Volume 112, Issue 23, 15 June 2000
 COMMUNICATIONS


On the hyperfine structure of levels near dissociation threshold
View Description Hide DescriptionWe report the first direct measurement of the hyperfine structure of single molecular eigenstates in the 2.53 cm^{−1} region below dissociation threshold using the method of polarizationquantum beatspectroscopy (QBS). The hyperfine interaction of these loosely bound states is substantially weaker (on the average by a factor of ∼5) than found at energies below 22 000 cm^{−1}, but is similar on the average to that observed 50–150 cm^{−1} below threshold. The implications of our results regarding the participation of additional electronic states near are discussed.
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 ARTICLES

 Theoretical Methods and Algorithms

Basis sets in correlated effective potential calculations
View Description Hide DescriptionDue to the behavior of the pseudoorbitals near nuclei, basis set selection in shapeconsistent effective potential calculations can be problematic in studies using correlation techniques based on virtual orbital expansions (configuration interaction, etc.). In this paper we quantify the magnitude of the problem and give simple rules for the selection of correlating functions in a manner that parallels the use of simple diffuse primitives in allelectron work. Our calculations show the problem to be substantial for s and pbasis sets, and to involve both one and twocenter effects, but is negligible for higher l. We also show that the problems can be avoided by the inclusion of one additional high exponent s primitive in the basis set and by augmenting p primitives with a higher exponent function so as to give zero first derivatives at the nucleus. By this recipe, computed s and p shell correlation energies in single and double promotion configuration interaction calculations can be increased by 3%–7%, as compared to basis sets using simple diffuse primitives for correlation.

New approach to the statespecific multireference coupledcluster formalism
View Description Hide DescriptionA new development is presented in the framework of the statespecific multireference (MR) coupledcluster (CC) theory (MRCC). The method is based on the CASSCF (complete active space selfconsistent field) wave function and it is designed specifically for calculating excited electronic states. In the proposed approach, the cluster structure of the CC wave operator and the method to determine this operator are the key features. Since the general formulation of the CASCC method is uncontracted, i.e., allows the interaction between the nondynamic and dynamic correlation effects to affect both the CAS reference function and the CC correlation wave operator, the method is expected to perform better than contracted perturbative approaches such as the CASPT2 (secondorder perturbation theory based on the CAS wave function) method. Also, the CASCC method is not a perturbative approach and is not based on selection of an unperturbed Hamiltonian, which in the case of the CASPT2 method often leads to the “intruder state” problem. CASCC calculations of the lowest totally symmetric excited state of the model system using the internally contracted and uncontracted approaches reveal some interesting features of the methodology.

Singularities in the behavior of density functionals in predictions of singlet biradicals: The 1,2dichalcogenins
View Description Hide DescriptionThe performance of conventional exchangecorrelation functionals for the description of singlet biradicals which possess a small admixture of an auxiliary electronic state was examined using a broken symmetry spin unrestricted density functional approach. A pure density functional, BLYP, and the hybrid B3LYP and BHandHLYP exchangecorrelation functionals were employed to study the thermal ring opening of 1,2dichalcogenins and the subsequent formation of the bicyclic products. A stepwise mechanism was predicted for the reaction of the 1,2dithiin and 2selenathiin rings and no biradical structures were located. For 1,2diselenin, the biradical stepwise mechanism competes energetically with a concerted reaction which is slightly favored. For 1,2ditellurin, a highenergy open intermediate with considerable biradical character was located. The hybrid functionals show an increase in biradical character with an increase in the percentage of Hartree–Fock exchange incorporated into the exchange functional. The instability of the restricted Kohn–Sham solutions was used to indicate the existence of biradical structures with lower energy. Interesting incorrect behavior of certain of the hybrid functionals was noted. The instability of the restricted BHandHLYP solution results from too large a contribution of Hartree–Fock exchange. An unexpected stability of the restricted B3LYP solution was found and attributed to cancellation of two different sources of instability: one from the pure density functional and the other from the inclusion of Hartree–Fock exchange.

