Jahn-Teller Activity Research Articles

Superconducting first‐order pairing: Finite‐temperature simulations

AbstractA recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Direct superconducting pairing versus Jahn–Teller distortions; an analysis of a competition

The competition between a direct, i.e. first-order, superconducting pairing interaction and Jahn–Teller (JT) distortions has been studied theoretically. Finite cluster simulations have been performed for systems which exhibit JT activity or which are pseudo JT active. The first-order pairing employed does not necessarily involve second-order elements such as the electron–phonon coupling or specific magnetic interactions. The pairing is defined only by parameters of the electronic Hamiltonian. In the first-order approach suggested the mixed quantum statistics of Cooper pairs is correctly taken into account. The quantum statistics of superconducting pairs combines fermionic on-site and bosonic intersite properties. Moves of Cooper pairs are not influenced by constraints caused by the Pauli antisymmetry principle (PAP) while the moves of unpaired fermions are. Driving force for the first-order pairing is the suppression of the PAP influence. Such a reduction of antisymmetry constraints is also feasible by JT distortions. It is demonstrated that JT activity and direct superconducting pairing compete in order to reduce the destabilizing influence of the PAP. Model calculations have been performed for a square-planar cluster of D 4h symmetry, a bicyclic network of D 2h symmetry and a tetrahedral T d cluster. JT distortions lower these point symmetries to D 2h, C 2h and D 2d. All calculations have been performed in the simple Hubbard approximation with a two-electron repulsion of the density–density on-site type and nearest-neighbour hoppings. We suggest that both JT distortions and the superconducting pairing can be explained without electron–phonon coupling. Both processes are electronically driven.

Theoretical Investigation of Jahn−Teller Dynamics in the 2E‘ Electronic Ground State of the Cyclopropane Radical Cation

The static and dynamic aspects of (E x e)-Jahn-Teller (JT) interactions in the electronic ground state (X 2 E') of the cyclopropane radical cation are investigated with the aid of an ab initio based quantum dynamical approach. The valence photoelectron spectrum of cyclopropane pertinent to an ionization to the X 2 E' electronic manifold of its radical cation is calculated and compared with the most recent experimental recording of Holland and co-workers using He I and synchrotron radiation as excitation sources [J. Electron Spectrosc. Relat. Phenom. 2002, 57, 125]. A model diabatic Hamiltonian up to a quadratic vibronic coupling scheme and ab initio calculated coupling parameters are employed in the quantum dynamical simulations. Despite some minor details, the theoretical results are in good accord with the observed bimodal shape of the photoelectron band. The observed splitting of the maxima of ∼0.78 eV in the bimodal profile compares well with our theoretical value of ∼0.76 eV. A strong first-order JT activity of the degenerate vibrational modes is discovered, which results in the distinct twin structure of the photoelectron band, indicating transitions to both the sheets of the so-called Mexican hat potential energy surface of the X 2 E' electronic ground state of the radical cation. Two Condon active (A' 1 ) and three JT active (E') vibrational modes are found to contribute mostly to the nuclear dynamics in this electronic manifold. The low-energy progression in the photoelectron band is found to be mainly caused by the degenerate CH 2 wagging and ring deformation modes. While the linear vibronic coupling scheme overestimates the observed spacing in the low-energy progressions, it leads to a very good agreement with the overall shape of the observed band. The effect of quadratic coupling terms of the Hamiltonian on this low-energy progression is also discussed.

Electronic absorption spectra of B3 and B3− in neon matrices and ab initio analysis of the vibronic structure

Mass selected B3− ions have been isolated in 6 K neon matrices and their absorption spectra measured. A band system with origin at 467 nm is assigned as the E′1←X 1A1′ electronic transition of the cyclic anion. After photobleaching, the 1 2E′←X 2A1′ and 2 2E′←X 2A1′ band systems of neutral cyclic B3 are observed which start around 736 and 458 nm, respectively. Large scale ab initio calculations have provided potential energy surfaces for a variational treatment of the vibrational motion. Calculated band origins leave no doubt about the electronic symmetry assignments. The complex vibrational structure in the 1 2E′ state, which is due to relatively strong Jahn–Teller distortions, appears to be closely reproduced by the calculated vibrational energies and intensities, if the first observed stronger line is identified with the first vibrationally excited state, placing the “true” band origin of the 1 2E′ state at 775 nm where no signal with significant strength is apparent. The 2 2E′ state undergoes only a relatively weak Jahn–Teller distortion and shows a short progression with an observed frequency of 981(10) cm−1 that compares favorably with the theoretical frequency of 973 cm−1. The E′1 system of B3− shows a Jahn–Teller activity comparable to that of the 1 2E′ state of B3.

