pseudo-Jahn-Teller Effect Research Articles

Theoretical analysis of the Jahn-Teller distortions in tetrathiolato iron(II) complexes.

Crystallographic studies of [Fe(SR)(4)](2-) (R is an alkyl or aryl residue) have shown that the Fe(II)S(4) cores of these complexes have (pseudo) D2d symmetry. Here we analyze the possibility that these structures result from a Jahn-Teller (JT) distortion that arises from the e(3z(2) - r(2), x(2) - y(2)) orbital ground state of Fe(II) in T(d)symmetry. Special attention is paid to the influence of the second-nearest neighbors of Fe, which lowers the symmetry and reduces the full JT effect to a smaller, pseudo JT effect (PJT). To estimate the size of the PJT distortion, we have determined the vibronic parameters and orbital state energies for a number of [Fe(SR)(4)](2-) models using density functional theory (DFT). Subsequently, this information is used for evaluating the adiabatic potential surfaces in the space of the JT-active coordinates of the FeS(4) moiety. The surfaces reveal that the JT effect of Fe(II) is completely quenched by the tetrathiolate coordination.

Electron–phonon interaction and Jahn–Teller effect in the SbSI atomic chain

The quasi-one-dimensional SbSI atomic chain consisting of up to 60 atoms is considered theoretically. One-electron energies, interatomic bond strengths, and ionic charges of atoms have been calculated using the unrestricted Hartree–Fock method within the Hw basis set employing the pseudopotential. The symmetry of normal vibrational modes of the SbSI chain in the paraelectric and ferroelectric phases has been determined. As shown, the A u and B g symmetry top electronic levels of the highest valence band are degenerate in the paraelectric phase. The A ̄ u symmetry normal mode interacting with the degenerate A u symmetry electronic states in the valence band top induce the Jahn–Teller effect. The same mode interacting with A u symmetry electronic states in the valence band and B g symmetry that states in the conduction band bottom induces the pseudo-Jahn–Teller effect (JTE). Due to both JTE, the normal mode force constant K decreases. The polynomial expansion coefficients of the normal mode A ̄ u total energy dependence upon normal coordinate, E T= E T0+ K( z) 2+ c( z) 4, demonstrate anomalous variation in the phase transition region. The anomalies of E T0, of the harmonic coefficient K and anharmonicity factor c are caused by the anomalies of the unit cell volume V 0, and both the Jahn–Teller and pseudo-Jahn–Teller vibrational constants undergo changes during the phase transition.

Multimode Jahn–Teller and pseudo-Jahn–Teller coupling effects in the photoelectron spectrum of CH3F

Abstract The multimode Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) coupling effects in the photoelectron spectrum of methylfluoride are theoretically investigated with the aid of an ab initio quantum dynamical approach. The theoretical findings are compared with the experimental results of Karlsson et al. [Phys. Scripta 16 (1977) 225]. At the vertical configuration, the ground, first and second excited electronic states of the methylfluoride radical cation belong to the 2 E, 2 A 1 and 2 E symmetry species. The three doubly degenerate vibrational modes cause a splitting of the degeneracy of the E electronic states of the radical cation and exhibit the (E⊗e)-JT effect. The same vibrational modes may also cause a coupling of the degenerate and the non-degenerate electronic states (PJT effect). In our theoretical approach we devise a model diabatic vibronic Hamiltonian within a quadratic vibronic coupling scheme. The parameters of the Hamiltonian are derived by performing extensive ab initio calculations at the CASSCF-MR-AQCC level of theory. The photoelectron bands are calculated by a quantum dynamical approach based on the Lanczos algorithm. A detailed examination of the various static and dynamic aspects of the problem reveals an interesting interplay of JT and PJT coupling effects in the photoelectron-induced dynamics of CH 3 F + . The resolved progression in the first photoelectron band corresponding to the ground X 2 E electronic manifold of CH 3 F + is found to be mainly caused by the C–F stretching (a 1 ), C–F bending (e) and CH 3 deformation (e) modes. The JT coupling effects are not particularly strong in this electronic manifold. This also holds for the second photoelectron band attributed to the vibronic structure of the A 2 A 1 and B 2 E electronic states of CH 3 F + . However, the extremely large Condon activity of the symmetric vibrational modes in the A 2 A 1 electronic state contributes much to the broad and highly diffuse nature of this band which is also observed experimentally. The PJT activity of the anti-symmetric C–F bending (e) vibration in the X 2 E and B 2 E electronic states is also discussed.

