The paper investigates the role of the exchange-correlation (XC) potential and kernel in calculating excitation energies using time-dependent density functional theory (TDDFT). The authors focus on the helium and beryllium atoms, comparing results obtained from exact and approximate XC potentials, as well as different approximations for the XC kernel. They find that the choice of the ground-state XC potential has the most significant impact on the absolute position of excitation energies, with orbital-dependent approximate potentials leading to a uniform shift of transition energies to Rydberg states. The study also explores the effects of various approximations for the XC kernel, including the adiabatic local density approximation (ALDA) and self-interaction corrected local density approximation (SIC-LDA). The results highlight the importance of accurate XC potentials and kernels in obtaining reliable excitation energy calculations.The paper investigates the role of the exchange-correlation (XC) potential and kernel in calculating excitation energies using time-dependent density functional theory (TDDFT). The authors focus on the helium and beryllium atoms, comparing results obtained from exact and approximate XC potentials, as well as different approximations for the XC kernel. They find that the choice of the ground-state XC potential has the most significant impact on the absolute position of excitation energies, with orbital-dependent approximate potentials leading to a uniform shift of transition energies to Rydberg states. The study also explores the effects of various approximations for the XC kernel, including the adiabatic local density approximation (ALDA) and self-interaction corrected local density approximation (SIC-LDA). The results highlight the importance of accurate XC potentials and kernels in obtaining reliable excitation energy calculations.