  In this letter we report the singlet ground state structure of the full
carotenoid peridinin by means of variational Monte Carlo (VMC) calculations.
The VMC relaxed geometry has an average bond length alternation of 0.1165(10)
{\AA}, larger than the values obtained by DFT (PBE, B3LYP and CAM-B3LYP) and
shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD
calculations on a reduced peridinin model confirm the HOMO-LUMO major
contribution of the Bu+-like (S2) bright excited state. Many Body Green's
Function Theory (MBGFT) calculations of the vertical excitation energy of the
Bu+-like state for the VMC structure (VMC/MBGFT) provide excitation energy of
2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The
dependence of the excitation energy on the bond length alternation in the MBGFT
and TDDFT calculations with different functionals is discussed.
