A recent JACS paper Mechanism for Singlet Fission in Pentacene and Tetracene: From Single Exciton to Two Triplets from Martin Head-Gordon's group is not as transparent as it could be about whether it is ab initio. It states
The originally proposed mechanism for SF [Singlet Fission] is based on model Hamiltonians that couple of monomer states between adjacent molecules. The low coupling in the model between the single-exciton and ME states requires that a CT state be invoked as an intermediate (i.e., an indirect mechanism). This requires the assumption that the CT state is relatively low in energy and thus energetically accessible. Herein, systematic ab initio study of the low-lying excited states in tetracene and pentacene provides an alternative mechanism for the photophysics of these materials. This study provides evidence that CT states need not be directly relevant to SF in acenes.
Because these ab initio simulations capture the correlation of many electrons, they are distinct from model Hamiltonian studies (for instance ref 22). The current understanding of SF comes from model Hamiltonians, where certain electronic states of two monomers are employed as basis sets. While model Hamiltonian studies can yield deep insights into complex physical processes such as SF [Singlet Fission], these invariably require assumptions about the physics which are embedded as model parameters. By contrast, ab initio calculations in principle allow the essential features to emerge directly from simulations....However, if one looks at the Computational Details section of the paper (which comes after the Conclusion) one finds the statement.
One deficiency of CASSCF and RAS-2SF theories is the overestimation of excitation energies due to the limited degree of dynamic correlation. To overcome this difficulty, we shift the excitation energies of T1 and S1 at the equilibrium geometry to the experimental values for the acene crystals.Surely, this fitting to experiment [of two key observables] undermines the authors claim to be doing ab initio calculations or to be superior to model calculations. Furthermore, most of the calculations in the paper involve a small number of molecules, which is surely a model for the infinite solid, in which significant screening effects may be present. Arguably, ignoring this is comparable to the significant physical assumptions present in model calculations.