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Academic literature on the topic 'Orbital structure'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Orbital structure"

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CHEN, ZHENHUA, JINSHUAI SONG, LINGCHUN SONG, and WEI WU. "A VALENCE BOND APPROACH BASED ON LEWIS STRUCTURES." Journal of Theoretical and Computational Chemistry 07, no. 04 (August 2008): 655–68. http://dx.doi.org/10.1142/s0219633608004039.

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In this paper, a valence bond method based on Lewis structures, called LVB, is presented. The method uses a Slater determinant expansion of doubly occupied orbitals for describing a Lewis structure, where two orbital sets, semi-localized orbitals, called bond orbitals, and localized hybrid atomic orbitals (HAOs), are employed. The levels of LVB method are fashioned as LVBS, LVBSD, etc. LVBS involves only the single bond orbital replacements with HAOs, while LVBSD involves also double replacements, and so on. Tests of three examples, methane, methylene, and benzene, show that the LVB method at both of LVBS and LVBSD levels gives results that match those of the VBSCF method very well, even though the form of LVB wave function is much compact.

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Ghosh, U. S., B. Mukherjee, and S. Rai. "Shell model study of nuclear structure in 63,65,67Ga." International Journal of Modern Physics E 29, no. 07 (July 2020): 2050045. http://dx.doi.org/10.1142/s0218301320500457.

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Shell model calculations have been performed in [Formula: see text] model space using two different interactions viz. jj44bpn and jun45pn to explore nuclear structure in [Formula: see text]Ga. Calculated excitation energies are compared with previously reported experimental values and a good agreement has been observed. Transitions strengths are also calculated using two sets of effective charges for proton and neutron and are compared with nearby [Formula: see text]Zn isotopes. Occupation probabilities of protons and neutrons corresponding to individual orbitals (namely [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] orbital), and dominant particle configurations for individual spin states have been presented as well. Calculations suggest major role of intruder [Formula: see text] orbital in constructing the wave functions of higher angular momentum states, whereas, the lower excited states are mainly dominated by contributions from [Formula: see text] orbitals.

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Baldev, Vibha, and Shailja Tibrewal. "Anomalous orbital structure mimicking fracture of orbital floor." Journal of American Association for Pediatric Ophthalmology and Strabismus 24, no. 3 (June 2020): 175–77. http://dx.doi.org/10.1016/j.jaapos.2020.01.016.

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Hotta, Takashi, Elbio Dagotto, Hiroyasu Koizumi, and Yasutami Takada. "STRIPES IN MANGANITES." International Journal of Modern Physics B 14, no. 29n31 (December 20, 2000): 3494–99. http://dx.doi.org/10.1142/s021797920000399x.

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Topological aspects of the stripe structure in manganese oxides are discussed in terms of the "winding number" w associated with the Berry-phase conncection for e g orbitals acquired by the parallel transport through the periodic array of Jahn-Teller centers. For La 1-x Ca x MnO 3, w is shown to characterize both the three-dimensional spin-charge-orbital structures in the antiferromagnetic phase for x≥1/2 and the charge-orbital stripes in the two-dimensional ferromagnetic phase for <1/2.

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Li, Yu-Qiong, Qian He, Jian-Hua Chen, and Cui-Hua Zhao. "Electronic and chemical structures of pyrite and arsenopyrite." Mineralogical Magazine 79, no. 7 (December 2015): 1779–89. http://dx.doi.org/10.1180/minmag.2015.079.7.05.

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AbstractThe first-principles plane-wave pseudopotential method is used to study the electronic and chemical structures of pyrite (FeS2) and arsenopyrite (FeAsS). The results indicate that an antibonding interaction occurs between Fe and As atoms in arsenopyrite. This interaction results in the Fe atom being repelled towards the S atom to stabilize antibonding orbitals, causing a larger S–Fe–S angle in arsenopyrite than in pyrite and a distortion in the arsenopyrite structure. In arsenopyrite, Fe–Fe distances are alternately long and short. The low spin density of the Fe d electrons supports this configuration in arsenopyrite. However, electron density calculations indicate that there is negligible electron density present between Fe atoms. This result indicates that cation-anion interactions are dominant in arsenopyrite. The pyrite Fe 3d orbital is split below the Fermi level, whereas the arsenopyrite Fe 3d orbital is not split, which can be attributed to the stronger interatomic bonding effects between Fe and S atoms in pyrite compared to arsenopyrite. It is found that the d-p orbital interactions between Fe and S atoms lead to bonding-antibonding splitting in both pyrite and arsenopyrite. However, the bonding effects between pyrite Fe and S atoms are stronger than in arsenopyrite. In arsenopyrite, the bonding interaction between the As 4p and Fe 3d orbitals is very weak, while the antibonding effect is very strong. The p-p orbital interaction is the dominant effect in As–S bonding. Frontier orbital calculations indicate that the Fermi levels of pyrite and arsenopyrite are notably close to each other, resulting in similar electrochemical activities. Orbital coefficient results show that the pyrite Fe 3d and S 3p orbitals are the active orbitals in the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively. In the case of arsenopyrite, Fe 3d orbitals are very active in both the HOMO and LUMO. Moreover, the activity of the As 4p in the HOMO is greater than S 3p, whereas the opposite situation occurs in the LUMO. Based on these results, As atoms could be one of the active sites for the oxidation of arsenopyrite. In addition, separation of arsenopyrite and pyrite could be achieved by utilizing the difference in chemical reactivities of iron in the two minerals.

