Low-lying excited states of linear all-<i>trans</i> polyenes: the σ–π electron correlation and the description of ionic states

In this work, the electronic spectra of all-<i>trans</i> polyenes, from hexatriene to dodecahexaene are investigated. Special attention is given to the challenging description of the ionic 1¹B+u state. A comprehensive wavefunction analysis of both singlet (2¹A-g, 1¹B+u, and 2¹B-u) and triplet excited states (1³A-g and 1³B-u) is performed using a range of multireference correlated methods, including multireference configuration interaction with singles and doubles (MR-CISD) including <i>a posteriori</i> size-extensivity Pople correction (+P), and the multireference averaged quadratic coupled-cluster (MR-AQCC) method. While covalent states are well described by multi-configurational self-consistent field (MCSCF) theory, accurately describing the ionic state requires addressing size-extensivity errors, basis set effects, and, most importantly, σ-π electron correlation. Taking these factors into account, MR-CISD+P and MR-AQCC results mutually corroborate that the ionic 1¹B+u state is the first vertically excited state in hexatriene and octatetraene. In decapentaene, extrapolated MR-CISD+P results indicate that the 2¹A-g and 1¹B+u states are nearly degenerate, while MR-AQCC suggests that the ionic state lies approximately 0.2 eV below the covalent state. From a wavefunction perspective, the ionic state is consistently well-represented by a single HOMO-LUMO excitation, whereas the contribution of doubly excited configurations increases with chain length for both covalent states.