On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study.

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

Computational analysis of thermal-motion effects on the topological properties of the electron density.

The distributions of bond topological properties (BTPs) of the electron density upon thermal vibrations of the nuclei are computationally examined to estimate different statistical figures, especially uncertainties, of these properties. The statistical analysis is based on a large ensemble of BTPs of the electron densities for thermally perturbed nuclear geometries of the formamide molecule. Each bond critical point (BCP) is found to follow a normal distribution whose covariance correlates with the displacement amplitudes of the nuclei involved in the bond. The BTPs are found to be markedly affected not only by normal modes of the significant bond-stretching component but also by modes that involve mainly hydrogen-atom displacements. Their probability distribution function can be decently described by Gumbel-type functions of positive (negative) skewness for the bonds formed by non-hydrogen (hydrogen) atoms.

The IMAGINE instrument: first neutron protein structure and new capabilities for neutron macromolecular crystallography.

The first high-resolution neutron protein structure of perdeuterated rubredoxin from Pyrococcus furiosus (PfRd) determined using the new IMAGINE macromolecular neutron crystallography instrument at the Oak Ridge National Laboratory is reported. Neutron diffraction data extending to 1.65 Šresolution were collected from a relatively small 0.7 mm(3) PfRd crystal using 2.5 d (60 h) of beam time. The refined structure contains 371 out of 391, or 95%, of the D atoms of the protein and 58 solvent molecules. The IMAGINE instrument is designed to provide neutron data at or near atomic resolution (1.5 Å) from crystals with volume <1.0 mm(3) and with unit-cell edges <100 Å. Beamline features include novel elliptical focusing mirrors that deliver neutrons into a 2.0 × 3.2 mm focal spot at the sample position with full-width vertical and horizontal divergences of 0.5 and 0.6°, respectively. Variable short- and long-wavelength cutoff optics provide automated exchange between multiple-wavelength configurations (λmin = 2.0, 2.8, 3.3 Što λmax = 3.0, 4.0, 4.5, ∼20 Å). These optics produce a more than 20-fold increase in the flux density at the sample and should help to enable more routine collection of high-resolution data from submillimetre-cubed crystals. Notably, the crystal used to collect these PfRd data was 5-10 times smaller than those previously reported.

Experimental charge density studies of disordered N-phenylpyrrole and N-(4-fluorophenyl)pyrrole.

The static electron densities of the title compounds were extracted from high-resolution X-ray diffraction data using the nucleus-centered finite multipole expansion technique. The interpretation of the data collected for the N-phenylpyrrole crystal revealed a static disorder that could be successfully resolved within the aspherical-atom formalism. The local and integrated topological properties of the density obtained via a constrained multipole refinement are in statistical agreement with those calculated at the B3LYP/cc-pVTZ level of theory for the isolated molecule and for those derived from the experimental density of the para-fluorinated derivative N-(4-fluorophenyl)pyrrole. The topological analysis of the densities indicates neither pyramidal character of the pyrrole N-atom nor a quinoidal structure of the phenyl rings in either molecule. The fluorine substitution appears to have only a minor effect on the density of the remaining constituents but it results in markedly different features of the electrostatic potential of the two compounds. The consistency of the multipole refinement is validated by residual density analysis.

On the basis-set dependence of local and integrated electron density properties: Application of a new computer program for quantum-chemical density analysis.

A new computer program for post-processing analysis of quantum-chemical electron densities is described. The code can work with Slater- and Gaussian-type basis functions of arbitrary angular momentum. It has been applied to explore the basis-set dependence of the electron density and its Laplacian in terms of local and integrated topological properties. Our analysis, including Gaussian/Slater basis sets up to sextuple/quadruple-zeta order, shows that these properties considerably depend on the choice of type and number of primitives utilized in the wavefunction expansion. Basis sets with high angular momentum (l = 5 or l = 6) are necessary to achieve convergence for local properties of the density and the Laplacian. In agreement with previous studies, atomic charges defined within Bader's Quantum Theory of Atoms in Molecules appear to be much more basis-set dependent than the Hirshfeld's stockholder charges. The former ones converge only at the quadruple-zeta/higher level with Gaussian/Slater functions.

Bond orders and atomic properties of the highly deformed halogenated fullerenes C60F18 and C60Cl30 derived from their charge densities.

The experimental charge densities of the halogenated C(60) fullerenes C(60)F(18) and C(60)Cl(30) were determined from high-resolution X-ray data sets measured with conventional Mo(Kalpha) radiation at 20 K for C(60)Cl(30) and with synchrotron radiation at 92 K for the fluorine compound. Bond topological and atomic properties were analyzed by using Bader's AIM theory. For the different C--C bonds, which vary in lengths between 1.35 and 1.70 A bond orders n between n=2 and significantly below n=1 were calculated from the bond topological properties at the bond critical points (BCP's). The low bond orders are seen for 5/6 bonds with each contributing carbon carrying a halogen atom. By integration over Bader's zero flux basins in the electron density gradient vector field atomic properties were also obtained. In contrast to free C(60), in which all carbon atoms have a uniform volume of 11 A(3) and zero charge, atomic volumes vary roughly between 5 and 10 A(3) in the halogenated compounds. Almost zero atomic charges are also found in the Cl derivative but a charge separation up to +/-0.8 e exists between C and F in C(60)F(18) due to the higher fluorine electronegativity, which is also seen in the electrostatic potential for which the electronegativity difference between carbon and fluorine, and the addition to one hemisphere of the fullerene cage leads to a strong potential gradient along the C(60)F(18) molecule. From the summation over all atomic volumes it follows that the halogen addition does not only lead to a dramatic distortion of the C(60) cage but also to a significant shrinkage of its volume.

