We report on the formation of the high-energy empty-state resonance in the electronic spectrum of the iron adatom on the Pt(111) surface. By using the combination of the first-principles methods and the finite-temperature exact diagonalization approach, we show that the resonance is the result of the valence fluctuations between atomic configurations of the impurity. Our theoretical finding is fully confirmed by the results of the scanning tunneling microscopy measurements [M. F. Crommie et al., Phys. Rev. B 48, 2851 (1993)]. In contrast to the previous theoretical results obtained by using local spin density approximation, the paramagnetic state of the impurity in the experiment is naturally reproduced within our approach. This opens a way for interpretation of STM data collected earlier for metallic surface nanosystems with iron impurities.