In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In particular we will discuss: 1) the derivation of the MCDE and the definition of the space in which it is to be solved; 2) the rationale of the approximation to the multichannel self-energy; 3) a diagrammatic analysis of the MCDE; 4) the recasting of the MCDE on an eigenvalue problem with an effective Hamiltonian that can be solved using standard numerical techniques. This work mainly focuses on the coupling between the one-body Green's function and the three-body Green's function to describe photoemission spectra, but the MCDE method can be generalized to the coupling of other many-body Green's functions and to other spectroscopies.

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Galvinoxyl, as one of the most extensively studied organic stable free radicals, exhibits a notable phase transition from a high-temperature (HT) phase with a ferromagnetic (FM) intermolecular interaction to a low-temperature (LT) phase with an antiferromagnetic (AFM) coupling at 85 K. Despite significant research efforts, the crystal structure of the AFM LT phase has remained elusive. This study successfully elucidates the crystal structure of the LT phase, which belongs to the P[1 with combining macron] space group. The crystal structure of the LT phase is found to consist of a distorted dimer, wherein the distortion arises from the formation of short intermolecular distances between anti-node carbons in the singly-occupied molecular orbital (SOMO). Starting from the structure of the LT phase, wave function calculations show that the AFM coupling 2J/kB varies significantly from −1069 K to −54 K due to a parallel shift of the molecular planes within the dimer.

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We performed several types of ab initio calculations, from Hartree-Fock to Complete-Active-Space second-order perturbation theory and Coupled Cluster, on compact clusters of stoichiometry XY, where X and Y are atoms belonging to the second row of the periodic table. More precisely, we considered the “cubic” structures of three isoelectronic groups, having a total of 48, 52, and 56-electrons, respectively. Notice that the highly symmetric cubic clusters of type X are characterized by an symmetry group, while the XY structures, with XY, have at most a symmetry. Binding energies and wave function analysis of these clusters have been performed, in order to investigate the nature, and the electron delocalization of these systems and establish a comparison between them. To this purpose, we also computed the Total-Position Spread tensor for each structure, a quantity which is related to the multi-reference nature of a system wave function.

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Recently, some of us reviewed and studied the photoionization dynamics of C₆₀ that are of great interest to the astrochemical community as four of the diffuse interstellar bands (DIBs) have been assigned to electronic transitions in the C₆₀$^+$ cation. Our previous analysis of the threshold photoelectron spectrum (TPES) of C₆₀ [Hrodmarsson et al., Phys. Chem. Chem. Phys. 22, 13880–13892 (2020)] appeared to give indication of D_3d$^+$ ground state symmetry, in contrast to theoretical predictions of D_5d$^+$ symmetry. Here, we revisit our original measurements taking account of a previous theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), obtained within a vibronic model parametrized on density functional theory/local-density approximation electronic structure involving all h_g Jahn–Teller active modes, which couple to the $^2$H_u components of the ground state of the C₆₀$^+$ cation. By reanalyzing our measured TPES of the ground state of the C₆₀ Buckminsterfullerene, we find a striking resemblance to the theoretical spectrum calculated in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), and we provide assignments for many of the hg modes. In order to obtain deeper insights into the temperature effects and possible anharmonicity effects, we provide complementary modeling of the photoelectron spectrum via classical molecular dynamics (MD) involving density functional based tight binding (DFTB) computations of the electronic structure for both C₆₀ and C₆₀$^+$. The validity of the DFTB modeling is first checked vs the IR spectra of both species which are well established from IR spectroscopic studies. To aid the interpretation of our measured TPES and the comparisons to the ab initio spectrum we showcase the complementarity of utilizing MD calculations to predict the PES evolution at high temperatures expected in our experiment. The comparison with the theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), furthermore, provides further evidence for a DC_5d symmetric ground state of the C₆₀$^+$ cation in the gas phase, in complement to IR spectroscopy in frozen noble gas matrices. This not only allows us to assign the first adiabatic ionization transition and thus determine the ionization energy of C₆₀ with greater accuracy than has been achieved at 7.598 ± 0.005 eV, but we also assign the two lowest excited states ($^2E$_1u and $^2E$_2u) which are visible in our TPES. Finally, we discuss the energetics of additional DIBs that could be assigned to C₆₀$^+$ in the future.

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