First-principles calculations on Li xNiO 2: phase stability and monoclinic distortion

The phase diagram of Li x NiO 2 (0< x<1) and the evolution of the monoclinic distortion as a function of the lithium content are calculated using a combination of first-principles energy methods and statistical–mechanics techniques. As a function of the temperature different ordered Li x NiO 2 structures appear in the phase diagram at x=0.25, 0.33, 0.4, 0.5 and 0.75. Noteworthy, a new and unsuspected phase, Li 0.4NiO 2, dominates the low-lithium region of the phase diagram. In agreement with experimental results, maxima in monoclinicity ( a m/ b m) are predicted to occur near Li 0.75NiO 2 and Li 0.4NiO 2. The coupling between the Li-vacancy ordering and the Jahn–Teller activity of Ni 3+ ions plays a crucial role in the stability of ordered Li x NiO 2 structures and is at the origin of the monoclinic distortion. As a result, the different electrochemical behavior of Li x NiO 2 versus Li x CoO 2 lies in the electronic nature of the involved transition metal cation.

Calculation of the Jahn-Teller effect in benzene cation: Application to spectral analysis

Ab initio calculations have been performed for the cations of benzene, C6H6, and its fluorinated analogs, C6F6 and C6H3F3. Calculated molecular parameters characterizing the Jahn-Teller potential energy surface (PES) are very consistent with those derived from the spectra of C6F6+ and C6H3F3+. However the calculated Jahn-Teller stabilization energy for the benzene cation is roughly three times greater than that previously reported experimentally. With the aid of the calculated values, a more complete analysis of the available spectral data for C6H6+ and C6D6+ is performed, with an emphasis on the data from ZEKE experiments and IR spectra of the Ar⋅C6H6+, Ne⋅C6H6+, and Ar⋅C6D6+ complexes. The comprehensive analysis reveals Jahn-Teller activity in 3 e2g modes for C6(H/D)6+ and provides values for their vibrational frequencies, linear and quadratic Jahn-Teller coupling constants, as well as quadratic coupling constants for several other degenerate modes. These new molecular parameters are generally in good agreement with the corresponding values derived from the ab initio calculations and produce a total Jahn-Teller stabilization energy in good agreement with the computed value.

First-principles calculations of lithium ordering and phase stability onLixNiO2

The phase diagram of ${\mathrm{Li}}_{x}{\mathrm{NiO}}_{2}$ $(0lxl1)$ is calculated using a combination of first-principles energy methods and Monte Carlo simulations. The energy dependence of the Li-vacancy configurational disorder is parametrized with a cluster expansion. At room temperature ordered ${\mathrm{Li}}_{x}{\mathrm{NiO}}_{2}$ phases appear in the phase diagram at $x=1/4,$ 1/3, 2/5, 1/2, and 3/4. The predicted lithium-vacancy ordering at $x=1/4$ and 1/3 are in good agreement with experiments, while for the other phases no detailed experimental evidence has been reported. We predict a previously undetected phase at $x=2/5$ to dominate the phase diagram at low lithium content. The stability of ordered ${\mathrm{Li}}_{x}{\mathrm{NiO}}_{2}$ structures is determined by short-ranged repulsive in-plane Li-Li interactions and long-range attractive interplane Li-Li interactions. These attractive interplane Li-Li interactions are due to the Jahn-Teller activity of ${\mathrm{Ni}}^{+3}$ ions. As a result, ${\mathrm{Li}}_{x}{\mathrm{NiO}}_{2}$ behaves fundamentally different from ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ even though their host structures are identical and Co and Ni have similar ionic sizes.

