Quantum dynamics of the Li+HF-->H+LiF reaction at ultralow temperatures

Quantum mechanical calculations are reported for the Li+HF(v=0,1,j=0)-->H+LiF(v',j') bimolecular scattering process at low and ultralow temperatures. Calculations have been performed for zero total angular momentum using a recent high accuracy potential energy surface for the X 2A' electronic ground state. For Li+HF(v=0,j=0), the reaction is dominated by resonances due to the decay of metastable states of the Li...F-H van der Waals complex. Assignment of these resonances has been carried out by calculating the eigenenergies of the quasibound states. We also find that while chemical reactivity is greatly enhanced by vibrational excitation the resonances get mostly washed out in the reaction of vibrationally excited HF with Li atoms. In addition, we find that at low energies, the reaction is significantly suppressed due to the formation of rather deeply bound van der Waals complexes and the less efficient tunneling of the relatively heavy fluorine atom.Comment: 24 pages, 8 figures, 1 table, submitted to J. Chem. Phy

Dimension dependence of correlation energies in two‐electron atoms

Correlation energies (CEs) for two‐electron atom ground states have been computed as a function of the dimensionality of space D. The classical limit D→∞ and hyperquantum limit D→1 are qualitatively different and especially easy to solve. In hydrogenic units, the CE for any two‐electron atom is found to be roughly 35% smaller than the real‐world value in the D→∞ limit, and about 70% larger in the D→1 limit. Between the limits the CE varies almost linearly in 1/D. Accurate approximations to real CEs may therefore be obtained by linear interpolation or extrapolation from the much more easily evaluated dimensional limits. We give two explicit procedures, each of which yields CEs accurate to about 1%; this is comparable to the best available configuration interaction calculations. Steps toward the generalization of these procedures to larger atoms are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70213/2/JCPSA6-86-6-3512-1.pd

Dimensional expansions for two‐electron atoms

Approximate expansions in inverse powers of the dimensionality of space D are obtained for the ground‐state energies of two‐electron atoms. The method involves fitting polynomials in δ=1/D to accurate eigenvalues of the generalized D‐dimensional Schrödinger equation. To the maximum order obtainable from the data, about δ7, the power series for nuclear charges Z=2, 3, and 6 all diverge at D=3. Asymptotic summation yields an energy for the Z=2 atom 1% in excess of the true value at D=3. However, expansions with a shifted origin, i.e., expansions in (δ−δ0), show improved convergence. Of particular interest is the case δ0=1, because the expansion coefficients can in principle be calculated by perturbation theory applied to the one‐dimensional atom. Series in powers of (δ−1) appear to converge rapidly. Also the series in (δ−1) can be evaluated even for the hydride ion, with Z=1. For helium, this series is quite comparable to the more familiar expansion in powers of λ=1/Z, with errors in the partial sums decreasing by roughly an order of magnitude per term. Thus, for Z=2 the first four terms of the expansion in (δ−1) yield an energy within 0.02% of the true value at D=3. Similar results are found in an analogous treatment of accurate eigenvalues for the Hartree–Fock approximation. This provides a rapidly convergent dimensional expansion for the correlation energy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70931/2/JCPSA6-86-4-2114-1.pd

On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem

Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spatial dimensions. The symmetric structure at lowest order has a point group isomorphic with the S_N group, the symmetric group of N particles, and the resulting perturbation expansion of the Hamiltonian is order-by-order invariant under the permutations of the S_N group. This invariance under S_N imposes severe symmetry requirements on the tensor blocks needed at each order in the perturbation series. We show here that these blocks can be decomposed into a basis of binary tensors invariant under S_N. This basis is small (25 terms at first order in the wave function), independent of N, and is derived using graphical techniques. This checks the N^6 scaling of these terms at first order by effectively separating the N scaling problem away from the rest of the physics. The transformation of each binary tensor to the final normal coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N for arbitrary N. This has been accomplished using the group theory of the symmetric group. This achievement results in an analytic solution for the wave function, exact through first order, that scales as N^0, effectively circumventing intensive numerical work. This solution can be systematically improved with further analytic work by going to yet higher orders in the perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and is under revie

