Volume 114, Issue 3, 15 January 2001
 ARTICLES

 Theoretical Methods and Algorithms

Semiclassical application of the Mo/ller operators in reactive scattering
View Description Hide DescriptionMo/ller operators in the formulation of reaction probabilities in terms of wave packet correlation functions allow us to define the wave packets in the interaction region rather than in the asymptotic region of the potential surface. We combine Mo/ller operators with the semiclassical propagator of Herman and Kluk. This does not involve further approximations and can be used with any initial value representation (IVR) semiclassical propagator. Time propagation in asymptotic regions of the potential due to Mo/ller operators reduces the oscillations of the propagator integrand and improves convergence of the results with respect to the number of trajectories. The effectiveness of Mo/ller operators for semiclassical reaction probability calculation is demonstrated for the collinear hydrogen exchange reaction. Full convergence is achieved and the number of classical trajectories is reduced by a factor of compared to the calculation without Mo/ller operators.

Classical mapping approaches for nonadiabatic dynamics: Short time analysis
View Description Hide DescriptionA systematic approach to improve the short time dynamics for classical mapping treatments of nonadiabatic dynamics is developed. This approach is based on the Taylor expansion of timedependent observables around By sampling initial conditions in a manner that renders accurate static moments of the electronic population, it is shown that the short time electronic population dynamics described by classical mapping approaches for nonadiabatic dynamics can be greatly improved. The approach is illustrated on the example of the spinboson model. For this problem, the analysis of the expansion coefficients reveals why classical mapping approaches to nonadiabatic dynamics often perform much worse for energetically biased reactions than they do for reactions with zero bias. The analysis presented here not only allows for the improvement of short time (and often long time) behavior, but also points to a systematic way of accessing how accurate a given classical mapping approach should be for a given problem.

Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach
View Description Hide DescriptionWe present a way of combining realtime path integral Monte Carlo simulations with a maximum entropy numerical analytic continuation scheme in a new approach for calculating time correlation functions for finite temperature many body quantum systems. The realtime dynamics is expressed in the form of the symmetrized time correlation function, which is suitable for Monte Carlo methods, and several simulation techniques are presented for evaluating this function accurately up to moderate values of time. The symmetrized time correlation function is then analytically continued in combination with imaginary time data to obtain the realtime correlation function. We test this approach on several exactly solvable problems, including two onedimensional systems, as well two cases of vibrational relaxation of a system coupled to a dissipative environment. The computed time correlation functions are in good agreement with exact results over several multiples of the thermal time and exhibit a significant improvement over analytic continuation of imaginary time correlation functions. Moreover, we show how the method can be systematically improved.

A quantum electrodynamical theory of threecenter energy transfer for upconversion and downconversion in rare earth doped materials
View Description Hide DescriptionThreecenter energy transfer affords the basic mechanism for a variety of multiphoton processes identified within materialsdoped with rare earths. Addressing the theory using quantum electrodynamics, general results are obtained for systems in which the fundamental photophysics engages three ions. Distinct cooperative and accretive mechanistic pathways are identified and the theory is formulated to elicit their role and features in energy transfer phenomena of pooling upconversion, sensitization, and downconversion or quantum cutting. It is shown that although the two mechanisms play significant roles in pooling and cutting, only the accretive mechanism is responsible for sensitization processes. Both mechanisms are shown to invoke Raman selection rules, which govern transitions of the mediator ions in the accretive mechanisms and transitions of the acceptor ions in the cooperative mechanisms. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structuraleffects. Attention is drawn to a general implication of implementing a multipolar description for the optical properties of doped solidstate ionic materials.

