Relativistic Jahn—Teller effect G<Subscript>g</Subscript>[3/2]×(t<Subscript>2g</Subscript> + e<Subscript>g</Subscript>) in cubic and octahedral molecules

The properties of the symmetry of the vibronic Hamiltonian of the multimode relativistic Jahn—Teller effect G_g[3/2]×(t_2g + e_g) in cubic and octahedral molecules are studied. The Hamiltonian considered corresponds to the half-integer spin of the electron shell and the linear approximation on the vibrational normal modes t_2g and e_g. The angular variables were separated, and biradial dynamic equations and analytical expressions for the biradial potential energy surfaces were obtained. The positions of the low-lying resonances in two upper potential “bowls” were found.     

Superconducting first‐order pairing: Finite‐temperature simulations

A 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     

VIBPACK: A package to treat multidimensional electron‐vibrational molecular problems with application to magnetic and optical properties

We present a FORTRAN code based on a new powerful and efficient computational approach to solve multidimensional dynamic Jahn–Teller and pseudo Jahn–Teller problems. This symmetry‐assisted approach constituting a theoretical core of the program is based on the full exploration of the point symmetry of the electronic and vibrational states. We also report some selected examples of increasing complexity aimed to display the theoretical background as well as the advantages and capabilities of the program to evaluate of the energy pattern, magnetic and optical properties of large multimode vibronic systems. © 2018 Wiley Periodicals, Inc.     

Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

Density functional theory of born couplings: Consequences for electron flow in Jahn–Teller molecules and superconductors

The dynamics of Jahn–Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear-coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a densitybased treatment of Born couplings is derived from first-principles quantum mechanics beyond the Born–Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn–Teller molecule, there are an infinite number of ways in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecule in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn–Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. © 1995 John Wiley & Sons, Inc.     

Superconductivity in cuprates: Details of electron phonon coupling

The Bardeen‐Cooper‐Schrieffer (BCS) model explains superconductivity (SC) as due to correlation between electronic momentum and nuclear momentum (phonons) in a free electron gas. The BCS model lacks chemical specificity, however, since the coupling mechanism is left unspecified. After the discovery of high T_C superconductivity in 1986 it was concluded that electron–phonon interactions are insufficient to explain electron pairing. A large part of theoretical research has since been aiming at finding another mechanism that would allow us to consider the superconducting system as a gas of charged free bosons. However, there appears to be no reason to assume free electrons in oxides. In this article the free‐electron criterion is therefore replaced by the criterion that a pair of electrons can move freely between sites without resistance, i.e., without activation energy. Electron pair transfer is treated in a many‐electron real space approach using standard mixed‐valence theories. Mott‐Hubbard‐U is strictly defined, its dependence on breathing mode coordinates analyzed, and the connection between U and the energy gap for superconductivity clarified. d‐wave gap anisotropy is found to be consistent with the general atomic level model presented here. Softening of phonon half‐breathing modes in inelastic neutron scattering (INS) is connected to mixed‐valency. The fundamental vibronic interaction between spin density wave (SDW) and charge density wave (CDW) states leads to a new phase with energy gap and electron pair carriers that can only be the superconducting phase. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin–orbit couplings in Π electronic states of linear tetra‐atomic molecules

Avariational and a perturbative approach are developed to handle the combined effect of the vibronic and spin–orbit couplings in Π electronic states of tetra‐atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin–orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth‐order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second‐order formulae when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin–orbit structure in the X²Π electronic state of HCCS by employing the ab initio‐computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

A Chemist's View of BCS Theory for Low Tc Superconductivity and Its Relationship to Charge Transfer and High Tc Superconductivity

Based on a chemist's understanding of electron transfer, attempts are made to interpret the physicists' BCS theory for low Tc superconductivity in terms of quantum chemical views. To show how to improve and apply some of the principles of the BCS theory for high Tc superconductors, especially those having to do with many-body aspects of correlation, coherence and long-range order, we (1) extend the two-partner, donor-acceptor electron transfer to large periodic systems with cyclic boundary conditions and with double-well potentials beyond Peierls distortion. (2) introduce second-order Jahn-Teller stabilization and introduce vibronic mixing as configuration interaction. To take advantage of existing bonds in high Tc superconductors we propose a linear combination of bonding (two-electron) geminals to form molecular bonding geminals which we call “Vibronic Geminals” after mixing with different running waves of bond structure vibrations. To take advantage of the valence bonds and double-well potentials due to anti-symmetric and other vibrations, we propose a ‘Covalon’ type model for the propagation and tunneling of such bonds which transform as Bosons.     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Jahn—Teller effects in substituted benzene cations. IV. Intermode interactions and intensity anomalies in sym-trifluorobenzene ions