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Masan, Samuel E. P. P., Fitri N. Febriana, Andi H. Zaidan, Ira Puspitasari, and Febdian Rusydi. "Evaluation of the Electronic Structure Resulting from ab-initio Calculations on Simple Molecules Using the Molecular Orbital Theory." Jurnal Penelitian Pendidikan IPA 7, no. 1 (January 28, 2021): 107. http://dx.doi.org/10.29303/jppipa.v7i1.545.

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Hartree Fock (HF) and Density Functional Theory (DFT) have been commonly used to model chemical problems. This study uses the Molecular Orbital Theory (MOT) to evaluate the electronic structure of five diatomic molecules generated by HF and DFT calculations. The evaluation provides an explanation of how the orbitals of a molecule come to be and how this affects the calculation of the physical quantities of the molecule. The evaluation is obtained after comparing the orbital wave functions calculated by MOT, HF, and DFT. This study found that the nature of the Highest Occupied Molecular Orbital (HOMO) of a molecule is determined by the valence orbital properties of the constituent atoms. This HOMO property greatly influences the precision of calculating the molecular electric dipole moment. This shows the importance of understanding the orbital properties of a molecule formed from the HF and DFT calculations

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Bryar, Traci R., and Donald R. Eaton. "Electronic configuration and structure of paramagnetic iron dinitrosyl complexes." Canadian Journal of Chemistry 70, no. 7 (July 1, 1992): 1917–26. http://dx.doi.org/10.1139/v92-240.

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The electronic and geometric structures of paramagnetic iron dinitrosyl complexes have been investigated using electron spin resonance, infrared spectroscopy, and X-ray crystallography. It is concluded that these compounds are best described as 17 electron complexes with a d9 configuration rather than the d7 configuration assumed by most previous investigators. The anisotropy of the g values, determined from the electron spin resonance spectra of frozen solutions, varies considerably from complex to complex. The results are consistent with the supposition that all of the complexes have a distorted tetrahedral geometry, but the nature of the distortion changes as the ligands are varied. As a result of this variation there are changes in the nature of the spin-containing d orbital. Ligands containing hard, nonpolarizable donor atoms such as oxygen or fluorine produce a distortion towards a planar geometry, placing the odd electron in a predominantly [Formula: see text] orbital, while those containing softer donor atoms such as phosphorus or sulfur give complexes with a different type of distortion, leading to placement of the odd electron in a predominantly [Formula: see text] orbital. Nitrogen and halide donor ligands produce smaller distortions, leading to spin-containing molecular orbitals with contributions from a mixture of d orbitals. In accordance with this model, the crystal structure of [Fe(NO)2I2]− has been found to be only slightly distorted from regular tetrahedral coordination about the iron atom.

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Cargnoni, Fausto, Simone Cenedese, Paolo Ghigna, Mario Italo Trioni, and Marco Scavini. "Electronic Structure and Magnetic Coupling of Pure and Mg-Doped KCuF3." Advances in Condensed Matter Physics 2018 (August 15, 2018): 1–10. http://dx.doi.org/10.1155/2018/9164270.

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We investigated the electronic and magnetic properties of KCuF3 and KCu0.875Mg0.125F3 crystals by means of Density Functional periodic computations at the B3LYP level of theory. We considered four possible magnetic ordering of the unpaired electrons on copper ions. Both materials are correctly predicted as being 1D antiferromagnetic insulators, and the superexchange parameters in the crystallographic ab planes and along the c direction measure +10 and -600 K, respectively. Residual spin polarization is found also on fluorine atoms, in agreement with literature results. We found a complete orbital ordering at Cu sites: in the copper reference frame dxy, dyz, dxz, and dz2 orbitals contain about 2 electrons each, while the dx2-y2 orbital is only partially filled. The perturbation induced by doping of KCuF3 with Mg is very strong and localized on the first shell of F neighbours. Mg has a very small influence on the ordering of the 3d orbitals of copper and on the Cu-Cu magnetic superexchange parameters but reduces significantly the absolute energy differences between the antiferromagnetic ground state and the ferromagnetic phase, in agreement with the experiment. The absence of long range effects makes Mg a suitable dopant for the investigation of strongly correlated electronic systems by means of orbital dilution.

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Guimon, C., G. Pfister-Guillouzo, D. Ilavsky, M. Marchalin, and A. Martvon. "Structure électronique et réactivité des pyridyl-isothiocyanates. Étude quantique et photoélectronique." Canadian Journal of Chemistry 64, no. 8 (August 1, 1986): 1467–73. http://dx.doi.org/10.1139/v86-242.

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On the basis of molecular orbital calculations made in association with ultraviolet photoélectron spectroscopy (ups), it is demonstrated that the regioselectivity of the cycloadditions of pyridyl-2-isothiocyanate with 1,3-dipoles is directed by frontier orbitals. The different cycloadditions (4 + 2, 2 + 3, 2 + 2) vary with the overlap of these orbitals and this shows the importance of secondary interactions, namely the localization of the orbitals on the atoms adjacent to the bonds that are formed during the addition.

