New experimental and theoretical assessment of the dissociation energy of C2

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.

Carbon Clusters: Thermochemistry and Electronic Structure at High Temperatures

This paper studies the thermochemistry and electronic structure of small carbon clusters and hydrocarbons, which are major constituents of pyrolysis gases released into the boundary layer of ablating heat shields. Our focus lies on clusters of up to four carbon atoms. Among other molecules, thermochemistry data for molecules such as C₃H and C₄H have been determined using the Weizmann-1 (W1) method. These molecules have very limited thermochemistry data recorded in the literature, thereby necessitating new and accurate computations of required properties such as electronic energies of low-lying states, heats of formation, harmonic frequencies, and rotational constants. A study of electronically excited states of these molecules computed using the equations of motion coupled cluster singles doubles method revealed C₄ and C₄H to be potential sources of radiation absorption in the boundary layer. The excited electronic states of interest are studied further to obtain their optimum geometries, rotational constants, and vibrational frequencies. Moreover, we also study the effect of low-lying excited electronic states on the partition function to assess their effect on the thermodynamics of these pyrolysis gases in the high-temperature regime. Neglecting the excited electronic states records a maximum difference of 12% in the computed specific heat capacity values, C_p values. Finally, comparisons of the equilibrium mole fractions obtained using the thermodynamics computed in this paper with the existing state-of-the-art tables used for hypersonic applications (e.g., JANAF and Gurvich Tables) show an order of magnitude difference in the mixture compositions. It is shown that the rhombic isomer of C₄ (¹A_g), which is energetically close to the ground state (³Σ_g^-) and usually neglected in composition calculations, contributes to a 28% increase in the equilibrium mole fraction of the C₄ molecule.

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.

Accurate ground state potential of Cu2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing

Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X ¹Σ_g ⁺ (0_g ⁺) ground state of Cu₂. Rotationally resolved transitions up to v^″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of D_e = 16 270(7) hc cm^-1 is determined, and an accurate potential energy function for the X ¹Σ_g ⁺ (0_g ⁺) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas-Kroll-Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.