Second-order Jahn-Teller Effect Research Articles

The Electronic Structure of the Fulvalene Trication Radical. A Localization of the Unpaired Electron

Abstract The restricted Hartree-Fock (RHF) solution for the trication radical of fulvalene, obtained by using the open-shell SCF formalism of the Pariser-Parr-Pople-type MO method, is found to be doublet unstable at the conventional D2h nuclear arrangement. We calculate the broken-symmetry charge-density wave solution lower in energy than the usual symmetry-adapted RHF solution and examine its properties. It is predicted that the unpaired electron should be localized on the single five-membered ring having a smaller positive charge. Finally, on the basis of the second-order Jahn-Teller effect, we examine the molecular-symmetry reduction of the trication radical from the fully-symmetrical D2h to the C2v nuclear arrangement.

Theory of the structural phase transition inA15compounds

The structural phase transition in the $A15$ compounds are investigated theoretically with the standpoint that the band Jahn-Teller effect of the twofold-degenerate ${\ensuremath{\Gamma}}_{12}$ subbands crossing the Fermi level is responsible for the instability. On the basis of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ perturbation theory, the ${\ensuremath{\Gamma}}_{12}$ subbands are revealed to be well described by two parabolic bands which couple not only to the bulk distortions, but also to the displacements of the ${\ensuremath{\Gamma}}_{12}$ optic modes. It is found that when the electron-lattice coupling exceeds the threshold of strength, the tetragonal phase with almost the same stabilities of $\frac{c}{a>1}$ and $\frac{c}{a<1}$ appears, accompanying one of the ${\ensuremath{\Gamma}}_{12}$ optic modes below a weak first-order phase transition temperature ${T}_{M}$. The temperature dependences of the elastic moduli are calculated; it is found that ${c}_{11}\ensuremath{-}{c}_{12}$ vanishes below ${T}_{M}$ while ${c}_{33}\ensuremath{-}{c}_{13}$ recovers from its softening partially or completely with decreasing temperature below ${T}_{M}$. The long-wavelength acoustic phonons are also investigated in order to clarify the relation between the phonon anomalies and the structural transition. The [110]${\mathrm{T}}_{1}$ mode ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\parallel}[110]$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{e}}\ensuremath{\parallel}[1\overline{1}0]$) is considerably softened in the range $0<q\ensuremath{\lesssim}2{k}_{F}$. This softening begins at high temperatures, remaining even at absolute zero. The theory explains successfully the various aspects of the phase transitions in ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn. The comparison between them proves that the second-order Jahn-Teller effect occurs in both compounds.

The second-order Jahn-Teller effect

The second-order Jahn-Teller effect is an example of reactions proceeding by an interaction between the HOMO and the LUMO within the same molecule. The consequences can be decomposition of the molecule or a structural change. First the general theory is given, and then a number of examples are presented.

Ligands of low electronegativity in the VSEPR model: Molecules and ions isoelectronic with primary, secondary and tertiary amines

Equilibrium geometries, skeletal bending force constants, and inversion barriers have been calculated for 15 molecules and ions of type (MH 3) 3YE n+ : the results are consistent with interpretations of molecular configurations based upon the second-order Jahn—Teller effect. Molecules and ions of types H 2NMH n+ 2 and HN(MH 3) n+ 2 are also described.

Ligands of low electronegativity in the VSEPR model: Molecules and ions isoelectronic with primary, secondary and tertiary amines

Equilibrium geometries, skeletal bending force constants, and inversion barriers have been calculated for 15 molecules and ions of type (MH 3) 3YE1 n+ : the results are consistent with interpretations of molecular configurations based upon the second-order Jahn-Teller effect. Molecules and ions of types H 2NMH 3 n+ and HN(MH 3) 2 n+ are also described.

