Analysis of crystal field effects and interactions using X-ray restrained ELMOs

Abstract

The purpose of this study is to assess the capability of X-ray restrained molecular wavefunction methods to reproduce the perturbation due to the crystal field. The effect of the crystal environment on the molecular charge densities has been thoroughly investigated experimentally and theoretically. However, the same analysis in terms of molecular orbitals is unprecedented. We specifically analysed the extremely localized molecular orbitals (ELMOs) because they allow for a valence bond like interpretation that is closer to the typical chemical reasoning. For a set of test molecules, we calculated first principles wavefunctions (called primary wavefunctions) and the corresponding scattered intensities (primary structure factors), that we afterwards used for X-ray restrained Hartree-Fock and ELMO calculations. This mimics the typical procedure of modelling wavefunctions from experimental X-ray diffraction, having the primary wavefunction as benchmark. This study follows a previous investigation concerning the effects of electron correlation, where it was shown that those subtle features could be retrieved only to a minor extent. The electric field generated by surrounding molecules is instead more substantial. Therefore, retrieving this information should be more successful and, in case, extremely useful for supramolecular chemistry and crystal engineering. The work also provides useful indications to experimentalists who want to exploit the potentialities offered by the X-ray restrained wavefunction methods.

HgH2meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

“…The option to study crystal field effects is also considered by Ernst et al (2020). These effects are found to be subtle, as shown previously by Bučinský et al (2019), but important (Ernst et al, 2020). This indicates the capability of XCW to transfer information from structure factors to the XC wavefunction (XC electron density).…”

“…In addition, it was shown that XCW is able to account for polarization effects from the crystal environment for the ammonia crystal test case (Bytheway et al, 2002a). The option to study crystal field effects is also considered by Ernst et al (2020). These effects are found to be subtle, as shown previously by Bučinský et al (2019), but important (Ernst et al, 2020).…”

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

“… 4 a/5 b,c: model P minus model G at the QM/MM‐optimized geometry of P ; 4 b/5 e,f: model C minus model G at the QM/MM‐optimized geometry of C ; 4 c/5 h,i: polarization of 1 with a cluster of Hirshfeld‐atom point charges and dipoles (model CC , cluster charges) minus model G at the experimental geometry from X‐ray diffraction; 4 d/5 k,l: effect of X‐ray constrained wavefunction fitting: [22, 28] X‐ray constrained model X minus model G at the experimental geometry from X‐ray diffraction. …”

“…4 d/5 k,l: effect of X‐ray constrained wavefunction fitting: [22, 28] X‐ray constrained model X minus model G at the experimental geometry from X‐ray diffraction.…”

“…[27] Only very recently,a na lternative approacht othe derivation of the interaction density was discussed, namely the comparison of the non-fitted and maximally fittedm olecular wavefunction according to the X-ray constrained wavefunction fitting technique. [28] The non-fitted wavefunctionp roduces the in vacuo electron density of the molecule under examination, whereas the fitted wavefunction includes the polarization of the molecule by the crystalline environmentv ia the measured X-ray structure factors. This new methodw as described mainly for an application to theoretically calculated X-ray structuref actors.…”