Cumulenic Chains Research Articles

Comparative analysis of absorption resonances between carbynes and cyclo [n] carbons

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo [n] carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and the ab initio time-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following the Nring=2Nchain+2 rule, which states that the number of atoms in an atomic ring Nring is twice the number of atoms on a finite chain Nchain with two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes with N=7and8 carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynes N = 7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo [n] carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

One-dimensional carbon chains encapsulated in hollandite

One-dimensional carbon chains are highly reactive allotropes that are stabilized inside the protective environment of carbon nanotubes. Here we show that carbon chains can be encapsulated in metal oxides containing open structural channels, exemplified by hollandite α-MnO2. The α-MnO2 channels stabilize cumulene chains due to their structural commensurability, whereas the triple bonds in polyyne chains exhibit excessive steric repulsion to the oxide ions bordering the channel. Cumulene exhibits an interaction energy of only 0.065 eV per carbon atom, obtained by first-principles calculations, which is significantly more favorable than for encapsulation in a similarly sized carbon nanotube. Encapsulation of carbon chains is associated with lateral expansion of the α-MnO2 channel and polarization of the manganese and oxygen charge densities adjacent to the chains. Accordingly, the interaction energy is governed by a balance between van der Waals attraction and steric repulsion between the materials.

Low Energy Isomers and Infrared Spectra Simulations of C4H3N, C4H4N, and C4H5N and Related Ions

The relative stability of pyrrole derivatives were investigated by applying a global minimum (GM) search for the low-lying energy structures of C4HnN (n = 3-5) clusters at neutral, anionic, and cationic states. Several low-energy structures, previously not reported, were identified. The present results reveal a preference for cyclic and conjugated systems for the C4H5N and C4H4N compounds. In particular, the structures of the cationic and neutral C4H3N species are different from the anionic ones. For the neutrals and cations, cumulenic carbon chains were found, while for the anions, conjugated open chains were obtained. Of particular relevance, the GM candidates C4H4N+ and C4H4N are different from those reported previously. For the most stable structures, infrared spectra were simulated and the main vibrational bands were assigned. Also, a comparison with available laboratory data was done aiming to corroborate with experimental detection.

Structural and electronic properties of polyyne and cumulene chains with phenylene as central aromatic group: a density functional theory study

Structural and electronic properties of polyyne and cumulene chains with phenylene as central aromatic group: a density functional theory study

Highly delocalised molecular orbitals in boron-, carbon- and nitrogen-based linear chains: a DFT study

In the present work a comparison of the electronic structures of the Linear carbon chains (LCC) with Boron linear chains (BnH2 and BnH4) and boron–nitrogen linear chains (Bn/2Nn/2H2 and Bn/2Nn/2H4) is made using B97X-D/6-311++G** level of theory. BnH2 and BnH4 show comparatively more delocalised molecular orbitals and lower electron densities than CnH2 and CnH4. CnH2 and CnH4 show much more efficient charge delocalisation than the other chains. For the first time it is reported that BnH4 chains also show helical molecular orbitals for n = 2,6,10. Modification of the helical orbitals of the cumulene chains was observed upon the introduction of boron atoms.

Geometrical, electrical, and energetic parameters of hetero-disubstituted cumulenes and polyynes in the presence and absence of the external electric field

Cumulenes and polyynes have the potential to be applied as linear, sp-hybridized, one-dimensional all-carbon nanowires in molecular electronics and optoelectronics. The delocalization and conductivity descriptors of the two π-conjugated systems, heterodisubstituted with the NO2, CN, NH2, and OH groups, were studied using the B3LYP, B3LYP/D3, CAM-B3LYP, and ωB97XD DFT functionals, combined with the aug-cc-pVTZ basis set. Three independent types of molecular descriptors, based on geometry (the HOMA index), electrical properties (trace of the polarizability tensor), and energetic (the HOMO-LUMO energy gap) were shown to be mutually correlated and provided concordant indication that communication through the cumulene chain was considerably better than through the polyyne one. The communication can be tuned by using substituents of significantly different π-electron donor-acceptor properties as well as by the external electric field directed along the carbon chain.

