General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

According to the Jahn-Teller theorem, symmetrical molecules with degenerate electronic states are unstable. Such molecules therefore take up a distorted shape. If there is near-degeneracy, the symmetrical shape may also be unstable. We have studied the distortion in some particular cases. The approach is to minimize the total electronic energy with respect to distortions of the nuclear framework, the latter being considered to be static. There are always several equivalent distortions of equal energy, so that a static distortion fails to remove the degeneracy. The discussion of dynamic effects is postponed to a subsequent paper. A linear molecule of formula BAB , for which two electronic states of opposite symmetry are sufficiently nearly degenerate, will be stable in a configuration with unequal A—B separations, and unstable when symmetrical. This example illustrates some of the main physical features of Jahn-Teller distortions in a simple manner. Although we know of no example where the symmetrical structure is actually unstable, there are examples where the tendency towards distortion noticeably reduces the force constant of the asymmetric vibration. Octahedral complexes AB 6 with degenerate electronic states occur in many situations (e. g. paramagnetic crystals, F-centres, luminescent centres and exciton states in cubic crystals). The orbital degeneracy may be threefold ( T 1 and T 2 ) or twofold. In the former case the stable distortion is found to be either of tetragonal symmetry about a [100] direction, or of trigonal symmetry about a [111] direction. The twofold degenerate situation leads to a more complicated situation. If one neglects anharmonic effects there appears to be an infinity of distortions minimizing the energy; a more detailed consideration of the anharmonic terms shows that the stable distortions are of elongated tetragonal character. This result has an important bearing on complexes involving the cupric ion.

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A Study of Spin-Hamiltonian Parameters and Defect Structure for Co2+ Ion in the Tetragonal Zn2+ Site of Ba2ZnF6 Crystal

Zeitschrift für Naturforschung A ◽

10.1515/zna-2010-1016 ◽

2010 ◽

Vol 65 (10) ◽

pp. 877-881

Author(s):

Bang-Xing Lia ◽

Wen-Chen Zheng ◽

Wei-Qing Yang

Keyword(s):

Defect Structure ◽

Reduction Factor ◽

Teller Effect ◽

Tetragonal Symmetry ◽

Spin Hamiltonian ◽

Effective Spin ◽

Jahn Teller ◽

Jahn Teller Effect ◽

Experimental Values ◽

Hamiltonian Parameters

The spin-Hamiltonian (SH) parameters (g factors g∥ , g⊥ and hyperfine structure constants A∥, A⊥) for the Co2+ ion in the tetragonal Zn2+ site of a Ba2ZnF6 crystal are calculated from the secondorder perturbation formulas based on the cluster approach for the SH parameters of 3d7 ions in tetragonal symmetry with the effective spin S = 1/2. In the calculations, a reduction factor due to the dynamical Jahn-Teller effect is used. The calculated results are in reasonable agreement with the experimental values, suggesting that the dynamical Jahn-Teller effect should be considered here. The defect structure of the Co2+ center in Ba2ZnF6:Co2+ is also obtained from the calculations. The results are discussed.

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Magnetic Dipole Origins of the 3A2g→3T2g Transition in Ni(II) Doped MgO

Australian Journal of Chemistry ◽

10.1071/ch12104 ◽

2012 ◽

Vol 65 (9) ◽

pp. 1298 ◽

Cited By ~ 6

Author(s):

Mark J. Riley ◽

Jeremy Hall ◽

Elmars R. Krausz

Keyword(s):

Magnetic Dipole ◽

Near Infrared ◽

Magnetic Circular Dichroism ◽

Linear Dichroism ◽

Tetragonal Symmetry ◽

Double Quantum ◽

Spin Orbit ◽

Paramagnetic Resonance ◽

Magnetic Linear Dichroism ◽

Jahn Teller

Magnetic circular dichroism and magnetic linear dichroism spectroscopy have been used to study the near infrared 3A2g → 3T2g transition of Ni(ii) doped MgO. Two sharp electronic origins are observed and it is show that their polarisation behaviour follows that expected from calculations in detail for magnetic dipole allowed transitions in octahedral symmetry. Not all transitions to the spin-orbit components of the 3T2g state are observed. We put forward an explanation for why some components are missing, even though they are expected to be of comparable intensity, in terms of the different coupling to the Jahn–Teller active tetragonal distortion in the excited state. The two lower energy spin-orbit split components are nearly independent of this distortion, while the two higher energy components are strongly dependent. We also examine the double quantum transition in the electron paramagnetic resonance spectrum and estimate the magnitude of the random strain of tetragonal symmetry in the MgO lattice.

