Long-range interactions and the sign of natural amplitudes in two-electron systems.

@article{Giesbertz2013LongrangeIA,
  title={Long-range interactions and the sign of natural amplitudes in two-electron systems.},
  author={Klaas J. H. Giesbertz and Robert van Leeuwen},
  journal={The Journal of chemical physics},
  year={2013},
  volume={139 10},
  pages={
          104110
        }
}
In singlet two-electron systems, the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work, we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical… 

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References

SHOWING 1-10 OF 47 REFERENCES

Natural occupation numbers: when do they vanish?

It is shown that for a two-particle system of harmonically confined electrons with a Coulombic interaction the natural orbital occupations never vanish, and a more general criterium for the non-vanishing of NO occupations for two- particle wavefunctions with a certain separability structure is derived.

An approximate exchange-correlation hole density as a functional of the natural orbitals

The Fermi and Coulomb holes that can be used to describe the physics of electron correlation are calculated and analysed for a number of typical cases, ranging from prototype dynamical correlation to

Double ionization of a two-electron system in the time- dependent extended Hartree-Fock approximation

The dynamics of a two-electron system in a strong laser pulse is described by the time-dependent extended Hartree-Fock ~TDEHF! scheme. Ionization yields for a one-dimensional helium model are

Long‐range behavior of natural orbitals and electron density

Given an exact eigenfunction ψ for some system with N electrons, a procedure is developed for determining ionization potentials of the system to various states of the corresponding system having N−p

Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction

In order to calculate the average value of a physical quantity containing also many-particle interactions in a system of $N$ antisymmetric particles, a set of generalized density matrices are

EFFECT OF ELECTRON CORRELATION ON THE TWO-PARTICLE DYNAMICS OF A HELIUM ATOM IN A STRONG LASER PULSE

This review discusses the complicated two-electron dynamics of a helium atom in an intense, short laser pulse. A helium gas in femtosecond laser pulses at long wave lengths (lambda similar to 700 nm)

Generalized overlap amplitudes using the extended Koopmans’ theorem for Be

Approximate generalized overlap amplitudes (GOAs), also called Feynman–Dyson amplitudes, have been calculated from a full configuration interaction (CI) wave function for the ground state of

The ground state of harmonium

A detailed analysis that benefits from a slate of new approximate numerical and exact asymptotic results produces highly accurate properties of the ground state of the harmonium atom as functions of

Short-range correlations and the structure factor and momentum distribution of electrons

It is shown that for any system of non-relativistic electrons and nuclei the large-wavevector limit of the probability of finding an electron with momentum h(cross)k is proportional to 1/k8, and the

Natural Orbital Functional Theory

One of the central problems of solid state physics and quantum chemistry is to find an accurate and computationally affordable method for the description of electronic correlation that can be applied to large systems, particularly those with deep core electrons.