^{1}, A. W. Castleman Jr.

^{2}and J. O. Sofo

^{3,a)}

### Abstract

Calculations are presented for the structural, electronic, and vibrational properties of the different metallocarbohedrynes. (Please note that we adopt the name “metallocarbohedrynes” instead of “metallocarbohedrenes” to denote the acetylenic nature of units in this class of clusters demonstrated by several contributions in literature.) The density-functional theory(DFT) calculations are performed with the all-electron projector augmented-wave method and generalized gradient approximation for the exchange-correlation functional. We study the seven low-energy isomers of the metallocarbohedrynes using spin-polarized DFT, where we find a correlation between the number of rotated carbon dimers and the cohesive energy of the structure. The electronic density of states (eDOS) show that , , and isomers are spin polarized. The partial eDOS shows that, depending on the dimer orientation, carbon atoms and a subgroup of the metal atoms form a covalent framework while other metal atoms are bonded to this framework more ionically. This picture is further supported by the charge density of the different structures, where we see that the Ti atoms with higher charge density show less contribution to the covalent bonding of the Ti–C framework. The vibrational spectra of the different structures are calculated using the frozen-vibration method. Also, we calculate the vibrational spectra of the and structures using molecular-dynamics simulations at two different temperatures. The results of the simulations demonstrate the local stability of the structures beyond the harmonic limit explored by the frozen-vibration method.

The authors are grateful to Dr. M. R. Pederson, Dr. T. Baurah, and Dr. J. T. Muckerman for supplying them with the coordinate files of their published structures. Financial support from the Air Force Office of Scientific Research, Grant No. FA 9550-04-1-0066 is gratefully acknowledged. One of the authors (M.S.) would also like to thank K. M. Davis and K. L. Knappenberger, Jr. for their helpful suggestions.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSION

A. Atomic structure

B. Electronic and magnetic properties

1. Electronic properties

2. Magnetic properties

C. Vibrational frequencies

D. Molecular dynamics

IV. CONCLUSION

### Key Topics

- Carrier density
- 26.0
- Carbon
- 15.0
- Density functional theory
- 15.0
- Jahn Teller effect
- 12.0
- Magnetic moments
- 9.0

## Figures

The figure shows the different metallocarbohedryne structures [Ref. 17(a)]. For demonstration, we specify the unit rotated in the figure to obtain one isomer from the other. The energy differences between the different structures are given in the text. The number at each vertex of the cube is the coordination number of the Ti atom and represents the sum of the carbons facing the Ti atom located at each vertex. If the unit is diagonally facing the Ti atom at the vertex, then it is counted as two. If one carbon from the unit is bonded to the Ti at the vertex, then it is counted as one.

The figure shows the different metallocarbohedryne structures [Ref. 17(a)]. For demonstration, we specify the unit rotated in the figure to obtain one isomer from the other. The energy differences between the different structures are given in the text. The number at each vertex of the cube is the coordination number of the Ti atom and represents the sum of the carbons facing the Ti atom located at each vertex. If the unit is diagonally facing the Ti atom at the vertex, then it is counted as two. If one carbon from the unit is bonded to the Ti at the vertex, then it is counted as one.

The plot shows the total electronic density of states of the metallocarbohedryne structures. The vertical dotted line denotes the Fermi level for the different structures. The respective HOMO-LUMO gap in eV is shown on the right side of the eDOS plot of each structure.

The plot shows the total electronic density of states of the metallocarbohedryne structures. The vertical dotted line denotes the Fermi level for the different structures. The respective HOMO-LUMO gap in eV is shown on the right side of the eDOS plot of each structure.

The plot shows the partial density of states of the Ti and C atoms in the structure. The Fermi level is denoted by the vertical dotted line at 0 eV.

The plot shows the partial density of states of the Ti and C atoms in the structure. The Fermi level is denoted by the vertical dotted line at 0 eV.

The plot shows the partial density of states of the Ti and C atoms in the structure. The Fermi level is denoted by the vertical dotted line at 0 eV.

The plot is an expansion of the total electronic density of states of the and structures close to the Fermi level. The dashed lines mark the Fermi level for both structures.

The plot is an expansion of the total electronic density of states of the and structures close to the Fermi level. The dashed lines mark the Fermi level for both structures.

The plot is a depiction of the charge-density isosurfaces of the different metallocarbohedryne structures in two different perspectives.

The plot is a depiction of the charge-density isosurfaces of the different metallocarbohedryne structures in two different perspectives.

The plot is a depiction of the spin-polarization isosurfaces of the , , and structures in two different perspectives.

The plot is a depiction of the spin-polarization isosurfaces of the , , and structures in two different perspectives.

The plot shows the vibrational spectra of the different metallocarbohedrynes arranged in ascending order of their cohesive energies.

The plot shows the vibrational spectra of the different metallocarbohedrynes arranged in ascending order of their cohesive energies.

The plot shows the vibrational spectra of the structure calculated from the MD simulations at 300 and 100 K.

The plot shows the vibrational spectra of the structure calculated from the MD simulations at 300 and 100 K.

The plot shows the vibrational spectra of the structure calculated from the MD simulations at 300 and 100 K.

## Tables

The cohesive and relative energies of the different metallocarbohedryne structures are shown, with the structures arranged in ascending order by their respective energies. The table shows the symmetry group recognized by VASP, magnetic moment, Fermi energy, and the HOMO-LUMO gap for the different metallocarbohedryne structures.

The cohesive and relative energies of the different metallocarbohedryne structures are shown, with the structures arranged in ascending order by their respective energies. The table shows the symmetry group recognized by VASP, magnetic moment, Fermi energy, and the HOMO-LUMO gap for the different metallocarbohedryne structures.

Interatomic distances (Å) approximated to the third decimal place, for the different metallocarbohedryne structures are given in the table. C–C denotes the distance between the two carbon atoms in the unit. denotes the distance between two Ti atoms, one with coordination number and the other with coordination number (where and are integers from 3 to 6, can be equal or different from ). denotes the bond length between a carbon atom and Ti atom of coordination number .

Interatomic distances (Å) approximated to the third decimal place, for the different metallocarbohedryne structures are given in the table. C–C denotes the distance between the two carbon atoms in the unit. denotes the distance between two Ti atoms, one with coordination number and the other with coordination number (where and are integers from 3 to 6, can be equal or different from ). denotes the bond length between a carbon atom and Ti atom of coordination number .

The harmonic-vibrational frequencies in of the carbon dimers and the Ti–C bonds are shown in the table. The frequencies are calculated using the frozen-vibration method.

The harmonic-vibrational frequencies in of the carbon dimers and the Ti–C bonds are shown in the table. The frequencies are calculated using the frozen-vibration method.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content