Watching soot inception via online Raman spectroscopy

In this work, online spontaneous Raman spectroscopy was applied to study the soot inception and growth zones of a low pressure premixed ethylene/oxygen flame. Firstly, we measured online Raman spectrum of aerosol soot extracted from the flame. The spectrum was compared to ex situ Raman measurements of the same soot after being deposited on a window. In the aerosol soot particles, the presence of an abundant sp hybridized carbon chain component is inferred accompanying a polycyclic aromatic component. Both cumulenic and polyynic chains are affected by the deposition under vacuum and by the pressure as it is raised to atmospheric, revealing that the sp phase is no longer visible in the ex situ characterization of the sampled soot. Secondly, we monitored the Raman spectra of aerosol soot as a function of the height above the burner. Comparing spectral differences of by-products along the blue to orange zone of the flame permitted the soot formation and evolution to be probed. The online spectra, by avoiding structural modifications of the real soot structures by deposition, highlight the role of unsaturated carbon chains in the chemical condensation scenario.

ANISOTROPY OF THE SURFACE OF CARBON MATERIALS

In this work, a model of the surface layer of perfect single crystals is used and the role of surface energy in physical processes occurring in the region of nanosized carbon materials is clarified. Of these, diamond, graphite, carbyne and fullerenes have been investigated. The thickness of the surface layer of diamond with cubic symmetry is 8.2 nm and is a nanostructure. The average size of the synthesized nanodiamond is of the order of ~ 8 nm. The value of the surface energy σhkl calculated by us along the diamond planes (100), (110), and (111) is in good agreement with experiment and other calculations. The thickness of the surface layer of graphite along the a axis is equal to R(I)a = 8.0 nm and also represents a nanostructure. But along the c axis we have a layer thickness of about 1.5 nm and the number of monolayers is only 2. On this c axis, graphite can be created a monolayer by turning it into graphene. The σhkl value calculated by us along the a and c planes of graphite is 25957 and 5515 mJ/m2 , respectively. Carbines represent a polymeric polyyne or cumulene chain composed of sp-hybridized carbon atoms. If we imagine that the thickness of the surface layer of carbyne is stretched into a one-dimensional chain along the c axis, then the length of this chain is up to 200 nm for α-carbyne. The thickness of the surface layer of fullerenes significantly exceeds the thickness of the surface layer of pure metals. The surface energy of fullerenes σhkl increases with an increase in the number of carbon atoms С36 → С96. It also changes in the series (111) → (100) → (110).

Spin-Spin Interactions in One-Dimensional Assemblies of a Cumulene-Based Singlet Biradical.

The synthesis of phenalenyl-endcapped [5]cumulene as a cumulene-based singlet biradical and the spin correlation changes of one-dimensional aggregates are described. The high propensity for self-aggregation of phenalenyl rings and the introduction of bulky substituents into the appropriate positions led to the formation of a one-dimensional chain assembly. Single-crystal X-ray structural analysis indicated that the bond length alternation of the cumulene chain increased with decreasing temperature, along with improved overlapping of the phenalenyl rings. Variable-temperature Raman spectroscopy and magnetic susceptibility measurements revealed that a localized spin pair within the molecule decouples at low temperatures, and a continuum spin system involving intra- and intermolecular spin-spin interactions emerges in the one-dimensional chain.

Spin–Spin Interactions in One‐Dimensional Assemblies of a Cumulene‐Based Singlet Biradical

AbstractThe synthesis of phenalenyl‐endcapped [5]cumulene as a cumulene‐based singlet biradical and the spin correlation changes of one‐dimensional aggregates are described. The high propensity for self‐aggregation of phenalenyl rings and the introduction of bulky substituents into the appropriate positions led to the formation of a one‐dimensional chain assembly. Single‐crystal X‐ray structural analysis indicated that the bond length alternation of the cumulene chain increased with decreasing temperature, along with improved overlapping of the phenalenyl rings. Variable‐temperature Raman spectroscopy and magnetic susceptibility measurements revealed that a localized spin pair within the molecule decouples at low temperatures, and a continuum spin system involving intra‐ and intermolecular spin–spin interactions emerges in the one‐dimensional chain.