Product Jahn-Teller systems: The{T1⊗H}⊗(g+2h)icosahedral exciton

The ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(g+2h)$ product Jahn-Teller (JT) system offers a model Hamiltonian for the excited configuration of ${\mathrm{C}}_{60}.$ It describes the combined JT activity of two open shells transforming as the threefold and fivefold degenerate icosahedral representations ${T}_{1}$ and H. The two separate JT problems interfere via the interaction with common vibrational modes. In this paper we examine the structure of the resulting potential energy surface. The treatment first considers the simplified ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(2h)$ problem. The coupling conditions for this problem can be represented in a two-dimensional phase diagram with a rich structure. The diagram is separated in four domains by four trough lines. These correspond to different embeddings of $\mathrm{SO}(3)$ in $\mathrm{SO}(5)$ and describe the possible spherical couplings between a three vector and a five tensor. Outside the trough lines symmetry is broken to ${D}_{5d},$ ${D}_{3d},$ ${D}_{2h},$ and even ${C}_{2h}.$ Several tables offer a description of the structural aspects of these low-symmetry solutions. In the second part the full multimode Hamiltonian is treated by the method of the isostationary function. It is shown that the interconfigurational coupling term of this Hamiltonian reduces to the same tensorial form as for the simplified single mode ${{T}_{1}\ensuremath{\bigotimes}H}\ensuremath{\bigotimes}(2h)$ case.

Theoretical investigation of Jahn–Teller and pseudo-Jahn–Teller coupling effects on the photoelectron spectrum of allene

The valence photoelectron spectrum of allene (C3H4) pertinent to the à 2E/B̃ 2B2 interacting electronic manifold of the corresponding cation (C3H4+) is theoretically calculated and compared with the most recent high resolution He I excited experimental recording of Baltzer et al.[Chem. Phys. 196, 551 (1995)]. A model diabatic Hamiltonian within the linear vibronic coupling scheme and ab initio calculated coupling parameters are employed in our investigations. While the resolved vibrational progressions in the photoelectron band at low energies can be attributed to the E⊗B Jahn–Teller activity within the à 2E electronic manifold, the diffuse structure in the photoelectron band at high energies is found to emerge from the mixing of the à 2E electronic manifold with the B̃2B2 electronic state via degenerate vibrational modes. The latter demonstrates the importance of the pseudo-Jahn–Teller type of interactions in the photoelectron spectrum of allene.

Jahn–Teller effects in solid-state co-ordination chemistry

Jahn–Teller-active systems continue to yield unforeseen effects in the solid state. The use of conceptually simple potential energy surfaces, an approach developed by several investigators in recent decades, facilitates the understanding of diverse phenomena driven by Jahn–Teller activity. The background of this approach and its recent use in understanding dynamic Jahn–Teller systems, solid solutions of Jahn–Teller compounds in host lattices, and molecular shape switching in Jahn–Teller complexes are presented.

Experimental study of vibrational excitation of allene by slow electron impact: Vibronic coupling in the short-lived negative ion states

Vibrational electron energy loss spectra, vibrational excitation functions, and angular dependence of vibrational energy losses were measured in relative units for propadiene (allene, H2C=C=CH2) in an incident energy range up to 16 eV. Resonant excitation via the 2 eV resonance is not very selective; symmetric and antisymmetric C–C–C stretch, CH2 twist and scissoring, CH stretch, and C–C–C bending are all excited. The antisymmetric C–C–C stretch and CH2 twist are excited by Jahn–Teller activity of the degenerate 2E resonance, the bending by vibronic coupling with higher lying resonances. The essential features of the excitation are qualitatively rationalized by a Hartree–Fock (HF)/6-31G* anion potential energy surface. Unspecific excitation of high vibrational levels, accompanied by detachment of slow electrons, is also observed to result from attachment of 2 eV electrons, and is rationalized as a consequence of temporary trapping of part of the nuclear wave packet on the bound (not autodetaching) part of the anion potential surface. Very broad resonance features are observed in the 2–16 eV range, mainly in the excitation functions of the C–H stretch and the CH2 scissoring vibrations. A moderately broad resonance peak at 11.5 eV, observed in the excitation of the symmetric and antisymmetric C–C–C stretch vibrations, is assigned to two overlapping σ* shape resonances. Absolute elastic cross sections are given for reference.

