Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Abstract

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational–rotational–vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C 60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H 2 O@C 60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n -mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H 2 O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H 2 O@C 60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest–host interactions.

First principles molecular dynamics calculations of the mechanical properties of endofullerenes containing noble gas atoms or small molecules

“…57,58 We also find that the O atom of the H 2 O molecule remains close to the C 60 center during the 300 K run, and that the molecule rotates easily as expected. 29,59 DQ is only Table 1 Vinet EOS parameters for the atom or molecule X, and data for the endofullerene X@C 60 computed at 300 K. V 0 , B 0 and B 0 0 are the volume, bulk modulus, and bulk modulus derivative published values for X in solid phase: He, 44 Ne, 45 Ar, 46 Kr, 47 Xe, 48 H 2 O, 49 CH 4 . 50 V 0 for He 6 and He 10 are the He value multiplied by the number of helium atoms.…”

Unraveling the Origin of Symmetry Breaking in H2O@C60 Endofullerene Through Quantum Computations

“…In our previous work, [44] the exact kinetic energy operator has been derived for a nanoconfined light‐heavy‐light molecule, such as the water, and thus the Hamiltonian operator of the fully coupled H 2 O@C 60 reads: , with being the total mass of the H 2 O, being the coordinates, defined as ( ) the spherical coordinates of the H 2 O mass center with respect the space‐fixed xyz coordinate system, the Radau coordinates describe the water molecule, and the Euler angles. The potential operator is expressed as, , where the potential is generated as a sum over the H 2 O−C pairwise interactions, modeled with the H−C and O−C Lennard‐Jones (LJ) 12–6 potentials adjusted to DFT‐SAPT ab initio graphene‐water reported in Ref.…”

“…In our previous work, [44] the exact kinetic energy operator has been derived for a nanoconfined light-heavy-light molecule, such as the water, and thus the Hamiltonian operator of the fully coupled H 2 O@C 60 reads:…”

“…Thus, recently we have reported such computational scheme, within the multiconfiguration time-dependent Hartree (MCTDH) framework, [41,42] to perform in an efficient manner quantum dynamics calculations of any encapsulated triatomic molecule. [27,43,44] As mentioned, distinct suggestions have been reported for symmetry-lowering interaction, [3,9,16,[25][26][27][28][29] including electrostatic charge-transfer, dipoles and quadrupoles between neighbor filled or empty cages, present of impurities, as well as crystal field effects, with the origin of such reduction in symmetry (from the I h of the C 60 molecule [45] ) being of fundamental interest, whether it arises from inter-cage or intra-cage interactions or both.…”

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

“…For HF@C 60 , bond elongation and a quenching of the vibrational frequency have been predicted. 32 Besides the electronic and vibrational states studied here, rotational coupling can lead to additional splittings; see, e.g., refs ( 33 − 39 ) for details.…”