as the test function. The variational energy of the product is given by equation ( ) with modifications (18). Note that, if the GS product is not an eigenstate of Ŝ2 , it should be spin-adapted before being used as the test function. In this case, the spin-adapted GS product is a linear combination of several ESDs, and hence its variational energy will be a linear combination of matrix elements that can be calculated using the ECI formulas.