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Carbon–sulfur chains: A high‐resolution infrared and quantum‐chemical study of C3S and SC7S

AbstractIn the course of a 5 μm high‐resolution infrared study of laser ablation products from carbon–sulfur targets, the ν1 vibrational mode region of linear C3S has been studied continuously from 2046 to 2065 cm−1. Besides the prominent vibrational fundamental, the region was found to feature the , and even hot bands, the latter two of which were observed for the first time. Owing to the high signal‐to‐noise ratio obtained, the ν1 mode of S could also be observed in natural abundance for the first time at high spectral resolution in the infrared. At 2061 cm−1, hidden inside the branch of the C3S ν1 fundamental mode, a weak new band is observed which exhibits very tight line spacing and stems from a heavy both carbon and sulfur containing carrier. On the basis of high‐level quantum‐chemical calculations of selected carbon–sulfur chains and other carbon‐rich cumulenes, this feature is attributed to the ν5 vibrational fundamental of linear SC7S, which stands for the first gas‐phase spectroscopic detection of this long cumulenic chain.

Electronic torsional sound in linear atomic chains: Chemical energy transport at 1000 km/s.

We investigate entirely electronic torsional vibrational modes in linear cumulene chains. The carbon nuclei of a cumulene are positioned along the primary axis so that they can participate only in the transverse and longitudinal motions. However, the interatomic electronic clouds behave as a torsion spring with remarkable torsional stiffness. The collective dynamics of these clouds can be described in terms of electronic vibrational quanta, which we name torsitons. It is shown that the group velocity of the wavepacket of torsitons is much higher than the typical speed of sound, because of the small mass of participating electrons compared to the atomic mass. For the same reason, the maximum energy of the torsitons in cumulenes is as high as a few electronvolts, while the minimum possible energy is evaluated as a few hundred wavenumbers and this minimum is associated with asymmetry of zero point atomic vibrations. Theory predictions are consistent with the time-dependent density functional theory calculations. Molecular systems for experimental evaluation of the predictions are proposed.

Properties of π-mode vibrations in strained carbon chains

Nonlinear vibrations in strained monoatomic carbon chains are studied with the aid of ab initio methods based on the density functional theory. An unexpected phenomenon of structural transformation at the atomic level above a certain value of the strain was revealed in cumulene chain (carbyne-β). This phenomenon is a consequence of stability loss of the old equilibrium atomic positions that occur at small strain, and appearance of two new stable equilibrium positions near each of them. The aforementioned restructuring gives rise to a softening of π-mode whose frequency tends to zero in a certain region of amplitudes when carbon atoms begin to vibrate near new equilibrium positions. This resembles the concept of soft mode whose “freezing” is postulated in the theory of phase transitions in crystals to explain the transitions of displacement type. The dynamical modeling of mass point chains whose particles interact via Lennard-Jones potential can approximate our ab initio results well enough. In particular, this study demonstrates an essential role of dipole-dipole interactions between carbon atoms in formation of their new equilibrium positions in the cumulene chain. We believe that computer studying of Lennard-Jones chains enables to predict properties of various dynamical objects in carbon chains (different nonlinear normal modes and their bushes, discrete breathers etc.) which then can be verified by ab initio methods.

On stability of nonlinear atomic vibrations in strained carbon chains

Monoatomic carbon chain (carbyne) can exist in two different modifications: cumulene with double chemical bonds between its atoms, and polyyne with alternation of single and triple bonds. In our previous paper [Letters on materials 6 (2), 146-151 (2016)], we have discussed new physical phenomenon which was revealed in cumulene chains under uniform strain. It was found that above 11.2% strain softening of π-mode atomic vibrations takes place in some range of its amplitude. Condensation ("freezing") of this soft mode leads to structural phase transition of displacement type. It is the Peierls phase transition which was found earlier in [Nano Lett. 14, 4224-4229 (2014)] with the aid of a different approach. The above phenomenon occurs due to the fact that old atomic equilibrium positions (EQPs), near which atoms vibrate in the case of small strain, lose their stability and two new EQPs appear near each of them. The π-mode softening corresponds to vibrations in the vicinity of these new EQPs. In the present paper we discuss the problem of stability of the new EQPs, as well as a possibility of condensation in cumulene of two other symmetry-determined nonlinear normal modes, different from π-mode. Inferences of this paper may be useful for comparison of the results, obtained by methods of molecular dynamics, with those obtained with the aid of ab initio simulations based on the density functional theory in studying different physical phenomena.

Ballistic Thermal Transport in Carbyne and Cumulene with Micron-Scale Spectral Acoustic Phonon Mean Free Path.

