The Noncommutative Quadratic Stark Effect For The H-Atom

Using both the second order correction of perturbation theory and the exact computation due to Dalgarno-Lewis, we compute the second order noncommutative Stark effect,i.e., shifts in the ground state energy of the hydrogen atom in the noncommutative space in an external electric field. As a side result we also obtain a sum rule for the mean oscillator strength. The energy shift at the lowest order is quadratic in both the electric field and the noncommutative parameter $\theta$. As a result of noncommutative effects the total polarizability of the ground state is no longer diagonal.Comment: 7 pages, no figure

The Electronic Origin of Geometrical Deformations in Cyclohexadienyl and Cyclobutenyl Transition Metal Complexes

(40) (a) Davies4' has stated the opinion that ". . . the comparatlve success of London's method for aromatic hydrocarbons may be attributed to the dependence of the theoretical anisotropy on the square of the area of the rings in a molecule'' and that ". . . any method that takes this into account is likely to give reasonable results for the ratio . . ." of a given calculated anisotropy to that calculated, by the same method, for benzene. We might also add that, at least for paramagnetic systems of the type considered here, another important requirement for obtaining 'reasonable' ratios is the use of a a-electron wave function which is Iteratively self-consistent with respect to atomic charges and bond orders. (see subsection 4 of this section). The Electronic Origin of Geometrical Deformations in Cyclohexadienyl and Cyclobutenyl Transition Metal Complexes Roald Hoffmann* and Peter Hofmann Contribution from the Department of Chemistry. Cornell University, Ithaca, New York 14850. Received May 19,1975 Abstract: A case is presented for an electronic factor in the out-of-plane bending of the saturated carbon in cyclohexadienyl-M(CO)3 complexes, M = Fe+, Mn, Cr-. In the cyclohexadienyl ligand hyperconjugation extends the nonbonding MO wave function to the methylene hydrogens. The phase of the CH2 hydrogen contributions to that MO is such that when the C6H7 ligand is bound to the M(C0)3 group there arises a secondary M-CHz interaction which is destabilizing. In cyclobutenyl and cyclooctatrienyl complexes this interaction is lacking and thus these should be less bent than cyclohexadienyl complexes. A similar analysis rationalizes the bending away from the metal in cyclopentadiene-Fe(C0)3 complexes, its lessening in cyclopentadienone complexes, and the bending toward the metal in fulvene or cyclopentadienyl-carbonium ion complexes. The charge distribution and substituent effects in C6H,M(CO)3 complexes are examined, as well as a case of hypothetical isomerism in benzyl-M(C0)3. There exists a substantial chemistry of transition metal complexes of cyclohexadienyl and cyclobutenyl ligands, exemplified by structure 1. Examples exist for M = Fe+, Mn, Cr-, and their lower transition series analogues. The assign- 3 . 4 1 ment of a formal charge to the metal is, of course, arbitrary. Nevertheless it focuses on the basic electronic similarity of these complexes, an aspect that might be obscured by an argument over the cationic or anionic nature of the coordinated cyclohexadienyl ligand. In all known structures of type 1 the six-membered organic ring is highly nonplanar, and distorted in the same way-atoms 1 through 5 remain in an approximate plane, but the saturated carbon 6 moves out of that plane and away from the metal. It should be noted that the free organic ligand is either planar or only moderately distorted. In the crystal structure of the tetrachloroaluminate salt of the heptamethylbenzenonium cation, 2, the six-membered ring is essentially planar.' However, in three recent structures of stabilized u complexes, 3,1° dihedral angles up to 17' have been found.'' Stabilized anionic u complexes, that is Meisenheimer complexes, have been known for some time.l* Several crystal structures of such highly substituted cyclohexadienyl anions are a~a i l a b l e , '~ and in all the six-membered ring is approximately planar. The problem of potential nonplanarity of cyclohexadienyl radicals has been discussed re~e n t 1 y . I~ At any rate it is clear that upon formation of a transition metal complex there is a significant enhancement of th

Hyperfine structure of the ground state muonic He-3 atom

On the basis of the perturbation theory in the fine structure constant $\alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(\mu\ e \ ^3_2He)$. We obtain total result for the ground state hyperfine splitting $\Delta \nu^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $\alpha^5$ and $\alpha^6$. The remaining difference between our theoretical result and experimental value of the hyperfine splitting lies in the range of theoretical and experimental errors and requires the subsequent investigation of higher order corrections.Comment: Talk on poster section of XXIV spectroscopy congress, 28 February-5 March 2010, Moscow-Troitsk, Russia, 21 pages, LaTeX, 8 figure

An exactly solvable model for the Fermi contact interaction

A model for the Fermi contact interaction is proposed in which the nuclear moment is represented as a magnetized spherical shell of radius r 0 . For a hydrogen-like system thus perturbed, the Schrödinger equation is solvable without perturbation theory by use of the Coulomb Green's function. Approximation formulas are derived in terms of a quantum defect in the Coulombic energy formula. It is shown that the usual Fermi potential cannot be applied beyond first-order perturbation theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46454/1/214_2004_Article_BF00548828.pd

Fine and hyperfine structure of the muonic ^3He ion

On the basis of quasipotential approach to the bound state problem in QED we calculate the vacuum polarization, relativistic, recoil, structure corrections of orders $\alpha^5$ and $\alpha^6$ to the fine structure interval $\Delta E^{fs}=E(2P_{3/2})-E(2P_{1/2})$ and to the hyperfine structure of the energy levels $2P_{1/2}$ and $2P_{3/2}$ in muonic $^3_2He$ ion. The resulting values $\Delta E^{fs}= 144803.15 \mu eV$, $\Delta \tilde E^{hfs}(2P_{1/2})=-58712.90 \mu eV$, $\Delta \tilde E^{hfs}(2P_{3/2})=-24290.69 \mu eV$ provide reliable guidelines in performing a comparison with the relevant experimental data.Comment: 15 pages, 4 figures, 3 table

Environment influences on the aromatic character of nucleobases and amino acids

Geometric (HOMA) and magnetic (NICS) indices of aromaticity were estimated for aromatic rings of amino acids and nucleobases. Cartesian coordinates were taken directly either from PDB files deposited in public databases at the finest resolution available (≤1.5 Å), or from structures resulting from full gradient geometry optimization in a hybrid QM/MM approach. Significant environmental effects imposing alterations of HOMA values were noted for all aromatic rings analysed. Furthermore, even extra fine resolution (≤1.0 Å) is not sufficient for direct estimation of HOMA values based on Cartesian coordinates provided by PDB files. The values of mean bond errors seem to be much higher than the 0.05 Å often reported for PDB files. The use of quantum chemistry geometry optimization is strongly advised; even a simple QM/MM model comprising only the aromatic substructure within the QM region and the rest of biomolecule treated classically within the MM framework proved to be a promising means of describing aromaticity inside native environments. According to the results presented, three consequences of the interaction with the environment can be observed that induce changes in structural and magnetic indices of aromaticity. First, broad ranges of HOMA or NICS values are usually obtained for different conformations of nearest neighborhood. Next, these values and their means can differ significantly from those characterising isolated monomers. The most significant increase in aromaticities is expected for the six-membered rings of guanine, thymine and cytosine. The same trend was also noticed for all amino acids inside proteins but this effect was much smaller, reaching the highest value for the five-membered ring of tryptophan. Explicit water solutions impose similar changes on HOMA and NICS distributions. Thus, environment effects of protein, DNA and even explicit water molecules are non-negligible sources of aromaticity changes appearing in the rings of nucleobases and aromatic amino acids residues