Then 𝜌𝜌 � 𝑎𝑎 (𝐫𝐫) is defined according to eq 9 using the newly defined 𝜌𝜌 � 𝑏𝑏 (𝐫𝐫). Note that eq 10 can be expanded in a series by Equation 11 agrees with eq 9 through the leading two terms in a Taylor series of the exponential, but it has continuous derivatives and is always non-negative; this is the motivation for using eq 10.