In this talk I will start with a sketch of a general perspective on theory as used in molecular science. I will then focus on the finite basis, second quantized representation of the Hamiltonian and describe a fairly general recipe to obtain efficient approaches to obtain a large number of electronic states at a fair level of accuracy, which has been a focal point of my research for many years. This requires i) a model space that targets the states of interest, ii) identification of the second quantized elements in the Hamiltonian that excite out of the model space, iii) the solution of amplitudes that define a corresponding many-body similarity transform of the Hamiltonian, using a normal ordered exponential transformation, iv) the diagonalization of a (non-Hermitean) transformed Hamiltonian over a compact subspace.
For single reference problems, with a well-behaved Hartree-Fock ground state, the approach results in the so-called Similarity Transformed Equation of Motion Coupled Cluster approach, STEOM-CC, while for multireference problems the method is referred to as multireference EOMCC, MR-EOMCC. These methods are readily available in the ORCA suite of electronic structure programs.
In the final part of the talk I will discuss generalizations of normal ordered exponential approaches to the direct calculation of thermal (electronic) properties and time-correlation functions in vibronic spectroscopy. The focus of the talk will be conceptual / theoretical with only a few examples to illustrate methodologies.