A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Feshbach resonances in ultracold gases

Feshbach Resonances in Ultracold Gases

Starting from our earlier model [J. Chem. Phys. 66, 1496 (1977)] a simple expression is derived for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n. The damping functions are only a function of the Born–Mayer range parameter b and thus can be applied to all systems for which this is known or can be estimated. For H(1S)–H(1S) the results are in almost perfect agreement with the very accurate recent ab initio damping functions of Koide, Meath, and Allnatt. Comparisons with less accurate previous calculations for other systems also show a satisfactory agreement. By adding a Born–Mayer repulsive term [A exp(−bR)] to the damped dispersion potential, a simple universal expression is obtained for the well region of the atom–atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10. The model has been tested for the following representative systems: H2 3Σ, He2, and Ar2 as well as NaK 3Σ and LiHg, which include four che...

An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients

A simple realistic and precise empirical intermolecular potential is proposed for helium. It possesses nearly the correct Hartree–Fock repulsion as well as the correct long range behavior. It was fitted to recent accurate intermediate temperature second virial coefficients and thermal conductivity data as well as high temperature viscosity values. It is able to predict second virial coefficients over an extended temperature range from 1.5 to 1475 K. Above 100 K it reproduces substantially all of the transport properties to within experimental error in a manner superior to all other potentials in existence. Below 100 K where the transport data are less reliable, it produces a good representation of the isotopic differences in the viscosity. It also predicts differential cross sections reasonably well. In spite of a few remaining discrepancies, when all the different macroscopic properties are considered, the potential produces the best representation of the helium interaction available at this time.

An accurate intermolecular potential for helium

Upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established. Nonadditive three‐body coefficients involving dipole, quadrupole, and octupole interactions are also determined. For the dipole polarizabilities a three‐term, two‐point Pade approximant is used to obtain the upper bound and a two‐term Pade approximant is used to obtain the lower bound. For the quadrupole and octupole polarizabilities a one‐term approximation of the dynamic polarizability is used, except for the helium quadrupole polarizability, where extended approximations are possible.

Upper and lower bounds of two‐ and three‐body dipole, quadrupole, and octupole van der Waals coefficients for hydrogen, noble gas, and alkali atom interactions

P. R. Certain

Papers

Upper and lower bounds of two‐ and three‐body dipole, quadrupole, and octupole van der Waals coefficients for hydrogen, noble gas, and alkali atom interactions