integrals between molecules and of the Coulomb interactions between atomic fractional charges. The parameters of the PEF are easily determined in order to reproduce the ab initio pair interaction energies. The lack of manybody interactions, however, prevents the reproduction of the liquid structures. The PEF consists of some physically meaningful terms, and using the characteristics of the function, it is found that the enhancement of a component in the PEF reasonably succeeds in producing the liquid structures. The general procedure for obtaining an effective pair potential function for the hydrogenbonding systems is reported by a simple modification to the PEF.

Screening and the quantitative πmodel description of the optical spectra and polarizations of phenyl based oligomers
View Description Hide DescriptionThe long standing problem of the inability of many semiempirical models to correctly predict the polarization of the higher dipole allowed optical transitions of phenyl based πconjugated polymers and molecules is examined and related to the issue of internal and external screening of π–π electron Coulomb interactions within the molecules. Following a review of previous theoretical and experimental work, π electron only the Complete Neglect of Differential Overlap (CNDO) model is presented which, for the first time, is able to predict accurately the energies and symmetries of all the observed optical transitions of benzene, biphenyl and transstilbene, up to ∼8–10 eV. In so doing, it is demonstrated that the problem with previous calculations was the noninclusion of screening from outside the π electron system itself. By fitting separately the spectra in hydrocarbon based condensed phases, in the gas phase and in solid rare gas matrices, and comparing the resulting model parameters, we show that, while the effects of screening from the environment are certainly noticeable, the most important spectral features—in particular the ordering of dipole allowed transitions—come from effective screening by the σ electrons. We find that both of these effects can be adequately accounted for within a π electron only model by using a dielectric constant and appropriate parameter renormalization.

Rotational Brownian motion of a pair of linear molecules or dipoles with anisotropic interaction
View Description Hide DescriptionThe rotational Smoluchowski equation for the orientational distribution function of two identical linear molecules or dipoles with anisotropic interaction is solved by expansion in terms of a limited set of eigenfunctions of the operator for free rotational diffusion. The equilibrium selfcorrelation and pair timecorrelation functions of the two axial unit vectors or dipole moments are evaluated for the special case of electrostatic or magnetostatic dipole interaction. The interactions appreciably influence the relaxation behavior.

Thirdorder Douglas–Kroll ab initio model potential for actinide elements
View Description Hide DescriptionA relativistic ab initiomodel potential (AIMP) method with the thirdorder Douglas–Kroll (DK3) approximation has been developed for the whole series of the actinide elements from Th to Lr. Two different cores, i.e., [Xe, and [Xe, have been employed and the corresponding valence basis sets, and are presented for all actinides. The mean absolute errors of the AIMP relative to the allelectron results for the atomic SCF valence orbital energies (ε) and the radial expectation values are 0.003 (0.001) hartree and 0.004 (0.006) bohr with the small (large) core set. The spectroscopic properties of the ground state of thorium monoxide, ThO, are calculated at the SCF and complete active space SCF levels. The DK3AIMP results again satisfactorily reproduce the allelectron DK3 results. The large core set gives almost the same results as the small set for atomic and molecular calculations, suggesting that the electrons can safely be omitted from the valence electrons in actinide chemistry.

Theory of solutions in the energy representation. II. Functional for the chemical potential
View Description Hide DescriptionAn approximate functional for the chemical potential of a solute in solution is presented in the energy representation. This functional is constructed by adopting the Percus–Yevicklike approximation in the unfavorable region of the solute–solvent interaction and the hypernettedchainlike approximation in the favorable region. The chemical potential is then expressed in terms of energy distribution functions in the solution and pure solvent systems of interest, and is given exactly to second order with respect to the solvent density and to the solute–solvent interaction. In the practical implementation, computer simulations of the solution and pure solvent systems are performed to provide the energy distribution functions constituting the approximate functional for the chemical potential. It is demonstrated that the chemical potentials of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions.