DENSITY FUNCTIONAL ELECTRONIC SPECTRUM OF THE CuO6-10 CLUSTER AND POSSIBLE LOCAL JAHN–TELLER DISTORTIONS IN THE La–Ba–Cu–O SUPERCONDUCTOR

We present a density functional theory (DFT) calculation in the generalized gradient approximation to study the possibility for the existence of Jahn–Teller (JT) or pseudo Jahn–Teller (PJT) type local distortions in the La – Ba – Cu – O superconducting system. We performed the calculation and correspondingly group theory classification of the electronic ground state of the CuO 6-10 elongated octahedra cluster, immersed in a background simulating the superconductor. Part of the motivation to do this study is that the origin of the apical deformation of the CuO 6-10 cluster is not due to a pure JT effect, having therefore a non a priori condition to remove the degeneracy of the electronic ground state of the parent regular octahedron. We present a comparative analysis of the symmetry classified electron spectrum with previously reported results using unrestricted Hartree–Fock calculations (UHF). Both the DFT and UHF calculations produced a non-degenerate electronic ground state, not having therefore the necessary condition for a pure JT effect. However, the appearance of a degenerate E g state near to the highest occupied molecular orbital in the DFT calculation, suggests the possibility for a PJT effect responsible for a local distortion of the oxidized [Formula: see text] cluster.

Multimode Jahn?Teller and pseudo-Jahn?Teller coupling effects in the photoelectron spectrum of CH3F

The multimode Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) coupling effects in the photoelectron spectrum of methylfluoride are theoretically investigated with the aid of an ab initio quantum dynamical approach. The theoretical findings are compared with the experimental results of Karlsson et al. [Phys. Scripta 16 (1977) 225]. At the vertical configuration, the ground, first and second excited electronic states of the methylfluoride radical cation belong to the 2 E, 2 A 1 and 2 E symmetry species. The three doubly degenerate vibrational modes cause a splitting of the degeneracy of the E electronic states of the radical cation and exhibit the (E⊗e)-JT effect. The same vibrational modes may also cause a coupling of the degenerate and the non-degenerate electronic states (PJT effect). In our theoretical approach we devise a model diabatic vibronic Hamiltonian within a quadratic vibronic coupling scheme. The parameters of the Hamiltonian are derived by performing extensive ab initio calculations at the CASSCF-MR-AQCC level of theory. The photoelectron bands are calculated by a quantum dynamical approach based on the Lanczos algorithm. A detailed examination of the various static and dynamic aspects of the problem reveals an interesting interplay of JT and PJT coupling effects in the photoelectron-induced dynamics of CH 3 F + . The resolved progression in the first photoelectron band corresponding to the ground X ̃ 2 E electronic manifold of CH 3 F + is found to be mainly caused by the C–F stretching (a 1 ), C–F bending (e) and CH 3 deformation (e) modes. The JT coupling effects are not particularly strong in this electronic manifold. This also holds for the second photoelectron band attributed to the vibronic structure of the A ̃ 2 A 1 and B ̃ 2 E electronic states of CH 3 F + . However, the extremely large Condon activity of the symmetric vibrational modes in the A ̃ 2 A 1 electronic state contributes much to the broad and highly diffuse nature of this band which is also observed experimentally. The PJT activity of the anti-symmetric C–F bending (e) vibration in the X ̃ 2 E and B ̃ 2 E electronic states is also discussed.

Phase transitions in the magnetoelastic crystals CsDy1−xGdx(MoO4)2

Based on the data of ultrasonic studies and on the temperature behavior of the absorption spectra, a study of the phase diagram of the crystals CsDy1−xGdx(MoO4)2 is made and the structural distortions occurring as a result of the pseudo-Jahn–Teller effect are discussed. It is shown that in the presence of impurities there are several lines of phase transitions on the x–T phase diagram. It is established that one of the phase transitions these found is essentially of a magnetoelastic origin.

