Molecular electrostatic potentials from crystal diffraction: the neurotransmitter gamma-aminobutyric acid

Given the electronic charge parameters obtained from a diffraction study of the charge density distribution in a crystal, a mathematical procedure is presented for deriving the electrostatic potential. The procedure allows the mapping of electrostatic potential for a molecule or group of molecules removed from the crystal structure but with each molecule retaining the effects of polarization owing to the original crystal environment. The method is applied for the neurotransmitter gamma-aminobutyric acid. The potential for a gamma-aminobutyric acid molecule is analyzed in terms of a simple model that is suitable for rapid computations concerned with Coulombic molecular interactions. Outside the molecular envelope at 1.2 A from the atomic nuclei, the total potential is well represented by a sum of spherical atom contributions with V(r) = (q/r) + exp(-beta r2). The most important aspherical component in the potential is the dipole contribution from the hydrogen atoms. This can be represented as V(r, phi) = (0.162 cos phi)/(r2 + 0.615). Here, V is in e/A, r is the distance from each nucleus in A, q is the experimentally determined net atomic charge in electron units, and phi is the angle between r and the bond X-H. We obtain beta = 1.47, 1.66, 1.83 A-2 for C, N, and O respectively. For H, no term in beta is needed.