https://arxiv.org/pdf/cond-mat/0410417.pdf

Universality in few-body systems with large scattering length

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose and two-spin-component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled-channels theory provides a rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, and the classification in terms of entrance- and closed-channel-dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic-field sweeps in cold Bose and Fermi gases and pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean-field, as well as beyond mean-field approaches are reviewed in detail, including the associated ranges of validity.

Production of cold molecules via magnetically tunable Feshbach resonances

▪ Abstract Laser ablation of in situ metals has recently made it possible to immerse a large number of different metal atoms and ions and small clusters of metal atoms in liquid helium (He) and thus study their absorption and emission spectra in the visible region. Atoms and molecules are readily picked up by large ( ≥ 103 atoms) He droplets, and their spectra are sensitively detected through the use of either beam depletion following absorption or laser-induced fluorescence. Within the past three years, a wide variety of molecules, ranging from OCS to large organic molecules such as amino acids and a number of van der Waals complexes and even large metal clusters, have been embedded in He droplets and studied either in infrared or in the visible region. These results are discussed here in detail, and the evidence for the effect of superfluidity on the spectral features is reviewed.

Spectroscopy of atoms and molecules in liquid helium

A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one‐dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two‐dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three‐dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Rohse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Rohse et al. using a low order polynomial fitting procedure.

A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations

Standard density functional approximations cannot accurately describe interactions between nonoverlapping densities. A simple remedy consists in correcting for the missing interactions a posteriori, adding an attractive energy term summed over all atom pairs. The density-dependent energy correction, dDsC, presented herein, is constructed from dispersion coefficients computed on the basis of a generalized gradient approximation to Becke and Johnson’s exchange-hole dipole moment formalism. dDsC also relies on an extended Tang and Toennies damping function accounting for charge-overlap effects. The comprehensive benchmarking on 341 diverse reaction energies divided into 18 illustrative test sets validates the robust performance and general accuracy of dDsC for describing various intra- and intermolecular interactions. With a total MAD of 1.3 kcal mol–1, B97-dDsC slightly improves the results of M06-2X and B2PLYP-D3 (MAD = 1.4 kcal mol–1 for both) at a lower computational cost. The density dependence of both ...

Comprehensive Benchmarking of a Density-Dependent Dispersion Correction.

A simple analytical expression for the entire van der Waals potential curve of the helium dimer is derived from perturbation theory. The repulsive part is essentially from Duman and Smirnov [Opt. Spectrosc. 29, 229 (1970)] who assume the exchange of only one pair of electrons at any one time. The potential depends only on the known dispersion coefficients and the amplitude of the asymptotic wave function and the ionization energy of the atoms. Without any adjustable parameters the potential is in excellent agreement with the latest experimental and theoretical results and predicts the existence of the He dimer. The same method can be applied to heavier rare gases.

Accurate analytical He-He van der Waals potential based on perturbation theory.

The surface integral method of Holstein and Herring is applied to the calculation of the exchange energy of the H2 molecule. This theory provides a means for calculating the exchange energy by taking into account the physical exchange of the two electrons with respect to the nuclei. Problems associated with symmetrization of the polarized wave functions which have encumbered previous attempts at developing a perturbation theory of the chemical bond are circumvented. Whereas the previous calculations using this method by Gor’kov and Pitaevski and Herring and Flicker were restricted to the asymptotic (R→∞) limit, in the present calculation we have used an extended formula to examine the validity also for the short range region down to R=0.5 a.u. In order to compare with the results of Heitler–London theory we have used the undisturbed zeroth order wave function of the H atoms in the calculations. An analytic expression is obtained for the exchange energy and the numerical results are found to be in good agr...

Exchange energy of H2 calculated by the surface integral method in zeroth order approximation

The unsymmetrized perturbation theory for interaction potentials is reformulated in such a way that the overlap and exchange effects can be taken into account in a satisfactory and conceptually simple way. This formulation, known as the generalized Heitler-London theory, its shown to be valid regardless of the ultimate limit to which the polarization approximation converges. Within the framework of this theory, the van der Waals potential of the triplet H2(3Σu) state is calculated and shown to be in excellent agreement with the exactab initio results. Both the exchange energy and the polarization energy are obtained from a perturbation calculation.

C. L. Yiu

Papers

Accurate analytical He-He van der Waals potential based on perturbation theory.

Exchange energy of H2 calculated by the surface integral method in zeroth order approximation

The perturbation calculation of van der Waals potentials