Quantum Chemical Calculation of the Ground State Geometry and Vibrational Frequencies for the C60+ Ion (original) (raw)
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Internet Electronic Journal of …, 2003
Theoretical calculations for the fullerene cation are important for several aspects. Jahn-Teller vibronic interactions are symmetry-allowed in this ion and the expectation is that such interactions lead to static geometrical effects. In addition it is interesting to study the change of the vibrational spectrum of C 60 upon ionization. We have used semi-empirical AM1/UHF and PM3/UHF and density functional theoretical methods (B3LYP and LDA) to calculate the electronic ground state equilibrium geometry and vibrational frequencies for C 60 +. A small but significant reduction from icosahedral symmetry to D 5d obtained from DFT calculations without symmetry constraints supports the presence of static Jahn-Teller distortions. Structure optimizations constrained to D 5d and D 3d symmetry have also been carried out. The JT stabilization energy in the D 5d and D 3d structures is estimated according to two different methods. Vibrational frequencies calculated at B3LYP/6-31G level for the fullerene cation of D 5d geometry are reported and compared to literature values of neutral C 60 .
Theoretical calculations for the fullerene cation are important for several aspects. Jahn-Teller vibronic interactions are symmetry-allowed in this ion and the expectation is that such interactions lead to static geometrical effects. In addition it is interesting to study the change of the vibrational spectrum of C 60 upon ionization. We have used semi-empirical AM1/UHF and PM3/UHF and density functional theoretical methods (B3LYP and LDA) to calculate the electronic ground state equilibrium geometry and vibrational frequencies for C 60 + . A small but significant reduction from icosahedral symmetry to D 5d obtained from DFT calculations without symmetry constraints supports the presence of static Jahn-Teller distortions. Structure optimizations constrained to D 5d and D 3d symmetry have also been carried out. The JT stabilization energy in the D 5d and D 3d structures is estimated according to two different methods. Vibrational frequencies calculated at B3LYP/6-31G level for the fullerene cation of D 5d geometry are reported and compared to literature values of neutral C 60 .
The Journal of Physical Chemistry A, 2000
Traditional vibrational assignment in terms of bond stretching, angle bending, and torsion is not possible in fullerenes due to the very large number of coupled internal coordinates. Large scale density functional calculations of the vibrational properties of C 60 and C 60 6have been carried out with Becke3LYP and BeckeLYP exchange-correlation functionals in the pursuit of obtaining a reliable set of 174 normal modes (46 fundamental frequencies) and understanding the effect of charge transfer (doping) on the vibrational modes. The calculations involve scaling of the force field in redundant internal coordinates as proposed by Pulay et al. The scaled quantum mechanical (SQM) calculations yield excellent agreement with experiment for the 14 allowed frequencies. This provides the basis for an accurate assignment of all nonallowed fundamentals and the reassignment of the observed overtone and combination bands of the high-resolution Raman and IR (Martin et al. 1994) spectra. The calculated intensity ratios for the four IR active bands agree with experiment. The large IR intensity enhancements observed for C 60 6relative to C 60 are explained by the enhancement of certain components of the atomic polar tensor that is partially due to bond equalization in the charged fullerene. This enhancement appears to be largely a molecular rather then a solid state effect.
2003
Theoretical calculations for the fullerene cation are important for several aspects. Jahn-Teller vibronic interactions are symmetry-allowed in this ion and the expectation is that such interactions lead to static geometrical effects. In addition it is interesting to study the change of the vibrational spectrum of C 60 upon ionization. We have used semi-empirical AM1/UHF and PM3/UHF and density functional theoretical methods (B3LYP and LDA) to calculate the electronic ground state equilibrium geometry and vibrational frequencies for C 60 +. A small but significant reduction from icosahedral symmetry to D 5d obtained from DFT calculations without symmetry constraints supports the presence of static Jahn-Teller distortions. Structure optimizations constrained to D 5d and D 3d symmetry have also been carried out. The JT stabilization energy in the D 5d and D 3d structures is estimated according to two different methods. Vibrational frequencies calculated at B3LYP/6-31G level for the ful...