Bis(N,N-dimethylethylenediamine-κ2N,N′)bis(perchlorato-κO)copper(II)

In the title compound, [Cu(ClO4)2(C4H12N2)2], the Cu atom is located at a center of symmetry. It adopts an elongated octahedral trans-[CuN4O2] coordination geometry, which is a typical feature of the pseudo-Jahn–Teller effect. The axial Cu—O bond length is 2.605 (4) A, while the in-plane Cu—N bond lengths are 1.987 (2) and 2.098 (2) A.

Terminal and four-coordinate vanadium(IV) phosphinidene complexes. A pseudo Jahn-Teller effect of second order stabilizing the V-P multiple bond.

Treatment of the four-coordinate vanadium neopentylidene (Nacnac)V=CHtBu(I) (Nacnac- = [Ar]NC(Me)CHC(Me)N[Ar], Ar = 2,6-iPr2C6H3) with a bulky primary lithium phosphide LiPHR (R = 2,4,6-iPr3C6H2, 2,4,6-tBu3C6H2) leads to alpha-hydrogen migration concomitant with the formation of a four-coordinate vanadium complex containing a terminal phosphinidene functionality (Nacnac)V=PR(CH2tBu). The crystal structures for the vanadium phosphinidene complexes prepared herein were determined by single-crystal X-ray diffraction methods. Solution EPR and magnetic measurements of the vanadium phosphinidenes are also in accordance with such systems containing a V(IV) metal center, and DFT calculations indicate the V=P bond to be stabilized through a pseudo Jahn-Teller effect of second order.

Generalization of the shell model and correlation effects in strongly correlated oxides

Direct analytical and numerical calculation show that the two-electron atomic configuration can be unstable with respect to a static or dynamic displacement of the electron shells. This enables us to develop a so-called nonrigid shell model for a partial account of the intra-atomic electron correlations. In frames of the model a correlated state of two-electron molecular configuration is described by a set of symmetrized shell displacements similarly to the well-known shell model developed for a description of the lattice dynamics. The former relate to the latter as the optical phonon modes relate to the acoustical one. The effect under consideration is expected to be of particular importance for anionic ${2p}^{6}$ background in oxides. The nonrigid anionic background forms an unconventional magnetoelectric system characterized by a set of independent orbital order parameters and competition of paramagnetic and diamagnetic responses. The model allows an introduction of the pseudospin formalism and effective ``spin Hamiltonian'' for a description of the short- and long-range ordering of nonrigid atomic backgrounds in crystals. We predict a number of unconventional correlation effects including: (i) a formation of polaronlike holes and charge-transfer excitons; (ii) the mechanism of the self-trapping for holes and/or charge-transfer excitons; (iii) a purely electronic (pseudo)Jahn-Teller effect due to a coupling between valent hole and a nonrigid anionic background; (iv) a combined (pseudo)Jahn-Teller effect provided by a joint account both of the electron shell displacements and conventional nuclear ones; (v) an appearance of the soliton chiral correlation states; (vi) unconventional magnetic response; (vii) unconventional hyperfine coupling.

Strong Jahn–Teller effect in the excited state: Anomalous temperature dependence of the zero-phonon line

We are studying the optical spectra of impurity centers in the case when the optical transition takes place between nondegenerate and two-fold degenerate electronic E-states characterized by a strong vibronic coupling. In the latter state the adiabatic surface has a shape of a deformed Mexican hat with three flat minima on the trough of the “hat.” We have found that in this case the usual T7-dependence of the homogeneous width of the zero-phonon line at low temperatures is replaced by a dependence close to the T3-one. Besides, the usual T4-dependent redshift of the line is replaced by the T2-dependent shift. Depending on the flatness of the adiabatic surface, the latter shift may be to the red or to the blue. The theory is applied to the zero-phonon line 637 nm of the nitrogen-containing N-V center in a diamond. In this system the temperature dependence of the ZPL results from the common action of the Jahn–Teller effect and the pseudo-Jahn–Teller effect in the excited E-state: the pseudo-Jahn–Teller effect “helps” to get the system close to the dynamical instability due to the enlargement of the Jahn–Teller distortion.

