Exploration of interlacing and avoided crossings in a manifold of potential energy surfaces by a Unitary Group Adapted State Specific Multi-Reference Perturbation Theory (UGA-SSMRPT).

The Unitary Group adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT) developed by Mukherjee et al has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving and size-consistent manner. The theory belongs to a suite of Unitary Group Adapted SS-MR theories developed by the group, starting with coupled cluster (CC) and then it's second order PT (UGA-SSMRPT2) which possesses all of the desirable features of generating a manifold of PES of same or different spatial symmetries. However, they lack invariance with respect to transformation of orbitals in the active space. UGA-SSMRPT2 displays remarkable predictability, yet being computationally much cheaper than it's CC counterpart. It is not immediately obvious how a state-specific theory, generating successively higher-lying PES one at a time, would retain sufficiently accurate information of other close lying PES of the same symmetry to demonstrate interlacing of the PES and also of the possible strong/weak avoided crossings. In state-specific formalism, since each state is an eigenstate of its own effective operator, to include the information of the other states require the theory to be sufficiently accurate. We present here the results for a variety of electronic states of a set of molecules in their various spin multiplicities which display the striking accuracy of UGA-SSMRPT2 for all the states studied by us. Accuracy of our results has been benchmarked against IC-MRCISD+Q. This bolsters our belief in the intrinsic accuracy of the formalism in sensing the interactions of the PES of same symmetry. The validation of the sufficiency we had used in our theory, which had helped us bypass the projection of our equations by strictly orthogonal excited functions, has also been demonstrated.