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Purton, J., and D. S. Urch. "High-resolution silicon Kβ X-ray spectra and crystal structure." Mineralogical Magazine 53, no. 370 (April 1989): 239–44. http://dx.doi.org/10.1180/minmag.1989.053.370.11.

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AbstractHigh-resolution X-ray emission spectra (XES) are presented for minerals with a variety of structures. The participation of the Si 3p orbitals in bonding is influenced by the local structure around the silicon atom. In orthosilicates the distortion of the SiO44--tetrahedron influences both peak-width and the intensity of the high-energy shoulder of the Si-Kβ spectrum. In minerals containing Si-O-Si bonds there is mixing of the Si 3s and 3p orbitals giving rise to a peak on the low-energy side of the main Si-Kβ peak. When combined with X-ray photoelectron spectra (XPS), a complete molecular orbital picture of bonding can be established.

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Dissertations / Theses on the topic "Orbital structure"

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Tyer, Richard. "Ab initio study of charge, spin and orbital ordering in manganites." Thesis, University of Sheffield, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246901.

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Kimber, Simon A. J. "Spin and orbital ordering in ternary transition metal oxides." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/3487.

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Spin and orbital orderings are amongst the most important phenomena in the solid state chemistry of oxides. Physical property and powder neutron and X-ray diffraction measurements are reported for a range of mostly low dimensional ternary transition metal oxides which display spin or orbital order. Extensive studies of the physical properties and crystal structure of In2VO5 are reported. The structure of this material consists of one dimensional zig-zag chains of orbitally ordered S = 1/2 V4+. Magnetic susceptibility measurements show an unusual crossover from dominant ferromagnetic (θ = 17 K) to antiferromagnetic (θ = -70 K) exchange at 120 K, which is attributed to ferromagnetic dimerisation driven by magnetic frustration. The magnetic moment also increases from 1.81 to 2.2μB at the 120 K crossover. Heat capacity measurements confirm this scenario as the magnetic entropy tends towards 1/2 Rln3 below 120 K before approximating to Rln2 at high temperature. Synchrotron x-ray diffraction and high resolution neutron powder diffraction show no bulk structural changes, but the b axis, along which the VO6 chains run, shows an anomalous expansion below 120 K. At low temperatures, a downturn in the magnetic susceptibility is seen at 2.5 K, signifying a spin freezing transition. Heat capacity and powder neutron diffraction measurements show no evidence for long range magnetic order down to 0.42 K. The low dimensional brannerite materials MV2O6 (M = Mn, Co, Ni) were synthesised by a sol-gel method. Magnetic properties were investigated by magnetisation, powder neutron diffraction and in the case of CoV2O6, heat capacity measurements. The structure of these materials consists of linear chains of edge sharing MO6 octahedra. Monoclinic MnV2O6 is an isotropic antiferromagnet with TN = 20 K and a reduced magnetic coherence length due to 3 % Mn/V antisite disorder. The magnetic structure consists of ferromagnetic edge-sharing chains with k = (0,0,1/2) and a refined Mn moment of 4.77(7) μB. The triclinic materials CoV2O6 and NiV2O6 are also antiferromagnetic with TN = 7 and 14 K respectively and both show metamagnetic type transitions. Unusually, M(H) isotherms recorded below 5 K for CoV2O6 show a plateau at 1/3 of the saturation magnetisation. This feature, together with a long period modulated magnetic structure, is attributed to strong single ion (Ising) type anisotropy and nearest neighbour ferromagnetic exchange. Preliminary high pressure experiments on NiV2O6 have confirmed a previously reported transition to a columbite phase at 6 GPa and 900 °C. The high pressure polymorph is also antiferromagnetic with TN = 2.5 K. The previously uncharacterised perovskite, PbRuO3 has been prepared using high pressure/temperature synthesis techniques (10 GPa, 1000 °C). Synchrotron powder X-ray diffraction measurements show that the room temperature structure is orthorhombic, Pnma. A first order orbital ordering transition occurs at 75 K with an associated metal insulator transition. Below 75 K, the dxz orbitals are preferentially occupied and the structure is orthorhombic Imma. The transition may be driven by an increase in antiferroelectric Pb2+ displacements, whcih reach a peak at ~ 125 K. A further structural transition to a larger monoclinic cell is also identified at 9.7 K. The physical properties and crystal structures of two low dimensional lead manganese oxides have also been investigated. Acentric Pb2MnO4, which has a structure consisting of edge sharing chains, is antiferromagnetic with TN = 18 K. Powder neutron diffraction shows the magnetic structure consists of antiferromagnetic chains with k = (0,0,0) and a refined Mn moment of 2.74(2) μB. The crystal point group allows piezoelectricity and the magnetic point group symmetry allows piezomagnetism. We speculate that coupled magnetic and electric properties may be observed in this material. The layered material, Pb3Mn7O15, with a structure consisting of 1/2 filled Kagomé layers has also been studied. Single crystals were prepared by a flux growth method and polycrystalline material was prepared by the ceramic method. Powder neutron and synchrotron x-ray diffraction studies show that the single crystals are hexagonal and that the polycrystalline material is orthorhombic. Furthermore, heat capacity measurements show that the hexagonal single crystal material undergoes a glassy magnetic transition. In contrast, powder neutron diffraction shows that the orthorhombic polycrystalline material has coherent long range magnetic order. These differences are attributed to an oxygen deficiency in the polycrystalline magnetic order. These differences are attributed to an oxygen deficiency in the polycrystalline material.