A diagrammatic theory of time correlation functions of facilitated kinetic Ising models
View Description Hide DescriptionWe present a diagrammatic formulation of the kinetic theory of time correlation functions for facilitated kinetic Ising models with directed constraints. Such models have been studied because their relaxation properties are similar to those of glass forming liquids and because some of them undergo ergodic–nonergodic transitions. Using a Hilbert space formulation of the dynamics of Markov processes that satisfy a detailed balance condition, we derive a diagrammatic series for the spin autocorrelation function, its memory function, and its irreducible memory function. Using graphical methods we derive various approximations for the irreducible memory function, including approximations equivalent to various versions of the simplified and extended mode coupling theory of Götze and coworkers. An extended mode coupling theory for the “East model” is compared with simulation data. The theory is accurate at short and intermediate times for all upspin concentrations and for all times at high upspin concentrations. The major failing of the extended mode coupling theory for this model is the prediction of long time decay that is too rapid and too exponential, as compared with the simulation results.

Computational method of manyelectron integrals over explicitly correlated Cartesian Gaussian functions
View Description Hide DescriptionDerivation of recurrence formulas for general manyelectron overlap, nuclear attraction, and electron repulsion integrals over explicitly correlated Cartesian Gaussian functions is presented. The recurrence formulas are derived in a similar way as the derivation of molecular twoelectron integrals over Cartesian Gaussian functions by Obara and Saika. As a result, the formulas expressing the manyelectron integrals of higher angular momentum as a linear combination of those of lower angular momentum are obtained. An algorithm for computation of the general manyelectron integrals by means of the recurrence formulas is also shown.

Compact parameter set for fast estimation of proton transfer rates
View Description Hide DescriptionSeveral proton transfer systems were studied by quantum chemical calculations in the presence of further ligand waters. The calculated proton transfer barriers are fitted by an analytical expression, which allows for fast calculation of proton transfer rates between common donor–acceptor pairs in biological systems under the influence of surrounding chemical groups. The only information required is the chemical nature of the donor and acceptor, the distance between donor and acceptor, and the environmental influence in the acceptor and donor bound states. The quantum nature of the transferred proton is approximated at the level of an effective zeropoint energy along the reaction coordinate. The approach presented allows efficient calculation of transfer rates and allows to include proton hopping events between titratable sites in classical molecular dynamics simulations.

Secondorder quasidegenerate perturbation theory with quasicomplete active space selfconsistent field reference functions
View Description Hide DescriptionA quasidegenerate perturbation theory (QDPT) is presented that is based on quasicomplete active space selfconsistent field (QCASSCF) reference functions. The perturbation method shown here is an extension of a previously proposed QDPT with CASSCF reference functions (CASQDPT) but is a more compact perturbation method that can employ a much smaller reference configuration space with the same number of active electrons and orbitals as the CAS case. A computational scheme to secondorder using a diagrammatic approach is described. The secondorder effective Hamiltonian consists of the contribution from external excitations, which involve core or/and virtual orbitals, and internal excitations, which involve only active orbitals. The importance of the internal excitation contribution is emphasized. The method is tested on the potential energy curves of the LiF molecule, the Rydbergexcitation energies of furan, and the transition state barrier height of the reaction, The results are in very good agreement with the corresponding CASSCF reference QDPT results and available experimental data. The deviations from the CASQDPT values in the energy are less than 0.1 eV on the average for the excitation energies of furan and less than 1 kcal for the barrier height of the reaction, The deviation from the experimental values is 0.11 eV at most for the excitation energies, and 1.2 kcal/mol, which is within the twice the experimental uncertainty, for the barrier height.

Statistics of the bleaching number and the bleaching time in singlemolecule fluorescence spectroscopy
View Description Hide DescriptionThe kinetics of bleaching in singlemolecule fluorescence spectroscopy (SMS) is studied using renewal theory. A fivestate model of a dye molecule is considered where bleaching occurs from the excited triplet states. An exact formalism is developed to calculate the distributions of the bleaching number (i.e., the number of photon counts) and bleaching time (i.e., the time before photobleaching). For photostable dyes those distributions are well approximated by exponential distributions determined by the average bleaching number ν and the average bleaching time τ respectively. Exact formulation is developed to calculate ν and τ in terms of the transition rate constants. For photostable dyes the exact ν and τ are well approximated by expressions derived from a steadystate solution to the kinetic rate equations describing the molecule. The theory implies that experimental multiexponential fits to the distributions of the bleaching number and bleaching time are an indication that the SMS system is heterogeneous.

Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of
View Description Hide DescriptionThe theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of faceshared bioctahedral dimer (overall symmetry). The effective kinetic exchange Hamiltonian is found for a system taking into account all relevant transfer pathways and chargetransfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and the technique of the irreducible tensor operators of group we give a general outlook on the nontrivial symmetry properties of the effective Hamiltonian for the pair, and on the magnetic anisotropy arising from the orbital interactions specific for the case of orbital degeneracy. The magnetic properties of the binuclear unit in are discussed with a special emphasis on the magnetic anisotropy experimentally observed in this system. The existing exchange models for and the concept of the effective Hamiltonian are discussed in the context of the present study.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Reactivity and electronic structure of aluminum clusters: The aluminum–nitrogen system
View Description Hide DescriptionThe stability of anionic aluminum–nitrogen clusters has been examined and and are found to be particularly stable. Theoreticaldensity functional calculations on neutral and anionic clusters were performed and the stability and reaction energetics with oxygen examined. Clusters requiring less than 5.7 eV to remove an electron and an Al atom are shown to be resistant to the reaction with oxygen.

Absolute total and partial cross sections for the electron impact ionization of tetrafluorosilane
View Description Hide DescriptionWe measured absolute partial cross sections for the formation of various singly charged and doubly charged positive ions produced by electron impact on from threshold to 900 eV using a timeofflightmass spectrometer.Dissociativeionization was found to be the dominant process, although we found evidence of the presence of the parent ion in our experiment. The fragment ion has the largest partial ionization cross section with a maximum value of at 90 eV. All other singly charged fragment ion cross sections are about one order of magnitude smaller at this impact energy. The crosssection values of the doubly charged ions with the exception of are about two orders of magnitude smaller. A comparison is made with available previously measured data. Additional measurements using a sectorfield mass spectrometer revealed that all fragment ions are formed with excess kinetic energy. The experimentally determined total single ionization cross section of is compared with results of semiempirical and semiclassical calculations and reasonable agreement is found.

Optical pumping studies of vibrational energy transfer in highpressure diatomic gases
View Description Hide DescriptionSpontaneous Raman scattering is used to experimentally determine the vibrational distribution functions of diatomic species in and gas mixtures optically pumped by a CO laser in the pressure range 410–760 torr. In mixtures, as many as 38 vibrational levels of CO are observed, in addition to six levels of The CO vibrational distribution function is highly nonBoltzmann, exhibiting the wellknown Treanor plateau. In mixtures, up to 13 vibrational levels of are observed, which also exhibit a highly nonBoltzmann distribution. Experimental data are compared to predictions of a master equation kinetic model, which incorporates absorption of the laser radiation, species, and quantum statespecific vibration–vibration and vibration–translation energy exchange, as well as diffusion of vibrationally excited species out of the laserexcited volume. It is shown for the first time that modest power continuous wave lasers can be used to establish highly excited steadystate vibrational distributions of all three major diatomic species in COseeded atmospheric pressure dry air. This has implications for the energyefficient creation of lowtemperature, highpressure air plasmas, in which the principal free electron loss mechanism is known to be threebody attachment to molecular oxygen.

Spectra of jetcooled and in systems and Rotational structure of perturbed
View Description Hide DescriptionSpectra of and of and are obtained in a supersonic jet at a resolution The rotational structures are analyzed for both isotopic species to obtain precise rotational and spin constants. Two new bands at 27 032.222(1) and 27 515.41(1) cm^{−1} arising from vibronic interaction separately with vibrational state (110) and (200) of are assigned to transitions to and (101). The rotational structure of is observed and analyzed for the first time. The two vibrational states are analyzed to yield effective rotational constants 1.89(3), 0.412(3), and respectively. Then the difference of vibrational frequency of is obtained to be Because of interaction to the observed spacing of K stack and spin constants α and β for are smaller whereas the state is relatively unaffected and only spin constants vary significantly.

