Modeling electron density distributions from X-ray diffraction to derive optical properties: Constrained wavefunction versus multipole refinement

Abstract

The rational design of next-generation optical materials requires an understanding of the connection between molecular structure and the solid-state optical properties of a material. A fundamental challenge is to utilize the accurate structural information provided by X-ray diffraction to explain the properties of a crystal. For years, the multipole refinement has been the workhorse technique for transforming high-resolution X-ray diffraction datasets into the detailed electron density distribution of crystalline material. However, the electron density alone is not sufficient for a reliable calculation of the nonlinear optical properties of a material. Recently, the X-ray constrained wavefunction refinement has emerged as a viable alternative to the multipole refinement, offering several potential advantages, including the calculation of a wide range of physical properties and seeding the refinement process with a physically reasonable starting point. In this study, we apply both the multipole refinement and the X-ray constrained wavefunction technique to four molecules with promising nonlinear optical properties and diverse structural motifs. In general, both techniques obtain comparable figures of merit and generate largely similar electron densities, demonstrating the wide applicability of the X-ray constrained wavefunction method. However, there are some systematic differences between the electron densities generated by each technique. Importantly, we find that the electron density generated using the X-ray constrained wavefunction method is dependent on the exact location of the nuclei. The X-ray constrained wavefunction refinement makes smaller changes to the wavefunction when coordinates from the Hartree-Fock-based Hirshfeld atom refinement are employed rather than coordinates from the multipole refinement, suggesting that coordinates from the Hirshfeld atom refinement allow the X-ray constrained wavefunction method to produce more accurate wavefunctions. We then use the experimentally derived wavefunctions to calculate the molecular dipole moment, polarizability, hyperpolarizability, and refractive index and show that these are in good agreement with the values calculated using ab initio methods. Thus, this study shows that experimental wavefunctions can be reliably generated from X-ray diffraction datasets, and that optical properties can be reliably calculated from these wavefunctions. Such a concerted interplay of experiment and computation via the X-ray constrained wavefunction refinement stands to enable the molecular engineering of tailor-made next-generation optical materials.

Electron Density Studies in Materials Research

“…Interesting tools for combining experimental and theoretical information exist, such as the XCW method, [106] which among other things hass hown promise in evaluating opticalp roperties of materials. [107,108] This is part of the emergentf ield of quantum crystallography, which in its original definition considers approaches, where theoretical information is used to enhance the information content in the diffractiond ata, for example,H irshfeld atom refinement, [120] or where experimental information is used to enhancet he information of the calculation, as in the XCW method. [121] In the contextr eviewed here, especially the XCW methodp rovides interesting perspectives for combining experimental and theoretical information for analysiso fc hemical bonding in materials, but severalc onceptual as well as technical difficulties exist for the techniques as describedi narecent review.…”

“…[107] Thisg ave rise to in-crystal dipole moments for small molecules in good agreement with much higher level MP2 calculations including ac rystal field, and refractivei ndices from the XCW method generally gave better agreement with experiment than molecular HF and MP2 calculations.T his shows that some information about the influence of the crystalline environment is available through the X-ray structure factors, which perturbs the molecular calculations to give betterr esultsf or crystalline properties.M ore recently,a lso hyperpolarizability tensors were derived based on the XCW methodf or four NLO materials, and agreement with theory was shown to be better than the ones based purely on the ground state ED. [105,108] Sincet hese tensorial components are not easily measureable, no comparison with other experiments could be made. In af ollow up study,t he same authors investigated zinc tris(thiourea)sulfate (ZTS) in more detail.…”

Quantum Crystallography: Current Developments and Future Perspectives

“…It was initially developed in the framework of the RestrictedH artree-Fock formalism [28,29,31] and was afterwards extended to othera pproaches (e.g.,D ensityF unctional Theory, [32] relativistic Hamiltonians, [33,34] ExtremelyL ocalized Molecular Orbitals (ELMOs), [35][36][37][38] etc.). Severali nvestigations have shown that XCW fitting allows not only to obtain reliable charge density distributions, but also to determine physical properties of materials [126][127][128][129] (e.g.,n on-linear opticalp roperties) and to consistently capture electronc orrelation, [130] polarization and crystal fielde ffects. Other ongoing studies also focus on the capability of the method in capturing relativistic effects [34] and in reliably determining experimental spin densities for interesting open-shell systems, such as the cyclic alkylaminocarbene radicalc AAC-SiCl 3 , [131] for which preliminaryr esults are available.…”

The Role of Hydrogen Bond in Designing Molecular Optical Materials

“…Indeed, it was later shown that the one-electron density ρprq, obtained from the usual multipolar pseudo-atom formalisms, does not yield accurate response properties because electronic correlation is included only partially [22]. Instead, Jayatilaka and Cole [23] have pursued an X-ray constrained wavefunction approach to derive much more accurate ρprq distributions for a few optical materials, including a metal-organic non-linear optical compound. The "experimental" wavefunctions yielded remarkably accurate electric properties, indicating the possibility to use X-ray constrained molecular orbitals for engineering this kind of materials.…”