Explicitly correlated Helium wave function and hyperspherical coordinates

Spherical and hyperspherical harmonics representation of van der Waals aggregates

The representation of the potential energy surfaces of atom molecule or molecular dimers interactions should account faithfully for the symmetry properties of the systems, preserving at the same time a compact analytical form. To this aim, the choice of a proper set of coordinates is a necessary precondition. Here we illustrate a description in terms of hyperspherical coordinates and the expansion of the intermolecular interaction energy in terms of hypersherical harmonics, as a general method for building potential energy surfaces suitable for molecular dynamics simulations of van der Waals a…

Universal temperature dependence of the ion-neutral-neutral three-body recombination rate

A classical approach based on hyperspherical coordinates is used to derive a first principle formulation of the the ion-neutral-neutral three-body recombination rate, A$^+$ + A + A $\rightarrow$ $\text{A}_2^+$ + A, in terms of the mass of the atom and its polarizability. The robustness and predictive power of our approach have been checked in comparison with experimental data of rare gas three-body recombination as well as previous theoretical frameworks, which need one or two atom-dependent fitting parameters. Thus, our approach is general and applicable to any ion-atom-atom system.

Experimental Determination of the Interaction Potential between a Helium Atom and the Interior Surface of a C60 Fullerene Molecule

The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Non-bonded interactions are dominated by repulsive forces at short range and attractive dispersion forces at long range. Experimental data on the detailed interaction potentials for non-bonded interatomic and intermolecular forces is scarce. Here we use terahertz spectroscopy and inelastic neutron scattering to determine the potential energy function for the non-bonded interaction between single He atoms and encapsulating C60 fullerene cages, in the helium endofullerenes 3He…

Variational calculation of many-body wave functions and energies from density-functional theory

A generating coordinate is introduced into the exchange-correlation functional of density-functional theory (DFT). The many-body wave function is represented as a superposition of Kohn-Sham (KS) Slater determinants arising from different values of the generating coordinate. This superposition is used to variationally calculate many-body energies and wave functions from solutions of the KS equation of DFT. The method works for ground and excited states, and does not depend on identifying the KS orbitals and energies with physical ones. Numerical application to the Helium isoelectronic series il…

电场中原子-分子化学反应的严格量子计算：从单分波到多分波区域

Rigorous quantum calculations for atom-molecule chemical reactions in electric fields: from single to multiple partial wave regimes

本文提出了一种在直流电场下严格计算原子-分子反应散射截面的高效方法，通过超球面与Jacobi坐标间的渐近变换解决了计算难题，并利用精确势能面揭示了电场对不同化学反应截面的影响及基组收敛性的关键作用。

Lifetimes and wave functions of ozone metastable vibrational states near the dissociation limit in full symmetry approach

Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of $^{16}$O$_3$ were determined using a previously-developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently-computed potential energy surface of ozone determined with a spectroscopic accuracy [J. Chem. Phys. {\bf 139}, 134307 (2013)]. The effect of permutational symmetry on rovibrational dynamics and the density of resonance states in O$_3$ is discussed in detail. Correspondence between quantum numbers appropriate f…