Numerical Estimation of the Pseudo-Jahn–Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules

Abstract

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.

Jahn–Teller and Pseudo-Jahn–Teller Effects: From Particular Features to General Tools in Exploring Molecular and Solid State Properties

“…This section is to introduce the JTE and PJTE (jointly, vibronic effects) in a (somewhat pedagogical) manner (using simple cases as examples), which allow us to demonstrate the main origins of these effects and their most important features that contribute to the observable phenomena in mater, emphasizing the latest achievements. In so doing, as mentioned above, we avoid bulk mathematical deduction for the more complicated cases, which can be find in the cited publications, ,,− ,− …”

“…There is a series of other JTE and PJTE problems (some of them considered below in this review), with many applications to studies of molecular and solid state phenomena, reflected in original publications, reviews, and books cited in the introduction, notably refs , , , and − for books, refs , , , and − for major reviews, and refs − for more recent developments of the vibronic coupling theory in relation to the JTE and PJTE. In addition to the noted above E⊗e problem of systems with 2-fold degenerate states, widespread are also problems T⊗ e , T⊗ t 2 , T⊗( e+t 2 ) of cubic systems with 3-fold degenerate T terms interacting with e and t 2 displacements, and higher level of degeneracy in icosahedral systems, as well as combined and multimode JTE problems <...…”

“…The development of the theory of the JTE and PJTE continues, including both higher order vibronic coupling (higher terms in the Hamiltonian expansion in nuclear displacements in eq ) and higher electronic degeneracies and pseudodegeneracies with spin–orbital coupling implications and other relativistic effects, as well as nonadiabatic effects, which involve more complicated analytical deductions and ab initio calculations (see refs − and references therein). The novel achievements of the theory, in addition to producing quantitative estimates of the expected vibronic effects, reveal also novel features in the observable properties of the system.…”

“…The theoretical background of all these effects in atomic systems emerges from the first-principles as a delicate addition to the coupling between the electronic states and nuclear displacements, which occurs beyond the adiabatic approximation (vibronic coupling). The theory of the JTE and PJTE with many of their manifestations in molecular and solid state properties are rather well studied and continues developing. − Less attention has been paid so far to the PJTE, especially to its use as a tool in the study of the structure and properties of polyatomic syst...…”

“…As in any theoretical work, mathematical proofs of the origin of the JTE and PJTE structural instabilities based on first-principles are most important, but in detail they are of primary interest to more specialized readers and deserve separate consideration. For the more significant achievements in this field, see refs , , , and − for books; refs , , , and − for major reviews; refs − for JTE conference proceedings; and refs − …”