Theoretical studies on the variational transitional state theory rate constants for the hydrogen abstraction reaction of O (3P) with CH3Cl and CH2Cl2

The hydrogen abstraction reactions of atomic O (3P) with CH3Cl and CH2Cl2 have been studied theoretically using ab initio molecular orbital theory for the first time. In the Cs symmetry, both reactions proceed over two potential-energy surfaces, A″3 and A′3 generated by the pseudo-Jahn–Teller effect. Two nearly degenerate transition states of A″3 and A′3 symmetries have been located for each hydrogen abstraction reaction from the C–H bonds. Geometries of the reactants, transition states, and products have been optimized at the second-order Møller–Plesset (MP2) level with the 6-311G(2d,p) basis set. The single-point energy calculations have been carried at the [QCISD(T)]/6-311+G(3df,2p) level. Changes of geometries, generalized normal-mode vibrational frequencies, and potential energies along the reaction paths are discussed and compared. The total thermal rate constants were obtained from the sum of the calculated rate constants for the two surfaces using canonical variational transition-state theory (CVT) with small curvature tunneling effect (SCT). The results show that the variational effect is small and in the lower-temperature range, the small curvature tunneling contribution is important for each reaction. The calculated CVT/SCT rate constants show reasonable agreement with the recent experimental values, with a more pronounced curvature in the Arrhenius plot than in the experimental data.

Evaluation of the Analogy between Exceptions to the Generalized Maximum Hardness Principle for Non-Totally-Symmetric Vibrations and the Pseudo-Jahn−Teller Effect

Exceptions to the generalized maximum hardness principle (MHP) for nitrogen heterocycles, along non-totally-symmetric vibrations (bond-length alternating modes), are caused by pseudo-Jahn−Teller (PJT) coupling between the ground and the excited state along those modes. Thus, the PJT effect causes an increase of the energy gap between the ground and the excited state, and this is reflected in an increase of hardness. This relationship is based on the assumption that the hardness (defined as difference between ionization potential and electron affinity) is approximately equal to the HOMO−LUMO gap (Koopmans' approximation), and this is in turn assumed to be approximately equal to the energy difference between the ground and excited state. The analogy is valid here because the excited state and the relevant vibration have the same symmetry, and the geometry and force constants of the optimized minima for the two coupled states are reasonably similar.

A pseudo-Jahn–Teller model of the photochromic effect in sodium nitroprusside

A new model for the photochromic effect in sodium nitroprusside Na2[Fe(CN)5(NO)]·2H2O based on the concept of the pseudo-Jahn–Teller effect is proposed. The model takes into account the electron transfer from the Fe2+ ion to the π* orbitals of the NO-ligand as well as the vibronic mixing of three electronic states of the FeNO fragment through the non-symmetric and full-symmetric modes. The problem is solved within the adiabatic approximation. Under certain conditions the lower sheet of the adiabatic potential is shown to possess three minima with the increasing energies that correspond to the N-bound, sideways bound and O-bound NO group. The barriers between the minima are estimated and the excited minima are attributed to the MS2 and MS1 metastable states observed experimentally.

Vibronic coupling in ionized organic molecules: structural distortions and chemical reactions

Ionized organic molecules (radical cations) in radiation chemistry are liable to undergo vibronic coupling whenever there is a relatively small energy gap (≈0.5–1.5 eV) between their ground and excited states. As a result of this mixing, the force constant for the symmetry-allowed vibrational mode that couples these states is lowered in the ground state of the radical cation so that deformation can take place more easily along this specific mode. This pseudo-Jahn–Teller effect can then result in a permanent structural distortion of the radical cation relative to the symmetry of the parent neutral molecule. It can also bring about an energetically favored pathway for a facile chemical rearrangement along a reaction coordinate defined by the coupling mode. Examples taken from matrix-isolation studies are used to illustrate these dramatic consequences of vibronic coupling in radical cations. Thus, the bicyclo[2.2.2]oct-2-ene and tetramethylurea radical cations are found to have twisted structures departing from the C 2v symmetry of their parent molecules, while the oxirane and bicyclo[1.1.1]pentane radical cations undergo ring-opening rearrangements along reaction coordinates that correspond to the deformational modes predicted by the pseudo-Jahn–Teller effect.