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Senn, Mark Stephen. "Charge, orbital and magnetic ordering in transition metal oxides." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/7828.

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Neutron and x-ray diffraction has been used to study charge, orbital and magnetic ordering in some transition metal oxides. The long standing controversy regarding the nature of the ground state (Verwey structure) of the canonical charge ordered material magnetite (Fe3O4) has been resolved by x-ray single crystal diffraction studies on an almost single domain sample at 90 K. The Verwey structure is confirmed to have Cc symmetry with 56 unique sites in the asymmetric unit. Charge ordering is shown to be a useful first approximation to describe the nature of the ground state, and the conjecture that Verwey made in 1939 has finally been confirmed. However, three-site distortions which couple to the orbital ordering of the Fe2+ ordered states (trimerons) are shown to provide a more complete description of the low temperature structure. Trimerons explain the rather continuous distribution of the valence states observed in magnetite below Tv, anomalous shortening of Fe-Fe distances and the off-centre distortions resulting in ferroelectricity. DFT+U electronic structure calculations on the experimental coordinates support the conclusion of this crystallographic study, with the highest electron densities calculated for those Fe-Fe distances predicated to participate in the trimeron bonds. The 6H-perovskites of the type Ba3ARu2O9 have been reinvestigated by high resolution neutron and x-ray power diffraction. The charge ordered state of Ba3NaRu2O9 has been characterised at 110 K (P2/c, a =5.84001(2) Å, b = 10.22197(4) Å, c = 14.48497(6) Å, β = 90.2627(3) °) and shown to consist of a structure with near integer charge ordering of Ru5+ 2O9 / Ru6+ 2O9 dimers. The ground state has been shown to be very sensitive to external perturbations, with a novel melting of charge ordering observed under x-ray irradiation below 40 K (C2/c, a =5.84470(2) Å, b = 10.17706(3) Å, c = 14.45866(5) Å, β = 90.2151(3)-° at 10 K). High pressure studies reveal that the Ru-Ru intra-dimer distance may dictate the response of the system to pressure. Empirical trends in the Ba3ARu2O9 series of compounds have shown that change in ‘chemical pressure’ in these systems may be rationalised in terms of Coulomb’s law. In A = La and Y the magnetic ordering is shown to be FM within the Ru2O9 dimers (1.4(2) μB and 0.5(1) μB, respectively per Ru), representing the first case of intra dimer FM coupling reported in a system containing face-sharing RuO6 octahedra . The overall AFM coupling of the dimers implies an as yet unobserved breaking of the parent symmetry. In A = Nd, a complex competition between the crystal field effect of Nd3+ and the magnetic ordering of the Ru2O9 FM moments has been observed, leading first vi to FM order of Nd at 25 K (1.56(7) μB) followed by ordering of Ru moments (0.5(1) μB) and a spin reorientation transition of Nd moments at 18 K. In A = Ca, the formation of a singlet ground state is observed in Ru2O9 rather than the expected AFM coupling and below 100 K Ba3CaRu2O9 is diamagnetic. All five systems indicate that the Ru2O9 dimer is the physically significant unit in these systems when considering structural trends and the ordering of charge, spin and orbital degrees of freedom.

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Jesseit, Roland. "The orbital structure of galaxies and dark matter halos in N-body simulations." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970059388.

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Graham, John Patrick. "Applications of molecular orbital theory in the structure, bonding and reactivity of inorganic molecules /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487941504295077.

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Sonnenberg, Jason Louis. "Structure and reactivity studies of environmentally relevant actinide-containing species using relativistic density functional theory." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124308219.

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Thesis (Ph. D.)--Ohio State University, 2005.
Title from second page of PDF file. Document formatted into pages; contains xxiii, 151 p.; also includes graphics (some col.). Includes bibliographical references (p. 140-151). Available online via OhioLINK's ETD Center

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Ghosh, Swarnava Ghosh. "Orbital-free density functional theory using higher-order finite differences." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53603.

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Density functional theory (DFT) is not only an accurate but also a widely used theory for describing the quantum-mechanical electronic structure of matter. In this approach, the intractable problem of interacting electrons is simplified to a tractable problem of non-interacting electrons moving in an effective potential. Even with this simplification, DFT remains extremely computationally expensive. In particular, DFT scales cubically with respect to the number of atoms, which restricts the size of systems that can be studied. Orbital free density functional theory (OF-DFT) represents a simplification of DFT applicable to metallic systems that behave like a free-electron gas. Current implementations of OF-DFT employ the plane-wave basis, the global nature of the basis prevents the efficient use of modern high-performance computer archi- tectures. We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a gener- alized framework suitable for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we develop a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In doing so, we make the calculation of the electronic ground-state and forces on the nuclei amenable to computations that altogether scale linearly with the number of atoms. We develop a parallel implementation of our method using Portable, Extensible Toolkit for scientific computations (PETSc) suite of data structures and routines. The communication between processors is handled via the Message Passing Interface(MPI). We implement this formulation using the finite-difference discretization, us- ing which we demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson mixing. We verify the accuracy of our results by comparing the energies and forces with plane-wave methods for selected examples, one of which is the vacancy formation energy in Aluminum. Overall, we demonstrate that the proposed formulation and implementation is an attractive choice for performing OF-DFT calculations.

