pseudo-Jahn-Teller Effect Research Articles

The Elusive Structure of CrCl2—A Combined Computational and Gas-Phase Electron-Diffraction Study

Chromium dichloride poses a challenge to the structural chemist. Its different forms of aggregation and association display all well-known structural distortions induced by vibronic interactions. The monomeric molecule has a Renner-Teller distorted bent geometry, the crystal exhibits strong Jahn-Teller distortion, and the oligomers have slightly distorted four-membered-ring structures due to the pseudo-Jahn-Teller effect. In this paper we report on the low-energy structures of the monomer and its clusters, Cr(2)Cl(4), Cr(3)Cl(6), and Cr(4)Cl(8), from unrestricted Kohn-Sham (broken-symmetry) density functional calculations. CrCl(2) was also investigated at higher level, including coupled-cluster and state-average CASSCF computations. The global minima of the gas-phase clusters consist of two-dimensional, antiferromagnetically coupled chains of CrCl(2) units forming four-membered, doubly bridged Cr(2)Cl(2) rings, closely resembling the solid-state structure of alpha-CrCl(2). Each Cr atom in these chains has spin quantum number S=2. This suggests that the CrCl(2) nucleation starts very early on the structural chain motif found in the solid. There is only a very small change in energy from the antiferromagnetically to the ferromagnetically coupled Cr atoms, which indicates little spin-coupling between the metal centers. There is an approximately constant change in energy, about 50 kcal mol(-1), with every new CrCl(2) unit during cluster formation. Information about the structure of these clusters was used in the re-analysis of high-temperature electron-diffraction data. The vapor at 1170 K contained about 77 % monomeric molecules, 19 % dimers, and a small amount of trimers. Monomeric CrCl(2) was found to be bent with a bond angle of 149(10) degrees, in good agreement with our computations, which resulted in a Renner-Teller distortion of the lowest-energy (5)Pi(g) electronic state into the bent (5)B(2) ground state. The vibrational spectrum of chromium dichloride is discussed and the thermodynamics of cluster formation from 1000-2000 K is examined.

Dynamic Pseudo Jahn−Teller Effect and the Phase Transition Induced by Absorption of Molecules in Metal−Organic Nanotube Framework

A second-order phase transition induced by absorption of acetone in nanoporous zinc terephthalate, Zn2(C 8 H 4 O 4 )2(C 6 H 12 N 2 ), has been studied by 2 H NMR and DSC data. The heterogeneous system [Zn 2 (C 8 H 4 O 4 ) 2 -(C 6 H 12 N 2 )·n(CH 3 ) 2 CO (n = 0-5) is tetragonal at n n e (to orthorhombic). The breaking of symmetry is related to a combination of a pseudo Jahn-Teller effect and the influence of quantum confinement on the dynamic behavior of the absorbed molecules in the metal-organic nanotube framework.

Why Are Some ML2 Molecules (M: Ca, Sr, Ba; L: H, F, Cl, Br) Bent While Others Are Linear? Implications of the Pseudo Jahn—Teller Effects.

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Why Are Some ML2Molecules (M = Ca, Sr, Ba; L = H, F, Cl, Br) Bent while Others are Linear? Implications of the Pseudo Jahn−Teller Effect

The unexpected bent geometries of some alkaline earth dihalides and dihydrides, ML(2) (M = Ca, Sr, Ba; L = H, F, Cl, Br) have been explained in the literature using various models that attribute the effect to different phenomena like covalency, metal core polarization, sd-hybridization, and electron pair repulsion. We employ (based on first principles) the pseudo Jahn-Teller effect, as the only source of instability of high-symmetry configurations in nondegenerate states, to analyze the origin of the geometry of these systems and show that this approach explains all of their main structural features, including the topology of the Laplacian of the electron density and the vibrational frequencies. The main contribution to the distortion of the linear configuration is due to the pseudo Jahn-Teller mixing by bending of the sigma(u) HOMO formed by the ligand orbitals with the unoccupied pig orbitals of the metal (with main d(xz) and d(yz) character), resulting in new covalency which stabilizes the bent configuration. We show that the model approaches to the problem, mentioned above, are either restricted particular cases of the pseudo Jahn-Teller interaction, or they yield very small contributions to the instability that do not explain the origin of the bending. All of our conclusions are supported by high-quality ab initio calculations.

