We investigate the isomerization enthalpy of the Dihydroazulene/Vinylheptafulvene (DHA/VHF) molecular photoswitch system derivatives using electronic structure calculation methods including Density Functional Theory (DFT), Quantum Monte Carlo (QMC) and Coupled Cluster (CCSD(T)). Recent efforts have focused on tuning the isomerization enthalpy of the photoswitch for solar thermal energy storage applications using substitutional functional groups on its five and seven membered carbon rings, predominantly using DFT for the energy predictions. However, using the higher accuracy QMC and CCSD(T) methods, we show that in many cases DFT incorrectly predicts the isomerization enthalpy and the errors depends on the functional groups substituted and the choice of the DFT functional. Isomerization of the DHA to VHF molecule is a ring-opening reaction on the five membered ring of the DHA isomer. We find that the DFT errors are correlated to the ring-opening reactions of cyclobutene and cyclo-1,3-hexadiene, such that the DFT error changes monotonically with the size of the carbon ring, although QMC and CCSD(T) results are in a good agreement irrespective of the ring size. Using the QMC and CCSD(T) isomerization enthalpies, we predict gravimetric energy densities of the DHA derivatives for solar thermal storage applications. Our results show that suitable substitutions on DHA can yield gravimentric storage densities as large as 732 kJ/kg. 1