X-ray restrained extremely localized molecular orbitals for the embedding of quantum mechanical calculations

The X-ray restrained wavefunction (XRW) method is a quantum crystallographic technique that allows the calculation of molecular wavefunctions adapted to minimize the difference between computed and reference structure factor amplitudes. The latter result from experimental measurements on crystals or from advanced theoretical calculations with periodic boundary conditions, and are used as external restraints in a traditional least-squares structural refinement. Detailed investigations have shown that the technique is able to reliably capture the effects of the crystal field on the molecular electron density. In a recent application, electron distributions obtained from preliminary X-ray restrained wavefunction calculations have been employed in the framework of frozen density embedding theory to embed excited state computations of well defined subsystems. Inspired by these results, it was decided to test, for the first time, the X-ray restrained extremely localized molecular orbitals (XR-ELMOs) along with the recently developed quantum mechanics/extremely localized molecular orbital multiscale embedding approach. By exploiting XR-ELMOs obtained through XRW calculations that used structure factor amplitudes resulting from periodic ab initio computations, excited state calculations of acrylamide in an environment mimicking the one of the crystal structure were performed. In all these computations, the QM region coincides with the crystal asymmetric unit and the ELMO subsystem consisted of two other acrylamide molecules involved in direct hydrogen bonds with the reference unit. The shifts of the excitation energies with respect to the corresponding gas-phase values were evaluated as a function of different parameters on which the computations with XR-ELMOs depend. For instance, the dependence on the resolution of the sets of structure factors that were used to determine the embedding XR-ELMOs were assessed in particular. The results have shown that the use of XR-ELMOs slightly (but not negligibly) improves the description of excited states compared to the gas-phase ELMOs. Once again, these results demonstrate the efficiency of the XRW approach in incorporating environment effects into the calculated molecular orbitals and, hence, into the corresponding electron densities.