Periodically, there are milestone developments in a field that dramatically accelerate its progress. Such an advance in quantum chemistry is coupled-cluster theory and its equation-of-motion (EOM-CC) extensions. Today, these methods typically provide the best numerical treatment of the chemically essential electron correlation effects for the largest number of computationally accessible molecular problems. How and why did this occur?<br/>Prior to the dramatic transition (1972-1985) to ‘Many-body methods in quantum chemistry,’ i.e. CC/MBPT/EOM-CC, variational configuration interaction (CI) was the method of choice for the correlation problem. Variational methods that provide an upper bound to a given approximation differ from “Many-body” ones, in that the latter must scale appropriately with the size of a molecule and its number of electrons. This scaling also makes it possible to treat correlation in infinite systems like polymers and crystalline solids. This property is termed ‘size-extensivity’, now recognized as a critical property for quantum chemical methods. Variational methods like CI (short of full CI) do not have this property, causing their approximations for a comparable effort to be typically poorer than the CC ones. The power of CC methods is that they rapidly converge to the best possible ab initio result, the full CI, as the CCSD, CCSD, CCSDT, CCSDTQ sequence gets there far faster than the CI equivalents. The latter, single or multi-reference retain ‘unlinked-diagrams’ that the full CI would not have yet are only cancelled in the limit. These terms scale incorrectly with the number of electrons and are responsible for the variational upper bound in CI approximations and its poorer performance.<br/>This talk will communicate how many-body methods evolved to become the choice for the application of ab initio methods to molecular structure and spectra. This required new theory for analytical gradients, density matrices, and excited states, and computational implementations to solve the highly non-linear CC equations.<br/>Some new advances in our group will also be summarized: the robust treatment of ‘doubly’ excited ‘dark’ states in electronic spectra; the use of the CC response density matrix to quantify potential errors in single-reference CC/EOM-CC calculations; and the time propagation of EOM-CC dipole and quadrupole transitions to conveniently obtain electronic spectra from high-energy core excitations to low-lying valence states.

Coupled cluster revolution

ACS Fall 2021

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