^{1,a)}, Isaac B. Bersuker

^{1}and James E. Boggs

^{1}

### Abstract

It is shown that in systems with electronic half-closed-shell configurations of degenerate orbitals, and (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 [ and in the and 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 for and for 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 and 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 , , , , , , , and , which are in agreement with the experimental data available.

This work was supported by the Welch Foundation with Grant No. F-100.

I. INTRODUCTION

II. PJTE AND DISPROPORTIONATION IN ELECTRONIC CONFIGURATIONS

III. PJTE AND DISPROPORTIONATION IN ELECTRONIC CONFIGURATIONS

IV. ORBITAL DISPROPORTIONATION IN SPECIFIC MOLECULES: AB INITIO CALCULATIONS FOR , , , , , , , AND

A. Ground electronic structure and geometry of

B. The electronic structure and ground state geometry of

C. Electronic structure and ground state geometry of

D. Excited states of

E. The electronic structures and ground state geometries of and

F. Geometry and electronic states of

G. Electronic structure and ground state geometry of

V. SPIN CROSSOVER

VI. CONCLUSIONS

### Key Topics

- Ground states
- 26.0
- Excited states
- 22.0
- Sodium
- 22.0
- Spin crossover
- 18.0
- Ab initio calculations
- 15.0

## Figures

Cross section of the APES along the coordinate for the states arising from the electronic configuration of . Its main features are (as predicted by the theory) a very weak JTE in the excited state, a strong PJTE between the excited and states that produces the global minimum with a distorted configuration, and a second conical intersection along (with two more, equivalent, in the full space). The spin-triplet state is shown by dashed line.

Cross section of the APES along the coordinate for the states arising from the electronic configuration of . Its main features are (as predicted by the theory) a very weak JTE in the excited state, a strong PJTE between the excited and states that produces the global minimum with a distorted configuration, and a second conical intersection along (with two more, equivalent, in the full space). The spin-triplet state is shown by dashed line.

Conventional energy level scheme for electronic configurations in tetrahedral (also valid for octahedral) vs icosahedral geometries. The and states in tetrahedral symmetry merge to form the fivefold state in symmetry. Vertical arrows show allowed PJT coupling via the indicated normal modes.

Conventional energy level scheme for electronic configurations in tetrahedral (also valid for octahedral) vs icosahedral geometries. The and states in tetrahedral symmetry merge to form the fivefold state in symmetry. Vertical arrows show allowed PJT coupling via the indicated normal modes.

Calculated relative contribution (weight) of the two possible disproportionate distributions the state (that produces the global minima of ) represented by the two Slater determinants, and , in the wave function. At (undistorted configuration) the weights of both components are equal and the electronic density distribution is totally symmetric. As a result of the PJT distortion one of the components becomes dominant, producing an orbitally disproportionate electron distribution.

Calculated relative contribution (weight) of the two possible disproportionate distributions the state (that produces the global minima of ) represented by the two Slater determinants, and , in the wave function. At (undistorted configuration) the weights of both components are equal and the electronic density distribution is totally symmetric. As a result of the PJT distortion one of the components becomes dominant, producing an orbitally disproportionate electron distribution.

The molecule in symmetry.

The molecule in symmetry.

Calculated cross section of the APES of using CASSCF along the angle in Fig. 4 showing the very weak JTE in the excited state and a strong PJTE between the and states. The inset shows in more detail the two conical intersections in the state in this direction.

Calculated cross section of the APES of using CASSCF along the angle in Fig. 4 showing the very weak JTE in the excited state and a strong PJTE between the and states. The inset shows in more detail the two conical intersections in the state in this direction.

Ground and excited states of along the coordinate. The PJTE pushes down the component of the degenerate term, which has also a weak linear JTE resulting in two conical intersections in this direction, one at and the other nearby, seen in the more detailed picture in the inset.

Ground and excited states of along the coordinate. The PJTE pushes down the component of the degenerate term, which has also a weak linear JTE resulting in two conical intersections in this direction, one at and the other nearby, seen in the more detailed picture in the inset.

Cross section of the APES of along the mode that distorts the system from square-planar to rhombic geometry due to the PJT coupling.

Cross section of the APES of along the mode that distorts the system from square-planar to rhombic geometry due to the PJT coupling.

Cross section of the APES of along the -mode distortion transforming the system from tetrahedral to square-planar geometry due to the PJT coupling.

Cross section of the APES of along the -mode distortion transforming the system from tetrahedral to square-planar geometry due to the PJT coupling.

Cross section of the APES of along the *effective mode* that takes the system from the undistorted high-spin minimum to the distorted low-spin minimum due to the multimode PJT coupling. The zero-point energies (ZPEs) *along this mode* (which are different from the global ZPEs) are to show that the lowest vibronic state associated with the electronic spin-doublet state is lower than that of the spin-quadruplet state.

Cross section of the APES of along the *effective mode* that takes the system from the undistorted high-spin minimum to the distorted low-spin minimum due to the multimode PJT coupling. The zero-point energies (ZPEs) *along this mode* (which are different from the global ZPEs) are to show that the lowest vibronic state associated with the electronic spin-doublet state is lower than that of the spin-quadruplet state.

## Tables

Vibronic and force constants of in the states arising from the splitting of the term of electronic , , and configurations (in notations).

Vibronic and force constants of in the states arising from the splitting of the term of electronic , , and configurations (in notations).

The parameters of the JT spin crossover in several systems. is the energy difference between the ground states of the high-spin and low-spin configurations, and and are the respective energy barriers, the energy difference between the minima and the crossing point between the two spin states (Fig. 9). All the energies are read off the zero-point vibrations.

The parameters of the JT spin crossover in several systems. is the energy difference between the ground states of the high-spin and low-spin configurations, and and are the respective energy barriers, the energy difference between the minima and the crossing point between the two spin states (Fig. 9). All the energies are read off the zero-point vibrations.

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