On the vibrational assignment of fullerene C60
The Journal of Chemical Physics, 1994
A recent density functional perturbation theory calculation of the vibrational frequencies of Cc0 is compared with the infrared spectrum of the crystal. The vibrational assignment of C,, is completed with the help of the calculation plus the available infrared, Raman, and inelastic neutron scattering spectra.
Totally symmetric vibrational modes of fullerene C60
Journal of Experimental and Theoretical Physics Letters, 2000
Because of high symmetry, the C 60 molecule is subject to various instabilities associated with both interaction between electronic and nuclear degrees of freedom (Jahn-Teller effect ) and interaction of various vibrational modes with one another (Fermi resonance ). These instabilities determine the properties of fullerene-based materials, in particular, the superconducting transition temperature of fullerites M 3 C 60 , where M stands for an alkali-metal atom .
Electronic excitations in fullerenes: Jahn-Teller distorted structures of C60
Journal of Molecular Structure, 1994
The ground state wavefunction of the neutral icosahedral C 60 molecule belongs to the total symmetric one-dimensional A g representation. However, the degeneracy of the HOMO is five-fold while the LUMO is triply degenerate. This means that the lowest excited and ionized many-electron states will also be degenerate, and thus they are subjected to Jahn-Teller distortions. In this work we used a simple model Hamiltonian to study the extent and energy of the distortions arising due to excitations. For the -r-electrons we used a Pariser-Parr-Pople type wavefunction augmented by an empirical potential to describe the (J cores. The zr-electron part of the Hamiltonian depends on the bond lengths which can be optimized by means of simple gradient techniques. The excited states are described by the Tamm -Dancoff approximation (all single CI). In order to locate the distorted states on the energy hypersurface, the degenerate excited states were reduced according to those subgroups of the I h group that contain one-dimensional (that is, Jahn--Teller inactive) irreducible representations in an excitation subspace. Distorted structures of D 2h , D 3d , D Sd and T h symmetries were determined. The extent of the distortions is small, the largest change in bond lengths being 0.02 A. The Jahn Teller distortion energies were found to be typically I~3 kcal mol": Singlet and triplet excited state spectra were computed using the CNDO/S-CI method. Comparison of the calculated spectra with experimental results shows evidence of JahnT eller distortions.
Journal of Molecular Structure: THEOCHEM, 1998
Ionization energies (PES), excitation energies (UV) and electron affinities (EA) of fullerene Cbo have been calculated with the semiempirical HAM/3 method. The first few ionization energies calculated with HAM/3 show errors as great as 1.4 eV. The HAM/3-CI method has reproduced the observed UV spectrum fairly well. The HAM/~-AC method has given fairly good energies for the forbidden lowest singlet and triplet transitions but rather poor results for the allowed transitions. The correlation between calculated PES, UV and EA values is discussed. A method to ectimate accurate electron affinity is proposed. The CNDO/S method, on the other hand, has given good values for some of the ionization energies and electron affinities. 0 1998 Elsevier Science B.V.
The Vibrational Spectrum of Fullerene C 60
The Journal of Physical Chemistry A, 2001
Using an improved DFT calculation of the vibrational frequencies based on the B3-LYP functional and the 6-31G* basis set, the infrared, Raman, neutron inelastic and luminescence spectra of C 60 are rediscussed, and a revised assignment of all the silent modes is obtained and compared with the most recent assignments.
Electron-vibration coupling constants in positively charged fullerene
Philosophical Magazine Part B, 2001
Recent experiments have shown that C 60 can be positively field-doped. In that state, fullerene exhibits a higher resistivity and a higher superconducting temperature than the corresponding negatively doped state. A strong intramolecular hole-phonon coupling, connected with the Jahn-Teller effect of the isolated positive ion, is expected to be important for both properties, but the actual coupling strengths are so far unknown. Based on density functional calculations, we determine the linear couplings of the two a g , six g g , and eight h g vibrational modes to the H u HOMO level of the C 60 molecule. The couplings predict a D 5 distortion, and an H u vibronic ground state for C + 60 . They are also used to generate the dimensionless coupling constant λ which controls the superconductivity and the phonon contribution to the electrical resistivity in the crystalline phase. We find that λ is 1.4 times larger in positively-charged C 60 than in the negatively-doped case. These results are discussed in the context of the available transport data and superconducting temperatures. The role of higher orbital degeneracy in superconductivity is also addressed. *