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THE SYNTHESIS OF COPPER(II)-CONTAINING 1,2,4-TRIAZOLE COMPLEXES

Bulletin of Taras Shevchenko National University of Kyiv Chemistry ◽

10.17721/1728-2209.2017.2(54).4 ◽

2017 ◽

pp. 35-36

Author(s):

I. Petrenko ◽

D. Khomenko ◽

R. Doroschuk ◽

R. Lampeka

Keyword(s):

Coordination Compounds ◽

Coordination Complexes ◽

Octahedral Complex ◽

Tetragonal Symmetry ◽

X Ray Diffraction ◽

X Ray ◽

Mononuclear Complexes ◽

Jahn Teller ◽

Jahn Teller Effect ◽

Metal Ligand

Methods of the synthesis of the copper(II) containing 3-(2-pyridinyl)-1H-1,2,4-triazole complexes are reported. Systematic studies were devoted to the investigating an importance of triethylamine towards the сomplexation. The various coordination modes that have been observed in complexes were discussed. We noticed the correlations of coordination complexes structure and the metal-ligand correlation. Two mononuclear complexes and one dinuclear complex of a 2:2 composition were obtained. The deprotonation of the ligand in the complex namely [Cu(L)2](H2O)2 was eased by adding triethylamine. The octahedral complex [Cu(HL)2(NO3)](NO3) was synthesized without triethylamine. In excess of ligands, mononuclear coordination compounds formed mostly. By adding the equal to ligand amount of triethylamine we obtained complex in a lower tetragonal symmetry. Deprotonated triazole is the high field ligand, therefore, due to the Jahn–Teller effect, square coordination is more desirable. In all coordination compounds formation of the 5-membered chelate cycle realizes through a pyridine-triazole binding site.The structures of three complexes have been determined by single crystal X-ray diffraction.

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The Local Structure Distortion of Chromium-Phosphorus Clusters as Cr2+ Impurity in InP Semiconductors

Zeitschrift für Naturforschung A ◽

10.1515/zna-2006-7-810 ◽

2006 ◽

Vol 61 (7-8) ◽

pp. 371-374

Author(s):

Xiao-Ming Tan ◽

Xiao-Yu Kuang ◽

Kang-Wei Zhou ◽

Cheng Lu ◽

Qin-Sheng Zhu

Keyword(s):

Local Structure ◽

Tetragonal Symmetry ◽

Zero Field ◽

Energy Matrix ◽

Zero Field Splitting ◽

Field Splitting ◽

Jahn Teller ◽

Phosphorus Clusters ◽

Complete Energy Matrix ◽

Distortion Parameters

By diagonalizing the complete energy matrix of a d4 configuration ion in tetragonal symmetry, the zero-field-splitting parameters a, D and F of InP:Cr2+ have been studied. The local structure distortion parameters ΔR = 0.08 Å and Δθ = 1.01◦ were estimated. They show an expansion distortion around Cr2+ in the InP semiconductor. The Jahn-Teller energy EJT is found to be about 413 cm−1, which agrees well with the experiment. - PACS numbers: 75.10.Dg; 76.30.-v

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Formation of the C-type Orbital-Ordered State in the Simple Perovskite Manganite Sr1-xSmxMnO3

MRS Advances ◽

10.1557/adv.2016.217 ◽

2016 ◽

Vol 1 (9) ◽

pp. 615-620 ◽

Cited By ~ 2

Author(s):

Misato Yamagata ◽

Ayumi Shiratani ◽

Yasuhide Inoue ◽

Yasumasa Koyama

Keyword(s):