ChemInform Abstract: A SECOND‐ORDER JAHN‐TELLER EFFECT IN A TETRANUCLEAR METAL ATOM CLUSTER COMPOUND

Chemischer InformationsdienstVolume 13, Issue 15 Physical Inorganic Chemistry ChemInform Abstract: A SECOND-ORDER JAHN-TELLER EFFECT IN A TETRANUCLEAR METAL ATOM CLUSTER COMPOUND F. A. COTTON, F. A. COTTONSearch for more papers by this authorA. FANG, A. FANGSearch for more papers by this author F. A. COTTON, F. A. COTTONSearch for more papers by this authorA. FANG, A. FANGSearch for more papers by this author First published: April 13, 1982 https://doi.org/10.1002/chin.198215008AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume13, Issue15April 13, 1982 RelatedInformation

Ligands of low electronegativity in the VSEPR model: The structures of singlet carbenes

Equilibrium structures and force constants for skeletal bending from linearity have been calculated, in the MNDO approximation, for twenty five singlet carbenes CX 2. When the substituent X bears neither vacant orbitals nor lone pairs, the force constant becomes steadily more negative as the electronegativity of X increases; when X bears vacant orbitals, the C→ X π bond order and the force constant both increase with the electronegativity of X. When X bears lone pairs, the force constant parallels the HOMO—LUMO gap at linearity. Previous discussions of the structures of singlet carbenes are shown to be inadequate: the reported results support the interpretation in terms of the second-order Jahn-Teller effect of the observed stereochemical inactivity of lone pairs in the presence of ligands of low electronegativity.

Ligands of low electronegativity in the vsepr model: electron-rich hydrides MH 3E 2, MH 4E, MH 5E, and MH 6E

Hydrides FH 3, ClH 3, and OH − 3 of type MH 3E 2 are calculated to adopt D 3h structures: NH 3 2−, PH 3 2−, and SH 3 − each have two energy minima, one at D 3h and the other at a T-shaped geometry, of which the D 3his the more stable for SH 3 − but the less stable for NH 3 2− and PH 3 2−. Hydrides NH 4 2−, OH 4, and ClH 4 + of type MH 4E have a single energy minimum at T d: CH 4 2−, SiH 4 2−, PH 4 −, and SH 4 each have two minima, one at T d (more stable for SH 4 only) and one at an SF 4-like C 2v geometry, which is the more stable for CH 4 2−, SiH 4 2− and PH 4 −. D 3h and C 4V structures are very close in energy for all hydrides of type MH 5E, with no activation barrier between the two configurations: D 3h is the more stable configuration for OH 5 −, FH 5, SH 5, and ClH 5, but C 4V is the more stable for NH 5 2−, SiH 5 3−, and PH 5 −. The T 1u bending force constant in hydrides MH 6E becomes negative, for C 3V distortion, in PH 6 3− and SiH 6 4−. Both the equilibrium geometries and the force constants strongly support an interpretation, in terms of the second-order Jahn-Teller effect, of the observed stereochemical inactivity of non-bonding electrons in the presence of ligands of low electronegativity. Molecular energies, equilibrium geometries, orbital energies and electron populations are reported for all species considered in this study. Three molecular states of ClH 4 −, of type MH 4E 2, were also briefly investigated.

Gas-phase electron diffraction study of tris(trimethylstannyl)amine, N(SnMe 3) 3

The geometrical parameters of tris(trimethylstannyl)amine have been determined by gas-phase electron diffraction. The a structure has been refined using mean amplitude values calculated from the force fields of a number of tin derivatives. The experimental data are consistent with a planar bond configuration at the nitrogen in N(SnMe 3) 3. The final set of geometrical parameters is as follows (average bond distances, r g , in Å, angles in degrees): SnC 2.166(5), SnN 2.038(3), CH 1.117(17). NSnC 108.5(1.5), SnCH 112.1(1.6). Mean amplitude values have been varied for those distances which give considerable contributions to scattering. The results obtained fill a gap in the knowledge of structures of Group IV element μ-nitrido derivatives. They confirm the conclusion that lowering of ligand MR n electro-negativity weakens the tendency to deviation from planarity in the central fragment NM 3. This tendency may be considered as a manifestation of the second-order Jahn-Teller effect.