Chemical Accelerator Studies of Isotope Effects on Collision Dynamics of Ion–Molecule Reactions: Elaboration of a Model for Direct Reactions

This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/53/2/10.1063/1.1674042.Crossed‐beam studies on isotopic variants of the reaction Ar+ + H2→ArH+ are reported. Both velocity and angular distributions of the ionic product as a function of initial translational energy, down to 0.1 eV (center of mass), have been measured. At lowest energies there is a gain in the translational energy of the products over that of the reactants, but at higher energies there is increasing conversion of kinetic into internal energy. While this represents the most probable course of the reaction there is a fairly wide distribution about the median values. Results confirm that this reaction is predominantly direct at all energies and provide no evidence for intermediate persistent complex formation. They are also consistent with a model for direct reactions previously proposed. The data on reaction with HD permit further development of this mechanism. The reactants are mutually accelerated by their long‐range attractive potential until hydrogen atom transfer occurs. The liberated H (or D) atom is reflected from the ArD+(ArH+ and the products separate, being decelerated in the process by the attractive potential acting between them. This “polarization–reflection” model yields a reasonable value for the radius at which transfer occurs, and it accounts quantitatively for the magnitudes of, and isotopic effects on, the median product velocities. It also predicts the significant back scattering observed at very low as well as very high energies. With appropriate modification for the attractive potentials involved the model can provide a simple representation of direct reactions in general

Two and three electrons in a quantum dot: 1/|J| - expansion

We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular momentum, J, and a low number of vibrational quanta may be systematically computed as power series in 1/|J|. These states are relevant in the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

Entropic uncertainty measures for large dimensional hydrogenic systems

The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the entropic uncertainty measures of R\'enyi type which allow one to find the most relevant mathematical formalizations of the position-momentum Heisenberg's uncertainty principle, the entropic uncertainty relations. It is known that the solution of difficult three-dimensional problems can be very well approximated by a series development in $1/D$ in similar systems with a non-standard dimensionality $D$; moreover, several physical quantities of numerous atomic and molecular systems have been numerically shown to have values in the large-$D$ limit comparable to the corresponding ones provided by the three-dimensional numerical self-consistent field methods. The $D$-dimensional hydrogenic atom is the main prototype of the physics of multidimensional many-electron systems. In this work we rigorously determine the leading term of the R\'enyi entropies of the $D$-dimensional hydrogenic atom at the limit of large $D$. As a byproduct, we show that our results saturate the known position-momentum R\'enyi-entropy-based uncertainty relations.Comment: Accepted in J. Math. Phy

Pulsed rotating supersonic source used with merged molecular beams

We describe a pulsed rotating supersonic beam source, evolved from an ancestral device [M. Gupta and D. Herschbach, J. Phys. Chem. A 105, 1626 (2001)]. The beam emerges from a nozzle near the tip of a hollow rotor which can be spun at high-speed to shift the molecular velocity distribution downward or upward over a wide range. Here we consider mostly the slowing mode. Introducing a pulsed gas inlet system, cryocooling, and a shutter gate eliminated the main handicap of the original device, in which continuous gas flow imposed high background pressure. The new version provides intense pulses, of duration 0.1-0.6 ms (depending on rotor speed) and containing ~10^12 molecules at lab speeds as low as 35 m/s and ~ 10^15 molecules at 400 m/s. Beams of any molecule available as a gas can be slowed (or speeded); e.g., we have produced slow and fast beams of rare gases, O2, Cl2, NO2, NH3, and SF6. For collision experiments, the ability to scan the beam speed by merely adjusting the rotor is especially advantageous when using two merged beams. By closely matching the beam speeds, very low relative collision energies can be attained without making either beam very slow.Comment: 26 pages, 10 figure