Implementation of the CCSD(T)-F12 method using cusp conditions

A new united atom perturbation theory of the interaction of two atoms at small separations is described. The key feature is a similarity transformation of the Schrödinger equation which enables the cusp conditions to be satisfied at both nuclei and preserves the correct molecular symmetry. The first-order theory is examined in detail and compared with other united atom theories. Numerical calculations are presented for the ground states of the systems H + 2 , HeH 2+ HeH, He 2 and Li + He, based mainly on Hartree-Fock wavefunctions for the united atoms, and are compared with accurate molecular calculations. The agreement is remarkably good for separations up to 1 bohr.

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CUSP conditions in extended SCF methods

Chemical Physics Letters ◽

10.1016/0009-2614(72)87008-8 ◽

1972 ◽

Vol 15 (1) ◽

pp. 31-33 ◽

Cited By ~ 9

Author(s):

Sten Lunell

Keyword(s):

Cusp Conditions

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Polarizabilities and other properties of the tdµ molecular ion

Canadian Journal of Physics ◽

10.1139/p01-075 ◽

2001 ◽

Vol 79 (9) ◽

pp. 1149-1158

Author(s):

A K Bhatia ◽

R J Drachman

Keyword(s):

Energy Levels ◽

Molecular Ions ◽

Muon Catalyzed Fusion ◽

Oppenheimer Approximation ◽

Good Energy ◽

Cusp Conditions ◽

Fermi Contact ◽

Muonic System ◽

Three Body ◽

Contact Parameters

Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+, and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the BornOppenheimer approximation. We tried the same approach in a muonic system, tdµ (triton, deuteron, and muon). Improved convergence was obtained for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the two lowest J = 0 and 1 states and compared them with the best earlier calculations. Expectation values were obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with tdµ acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results. PACS Nos.: 30.00, 36.10-k, 02.70-c

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Incorporation of Threshold Phenomena in Three-body Coulomb Continuum Wavefunctions

Australian Journal of Physics ◽

10.1071/ph961095 ◽

1996 ◽

Vol 49 (6) ◽

pp. 1095 ◽

Cited By ~ 13

Author(s):

Jamal Berakdar

Keyword(s):

Spin Asymmetry ◽

Excess Energy ◽

Absolute Value ◽

Threshold Phenomena ◽

Cusp Conditions ◽

Wannier Threshold ◽

Coulomb Boundary Conditions ◽

Three Body ◽

Energy Sharing ◽

First Time

In this work a three-body Coulomb wavefunction for the description of two continuum electrons moving in the field of a nucleus is constructed such that the Wannier threshold law for double escape is reproduced and the asymptotic Coulomb boundary conditions as well as the Kato cusp conditions are satisfied. It is shown that the absolute value of the total cross section, as well as the spin asymmetry, are well described by the present approach. Further, the excess-energy sharing between the two escaping electrons is calculated and analysed in light of the Wannier theory predictions. This is the first time an analytical three-body wavefunction is presented which is asymptotically exact and capable of describing threshold phenomena.

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