Pseudopotential SCF–MO studies of hypervalent compounds. II. XeF+5 and XeF6

New evidence bearing upon the anomalous properties of xenon hexafluoride has been obtained via the ab initio molecular orbital approach applied successfully to the di- and tetrafluorides in paper I. Structures of both XeF+5 and XeF6 are governed by a stereochemically active lone pair. In the case of the square–pyramidal cation the Fax–Xe–Feq angle calculated for the bare ion is within 2° of the value observed in the crystalline complex. For the hexafluoride, however, the calculated deformation from Oh symmetry is appreciably greater than that deduced from electron diffraction intensities. Nevertheless, the results of calculations are in sufficient conformity with the Bartell–Gavin, Pitzer–Bernstein interpretation and at variance with the ’’electronic-isomers’’ interpretation to leave little doubt about the answer. With increasing fluorination in the XeFn series the HOMO–LUMO energy difference decreases and the second-order Jahn–Teller effect is enhanced. Increasing fluorination (and increased positive charge on Xe) also shortens bond lengths; calculated shortenings parallel observed shortenings. The deformation of XeF6 from Oh is along t1u bend and stretch coordinates to a C3v structure with long bonds adjacent to the lone pair, as expected according to the valence-shell–electron-pair-repulsion model. Pure t2g deformations are destabilizing but anharmonic t1u–t2g coupling significantly stabilizes the deformation. Steric aspects of the structure and force field are diagnosed and found to be minor. Values for the force constants f44, f55, f̄4444, f̄444′4′, and f̄445 are derived and found to be of the magnitude forecast in the Bartell–Gavin and Pitzer–Bernstein treatments except that the calculations do not reproduce the delicate balances believed to lead to almost free pseudorotation in XeF6.

Skeletal structures of hexa-organo substituted triatomics R 3XYZR 3: A rationalisation using the second-order Jahn—Teller effect

In compounds of type R 3XYZR 3 (R  phenyl, methyl, benzyl; X, Z  Al, Si, P, Ge, Sn; Y  C, N, O, F) linearity of the XYZ skeleton is predicted by the second-order Jahn—Teller effect in those examples where the valence orbitals of X and Z are much less tightly bound than those of Y. When the X and Z orbitals are bound more tightly than those of Y, the XYZ skeleton is predicted to be non linear at Y. The effects of varying R, X and Z, and the contribution of π-interactions are discussed.

A link between the second-order Jahn-Teller effect and the highest occupied molecular orbital postulate for molecular shapes

For a closed-shell molecule, a connection is drawn between two recent models for molecular shapes, namely, those based on the second-order Jahn-Teller (SOJT) effect and the highest occupied molecular orbital (HOMO) postulate respectively. Two necessary and sufficient conditions are derived within the molecular orbital framework for the approximation inherent in the SOJT model to be valid. One of these conditions is akin to the HOMO postulate.

ESR spectra of AsF 2−6 and SbF 2−6

ESR spectra observed in γ-irradiated CsAsF 6 and CsSbF 6 matrices have been assigned to the free radicals AsF 2− 6 and SbF 2− 6 respectively. The large, isotropic central-atom hyperfine interactions and isotropic g-values of these species suggest that they possess 2A tg ground-states in O h symmetry. The contribution to the semi-occupied orbital of the central-atom valence s atomic orbital is ≈ 0.6, greater than in the halogen hexafluorides (≈0.4) and the chalcogen hexafluoride anions (≈ 0.5). Variation of the central-atom hyperfine interaction with temperature is interpreted in terms of a second-order Jahn-Teller effect involving a low-lying 2T 1u excited state.

The crystal structure of germanium dibromide*

Abstract Germanium dibromide (GeBr2) is monoclinic, P21/c, with a = 11.68, b = 9.12, c = 7.02 Å, β = 101.9°, and eight formula weights per cell. The crystal structure as determined by x-ray diffraction consists of layers of edge-sharing distorted GeBr6 octahedra parallel to {100} with bromine bridges linking the layers. Distortion of the octahedra gives rise to chains of vertex-sharing GeBr3 trigonal pyramids within the octahedral layers. The octahedral distortion in GeBr2 and other germanium halides may be an example of the second-order Jahn-Teller effect.

