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Effective potential in density matrix functional theory.

A Nagy1, C Amovilli

  • 1Department of Theoretical Physics, University of Debrecen, and Atomic and Molecular Physics Research Group of the Hungarian Academy of Sciences, H-4010 Debrecen, Hungary.

The Journal of Chemical Physics
|October 12, 2004
PubMed
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This study reduces complex electron systems to a two-particle problem, simplifying calculations. An effective potential term of kinetic origin is analyzed, offering new approximation methods.

Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Many-body physics

Background:

  • The diagonal of the spin-independent second-order density matrix (n) is crucial for understanding electronic systems.
  • Previous work established that n can be found by solving a two-particle auxiliary equation for systems with an even number of electrons.

Purpose of the Study:

  • To analyze the properties of the effective potential in the reduced two-particle problem.
  • To derive and propose approximations for a kinetic-origin potential term, v(p).
  • To establish a connection between v(p) and the effective potential u(p) of the shape function equation.

Main Methods:

  • Solving a single auxiliary equation for a two-particle problem.
  • Deriving the virial theorem and a hierarchy of equations for v(p).

Related Experiment Videos

  • Developing simple approximation schemes for v(p).

    • Main Results:

    • The problem of arbitrary even-electron systems is successfully reduced to a two-particle problem.
    • An effective potential term, v(p), of purely kinetic origin was identified within the two-particle equation.
    • The virial theorem and hierarchy of equations for v(p) were derived, alongside proposed approximations.
    • A relationship between v(p) and the shape function effective potential u(p) was established.

    Conclusions:

    • The reduction to a two-particle problem provides a significant simplification for studying complex electronic systems.
    • The kinetic-origin potential v(p) and its properties are key to understanding the behavior of these systems.
    • The established relationship between v(p) and u(p) offers further avenues for theoretical development and approximation.