A theoretical treatment of coupling between Jahn—Teller modes is given which includes both linear and quadratic Jahn—Teller coupling. Effects of two and three mode interactions on the B?²A″₂ → X?²E″ transition of the sym-trifluorobenzene ions are studied, within the linear coupling approximation, for modes 6, 7, 8 and 9. Quadratic coupling effects are considered in a companion paper (part V). The results show that discrepancies previously noted between observed relative band intensities and those calculated on the basis of single Jahn—Teller modes cannot be accounted for by multimode interactions or by Fermi resonance effects operating in conjunction with Jahn—Teller effects. Jahn—Teller combination bands are shown to have several components, the most intense of which are assigned. Particular attention is paid to various possible assignments of the 8^0,0_{1,$\text{1}\text{2}$} and 6^0,0_{3,$\text{1}\text{2}$} vibronic transitions in the light of the multimode interaction analyses.     

Vibronic polarons: Self‐trapping,local rotation,and band features

We revisit basic theoretical concepts of local and itinerant vibronic polarons in crystals. The following results may be regarded as novel: (1) The electron self‐trapping rate to a small polaron is calculated via the reaction rate method; subsequently, self‐trapped on‐center small polarons relax to an off‐center vibronic polaron state. (2) The general vibronic Hamiltonian is redefined so as to incorporate both local and itinerant behavior and pairing into bipolarons or Cooper pairs. (3) The planar rotation and diametral tunneling of an off‐center polaron around and across its centrosymmetrical site are dealt with to adiabatic approximation. (4) Variational calculations are made for vibronic polarons itinerant along 1‐D chains by means of a two‐band extension of Merrifield's ansatz. This investigation of vibronic polarons is undertaken in view of their presumed role in high‐temperature superconductivity and colossal magnetoresistance. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Jahn—Teller effects in substituted benzene cations. V. Quadratic coupling

A calculation model is derived for taking into account quadratic, in addition to linear, coupling Jahn—Teller effects in determining vibronic energy levels and transitions. Procedures are developed for analysis of Jahn—Teller electronic spectra on this basis and the new features, with respect to the linear coupling approximation, brought about by introduction of quadratic coupling, are discussed. Vibronic analyses of the B?² A″₂-X?²E″ transitions of 1,3,5-C₆F₃H⁺₃, 1,3,5-C₆F₃D⁺₃ and 1,3,5-C₆Cl₃H⁺₃ are carried out, in particular for bands involving excitation of the mode 6 vibration. Experimental evidence for quadratic Jahn—Teller effects is obtained for the sym-trifluorobenzene ions and the linear coupling parameters D₆, ω₆ and quadratic coupling parameter q₆ are derived. Two possible orders of magnitude of the quadratic coupling strength are found to be compatible with the spectra of 1,3,5-C₆Cl₃H⁺₃. The analyses are consistent between the three ions and are not in contradiction with the general findings based on the linear approximation alone.     

A Genuine Jahn–Teller System with Compressed Geometry and Quantum Effects Originating from Zero‐Point Motion

First‐principle calculations together with analysis of the experimental data found for 3d⁹ and 3d⁷ ions in cubic oxides proved that the center found in irradiated CaO:Ni²⁺ corresponds to Ni⁺ under a static Jahn–Teller effect displaying a compressed equilibrium geometry. It was also shown that the anomalous positive g_∥ shift (g_∥?g₀=0.065) measured at T=20 K obeys the superposition of the |3 z²?r²? and |x²?y²? states driven by quantum effects associated with the zero‐point motion, a mechanism first put forward by O'Brien for static Jahn–Teller systems and later extended by Ham to the dynamic Jahn–Teller case. To our knowledge, this is the first genuine Jahn–Teller system (i.e. in which exact degeneracy exists at the high‐symmetry configuration) exhibiting a compressed equilibrium geometry for which large quantum effects allow experimental observation of the effect predicted by O'Brien. Analysis of the calculated energy barriers for different Jahn–Teller systems allowed us to explain the origin of the compressed geometry observed for CaO:Ni⁺.     

