The case of protease inhibitor model compounds incorporating an aziridine or epoxide ring is used to exemplify how application of experimental electron-density techniques can be used to explain the biological properties of low-molecular weight enzyme ligands. This is * Dr. S. Grabowsky 1905 furthermore seen in the light of a comparison of crystal and enzyme environments employing QM/MM computations to elucidate to which extent the properties in the crystal can be used to predict behavior in the biological surrounding. bidden 222 reflection in diamond. [9] Further major contributions to the development of the multipole model (incomplete list) were made by Kurki-Suonio, [10] Stewart, [11] Hirshfeld, [12] and Coppens. [13] The model developed by Hansen and Coppens in 1978 [1] has proven to be most flexible and is implemented in the most frequently used program packages for experimental electron-density investigations (XD, [14] Mo-Pro, [15] Jana [16] ). The Hansen-Coppens formula for an aspherical pseudoatom used in the refinement is ρ c (r Ǟ ) and ρ v (κ,r Ǟ ) represent the spherical core and spherical valence electron densities, respectively, which are derived from Hartree-Fock wavefunctions expanded over Slater-type basis functions, [17] and are contractible and expansible by the κ parameter. The last term of the sum describes the aspherical deformation of the valence electron density. It consists of a linear combination of real spherical harmonics Y lmϮ with radial functions R l taken as single-zeta orbitals with fixed energy-optimized Slater exponents, [18] contractible and expansible by the κЈ parameter. The populations P v and P lmϮ as well as κ and κЈ are the refinable electron-density parameters. In recent developments, these valence parameters have been transferred to a description of core polarization, i.e. they have been used in an additional refinement of the core electron densities to improve the final density model. [19] Koritsanszky et al. are currently working on an upgraded multipole formalism employing a stockholder-partitioned quantum-mechanical molecular density projected onto nucleus-centered spherical harmonics yielding so-called bonded-atom radial functions analogous to the R l term. [20]
X-ray Wavefunction RefinementIn this technique developed by Jayatilaka during the last 15 years, structure and electron-density refinement comparable to