Constrained LDFT To stabilize a nucleus,we introduced a suitable constraint in the framework of the LDFT Volume constraint E=2+2'=kT>[e,In p:+(1-p.)In(1-p.)] 0, P,∈vapor -号∑∑Pp,+∑AA-+g-Σx1-们 p,∈liquid Surface constraint E=2+2'=kT∑[p,lnp,+(I-p)ln(l-p】 [0. P,∈vapO -受∑∑P.P+∑A(-)+N-∑】= P,∈surface 0, p,∈liquid Men,Zhang and Wang,Phys.Rev.E 2009,79,051602Constrained LDFT • To stabilize a nucleus, we introduced a suitable constraint in the framework of the LDFT – Volume constraint – Surface constraint ( ) [ ] 2 [ ln (1 )ln(1 )] i i 0 i i i i a i i a ff i i i i i ∑ ∑ ∑ ∑ ∑ − + − + − = Ω + Ω′ = + − − ρ ρ + ρ φ µ κ χ ε ρ ρ ρ ρ N L E kT ( ) [ ] 2 [ ln (1 )ln(1 )] i Si 0 i i i i a i i a ff i i i i i ∑ ∑ ∑ ∑ ∑ − + − + − = Ω + Ω′ = + − − ρ ρ + ρ φ µ κ χ ε ρ ρ ρ ρ Ns E kT liquid vapor i i i ∈ ∈ ⎩ ⎨ ⎧ = ρ ρ χ , , 1 0 liquid surface vapor i i i Si ∈ ∈ ∈ ⎪ ⎩ ⎪ ⎨ ⎧ = ρ ρ ρ χ 0, 1, 0, Men, Zhang and Wang, Phys. Rev. E 2009, 79, 051602