KS meaning in Academic & Science ?

Answer:

What is Kohn-Sham mean?

In physics and quantum chemistry, specifically density functional theory, the Kohn–Sham equation is the one-electron Schrödinger equation (more clearly, Schrödinger-like equation) of a fictitious system (the "Kohn–Sham system") of non-interacting particles (typically electrons) that generate the same density as any given system of interacting particles. The Kohn–Sham equation is defined by a local effective (fictitious) external potential in which the non-interacting particles move, typically denoted as vs(r) or veff(r), called the Kohn–Sham potential. As the particles in the Kohn–Sham system are non-interacting fermions, the Kohn–Sham wavefunction is a single Slater determinant constructed from a set of orbitals that are the lowest-energy solutions to

( − ℏ 2 2 m ∇ 2 + v eff ( r ) ) φ i ( r ) = ε i φ i ( r ) . {\displaystyle \left(-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}+v_{\text{eff}}(\mathbf {r} )\right)\varphi _{i}(\mathbf {r} )=\varepsilon _{i}\varphi _{i}(\mathbf {r} ).}

This eigenvalue equation is the typical representation of the Kohn–Sham equations. Here εi is the orbital energy of the corresponding Kohn–Sham orbital φ i {\displaystyle \varphi _{i}} , and the density for an N-particle system is

ρ ( r ) = ∑ i N | φ i reference

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