can nonlinear optical properties be extracted from charge density analysis of x-ray diffraction data?

 

Mark Spackman,a Andrew Whittena and Dylan Jayatilakab

 

aChemistry, School of Biological, Biomedical and Molecular Sciences, University of New England, Armidale NSW 2351, Australia;  bChemistry, School of Biomedical & Chemical Sciences, University of Western Australia, Crawley WA 6009, Australia. (mspackma@une.edu.au)

 

 

In the mid-1990s it was proposed to derive the static polarisabilities a and b (and potentially, g) from the different multipolar moments of experimental determined charge distributions[1]. In the most recent work of this kind, static a and b tensors were derived for molecules of N-(4-nitrophenyl)-(L)-prolinol (NPP) in the single crystal.  However, the results obtained were not promising. We have re-examined the basic equations, and discovered that the expressions used by those workers were over-simplified.  To obtain meaningful information on response properties such as polarisabilities, the ground state one-electron distribution is insufficient. 

Virtually all quantitative charge density analyses of X-ray diffraction data employ the rigid pseudoatom model, where the electron density of the crystal is described by a multipole expansion about the atomic nuclei. This has become a straightforward procedure, but it results in only a one-electron density function. In 1998 Jayatilaka described a procedure for extracting "experimental wavefunctions" from X-ray diffraction data[2], which enables computation of the relevant two-electron expectation values and hence the possibility of obtaining meaningful estimates of the electronic part of in-crystal static molecular (hyper)polarisabilities.

We have begun investigating an approach based on that of Sylvain & Csizmadia[3], where the usual sum-over-states expression for the static dipole polarisability can be written in terms of expectation values of the ground state wavefunction,  

                                                     

where D is a mean excitation energy and  is the v-component of the dipole moment operator.  For a single-determinant wavefunction the dipole polarisability can then be expressed in the rather simple form

                                                                                  

where  represents a two-electron generalisation of the one-electron expectation values. The ultimate success of the method depends on being able to determine suitable values of the mean excitation energy D, which, together with the appropriate integrals in equations (8) and (11), yield meaningful (hyper)polarisabilities.  Progress in this direction, based on ab initio calculations on isolated molecules, will be presented.

 

References

1.   Fkyerat, A., Guelzim, A., Baert, F., Paulus, W., Heger, G., Zyss, J. and Pˇrigaud, A. (1995) Acta Cryst., B51, 197; Fkyerat, A., Guelzim, A., Baert, F., Zyss, J. and Pˇrigaud, A. Phys. Rev. (1996) B53, 16236.

2.   Jayatilaka, D. Phys. Rev. Lett. (1998) 80, 798; Jayatilaka, D. and Grimwood, D.J. (2001) Acta Cryst. A57, 76.

3.   Sylvain, M. G. and Csizmadia, I. G. (1987) Chem. Phys. Lett., 136, 575.