The d-L(π)-π type of charge-transfer salt [Cu(Me-tri)2][Ni(dmit)2]2: Interaction between copper(ii) d- and Ni(dmit)2π-electrons via π-conjugated macrocyclic ligands

In order to correlate d-electrons of copper(II) ions with π-electrons of Ni(dmit)2 (dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate) acceptors, we prepared the d-L(π)-π type of charge-transfer salt [Cu(Me-tri)2][Ni(dmit)2]2(Me-tri = methyl-substituted tribenzo[b, f, j][1, 5, 9]triazacycloduodecine), where the π-conjugated system of ligand Me-tri (L(π)) is expected to behave as a mediator to link the d- and the π-electrons. In the crystal, Ni(dmit)2 anions with S = 1/2 π-spin form face-to-face dimers, and divalent Cu(Me-tri)2 cations exist with their L(π) planes almost parallel to the dimers. From magnetic susceptibility measurements, it was revealed that spins on the Ni(dmit)2 dimer relax from a triplet to a singlet state with decreasing temperature, and copper spins remain uncoupled below 75 K. The presence of weak anti-ferromagnetic interactions between the copper spins was confirmed below 25 K, although the copper ions are quite far apart. These phenomena are explained in terms of superexchange coupling via anti-parallel spins on the Ni(dmit)2 dimer. As evidence to support this, the EPR spectrum at 4 K had narrow linewidth without hyperfine structure. At 75 K, the EPR signal is isotropic, which means that the Jahn–Teller distortion of Cu(Me-tri)2 is fluxional. Compared with the results for [Cu(Me-tri)2](BF4)2, Cu(Me-tri)2 in the Ni(dmit)2 salt was found to maintain fluxionality even at lower temperature. Semi-empirical molecular orbital calculations suggest that the distortion of Cu(Me-tri)2 is more properly described as a pseudo-Jahn–Teller effect, in which the magnetic L(π) orbital is involved. Assuming charge-transfer interactions of this L(π) orbital with the unoccupied π-orbital of the Ni(dmit)2 dimer, reasonable explanations are provided both for the superexchange coupling and for the persistence of the fluxional distortion at lower temperatures.

Synthesis and crystal structure of bis(2,2'-bipyridyl)mononitritozinc(II) perchlorate. An example of a six-coordinate cis-octahedral ZnN4O2 chromophore

The crystal structure of bis(2,2′-bipyridyl)mononitritozinc(II) perchlorate, [Zn(bipy)2 (ONO)][ClO4] (1) has been determined. The complex is monoclinic, with a = 10.9195(4) A, b = 12.2320(5) A, c = 16.5477(8) A, β = 105.6150(10)○, P21/n space group, with final R1 = 0.0657 and wR2 = 0.1630. The complex involves a [Zn(bipy)2 (ONO)]+ cation and a [ClO4]− anion. The ZnN4O2 chromophore is six-coordinate, with a cis-distortion of the two oxygens of the nitrite, O(1) and O(2), at distances 2.216(5) and 2.197(5) A from the zinc (Zn– Omean = 2.206(5) A, ΔO = 0.019(5) A) and two out of plane Zn–N bonds, Zn–N(2) and Zn–N(3), at 2.129(4) and 2.135(4) A (Zn–nmean/out = 2.132(4) A, Δn2,3 = 0.006(4) A). The two inplane nitrogens, N(1) and N(4), at distances Zn–N(1) = 2.090(4) and Zn–N(4) = 2.085(4) A (Zn–nmean/in = 2.087(4) A, Δn1,4 = 0.005(4) A) are greater than 2.0 A, but slightly shorter than the axial bonds. The inplane angles α1, α2, and α3 in 1 have values 150.33(18)○, 108.98(17)○, and 99.73(18)○ respectively. The stereochemistry is cis-distorted octahedral, with an α3 = 99.37(18)○, which is lower than α3 = 103.4(1)○ observed in [Zn(bipy)2(ONO)][NO3] (5). Comparison with the corresponding [Cu(bipy)2(ONO)][Y] complexes suggested that the cis-distortion of the CuN4O2 chromophore in the copper(II) series does not originate in the Jahn–Teller or pseudo-Jahn–Teller effect.

