Isaac B. Bersuker

The Jahn-Teller effect

1. Introduction 2. Vibronic interactions 3. Formulation of Jahn-Teller problems. Adiabatic potentials 4. Pseudo Jahn-Teller, Product Jahn-Teller, and Renner-Teller effects 5. Solutions of vibronic equations. Energy spectra and Jahn-Teller dynamics 6. The Jahn-Teller Effect in spectroscopy: general theory 7. Geometry, spectra, and reactivity of molecular systems 8. Solid-state problems: local properties and cooperative phenomena Appendices Subject index Formula index.

On the origin of dynamic instability of molecular systems

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH3, planar square CH4 and linear H3+) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.

LIMITATIONS OF DENSITY FUNCTIONAL THEORY IN APPLICATION TO DEGENERATE STATES

It is shown that the claims that density functional theory (DFT) can handle orbitally degenerate states are ungrounded. The constraint search formulation of DFT allows one to determine a set of densities and eigenvalues for the degenerate term that, however, are neither observables, nor can they be used to solve the system of coupled equations for the nuclear motions to obtain observables, as in the wave function presentation. A striking example of the failure of the existing versions of DFT to describe degenerate states is provided by the Berry phase problem: the strong dependence of the results on the phase properties of the electronic wave function that are smeared out in the density formulation. The solution of the Jahn‐Teller E‐e problem illustrates these statements. For nondegenerate states with the full wave function taken in the adiabatic approximation as a product of the electronic and nuclear parts, the formulation of DFT is rigorous if and only if the dependence of the electronic wave function on nuclear coordinates is ignored. This lowers the accuracy of the results, in general, and may lead to erroneous presentation as in the case of molecular systems in strong magnetic fields.

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 Hunds 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.

Pseudo Jahn-Teller origin of nonplanarity and rectangular-ring structure of tetrafluorocyclobutadiene.

It is shown that the pseudo Jahn-Teller effect (PJTE) in combination with ab initio calculations explains the origin of instability of the planar configuration of tetrafluorocyclobutadiene, C(4)F(4), with respect to a puckered structure and square-to-rectangle distortion of the carbon ring, and rationalizes its difference from the planar-rectangular geometry of C(4)H(4) and nonplanar (puckered) structure of Si(4)H(4). The two types of instability and distortion of the high-symmetry D(4h) configuration in these systems emerge from the PJT coupling of the ground B(2g) state with the excited A(1g) term producing instability along the b(2g) coordinate (elongation of the carbon or silicon square ring), and with the excited E(g) term resulting in e(g) (puckering) distortion. A rhombic distortion b(1g) of the ring is also possible due to the coupling between excited A(1g) and B(1g) terms. For C(4)F(4), ab initio calculations of the energy profiles allowed us to evaluate the PJTE constants and to show that the two instabilities, square-to-tetragonal b(2g) and puckering e(g) coexist, thus explaining the origin of the observed geometry of this system in the ground state. The preferred cis-trans (e(g) type) puckering in C(4)F(4) versus trans-trans puckering (b(2u) distortion) in Si(4)H(4) follows from the differences in the energy gaps to their excited electronic E(g) and A(1u) terms causing different PJTE in these two cases.

Pseudo Jahn–Teller origin of instability of molecular high-symmetry configurations: Novel numerical method and results

The pseudo Jahn–Teller (PJT) effect as the only source of instability of molecular high-symmetry configurations in nondegenerate states is given a deeper insight by means of a novel method of ab initio evaluation of the vibronic Kv and nonvibronic K0 contributions to the curvature K=K0+Kv of the adiabatic potential energy surface in the direction of distortion. The method overcomes two essential difficulties: (1) the low accuracy in calculation of K0 because of the singularities at the nuclei where existing basis sets yield inadequate results, and (2) the lack of sufficiently accurate data on excited states (including the continuum spectrum) for calculation of Kv. This is achieved by summing up the contributions of the excited states to result in expressions with only the ground state wave function and its derivatives, and excluding the singularities by canceling mutually compensating diagonal matrix elements in K0 and Kv. After these essential changes K=K0+Kv is no longer a small difference between two l...

Symmetry breaking in the ground state of BNB: a high level multireference study.

A series of multireference approaches based on the SA-CASSCF wave function, i.e., CASPT2, MRCI, MRCI + Q, and MRAQCC with single- or multireference states, have been employed to investigate the symmetry breaking effect in the ground state X (2)Sigma(u)(+) of the triatomic BNB radical. We found that the mixing of the reference states contributes significantly to the dynamical correlation energy, which strongly affects the geometry of the ground state. Our results show that BNB in its ground state has a linear noncentrosymmetric structure with two equivalent global minima of the adiabatic potential energy surface and, respectively, two oppositely directed dipole moments of about 2 D. The barrier between the minima is about 20 cm(-1). The origin of the double-minimum potential in the ground state of BNB is explained as due to the pseudo-Jahn-Teller effect involving vibronic interaction with the first excited state A (2)Sigma(g)(+) via the asymmetric stretching vibrations.

