Stewart atoms

When doing the molecular fitting of ASA coefficients compared with promolecular ASA, the ASA coefficients no longer sum to 1 for all atoms in the molecule, because the sum of the coefficients reflects the effect of polarization. In other words, rather than having Pa = Za in promolecular ASA, the values of Pa Za in fitted ASA reflect the internal electron density redistribution. In such a way, fitted ASA coefficients are reminiscent of the Stewart atoms idea, where atoms in molecules are considered as radially distorted atoms and are connected with so-called Stewart charges. Contrary to common promolecular ASA where the atomic densities of Eq. [41] integrate to Za ... 

Hehre W J, Stewart R F and Popie J A 1969 Seif-consistent moiecuiar-orbitai method i. Use of Gaussian expansions of Siater-type atomic orbitais J. Chem. Phys. 51 2657-64... 

STO-3G bases were employed some years ago (W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51, 2657 (1969)) but are less popular recently. These bases are constructed by least squares fitting GTOs to STOs which have been optimized for various electronic states of the atom. When three GTOs are employed to fit each STO, a STO-3G basis is formed. 

Alkyl groups attached to aromatic rings are oxidized more readily than the ring in alkaline media. Complete oxidation to benzoic acids usually occurs with nonspecific oxidants such as KMnO, but activated tertiary carbon atoms can be oxidized to the corresponding alcohols (R. Stewart, 1965 D. Arndt, 1975). With mercury(ll) acetate, allyiic and benzylic oxidations are aJso possible. It is most widely used in the mild dehydrogenation of tertiary amines to give, enamines or heteroarenes (M. Shamma, 1970 H. Arzoumanian. 1971 A. Friedrich, 1975). 

Hehre, W.J. Stewart, R.F. Pople, J.A. Self-consistent molecular-orbital methods. I. Use of Gaussian expressions of Slater-Type Atomic Orbitals 7 Chem. 51 2657-2664, 1969. 

Stewart, A. L., Proc. Phys. Soc. A70, 756, "Wave functions for He and similar atomic systems. Perturbation treatment of second order, based on complete set of Laguerre functions. 

The MaxEnt valence density for L-alanine has been calculated targeting the model structure factor phases as well as the amplitudes (the space group of the structure is acentric, Phlih). The core density has been kept fixed to a superposition of atomic core densities for those runs which used a NUP distribution m(x), the latter was computed from a superposition of atomic valence-shell monopoles. Both core and valence monopole functions are those of Clementi [47], localised by Stewart [48] a discussion of the core/valence partitioning of the density, and details about this kind of calculation, may be found elsewhere [49], The dynamic range of the L-alanine model... 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

K. Stewart, and J. Taggert, analysts. Analysis for Li by induction-coupled plasma spectroscopy, S. Wilson, analyst. Analysis for Na, K, and Sr by atomic-absorption spectroscopy, D. D. Eberl, analyst. 

Mkhoyan KA, Contryman AW, SiicoxJ, Stewart DA, Eda G, Mattevi C, Miller S, Chhowalla M, Atomic and electronic structure of graphene-oxide, Nano Lett., 2009, 9,1058 1063. 

According to Stewart et al. (1980), the fractional ionic character thus defined is in agreement with the value deduced from electronegativity theory for molecular orbitals. The energy of a generic atom A is defined as... 

FIG. 3.1 Scattering Factors for the hydrogen atom. IAM, free atom SDS bonded atom as in H2, according to Stewart et al. (1965) k = 1.4, IAM density contracted with a kappa parameter equal to 1.4. 

The coefficients n, have to obey the condition n, f, imposed by Poisson s electrostatic equation, as pointed out by Stewart (1977). The radial dependence of the multipole density deformation functions may be related to the products of atomic orbitals in the quantum-mechanical electron density formalism of Eq. (3.7). The ss, sp, and pp type orbital products lead, according to the rules of multiplication of spherical harmonic functions (appendix E), to monopolar, dipolar, and quadrupolar functions, as illustrated in Fig. 3.6. The 2s and 2p hydrogenic orbitals contain, as highest power of r, an exponential multiplied by the first power of r, as in Eq. (3.33). This suggests n, = 2 for all three types of product functions of first-row atoms (Hansen and Coppens 1978). 

The multipole formalism described by Stewart (1976) deviates from Eq. (3.35) in several respects. It is a deformation density formalism in which the deformation from the IAM density is described by multipole functions with Slater-type radial dependence, without the K-type expansion and contraction of the valence shell. While Eq. (3.35) is commonly applied using local atomic coordinate systems to facilitate the introduction of chemical constraints (chapter 4), Stewart s formalism has been encoded using a single crystal-coordinate system. 

International Tables for Crystallography 1992). The function <]/> for Slater-type radial functions can be expressed in terms of a hypergeometric series (Stewart 1980), or in closed form (Avery and Watson 1977, Su and Coppens 1990). The latter are listed in appendix G. As an example, for a first-row atom quadrupolar function (/ = 2) with n, = 2, the integral over the nonnormalized Slater function is... 

The promolecule density shows (3, — 1) critical points along the bond paths, just like the molecule density. But, as the promolecule is hypothetical and violates the exclusion principle, it would be incorrect to infer that the atoms in the promolecule are chemically bonded. In a series of topological analyses, Stewart (1991) has compared the model densities and promolecule densities of urea,... 

The first electrostatic moment from X-rays was obtained by Stewart (1970), who calculated the dipole moment of uracil from the least-squares valence-shell populations of each of the constituent atoms of the molecule. Stewart s value of... 

Stewart s conclusion underscores the need for short-wavelength, low-temperature studies, if very high accuracy electrostatic properties are to be evaluated by Fourier summation. But, as pointed out by Hansen (1993), the convergence can be improved if the spherical atoms subtracted out are modified by the k values obtained with the multipole model. Failure to do this causes pronounced oscillations in the deformation density near the nuclei. For the binuclear manganese complex ( -dioxo)Mn(III)Mn(IV)(2,2 -bipyridyl)4, convergence of the electrostatic potential at the Mn nucleus is reached at 0.7 A" as checked by the inclusion of higher-order data (Frost-Jensen et al. 1995). 

Spackman, M. A. and Stewart, R. F., in Chemical Applications of Atomic and Molecular Electrostatic Potentials, P. Politzer and D. G. Truhlar (eds.), Plenum Press New York, London (1981), pp. 407-425. 

Maitani MM, Allara DL, Ohlberg DAA, Li Z, Williams RS, Stewart DR (2010) High integrity metal/organic device interfaces via low temperature buffer layer assisted metal atom nucleation. Appl Phys Lett 96(17) 173109-173113... 

The current health risks associated with exposure to low-dose radiation are extrapolated from high-dose data taken from the Life Span Study of the Japanese atomic bomb survivors. Currently, a linear no threshold extrapolation is recommended. The numerous technical reports and scientific papers about the Japanese A-bomb survivors were widely interpreted as showing that the effects of occupational exposures to radiation would be too small to detect in epidemiological studies. However, questions about the reliability of the A-bomb results were presented by Stewart and Kneale [2]. Their Oxford Childhood Study observed that children whose in utero exposures were as little as 10 to 20 mSv had 40% more childhood leukemias than those who were not exposed. No similar effects are reported in the A-bomb data. Of course, the finding of no effect is not a compelling argument for or against a safe dose. 

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