Electronic continua in timeresolved photoelectron spectroscopy. I. Complementary ionization correlations
View Description Hide DescriptionWe examine the role of electronic continua in timeresolvedphotoelectron spectroscopy studies of polyatomic nonadiabatic dynamics. We have investigated the two limiting cases for such studies. We consider here the limiting case of complementary ionizationcorrelations where the two nonadiabatically coupled excited electronic states and correlate (in the Koopmans’ picture) to different cation electronic states. We show, using an example of ultrafast internal conversion a linear polyene, that this favorable case allows for disentangling of the electronic population dynamics from the coupled vibrational dynamics. In the following paper, we investigate the unfavorable case of corresponding ionizationcorrelations.

Electronic continua in timeresolved photoelectron spectroscopy. II. Corresponding ionization correlations
View Description Hide DescriptionWe investigate further the role of ion electronic continua in timeresolved photoelectron spectroscopicmeasurements of ultrafast nonadiabatic coupling. In the preceding paper [Blanchet, Zgierski, and Stolow, J. Chem. Phys. 114, 1194 (2000)], the limiting case of complementary ionizationcorrelations permitted a disentangling of electronic from vibrational dynamics. Here we examine the other limiting case in which the nonadiabatically coupled sates (e.g., and correlations correspond to the same ionic continua, presumably an unfavorable case. We use ultrafast internal conversion in the polyaromatic hydrocarbons phenanthrene and naphthalene as examples. In this situation, the geometry changes (displacements) upon nonadiabatic crossing and upon ionization will strongly affect the ability to disentangle electronic from vibrational dynamics. Particularly, phenanthrene and naphthalene are both very rigid molecules and have small displacements upon internal conversion and ionization, still allowing for direct monitoring of the state internal conversion rate.

Mechanism of the reaction, studied by ultrafast and stateresolved photolysis/probe spectroscopy of the van der Waals complex
View Description Hide DescriptionThe mechanism of the reaction was investigated by ultrafast, timeresolved and stateresolved experiments. In the ultrafast experiments, short ultraviolet pulses photolyzedozone in the van der Waals complex to produce The ensuing reaction with was monitored by measuring the appearance rate of by laserinduced fluorescence, through the transition, using short probe pulses. These spectrally broad pulses, centered between 307 and 316 nm, probe many different OH rovibrational states simultaneously. At each probe wavelength, both a fast and a slow rise time were evident in the fluorescence signal, and the ratio of the fasttoslow signal varied with probe wavelength. The distribution of states, was determined by laserinduced fluorescence using a highresolution, tunable dye laser. The data and the timeresolved data were analyzed under the assumption that different formation times represent different reaction mechanisms and that each mechanism produces a characteristic rovibrational distribution. The stateresolved and the timeresolved data can be fit independently using a twomechanism model: can be decomposed into two components, and the appearance of OH can be fit by two exponential rise times. However, these independent analyses are not mutually consistent. The timeresolved and stateresolved data can be consistently fit using a threemechanism model. The OH appearance signals, at all probe wavelengths, were fit with times and The slowest of these three is the rate for dissociation of a vibrationally excited methanol intermediate predicted by statistical theory after complete intramolecular energy redistribution following insertion of into The was decomposed into three components, each with a linear surprisal, under the assumption that the mechanism producing OH at a statistical rate would be characterized by a statistical prior. Dissociation of a intermediate before complete energy randomization was identified as producing OH at the intermediate rate and was associated with a population distribution with more rovibrational energy than the slow mechanism. The third mechanism produces OH promptly with a cold rovibrational distribution, indicative of a collinear abstraction mechanism. After these identifications were made, it was possible to predict the fraction of signal associated with each mechanism at different probe wavelengths in the ultrafast experiment, and the predictions proved consistent with measured appearance signals. This model also reconciles data from a variety of previous experiments. While this model is the simplest that is consistent with the data, it is not definitive for several reasons. First, the appearance signals measured in these experiments probe simultaneously many states, which would tend to obfuscate differences in the appearance rate of specific rovibrational states. Second, only about half of the states populated by this reaction could be probed by laserinduced fluorescence through the band with our apparatus. Third, the cluster environment might influence the dynamics compared to the free bimolecular reaction.

