Spherical Electron Density Research Articles

Complementary spherical electron density model and its implications for the 18 electron rule

The Complementary Spherical Electron Density Model developed by Mingos and Hawes in 1985 is reviewed and its implications to 18 electron complexes and co-ordinatively unsaturated complexes are developed. These conclusions are particularly germane in view of the recent proposal by Landis that transition metal complexes are governed by a 12 rather than an 18 electron rule, Hall’s recent OSRAM model and the availability of additional structural data.

Structure and energetics of He2* bubble-states in superfluid 4He

Structure and energetics of solvation of the triplet Rydberg states of the He2* excimer in liquid He4 (LHe) are analyzed using ab initio potentials and density functional methods. The results are used to interpret the known spectroscopy. Having established the reliability of the various semiempirical functionals, interfacial properties of the superfluid on molecular scales are discussed. Due to its spherical electron density, the a(Σu3) state solvates in a spherical bubble of 7 Å radius in which the excimer freely rotates. This explains the observed rotationally resolved b3←a3 and c3←a3 absorption spectra. A deep potential minimum occurs at the equatorial node of the a(Σu3) state, where a radially frozen belt of six He atoms can be sustained at R=2.3 Å, inside an ellipsoidal cavity with major axis of 8 Å and a more diffuse minor axis of 6 Å. Despite the absence of a potential energy barrier, or a many-body interfacial tension preventing the wetting of the belt, the bare c3 state is observed in emission. It is argued that in the superfluid, wetting is prevented by the hindered rotation of the excimer, hence the sensitivity of the c3→a3 emission to pressure induced quenching. The nodal plane in the b(3Πg3) state passes through the molecular axis, as such, rotation cannot provide protection against wetting and subsequent quenching of the b3 state via the He3* manifold; hence the absence of b3→a3 emission despite its large transition dipole. In its global minimum, the d3 excimer sustains a shell of 16 He atoms, localized at the radial node of its Rydberg electron, at R∼2.5 Å. The shell, in turn, is contained in a nearly spherical bubble held at a radius of 13 Å by the extra-nodal electron density. The repulsion between extra-nodal electron density and LHe provides a barrier to filling of the deep nodal well, ensuring the stability of the bare d3 excimer in a large spherical bubble. This explains the free-rotor envelopes of the d3→b3 and d3→c3 emissions, and their negligible spectral shifts relative to the gas phase. The predicted minimum energy structures, the belted c3 state and the crusted d3 state, if formed, should be metastable.

The origin of the electron distribution in SnO

Gradient corrected density functional theory calculations have been performed on SnO in the litharge and idealized CsCl structures with the litharge structure in good agreement with experiment. The CsCl structured SnO has a spherical electron density whereas the litharge structured SnO has a nonspherical electron distribution. Such asymmetry is often attributed to a sterically active lone pair formed by the 5s2 electrons which does not take part in chemical bonding. However, analysis of the density of states and band structures indicates that the situation is more complicated. In CsCl structured SnO mixing of the Sn 5s with the oxygen 2p electronic states results in filled bonding and antibonding combinations. The antibonding combinations, at the top of valence band, can interact with Sn 5p to stabilize the structure, only when in the distorted litharge structure resulting in the asymmetric electron density. This is in contrast to the classical theory of hybridization of the tin 5s and 5p orbitals to form a “lone pair” as the asymmetric electron distribution is the result of the tin–oxygen covalent interactions.

Molecular surfaces from the promolecule: A comparison with Hartree–Fock ab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

Towards the charge-density study of proteins: a room-temperature scorpion-toxin structure at 0.96 A resolution as a first test case.

The number of protein structures refined at a resolution higher than 1.0 A is continuously increasing. Subatomic structures may deserve a more sophisticated model than the spherical atomic electron density. In very high resolution structural studies (d < 0.5 A) of small peptides, a multipolar atom model is used to describe the valence electron density. This allows a much more accurate determination of the anisotropic thermal displacement parameters and the estimate of atomic charges. This information is of paramount importance in the understanding of biological processes involving enzymes and metalloproteins. The structure of the scorpion Androctonus australis Hector toxin II has been refined at 0.96 A resolution using synchrotron diffraction data collected at room temperature. Refinement with a multipolar electron-density model in which the multipole populations are transferred from previous peptide studies led to the observation of valence electrons on covalent bonds of the most ordered residues. The refined net charges of the peptide-bond atoms were of the correct sign but were underestimated. Such protein-structure refinements against higher resolution data collected at cryogenic temperature will enable the calculation of experimental atomic charges and properties such as electrostatic potentials.

Molecular surfaces from the promolecule: A comparison with Hartree-Fockab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

Hydrogen bond energetics from topological analysis of experimental electron densities: Recognising the importance of the promolecule

In a recent paper [E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 285 (1998) 170] the kinetic energy density G( r c) and potential energy density V( r c) at the bond critical point r c in X–H⋯O hydrogen bonds were deduced from topological analyses of experimental electron distributions extracted from accurate X-ray diffraction experiments. We show that the promolecule, a model of non-interacting overlapping spherical atomic electron densities, can explain many of the observed results as well as the exponential dependence on the H⋯O distance. This raises the question of whether present experimental results differ from a simple reference model for weak interactions.

