Struct. Chem., Vol. 2, pp. 3-9. ISSN 1040-0400 An Ab Initio Study of Crystal Field Effects, Part 3t: Solid- and Gas-Phase Geometry of Formamide, Modeling the Changes in a Peptide Group Due to Hydrogen Bonds P. Popelier, A. T. H. Lenstra, C. Van Alsenoy, and H. J. Geise* University of Antwerp [UIA), Department of Chemistry, B-2610 Wilrijk, Belgium A model of the solid state of formamide is con- structed by optimizing a central molecule in an elec- trostatic field of the proper symmetry. Attention is paid to the way the electrostatic charges are ob- tained. Point charges obtained from a Mulliken pop- ulation analysis yield a final set of atomic charges in the central molecule that agree reasonably well with those obtained experimentally after a K-refine- ment of formamide. Point charges from a so-called stockholder partitioning agree slightly less. Fur- thermore, the simple crystal field adaptation of standard ab initio methods reproduces within ex- perimental limits the differences in C--O and C--N lengths, observed between the gas-phase and the solid state geometry. Again, a Mulliken field agrees slightly better than a stockholder field, but the dif- ference in performance is statistically insignificant. In a survey of 221 high-quality single-crystal x-ray determinations of compounds containing the peptide group N--C=O, we found evidence supporting quantitatively the conclusion that the increase of C=O and the decrease of C--N bond length in the gas-to-solid transition is dominated by the effects of hydrogen bonding. It was shown that the C=O bond lengthens by about 0.011 • per H-bond it ac- cepts, while the N--C bond diminishes by about 0.015 A per H-bond it donates. INTRODUC~ON A molecule in the solid phase often has a geometry slightly different from the one in the gaseous phase, ?Part 2, see Ref. [5]. *To whom correspondence should be addressed. particularly when intermolecular hydrogen bonds are present. A theoretical technique that gives such dif- ferences reliably would be most welcome. A method based on the incorporation of a simple electro,,~tatic crystal field model of the solid state into standard ab initio calculations has attracted increasing interest [ 1-6]. It is computationally inexpensive and has been suc- cessfully applied, e.g., in the conformational analysis of cyanoformamide [3], cyanamide [4], and acetamide [5]. A number of methodological aspects, however, have not yet been investigated. One of them, namely, the influence of the manner in which the electrostatic crystal field charges are computed, is addressed in this work. Formamide is taken as the test molecule, be- cause it is one of the very few molecules for which the geometry differences in going from the gaseous to the crystalline state have been determined with sufficient accuracy. Furthermore, it is the simplest model com- pound containing a peptide unit engaged in hydrogen bonding. Therefore, another aim of this work is to investigate the response of the peptide geometry to hydrogen bonding conditions. Kitano and Kuchitsu analyzed the molecular structure of formamide in the gas phase by electron diffraction [7]. Stevens determined the structure as well as the electron density distribution in the solid ~rom low-temperature, high-order x-ray data [8]. The mol- ecule is within experimental accuracy planar in both phases, but the C=O bond is 0.027(5) A longer and the C--N bond 0.042(5) shorter in the crystal. We will show that the crystal field approach reproduces the geometric features and the experimental atomic charges satisfactorily. Finally, a statistical analysis is per- Manuscript received 11/13/89; accepted 4/18/90. 3 9 1991 VCH Publishers, Inc. 1040-0400/91/$3.50 + .25