Photodissociation of dicarbon: How nature breaks an unusual multiple bond

Strongly Rotationally Dependent Lifetimes of C2 in the 23Σg- State: Implications for Predissociation in the Vacuum Ultraviolet Region

The radiative and photodissociative properties of the dicarbon molecule, C2, in high-lying electronic states are of utmost importance for modeling the photochemical processes that occur in various astronomical environments. Despite extensive spectroscopic studies in the last two centuries, the photodissociation properties of C2 are still largely unknown, particularly for quantum states in the vacuum ultraviolet (VUV) region. Here, the lifetimes of C2 for each individual rovibrational level in the recently identified 23Σg- state are measured for the first time using a VUV-pump-UV-probe photoionization scheme. The lifetimes are found to be strongly dependent on the rotational and vibrational quantum levels in the 23Σg- state. The strongly rotationally dependent lifetimes observed here indicate that the 23Σg- state may mainly undergo a predissociation process through couplings with nearby repulsive electronic states. The current observation could have important applications in modeling the interstellar medium and cometary comae.

Diabatic Valence-Hole Concept

A global diabatization scheme, based on the "valence-hole" concept, has been previously applied to model webs of avoided crossings that exist in four electronic-state symmetry manifolds of C2 (1Πg, 3Πg, 1Σu+, and 3Σu+). Here, this model is extended to the electronically excited states of four more molecules: CN (2Σ+), N2 (3Πu), SiC (3Π), and Si2 (3Πg). Many strangenesses in the spectroscopic observations (e.g., energy level structure, predissociation linewidths, and radiative lifetimes) for all four electronic state systems discussed here are accounted for by this unified model. The key concept of the model is valence-hole electron configurations: 3σ24σ11π45σ2 in CN (2Σ+), 2σg22σu11πu43σg21πg1 in N2 (3Πu), 5σ26σ17σ22π3 in SiC (3Π), and 4σg24σu15σg22πu3 in Si2 (3Πg), all of which have a triply occupied "valence-core" (i.e., 2σg22σu1 or the equivalent). These valence-hole configurations have a nominal bond order of three or higher and correlate with high-energy separated-atom limits with an np ← ns (n = 2, 3) promotion in one of the atomic constituents. On its way to dissociation, the strongly bound diabatic valence-hole state crosses multiple weakly bound or repulsive states, which belong to electron configurations with a completely filled valence-core. These curve crossings between diabatic potentials result in a network of many avoided crossings among multiple electronic states, analogous to the well-studied electronic structure landscape of ionic-covalent crossings in strongly ionic molecules. Considering the unique role of valence-hole states in shaping the global electronic structure, the valence-hole concept should be added to our intuitive framework of chemical bonding.

Spectroscopic Study of a New Electronic Band System 33Δg-a3Πu of C2

As one of the most important diatomic molecules in the universe, the spectroscopic characterizations of C2 have attracted wide attention in various fields, such as interstellar chemistry, planetary atmospheric chemistry, and combustion. In recent years, a systematic spectroscopic study of C2 in the vacuum ultraviolet (VUV) region has been carried out in our laboratory by using the (1VUV+1'UV) resonance-enhanced multiphoton ionization method based on the combination of a tunable VUV laser source and a time-of-flight mass spectrometer. Two new electronic transition band systems have been reported, following the pioneering work of Herzberg and co-workers in 1969. In the current study, a total of 18 vibronic transition bands of C2 from the lower a3Πu state are experimentally observed in the VUV photon energy range 72000-81000 cm-1, and 6 new upper vibronic levels of 3Δg symmetry are identified, which are assigned as the v' = 0-5 vibrational levels of the 33Δg state of C2. The term energy Te of the 33Δg state is determined to be in the range of 78425-78475 cm-1 (9.724-9.730 eV) with respect to the ground X1Σg+ state, and the molecular constants such as vibrational and rotational constants are also determined, which are in reasonable agreement with those predicted by high-level ab initio theoretical calculations. Irregular vibrational energy level spacings in the 33Δg state are observed, which is tentatively attributed to the strong perturbations between the 33Δg and 23Δg states, as previously predicted by theory.

Observation of the electronic band system 23Σg--a3Πu of C2 in the vacuum ultraviolet region

A systematic spectroscopic study of the dicarbon molecule C2 has important applications in various research fields, such as astrochemistry and combustion. In the short vacuum ultraviolet (VUV) wavelength region, recent theoretical calculations have predicted many absorption band systems of C2, but only few of them have been verified experimentally yet. In this work, we employed a tunable VUV laser radiation source based on the two-photon resonance-enhanced four-wave mixing method and a time-of-flight mass spectrometer to investigate the absorption bands of C2 in the VUV range of 64 000-66 000 cm-1. The electronic transition 23Σg-(v')-a3Πu(v″) of C2 has been observed and identified experimentally for the first time. The term value Te for the 23Σg- state is determined to be 66 389.9 ± 0.5 cm-1 above the ground state X1Σg+, and the vibrational and rotational constants are also determined. The experimentally measured spectroscopic parameters in this study are in excellent agreement with the theoretical results based on high-level ab initio calculations.

Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C2

The ¹Σ_g⁺ ground state of C₂ is investigated using truncated CIPSI-Jastrow CSF wave functions with Hartree-Fock orbitals within the framework of variational and diffusion quantum Monte Carlo. The truncation is performed based on the absolute value of the CI coefficients, and the Jastrow, molecular orbitals, and CI parameters are either partially or fully reoptimized with respect to the variational energy. Excellent absolute as well as bond dissociation energies are obtained at DMC level with very compact, fully optimized wave functions. By studying the expansions in more detail, we observe a change in the CI picture when reoptimizing the antisymmetric part of the CIPSI-Jastrow wave functions. Furthermore, we demonstrate that a decrease in the VMC energy as well as an improvement of the nodal surface quality can be achieved─with the same expansion size─if the CSFs are selected in the presence of a Jastrow correlation function, laying the foundation for a Jastrow selected CI scheme with quantum Monte Carlo.

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C₂ singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B₂, C₂, O₂, and F₂ in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C₂. This work shows that spin symmetry breaking in singlet C₂, which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

A New Band System of the Dicarbon Molecule in the Vacuum Ultraviolet Region

As one of the most abundant molecules in the universe, the long history of spectroscopic studies of the dicarbon molecule, C₂, reaches back two centuries. While many electronic band systems with upper states below the lowest dissociation threshold have been well characterized, much less is known about transitions to higher-lying states. Here, we report the observation of a new band system of C₂ from the lowest triplet state a³Π_u through a resonance-enhanced multiphoton ionization scheme. The upper state is identified as 1³Σ_g⁺, which is determined to be 61539.0 cm^-1 (7.630 eV) above ground state X¹Σ_g⁺. The spectroscopic parameters determined for the 1³Σ_g⁺ state are in excellent agreement with those predicted by the high-level ab initio calculations. This study paves the way for systematic investigations of the photoabsorption and photodissociation of C₂ in the vacuum ultraviolet region, which has important applications in the field of astrochemistry.

Multireference configuration interaction study of the predissociation of C2 via its F 1Πu state

Photodissociation is one of the main destruction pathways for dicarbon (C2) in astronomical environments such as diffuse interstellar clouds, yet the accuracy of modern astrochemical models is limited by a lack of accurate photodissociation cross sections in the vacuum ultraviolet range. C2 features a strong predissociative F 1Πu-X 1Σg+ electronic transition near 130 nm originally measured in 1969; however, no experimental studies of this transition have been carried out since, and theoretical studies of the F 1Πu state are limited. In this work, potential energy curves of excited electronic states of C2 are calculated with the aim of describing the predissociative nature of the F 1Πu state and providing new ab initio photodissociation cross sections for astrochemical applications. Accurate electronic calculations of 56 singlet, triplet, and quintet states are carried out at the DW-SA-CASSCF/MRCI+Q level of theory with a CAS(8,12) active space and the aug-cc-pV5Z basis set augmented with additional diffuse functions. Photodissociation cross sections arising from the vibronic ground state to the F 1Πu state are calculated by a coupled-channel model. The total integrated cross section through the F 1Πu v=0 and v=1 bands is 1.198×10−13 cm2cm-1, giving rise to a photodissociation rate of 5.02×10−10 s−1 under the standard interstellar radiation field, much larger than the rate in the Leiden photodissociation database. In addition, we report a new 2 1Σu+ state that should be detectable via a strong 2 1Σu+-X 1Σg+ band around 116 nm.

Orbital contraction and covalent bonding

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H₂ ⁺ and H₂. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H₂, Li₂, B₂, C₂, N₂, O₂, F₂, CO, P₂, and Cl₂ and the polyatomics CH₃-CH₃, CH₃-SiH₃, CH₃-OH, and C₂H₅-C₂H₅ (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

Diabatic Valence-Hole States in the C2 Molecule: "Putting Humpty Dumpty Together Again"

Despite the long history of spectroscopic studies of the C₂ molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C₂ is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions that occur within four symmetry manifolds of excited states of C₂ (¹Π_g, ³Π_g, ¹Σ_u⁺ , and ³Σ_u⁺ ). The key concept of our model is the existence of two "valence-hole" configurations, 2σg22σu11πu33σg2 for ^1,3Π_g states and 2σg22σu11πu43σg1 for ^1,3Σ_u⁺ states, that are derived from 3σ_g ← 2σ_u electron promotion. The lowest-energy state from each of the four C₂ symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s²2p² + 2s2p³ separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the global electronic structure and unimolecular dynamics of C₂.

The dynamics of CO production from the photolysis of acetone across the whole S1 ← S0 absorption spectrum: Roaming and triple fragmentation pathways

The unimolecular photodissociation dynamics of acetone spanning the entire S1 ← S0 absorption spectrum have been reinvestigated, with a focus on mechanisms that produce CO. At excitation wavelengths of λ > 305.8 nm, all photoproducts are formed on the S0 state after internal conversion. A roaming mechanism forming C2H6 + CO is active in the window λ = 311.2–305.8 nm. From λ = 305.8 to 262 nm, little or no CO is produced with the photochemistry dominated by the Norrish-type I C–C bond cleavage on the lowest excited triplet state, T1. At higher energy ( λ < 262 nm), an increasing fraction of CH3CO radicals from the primary reaction have sufficient internal energy to spontaneously decompose to CH3 + CO. A new model is presented to account for the kinetic energy distribution of the secondary CH3 radical, allowing us to determine the height of the energetic barrier to CH3CO decomposition as 68 ± 4 kJ mol−1, which lies midway between previous measurements. The fraction of CO from triple fragmentation rises smoothly from 260 to 248 nm. We see no evidence of the return of roaming, or any other S0 reaction, in this higher energy region of the first electronic absorption band.