A multiconfigurational approach of the symmetry breaking problem in the cyclic C 3H radical

The ground state of the cyclic C 3H radical is prone to symmetry breaking due to a peculiar structure that require to distribute three electrons on two centers which are equivalent by symmetry. A pseudo Jahn–Teller effect is also observed due to the non-adiabatic interaction with the first excited state. The multiconfigurational self-consistent-field method is used to calculate wavefunctions free from symmetry breaking. The weakening of the pseudo Jahn–Teller effect is observed when the correlation energy is increased. The equilibrium geometry and harmonic vibrational frequencies are calculated with the multireference configuration interaction method and a good agreement with experimental results is obtained. The present work confirms that the ground state of the cyclic C 3H has the C 2 v symmetry.

Symmetry of the electronic and geometric structures of metallofullerene M@C 74 (M = Be, Mg, Ca, Sr, and Ba) in terms of vibronic coupling

Motion of the encapsulated metal in M@C 74 (M = Be, Mg, Ca, Sr, and Ba) is studied in terms of vibronic coupling using group theory approach. The selection rule for the symmetry of metal motion is presented. This agrees well with experimental findings for Ca@C 74. The metal motion can be regarded as a pseudo-Jahn–Teller effect. The electronic structures and adiabatic potential surfaces of M@C 74 are calculated using the tight-binding approximation.

Vibronic origin of the H 3O [rad] metastability

The vibronic origin of the metastability of the hydronium radical H 3O in its planar D 3h and pyramidal C 3v nuclear configurations is revealed by solving the three-mode ( A 1 ′ + A 2 ″ + E ′ ) ⊗ ( a 2 ″ + e ′ + e ′ ) Jahn–Teller problem. The vibronic constants in this model were estimated by fitting of the ab initio calculated adiabatic potential in the vicinity of the high-symmetry D 3h and C 3v nuclear configurations to its analytical expression. It was shown that the planar D 3h configuration is unstable with the respect to the out-of-plane distortions (leading to the C 3v nuclear configuration) because of the pseudo Jahn–Teller effect (PJTE). The barriers to dissociation H 3O → H 2O + H from both metastable nuclear configurations ( D 3h and C 3v) are due to the common action of the PJTE in the ground state and the Jahn–Teller effect (JTE) in the first degenerate excited state.

The Jahn–Teller effect as a general tool for solving molecular and solid state problems: Novel findings

In this (partly review) paper several important situations are analyzed in which molecular systems are distorted, but there are no apparent degeneracies or close in energy states to justify their origin as due to the Jahn–Teller effect (JTE) or pseudo JTE (PJTE). It is shown that in all these cases above the JTE are “hidden” in the excited states of the undistorted configuration even when the energy gap to these states is very large, and the involvement of these states in the vibronic coupling explains the JT origin of the distortions. This confirms the general validity of the JTE as the only source of instabilities and distortions of high-symmetry configurations of polyatomic systems. For the example of the ozone molecule, which has no degenerate ground state, neither in the distorted (obtuse-triangular), nor in the undistorted (regular triangular) configurations, and there are no low-lying excited states, the distortion is shown to emerge from the JTE in the excited E state situated at ∼8.3 eV above the ground state. The JT stabilization energy is more than ∼9 eV which makes the distorted configuration the lowest in energy. For molecular systems with half-closed-shell electronic configurations e 2 and t 3 (with degenerate orbitals), which produce totally symmetric charge distribution and are not subject to the JTE (neither in the ground high-spin (HS) state, nor in the excited low-spin (LS) states formed from these configurations by interelectron interaction), distortions were shown to occur due to a strong PJT mixing of two excited states. Again, the PJT stabilization energy in these cases is larger than the energy gap to the ground state, so the low-spin excited state of the undistorted geometry becomes the lowest in energy in the distorted configuration, and it is shown that this distortion is accompanied by orbital disproportionation that makes the charge distribution lower in symmetry. Since the two spin-states are stable in two different nuclear configurations, distorted (LS) and undistorted (HS), a novel phenomenon emerges in these systems: JT-induced spin-crossover. Distinguished from the known spin-crossover in transition metal compounds, the JT-induced spin-crossover takes place in a large variety of molecular systems from different classes including organic compounds, and it has a much lower rate of relaxation between the two states; this makes them candidates for single-molecule materials for electronic devices.

