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How to calculate an atoms ionization energy? 

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To calculate an atom's ionization energy, various methods and models can be employed. One approach involves using empirical equations and corrections for relativistic and Lamb shift effects to estimate ionization energies with excellent agreement with literature values . Another method involves implementing the GW approximation, which considers the highest occupied molecular orbital energies of atoms to provide accurate estimates of ionization energy, especially when using the total energy differences within the random phase approximation functional . Additionally, a simplified atomic geometrical model has been proposed to estimate inter-electronic repulsion in multi-electronic atoms, with modifications suggested to improve ionization energies while maintaining good agreement with experimental and theoretical calculations for total energies . Another technique involves parameter scaling of nuclear and electronic charges to calculate ionization energies of atoms and ions, adjusting coefficients to optimize energy differences based on experimental values .

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To calculate an atom's ionization energy, use a simple equation proposed by Lang and Smith, which considers potential energy and electron relaxation transition for accurate results.
To calculate an atom's ionization energy, use complex kinetic energy expressions with corrections for relativity and Lamb shift effects, or substitute coefficients into simple quadratic equations for multielectron ions.
Ionization energy of atoms can be calculated using GW approximation, specifically through total energy differences within the random phase approximation functional corresponding to the GW self-energy.
The paper proposes a simple atomic model to estimate ionization energies. It suggests modifications for alkali metals and alkaline earths to enhance accuracy while maintaining good agreement with experimental and theoretical values.

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