# Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components

@article{Liverts2016TwoparticleAC, title={Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components}, author={Evgeny Z. Liverts}, journal={Physical Review A}, year={2016}, volume={94}, pages={022506} }

The exact values of the presently determined components 26of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in the hyperspherical angular coordinates, which follows from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The…

## 6 Citations

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The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius r, and angle θ characterizes their positions on sphere, are…

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## References

SHOWING 1-10 OF 21 REFERENCES

Boundary solutions of the two-electron Schrödinger equation at two-particle coalescences of the atomic systems

- Physics
- 2006

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate correlation function…

General coalescence conditions for the exact wave functions: higher-order relations for two-particle systems.

- PhysicsThe Journal of chemical physics
- 2013

The necessary conditions that the non-relativistic time-independent exact wave functions for two-particle systems must satisfy at a coalescence (or cusp) point are derived, calling them generalized coalescence conditions (GCCs).

Coordinate systems and analytic expansions for three-body atomic wavefunctions. I. Partial summation for the Fock expansion in hyperspherical coordinates

- Mathematics
- 1987

A survey of analytic techniques for solving the two-electron atomic Schrodinger equation is presented. The hyperspherical formalism is introduced and specialised to the case of two electrons and zero…

Coordinate systems and analytic expansions for three-body atomic wavefunctions. III. Derivative continuity via solutions to Laplace's equation

- Physics
- 1987

Terms in a few-particle wavefunction, written as an expansion of homogeneous functions, are derived by a method which resembles standard techniques for solving differential equations in one variable.…

Compact representation of helium wave functions in perimetric and hyperspherical coordinates

- Physics
- 2004

Variational calculations of the ground-state energy of helium are performed using a basis set representation that includes an explicit treatment of the Fock expansion in hyperspherical coordinates.…

Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r

- Physics
- 1987

For pt.I, see ibid., vol.20, no.8, p.2043-75 (1987). Several coordinate systems for solving the few-electron Schrodinger equation are presented. Formal solutions corresponding to each coordinate…

Convergence properties of Fock's expansion for S-state eigenfunctions of the helium atom

- Mathematics
- 1986

It is proved by functional analytic methods that for S-state solutions of Schrödinger's equation for the helium atom, Fock's expansion in powers of R1/2 and R ln R, where R is the hyperspherical…

Use of the Fock expansion for 1S-state wave functions of two-electron atoms and ions.

- PhysicsPhysical review. A, General physics
- 1985

The first numerical solution of the equations for the Fock coefficients is presented, and a general procedure for matching a linear combination of Fock-series solutions onto a basis of adiabatic hyperspherical functions at a matching radius is presented.

Impact of Electron-Electron Cusp on Configuration Interaction Energies

- Physics
- 2001

The effect of the electron–electron cusp on the convergence of configuration interaction (CI) wave functions is examined. By analogy with the pseudopotential approach for electron–ion interactions,…

Cusp constraints for atomic wavefunctions

- Physics
- 1970

A hierarchy of cusp constraints, from necessary to sufficient, is examined. A flexible approach of cusp-satisfying orbitals is proposed. This is tested on some simple wavefunctions for the ground…