The STO-3G basis without orbital frozen is adopted in the simulations. The operator pool contains all spin-adapted single and double excitation operators which are from occupied to virtual orbitals. For example, LiH has 2 double occupied spatial orbitals and 4 virtual spatial orbitals, hence the spin-adapted single and double excitation operator pool of LiH contains 2 1 • 4 1 = 8 single excitation operators and 8 2 +8 = 36 double excitation operators, sum to 8 + 36 = 44 operators in the pool. All calculations are performed by a code based on SPOCK, which uses Openfermion-Psi4 for Jordan-Wigner transformation as well as all electron integral calculations, and Scipy package to implement the Broyden-Fletcher-Goldfarb-Shannon(BGFS) algorithm for parameter optimization with a convergence criterion of ϵ v = 10 -7 . In each AR iteration, the parameters are initialized with the values obtained in the previous AR iteration, to make sure they are following descending order. In contrast, in each adaptive iteration, all the initial parameters are set to be zero.