This talk will discuss the problem of reducing the complexity of the many-electron problem, focusing on applications to bond-breaking reactions, spin states, and excited states of molecules with near-degenerate electronic structures. Starting from the similarity renormalization group (SRG)—a many-body formalism to diagonalize operators using a series of infinitesimal unitary transformations—we will motivate the development of the driven SRG, an integral version of the SRG. Because of its renormalization group structure, the DSRG naturally avoids divergences due to small energy denominators characteristic of perturbative approaches. Several examples will be used to illustrate how the DSRG provides a convenient framework to derive numerically-robust electronic structure theories with electron correlation treated perturbatively or at a level comparable to that of nonperturbative many-body methods.
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