Jahn-teller effects in (3d) 2 ions in Al 2O 3

APR experiments have been carried out on V 3+ and Cr 4+ ions in Al 2O 3 partly to remove discrepancies in earlier measurements, and partly to provide additional information necessary for the theoretical analysis which follows. We find | G -| ∼ 45± 10 cm −1 and ∼ 160±30 cm −1 for V 3+ and Cr 4+ respectively. It is shown that all the data for both ions can only be explained satisfactorily if a moderately strong Jahn-Teller effect operates in the cubic 3 T 1, ground state of the ion. Full details are given, γ is found to be 0.14 and 0.36 for V 3+ and Cr 4+ respectively and important contributions from second-order Jahn-Teller effects are also present. The results also show that it is necessary to use a multimode full-lattice model of the Jahn-Teller effect as the constraints of the cluster model are broken. The implications of the proposed model on thermal conductivity, phonon spectroscopy and optical measurements are also briefly discussed. It is also pointed out that some important errors exist in the literature concerning the interpretation of experimental data for these systems.

ChemInform Abstract: A MODEL FOR CATALYSIS BY NICKEL(II) COMPLEXES

AbstractDie Isomerisierung von der tetraedrischen zur planaren Form vierfach koordinierter Komplexe vom Typ (I) wird inbezug auf den Jahn‐Teller Effekt zweiter Ordnung diskutiert.

Concerning Jahn-Teller Effects

Jahn-Teller effects are grouped into two categories. The first arises from incomplete shells of degenerate orbitals. It includes the first-order Jahn-Teller effect, and the pseudo Jahn-Teller effect. The second arises from filled and empty molecular orbitals that are close in energy, and is the second-order Jahn-Teller effect. The two categories have quite different physical bases. As a result, geometric distortions produced by the first are quite small and normally lead to dynamic effects only. In favorable cases, the second-order Jahn-Teller effect produces very large distortions, including complete dissociation of a molecule. This can occur even when the relevant molecular orbitals are separated in energy by as much as 4 eV.

A model for catalysis by nickel(II) complexes

The tetrahedral-planar isomerisation of four-co-ordinate complexes of the nickel(II) ion of the type [L2NiX2](L is a neutral ligand and X an anionic ligand) is discussed in terms of the second-order Jahn–Teller effect. It is shown that when the ligands L possess π-acceptor orbitals the isomerisation may be facilitated and it is suggested that a ready isomerisation may account for the catalytic activity of these, and possibly other, transition-metal complexes with π-bonding ligands.

Molecular-symmetry Reduction in CmHm−2 Cata-condensed Nonalternant Hydrocarbons

Abstract On the basis of the second-order Jahn-Teller effect and the semiempirical SCF MO method, we examined the energetically most favorable molecular-symmetry groups and geometrical structures with respect to C–C bond lengths of the CmHm−2 cata-condensed nonalternant hydrocarbons. In the 4n π-electron systems the first excitation energies in the fully-symmetrical nuclear arrangements were predicted to be significantly smaller than a certain critical value, and a molecular-symmetry reduction accompanied by a marked double-bond fixation in the peripheral carbon skeleton to occur. On the other hand, in the 4n+2 π-electron systems, such energies were found to be considerably large for small members and to decrease rapidly with the number of carbon atoms, resulting in the molecular-symmetry reduction for members larger than a certain critical size. The electronic spectra were calculated using the most stable geometrical structures obtained by the SCF MO method.

ChemInform Abstract: BOND DISTORTIONS AND RELATED PHENOMENA IN PERI‐CONDENSED TETRACYCLIC NONBENZENOID AROMATIC HYDROCARBONS

Chemischer InformationsdienstVolume 4, Issue 44 Physical Organic Chemistry ChemInform Abstract: BOND DISTORTIONS AND RELATED PHENOMENA IN PERI-CONDENSED TETRACYCLIC NONBENZENOID AROMATIC HYDROCARBONS AZUMAO TOYOTA, AZUMAO TOYOTASearch for more papers by this authorTAKESHI NAKAJIMA, TAKESHI NAKAJIMASearch for more papers by this author AZUMAO TOYOTA, AZUMAO TOYOTASearch for more papers by this authorTAKESHI NAKAJIMA, TAKESHI NAKAJIMASearch for more papers by this author First published: October 30, 1973 https://doi.org/10.1002/chin.197344083Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume4, Issue44October 30, 1973 RelatedInformation