Molecular origins of nonlinear optical activity in zinc tris(thiourea)sulfate revealed by high-resolution x-ray diffraction data and<i>ab initio</i>calculations

Structure-property relationships are established in the nonlinear optical (NLO) material, zinc tris(thiourea)sulfate (ZTS), via an experimental charge-density study, x-ray constrained wave-function refinement, and quantum-mechanical calculations. The molecular charge-transfer characteristics of ZTS, that are important for NLO activity, are topologically analyzed via a multipolar refinement of high-resolution x-ray diffraction data, which is supported by neutron diffraction measurements. The extent to which each chemical bond is ionic or covalent in nature is categorized by Laplacian-based bonding classifiers of the electron density; these include bond ellipticities, energy densities, and the local source function. Correspondingly, the NLO origins of ZTS are judged to best resemble those of organic NLO materials. The molecular dipole moment, ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, and (hyper)polarizability coefficients, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$ and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, are calculated from the experimental diffraction data using the x-ray constrained wave-function method. Complementary gas-phase ab initio quantum-mechanical calculations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ offer a supporting comparison. When taken alone, the experimental charge-density analysis does not fare well in deriving ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, or ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, which is not entirely surprising given that the associated calculations are only generally valid for organic molecules. However, by refining the x-ray data within the constrained wave-function method, the evaluations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ are shown to agree very well with those from ab initio calculations and show remarkable normalization to experimental refractive index measurements. The small differences observed between ab initio and x-ray constrained wave-function refinement results can be related directly to gas- versus solid-state phase differences. ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$ is found to be 28.3 Debye (gas phase) and 29.7 Debye (solid state) while ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ coefficients are not only significant but are also markedly three dimensional in form. Accordingly, substantial octupolar as well as dipolar NLO contributions in ZTS are indicated, which challenges the traditional focus on dipolar NLO molecules. This evaluation of NLO properties and their relation to the molecular structure offers several ways by which ZTS may be more widely functionalized as a NLO material. More generally, this case study on ZTS demonstrates how experimental and computational techniques can be combined to understand NLO structure-property relationships, an important tool for the quantum-tailored molecular design of next-generation metalorganic NLO materials.

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