Renormalized coupledcluster calculations of reactive potential energy surfaces: A comparison of the CCSD(T), renormalized CCSD(T), and full configuration interaction results for the collinear BeFH system
View Description Hide DescriptionThe recently proposed renormalized (R) and completely renormalized (CR) coupledcluster singles, doubles, and noniterative triples (CCSD(T)) methods have been used to calculate the groundstatepotential energy surface (PES) for the collinear BeFH system corresponding to the reaction. It has been demonstrated that the groundstate PES obtained in the CRCCSD(T) calculations is in perfect agreement with the exact PES obtained in the full configuration interaction calculations, whereas the PES resulting from the standard CCSD(T) calculations is qualitatively incorrect.

Wavelet approximation of correlated wave functions. II. Hyperbolic wavelets and adaptive approximation schemes
View Description Hide DescriptionWe have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wave functions. In order to analyze the consequences of reduced regularity of the wave function at the electron–electron cusp, we first considered a realistic exactly solvable manyparticle model in one dimension. Convergence rates of wavelet expansions, with respect to and norms and the energy, were established for this model. We compare the performance of hyperbolic wavelets and their extensions through adaptive refinement in the cusp region, to a fully adaptive treatment based on the energy contribution of individual wavelets. Although hyperbolic wavelets show an inferior convergence behavior, they can be easily refined in the cusp region yielding an optimal convergence rate for the energy. Preliminary results for the helium atom are presented, which demonstrate the transferability of our observations to more realistic systems. We propose a contraction scheme for wavelets in the cusp region, which reduces the number of degrees of freedom and yields a favorable cost to benefit ratio for the evaluation of matrix elements.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Potential energy curves and dipole transition moments for excited electronic states of XeKr and ArNe
View Description Hide DescriptionRelativistic corepotential calculations have been carried out on Ω states resulting from the interaction of Xe^{*} with groundstate Kr atoms as well as for the system Ar^{*} with groundstate Ne, using different basis sets and configuration interaction procedures. The present calculations on ArNe, employing larger sets of Rydberg functions than those of the previous calculations, yield totally repulsive potentials for the excited states of ArNe. Similar calculations on XeKr obtain shallow minima (600–860 cm^{−1}) in the potential energy curves of the excited states at large internuclear distances (6.9–7.8 bohr). Dipole transition moments have been calculated and strong radiative transitions are predicted from excited states to the ground state. The state, correlating with the metastable state of Xe is found to have a small but nonzero dipole transition moment at short and intermediate nuclear distances leading to a radiative lifetime for the level of this state of 21.0 μs.

Quantum dynamics of the reaction on the and surfaces: Reaction probabilities, cross sections, rate constants, and product distributions
View Description Hide DescriptionWe report real wave packet (WP) calculations of reaction probabilities, cross sections, rate constants, and product distributions of the reaction We propagate initial WPs corresponding to several levels, and employ reactant coordinates and a flux method for calculating initialstateresolved observables, or product coordinates and an asymptotic analysis for calculating statetostate quantities. Exact or Jshifting calculations are carried out at total angular momentum or respectively. We employ the recent S3 potential energy surface (PES) by Sayós et al. and the earlier PES by Duff et al. In comparing S3 results with the WP ones of a previous S2 PES, we find lower S3 energy thresholds and larger S3 probabilities, despite the higher S3 barrier. This finding is due to the different features of the doublet PESs in the reactant and product channels, at the transition state, and in the equilibrium region. We analyze the effects of the initial level and show that tunneling through the S3 barrier enhance the roomtemperature rate constant by ∼3.7 times with respect to the previous S2 WP rate. The agreement with the roomtemperature experimental result is thus notably improved. The NO vibrational distribution is inverted and the rotational ones are strongly oscillating. We explain these nonstatistical results showing that the reaction partners approach each other with a large impact parameter. The WP vibrational distribution is however different from that observed, which is oscillating. WP calculations show that the new S3 PES describes accurately several features of the state, although a lowering of its barrier height by ∼0.56 kcal/mol should bring calculated and observed rate constants in full agreement.

