VMC Parameters
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Jastrow Factor Physics
Jastrow wavefunction:
Ψ_J = exp(-½Σᵢ
u(r) = a·r/(1+b·r) (Padé form)
Metropolis sampling: Propose x→x', accept with probability min(1, |Ψ(x')|²/|Ψ(x)|²). Samples the exact wavefunction density.
Local energy: E_L(R) = Ψ⁻¹HΨ. VMC energy ⟨E⟩ = ∫|Ψ|² E_L dR / ∫|Ψ|²dR. Variance decreases when Ψ → exact eigenstate.
Pair correlation g(r): Measures how electrons avoid each other. Jastrow creates a correlation hole at r→0 (exchange-correlation).
Ψ_J = exp(-½Σᵢ
Metropolis sampling: Propose x→x', accept with probability min(1, |Ψ(x')|²/|Ψ(x)|²). Samples the exact wavefunction density.
Local energy: E_L(R) = Ψ⁻¹HΨ. VMC energy ⟨E⟩ = ∫|Ψ|² E_L dR / ∫|Ψ|²dR. Variance decreases when Ψ → exact eigenstate.
Pair correlation g(r): Measures how electrons avoid each other. Jastrow creates a correlation hole at r→0 (exchange-correlation).