### Abstract

We report on variational solutions to the twelve-dimensional (12D) Schrödinger equation appertaining to the translation-rotation (TR) eigenstates of H_{2}O@C_{60} dimer, associated with the quantized "rattling" motions of the two encapsulated H_{2}O molecules. Both H_{2}O and C_{60} moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR eigenstates of H_{2}O@C_{60} monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR eigenstates reported by us recently [P. M. Felker and Z. Bačić, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H_{2}O@C_{60} dimer for two values of the water dipole moment and for various dimer geometries. 12D TR eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of eigenstates, distinguished by the leading order (first or second) at which dipole-dipole coupling contributes to them. The two types of eigenstates differ in the general magnitude of their dipole-induced energy shifts and in the dependence of those shifts on the value of the water dipole moment and on the distance between the H_{2}O@C_{60} monomers. The dimer results are also found to be markedly insensitive to any change in the orientations of the C_{60} cages. Finally, the results lend some support for the interpretation that electric dipole-dipole coupling is at least partially responsible for the apparent reduced-symmetry environment experienced by H_{2}O in the powder samples of H_{2}O@C_{60} [K. S. K. Goh et al., Phys. Chem. Chem. Phys. 16, 21330 (2014)], but only if the water dipole is taken to have a magnitude close to that of free water. The methodology developed in the paper is transferable directly to the calculation of TR eigenstates of larger H_{2}O@C_{60} assemblies, that will be required for more extensive modeling of crystalline H_{2}O@C_{60}.

Original language | English (US) |
---|---|

Article number | 084303 |

Journal | Journal of Chemical Physics |

Volume | 146 |

Issue number | 8 |

DOIs | |

State | Published - Feb 28 2017 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Electric-dipole-coupled H _{2}O@C_{60} dimer : Translation-rotation eigenstates from twelve-dimensional quantum calculations.** / Felker, Peter M.; Bacic, Zlatko.

Research output: Contribution to journal › Article

_{2}O@C

_{60}dimer: Translation-rotation eigenstates from twelve-dimensional quantum calculations',

*Journal of Chemical Physics*, vol. 146, no. 8, 084303. https://doi.org/10.1063/1.4976526

}

TY - JOUR

T1 - Electric-dipole-coupled H2O@C60 dimer

T2 - Translation-rotation eigenstates from twelve-dimensional quantum calculations

AU - Felker, Peter M.

AU - Bacic, Zlatko

PY - 2017/2/28

Y1 - 2017/2/28

N2 - We report on variational solutions to the twelve-dimensional (12D) Schrödinger equation appertaining to the translation-rotation (TR) eigenstates of H2O@C60 dimer, associated with the quantized "rattling" motions of the two encapsulated H2O molecules. Both H2O and C60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR eigenstates of H2O@C60 monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR eigenstates reported by us recently [P. M. Felker and Z. Bačić, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H2O@C60 dimer for two values of the water dipole moment and for various dimer geometries. 12D TR eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of eigenstates, distinguished by the leading order (first or second) at which dipole-dipole coupling contributes to them. The two types of eigenstates differ in the general magnitude of their dipole-induced energy shifts and in the dependence of those shifts on the value of the water dipole moment and on the distance between the H2O@C60 monomers. The dimer results are also found to be markedly insensitive to any change in the orientations of the C60 cages. Finally, the results lend some support for the interpretation that electric dipole-dipole coupling is at least partially responsible for the apparent reduced-symmetry environment experienced by H2O in the powder samples of H2O@C60 [K. S. K. Goh et al., Phys. Chem. Chem. Phys. 16, 21330 (2014)], but only if the water dipole is taken to have a magnitude close to that of free water. The methodology developed in the paper is transferable directly to the calculation of TR eigenstates of larger H2O@C60 assemblies, that will be required for more extensive modeling of crystalline H2O@C60.

AB - We report on variational solutions to the twelve-dimensional (12D) Schrödinger equation appertaining to the translation-rotation (TR) eigenstates of H2O@C60 dimer, associated with the quantized "rattling" motions of the two encapsulated H2O molecules. Both H2O and C60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR eigenstates of H2O@C60 monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR eigenstates reported by us recently [P. M. Felker and Z. Bačić, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H2O@C60 dimer for two values of the water dipole moment and for various dimer geometries. 12D TR eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of eigenstates, distinguished by the leading order (first or second) at which dipole-dipole coupling contributes to them. The two types of eigenstates differ in the general magnitude of their dipole-induced energy shifts and in the dependence of those shifts on the value of the water dipole moment and on the distance between the H2O@C60 monomers. The dimer results are also found to be markedly insensitive to any change in the orientations of the C60 cages. Finally, the results lend some support for the interpretation that electric dipole-dipole coupling is at least partially responsible for the apparent reduced-symmetry environment experienced by H2O in the powder samples of H2O@C60 [K. S. K. Goh et al., Phys. Chem. Chem. Phys. 16, 21330 (2014)], but only if the water dipole is taken to have a magnitude close to that of free water. The methodology developed in the paper is transferable directly to the calculation of TR eigenstates of larger H2O@C60 assemblies, that will be required for more extensive modeling of crystalline H2O@C60.

UR - http://www.scopus.com/inward/record.url?scp=85014032296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014032296&partnerID=8YFLogxK

U2 - 10.1063/1.4976526

DO - 10.1063/1.4976526

M3 - Article

AN - SCOPUS:85014032296

VL - 146

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084303

ER -