vibronic spectra of benzene clusters revisited. I. The tetramer
View Description Hide DescriptionWe report the reinvestigation of the electronic transitions of clusters by twocolor massselective resonantly enhanced twophotonionization (R2PI) and UV–UV (ultraviolet) hole burning spectroscopies. The present paper describes the band system that has been assigned to the trimer for two decades. Hole burning measurements by monitoring the trimer ion isotopomer channels in the expansion of a mixture of and have shown the contribution of six spectral carriers in the R2PI spectra, two of which are isotopically pure clusters. The other hetero isotopic species containing at least one moiety appear in two adjacent isotopomer channels. It is argued that the band system should be reassigned to the neutral tetramer having four equivalent sites, which are detected in daughter ion mass channels due to efficient fragmentation after ionization even with twocolor excitation. The experimental results are consistent with a distorted tetrahedral structure with symmetry predicted as the global minimum by several model calculations. This conclusion is further supported by an analysis of exciton splittings in the localized origin band, and this analysis provides coupling constants for the excitation exchange in the state. Other experimental results reported so far pertaining to this species are reconsidered on the basis of the new assignment.

vibronic spectra of benzene clusters revisited. II. The trimer
View Description Hide DescriptionWe present a reexamination of the transition of the cluster that appears only in the dimer ion channel and thus has been assigned to an isomer of the neutral dimer other than the extensively studied Tshaped form. Massselective resonantly enhanced twophotonionization (R2PI) excitation and UV–UV (ultraviolet) hole burningspectra are measured in the and vibronic regions. It is established from the observed spectra monitoring three isotopomer channels, and that efficient fragmentation following ionization prohibits one to observe the twocolor R2PI spectra in the parent ion channels, similar to the case for the benzene tetramer as presented in Paper I [J. Chem. Phys. 117, 3656 (2002)]. Three neutral isotopomers containing at least one moiety are identified, and this result argues the reassignment of the band system to the neutral benzene trimer with a cyclic form, where the three benzene sites are equivalent. The spectra of the homo isotopomers and in the two vibronic regions exhibit small splittings due to the excitation exchange interactions, and this observation is discussed on the symmetry of the cluster geometry. Energetics pertaining to neutral and ionic benzene clusters are also discussed with previous experimental studies to assess a reason of the efficient fragmentation in the ionic states after R2PI for the trimer and larger clusters but not for the dimer.

Nondipole bound anions: and
View Description Hide DescriptionElectron affinities (EAs) of berylliumclusters are calculated up to the complete coupledcluster single double triple (CCSDT) level using reasonably large basis sets with many diffuse functions. At all levels of theory, the obtained values for the adiabatic EA are large enough to be observed with standard photodetachment techniques. The vertical electron detachment energy is 0.341 eV for and is 1.470 eV for at the most precise CCSDT level. All studied beryllium anions are valence bound but the nature of binding is different in and the two isomers. The only factor of stabilization of the excess electron in is the relaxation energy. is stabilized by the relaxation energy and the Koopmans electrostatic and exchange energies; in the main factors of stabilization are the correlation and relaxation energies. As was revealed in our study, in linear molecules the correlation contribution to the electron binding energy is negative, i.e., it decreases the EA.

Laser spectroscopy of NiBr: Ground and lowlying electronic states
View Description Hide DescriptionFour electronic states of NiBr have been studied using the technique of laser vaporization/reaction with supersonic cooling and laser induced fluorescence(LIF)spectroscopy. NiBr molecules were produced by reacting laser ablatednickel atoms and ethyl bromide High resolution LIF spectrum between 724 and 810 nm was recorded, which consists of the (2,0), (1,0), and (0,0) bands of the [13.2] system and the [13.2] system, and also the with bands of the [12.6] system. Spectra of four isotopic molecules: and were observed and analyzed. Least squares fit of rotationally resolved transition lines yielded accurate molecular constants for the [12.6] and [13.2] electronic states of NiBr. The bond length, measured for the and states is 2.196 28 and 2.164 45 Å, respectively. A molecular orbital diagram has been constructed to explain the four observed electronic states. This work represents the first highresolution spectroscopic study of NiBr.

