Symmetry Dilemma of Doubly Hybrid Density Functionals for Equilibrium Molecular Property Calculations

In electronic structure theory, when an approximate wavefunction tends to artifactually break the symmetry of the exact Hamiltonian, the corresponding method is referred to as having a "symmetry dilemma" problem. Such types of artifacts were often reported when Hartree-Fock (HF) and the low-level post-HF methods were used, while the traditional Kohn-Sham density functional theory (KS-DFT) methods were usually found to be more resistant to this breakdown. In this work, we present a systematic study on the reliability of the doubly hybrid (DH) DFT methods for several violable cases. Almost all the commonly used B2PLYP-type (bDH) functionals are shown to have a severe "symmetry dilemma" problem and yield dramatically unreliable molecular properties, such as dipole moment, vibrational frequency, and static polarizability at the equilibrium geometry. A one-parameter bDH functional model study demonstrates that such a problem is a combined effect of the inappropriate portion of the HF exchange (over 50%) for the self-consistent field (SCF) calculation and the augmentation of the second-order perturbative contribution. It is remarkable that the XYG3-type (xDH) functionals show a good capability to resist the artifactual symmetry breaking and yield reliable molecular properties when the same critical cases are calculated. In the xDH, there are two functionals of different purposes, namely, the SCF functional and the energy functional, which have different amounts of the HF exchange and different portions of the correlation contributions. The success of the xDHs can be attributed to this flexibility in xDH construction to avoid using an improperly large portion of the HF exchange in the SCF functional. The insights gained in this work are of significance for the development of an improved DH functional.