Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
J Chem Phys. 2013 Aug 14;139(6):064108. doi: 10.1063/1.4817662.
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.
新一代光学材料的合理设计需要了解分子结构与材料固态光学性质之间的联系。一个基本的挑战是利用 X 射线衍射提供的精确结构信息来解释晶体的性质。多年来，多极精修一直是将高分辨率 X 射线衍射数据集转换为晶体材料详细电子密度分布的主力技术。然而，仅电子密度对于可靠地计算材料的非线性光学性质是不够的。最近，X 射线约束波函数精修已成为多极精修的可行替代方法，具有多种潜在优势，包括计算广泛的物理性质和用物理上合理的起点播种精修过程。在这项研究中，我们将多极精修和 X 射线约束波函数技术应用于四个具有有前途的非线性光学性质和不同结构基序的分子。一般来说，两种技术都获得了可比的优值，并生成了大致相似的电子密度，证明了 X 射线约束波函数方法的广泛适用性。然而，两种技术生成的电子密度之间存在一些系统差异。重要的是，我们发现使用 X 射线约束波函数方法生成的电子密度取决于核的精确位置。当使用基于 Hartree-Fock 的 Hirshfeld 原子精修的坐标而不是多极精修的坐标时，X 射线约束波函数精修对波函数的变化较小，这表明 Hirshfeld 原子精修的坐标允许 X 射线约束波函数方法生成更准确的波函数。然后，我们使用实验得出的波函数来计算分子偶极矩、极化率、超极化率和折射率，并表明这些值与使用从头算方法计算的值吻合良好。因此，本研究表明，可以从 X 射线衍射数据集可靠地生成实验波函数，并且可以从这些波函数可靠地计算光学性质。通过 X 射线约束波函数精修的实验和计算的协同作用，有望实现定制下一代光学材料的分子工程。
