Multi-reference approaches

We anticipate that continued development of minimalist models, in conjunction with more efficient multi-reference approaches and a wider array of benchmark curves, will result in a better understanding of the theoretical challenges of bond breaking processes and increased ability of electronic structure theory to model them. 

The effects of intruder states are generally more severe for molecules than for atoms, due to more dense energy levels. Therefore, even if there are ways of avoiding - or at least reducing - the effect of intruder states in the multi-reference approach, it is when the interest lies entirely in one or a few particular states, more advantageous to study one state at a time in a state-specific approach. 

The S-T splitting is obtained as a difference of the two separate individual energy calculations for the singlet and triplet. Those individual singlet and triplet calculations do not necessarily have to be by the same method, and in fact, the majority of the results in Table 1 use composite methods in which the singlet and triplet are treated by two different methods (primarily the singlet as a MR state while the triplet is SR). RMR indicates the reduced multi-reference approach of Li and Paldus [58]. The TD-CCSD of Baikova and Bartlett [54], an early SU-CCSD application, provides two roots simultaneously at each geometry. This SU-CCSD calculation introduced GVB CCSD as a two-determinant reference. The MR-BW is a state-specific MR... 

Lastly, the SF approach implemented within the time-dependent. (TD) density functional theory (DFT) extends DFT to multi-reference situations with no cost increase relative to the non-SF TD-DFT. Similarly to DFT and TD-DFT, the SF-DFT model (27) is formally exact and therefore will yield exact answers with the exact density functional. With the available inexact ftmctionals, the SF-DFT represents an improvement over its non-SF counterparts. It has been shown to yield accurate equilibrium properties and singlet-triplet energy gaps in diradicals (27). 

Configuration interaction treatments can also be easily extended to multideterminant problems but these require even more care and an exorbitant computational effort [15]. Multi-reference Cl approaches are ideally suited to determining, for example, electronic spectra, as they can deal with excited states in a straightforward fashion [16]. 

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