Multiphoton ionization and density functional studies of clusters
View Description Hide DescriptionThe multiphoton ionization of clusters at conditions of supersonic expansion is studied using a timeofflightmass spectrometer at the wavelengths of 355 and 532 nm. At both wavelengths, a series of protonated cluster ions are obtained. The production of these protonated cluster ions requires an intracluster proton transferreaction. The protonated products are also suggested to relate to the excitation or ionization of water molecules. Ab initio calculations show that the dissociation of cluster ions prefer to produce protonated ions. Two ways of producing protonated cluster ions are discussed. The reaction mechanism of intracluster proton transfer and the geometricstructures of clusters were depicted. The proton pulling effect and the atomic charge changes in the protonated cluster ions are also discussed.

Vibrational structure in the optical response of small Licluster ions
View Description Hide DescriptionThe optical response of and exhibits three large maxima at photon energies between 1.9 and 3.6 eV, on which a fine structures could be resolved that has a peak to peak distance of about 30–40 meV. A high level ab initio calculation of shows that this feature is due to vibrational structure of the excited electronic state. It is pointed out that the lifetime of the excited states exhibits a dramatic shortening with increasing particle size.

Theoretical electronic structure of the lowestlying states of the LaF molecule
View Description Hide DescriptionCASSCF/MRCI calculations have been performed for nine molecular states in the representation (neglecting spin–orbit effects) for the molecule LaF. The corresponding 20 molecular states in the representation (including spin–orbit effects) have been calculated using a semiempirical spin–orbit pseudopotential built up for lanthanum. Calculated potential energy curves and spectroscopic constants are reported. To the best of our knowledge they are the first ones from ab initio methods for the excited states of LaF. Comparison to recent experimental data display a good agreement with averaged discrepancies and Predictions are provided for the new triplet transitions under investigation in our laboratory involving the excited state as well as for the yet unobserved state

Electron attachment timeofflight mass spectrometry reveals geometrical shell closings in van der Waals aggregates
View Description Hide DescriptionUsing electron attachment timeofflight mass spectrometry, we show how highprecision structural constants of van der Waals aggregates may be obtained for two kinds of homogeneous clusters, and Furthermore, we obtain sizespecific structural information over a wide range of aggregate sizes. Mass spectrometric data are presented regarding the size needed to facilitate the transition from “cluster packing,” dominated by nearestneighbor interactions, to bulklike packing. For both examples, it appears that the clustertobulk packing transition may occur even for aggregates where the majority of the molecules resides at the surface. The critical size for the clustertobulk transition may be related to the size at which molecules packed as bulk crystals can begin forming nearly spherical shapes. A discussion of the mechanism by which geometrical shell closings are visualized in electron attachment timeofflight mass spectrometry is also presented. We postulate that these observations reflect the dynamics of electron localization in ordered crystallites with and without defects.

Conical intersections and the nonadiabatic reactions
View Description Hide DescriptionIn this work the reaction and the reverse reaction were studied. and conical intersection seams were found that tie two reactantchannel potential energy surfaces to the two excited statepotential energy surfaces correlating with products. Near their lowest energy points, which occur for collinear geometries, these accidental symmetryallowed conical intersection seams have very similar geometries and are separated by <90 cm^{−1}. This close proximity may reflect a three state conical intersection not required by symmetry. The conical intersection seams were shown to be accessible from both the reactant and product channels without a barrier, above any reaction endoergicity, and provide in the case of the reverse reaction for branching to either or