The operator ∇ 2k : W 2k,1 R 3 -→ L 1 R 3 used in Equations 13a and 13b is shorthand notation for applying the Laplacian operator k consecutive times, thus, if k = 0 the operand is unchanged. Restricting each term of our functional in Equation 13a to even numbered consecutive applications of the Laplace operator guarantees (as can be seen from integration by parts) that interchanging the labels of ρ A and ρ B does not alter the result of the integral: XC