In this approach, the target state natural orbitals are generated by diagonalizing the virtual-virtual block of a second-order approximate one-particle reduced density matrix of the target states. D is the virtual-virtual block of MP2 one-particle reduced density matrix and k ab D is the one- particle reduced density matrix for k th ionized state calculated at ADC (2) level. The second-order algebraic diagrammatic construction (ADC (2)) theory, the ionization energy is calculated by diagonalization of the following Hermitian Jacobian ( )