Striking Enhancement and Retarding Effects in the Multi-quasi-resonance Evolvement in Electronic A → E ⊗ e Jahn-Teller Spectra

Completely unexpected and drastic enhancement and retarding effects are predicted to occur in the multi-quasi-resonance evolvement pertinent to the electronic bandshape pertaining to the orbitally allowed intensity of cold A → E ⊗ e Jahn-Teller spectra in the strong linear regime upon distorting the frequency of the e vibration during the radiative transition, while taking a fixed value for the strength of the linear Jahn-Teller activity in the E ⊗ e system. These dramatic effects together with other strong accompanying changes resulting in the theoretically calculated A ↔ E ⊗ e spectra are in complete contradiction with the long-standing conjecture, originating in the classic paper of Longuet-Higgins et al., stating that the vibronic structure associated with the bandshape of these spectra will be virtually independent of such vibrational frequency distortions.

Development of Orbitally Allowed Intensity along Vibronic Progressions of Linearly Inactive Doubly Degenerate Jahn-Teller Vibrations in A ↔ E Electronic Spectra

We introduce a novel "interstate" vibronic mechanism which may lead to a strong development of orbitally allowed intensity along the 0-0, 0-1, 0-2, 0-3, etc., vibronic progressions of a doubly degenerate (e) Jahn-Teller vibration in the spectra of A ↔ E electronic transitions. The mechanism is operative even in the complete absence of linear Jahn-Teller activity in the radiatively involved doubly degenerate electronic state, designated E(I). It involves a linear Herzberg-Teller vibronic coupling via the pertinent e Jahn-Teller mode connecting E(I) and a second doubly degenerate electronic state, E(II). The E(II) system, in turn, is simultaneously involved in linear J-T activity via the relevant e mode. The novel mechanism is highly effective in formation of well-developed vibronic progressions in the Jahn-Teller vibrations even in the far off-resonance weak-moderate coupling regime. In typical cases, its capability is comparable to that manifested by the classic orbitally allowed A ↔ E ⊗ e J-T spectra, as discussed by Longuet-Higgins et al. The latter spectra ensue via the direct action of the linear Jahn-Teller activity in the radiatively engaged E system. Note that we are only interested in the investigation of the development of orbitally allowed intensity pertinent to the A ↔ E(I) system and not in any contributions of vibronically borrowed forbidden intensity which, in principle, may be transferred to the A ↔ E(I) system via its linear vibronic coupling with the A ↔ E(II) system.

Magnetic circular dichroism of matrix-isolated Mo atoms: spin-orbit coupling and Jahn-Teller activity

The magnetic circular dichroism and absorption spectra of molybdenum atoms isolated in Ar, Kr, and Xe matrices have been measured. A method of moments analysis has been applied to the spectral results and the z 7P excited state spin-orbit (SO) coupling constants determined. In Ar the SO constant is 126 cm −1, greater than the gas value of 101 cm −1, while in Kr and Xe it is smaller, 84.5 and 57.5 cm −1, respectively. These results compare favorably with the values predicted by a recent theory of SO coupling for metals in matrices. It is further shown that matrix-enhanced second-order SO coupling, which was found to be important in Cr in the rare gas matrices, is negligible in the present systems. In addition, the method of moments was used to determine the contributions of the noncubic rare gas cage vibrational modes to the observed bandwidths, an approach which has been used previously to identify excited state Jahn-Teller activity. It is shown that Mo atoms in all three gas matrices exhibit a strong Jahn-Teller effect on the z 7P state.

Dispersed fluorescence spectroscopic study of the ground electronic state of silver trimer

Dispersed fluorescence spectra of Ag 3 have been recorded for the first time. The experimental data provide the first clear determination of the fundamental vibrational frequencies of the trimer in its ground electronic state, i.e. ν 1 ≈ 180 cm −1 and ν 2 ≈ 67 cm −1, and also lead to a reassignment of previous Raman work on the molecule. Evidence of significant Jahn—Teller activity in Ag 3 is clearly demonstrated by the observation of a progression in the nominally degenerate bending vibrational mode, ν 2, in both the excitation and dispersed fluorescence spectra. Our observations are consistent with ab initio calculations which have predicted that the triangular 2E′ ground electronic state should undergo significant Jahn—Teller distortion.