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Villanueva, Martha A. "Structures of small organic cluster ions computed using self-consistent field semiempirical molecular orbital methods." Thesis, Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/30323.

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Abuzaid, N. (Nuha). "Electronic structure according to the orbital approximation and the Hartree-Fock theory with electron correlation methods." Bachelor's thesis, University of Oulu, 2016. http://urn.fi/URN:NBN:fi:oulu-201611113017.

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Hartree-Fock theory, a computational method to solve electronic structure of molecules, is reviewed in this thesis. The emphasis is on spotlighting the physical reasoning behind the assumptions of the Hartree-Fock theory. Also, three post-Hartree-Fock electron correlation methods are introduced, configuration interaction, coupled cluster, and Møller-Plesset theory.

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Clement, Marjory Carolena. "In Pursuit of Local Correlation for Reduced-Scaling Electronic Structure Methods in Molecules and Periodic Solids." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/104588.

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Over the course of the last century, electronic structure theory (or, alternatively, computational quantum chemistry) has grown from being a fledgling field to being a ``full partner with experiment" [Goddard textit{Science} textbf{1985}, textit{227} (4689), 917--923]. Numerous instances of theory matching experiment to very high accuracy abound, with one excellent example being the high-accuracy textit{ab initio} thermochemical data laid out in the 2004 work of Tajti and co-workers [Tajti et al. textit{J. Chem. Phys.} textbf{2004}, textit{121}, 11599] and another being the heats of formation and molecular structures computed by Feller and co-workers in 2008 [Feller et al. textit{J. Chem. Phys.} textbf{2008}, textit{129}, 204105]. But as the authors of both studies point out, this very high accuracy comes at a very high cost. In fact, at this point in time, electronic structure theory does not suffer from an accuracy problem (as it did in its early days) but a cost problem; or, perhaps more precisely, it suffers from an accuracy-to-cost ratio problem. We can compute electronic energies to nearly any precision we like, textit{as long as we are willing to pay the associated cost}. And just what are these high computational costs? For the purposes of this work, we are primarily concerned with the way in which the computational cost of a given method scales with the system size; for notational purposes, we will often introduce a parameter, $N$, that is proportional to the system size. In the case of Hartree-Fock, a one-body wavefunction-based method, the scaling is formally $N^4$, and post-Hartree-Fock methods fare even worse. The coupled cluster singles, doubles, and perturbative triples method [CCSD(T)], which is frequently referred to as the ``gold standard" of quantum chemistry, has an $N^7$ scaling, making it inapplicable to many systems of real-world import. If highly accurate correlated wavefunction methods are to be applied to larger systems of interest, it is crucial that we reduce their computational scaling. One very successful means of doing this relies on the fact that electron correlation is fundamentally a local phenomenon, and the recognition of this fact has led to the development of numerous local implementations of conventional many-body methods. One such method, the DLPNO-CCSD(T) method, was successfully used to calculate the energy of the protein crambin [Riplinger, et al. textit{J. Chem. Phys.} textbf{2013}, textit{139}, 134101]. In the following work, we discuss how the local nature of electron correlation can be exploited, both in terms of the occupied orbitals and the unoccupied (or virtual) orbitals. In the case of the former, we highlight some of the historical developments in orbital localization before applying orbital localization robustly to infinite periodic crystalline systems [Clement, et al. textbf{2021}, textit{Submitted to J. Chem. Theory Comput.}]. In the case of the latter, we discuss a number of different ways in which the virtual space can be compressed before presenting our pioneering work in the area of iteratively-optimized pair natural orbitals (``iPNOs") [Clement, et al. textit{J. Chem. Theory Comput.} textbf{2018}, textit{14} (9), 4581--4589]. Concerning the iPNOs, we were able to recover significant accuracy with respect to traditional PNOs (which are unchanged throughout the course of a correlated calculation) at a comparable truncation level, indicating that our improved PNOs are, in fact, an improved representation of the coupled cluster doubles amplitudes. For example, when studying the percent errors in the absolute correlation energies of a representative sample of weakly bound dimers chosen from the S66 test suite [v{R}ez'{a}c, et al. textit{J. Chem. Theory Comput.} textbf{2011}, textit{7} (8), 2427--2438], we found that our iPNO-CCSD scheme outperformed the standard PNO-CCSD scheme at every truncation threshold ($tpno$) studied. Both PNO-based methods were compared to the canonical CCSD method, with the iPNO-CCSD method being, on average, 1.9 times better than the PNO-CCSD method at $tpno = 10^{-7}$ and more than an order of magnitude better for $tpno < 10^{-10}$ [Clement, et al. textit{J. Chem. Theory Comput.} textbf{2018}, textit{14} (9), 4581--4589]. When our improved PNOs are combined with the PNO-incompleteness correction proposed by Neese and co-workers [Neese, et al. textit{J. Chem. Phys.} textbf{2009}, textit{130}, 114108; Neese, et al. textit{J. Chem. Phys.} textbf{2009}, textit{131}, 064103], the results are truly astounding. For a truncation threshold of $tpno = 10^{-6}$, the mean average absolute error in binding energy for all 66 dimers from the S66 test set was 3 times smaller when the incompleteness-corrected iPNO-CCSD method was used relative to the incompleteness-corrected PNO-CCSD method [Clement, et al. textit{J. Chem. Theory Comput.} textbf{2018}, textit{14} (9), 4581--4589]. In the latter half of this work, we present our implementation of a limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) based Pipek-Mezey Wannier function (PMWF) solver [Clement, et al. textbf{2021}, textit{Submitted to J. Chem. Theory Comput.