Volume 111, Issue 11, 15 September 1999
 COMMUNICATIONS


Femtosecond timeresolved photoelectron imaging on ultrafast electronic dephasing in an isolated molecule
View Description Hide DescriptionUltrafast dephasing in an intermediate case of molecular radiationless transition has been visualized for the first time by femtosecondtimeresolved photoelectron imaging. The decay of photoexcited state of pyrazine in 100 ps and the corresponding buildup of triplet states were clearly observed.

Transfer of a pollutant molecule through a water film on a single crystal surface
View Description Hide DescriptionWe study the transfer of a molecule from the gas phase through a thin liquidwaterfilm supported on ionic single crystalsurfaces NaCl and MgO (001). The free energy profile for the is calculated at 300 K using constrained moleculardynamics simulation, and the detailed analysis of the competition between interaction and entropic contributions can help to the understanding of the pollution kinetic process of a water covered solid surface. It is shown that the solvation and its adsorption directly on the solid surface is easier for a NaCl supported film than for a MgO one.

On the connection between the reference interaction site model integral equation theory and the partial wave expansion of the molecular Ornstein–Zernike equation
View Description Hide DescriptionWe develop an integral equation theory based on the partial wave expansion of the molecular Ornstein–Zernike (OZ) equation. The theory provides a rigorous and transparent framework for multiple site treatments of molecular fluids. We examine freeenergy functional and closure expressions with pilot calculations of homonuclear diatomic LennardJones liquids.
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 THEORETICAL METHODS AND ALGORITHMS


Phase space optimization of quantum representations: Directproduct basis sets
View Description Hide DescriptionThe quantitative phase space similarities between the uniformly mixed ensembles of eigenstates, and the quasiclassical Thomas–Fermi distribution, are exploited in order to generate a nearly optimal basis representation for an arbitrary quantum system. An exact quantum optimization functional is provided, and the minimum of the corresponding quasiclassical functional is proposed as an excellent approximation in the limit of large basis size. In particular, we derive a stationarity condition for the quasiclassical solution under the constraint of strong separability. The corresponding quantum result is the phase space optimized directproduct basis—customized with respect to the Hamiltonian itself, as well as the maximum energy of interest. For numerical implementations, an iterative, selfconsistentfieldlike algorithm based on optimal separable basis theory is suggested, typically requiring only a few reduceddimensional integrals of the potential. Results are obtained for a coupled oscillator system, and also for the 2D Henon–Heiles system. In the latter case, a phase space optimized discrete variable representation (DVR) is used to calculate energyeigenvalues. Errors are reduced by several orders of magnitude, in comparison with an optimized sincfunction DVR of comparable size.

Reaction rates for fluctuating barriers with asymmetric noise
View Description Hide DescriptionThermally activated escape over a high barrier fluctuating randomly in time is investigated for asymmetric flipping rates. By means of the Fokker–Planck approach approximate methods developed for symmetric noise are applied to calculate the relaxation eigenvector and ultimate relaxation rate for piecewise linear potentials in the Smoluchowski limit. The ranges of validity of these approaches are discussed. Furthermore, the exact result for weak thermal noise but arbitrary barrier flipping rates is derived and its dependence on the asymmetry studied in detail.

Topological analysis of the molecular electrostatic potential
View Description Hide DescriptionThe topology of the molecular electrostatic potential of 18 molecules, calculated in the framework of Kohn–Sham density functional theory, is studied. For the location of the different kinds of critical points a newly developed search algorithm is applied. A chemical interpretation of the critical points in terms of lone pairs, bonds, hybrid orbitals and other electronic structure elements is suggested. A Poincaré–Hopf relationship for the molecular electrostatic potential is derived, connecting electronic structure elements and electrostatic reactivity via the topology of the molecular electrostatic potential.

Suppressing the geometric phase effect: Closely spaced seams of the conical intersection in
View Description Hide DescriptionIt is shown that for the Exε Jahn–Teller problem, the circulation, the line integral along a closed loop, of the actual, or an approximation to the, derivative coupling can be used to determine the number of closely spaced conical intersections in that closed loop. This approach has advantages over the use of the geometric phase theorem, which can only count conical intersections mod 2. The circulation is used to establish the locus of the seam of the conical intersection of the state of It is found that in addition to the seam of the conical intersection, three symmetry equivalent seams with symmetry exist in close proximity to the seam. The three seams intersect the seam. The netgeometric phase effect is largely suppressed and this ostensibly Jahn–Teller pair of electronic states is more like a Renner–Teller pair.