Improved electron-conformational method of pharmacophore identification and bioactivity prediction. Application to angiotensin converting enzyme inhibitors.

The electron-conformational (EC) method of pharmacophore (Pha) identification and bioactivity prediction, suggested earlier, is given here two major improvements. First, an atomic index of orbital and charge controlled interaction is introduced to better represent the ligand (substrate) in its interaction with the bioreceptor. Second, the multiconformational problem is considered in view of ligand-receptor binding states, resulting in essential simplification of the expression of bioactivity. The details of the improved EC method are demonstrated in application to the problem of angiotensin converting enzyme (ACE) inhibitors. The Pha of the latter is identified by separation of the heavily populated conformations of the chosen 51 compounds (the training set), calculation of the electronic structure, construction of their EC matrixes of congruity, and processing of the latter in comparison with the activities to reveal a common submatrix of all the active only compounds that describes the Pha. The latter contains three oxygen atoms plus a fourth atom X = S, N, O at certain interatomic distances and with restricted electronic parameters (within assumed tolerances), the position of the atom X being more changeable from one active compound to another. For quantitative prediction of the bioactivity, an expression is deduced which takes into account the duly parametrized influence of auxiliary groups (AG) which, being positioned outside the Pha, either diminish the activity (antipharmacophore shielding) or enhance it. It is shown that in case of many conformations of the same compound only one of them, that of the lowest energy which has the Pha, should be parametrized. The 15 parameters chosen to represent the AG in case of ACE inhibitors are weighted by variational (adjustable) coefficients which are determined from a regression treatment of the calculated versus known activities in the training set. Then the formulas with known coefficients are used to validate the method by calculating the bioactivity of other compounds not used in the training set. The prediction of the activity proved to be more than 90% (within experimental error and available compounds) qualitatively (yes, no) and about 60%-70% quantitatively.

An electron-conformational method of identification of pharmacophore and anti-pharmacophore shielding: application to rice blast activity.

In extension and improvement of previous results, a novel method is worked out for pharmacophore identification and activity prediction in structure-activity relationships. In this method, as in our previous works, each molecular system (conformation) of the training set is described by a matrix with both electron structural parameters (atomic charges, bond orders, etc.) and interatomic distances as matrix elements. This description includes a rather full geometry of charge and/or reactivity distribution thus providing a much better representation of the molecular properties in their interaction with the target. By multiple comparison of these matrices for the active and inactive compounds of the training set, a relatively small number of matrix elements are revealed that are common for all the active compounds and are not present in the same combination in the inactive ones. In this way a set of electronic and geometry parameters is obtained that characterize the pharmacophore (Pha). A major improvement of this scheme is reached by introducing the anti-pharmacophore shielding (APS) and a proper treatment of the conformational problem. The APS is defined as molecular groups and competing charges outside the basic skeleton (the Pha plus the inert neighbor atoms that do not affect the activity) that hinder the proper docking of the Pha with the bioreceptor thus diminishing (partially or completely) the activity. A simple empirical formula is derived to estimate the relative contribution of APS numerically. Two main issues are most affected by the APS: (1) the procedure of Pha identification is essentially simplified because only a small number of molecular systems with the highest activity and simplest structures (systems without APS) should be tried for this purpose; (2) with the APS known numerically, we can make a quantitative (or semiquantitative) prediction of relative activities. The contributions of different conformations (of the same molecular system) that possess the Pha and different APS is taken into account by means of a Boltzmann distribution at given temperatures. Applied to an example, rice blast activity, this approach proved to be rather robust and efficient. In validation of the method, the screening of 39 new compounds yields approximately 100% (within experimental error) prediction probability of the activity qualitatively (yes, no), and with r2=0.66 quantitatively.

MO LCAO analysis of the vibronic instability of the CuCl53− trigonal bipyramidal configuration. Critical view on the angular overlap model in vibronic problems

The vibronic origin of the instability of the CuCl53− trigonal-bipyramidal configuration (resulting in three equivalent square pyramidal stable configurations) is revealed by solving the three-mode (A′1 + E′)⊗(e′ + e′ + e′) problem, the electronic functions, vibronic constants and bare force constants being calculated in the semiempirical MO LCAO scheme. The three-mode problem is reduced to the one-mode one by means of the “interaction mode” presentation. The semiempirical calculations are based on the extended Huckel approach including self-consistency with respect to atomic charges and configuration (the SCCC MO LCAO method). It is shown that the main contribution to the instability is due to the pseudo Jahn-Teller mixing to three excited E′ states formed by one-electron excitations 1e′ → 5a1, 1e′ → 6a′1 and 1a′1 → 6e′ (in the frozen MO approximation excited states). By comparison with the results obtained earlier in the angular overlap model (AOM) and additional analysis, it is shown that the only (A′1 + E′)⊗e′ mixing considered in the AOM has a minor contribution to the instability; in general, the AOM is inapplicable to pseudo Jahn-Teller problems.