}]. Although orbital localization in the context of the linear combination of atomic orbitals (LCAO) representation of periodic crystalline solids is not new [Marzari, et al. textit{Rev. Mod. Phys.} textbf{2012}, textit{84} (4), 1419--1475; J`{o}nsson, et al. textit{J. Chem. Theory Comput.} textbf{2017}, textit{13} (2), 460--474], to our knowledge, this is the first implementation to be based on a BFGS solver. In addition, we are pleased to report that our novel BFGS-based solver is extremely robust in terms of the initial guess and the size of the history employed, with the final results and the time to solution, as measured in number of iterations required, being essentially independent of these initial choices. Furthermore, our BFGS-based solver converges much more quickly and consistently than either a steepest ascent (SA) or a non-linear conjugate gradient (CG) based solver, with this fact demonstrated for a number of 1-, 2-, and 3-dimensional systems. Armed with our real, localized Wannier functions, we are now in a position to pursue the application of local implementations of correlated many-body methods to the arena of periodic crystalline solids; a first step toward this goal will, most likely, be the study of PNOs, both conventional and iteratively-optimized, in this context.
Doctor of Philosophy
Increasingly, the study of chemistry is moving from the traditional wet lab to the realm of computers. The physical laws that govern the behavior of chemical systems, along with the corresponding mathematical expressions, have long been known. Rapid growth in computational technology has made solving these equations, at least in an approximate manner, relatively easy for a large number of molecular and solid systems. That the equations must be solved approximately is an unfortunate fact of life, stemming from the mathematical structure of the equations themselves, and much effort has been poured into developing better and better approximations, each trying to balance an acceptable level of accuracy loss with a realistic level of computational cost and complexity. But though there has been much progress in developing approximate computational chemistry methods, there is still great work to be done. textit{Many} chemical systems of real-world import (particularly biomolecules and potential pharmaceuticals) are simply too large to be treated with any methods that consistently deliver acceptable accuracy. As an example of the difficulties that come with trying to apply accurate computational methods to systems of interest, consider the seminal 2013 work of Riplinger and co-workers [Riplinger, et al. textit{J. Chem. Phys.} textbf{2013}, textit{139}, 134101]. In this paper, they present the results of a calculation performed on the protein crambin. The method used was DLPNO-CCSD(T), an approximation to the ``gold standard" computational method CCSD(T). The acronym DLPNO-CCSD(T) stands for ``domain-based local pair natural orbital coupled cluster with singles, doubles, and perturbative triples." In essence, this method exploits the fact that electron-electron interactions (``electron correlation") are a short-range phenomenon in order to represent the system in a mathematically more compact way. This focus on the locality of electron correlation is a crucial piece in the effort to bring down computational cost. When talking about computational cost, we will often talk about how the cost scales with the approximate system size $N$. In the case of CCSD(T), the cost scales as $N^{7}$. To see what this means, consider two chemical systems textit{A} and textit{B}. If system textit{B} is twice as large as system textit{A}, then the same calculation run on both systems will take $2^{7} = 128$ times longer on system textit{B} than on system textit{A}. The DLPNO-CCSD(T) method, on the other hand, scales linearly with the system size, provided the system is sufficiently large (we say that it is ``asymptotically linearly scaling"), and so, for our example systems textit{A} and textit{B}, the calculation run on system textit{B} should only take twice as long as the calculation run on system textit{A}. But despite the favorable scaling afforded by the DLPNO-CCSD(T) method, the time to solution is still prohibitive. In the case of crambin, a relatively small protein with 644 atoms, the calculation took a little over 30 days. Clearly, such timescales are unworkable for the field of biochemical research, where the focus is often on the interactions between multiple proteins or other large biomolecules and where many more data points are required. In the work that follows, we discuss in more detail the genesis of the high costs that are associated with highly accurate computational methods, as well as some of the approximation techniques that have already been employed, with an emphasis on local correlation techniques. We then build off this foundation to discuss our own work and how we have extended such approximation techniques in an attempt to further increase the possible accuracy to cost ratio. In particular, we discuss how iteratively-optimized pair natural orbitals (the PNOs of the DLPNO-CCSD(T) method) can provide a more accurate but also more compact mathematical representation of the system relative to static PNOs [Clement, et al. textit{J. Chem. Theory Comput.} textbf{2018}, textit{14} (9), 4581--4589]. Additionally, we turn our attention to the problem of periodic infinite crystalline systems, a class of materials less commonly studied in the field of computational chemistry, and discuss how the local correlation techniques that have already been applied with great success to molecular systems can potentially be applied in this domain as well [Clement, et al. textbf{2021}, textit{Submitted to J. Chem. Theory Comput.}].

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Books on the topic "Orbital structure"

1

Marie-Liesse, Doublet, and Iung Christophe, eds. Orbital approach to the electronic structure of solids. Oxford: Oxford University Press, 2012.

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Sevin, Alain. Liaisons chimiques: Structure et re activite. Paris: Dunod, 2006.