A cooperative pseudo Jahn–Teller effect in three phases of CeAlO 3

The sequence of phases of CeAlO 3, which experimentally have been found by lowering the temperature: Pm 3 ¯ m → R 3 ¯ c → Imma → I 4 / mcm , can be characterized by cooperative pseudo Jahn–Teller effects due to interaction of the ground state (4f) 1 with the excited state (5d) 1 from the Ce 3+-ion. The three phases, a tetragonal one, an orthorhombic one and a rhombohedral phase which are found from low temperature, successively to higher temperature, can be described by distortions from respectively a single T 2 u -component, a linear combination of two T 2 u -components and a linear combination of three T 2 u -components. Since in CeAlO 3 the distortions are at the Ce 3+-center, it is practical to name the distortion mode: T 2 u at the R-point (with respect to the center with a 12-environment of anions). The four short bonds around each Ce 3+-ion in the tetragonal phase point to covalent bonding. This bonding is in the tetragonal structure stronger than in the rhombohedral phase. This can explain the observation that the rhombohedral phase, with three short bonds, occurs at higher temperature, and is stabilized by entropy.

On the Jahn–Teller and pseudo-Jahn–Teller effects in the photoelectron spectrum of cyclopropane

We present a theoretical account of the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects in the photoelectron spectrum of cyclopropane. The PJT interactions between the two JT split X ˜ 2 E ′ and A ˜ 2 E ″ electronic states of the cyclopropane radical cation are examined. Nuclear dynamical simulations on the resulting four coupled electronic states including fourteen relevant vibrational modes are carried out by a wave packet propagation approach employing the multiconfiguration time-dependent Hartree algorithm. The theoretical results are compared with recent experimental photoelectron spectroscopic data.

A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si 6 ground state

We report a critical analysis of the performance of conventional ab initio and density functional methods in the computation of the ligand-free Si 6 “magic-number” cluster ground state, structure relying on the recent advances in modern pseudo-Jahn-Teller theory. Our study focuses on the equilibrium structures that have been concluded, at one point or another, as the true ground state structure in the literature. Namely, the distorted (compressed) octahedron of D 4h ( 1A 1g) symmetry which is indirectly supported by earlier experimental studies, the edge- and face-capped trigonal bipyramids of C 2v ( 1A 1) symmetry. Geometry optimizations have been carried out, with a vast selection of basis sets with methods that are extensively used for geometry optimizations such as Hartree–Fock, Møller–Plesset perturbation theory, coupled cluster techniques and the widely used B3LYP and B3PW91 density functional methods. Our results expose that the determination of Si 6 ground state structure is extremely sensitive to basis set effects and depends on the particular capabilities of each method in the treatment of the pseudo Jahn-Teller effect (PJTE). More specifically, geometry optimizations with methods based on Møller–Plesset perturbation theory, which have been demonstrated that do not treat the PJTE, predict that the distorted octahedron of D 4h ( 1A 1g) symmetry is the ground state structure, while methods which do provide PJTE treatment suggest that the distorted octahedron is unstable and undergoes PJTE distortions.