Rigorous and rapid calculation of the electron repulsion integral over the uncontracted solid harmonic Gaussiantype orbitals
View Description Hide DescriptionA rigorous general formula for calculating the electron repulsion integral (ERI) over the uncontracted solid harmonic (SH) Gaussiantype orbitals (GTOs) can be derived by the use of the “reducing mixed solid harmonics” defined in this paper. A general algorithm can be obtained inductively from this formula with the use of the “mixed solid harmonics” also defined in this paper. This algorithm is named as accompanying coordinate expansion (ACE) This is capable of computing very fast SHERIs. The floatingpoint operation (FLOP) count assessment is shown for the class of SHERIs It is found that the present algorithm is the fastest among all algorithms in the literature for the ERI over the uncontracted SHGTOs.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Photodissociation dynamics of the singlet and triplet states of the NCN radical
View Description Hide DescriptionThe spectroscopy and photodissociation dynamics of the NCN radical have been investigated by fast beam photofragment translational spectroscopy. The and transitions were examined. The major dissociation products for the and states are while the state dissociates to The dissociation channel, is observed for the state at photonenergies greater than 4.9 eV, where it comprises of the total signal. At all photonenergies, the photofragment translational energy distributions show a resolved progression corresponding to the vibrational excitation of the photofragment. The rotational distributions of the molecular fragments suggest that the dissociation pathway for the loss channel involves a bent transition state while the photofragments are produced via a linear dissociation mechanism. The distributions provide bond dissociation energies of and for the and CN loss channels, respectively, yielding eV.

Complex calculation of the variation of resonance widths of HOCl with total angular momentum
View Description Hide DescriptionComplex calculations of the variation of the resonance width of with total angular momentum,J, are reported, using a recently developed, accurate ab initiopotential energy surface [S. Skokov, J. M. Bowman, and K. A. Peterson, J. Chem. Phys. 109, 2662 (1998)]. The calculations are carried out using the adiabatic rotation approximation for the overall rotation and a truncation/recoupling method for the vibrational states. An ab initio calculation of the J and K dependence of the intensity of the absorptionspectrum of the Q branch in the neighborhood of the transition is presented, and compared to results of recent experiments of Rizzo and coworkers. The variation of the resonance width of the 6,0,0 and the 3,8,0 states with J and K is presented, and comparisons with recent doubleresonance experiments of the Rizzo and Sinha groups for the 6,0,0 state show encouraging qualitative agreement. The fluctuations of the dissociation rate with J is shown to be due to rotationinduced coupling of the state to a dense set of highly excited OCl stretch states. A simple model describing the coupling of with background states, using a coupling constant of 0.05 cm^{−1} is shown to give a qualitatively correct picture of the fluctuation of the resonance width with J. Finally, the energies of many nonoverlapping resonances, some of which are assigned, for and are presented and compared to Rice–Ramsperger–Kassel–Marcus (RRKM) theory. It is found that due to slow, rate limiting, intramolecular vibrational relaxation the RRKM overestimates the average dissociation rate by an order of magnitude.

Highly predissociative levels of the state of CH studied with the twocolor resonant fourwave mixing technique
View Description Hide DescriptionWe investigated highly predissociative transitions of CH in an oxyacetylene flame with twocolor resonant fourwave mixing, in which two grating beams are in resonance with the transition and the pump (and signal) beam is resonant with a selected transition. A total of 86 predissociative lines in six branches are observed, corresponding to excitation of the D state up to in previous experiments lines up to only were observed. Observed rovibronic transitions of the band are fitted to known Hamiltonians to yield improved spectral parameters of the state. The parameters for centrifugal distortion and Λ doubling of the state are deduced for the first time. The predissociative line width is about 2 cm^{−1} for the rotational level with and it gradually increases with for the width is about 7 cm^{−1}. Predissociation mechanisms of the state are discussed. A barrier height ∼5600 cm^{−1} for the D state is estimated based on observed predissociative lifetimes.

