Vibronic Coupling in Spherically Encapsulated, Diatomic Molecules: Prediction of a Renner-Teller-like Effect for Endofullerenes

Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes

Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly differ from those of free species. In this work, we employ the density-matrix renormalization group method to show that chains of fullerenes filled with polar molecules (LiF, HF, and H₂O) can form dipole-ordered quantum phases. In symmetry broken environments, these ordered phases are ferroelectric, a property that makes them promising candidates for quantum devices. We demonstrate that for a given guest molecule, the occurrence of these quantum phases can be enforced or influenced either by changing the effective electric dipole moment or by isotopic substitution. In the ordered phase, all systems under consideration are characterized by universal behavior that depends only on the ratio of the effective electric dipole and of the rotational constant. A phase diagram is derived, and further molecules are proposed as candidates for dipole-ordered endofullerene chains.

Probing the Interaction of NO with C60: Comparison between Endohedral and Exohedral Complexes

Recent advances in synthetic methodologies have opened new strategies for synthesizing stable metal-free electron spin systems based on fullerenes. Introducing nitric oxide (NO) inside a fullerene cage is one of the methods to attain this goal. In the present study, dispersion corrected density functional theory (B3LYP-D3) has been used to evaluate the structure, stability, and electronic properties of NO encapsulated fullerene NO@C₆₀ and compared those with its exohedral fullerene NO.C₆₀ analog. The calculated stabilization energy for NO@C₆₀ is appreciably higher than NO.C₆₀, and this difference is comprehended via the Quantum theory of atoms in molecules (QTAIM) and noncovalent interaction (NCI) topological analyses. The delocalization of electron density of NO and the C₆₀ cage in NO@C₆₀ is discussed using electrostatic potential analysis. In addition, an attempt has been made to understand the different locations and orientations involving the interaction of two NO radicals and the fullerene C₆₀. It is shown that the encapsulation of the NO dimer inside the C₆₀ cage is an energetically unfavorable process. On the other hand, stable structures are obtained upon the physisorption of other NO on the surface of NO@C₆₀ and NO.C₆₀. The present work provides an in-depth understanding of the interaction of NO and C₆₀ fullerene, its preferable position, and its orientation in both endohedral and exohedral complexes.

Neglected Importance of Anharmonicity in Quantifying the Renner-Teller Effect

Linear molecules in degenerate electronic states are influenced by the Renner-Teller (RT) effect. Currently the formula to quantify this vibronic interaction only considers the harmonic term. However, such a harmonic formula cannot well describe molecules that have double-well potential along the bending coordinate. In this work, we propose a new formula to quantify the RT effect by explicitly including the anharmonic term. A sign function and a delta function are additionally included to distinguish different scenarios. It is mathematically proved that the new formula is capable of differentiating different degrees of RT splitting. Representative molecules of different types are calculated. According to the new formula, molecules experiencing a weak RT effect have a positive parameter smaller than 1. For those experiencing a medium RT effect, the parameter will be negative. For others experiencing a large RT effect, the parameter will be larger than 1.

Vibronic Coupling in Spherically Encapsulated, Diatomic Molecules: Prediction of a Renner-Teller-like Effect for Endofullerenes

In the year 1933, Herzberg and Teller realized that the potential energy surface of a triatomic, linear molecule splits into two as soon as the molecule is bent. The phenomenon, later dubbed the Renner–Teller effect due to the detailed follow-up work of Renner on the subject, describes the coupling of a symmetry-reducing molecular vibration with degenerate electronic states. In this article, we show that a very similar type of nonadiabatic coupling can occur for certain translational degrees of freedom of diatomic, electronically degenerate molecules when trapped in a nearly spherical or cylindrical quantum confinement, e.g., realized through electromagnetic fields or molecular encapsulation. We illustrate this on the example of fullerene-encapsulated nitric oxide, and provide a prediction of its interesting, perturbed vibronic spectrum.