Charge density studies were conducted for both di(methoxy) gossypol and
di(propylamine) gossypol. The experimental electron distribution for the charge density was obtained from the crystallographic diffraction data by refinement with the Hansen-Coppens multipole deformation model as coded in the XD2006 computer program. In this model, the total density for each atom is fit by a spherical core and valance electron density calculated from Hartree-Fock atomic wavefunctions and an additional aspherical density contribution consisting of an expansion of Slater-type radial functions and spherical harmonic angular functions where the density for each atom is defined as
!"# %&8!"# ^ a_$86%8`b _$86%8!`"# ^ ¦$`bc$!`"#¦a$,h$,!T, U# where the spherical core density component, ρcore(r), is fixed, while the valance density
component, ρvalance(r), may be adjusted by the refinement of the valence population parameter, Pvalance, and the expansion/contraction parameter: κ. Components representing aspherical density contributions are obtained by refinement of the multipole population parameter, Pl,mfor each
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hexadecapolar (l = 4) level, and by further adjustment by a second expansion/contraction parameter: κ'. Refinement of the parameters for the electron configuration of each atom entails
three positional parameters; six anisotropic thermal displacement factors for each atom; the multipole model introduces an additional 27 parameters for the electronic distribution giving a total of 36 parameters for each atom.
Despite the high degree of parameterization defined with the multipole refinement process, the number of variables may be reduced in its implementation with restraints. For instance, chemically equivalent atoms may be constrained to have the same density. Naturally, the validity of such constraints must be tested by examining the quality of the fit to the x-ray data.
In general, the positional parameters for hydrogen atoms are highly correlated with the dipole density deformation directed along the covalent bonds, and concurrent refinement cannot reliably determine both parameters. In like manner, the hydrogen atomic temperature factors are correlated with both the monopoles and quadrapoles deformation parameters. The model used for multipole refinement of the hydrogen atoms included isotropic thermal parameters fixed at the experimental values obtained from the spherical atom refinement, and hydrogen positions fixed at positions calculated by extending along the X-H bond direction to a distance
corresponding to average X-H bond distances obtained from neutron diffraction experiments. With both the hydrogen positional and thermal parameters constrained, only the valance monopoles and the single monopole and quadrapole deformation parameters aimed along the major covalent bond axis are refined. Following each cycle of refinement, the hydrogen atom positions are reoriented to maintain the specified bond lengths.
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A total of nine sets of κ and κ' values are designated for di(methoxy) gossypol: one set for
the oxygen atoms in the aldehyde groups, one set for the oxygens in the alcohol groups, one set for the oxygen atom in the methoxy groups, one set for the carbon atoms, and one set for the hydrogens atoms bonded to carbon, and one set for the hydrogens bonded to oxygen. For PAG, a total of seven sets of κ and κ' values are designated: one set for the oxygen atoms in the
hydroxyl groups, one set for the oxide oxygen atoms, one set for the carbon atoms, one set for the nitrogen atoms, one set for the hydrogen atoms bonded to carbon, one set for the hydrogen atoms bonded to oxygen, and one set for the hydrogen atoms bonded to nitrogen. Moreover the small extinction coefficient from the spherical atom refinement is also included as a fixed value in the more complex multipole refinement.
To further test the validility of the deformation density models used in the multipole refinement process, and the successful completion of the deconvolution of the electronic density and thermal motion, electronic residual density maps are tested locally and globally throughout the refinement process. As stated, the residual density maps relate the difference between the observed density and the density calculated on the basis of the multipole model calculated by Fourier summation
¨ &8(5$ ¥( < 8$ !1/3#¦$@|+¥(| < |+8$|A-/!´u'u$µ# In general, where significant features corresponding to considerable electron density were observed in the residual density, site symmetry constraints on the deformation and/or chemical constraints parameters were relaxed and the refinement process continued until no areas
remained with significant density features that are greater than three times the estimated standard deviation in the residual density (estimated σ(∆ρ) = 0.051 e A−3).
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Further validity of the multipole refinement entails conformation of the deformation density via the rigid bond test [207]. Anisotropic thermal atomic displacement parameters that have been successfully deconvoluted from the molecular electron density organization should exhibit equal mean square amplitudes of vibration along the bond direction for covalently bonded pairs of atoms.
A static deformation density plot was calculated by taking the difference between the sum of the atomic densities given by ρmultipolemodel = Σρatom, and the sum of the isolated, neutral atomic densities, ρIAM = Σρsphericalatom, the independent atom model (IAM),
¨ 8¶&6 86(' 5$w$8 8$< ·¸¹
Topological properties and analysis of the electron density organization based on Bader's AIM theory were calculated with the XDPROP and TOPXD modules of XD2006. The
estimated standard deviations in the general properties are rigorously calculated based on the uncertainties of the multipole population parameters obtained by the least squares refinement of the X-ray data.
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