Exponentially correlated Gaussian functions in variational calculations. Momentum space properties of the ground state helium dimer

Generation of Basis Sets for Accurate Molecular Calculations: Application to Helium Atom and Dimer

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect.

Pendular alignment and strong chemical binding are induced in helium dimer molecules by intense laser fields

Intense pulsed-laser fields have provided means to both induce spatial alignment of molecules and enhance strength of chemical bonds. The duration of the laser field typically ranges from hundreds of picoseconds to a few femtoseconds. Accordingly, the induced "laser-dressed" properties can be adiabatic, existing only during the pulse, or nonadiabatic, persisting into the subsequent field-free domain. We exemplify these aspects by treating the helium dimer, in its ground [Formula: see text] and first excited [Formula: see text] electronic states. The ground-state dimer when field-free is barely bound, so very responsive to electric fields. We examine two laser realms, designated (I) "intrusive" and (II) "impelling." I employs intense nonresonant laser fields, not strong enough to dislodge electrons, yet interact with the dimer polarizability to induce binding and pendular states in which the dimer axis librates about the electric field direction. II employs superintense high-frequency fields that impel the electrons to undergo quiver oscillations, which interact with the intrinsic Coulomb forces to form an effective binding potential. The dimer bond then becomes much stronger. For I, we map laser-induced pendular alignment within the X state, which is absent for the field-free dimer. For II, we evaluate vibronic transitions from the X to A states, governed by the amplitude of the quiver oscillations.

Single photon double ionization of the helium dimer

We show that a single photon can ionize the two helium atoms of the helium dimer in a distance up to 10 A. The energy sharing among the electrons, the angular distributions of the ions and electrons, as well as comparison with electron impact data for helium atoms suggest a knockoff type double ionization process. The Coulomb explosion imaging of He2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing molecules.

Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data

Symmetry-adapted perturbation theory (SAPT) was applied to the helium dimer for interatomic separations R from 3 to 12 bohrs. The first-order interaction energy and the bulk of the second-order contribution were obtained using Gaussian geminal basis sets and are converged to about 0.1 mK near the minimum and for larger R. The remaining second-order contributions available in the SAPT suite of codes were computed using very large orbital basis sets, up to septuple-zeta quality, augmented by diffuse and midbond functions. The accuracy reached at this level was better than 1 mK in the same region. All the remaining components of the interaction energy were computed using the full configuration interaction method in bases up to sextuple-zeta quality. The latter components, although contributing only 1% near the minimum, have the largest uncertainty of about 10 mK in this region. The total interaction energy at R=5.6 bohrs is -11.000+/-0.011 K. For R< or =6.5 bohrs, the supermolecular (SM) interaction energies computed by us recently turned out to be slightly more accurate. Therefore, we have combined the SM results for R< or =6.5 bohrs with the SAPT results from 7.0 to 12 bohrs to fit analytic functions for the potential and for its error bars. The potential fit uses the best available van der Waals constants C(6) through C(16), including C(11), C(13), and C(15), and is believed to be the best current representation of the Born-Oppenheimer (BO) potential for helium. Using these fits, we found that the BO potential for the helium dimer exhibits the well depth D(e)=11.006+/-0.004 K, the equilibrium distance R(e)=5.608+/-0.012 bohrs, and supports one bound state for (4)He(2) with the dissociation energy D(0)=1.73+/-0.04 mK, and the average interatomic separation R=45.6+/-0.5 A.

Relativistic correction to the helium dimer interaction energy

The lowest-order relativistic correction to the helium-helium interaction energy has been calculated for the first time, using two independent methods based on expansions in explicitly correlated Gaussian functions. At the equilibrium interatomic distance of 5.6 bohr, this correction amounts to +15.4 +/- 0.6 mK. As a by-product, a new upper bound of -10.9985 K for the nonrelativistic Born-Oppenheimer interaction energy has been obtained.

On the acceleration of the convergence of singular operators in Gaussian basis sets

Gaussian type wave functions do not reproduce the interparticle cusps which result in a slow convergence of the expectation values of the operators involved in calculations of the relativistic and QED energy corrections. Methods correcting this deficiency are the main topic discussed in this paper. Benchmark expectation values of the singular operators for several few-electron systems are presented.