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.