Extended Hückel Molecular Orbital Calculations II. The Sigma and Pi Overlap Populations in Titanium Oxides

Hsia, Yu-Ping

doi:10.1002/jccs.197000001

J Chinese Chemical Soc

1970

DOI: 10.1002/jccs.197000001

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Extended Hückel Molecular Orbital Calculations II. The Sigma and Pi Overlap Populations in Titanium Oxides

Yu-Ping Hsia

Abstract: A method for analysis of separate sigma and pi overlap populations in a system of very low symmetry has been proposed. The calculations are performed in Ti3O3, rutile, anatase, brookite and tetragonal barium titanate. The examination of the various bond overlap populations has led to reasonable explanation on the infrared absorption spectra of CO and CO3 chemisorption on rutile and anatase and the relative heats of formation of anatase, rutile and brookite.

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1974

1979

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Cited by 3 publications

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Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Michel-Calendini¹,

Fichelle

1975

Physica Status Solidi (b)

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The energy levels of V4+ in a V0:-complex of Dzh symmetry are computed according t o an extended LCAO method with non-orthogonal orbitals. The substitutional impurity is trapped in TiO,, GeO,, and SnO, lattices. The results are compared with previous calculations on these structures. The interband transitions a t the centre of the Brillouin zone are related t o optical data with a good approximation. A first tentative is made to explain the X-ray spectra of TiO, according to the molecular diagram. The g-factors and the hyperfine structure constants are computed and the covalency of molecular orbitals is taken into account. Thefollowingresultsareobtainedfor g,, g,, andg,: 1.917,1.893, 1.966forV4+(Ti0,), 1.937,1.869, 1.953 for V4+ (SnO,) and 1.928, 1.911, 1.970 forV4+ (GeO,).The corresponding values of A,, A,, and A , in em-l units are: 35, 40, and 141 for V4+(Ti0,), 27, 40, and 148 for V4+ (SnO,), and 41,43, and 128 for V4+ (GeO,). A comparison is made with previous works using the point charge model. The LCAO calculations give results in agreement with the values deduced from E P R experiments. E s werden die Energieniveaus von V4+ in einem VO:--Komplex rnit Dzh-Symmetrie mit einer erweiterten LCAO-Methode mit nichtorthogonalen Orbitalen berechnet. Die Substitutionsstorstelle ist in Ti0,-, Ge0,-und Sn0,-Gittern eingebaut. Die Ergebnisse werden mit fruheren Berechnungen an diesen Strukturen verglichen. Die Interbandubergange im Zent,rum der Brillouinzone werden in guter abereinstimmung mit optischen Werten verkniipft. E s wird ein erster Versuch gemacht, die Rontgenspektren von TiO, entsprechend dem Molekulardiagramm zu erklaren. Die g-Faktoren und die Hyperfeinstrukturkonstanten werden berechnet, wobei die Kovalenz der Molekulorbitale berucksichtigt wird. Folgende Ergebnisse werden fur gs. g, und g, erhalten: 1,917; 1,893; 1,966 fur V4+ (TiO,), 1,937; 1,869; 1,953 fur V4+ (SnO,) und 1,928; 1,911; 1,970 fur V4+ (GeO,). Die entsprechenden Werte fur A,, A , und A , in Einheiten von cm-l sind: 35; 40 und 141 fur V4+ (TiO,), 27; 40 und 148 fur V4+ (SnO,) und 41 ; 43 und 128 fur V4+ (GeO,). Ein Vergleich des Punktladungsmodells rnit fruheren Arbeiten wird durchgefuhrt. Die LCAO-Rechnungen liefern Ergebnisse in ffbereinstimmung rnit den aus den EPR-Experimenten erhaltenen Werten.

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Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Michel-Calendini¹,

Fichelle

1975

Physica Status Solidi (b)

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Niveaux d'énergie et spectres de rayons X du rutile

Michel-Calendini

1974

Journal of Physics and Chemistry of Solids

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Transformation Enthalpies of the TiO₂ Polymorphs

Mitsuhashi

Kleppa

1979

Journal of the American Ceramic Society

110

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Extended Hückel Molecular Orbital Calculations II. The Sigma and Pi Overlap Populations in Titanium Oxides

Cited by 3 publications

References 16 publications

Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Niveaux d'énergie et spectres de rayons X du rutile

Transformation Enthalpies of the TiO₂ Polymorphs

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Extended Hückel Molecular Orbital Calculations II. The Sigma and Pi Overlap Populations in Titanium Oxides

Cited by 3 publications

References 16 publications

Electronic structure and EPR spectra of V4+ in TiO2, SnO2, and GeO2

Electronic structure and EPR spectra of V4+ in TiO2, SnO2, and GeO2

Niveaux d'énergie et spectres de rayons X du rutile

Transformation Enthalpies of the TiO2 Polymorphs

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Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Electronic structure and EPR spectra of V⁴⁺ in TiO₂, SnO₂, and GeO₂

Transformation Enthalpies of the TiO₂ Polymorphs