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Hellmann-Feynman Constraint on Charge Densities, an Experimental Test

A deformation density refinement on tetrafluoroterephthalonitrile against the low-temperature X-ray data of Seiler, Schweizer & Dunitz [Acta Cryst. (1984), B40, 319-327] has been constrained to yield vanishing electric fields at all nuclear positions. The constraint has produced sharp dipoles on the atoms, correlated with small atomic displacements, but has left the rest of the deformation map virtually unaltered. Schwarzenbach & Lewis (1982) have proposed that charge-density models for refinement against X-ray diffraction data may be constrained to make the electric field vanish at every nucleus in accordance with the Hellmann- Feynman theorem. Theoretical studies on small molecules have shown that a major contribution to the field at an atomic nucleus often arises from a very sharp polarization of its own cusp density (Hirshfeld & Rzotkiewicz, 1974). Hence the possibility of such polarization must be allowed in the deformation model if it is to satisfy the Hellmann-Feynman constraint in a realistic manner. However, the coefficients of any sharp dipole functions would, if refined against X-ray data alone, be strongly correlated with the corresponding atomic coordinates and thus virtually indeterminate. This means that we may expect these coefficients to be determined, in effect, solely by the Hellmann-Feynman constraint and to have no appreciable effect on the X-ray structure factors or on the other charge-density parameters. An excellent opportunity to check this expectation was provided by the very precise low-temperature X-ray data for tetrafluoroterephthalonitrile measured by Dunitz and coworkers (Dunitz, Schweizer & Seiler, F F