Abstract
<jats:p>Complete active space reduced density matrix theory (CASRDM) is presented in this work. A novel reconstruction of the two-electron reduced density matrix (2-RDM) is proposed via the anti-symmetrical variable dpq. Subject to the normalization constraint of dpq, variational minimization of total electronic energy at the ground state with respect to dpq leads to a standard eigenvalue problem with dpq as an eigenvector. Thus, solving the eigenvalue problem provides a direct way to calculate the 2-RDM and the electronic energy. Under the N-representability conditions, the minimum energy of CASRDM is obtained by optimizing a few parameters of active orbitals in the modified one-electron Hartree-Fock reduced density matrices. The ground-state energies of closed-shell molecules (NH3, HF, N2, CO, BF, SiO, CS, and P2) and open-shell molecules (CH, OH, NO, NH, PH, PH2, ClO, NF, and S2) are calculated with CASRDM. It is demonstrated that CASRDM energies of closed-shell molecules are in close agreement with complete active space configuration interaction (CASCI) values. No variational energy collapse is observed in all CASRDM calculations. The CASRDM method is further employed to calculate the spectroscopic constants of singlet states (LiH, AlH, BH, and BF), doublet states (CH and MgH), and triplet states (NH and PH), as well as the electronic affinities (EAs) of Br and SeH. These results are compared with experiments and with those from Hartree-Fock, MP2, MP3, CCSD, CCSD(T), and CASCI. This study indicates the reliability and high accuracy of CASRDM in calculating electronic structure properties at a low computational cost.</jats:p>