The elastic modulus of carbyne, a one-dimensional carbon chain, was recently predicted to be much higher than graphene. Inspired by this discovery and the fundamental correlation between elastic modulus and thermal conductivity, we investigate the intrinsic thermal transport in two carbon allotropes: carbyne and cumulene. Using molecular dynamics simulations, we discover that thermal conductivities of carbyne and cumulene at the quantum-corrected room temperature can exceed 54 and 148 kW/m/K, respectively, much higher than that for graphene. Such conductivity is attributed to high phonon energies and group velocities, as well as reduced scattering from non-overlapped acoustic and optical phonon modes. The prolonged spectral acoustic phonon lifetime of 30–110 ps and mean free path of 0.5–2.5 μm exceed those for graphene, and allow ballistic phonon transport along micron-length carbon chains. Tensile extensions can enhance the thermal conductivity of carbyne due to the increased phonon density of states in the acoustic modes and the increased phonon lifetime from phonon bandgap opening. These findings provide fundamental insights into phonon transport and band structure engineering through tensile deformation in low-dimensional materials, and will inspire studies on carbyne, cumulene, and boron nitride chains for their practical deployments in nano-devices.

π-Conjugation and End Group Effects in Long Cumulenes: Raman Spectroscopy and DFT Calculations

We have investigated the structure and spectroscopic properties of cumulenic carbon chains, focusing on the peculiar π-conjugation properties and end-group effects that influence their behavior. With support from Density Functional Theory (DFT) calculations, we have analyzed the IR and Raman spectra of cumulenes characterized by different end-capping groups and we have related them to the bond length alternation (BLA) pattern and local spectroscopic parameters associated with the CC bonds along the sp-carbon chain. For cumulenes we observe a breakdown of the correlation existing in polyynes among frequencies, Raman intensities of the R line (longitudinal CC stretching modes), and BLA. While the low R line frequency and equalized CC bonds would indicate the “metallic” character of cumulenic species, we obtain an unusually strong Raman intensity, which is typical of bond-alternated (semiconductive) structures. DFT calculations reveal that this is a consequence of π-electron conjugation, which markedly exten...

Tight Binding Model of Quantum Conductance of Cumulenic and Polyynic Carbynes

The linear carbon chains called the carbynes are possibly the most simple carbon molecular systems of interest as the potential materials for nanoelectronics. In a metallic cumulenic form of carbyne, the C atoms form the double bonds (...═C═C═...), but the single and triple bonds alternate in the semiconducting polyynic structure (...–C≡C–C≡C–...). In this work, the ballistic electrical conductance of cumulenic and polyynic carbon chains C40, C20, and C10 is calculated using the π-electron tight-binding methods. The transmission function and dependences of the current on the length of the carbon chain, the type of carbon bonds, material properties of the electrodes, bias voltage, and temperature are obtained. For the calculations of transmission function, we use the Schrödinger equation that meets the specified value of the energy E, the wave functions being the superposition of incident and reflected waves in the region of cathode, and describe the transmitted wave in the anode. For small bias voltages, the problem of calculating the transmission function in the cumulenic and polyynic chains is solved analytically by applying the difference schemes approach which permits us to pass from the tight-binding algebraic equations to the differential equations and to take advantage of their solutions. In the case of large voltages, we apply an iterative technique. The transmission functions τ(E,V) of the cumulenic and polyynic chains of similar composition differ dramatically. The energy regions of very high and low transparency of carbynes for electrons are obtained, and an oscillatory character of the energy dependence of transmission functions is pointed out. Each electronic level of the molecule corresponds to a peak in the energy dependence of transmission function with τ ≈ 1. The peaks are responsible for the resonant electron transfer between the electrodes. The voltage-dependent variations of the τ are initially quite weak, but at the higher voltages their effect is a drastic reduction of the carbyne transparency. One important feature of the current–voltage I–V characteristics is that the current initially increases with growth of the bias voltage, reaches a peak, and then drops to give rise to the negative conductance. On the typical I–V curves of the polyynic chains, there are both the peak and local minimum (valley) at higher voltages. Moreover, there are some oscillations of voltage dependences of conductance due to the discrete nature of the C chain electron energy levels. The π electron model results are compared with ab initio data on conductance of similar chains having only several C atoms. The presence of the negative resistance regions and valley in the curve I–V indicate the possibilities of design of the resonance tunneling devices based on the C chains.

Explicitly correlated benchmark calculations on C8H8 isomer energy separations: how accurate are DFT, double-hybrid, and composite ab initio procedures?