Properties of atoms in molecules: Transition probabilities
View Description Hide DescriptionThe transition probability for electric dipole transitions is a measurable property of a system and is therefore, partitionable into atomic contributions using the physics of a proper open system. The derivation of the dressed property density, whose averaging over an atomic basin yields the atomic contribution to a given oscillator strength, is achieved through the development of perturbation theory for an open system. A dressed density describes the local contribution resulting from the interaction of a single electron at some position r, as determined by the relevant observable, averaged over the motions of all of the remaining particles in the system. In the present work, the transition probability density expressed in terms of the relevant transition density, yields a local measure of the associated oscillator strength resulting from the interaction of the entire molecule with a radiation field. The definition of the atomic contributions to the oscillator strength enables one to determine the extent to which a given electronic or vibrational transition is spatially localized to a given atom or functional group. The concepts introduced in this article are applied to the Rydbergtype transitions observed in the electronic excitation of a nonbonding electron in formaldehyde and ammonia. The atomic partitioning of the molecular density distribution and of the molecular properties by surfaces of zero flux in the gradient vector field of the electron density, the boundary condition defining the physics of a proper open system, is found to apply to the density distributions of the excited, Rydberg states.

Effect of basis set superposition error on the electron density of molecular complexes
View Description Hide DescriptionThe Chemical Hamiltonian Approach (CHA) versions of the Roothaan and Kohn–Sham equations, labeled CHA/F and CHA/DFT, respectively, have been used to obtain the basis set superposition error (BSSE)corrected firstorder electron density of the hydrogen fluoride dimer with several basis sets. We have analyzed the effect of BSSE in terms of the electronic relaxation, i.e., the redistribution of the electron density due to the inclusion of the CHA correction at a frozen geometry, along with the subsequent nuclear relaxation process. Critical points of the charge density have been located and characterized to compare the conventional, uncorrected firstorder electron density against the BSSEcorrected density at each level of theory. Contour difference maps between BSSEcorrected and uncorrected densities on the molecular plane have also been plotted to gain insight into the effects of BSSE correction on the electron density.

Path integral molecular dynamics for Bose–Einstein and Fermi–Dirac statistics
View Description Hide DescriptionIn this paper, we propose a promising extension of the path integral molecular dynamics method to Bose–Einstein and Fermi–Dirac statistics. The partition function for the quantum statistics was rewritten in a form amenable to the molecular dynamics method with the aid of an idea of pseudopotential for the permutation of particles. Our pseudopotential, here, is a rigorous one describing the whole effect of Bose–Einstein and Fermi–Dirac statistics. For a model calculation, we chose a system consisting of three independent particles in a onedimensional harmonic well. The calculation has been performed for the particles obeying Bose–Einstein and Fermi–Dirac statistics. The calculated kinetic and potential energies were in excellent agreement with the analytical results even near the ground state. It was found that the pseudopotential shows attractive and repulsive characters for the static properties of Bose–Einstein and Fermi–Dirac particles, respectively. For interacting model particle systems, we studied a bosonic triatomic cluster. The calculated thermodynamic quantities were in qualitative agreement with those obtained by Fourier path integral Monte Carlo calculation.

Geminal functional theory: A synthesis of density and density matrix methods
View Description Hide DescriptionThe energy of any atom or molecule with an even number N of electrons is shown to be an exact functional of a single geminal where the functionals for both the kinetic energy and the external potential are explicitly known. We derive the foundations for geminal functionaltheory (GFT) through a generalized constrained search and the use of two theorems which demonstrate that all oneparticle properties of atoms and molecules with even N may be parametrized by a single geminal [A. J. Coleman, Int. J. Quantum Chem. 63, 23 (1997); D. W. Smith, Phys. Rev. 147, 896 (1966)]. By generalizing constrained search to optimize the universal functionals with respect to the 2RDM (two particle reduced density matrix) rather than the wave function, we closely connect the onedensity, the 1RDM (oneparticle reduced density matrix), and the geminal functionaltheories with 2RDM minimization of the energy. Constrained search with the 2RDM emphasizes that all energy functional methods must implicitly account for the Nrepresentability of the 2RDM within their universal functionals. An approximate universal functional for GFT, equivalent to a variational ansatz using the antisymmetrized geminal power wave function, yields energies that are significantly better than those from Hartree–Fock and yet rigorously above the exact energy.

Efficient pseudospectral methods for density functional calculations
View Description Hide DescriptionNovel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head–Gordan Jengine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical study of valence photoelectron spectrum of A spinorbit RESCCASPT2 study
View Description Hide DescriptionThe valence photoelectron spectrum (bands from A to E) of is studied by secondorder complete active space perturbation theory (CASPT2). The relativistic effects are included by the relativistic elimination of the small components (RESC) scheme. Spinorbit coupling is also considered. Both the electron correlation and relativistic effects are significant on the peak position and intensity of valence photoelectron spectrum of RESCCASPT2 gives values for the peak position and intensity in reasonable agreement with the resolved photoelectron spectrum data. The state ordering is predicted as Electron correlation shifts all peak positions by 2.5–3.5 eV to the highenergy side. Spinfree relativistic effects shift the band D by 0.8 eV again to the highenergy side due to the stabilization of Os orbital. The present study confirms that the band C arises from the spinorbit coupling in the ionic state. Under the E band, there are many twoelectron shakeup peaks in addition to the two oneelectron ionization peaks. The broad feature of the E band is due to the satellite peaks and can be well explained through the introduction of the relativistic effects.