Investigation of Monovalent Cation Activation of S-Adenosylmethionine Synthetase Using Mutagenesis and Uranyl Inhibition

S-Adenosylmethionine (AdoMet) synthetase catalyzes the formation of AdoMet from ATP and L-methionine with subsequent hydrolysis of the bound tripolyphosphate intermediate. Maximal activity requires the presence of two divalent and one monovalent cation per active site. Recently, the x-ray structure of the Escherichia coli AdoMet synthetase was solved, and the positions of the two Mg2+ binding sites were identified. Based on additional spherical electron density, the K+ binding site was postulated to be a nearby site where the uranyl heavy atom derivative also bound in the crystal. The side chain of glutamate 42 is within ligation distance of the metals. Mutagenesis of glutamate 42 to glutamine (E42QMetK) abolished monovalent cation activation and produced an enzyme that has kinetic properties virtually identical to those of K(+)-free wild type AdoMet synthetase in both the overall AdoMet synthetase reaction and in the hydrolysis of tripolyphosphate. Thus, there is a approximately 100-fold decrease in the Vmax for AdoMet synthesis and large increases in the Km values for both substrates. In contrast there is only a 2-fold decrease in Vmax for tripolyphosphate hydrolysis. The uranyl ion, UO2(2+), is a competitive inhibitor with respect to K+ (Ki = 350 nM) and is the first ion to bind at this site and inhibit the enzyme. The UO2(2+) inhibition is reversible and tight-binding, and results from UO2(2+) and not UO2(2+)-ATP. Analogous to K+ activation, UO2(2+) predominantly inhibits AdoMet formation rather than tripolyphosphate hydrolysis. The kinetic results indicate that UO2(2+) inhibition is likely to result from interference with productive ATP binding. UO2(2+) remains a tight-binding inhibitor of the E42Q mutant, which suggests that K+ and UO2(2+) have different ligation preferences when bound in the monovalent cation binding pocket. The results support the model that glutamate 42 provides ligands to the K+ and has a major role in monovalent cation binding.

Modelling electrostatic potential from experimentally determined charge densities. I. Spherical-atom approximation

Observations of the experimental electrostatic potential obtained from X − X spherical electron density can be used to derive point charges centred on the atoms. This is applied to a pseudopeptide, N-acetyl-α, β-dehydrophenylalanine methylamide. The experimentally determined charges are consistent whatever the sampling points and `follow' the atomic site when the conformation of the molecule changes. However, introduction of multipolar moments is necessary as soon as the aspherical part of the electron density is added.

Electron Density in a Half-Filled Shell Atom

It is found that wave functions belonging to a certain subspace in a half-filled shell yield spherical symmetric electron density. This result comes from the well-known disappearance rule in the atomic spectroscopy together with additional considerations.

Electron Density in a Half-Filled Shell Atom

It is found that wave functions belonging to a certain subspace in a half-filled shell yield spherical symmetric electron density. This result comes from the well-known disappearance rule in the atomic spectroscopy together with additional considerations

Complementary spherical electron density model for coordination compounds

Abstract

Complementary spherical electron density model for inorganic stereochemistries

The inert gas rule has been reformulated in terms of complementary and complete sets of central atom and ligand sphere wave-functions with s, p, and d nodal characteristics.

Die Wasserstoff-Palladium-Bindung bei Adsorption des Wasserstoffs an den (100)-und (111)-Oberflächen sowie Diffusion und Absorption im Kristallgitter aus der Sicht der SW-Xα-Methode / Investigation of the hydrogen-palladium bond of hydrogen being adsorbed on the (100)- and (111)-surfaces, diffusing and being absorbed in the crystal-lattice using the SW-Xα-method

Abstract SW-Xα-calculations pf PdnH-and Pdn-clusters of Oh -, Td -, C4v -and C3v -symmetry are carried out to investigate the bonding mechanism of hydrogen being chemisorbed at the (100)- and (111)-surfaces, entering the lattice and being absorbed at interstitial sites. Densities of states, local electron densities, spherical electron densities, integral electron charges as well as maps of the main H-Pd bonding orbital are compared in order to characterize the hydrogen-palladium bond.

Synaptic morphology and cytoplasmic densities: Rapid post-mortem effects

In the study of nervous tissue, the shift from the living state to the post-mortem condition affects the ultrastructure of the neuron in ways incompletely understood. We have observed rapid post-mortem changes associated with the synaptic region in the molecular layer of the rat dentate gyrus. These changes are evident in tissue taken from anesthetized animals in which perfusion was begun while the heart was beating but breathing had stopped. Such alterations were rarely in evidence if perfusion was started while the animal was breathing, either with or without artificial means. The following morphological alterations were observed: (a) an increase in spherical electron densities seen near the synapse as well as in the perinuclear cytoplasm; (b) a variation in the amount of density attached to the thickening of post-synaptic membrane; (c) a change in the curvature of the synaptic cleft. Because of these rapid alterations, caution is recommended in the interpretation of the in vivo morphology of the synapse and associated densities.

Repulsion Center of a Bonded Hydrogen Atom

The center of repulsion of a bonded hydrogen atom in a hydrogen molecule was found to be appreciably shifted from the proton into the bond. The magnitude of the shift was found to be 0.07–0.10 Å based on quantum-mechanical calculations of the energy of the He–H2 and H2–H2 systems. The shift of the repulsion center is in good agreement with the shift of the center of spherical electron density found by Stewart, Davidson, and Simpson.