Potential energy function and vibrational states of
View Description Hide DescriptionA sixdimensional potential energy function (PEF) for the electronic ground state of has been generated by electronic structure calculations using the restricted open shell coupled cluster RCCSD(T) approach. The ion has a planar trans equilibrium structure with: Å, Å, Å, and Variational calculations of the vibrational states have yielded the following anharmonic wavenumbers for the fundamentals: (NN stretch) 2287.2, (CO stretch) 2071.0, (CN stretch+NCO bend) 546.9, (CN stretch+NCO bend) 215.2, (inplane NNC bend) 123.4, (outofplane NNC bend) 133.8 (all values are in For fixed equilibrium coordinates except one, the barriers to linearity have been calculated to be 8 for the NNC and 2260 for the NCO moieties, the torsional barrier to be 35 It has been found that the and modes are strongly coupled, the inplane and outofplane bending modes possess an inverse anharmonicity and fall into clusters. Using complete active space selfconsitentfield CASSCF approach on the collinear cuts of the PEF for lowlying excited states several conical intersections between the and the states have been located.

Analysis of long range dispersion and exchange interactions between one Na atom and one K atom
View Description Hide DescriptionThis article critically surveys spectroscopic data for the two lowest states and of NaK. These states both dissociate to ground stateNa and K atoms. Since both states are known precisely to near dissociation, they can be used to determine experimental values of the separate Coulombic and exchange contributions to the longrange interaction potentials, which agree reasonably well with theory. We also discuss the dissociation energy of both of the states and recommend and

Analysis of exchange energy at long range for states of alkali diatomic molecules correlating to two ground state atoms
View Description Hide DescriptionRecently experimentallybased asymptotic exchange energies between ground state atoms in and NaK have been determined from spectroscopicallydetermined potential energy curves. These empirical results are shown to be well fit by the expression of Smirnov and Chibisov, where C is a positive constant and α and β can be readily calculated from the atomic ionization energies. The expression should be useful for estimating the exchange energy in other alkali dimers.

Ab initio potential energy surface for the ground state of and rotationally inelastic collision cross sections for circumstellar collisions
View Description Hide DescriptionAn ab initiopotential energy surface has been calculated for the ground electronic state of the system. The calculations were performed by first characterizing all the critical points of the system using ab initio complete active spaceself consistent field (CASSCF) methods. These preliminary calculations were followed by multireference configuration interaction (CI) calculations covering a grid of 1748 nuclear geometries. The surface has been fitted to a global analytic form, using the recently proposed Reproducing Kernel Hilbert Space Method of Ho et al., [J. Chem. Phys. 104, 2584 (1996)] and preliminary vibrationallyrotationally inelastic scattering cross sections have been computed using infinite order sudden quantum scattering methods. The motivation of the research is the evaluation of these inelastic cross sections which are needed in the modeling of circumstellar SiO maser radiation. Significant structure has been observed in the computed inelastic cross sections. This structure is of the form which might be expected to give rise to the vibrational–rotational quantum state population inversions which in turn leads to the observed circumstellar maser action. An interesting feature of the computed potential energy surface is a line of maxima in nonlinear geometries. These maxima appear to arise from a nonsymmetry related conical intersection.

State selected unimolecular dissociation of HOCl near threshold: The vibrational state
View Description Hide DescriptionThe spectroscopy and unimolecular dissociationdynamics of HOCl are examined by accessing rotational resonances of the vibrational level over the manifolds using overtone–overtone double resonance. The spectroscopicanalysis indicates that state mixing between the zerothorder “bright” O–H stretching overtone state, 6 0 0, and “dark” background vibrational levels is incomplete as the bright state couples to only a fraction of the available states. The coupling of 6 0 0 to a set of nearby dark states is mediated primarily by anharmonic coupling with the fourthorder vibrational resonance playing a particularly important role through its ability to couple the 6 0 0 state directly to the 5 2 1 vibration and indirectly to the 4 4 2 vibration. The measured statespecific unimolecular dissociation rates for 6 0 0 show large fluctuations with J and and are substantially slower than that expected on the basis of statistical theory. The rate fluctuations are interpreted on the basis of spectroscopic data which suggest that the fluctuations arise as a result of variation in state mixing as different dark vibrational states come in and out of resonance with the bright state for different values of J and

The electronic structure and chemical bonding of hypermetallic by ab initio calculations and anion photoelectron spectroscopy
View Description Hide DescriptionThe chemical structure and bonding of the hypermetallic and species have been studied by photoelectron spectroscopy and ab initio calculations. Both and are found to have planar structures that can be related to that of the planar square by adding one ion or one Al atom to an edge of the square. The planarity of and can be explained in terms of the structure of their highest occupied molecular orbitals which are ligand fivecenter one or twoelectron bonding MO, respectively, similar to the orbital responsible for the planarity of Four peaks were observed in the photoelectron spectra of with vertical binding energies of 2.67, 2.91, 3.19, and 4.14 eV which compare well with the 2.68, 2.96, 3.27, and 4.35 eV calculated by the Green function method The excellent agreement between the calculated and experimental electron affinity and excitation energies allow us to completely elucidate the geometrical and electronic structures of and suggest the most likely structure for the molecule.

