## 2 Experimental Details and Results  
The nuclear inelastic scattering [11; 12] experiment was carried out at the Dynamics Beamline P01 of PETRA III synchrotron (DESY, Hamburg, Germany) [13]. The measurements utilizing the nuclear gamma-resonance of \({}^{57}\)Fe at 14.413 keV were performed with an inline high-resolution monochromator providing an energy bandwidth of 0.9 meV full width at half maximum (FWHM). The sample with natural enrichment by \({}^{57}\)Fe was measured at 295 K. The Fe NIS spectrum of RbFeSe\({}_{2}\) is shown in Figure 1 (red dots) along with the instrumental function measured simultaneously with the spectrum (blue dots in Figure 1). The partial iron PDOS was evaluated from the NIS spectrum using the procedure described in [14]. The partial PDOS for the iron atoms in RbFeSe\({}_{2}\) is shown in Figure 2 (black dots). The ab initio calculations were carried out within the framework of density functional theory (DFT) utilizing the Vienna ab initio simulation package (VASP 5.3) [15; 16; 17; 18]. The Perdew-Burke-Ernzernhof (PBE) generalized gradient approximation (GGA) was applied for the exchange and correlation corrections [19]. The projector-augmented wave (PAW) method is used to take into account the electron-ion interactions. The PAW method is a frozen-core one in which the valence Rb (4p6 5s1), