where the trace Tr S in Eq. 35a is performed along the system DOF (which is the reaction coordinate R for the model considered here). In Eq. 35, ĥ = h( R -R ‡ ) is the Heaviside operator that projects onto the product states, where h(R) = 1 for R > R ‡ (in the product region) and h(R) = 0 for R < R ‡ (in the reaction region), R ‡ is the dividing surface. For the symmetric DW model considered here, we use R ‡ = 0. Under the system's eigen-representation {|ν i } in the truncated Fdimensional Hilbert subspace, it can be evaluated as