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Notes: Three-body interactions in a homonuclear van der Waals bound trimer (the 1 4A2′ state of Na3) are studied spectroscopically for the first time using laser induced emission spectroscopy on a liquid helium nanodroplet coupled with ab initio calculations. The van der Waals bound, spin polarized sodium trimers are prepared via pickup by, and selective survival in, a beam of helium clusters. Laser excitation from the 1 4A2′ to the 2 4E′ state, followed by dispersion of the fluorescence emission, allows for the resolution of the structure due to the vibrational levels of the lower state and for the gathering of precise information on the three-body interatomic potential. From previous experiments on Na2 we know that the presence of the liquid helium perturbs the spectra by a very small amount [see J. Higgins et al., J. Phys. Chem. 102, 4952 (1998)]. Ab initio potential energy calculations are carried out at 42 geometries of the lowest quartet state using the coupled cluster method at the single, double, and noniterative triple excitations level [CCSD(T)]. The full potential energy surface is obtained from the ab initio points using an interpolation procedure based on a Reproducing Kernel Hilbert Space (RKHS) methodology. This surface is compared to a second, constructed using an analytical model function for both the two-body interaction and the nonadditivity correction. The latter is calculated as the difference between the CCSD(T) points and the sum of the two-body interactions. The bound vibrational states are calculated using the two potential energy surfaces and are compared to the experimentally determined levels. The calculated bound levels are combined with an intensity calculation of the ν2″ mode of E′ symmetry derived from a Jahn–Teller analysis of the excited electronic state. The calculated frequencies of ν1″ and ν2″ are found to be 37.1 cm−1 and 44.7 cm−1, respectively, using the RKHS potential surface while values of 37.1 cm−1 and 40.8 cm−1 are obtained from the analytical potential. These values are found to be in good to fair agreement with those obtained from the emission spectrum and to be significantly different from any values calculated from additive potential energy surfaces. The 1 4A2′ Na3 potential energy surface is characterized by a D3h symmetry minimum of −850 cm−1 (relative to the three 3 2S Na atom dissociation limit) with a bond distance of 4.406 Å. This bond distance differs by about 0.8 Å from the value of 5.2 Å found for the sodium triplet dimer. This means that approximately 80% of the binding energy at the potential minimum is due to three-body effects. This strong nonadditivity is overwhelmingly due to the deformability of the valence electron density of the Na atoms which leads to a significant decrease of the exchange overlap energy in the trimer. © 2000 American Institute of Physics.

Notes: A formalism for relating dynamic observables of collision processes to the electronic structure of the colliding species is illustrated for the case of He collision-induced rotational excitation of H2. Expressions are presented for the functional derivative of transition cross sections and rate constants with respect to the electronic wave function. Regions of electronic coordinate space in which the electron probability densities have particularly strong influence on one or more inelastic transitions are identified. The possible role of functional derivatives of this sort for guiding electronic structure calculations to produce intermolecular potentials is discussed. © 1997 American Institute of Physics.

Notes: Proton spin relaxation times, T1/ρ (the slope of the longitudinal relaxation time, T1, vs density, ρ) in the infinite dilution limit as measured by Lemaire and Armstrong [J. Chem. Phys. 81, 5275 (1984)] at temperatures between 86 and 298 K are used to refine the anisotropic term of the Rodwell–Scoles HeH2 potential [J. Phys. Chem. 86, 1053 (1982)]. Prior to the refinement, a sensitivity study is performed which indicates that the data are primarily sensitive to the relative anisotropy of the repulsive wall. The inversion problem is posed as a first-order Fredholm integral equation with a kernel composed of functional sensitivities that relate potential perturbations to spin relaxation rate perturbations. The inversion scheme consists of a least-squares regularization procedure with singular system analysis and stabilization as used previously to refine atom–atom potentials [T.-S. Ho and H. Rabitz, J. Chem. Phys. 89, 5614 (1988); 90, 1519 (1989); 91, 7590 (1989)] with modifications which incorporate a priori information about the quality of the experimental data and the starting potential. The inversion yields a refined anisotropic term which in the repulsive region increases the anisotropic radial function V2(R) by approximately 10% and eliminates more than 80% of the discrepancy between the values of T1/ρ predicted by the potential and the values determined by experiment. The relative anisotropy, V2/V0, of the refined repulsive wall closely matches that of two potentials recently derived from ab initio calculation.© 1997 American Institute of Physics.

Notes: This work describes an extension of the Reproducing Kernel Hilbert Space (RKHS) method, in conjunction with the Tikhonov regularization, for constructing potential energy surfaces, with correct asymptotic forms, from high quality experimental measurements. The method is applied to the construction of new, global potential energy curves of the two lowest states X 1Σg+ and a 3Σu+ of the sodium dimer using rovibrational spectral measurements. The exchange interaction of Na2 at intermediate and long ranges is accordingly derived and adopted for determining the ionization energy of the corresponding valence electron. It is found that the resulting ground-state X 1Σg+ dissociation energy 6022.025 (±0.049) cm−1 of Na2 agrees within the experimental errors with the most recent experimental value [6022.0286 (±0.0053) cm−1, Jones et al., Phys. Rev. A 54, R1006 (1996)]. The well depth of the a 3Σu+ state is determined to be 174.96 (±1.18) cm−1, compared to the Rydberg–Klein–Rees (RKR) value of 174.45 (±0.36) cm−1 [Li et al., J. Chem. Phys. 82, 1178 (1985)]. Moreover, the equilibrium positions of both RKHS potential curves, 3.0796 (±0.0010) Å for the X 1Σg+ state and 5.089 (±0.062) Å for the a 3Σu+ state, are in excellent agreement with previously determined RKR results of 3.079 53 Å [Babaky and Hussein, Can. J. Phys. 67, 912 (1989)] and 5.0911 Å (Li et al.), respectively. The experimentally determined values of the equilibrium position and well depth for the a 3Σu+ state differ from recent theoretical values of 5.192 Å and 177.7 cm−1 obtained by highly accurate ab initio calculations [Gutowski, J. Chem. Phys. 110, 4695 (1999)]. Finally, both RKHS potential curves at large distances reproduce very recent theoretical dispersion coefficients within 1.0×10−5 percentage errors. © 2000 American Institute of Physics.

