## 1 Introduction
It is well known that a systematic overestimation of the atomic binding energies and lattice constants is inherent for the DFT calculations [7; 8]. It leads to the inaccuracy of the estimation of the eigenfrequencies of the phonon modes. The accurate quantitative estimation of the temperature dependence of the lattice specific heat by the PDOS needs a preliminary correction of its frequency scale. In the case of systematic underestimation of the force values, the frequency scale can be corrected by multiplying the frequencies of all phonon modes by a single parameter, i.e., the frequency correction factor [3]. There are different ways to determine the correction factor. For instance, Raman and infrared (IR) spectroscopy enable measuring the oscillation frequencies for Raman and IR-active phonon modes, respectively [2]. To a first approximation, the IR-active phonon oscillation frequency should coincide with the IR-absorption peak [3]. Therefore, a comparison of the calculated PDOS with the measured IR-absorption spectrum enables estimating the frequency correction factor for any solid with IR-active phonon modes. Nevertheless, such a way for estimation does not take into account the oscillator strength of the phonon modes. In the case of IR-absorption maxima of different phonon modes overlaying each other in the IR-spectrum, neglecting the oscillator strengths leads to possible errors of the phonon-mode frequency estimation. In the case of an iron-containing solid, \({}^{57}\)Fe Mossbauer spectroscopy methods also allow the estimation of the frequency correction factor (generally, the statement refers to a solid containing any kind of Mossbauer nuclei, which are not rare in the periodic table of elements, but only a few isotopes are suitable for practical application [9]). The Mossbauer effect is the resonant and recoilless absorption of gamma radiation by atomic nuclei bound into a solid. The probability of the effect is called the Lamb-Mossbauer factor [9]. It depends on the mean-square displacement of a nucleus, the temperature dependence of which is determined directly by the partial PDOS of the corresponding atom [9]. Besides, the Lamb-Mossbauer factor can be estimated as the relative total area under the Mossbauer spectrum [9]. So, the temperature dependence of the Lamb-Mossbauer factor can be obtained by measuring Mossbauer spectra at different temperatures. On the other hand, it can be modeled by calculating the partial PDOS of the corresponding atom. Hence, the comparison of the experimental and calculated temperature dependences of the Lamb-Mossbauer factor yields another estimate of the correction factor for the PDOS frequency. In our previous paper [3], we used both of these approaches to estimate the frequency correction factor for the ab initio calculated PDOS of the quasi-one-dimensional antiferromagnet RbFeSe\({}_{2}\). The value of 1.06 was obtained from the comparison of the high-frequency R-absorption peak frequencies with those in the calculated PDOS, while the fit to the temperature dependence of the Lamb-Mossbauer factor had given the value of 1.08. The approach to fit the temperature dependence of the Lamb-Mossbauer factor is quite indirect compared with the IR-spectroscopy method mentioned above, although the latter one cannot be regarded as absolutely accurate because of difficulties with determining the oscillator strengths. To resolve the dilemma of choosing one of the two methods, another experimental method to measure the PDOS is strongly desired. There are several methods to measure the PDOS in solids. Widely known is inelastic neutron scattering (INS), the advantage of which is its universality [10]. On the other hand, it is quite laborious and requires a large amount of sample, typically several dozens of grams, because of the small scattering cross-section of neutrons in solids. Another one is the nuclear inelastic scattering (NIS) method [11; 12], which is based on the Mossbauer effect, utilizing synchrotron radiation.