Cavity ringdown spectroscopy of the linear carbon chains and
View Description Hide DescriptionOptical bands from the transition of the linear carbon chains and have been measured in the gas phase by cavity ringdown spectroscopy. The bands exhibit well resolved P and R branches, which for are partially rotationally resolved. Comparisons between observed and simulated spectra indicate broadening in excess of that expected from the laser linewidth and Doppler width, suggesting rapid radiationless transitions in roughly 0.1–0.01 ns, a time scale consistent with the absence of observed fluorescence from these molecules. The and bands are of nearly equal strength, but those of the shorter chain are too weak to detect at the 1 ppm level. None of the bands observed here lies sufficiently close to any of the optical diffuse interstellar bands to provide positive identification.

Directions of transition dipole moments of tbutyl nitrite obtained via orientation with a strong, uniform electric field
View Description Hide DescriptionA strong, uniform electric field was used to orient supersonically cooled tbutyl nitrite for measurements of directions of transition dipole moments. The oriented sample was dissociated with linearly polarized light, and the NO fragments were studied by REMPI through the state. At photolysis wavelengths of 365.8 and 351.8 nm, there was a 47% enhancement in the NO signal when the photolysisbeam was polarized perpendicular to the orientation field, implying a perpendicular relationship between the transition dipole of the state and the permanent dipole. Photodissociation at 250 and 224 nm showed the opposite trend, with a 46% enhancement in the NO signal when the photolysisbeam was polarized parallel to the orientation field. The transition dipole of the state was therefore determined to be parallel to the permanent dipole. This experiment demonstrates the application of brute force orientation for obtaining directions of transition dipole moments.

Ab initio potential energy surface for the reactions between and H
View Description Hide DescriptionInterpolatedab initiopotential energy surfaces which describe abstraction and exchange reactions in collisions of hydrogen and water are reported. The electronic structure calculations are performed at the QCISD(T) level of theory, with an additivity approximation. A sufficiently large basis set is required to describe the Rydberg character of the electronic state for molecular configurations which are important for the exchange process. Classical and quantum dynamics calculations on the surfaces are presented.

Monte Carlo analysis of pyrazine collisional vibrational relaxation: Evidence for supercollisions
View Description Hide DescriptionThe collisional loss of vibrational energy from polyatomic molecules in triplet electronic states has been studied in new detail through a variant of the competitive radiationless decay (CRD) method. Experimental transient absorption kinetics for pyrazine vapor in the presence of helium relaxer reveals the competition between unimolecular radiationless decay and collisional vibrational relaxation. These data have been simulated with Monte Carlo stochastic calculations equivalent to full master equationsolutions that model the distribution of donor vibrational energies during relaxation. The simulations included energydependent processes of radiationless decay, optical absorption, and collisional energy loss. The simulation results confirm earlier findings of energy loss tendencies that increase strongly for pyrazine vibrational energies above ∼2000 cm^{−1}. It is also found that the experimental data are not accurately simulated over a range of relaxer pressures if a simple exponential stepsize distribution function is used to model collisional energy changes. Improved simulations are obtained by including an additional, lowprobability channel representing large energy changes. This second channel would represent “supercollisions,” which have not previously been recognized in the vibrational relaxation of triplet state polyatomics.

Reduced dimensionality wave packet study of the reaction
View Description Hide DescriptionThe reaction between and (or leading to (or is investigated using a quantum wave packet approach at a collision energy below 2.5 eV. The study is restricted to the collinear geometry preserving symmetry. Three degrees of freedom are explicitly treated: the reactive D–D and N–D distances, and the umbrella angle of The effects of the initial vibrational excitation of (or and of the umbrella motion of are studied. The reaction probability is found to be large and to decrease with internal excitation of the reagents. The statetostate reaction probabilities for the two isotopic variants differ qualitatively. This is related to the existence of a Fermi resonance in the geometrically constrained ion, which does not exist in The umbrella motion is found to play an active role in the reactivity at a collision energy above 1 eV.

