# Three-body contribution to the helium interaction potential

**ABSTRACT** Two nonadditive three-body analytic potentials for helium were obtained: one based on three-body symmetry-adapted perturbation theory (SAPT) and the other one on supermolecular coupled-cluster theory with single, double, and noniterative triple excitations [CCSD(T)]. Large basis sets were used, up to the quintuple-zeta doubly augmented size. The fitting functions contain an exponentially decaying component describing the short-range interactions and damped inverse powers expansions for the third- and fourth-order dispersion contributions. The SAPT and CCSD(T) potentials are very close to each other. The largest uncertainty of the potentials comes from the truncation of the level of theory and can be estimated to be about 10 mK or 10% at trimer's minimum configuration. The relative uncertainties for other configurations are also expected to be about 10% except for regions where the nonadditive contribution crosses zero. Such uncertainties are of the same order of magnitude as the current uncertainties of the two-body part of the potential.

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**ABSTRACT:**The triatomic 4He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: 4He + 4He + 4He → 4 He2 + 4He and 4He + 4He + 3He → 4He2 + 3He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is 4He2X with X = 7Li, 23Na, 39K, 85 Rb, and 133Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as 4He + 4He + 7Li → 4 He2 + 7Li and 4He + 4He + 7Li → 4 He7Li + 4He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.Few-Body Systems 08/2013; 54(7-10). DOI:10.1007/s00601-013-0708-z · 1.51 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Helium is the only substance that has been observed on macroscopic scale to form the fourth state of matter, the superfluid state. However, until recently superfluid helium had not found any practical applications, mainly because it expels all other atoms or molecules. Only in the 1990s was it discovered that it is possible to mix in other substances with superfluid helium if helium is prepared as small droplets, called nanodroplets, containing only a few thousand atoms. This discovery led to the development of a new and very powerful experimental technique, called helium-nanodroplet spectroscopy. Superfluid helium creates a gentle matrix around the impurities and - due to superfluidity and to very weak interactions of helium atoms with other atoms or molecules - allows measurements of the spectra with precision not much lower than in the gas phase. Consequently, helium-nanodroplet spectroscopy enables very accurate probing of molecules or clusters which cannot be investigated in the gas phase due to their instability. This category includes `fragile' molecules, isomers, radicals, and clusters in secondary minima. The major experimental developments will be described, emphasizing their importance for understanding basic principles of physics and new insights into chemically relevant processes. The experiments have been assisted by theoretical work on impurity-Hen clusters. Most such work involves first-principles quantum simulations. Although the number of helium atoms that can be included in such simulations is significantly smaller than in a typical nanodroplet, theory explains most of the observed trends reasonably well. Theoretical results can also be compared directly and much more precisely than in the case of the droplets with the results of molecular beam experiments on clusters of controllable size, with the number of helium atoms ranging from 1 to almost 100. Most of the simulations published to date will be discussed and the level of agreement with experiment will be critically evaluated. The results of the simulations are very sensitive to details of the He-He and impurity-He interaction potentials used, and most of the current discrepancies between theory and experiment can be traced down to the uncertainties of the potentials. Thus, an important component of this review will be an analysis of various sources of errors in potential energy surfaces.International Reviews in Physical Chemistry 04/2008; 27(2):273-316. DOI:10.1080/01442350801933485 · 4.92 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Nonrelativistic clamped-nuclei energies of interaction between two ground-state hydrogen molecules with intramolecular distances fixed at their average value in the lowest rovibrational state have been computed. The calculations applied the supermolecular coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and very large orbital basis sets-up to augmented quintuple zeta size supplemented with bond functions. The same basis sets were used in symmetry-adapted perturbation theory calculations performed mainly for larger separations to provide an independent check of the supermolecular approach. The contributions beyond CCSD(T) were computed using the full configuration interaction method and basis sets up to augmented triple zeta plus midbond size. All the calculations were followed by extrapolations to complete basis set limits. For two representative points, calculations were also performed using basis sets with the cardinal number increased by one or two. For the same two points, we have also solved the Schrodinger equation directly using four-electron explicitly correlated Gaussian (ECG) functions. These additional calculations allowed us to estimate the uncertainty in the interaction energies used to fit the potential to be about 0.15 K or 0.3% at the minimum of the potential well. This accuracy is about an order of magnitude better than that achieved by earlier potentials for this system. For a near-minimum T-shaped configuration with the center-of-mass distance R=6.4 bohrs, the ECG calculations give the interaction energy of -56.91+/-0.06 K, whereas the orbital calculations in the basis set used for all the points give -56.96+/-0.16 K. The computed points were fitted by an analytic four-dimensional potential function. The uncertainties in the fit relative to the ab initio energies are almost always smaller than the estimated uncertainty in the latter energies. The global minimum of the fit is -57.12 K for the T-shaped configuration at R=6.34 bohrs. The fit was applied to compute the second virial coefficient using a path-integral Monte Carlo approach. The achieved agreement with experiment is substantially better than in any previous work.The Journal of Chemical Physics 10/2008; 129(9):094304. DOI:10.1063/1.2975220 · 3.12 Impact Factor