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Structure and bonding. New York, NY: Wiley-Interscience, 2002.

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Burns, Rowland E. Forbidden tangential orbit transfers between intersecting Keplerian orbits. Washington, D.C: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1990.

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Yves, Jean. La structure électronique des molécules. 3rd ed. Paris: Dunod, 2003.

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AEleen, Frisch, and Gaussian Inc, eds. Exploring chemistry with electronic structure methods. 2nd ed. Pittsburgh, PA: Gaussian, Inc., 1996.

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Rhodes, Marvin D. Baseline tests of an autonomous telerobotic system for assembly of space truss structures. Hampton: National Aeronautics and Space Administration, Langley Research Center, 1994.

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Böhlig, Heinz. Molekülschwingungen und Kraftkonstanten. Halle: Deutsche Akademie der Naturforscher Leopoldina, 1988.

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Böhlig, Heinz. Molekülschwingungen und Kraftkonstanten. Halle: Deutsche Akademie der Naturforscher Leopoldina, 1988.

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Optimized LCAO method and the electronic structure of extended systems. Berlin: Springer-Verlag, 1989.

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Book chapters on the topic "Orbital structure"

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Helgaker, Trygve, Poul Jørgensen, and Jeppe Olsen. "Orbital Rotations." In Molecular Electronic-Structure Theory, 80–106. Chichester, UK: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781119019572.ch3.

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Linderberg, Jan. "Orbital Models and Electronic Structure Theory." In Structure and Bonding, 39–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/430_2011_50.

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Helgaker, Trygve, Poul Jørgensen, and Jeppe Olsen. "Short-Range Interactions and Orbital Expansions." In Molecular Electronic-Structure Theory, 256–86. Chichester, UK: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781119019572.ch7.

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Haken, Hermann, and Hans Christoph Wolf. "Orbital and Spin Magnetism. Fine Structure." In Advanced Texts in Physics, 181–203. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-98099-2_12.

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Haken, Hermann, and Hans Christoph Wolf. "Orbital and Spin Magnetism. Fine Structure." In Atomic and Quantum Physics, 173–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-97014-6_12.

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Haken, Hermann, and Hans Christoph Wolf. "Orbital and Spin Magnetism. Fine Structure." In The Physics of Atoms and Quanta, 181–203. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-97689-6_12.

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Haken, Hermann, and Hans Christoph Wolf. "Orbital and Spin Magnetism. Fine Structure." In The Physics of Atoms and Quanta, 175–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-97468-7_12.

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Haken, Hermann, and Hans Christoph Wolf. "Orbital and Spin Magnetism. Fine Structure." In The Physics of Atoms and Quanta, 177–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-97567-7_12.

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Nalewajski, Roman F. "Orbital Communication Theory of the Chemical Bond." In Perspectives in Electronic Structure Theory, 481–554. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20180-6_12.

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Ozawa, Tomonaga, Kosuke Okazaki, and Motohiro Nishio. "FMO as a Tool for Structure-Based Drug Design." In The Fragment Molecular Orbital Method, 217–44. Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742: CRC Press, 2009. http://dx.doi.org/10.1201/9781420078497-11.

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Conference papers on the topic "Orbital structure"

1

FANSON, J., C. C. CHU, R. SMITH, and E. ANDERSON. "Active member control of a precision structure with an H(infinity) performance objective." In Orbital Debris Conference: Technical Issues andFuture Directions. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1224.

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Závada, Petr. "Structure functions and intrinsic quark orbital motion." In Proceedings of the 17th International Spin Physics Symposium. AIP, 2007. http://dx.doi.org/10.1063/1.2750821.

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Zhang, Qinqiang, Takuya Kudo, and Ken Suzuki. "Theoretical Study of Electronic Band Structure of Dumbbell-Shape Graphene Nanoribbons for Highly-Sensitive Strain Sensors." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-88431.

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The authors have proposed the formation of dumbbell-shape graphene nanoribbon (GNR) for developing various semi-conductive materials with metallic electrode at both ends. The novel dumbbell-shape structure, which has a center narrow part and wide parts to sandwich the narrow part, can be considered as a composite structure consisting of two single GNRs with different ribbon width. In this study, the electronic band structure of this dumbbell-shape GNR was analyzed by using the first principle calculation method. All the first-principles calculations were performed using DFT. Throughout these calculations, the electronic band structures, densities of states, and orbital distributions of the new dumbbell-shape structure GNR were examined to describe the electronic properties of dumbbell-shape GNRs and predict the performance of strain sensors. The band gap of dumbbell-shape GNRs is different to that of single GNRs. The magnitude of the band gap of the dumbbell-shape GNR depends on the combination of the single GNRs and the difference in the width of narrow part and wide parts. The main change to the band gap is attributed to a change in the orbital distributions of the lowest unoccupied molecular orbitals (LUMO) and the highest occupied molecular orbitals (HOMO). In addition, when a dumbbell-shape GNR undergoes a uniaxial tensile strain, its band gap showed high strain sensitivity as was expected. Therefore, the GNR material with a dumbbell-shape structure has great potential for use in highly sensitive strain sensors.

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Izdebskaya, Ya, V. Shvedov, and A. Volyar. "Structure and Orbital Angular Momentum of Singular Arrays." In 2006 International Conference on Transparent Optical Networks. IEEE, 2006. http://dx.doi.org/10.1109/icton.2006.248232.