Low temperature luminescence spectra of the d10s2 complexes Cs2MX6 (M = Se,Te and X = Cl,Br). The Jahn—Teller effect in the Γ−4(3T1u) excited state

The emission spectra of the title compounds in microcrystalline form have been measured at 10 K. The extensive vibrational progression in the e_g mode is indicative of a tetragonal Jahn—Teller distortion in the Γ^?₄(³T_1u) excited state. The vibronic coupling of a threefold electronic state with a doubly degenerate e_g mode (T—e coupling), linear in the nuclear coordinates, has been reinvestigated considering spin—orbit coupling up to second order perturbation on energy levels which result from an a¹_1gt¹_1u electron configuration. For an estimation of Jahn—Teller coupling constants, the intensity distributions in the progressions were compared with the theoretical line shape functions which were obtained from a model which also permits the determination of potential energy minima and vibrational fundamentals of the excited state. The unusually large increase in the e_g vibrational frequency compared to the ground state is due to Jahn-Teller forces which distort the potential surface, yielding steeper excited state energy curves.     

Adjacent Lone Pair (ALP) Effect: A Computational Approach for Its Origin

The adjacent lone pair (ALP) effect is an experimental phenomenon in certain nitrogenous heterocyclic systems exhibiting the preference of the products with lone pairs separated over other isomers with lone pairs adjacent. A theoretical elucidation of the ALP effect requires the decomposition of intramolecular energy terms and the isolation of lone pair–lone pair interactions. Here we used the block‐localized wavefunction (BLW) method within the ab initio valence bond (VB) theory to derive the strictly localized orbitals which are used to accommodate one‐atom centered lone pairs and two‐atom centered σ or π bonds. As such, interactions among electron pairs can be directly derived. Two‐electron integrals between adjacent lone pairs do not support the view that the lone pair–lone pair repulsion is responsible for the ALP effect. Instead, the disabling of π conjugation greatly diminishes the ALP effect, indicating that the reduction of π conjugation in deprotonated forms with two σ lone pairs adjacent is one of the major causes for the ALP effect. Further electrostatic potential analysis and intramolecular energy decomposition confirm that the other key factor is the favorable electrostatic attraction within the isomers with lone pairs separated.     

Jahn–Teller Effects in Molecular Cations Studied by Photoelectron Spectroscopy and Group Theory

The traditional “ball‐and‐stick” concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn–Teller (JT) effect which is very common in open‐shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo‐Jahn–Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of “antiaromaticity” are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential‐energy surface are separated by substantial barriers.     

Theory of the Bose particle representation for geminals

An electron pair in a molecule is a complex entity and is incompletely described by the independent particle picture. Electron pairs are treated as Bose particles to include correlation of intrapair interaction effectively by the use of the Dyson transformation. The use of a Bose-type Hamiltonian permits a straight forward interpretation for geminals and facilitates the calculation of electronic energies. A Bose-type representation method is applied to the calculation of electronic energies of a lithium hydride molecule.     

Density functional theory for Jahn–Teller systems

The first discussion of the dynamics of Jahn–Teller systems in terms of the electronic density as the fundamental variable was given by W.J. Clinton in 1960, where the degenerate electronic configuration of a Jahn–Teller molecule was interpreted in terms of the infinite number of ways in which the charge distribution can be oriented for the same energy. The moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, with no activation energy required to put the charge cloud into motion. Recently, this notion of the electronic charge cloud in a Jahn–Teller molecule sweeping out the potential surface over which the nuclei move has found mathematical expression in our work in terms of a generalized electronic current density in nuclear-coordinate space [N. Sukumar and B.M. Deb, Int. J. Quantum Chem. 40 , 501 (1991)]. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, is a crucial component of this formulation. In the present work, the density-based treatment is extended to the nonadiabatic situation, with the Born couplings interpreted as nonadiabatic currents in parameter space. Abelian and non-Abelian gauge transformations of these currents are discussed. © John Wiley & Sons, Inc.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.     

The generalized separated electron pair model. III. An application to three localization schemes for CO

The separated electron pair (SEP ) model (strongly orthogonal geminals) and methods for its systematic extension have been applied to three different localization schemes for C?O. The optimum SEP wave function is obtained for the particular localization scheme that involves three equivalent bent bonds. The major corrections to the SEP model arise from one-electron transfer terms. Two-electron transfer terms were important only for those pairs that were not well localized. It was found that the separate definitions of the total intrapair and interpair correlation energies did not depend strongly on the choice of localization scheme.