Electronic System ◽

The State ◽

Tetragonal Symmetry ◽

Perovskite Manganite ◽

Orbital Ordering ◽

Teller Distortion ◽

Rotational Displacement ◽

Type Orbital ◽

Jahn Teller ◽

Jahn Teller Distortion

ABSTRACTThe simple perovskite manganite Sr1-xSmxMnO3 (SSMO) has been reported to have a highly-correlated electronic system for eg-electrons in a Mn ion. According to the previous studies, the C-type orbital-ordered (COO) state with the I4/mcm symmetry was found to be formed from the disordered-cubic (DC) state on cooling. The feature of the COO state is that its crystal structure involves both the Jahn-Teller distortion to orbital ordering and the R25-type rotational displacement of oxygen octahedra. Because of the involvement of both the distortion and the displacement, their competition should be expected in the formation of the COO state. However, the detailed features of the competition have not been understood yet. Thus, the crystallographic features of the COO state in SSMO have been examined by x-ray powder diffraction and transmission electron microscopy. It was found that, when the Sm content increased from x = 0 at room temperature, the DC state changed into the COO state with the tetragonal symmetry around x = 0.13. The notable feature of the COO state is that the state is characterized by a nanometer-scaled banded structure consisting of an alternating array of two tetragonal bands. One tetragonal band consisted of the COO state involving both the Jahn-Teller distortion and the R25-type rotational displacement. But, there was only the latter displacement in the other, the state of which could be identified as a disordered tetragonal (DT) state. Based on this, it is understood that the COO-state formation from the DC state should take place via the appearance of the DT state, which may involve fluctuations of the C-type orbital ordering.

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Dynamic Jahn-Teller Vibronic Coupling in Tetragonal Symmetry

Journal of the Physical Society of Japan ◽

10.1143/jpsj.44.1640 ◽

1978 ◽

Vol 44 (5) ◽

pp. 1640-1646 ◽

Cited By ~ 14

Author(s):

Shinji Muramatsu ◽

Nobuhiko Sakamoto

Keyword(s):

Vibronic Coupling ◽

Tetragonal Symmetry ◽

Jahn Teller

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Characteristic Features of the C-Type Orbital-Ordered State in the Simple Perovskite Manganite Sr1-xNdxMnO3

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.922.626 ◽

2014 ◽

Vol 922 ◽

pp. 626-631

Author(s):

Hiroki Sato ◽

Yasuhide Inoue ◽

Yasumasa Koyama

Keyword(s):

Crystal Structure ◽

Tetragonal Symmetry ◽

Perovskite Manganite ◽

Teller Distortion ◽

Rotational Displacement ◽

Type Orbital ◽

The Matrix ◽

Jahn Teller ◽

Coexistence State ◽

Jahn Teller Distortion

In the highly-correlated electronic system Sr1-xNdxMnO3, the C-type orbital-ordered (COO) state is present for 0.15<x<0.38, and its crystal structure with the tetragonal-I4/mcmsymmetry involves both theR25-type rotational displacement of MnO6octahedra and the Jahn-Teller distortion as a response of a lattice system to orbital ordering. To understand the details of the competition between the rotational displacement and the Jahn-Teller distortion, the formation of the COO state from the disordered cubic (DC) state with the space groupPm3mhas been investigated mainly by transmission electron microscopy. It was found that, when the temperature was lowered from the DC state forx= 0.20, for instance, COO regions with the tetragonal symmetry, exhibiting a {110}DCbanded structure, were locally formed in the matrix below about 330 K. The subsequent aging at 300 K resulted in the growth of COO regions; that is, the time-relaxation phenomenon. Because of the presence of antiphase boundaries for the rotational displacement in the matrix, the crystal structure of the matrix should also have the tetragonal symmetry. In other words, it is understood that the coexistence state appearing just after cooling from the DC state consists of two tetragonal regions with different c/a values. The coexistence state is apparently characteristic of the competition between the rotational displacement and the Jahn-Teller distortion for the formation of the COO state.

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