EPR of dynamic Jahn-Teller distortion in CuII doped magnesium Tutton's salt

The dynamic Jahn-Teller distortion in single crystals of CuII doped magnesium Tutton's salt, MgK2(SO4)2·6H2O was studied by EPR spectroscopy. The directions of the g tensor axes were found to coincide with those of A at room temperature as well as at 113 K and were correlated with the MgO directions in the lattice. Two spatially distinct sites of copper were detected in the crystal. The g and A values were also calculated from the polycrystalline samples at various temperatures. A dx2-y2 ground state has been assigned for CuII, as in the isomorphous zinc Tutton's salt. The Silver and Getz model was applied to understand the dynamics of Jahn-Teller (JT) activity. The system was found to undergo dynamic JT distortion at all temperatures. At low temperatures, the [Cu(H2O)6]2+ ion has three possible degenerate vibronic states corresponding to three possible directions for the long axis of the octahedron. The energy separations between the three inequivalent JT valleys were estimated as δ1,2 = 90 and δ1,3 = 370 cm−1. The lattice strain parameter V2 and the JT stabilization energy EJT were also estimated as 19,140 and 1030 cm−1 respectively. From the EJT value, the JT distortion present in the system was classified as a case of “strong” coupling.

Theoretical study of the photoelectron spectrum of allene

Multi-mode dynamical E⊗B Jahn-Teller coupling effects in the X 2E and A 2E states of the allene cation are systematically investigated. Ab initio electronic potential energies of the X 2E, A 2E and B 2B 2 states of C 3H + 4 have been obtained as a function of normal coordinates of A 1, B 1 and B 2 symmetry. The potential-energy functions reveal the Jahn-Teller activity (B 1, B 2 symmetry) and Condon activity (A 1 symmetry) of the normal modes. It is shown that the recently published (Yang et al. Chem. Phys. Letters 171 (1990) 9) high-resolution photoelectron spectrum of the X 2E band of allene can quantitatively be interpreted in terms of Jahn-Teller coupling involving the mode ν 4 (torsion) and the antisymmetric CC stretching mode ν 6. The vibronic fine structure of the A 2E band reported by Yang et al. is shown to arise primarily from the excitation of the Jahn-Teller active antisymmetric HCH bending mode ν 7 and the totally symmetric HCH bending mode ν 2.

The magnetic circular dichroism and absorption spectra of C 60 isolated in Ar matrices

The absorption and magnetic circular dichroism (MCD) spectra of C 60 isolated in Ar matrices have been measured in the visible and near-ultraviolet. The first two allowed bands (at ≈ 326 and ≈253 nm) show substantial negative A terms. Sharp, weak vibronic structure showing clear evidence of Jahn—Teller activity is observed in both the 400 and 600 nm regions. Detailed assignments are proposed for the resolved spectral features.

Jahn—Teller effect of the 2e 2g level of chemisorbed benzene

It is shown that the characteristic double-peak structure of the 2e 2g band in the photoelectron spectra of C 6H 6 and C 6D 6 chemisorbed on metal surfaces arises from a fairly strong intramolecular multi-mode dynamical Jahn—Teller effect. An ab initio treatment of the multi-mode Jahn—Teller effect in the isolated 2e 2g hole state of free benzene yields, after suitable broadening, a quantitative description of the band shape observed in the photoelectron spectra. In gas-phase benzene, the strong Jahn—Teller activity of the 2e 2g hole is concealed by its overlapping and strong pseudo-Jahn—Teller coupling with the adjacent 1a 2u hole state.

Ab initio investigation of the multimode dynamical Jahn-Teller effect in the X̃ 2E 1g state of the benzene cation

Linear-Jahn-Teller coupling parameters for the X̃ 2E 1g state of C 6H + 6 have been determined using beyond-Hartree-Fock ab initio methods. The vibronic structure of the first band of the photoelectron spectrum of benzene has been computed including up to three nonseparable Jahn—Teller-active modes and the totally symmetric C—C stretch mode. The calculated band-shape is in excellent agreement with the best-available photoelectron spectrum. The calculations reveal that the comparatively strong Jahn—Teller activity of model v 8 is hidden in the vibronic spectrum as a consequence of strong mode mixing with lower-frequency modes.