Charge density and experimental electrostatic potentials of two penicillin derivatives.

Two penicillin derivatives, the active penamecillin and the inactive penamecillin-1beta-sulfoxide, were used to study the relationship between their charge density and their activity. Single crystals of both compounds were measured at the synchrotron beamline F1 at the HASYLAB/DESY, at 100 K and up to resolutions of around 0.4 A. Experimental charge densities were obtained by using the Hansen-Coppens multipole formalism. The cleavage of the amide bond in the beta-lactam ring is of paramount importance in the mechanism of action of penicillins. Topological analysis of this bond in terms of Bader's AIM theory showed that its strength is equal in both compounds; therefore a direct influence of bond strength on the activity can be ruled out. However, the two derivatives differ significantly in their experimental electrostatic potentials. These differences are discussed and provide further insight into the chemistry and activity of penicillins.

The weakly coordinating trichloromethanesulfonate anion: NQR comparison of its coordinating abilities via oxygen with those of the chloroacetate ions.

Ionic and covalent derivatives of the chlorine analogue of the nonbasic, weakly coordinating triflate ion, Cl3CSO3(-) or "trichlate" ion, have been prepared and compared with the corresponding more strongly coordinated chloroacetates, Cl(x)CH(3-x)CO(2)M (x = 1-3), using 35Cl NQR (nuclear quadrupole resonance) spectroscopy. The (35)Cl NQR frequencies of all types of derivatives are sensitive to the nature of the metal ion or Lewis acid and are most sensitive in the case of monochloroacetates. In covalent (including zirconocene) derivatives, the average NQR frequencies fall as the Pauling electronegativity of M falls. The results for ionic derivatives contrast with previous results for ionic hexachlorometalates: the average (35)Cl NQR frequencies drop sharply as the ionic radius of the group 1 cation increases. Ab initio Gaussian 98 computations at the B3LYP/6-311++G(3df,3pd) level on isolated XCH2CO2M (M = Li, Na, K; X = F, Cl) molecules duplicate this trend, showing increasing polarization of the C-Cl bond and smaller electric field gradients for larger group 1 ions; the relevance of this to the solid state polymerization of chloroacetates (Herzberg, O.; Epple, M. Eur. J. Inorg. Chem. 2001, 1395-1406) is discussed. We have prepared the dihydrate and monohydrate of trichlic acid, Cl3CSO3H. Although trichlates have the highest average NQR frequencies of any of these salts, the NQR frequencies of trichlic acid dihydrate are anomalously lower than those of trichloroacetic acid, which suggests that it is a strong acid, ionized in the solid state to H5O2+ and Cl3CSO3(-) ions.

Aspherical-atom scattering factors from molecular wave functions. 1. Transferability and conformation dependence of atomic electron densities of peptides within the multipole formalism.

In this study, the feasibility of building a database of theoretical atomic deformation density parameters applicable to the construction of the densities of biomacromolecules and to the interpretation of their X-ray diffraction data is discussed. The procedure described involves generation of valence-only structure factors of tripeptides calculated from theoretical densities at the B3LYP level and the refinement of multipole parameters against these simulated data. Our results so far indicate that the backbone pseudoatoms extracted in such a way are highly transferable and fairly invariant with respect to rotations around single bonds in the peptide framework. The ultimate goal is to use the aspherical-atom database for improved macromolecular refinements that are based on high-resolution data and for prediction of electrostatic properties of larger molecules.

Electronic Insight into an Antithrombotic Agent by High-Resolution X-Ray Crystallography.

Five instead of 200 days measurement time are sufficient (thanks to area detection rather than conventional scintillation detection) to obtain the accurate charge density distribution of an antithrombotic agent with more than 50 atoms by a high-resolution X-ray diffraction experiment. The preferred sites of intermolecular interactions were identified from various topological properties, such as the reactive surface (zero Laplacian function, see picture) and the electrostatic potential.

Fast Experiments for Charge-Density Determination: Topological Analysis and Electrostatic Potential of the Amino Acids L-Asn, dl-Glu, dl-Ser, and L-Thr.

Synchrotron radiation and CCD detection give the possibility for fast diffraction experiments, which were employed to deduce the exact charge-density distributions of some amino acids. Their topological analysis (the figure shows the negative Laplacian function of dl-serine in the plane of the carboxylate group) yields not only comparable information about intramolecular but also about weak intermolecular interactions.