Outline Bands Paper Culmination of Synthesis 2011-2023- Coats-Gaskell (original) (raw)
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Ab initioGreen’s function formalism for band structures
Physical Review B, 2005
Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is formulated for crystal orbitals (CO-ADC). In this approach, the poles of the Green's function are determined by solving a suitable Hermitian eigenvalue problem. The method is not only applicable to the outer valence and conduction bands, it is also stable for inner valence bands where strong electron correlations are effective. The key to the proposed scheme is to evaluate the self-energy in terms of Wannier orbitals before transforming it to a crystal momentum representation. Exploiting the fact that electron correlations are mainly local, one can truncate the lattice summations by an appropriate configuration selection scheme. This yields a flat configuration space; i.e., its size scales only linearly with the number of atoms per unit cell for large systems and, under certain conditions, the computational effort to determine band structures also scales linearly. As a first application of the new formalism, a lithium fluoride crystal has been chosen. A minimal basis set description is studied, and a satisfactory agreement with previous theoretical and experimental results for the fundamental band gap and the width of the F 2p valence band complex is obtained.
Band structure built from oligomer calculations
The Journal of Chemical Physics, 2008
A method to build accurate band structures of polymers from oligomer calculations has been developed. This method relies on systematic procedures for ͑i͒ assigning k values, ͑2͒ eliminating strongly localized molecular orbitals, and ͑iii͒ connecting bands across the entire Brillouin zone. Illustrative calculations are carried out at the HF/STO-3G level for trans-polyacetylene ͑PA͒, poly͑para-phenylene͒ ͑PPP͒, and water chains. More stringent tests at several different levels are reported for polydiacetylene/polybutatriene.
The reaction between allylmagnesium bromide and imines 5a-l leads to the corresponding 4-substituted 4-N-benzylaminobut-1-enes 6a-l, which were oxidized in a regioselective manner to the alkenylnitrones 7a-l. The intramolecular 1,3-dipolar cycloaddition of these nitrones gave 2-spiroannulated or 2-substituted 6-exo-phenyl-1-aza-7-oxabicyclo[2.2.1]heptanes 8a-j. Reductive cleavage of the N-O bond of the obtained bicycles afforded the diverse substituted 4-hydroxypiperidines 9a-h in good yields. This stereoselective approach allowed the preparation of all-cis-4hydroxy-6-phenyl-2-nonylpiperidine (9i), a close analogue of dendrobatid frog alkaloid 241D. A. Varlamov et al. PAPER Synthesis 2002, No. 6, 771-783 ISSN 0039-7881 © Thieme Stuttgart · New York 1.23 (d, J 3a,3b = 11.3) 1.82 (dd, J 3b,4 = 5.3) 4.89 (dt, J 4,5b = 2.6, J 4,5a = 2.6) c~2 .04 (m, J 5a,6a = 6.3) c C 6 D 6 -0.58 (d, J 3a,3b = 11.3 1.34 (ddd, J 3b,4 = 5.2, J 3b,5b = 2.4) 4.31 (t, J 4,3b = 5.2, J 4,5b = 5.2) 1.41 (dd, J 5a,5b = 11.3, J 5a,6a = 8.2) 8c CDCl 3 -1.36 (d, J 3a,3b = 11.3) 1.77 (dd, J 3b,4 = 5.2) 4.86 (dt, J 4,5b = 2.6) c~2 .03 (m, J 5a,6a = 6.3) c N O Ph R 2 R 1 1 2 3 4 5 6 α β β 8a-j PAPER A Stereoselective Route to All-cis-2,6-Disubstituted 4-Hydroxypiperidines 779 Synthesis 2002, No. 6, 771-783 ISSN 0039-7881 © Thieme Stuttgart · New York
Keywords: chan nel-cut mono chro ma tor, asym met ric diffrac tion, X-ray beam shap ing, GISAXS, X-ray im ag ing
The and bending fundamental bands of
Journal of Molecular Spectroscopy, 2003
Infrared spectra of PD 3 have been recorded in the 600-1160 cm À1 range at a resolution of 0:0023 cm À1. About 2500 rovibrational transitions have been measured and assigned to the m 2 ðA 1 Þ and m 4 ðEÞ bending fundamentals, including 131 ''perturbation allowed'' transitions with selection rules Dðk À lÞ ¼ AE3 and AE6. Splittings of the K 00 ¼ 3, 6, and 9 lines were observed. The rotational structure in the v 2 ¼ 1 and v 4 ¼ 1 vibrational states up to J ¼ K ¼ 28 was reproduced by fitting simultaneously all experimental data. The adopted rovibrational Hamiltonian explicitly takes into account the Coriolis and k-type interactions between the v 2 ¼ 1 and v 4 ¼ 1 states, and includes also several essential resonances within these states. Two different reductions of the Hamiltonian were adopted in the fitting procedure. The 41 parameters in model 1 reproduced 2435 IR transitions retained in the final cycle with a standard deviation of the fit equal to 2:06 Â 10 À4 cm À1 (about the precision of experimental measurements); in model 2, 45 parameters reproduced 2428 transitions with the same value of standard deviation. The equivalence of the two sets of parameters has been demonstrated.
Edge-unfolding nested polyhedral bands
Computational Geometry, 2008
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Note on the generation of a new basis set for band structure calculations of infinite stacks
The band structures of a formamide stack (in the DNA B stacking arrangement), as well of cytosine (C) and uracil (U) stacks were calculated at the ab initio Hartree-Fock (HF) level using first a double basis set. The resulting valence and conduction bands were corrected for correlation on the basis of the inverse Dyson equation in the diagonal approximation with a MP2 selfenergy taking into account the relaxation effects.