Orbital disproportionation and spin crossover as a pseudo Jahn-Teller effect

It is shown that in systems with electronic half-closed-shell configurations of degenerate orbitals, e(2) and t(3) (which have totally symmetric charge distribution), ground state distortions from high-symmetry geometries may occur due to a strong pseudo Jahn-Teller effect (PJTE) in the excited states, resulting also in a novel phenomenon of PJT-induced spin crossover. There is no JTE neither in the ground state term nor in the excited terms (including degenerate terms) of these configurations but a strong PJT mixing between two excited states [((1)E+(1)A) [cross-filled circle] e and ((2)T(1)+(2)T(2)) [cross-filled circle] e in the e(2) and t(3) cases, respectively] pushes down the lower term to cross the ground state of the undistorted system and to form the global minimum with a distorted geometry. The analysis of the electronic structure of this distorted configuration shows that it is accompanied by orbital disproportionation: instead of proportional population of all degenerate orbitals by one electron each (as in the ground state of the undistorted system that follows Hund's rule), two electrons with opposite spins occupy one orbital, resulting in transformations of the type (e(theta);e(epsilon))-->(e(theta)e(theta)) for e(2) and (t(x);t(y);t(z))-->(t(x);t(x);t(z)) for t(3) systems. Since the two geometry configurations, undistorted and distorted, appertain to different electronic terms that have different spin states, the formation of the global minimum with the distorted configuration is accompanied by a spin crossover. Distinguished from the known spin-crossover phenomenon in some transition metal compounds, the two states with different spin in the PJT-induced spin crossover have also different nuclear configurations, undistorted and distorted, that coexist with a relatively small energy difference. The change of configuration reduces significantly the rate of relaxation between the two states; the relaxation is further reduced by the lower spin-orbital coupling in the light-atom systems as compared with transition metal compounds. This means that there may be systems for which the switch between the two states (in both directions) under perturbations may be observed as a single-molecule phenomenon. Systems with half-closed-shell electronic configurations e(2) and t(3) are available in a variety of molecules from different classes, organic and inorganic; the theory is illustrated here by ab initio calculations for a series of molecular systems, including Si(3), Si(3)C, CuF(3), Na(3), Si(4), Na(4), Na(4) (-), and C(60) (3-), which are in agreement with the experimental data available.

Carbon−Cobalt Bond Distance and Bond Cleavage in One-Electron Reduced Methylcobalamin: A Failure of the Conventional DFT Method

Geometry optimizations at the HF, B3LYP, and CASSCF levels of electronic structure theory have been performed for methylcobalamin (MeCbl) model compounds in both the Co(III) (MeCbl(III)) and Co(II) (MeCbl(II)) formal oxidation states. Since the HOMO-LUMO and C-Co sigma-sigma MO gaps are significantly smaller in the MeCbl(II) compounds compared with MeCbl(III), a pseudo-Jahn Teller effect is possible. CASSCF calculations show that there is strong coupling between C-Co sigma-sigma MOs for the MeCbl(II) models leading to strong state mixing with significant total charge density transfer (approximately 0.4 e-), mainly from the C-Co sigma MO to C-Co sigma MO (approximately 0.3 e-). CASSCF(9:7) calculations show that the strong state mixing leads to an increase in the C-Co bond length for MeCbl(II) model compounds from 1.969 A (DFT and HF calculations) to 2.164 A in the base-on MeCbl(II) model and from 1.938 A to 2.144 A in the base-off MeCbl(II) model. Concomitantly, the Co-N axial bond length increases from 2.121 A (DFT) to 2.344 A in the CASSCF calculation. This coupling interaction between states can be used to explain the much lower Co-C bond dissociation enthalpy and much faster bond cleavage rate for the one-electron reduced methylcobalamin radical anion compared to MeCbl(III). It may also be important for axial bond distances in other Co(II) compounds.

Multistate and multimode vibronic dynamics: The Jahn–Teller and pseudo-Jahn–Teller effects in the ethane radical cation

Multimode Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) coupling effects in the photoelectron spectrum of ethane are theoretically investigated. In this article, we focus on the vibronic structure of the second excited B ∼ 2 E u electronic manifold of the ethane radical cation which reveals an asymmetric band in the 14.5–16.5 eV ionization energy range in the experimental recordings. Ionization of an electron from the third occupied 1 e u molecular orbital of ethane produces the radical cation in the degenerate B ∼ 2 E u electronic manifold, which is prone to the JT instability when distorted along the degenerate e g vibrational modes. The theoretical formalism employed here is based on a model diabatic Hamiltonian and a quadratic vibronic coupling scheme with the parameters derived from ab initio electronic structure calculations. The photoelectron band is calculated by carrying out quantum dynamical simulations in the coupled manifold of electronic states. The B ∼ 2 E u electronic manifold of the radical cation is estimated to be ∼2.75 eV and ∼2.40 eV above its X ∼ 2 E g and the A ∼ 2 A 1 g electronic states, respectively. The symmetry selection rule suggests PJT coupling of these electronic states along the vibrational modes of e g/ e u symmetry. The quadratic JT spectrum simulated within the B ∼ 2 E u electronic manifold shows two maxima at ∼ 14.96 eV and ∼15.76 eV which are attributed to the two JT split adiabatic sheets of this electronic manifold. This is in good accord with their position observed at ∼15.0 eV and ∼15.8 eV, respectively, in the experimental recording. The diffuse structure of the overall band can be accounted to a large extent by considering the A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions. The overall shape of the theoretical band agrees very well with the experimental results. Further refinement of the theoretical results may be accomplished by including X ∼ 2 E g - A ∼ 2 A 1 g - B ∼ 2 E u PJT interactions in the theoretical model. Importance of the latter vibronic interactions is also discussed in the text.

Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na,Mg,Al,Si,P,S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.

Near degeneracy and pseudo Jahn-Teller effects in mixed-valence ladders: The phase transition inNaV2O5

We analyze the electronic structure of a mixed-valence ladder system. We find that structural anisotropy and complex electron correlations lead to on-rung charge localization and insulating character. Charge fluctuations within the rung of the ladder interact strongly to the lattice degrees of freedom, which gives rise to large pseudo Jahn--Teller effects. The phase transition in NaV$_2$O$_5$ should be driven by this kind of mechanism.

Pseudo Jahn–Teller effect observed in Eu@C60

Structures and electronic states in the ground state of endohedral fullerence are investigated by XAFS analysis and XANES spectrum. The distances between the Eu ion and the neighboring C atoms show clearly that the Eu ion is inside the C60 cage. The endohedral element, Eu, in C60 is located away from the central position of C60 cage by 1.4 Å. We show the detailed location of the Eu ion in the C60 cage by XAFS and the first principles calculation. The perturbation theory indicates that the distortion of C60 cage and the shift of the Eu ion are attributed to electron-nuclear interaction, pseudo-Jahn–Teller type interaction. XANES spectrum of Eu LIII-edge shows that the valence of the Eu ion is close to +2. The electron configuration is thus f7, showing the total symmetry (A1g) of Ih group. The details of the structures and the electronic states will be discussed with both the experimental and theoretical results.

Jahn-Teller effects in the SbSBr crystals atomic chain

The quasi-one-dimensional SbSBr atomic chain consisting of up to 60 atoms is considered theoretically. One-electron energies 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 SbSBr chain in the paraelectric and ferroelectric phases has been determined. It was shown that the A u and B g symmetry of the top electronic levels of the highest valence band are degenerated in the paraelectric phase. The low frequency and high frequency Au symmetry normal modes interacting with the degenerate Au symmetry electronic states in the top of valence band induce the Jahn-Teller effect. The same modes interacting with Au symmetry electronic states in the valence band and with B g symmetry states in the bottom of conduction band induce the pseudo Jahn-Teller effect. The total energy upon normal co-ordinates of modes and Au due to both Jan-Teller effects demonstrates anomalous variation of its vibrational frequency in the phase transition region.

Quantum non-adiabatic dynamics through conical intersections: Spectroscopy to reactive scattering

Some of the recent developments in the quantum dynamical studies at the conical intersections of molecular potential energy surfaces is briefly reviewed in this article. Particular emphasis is given to a variety of molecular processes studied by us in the recent past. The non-adiabatic effects due both to the electronic as well as relativistic spin–orbit coupling are considered. The discussions include the Jahn–Teller effect (and also the pseudo-Jahn–Teller effect whenever applicable) in the Rydberg emission spectrum of triatomic hydrogen and the photoelectron spectrum of cyclopropane and methyl fluoride, probing the conical intersections in ClO2 and the reagent van der Waals well in the Cl(2 P)+H2 reaction via the photodetachment spectroscopy of the negative ions, ClO and ClH , respectively, and the thermal scattering dynamics of H+H2 and Cl(2 P)+H2 reactions on multisheeted potential energy surfaces.

Symmetries, vibrational instabilities, and routes to stable structures of clusters of Al, Sn, and As.

We investigate the stability of small clusters using density functional theory to compute the total energy, forces, and vibrational frequencies using linear response. We exhibit an efficient and computationally low-cost route to finding stable structures, by starting with high-symmetry structures and distorting them according to their unstable modes. We illustrate this by application to 4-, 6-, and 13-atom clusters of Al, Sn, and As. This technique also naturally elucidates the origins of stability of the lower symmetry structures, which is variously due to the linear or pseudo Jahn-Teller effect, combined with a lowering of various contributions to the total energy. We show that the situation is more complex than has generally been appreciated.