Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins.

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.