Potential curves for several electronic states of the MgHe, and van der Waals complexes
View Description Hide DescriptionWe have estimated the potential curves of the and van der Waals states by means of ab initio calculations. Similar to the analogous doubly excited states of MgNe, MgAr, and MgKr, the state is found to be unusually strongly bound, a bond strength which is an astounding 165 times that of the singly excited state and 35 times that of the ion. The strong bonding is attributed primarily to the lack of a electron, so that all the attractive forces can extend to smaller internuclear distances because there is no repulsion. In fact, the and states have quite similar bond energies and bond lengths, indicating that for RG=He, the primary attractive force in all these states is the ion/induceddipole interaction of the core. This is consistent with the fact that the bond energy of the state is more than four times greater than that of the state, where there is substantial repulsion not present in the state.

Ab initio theoretical studies on photodissociation of HNCO upon excitation: The role of internal conversion and intersystem crossing
View Description Hide DescriptionPhotodissociation of isocyanic acid, HNCO, was studied with highlevel ab initio methods. Geometry optimizations of stationary points and surface crossing seams were performed with the complete active space selfconsistentfield (CASSCF) method, and the energetics were reevaluated with singlepoint secondorder multireference perturbation theory (CASPT2). The three product channels that participate in the photodissociation process are [1] at 86.0 (calculated 79.6) kcal/mol, [2] at 109.7 (108.7) kcal/mol, and [3] at 122.2 (120.8) kcal/mol. The four electronic states, and that interconnect these channels were studied in detail. exhibits dissociation barriers to both, channel [2] and [3], whose respective reverse heights are 11.3 and 1.2 kcal/mol, in good agreement with experiment as well as previous theoretical works. The two triplets, and show barriers of similar heights for HN bond fission, while has no barriers to either channel. Various key isomerization transition states as well as numerous minima on the seam of surface crossings (MSX’s) were also found. At photoexcitationenergies near channel [3] threshold, products to channel [3] are likely to be formed via (if enough energy in excitation) and Channel [2] can be formed via (HNmode quanta) and channel [1] via and At higher photoexcitationenergies the pathway is expected to be dominant while with the higher activation energy, is expected to drop rapidly. Also addressed are such important issues as the impact of a vibrationally excited HN mode on a channel [2] yield, and the band origin of the excitation spectrum.

Rydberg and pulsed field ionizationzero electron kinetic energy spectra of YO
View Description Hide DescriptionA spectroscopic study of the Rydberg states of YO accessed from particular rotational levels of the state has been combined with a pulsed field ionization, zero electron kinetic energy (PFIZEKE) investigation. The results provide accurate values of the ionization energy of YO, ionization energy I.E.(YO)=49 304.316(31) cm^{−1} [6.112 958(4) eV], and of the rotational constant (and bond length) of the cation in its ground state, The improved value of I.E.(YO) combined with the known ionization energy of atomic yttrium then leads to the result Combining this result with the value of obtained from guided ion beam mass spectrometry yields an improved value of The PFIZEKE spectra display an interesting channelcoupling effect so that all rotational levels with are observed with high intensity, where is the angular momentum of the cation that is produced and is the angular momentum of the state that is reached when the first photon is absorbed. This is thought to result from the interaction between the dipole moment of the rotating core and the Rydberg electron, which can induce changes in l and subject to the dipolar coupling matrix element selection rule, Δl=±1. The channelcoupling mechanism also appears to induce an inverse autoionization process in which an unbound electron with a low value of l is captured either by its low cation or by a second cation with the same value of This inverse autoionization process is extremely sensitive to the electron kinetic energy, leading to narrow peaks in the PFIZEKE spectrum which are only slightly broader than the laser linewidth employed for this study (0.25 cm^{−1}).
