The 15Πg state of C2

The Spectroscopy of C2: A Cosmic Beacon

ConspectusDicarbon, the molecule formed from two carbon atoms, is among the most abundant molecules in the universe. Said by some to exhibit a quadruple bond, it is bound by more than 6 eV and supports a large number of valence electronic states. It thus has a rich spectroscopy, with 19 one-photon band systems, four of which were discovered by the author and co-workers. Its spectrum was among the first to be described: Wollaston reported the emission spectra from blue flames in 1802.C₂ is observed in a variety of astronomical objects, including stars, circumstellar shells, nebulae, comets and the interstellar medium. It is responsible for the green color of cometary comae but is not observed in the comet tail. It can be observed in absorption and emission by optical spectroscopy in the infrared, visible, and ultraviolet regions of the spectrum, and because it has no electric-dipole-allowed vibrational or rotational transitions, its spectral signature is a sensitive probe of the local environment.Before the work described in this Account, models of C₂ photophysics included the thitherto-unobserved c³Σ_u⁺ state and parametrized the strength of spin-forbidden intercombination transitions. Furthermore, they did not account for photodissociation of C₂, even though it was identified in the 1930s as a key process. Inspired by the observation of C₂ in the Red Rectangle nebula, the author was motivated to instill rigor into C₂ models and embarked on a spectroscopic and computational journey that has lasted 15 years.We were the first to identify the c³Σ_u⁺ state through the d³Π_g-c³Σ_u⁺ transitions, which were to become known as the "Duck" system. This minor partner to the well-known Swan bands is a key part of astrophysical C₂ models and can now be included with rigor. We identified the e³Π_g-c³Σ_u⁺ system, and the c³Σ_u⁺ state is now well-studied. Meanwhile others described the singlet-triplet and triplet-quintet interactions in exquisite detail, allowing rigorous modeling of the a-X and c-X intercombination transitions.The final piece of the C₂ puzzle would be understanding how long it survives before being broken into carbon atom fragments. Though predicted by Herzberg, predissociation in the e³Π_g state had never been observed. To find it would require the complicated ultraviolet spectroscopy of C₂ to be disentangled. In so doing, we identified the 4³Π_g and 3³Π_g states of C₂, thus uncovering two new band systems. The 4³Π_g state allowed the first accurate determination of the ionization energy of C₂. With these new band systems secure, we extracted new levels of the D¹Σ_u⁺ state (Mulliken bands) and the e³Π_g state (Fox-Herzberg bands) from our spectra. Upon climbing the energy ladder in the e³Π_g state to v = 12, we finally identified the route to predissociation of C₂ via non-adiabatic coupling to the d³Π_g state. This observation provided the first laboratory evidence for why C₂ is observed in the coma of a comet but not the tail.

Cn (n=2-4): current status

The major aspects of the C₂, C₃ and C₄ elemental carbon clusters are surveyed. For C₂, a brief analysis of its current status is presented. Regarding C₃, 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 C₄, the most stable isomeric forms of both triplet and singlet spin states and their possible interconversion pathways are examined afresh by means of accurate ab initio calculations. The main strategies for modelling the ground triplet C₄ potential are also discussed. Starting from a truncated cluster expansion and a previously reported DMBE form for C₃, an approximate four-body term is calibrated from the ab initio energies. The final six-dimensional global DMBE form so obtained reproduces all known topographical aspects while providing an accurate description of the C₄ 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'.

Chemical bonding motifs from a tiling of the many-electron wavefunction

A method is presented to partition the 3N-dimensional space of a many-electron wavefunction into hyper-regions related by permutation symmetry. These hyper-regions represent unit cells, or "tiles" of the wavefunction from which the wavefunction may be regenerated in its entirety upon application of the set of permutations of like-spin electrons. The method, wherein a Voronoi diagram is constructed from the (even permutations of the) average position of a swarm of Monte Carlo walkers sampling |Ψ|(2), determines a self-consistent partitioning of the wavefunction. When one of the identical 3N-dimensional Voronoi sites is projected onto the coordinates of each electron, chemical motifs naturally appear, such as core electrons, lone-pairs, single-bonds and banana-bonds. The structures determined for N2, O2, F2, and other molecules correspond to the double-quartet theory of Linnett. When the procedure is applied to C2, we arrive at an interpretation of its bonding in terms of a near triple bond with singlet-coupled outer electrons.

Puzzles in bonding and spectroscopy: the case of dicarbon

The unstable molecule C₂ has been of interest since its identification as the source of the "Swan band" features observable in the spectra offlames, carbon arcs, white dwarf stars, and comets, and it continues to serve as a focal point for experimental and theoretical discovery. Recent spectroscopic work has identified a quintet state of the molecule for the first time, while new insights into the bond order of C₂ in its ground state have been provided by sophisticated computational methods based on valence bond theory. This article gives a review of spectroscopic and computational work on C₂ including both historical background and the most recent discoveries.