Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Abstract

Articles you may be interested inAlthough it was proposed some time ago that ͑hyper͒polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two-and three-electron terms for ␤, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, ͑1͒ , and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.

The Role of Hydrogen Bond in Designing Molecular Optical Materials

“…However, application of this method to organic non-linear optical materials revealed that many components of α and β tensors, calculated from X-ray diffraction, differ by more than an order of magnitude from theoretical results. 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.…”

Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

“…However, as already observed by Jayatilaka and co-workers Whitten et al, 2006;Jayatilaka et al, 2009;Hudá k et al, 2010), the convergence towards the desired agreement is not always fast and straightforward. In order to avoid large values of producing only minimal improvements in the 2 statistics and large unphysical changes of the energy, the following termination criteria have recently been proposed (Genoni, 2013b):…”

“…Therefore, for a definitive and fair comparison with the traditional multipole models, we should push the X-ray constrained computations beyond the usual 2 ¼ 1:0 limit (namely, we should consider larger ). Whitten et al (2006) have proposed pursuing the fitting until the weighted residual wR values approach those obtained in the multipole refinement of the same X-ray structure-factor magnitudes. This idea could be reformulated using 2 as a criterion, but, unfortunately, this is partially hampered by the problem of determining the optimal value for the Lagrange multiplier (see final discussion in x3.2).…”

Electron density building block approach for metal organic frameworks

“…A correction is necessary, however, in order to include the long range effects of a periodic distribution of polarizable building blocks, as suggested by Dunmur [48] and adopted by Spackman et al [49]. This means that each BB polarizability should be corrected for the apparent enhancement, caused by the electric field of the induced dipole moments of all other building blocks in the crystal.…”