Vibronic dynamic problem of the valence tautomeric interconversion [low-spin Co(III)(N∧N)(sq)(cat)] ↔ [high-spin Co(II)(N∧N)(sq)2]. Magnetic properties and charge-transfer band

For a single valence tautomeric complex the vibronic problem of pseudo-Jahn–Teller effect is solved. The vibronic (hybrid) wave-functions and energy levels are used for the calculation of the temperature dependence of the molecular magnetic moment and the shape of the optical band in the near infrared range. The magnetic moment is shown to increase gradually from 1.73μB to 4.34μB. The spectrum of the isolated complex in the near infrared range is revealed to represent a band related to the light induced transfer of an electron from the cat ligand to the metal ion. The suggested model is in qualitative agreement with the experimental data.

The pseudo-Jahn—Teller effect: a CASSCF diagnostic

A simple test for the pseudo-Jahn-Teller effect is proposed, based on the behaviour of a CASSCF frequency calculation when symmetry is restricted. The test suggests that the pseudo-Jahn-Teller effect operates at the D2h transition structure of S0 pentalene and the D8h transition structure of S0 cyclooctatetraene. The D4h transition structure of S0 cyclooctatetraene is not subject to a pseudo-Jahn-Teller distortion according to this test. Our interpretation of the pseudo-Jahn-Teller effect differs from the conventional one based on a single-transition (CIS-like) approximation.

Ionized bicyclo[2.2.2]oct-2-ene: a twisted olefinic radical cation showing vibronic coupling.

The bicyclo[2.2.2]oct-2-ene radical cation (1(.+)) exhibits matrix ESR spectra that have two very different types of gamma-exo hydrogens (those hydrogens formally in a W-plan with the alkene pi bond), a(2H) about 16.9 G and a(2H) about 1.9 G, instead of the four equivalent hydrogens as would be the case in an untwisted C(2v) structure. Moreover, deuterium substitution showed that the vinyl ESR splitting is not resolved (and under about 3.5 G); this is also a result of the twist. Enantiomerization of the C(2) structures is rapid on the ESR timescale above 110 K (barrier estimated at 2.0 kcalmol(-1)). Density functional theory calculations estimate the twist angle at the double bond to be 11-12 degrees and the barrier as 1.2-2.0 kcalmol(-1). Single-configuration restricted Hartree-Fock (RHF) calculations at all levels that were tried give untwisted C(2v) structures for 1(.+), while RHF calculations that include configuration interactions (CI) demonstrate that this system undergoes twisting because of a pseudo Jahn-Teller effect (PJTE). Significantly, twisting does not occur until the sigma-orbital of the predicted symmetry is included in the CI active space. UHF calculations at all levels that include electron correlation (even semiempirical) predict twisting at the alkene pi bond because they allow the filled alpha and the beta hole of the SOMO to have different geometries. The 2,3-dimethylbicyclo[2.2.2]oct-2-ene radical cation (2(.+)) is twisted significantly less than 1(.+), but has a similar temperature for maximum line broadening. Neither the 2,3-dioxabicyclo[2.2.2]octane radical cation (3(.+)) nor its 2,3-dimethyl-2,3-diaza analogue (5(.+)) shows any evidence of twisting. Calculations show that the orbital energy gap between the SOMO and PJTE-active orbitals for 3(.+) is too large for significant PJTE stabilization to occur.

Coupled-cluster theory, pseudo-Jahn–Teller effects and conical intersections

A detailed analysis of the strengths and weaknesses of coupled-cluster and many-body perturbation theories in treating strongly interacting potential energy surfaces is presented. Standard coupled cluster theory is shown to provide a qualitative treatment of Herzberg–Teller coupling that is vastly superior to that associated with perturbation theory. However, it also predicts unphysical effects that will always cause it to fail in describing the topology of potential energy surfaces in the immediate vicinity of conical intersections. To treat problems involving strong interstate coupling (notably those involving radicals subject to pseudo-Jahn–Teller effects), methods based on equation-of-motion (linear response) coupled-cluster theory appear to be considerably more suitable. In particular, they provide a description of intersecting surfaces that is qualitatively correct in all respects. It is also shown that there is no reason to believe that the noniterative inclusion of triple excitation contributions to the correlation energy should provide for any systematic improvement in describing this class of phenomena.