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The free complement (FC) theory accurately calculates Li atom properties by solving the scaled Schrödinger equation (SSE). This method provides exact solutions for wave functions, energies, and densities, validating the FC theory for atomic systems.

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Area of Science:

  • Quantum Chemistry
  • Atomic Physics
  • Computational Chemistry

Background:

  • The Schrödinger equation (SE) presents divergence challenges in variational calculations.
  • Accurate atomic property calculations require precise wave functions and energies.
  • The Li atom, a three-electron system, serves as a benchmark for theoretical methods.

Purpose of the Study:

  • To apply the free complement (FC) theory to solve the scaled Schrödinger equation (SSE) for the Li atom.
  • To calculate exact wave functions, energies, and properties of the Li atom's ground and excited states.
  • To validate the efficacy of the FC theory in obtaining exact solutions for atomic systems.

Main Methods:

  • Utilized the free complement (FC) theory to solve the scaled Schrödinger equation (SSE).
  • Employed a "correct" scaling function g = 1 - exp(-γr) for variational calculations.
  • Performed calculations to the eighth order of the FC theory for high accuracy.

Main Results:

  • Obtained essentially exact solutions for the SSE, equivalent to the SE.
  • Calculated exact energy, spin density, electron density, and cusp values for Li atom's doublet S and P states.
  • Results showed excellent agreement with experimental and established theoretical values.

Conclusions:

  • The free complement (FC) theory provides an effective and exact method for solving the scaled Schrödinger equation (SSE).
  • The chosen "correct" scaling function is crucial for achieving accurate results.
  • This study demonstrates the power of exact theories in yielding precise solutions for atomic structure and properties.