Accurate isomerization energies are obtained for a set of 45 C8H8 isomers by means of the high-level, ab initio W1-F12 thermochemical protocol. The 45 isomers involve a range of hydrocarbon functional groups, including (linear and cyclic) polyacetylene, polyyne, and cumulene moieties, as well as aromatic, anti-aromatic, and highly-strained rings. Performance of a variety of DFT functionals for the isomerization energies is evaluated. This proves to be a challenging test: only six of the 56 tested functionals attain root mean square deviations (RMSDs) below 3 kcal mol−1 (the performance of MP2), namely: 2.9 (B972-D), 2.8 (PW6B95), 2.7 (B3PW91-D), 2.2 (PWPB95-D3), 2.1 (ωB97X-D), and 1.2 (DSD-PBEP86) kcal mol−1. Isomers involving highly-strained fused rings or long cumulenic chains provide a ‘torture test’ for most functionals. Finally, we evaluate the performance of composite procedures (e.g. G4, G4(MP2), CBS-QB3, and CBS-APNO), as well as that of standard ab initio procedures (e.g. MP2, SCS-MP2, MP4, CCSD, and SCS-CCSD). Both connected triples and post-MP4 singles and doubles are important for accurate results. SCS-MP2 actually outperforms MP4(SDQ) for this problem, while SCS-MP3 yields similar performance as CCSD and slightly bests MP4. All the tested empirical composite procedures show excellent performance with RMSDs below 1 kcal mol−1.

Metal Complexes Containing Allenylidene and Higher Cumulenylidene Ligands: A Theoretical Perspective

Transition metal complexes containing unsaturated carbenes have enjoyed a recent surge in research interest. In addition to showing potential as molecular wires and as components of opto-electronic materials, they provide multifaceted reactive sites for organic synthesis. In this Account, we describe results of recent theoretical studies that delineate the main features of electronic structure and bonding in allenylidenes and higher cumulenylidene complexes, [L(m)M]═C(═C)(n)═CR(1)R(2) (where L represents the ligand, M the metal, and n ≥ 1). Although free cumulenylidene ligands, :C(═C)(n)═CR(1)R(2), are extremely unstable and reactive species, they can be stabilized by coordination to a transition metal. The σ-donation of the electron lone pair on the terminal carbon atom to an empty metal d-orbital, together with the simultaneous π back-donation from filled metal d(π)-orbitals to empty cumulene π* system orbitals, leads to the formation of a strong M═C bond with multiple character. Density functional theory studies on the model systems [(CO)(5)Cr(═C)(n)CH(2)] and [trans-Cl(PH(3))(4)Ru(═C)(n)CH(2)](+) (where n = 1-9) have been useful in interpreting the structural and spectroscopic properties and the reactivity of this class of complexes. Geometry optimizations significantly contributed to the generalization of the sparse structural data available for allenylidene, butatrienylidene, and pentatetraenylidene complexes to higher cumulenylidene complexes (with up to eight carbon atoms in the chain), which show a clear structural trend. In particular, the geometries of all even-chain cumulenes are consistent with an almost purely cumulenic structure, whereas the geometries of odd-chain cumulenes present a significant polyyne-like carbon-carbon bond length alternation. The calculated bond dissociation energies (BDEs) of the cumulenylidene ligand remain almost constant on lengthening the cumulene chain. These BDEs indicate that there is no thermodynamic upper limit to the cumulene chain length and suggest that the synthetic difficulties in preparing higher cumulenylidenes are due to an increase in reactivity. The calculated charges on the carbon atoms show no significant polarization along the cumulene chain, indicating that charge distribution is not important in determining the regioselectivity of either electrophilic or nucleophilic attack, which is instead determined by frontier orbital factors. The breakdown of the contributions from the metal and the carbon atoms along the chain to the HOMO and LUMO shows that the HOMO has contributions mainly from the metal and the carbon atoms in even positions along the chain (C(2), C(4), C(6), and higher). In contrast, the LUMO has contributions mainly from the carbon atoms in odd positions along the chain (C(1), C(3), C(5), and higher), thus explaining the experimentally observed regioselectivity of electrophilic and nucleophilic attacks, which are directed, respectively, to even and odd positions of the cumulenylidene chain. The study of the electronic structure of cumulenylidenes has allowed us not only to give a consistent rationale for the main structural and spectroscopic properties and for the reactivity of this emerging class of compounds but also to predict the effect of ancillary ligands on the metal center or substituents on the carbon end. The result is a useful guide to new developments in the still-underexplored fields of this fascinating class of compounds.