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Davis, Bruce A., Richard A. Hagen, Robert J. McCandless, Eric L. Christiansen, and Dana M. Lear. "Hypervelocity impact performance of 3D printed aluminum panels." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-055.

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Abstract NASA, JSC has been developing a light-weight, multi-functional sandwich core for habitable structure over the last several years. Typically honeycomb-based structures have been and still are a common structural component for many applications in the aerospace industry, unfortunately, honeycomb structures with an ordered, open path through the thickness have served to channel the micro-meteoroid or orbital debris into the pressure wall (instead of disassociating and decelerating). The development of a metallic open cell foam core has been explored to enhance the micro-meteoroid or orbital debris protection, which is heavier than comparable honeycomb-based structures when non-structural requirements for deep space environments (vacuum, micro-meteoroids/orbital debris, and radiation) have not been considered. While the metallic foam core represents a notable improvement in this area, there is an overwhelming need to further reduce the weight of space vehicles; especially when deep space (beyond low earth orbit, or LEO) is considered. NASA, JSC is currently developing a multi-functional sandwich panel using additive machining (3D printing), this effort evaluated the material response of a limited amount of 3D printed aluminum panels under hypervelocity impact conditions. The four 3D printed aluminum panels provided for this effort consisted of three body centric cubic lattice structure core and one kelvin cell structure core. Each panel was impacted once with nominally the same impact conditions (0.34cm diameter aluminum sphere impacting at 6.8 km/s at 0 degrees to surface normal). All tests were impacted successfully, with the aforementioned impact conditions. Each of the test panels maintained their structural integrity from the hypervelocity impact event with no damage present on the back side of the panel for any of the tests. These tests and future tests will be used to enhance development of 3D printed structural panels.

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Andersen, O. K., O. Jepsen, and G. Krier. "Exact Muffin-Tin Orbital Theory." In Proceedings of the Miniworkshop on “Methods of Electronic Structure Calculations” and Working Group on “Disordered Alloys”. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789814503778_0003.

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Arash, Firooz, and Fatemeh Taghavi-Shahri. "Polarized Structure Function of Nucleon and Orbital Angular Momentum." In Proceedings of the 17th International Spin Physics Symposium. AIP, 2007. http://dx.doi.org/10.1063/1.2750822.

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García-Álvarez, Rauĺ, and Miguel A. Porras. "Spatiotemporal structure of ultrafast pulses with orbital angular momentum." In Frontiers in Optics. Washington, D.C.: OSA, 2020. http://dx.doi.org/10.1364/fio.2020.jw6b.10.

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Boiko, Igor M. "On Loeb's criterion of orbital stability of self-excited periodic motions." In 2018 15th International Workshop on Variable Structure Systems (VSS). IEEE, 2018. http://dx.doi.org/10.1109/vss.2018.8460414.

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CHAMPION, K. "Atmospheric structure for low altitude satellites and aerobraked orbital transfer vehicles." In 24th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1986. http://dx.doi.org/10.2514/6.1986-186.

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Reports on the topic "Orbital structure"

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Straub, G., and J. Wills. Elastic moduli of copper: Electronic structure contributions from pseudopotentials and full-potential linear muffin-tin orbital band structure calculations. Office of Scientific and Technical Information (OSTI), November 1989. http://dx.doi.org/10.2172/5309013.

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Riley, Mark, and Akis Pipidis. The Mechanical Analogue of the "Backbending" Phenomenon in Nuclear-structure Physics. Florida State University, May 2008. http://dx.doi.org/10.33009/fsu_physics-backbending.

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This short pedagogical movie illustrates an effect in nuclear physics called backbending which was first observed in the study of the rotational behavior of rapidly rotating rare-earth nuclei in Stockholm, Sweden in 1971. The video contains a mechanical analog utilizing rare-earth magnets and rotating gyroscopes on a turntable along with some historic spectra and papers associated with this landmark discovery together with its explanation in terms of the Coriolis induced uncoupling and rotational alignment of a specific pair of particles occupying high-j intruder orbitals. Thus backbending represents a crossing in energy of the groundstate, or vacuum, rotational band by another band which has two unpaired high-j nucleons (two quasi-particles) with their individual angular momenta aligned with the rotation axis of the rapidly rotating nucleus. Backbending was a major surprise which pushed the field of nuclear structure physics forward but which is now sufficiently well understood that it can be used as a precision spectroscopic tool providing useful insight for example, into nuclear pairing correlations and changes in the latter due to blocking effects and quasi-particle seniority, nuclear deformation, the excited configurations of particular rotational structures and the placement of proton and neutron intruder orbitals at the Fermi surface.

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Zhou, Xin. Fourier transform photoelectron diffraction and its application to molecular orbitals and surface structure. Office of Scientific and Technical Information (OSTI), November 1998. http://dx.doi.org/10.2172/6458.

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Denman, Eugene, Timothy Hasselman, C. T. Sun, Jer-Nan Juang, and John Junkins. Identification of Large Space Structures on Orbit. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada173756.

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King, P. D. C. Subband Structure of a Two-Dimensional Electron Gas Formed at the Polar Surface of the Strong Spin-Orbit Perovskite KTaO3. Office of Scientific and Technical Information (OSTI), March 2012. http://dx.doi.org/10.2172/1035804.

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