Notes: A singular value decomposition of dynamical sensitivities provides insight into the relationship between a data set and the potential which is often not evident from the sensitivities of individual observables. An illustration is treated consisting of data sets drawn from reactive transition probabilities as a function of energy for the collinear H+H2 system. While the sensitivities of individual reactive transition probabilities to the two-dimensional potential are highly structured functions of the potential coordinates, a set of reactive transition probabilities is identified which collectively has localized sensitivity primarily to the saddle point region and secondarily to the slope along the H3 symmetric stretch line in the outer corner tunneling region and to the width of the barrier. Information of this type garnered from a principal component sensitivity analysis can be especially valuable when attempting to use dynamics data to refine potential surfaces. © 1998 American Institute of Physics.

Notes: This paper presents a method for inverting temporal experimental data from chemical models to obtain estimates of unknown parameters. Most of the models under consideration are deterministic and we assume that the measurements obtained from experimental observations are represented as the solution of a differential equation containing the variables of the model. To incorporate any extraneous laboratory effects that are not included in the model, we assume that these equations are perturbed by a white noise process so that the measurements become time-dependent stochastic variables. A particular measurement is then equivalent to a realization of these variables and applying stochastic estimation theory this realization can be used to obtain estimates of the unknown parameters in the model. As an example of this estimation method, we consider chemical kinetics models with various observational equations and construct an estimator for the unknown reaction rate constants. We also show the estimators for the structural constants in a laser model depending on the representation of the experimental data. In some cases the observations are simulated numerically and we present the parameter estimates as a function of time. The efficiency of the estimation process is calculated as the ratio of the a posteriori variance of the parameter estimator and the Rao–Cramer lower bound. Some issues in the numerical implementation of the filtering equations are discussed and a comparison is made between the minimum least-square estimation method and the filtering method.

Notes: It was recently proposed that the sudden approximation should be a powerful tool for the calculation of the angular intensity distribution in high-energy atom scattering from disordered surfaces. In the present study the sudden approximation is applied to scattering from one- and two-dimensional models of: (1) Isolated adsorbed impurities on crystalline surfaces (Ar on Cu); (2) Mixed overlayers on an underlying surface (Xe+Ar mixtures on a smooth surface). The results are tested against numerically exact quantum-mechanical wave packet calculations. Except for very low collision energies, the sudden approximation gives results of excellent quantitative accuracy for both types of noncrystalline surfaces. At low energies, several features of the intensity distribution are not produced correctly by the sudden: These are found to be due mainly to double collision effects. The accuracy and validity range of the method are discussed in the light of the results obtained in the test calculations.

Notes: The collinear dynamics of a model diatom–diatom system is investigated. The collision partners are harmonic oscillators for which the masses and force constants are chosen to correspond to those of the nitrogen and oxygen molecules. The interaction between the molecules arises from a Lennard-Jones 6-12 potential acting between the inside atoms in the collinear system. Quantum mechanical close coupled calculations are performed for several collision energies ranging from 1.0 to 2.25 eV. The state-to-state transition probabilities which are extracted from these calculations are then used as a benchmark for comparison. Semiclassical calculations are performed within the framework of a classical path approximation. A simple scheme to modify the classical path to reflect energy exchange between the collision coordinate and the internal degrees of freedom is found to improve the results. On the whole, the agreement between the semiclassical and the quantum mechanical results is surprisingly good. The classical trajectory calculations correctly display many of the qualitative features of the collisions but the numerical agreement is not as close. Unexpectedly, the classical results do not appear to be improving as the collision energy is increased.

Notes: We used a randomly corrugated hard wall model and the sudden approximation to analyze two experiments on atom scattering from disordered surfaces. In one, the structural surface disorder was caused by ion bombardment. In the other, the disorder was due to an incomplete overlayer of adsorbed atoms. We also present a study of the scattering of a rigid rotor by a randomly corrugated hard wall using the sudden approximation.

Notes: A recently developed global, nonlinear map-facilitated quantum inversion procedure is used to obtain the interaction potential for Ar–HCl(v=0) based on the rotationally resolved state-to-state inelastic cross sections of Lorenz, Westley, and Chandler [Phys. Chem. Chem. Phys. 2, 481 (2000)] as well as rovibrational spectral data. The algorithm adopted here makes use of nonlinear potential→observable maps to reveal the complete family of surfaces that reproduce the observed scattering and spectral data to within its experimental error. A nonlinear analysis is performed on the error propagation from the measured data to the recovered family of potentials. The family of potentials extracted from the inversion data is compared to the Hutson H6(4,3,0) surface [Phys. Chem. 96, 4237 (1992)], which was unable to fully account for the inelastic scattering data [Phys. Chem. Chem. Phys. 2, 481 (2000)]. There is excellent agreement with H6(4,3,0) in the attractive well, where Hutson's surface is considered most reliable. There is also good long-range agreement. However, it is shown that H6(4,3,0) predicts too soft a wall for the linear Ar–HCl configuration and significantly too steep a wall for linear Ar–ClH. These differences account for the systematically backscattered inelastic cross sections computed using the H6(4,3,0) surface. The new, nonlinear inversion results provide a global Ar–HCl interaction potential with reliable error bars that are consistent with all of the experimental data. © 2001 American Institute of Physics.