Thermochemical and kinetic parameters for hydrogen bonded clusters, derived from avalanche condensation flux measurements
View Description Hide DescriptionThe kinetic molecular model (KMM) was applied to recently reported extensive measurements of condensation flux levels developed under homogeneous conditions from supersaturated vapors of water and npentanol, in inert gas carriers. These data span wide ranges in temperatures and critical supersaturations (css). The calculated fluxes reproduced those observed (defined: number of droplets generated per cm^{3}s) within a factor 2, utilizing a narrow range of adjustable parameters. From the derived kinetic and thermochemical parameters one may derive estimates of sizedependent entropies for clusters. Thus, the derived entropy per mole of a 13 unit cluster of water molecules, at 233 K, is 233 eu.

Photothermodissociation of selenium clusters
View Description Hide DescriptionThe dissociation of selenium cluster ions containing from 7 up to 30 atoms has been studied using unimolecular decay of photothermoexcited clusters.Clusters containing more than 14 atoms evaporate and species, whereas smaller clusters with 7–10 atoms dissociate manly by loss. When the size increases, becomes the predominant channel showing a dissociation which evolves toward the bulk behavior. The changes in the observed channels correlate to changes in the dissociation energies which are deduced from the measured fractional dissociation rates and from the entropy contribution. Together with the previous study of telluriumclusters, this work provides comparative behavior of dissociation energies of group VI clusters and their convergence toward bulk properties.

Rotational energy transfer within CH and states by collisions with He, Ar, CO, and using a timeresolved Fourier transform spectrometer
View Description Hide DescriptionBy using a stepscan Fourier transform spectrometer, we have studied collisionallyinduced rotational energy transfer (RET) of the CH and states. The collision partners used for the B state are He, Ar, CO, and while He and Ar are for the A state. The timeresolved spectra obtained in the nanosecond regime may yield the RET information straightforward under a single pressure of the collider. The resultant RET rate constants for both states range from to comparable to the gas kinetic. The trend follows the order of for the B state, and for the A state. For the B state, the findings of multiquantum changing collisions up to and markedly large rate constants imply that the RET collisions are dominated by longrange attractive force. The collision complexes possibly formed between the and the colliders are longlived enough to allow for effective removal of the rotational energy more than a quantum level in a single collision. In contrast, a single quantum change in the RET collision found in the A state suggests dominance of a repulsive interaction between the colliding species, which has been verified previously in the measurements of temperature dependence of the electronic quenching.

Kscrambling in a nearsymmetric top molecule containing an excited noncoaxial internal rotor
View Description Hide DescriptionClassical trajectories on rotational energy surfaces and coherentstate quantum projections have been used to study an asymmetrictop molecule containing a freely rotating internal symmetric top whose symmetry axis is not coincident with a principal axis of the molecule. Stationary points on the rotational energy surface, which strongly influence the trajectories, increase in number from two to four to six as increases from zero to infinity (where J is the total and n is the freeinternalrotor angular momentum). For some values trajectories can arise that sample a large fraction of K values (where K is the zaxis projection of J), corresponding in quantum wave functions to extensive K mixing in the symmetrictop basis set J,K〉. When such mixing cannot be made small for any choice of z axis, we call it K scrambling. For typical values of the torsion–rotation coupling parameter ρ, rotational eigenfunctions for a given J and torsional state turn out to be quite different from eigenfunctions for the same J in some other torsional state. Nonzero rotational overlap integrals are then distributed among many rotational functions for each pair, which may, in turn, contribute to internal rotation enhancement of intramolecular vibrational energy redistribution. We have also examined nearfreerotor levels of our test molecule acetaldehyde, which arise for excitation of ten or more quanta of methyl group torsion, and find that barrier effects do not change the qualitative picture obtained from the freerotor treatment.

Molecular beam study of the electronic transition in FeCl
View Description Hide DescriptionThe band system of near 357 nm has been recorded at 0.3 and resolution by laser fluorescence excitation in a freejet supersonic expansion of photolyzed diluted in seed gases containing The subbands for 5/2, and 3/2 and of the 0, −1, and −2 sequences were assigned, and excitation energies and rotational constants were derived for the relevant upper and lower vibronic levels. With the exception of the (0,0) band, for which one subband could be rotationally analyzed, it was not possible to assign any of the subbands with −1/2, or −3/2; these finestructure components are expected to be strongly affected by homogeneous spin–orbit interactions with nearby sextet electronic states, leading to large Λ doubling in the and −1/2 components. A subband with a large upperstate Λ doubling was rotationally analyzed and assigned as the subband. The effect of the offdiagonal spin–orbit interactions is discussed in light of the present results and previous theoretical work.