On the electronic structure of small cyclic carbon clusters

Yousaf, Kazim E.; Taylor, Peter R.

doi:10.1016/j.chemphys.2008.02.059

Cited by 13 publications

(19 citation statements)

References 19 publications

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“…Typically, for such systems, cumulenic structures (C=C−C=C) are lower in energy than acetylenic (C ≡ C−C • • • C−C) bonding configurations [1,2,40,41]. More recently, supported by ab initio calculations, low-lying monocyclic isomers have also been conjectured as being isoenergetic or even more stable than linear arrangements [25][26][27][28][29]39]. In this work, we survey the current status on the smallest clusters (C 2 , C 3 and C 4 ) but keep the focal point on the trimer and tetramer.…”

Section: Introduction and Historical Remarksmentioning

confidence: 99%

C _n ( n =2−4): current status

Varandas¹,

Rocha²

2018

Phil. Trans. R. Soc. A.

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The major aspects of the C, C and C elemental carbon clusters are surveyed. For C, a brief analysis of its current status is presented. Regarding C, the most recent results obtained in our group are reviewed with emphasis on modelling its potential energy surface which is particularly complicated due to the presence of multiple conical intersections. As for C, the most stable isomeric forms of both triplet and singlet spin states and their possible interconversion pathways are examined afresh by means of accurate calculations. The main strategies for modelling the ground triplet C potential are also discussed. Starting from a truncated cluster expansion and a previously reported DMBE form for C, an approximate four-body term is calibrated from the energies. The final six-dimensional global DMBE form so obtained reproduces all known topographical aspects while providing an accurate description of the C linear-rhombic isomerization pathway. It is therefore commended for both spectroscopic and reaction dynamics studies.This article is part of the theme issue 'Modern theoretical chemistry'.

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Section: Introduction and Historical Remarksmentioning

confidence: 99%

C _n ( n =2−4): current status

Varandas¹,

Rocha²

2018

Phil. Trans. R. Soc. A.

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“…Small carbon clusters of this size are accessible to direct calculation of the harmonic frequencies with quantum chemical methods, including DFT, 25 coupled cluster theory 23 and multi reference based approaches. 26 These studies have shown that overall results from DFT are reasonably accurate compared to those from coupled cluster theory, 25,26 although some discrepancies have been identified where the minimum energy coupled cluster theory structure is a saddle point according to DFT. 26 Furthermore, it is probably necessary to account for both dynamical and non-dynamical correlation to accurately treat these systems.…”

Section: Introductionmentioning

confidence: 99%

“…26 These studies have shown that overall results from DFT are reasonably accurate compared to those from coupled cluster theory, 25,26 although some discrepancies have been identified where the minimum energy coupled cluster theory structure is a saddle point according to DFT. 26 Furthermore, it is probably necessary to account for both dynamical and non-dynamical correlation to accurately treat these systems. 26 The IR and Raman spectra for some fullerenes have been reported.…”

Section: Introductionmentioning

confidence: 99%

“…26 Furthermore, it is probably necessary to account for both dynamical and non-dynamical correlation to accurately treat these systems. 26 The IR and Raman spectra for some fullerenes have been reported. [27][28][29][30] The most studied fullerene is C 60 , and the IR spectrum of C 60 has four infrared active modes (T 1u ) and ten Raman active modes (two A g and eight H g ).…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials

Besley

2015

Phys. Chem. Chem. Phys.

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Vibrational frequencies for carbon clusters, fullerenes and nanotubes evaluated using empirical carbon-carbon potentials are presented. For linear and cyclic clusters, frequencies evaluated with the reactive empirical bond order (REBO) potential provide the closest agreement with experiment. The mean absolute deviation (MAD) between experiment and the calculated harmonic frequencies is 79 cm 1 for the bending modes and 76 cm 1 for the stretching modes. The effects of anharmonicity are included via second order vibrational perturbation theory and tend to increase the frequency of the bending modes while the stretching modes have negative shifts in the region of 20 -60 cm 1 , with larger shifts for the higher frequency modes. This results in MADs for the bending and stretching modes of 84 cm 1 and 58 cm 1 , respectively. For the fullerene molecule C 60 , the high frequency modes are predicted to have harmonic frequencies that are significantly higher than experiment, and this is not corrected by accounting for anharmonicity. This overestimation of experimental observed frequencies is also evident in the calculated frequencies of the G band in nanotubes. This suggests that the REBO potential is not optimal for these larger systems and it is shown that adjustment of the parameters within the potential leads to closer agreement with experiment, particularly if higher and lower frequency modes are considered separately.

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“…A recent CCSD study by Arulmozhiraja and Ohno 15 predicted a structure with both bond and angle alternation to be the most stable form for C 14 , C 18 , and C 22 , and the bondalternating structure to be more stable than the anglealternating cumulene. Yousaf and Taylor 24 have studies of some small C 4N and C 4N+2 clusters, demonstrating that single reference coupled cluster and multireference SCF struggle to describe the ground state structures, and that B3LP performs somewhat similarly to single reference coupled cluster. Watts and Bartlett 25 similarly considered detailed coupled cluster and many-body perturbation theory on the C 10 ring, suggesting the angle-alternating structure to be the most stable.…”

Section: Introductionmentioning

confidence: 99%

Structural manifestation of the delocalization error of density functional approximations: C4N+2 rings and C20 bowl, cage, and ring isomers

Heaton-Burgess

Yang

2010

The Journal of Chemical Physics

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The ground state structure of C 4N+2 rings is believed to exhibit a geometric transition from angle alternation ͑N Յ 2͒ to bond alternation ͑N Ͼ 2͒. All previous density functional theory ͑DFT͒ studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations ͑DFAs͒ and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C 10 and C 14 . The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Hückel aromaticity, of which the C 4N+2 rings provide a quintessential example. Additional examples are the relative energies of the C 20 bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD͑T͒ results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mecahnisms exist.

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On the electronic structure of small cyclic carbon clusters

Cited by 13 publications

References 19 publications

C _n ( n =2−4): current status

C _n ( n =2−4): current status

Calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials

Structural manifestation of the delocalization error of density functional approximations: C4N+2 rings and C20 bowl, cage, and ring isomers

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On the electronic structure of small cyclic carbon clusters

Cited by 13 publications

References 19 publications

C n ( n =2−4): current status

C n ( n =2−4): current status

Calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials

Structural manifestation of the delocalization error of density functional approximations: C4N+2 rings and C20 bowl, cage, and ring isomers

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Product

Resources

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C _n ( n =2−4): current status

C _n ( n =2−4): current status