Efficient calculation of molecular constants and transition intensities in weakly bound species from eigenstates: BenzeneAr as test case
View Description Hide DescriptionIn application to benzeneAr we test a procedure that makes use of conveniently calculated intermolecular eigenstates to compute molecular constants and transition intensities without requiring explicit diagonalization of the full rotational/intermolecular vibrational Hamiltonian of the species. The approach relies on the ability to calculate the orientation of an Eckart bodyfixed frame for each point on a grid over which a state is represented. That ability allows one to compute vibrational matrix elements of operators referred to the Eckart axes while working with eigenstates obtained in an entirely different bodyfixed frame. Generally excellent agreement is found between the Eckart results and those obtained by others via diagonalization of the full rotational/intermolecular vibrational Hamiltonian. Finally, a general prescription for the construction of an efficient rovibrational basis from solutions in a convenient bodyfixed frame is presented.

Rotational spectra and structures of the and symmetric tops
View Description Hide DescriptionRotational spectra of several isotopomers of and tetramers were obtained with a Balle–Flygare Fourier transformmicrowave spectrometer. Both were found to be symmetric tops, the former being an oblate and the latter a prolate one. The rotational constantsB, and were determined to be 1172.1323(1) MHz, 7.199(1) kHz, and −5.545(2) kHz for the and 819.0385(1) MHz, 3.346(1) kHz, and +3.145(2) kHz for the containing tetramer. Substitution analysis with the rotational constants of various isotopomers led to an Ar–Ar distance of 3.848 (3.865) Å and an distance of 3.675 (4.112) Å for complexes. The angle between the axis of the and the axis of the tetramer is estimated to be 74° for and 13° for the complex. No evidence for any excited tunneling/internal rotor states was found for either of the tetramer. MMC calculations show that the equilibrium geometry has the positioned above the plane of the with both the protons pointing towards one Ar each. The barrier for the “pseudorotation” in which the protons hop between the argons is determined to be about 6 (8) cm^{−1} only for making the moiety very mobile and effectively making both the tetramers symmetric tops. Rigid body diffusionquantum Monte Carlo (RBDQMC) calculations with the MMC potential have been carried out for vibrational analysis.

Quantummechanical study of vibrational relaxation of HF in collisions with Ar atoms
View Description Hide DescriptionVibrational relaxation cross sections and rate constants of by Ar are calculated on a recent semiempiricalpotential energy surface (PES) [J. Chem. Phys. 111, 2470 (1999)] using the quantummechanical coupled states approach. Accurate theoretical estimations of rate coefficients for vibrational relaxation of at temperatures between and K are obtained. The vibrational relaxation is shown to be of a quasiresonant character and occur mostly to two nearest rotational levels of the ground vibrational state. The weak isotope effect after substitution of HF by DF is investigated and explained. The cross sections for vibrational relaxation of where are calculated and shown to increase significantly as increases. In the same calculations we observe a dramatic increase of multiple quantum vibrational transitions as the difference between the initial and final states falls in close resonance with the collision energy. A comparison of the cross sections obtained from the coupled states calculations with those performed with rotational infiniteordersudden approximation proves a crucial role of molecular rotations for vibrational relaxation. Finally, we describe the close coupling coupled states calculations for relaxation and rotational excitation of with a reduced number of open channels in the basis set and show that it is possible to obtain converged results for rotationally inelastic transitions between the various levels of neglecting all states below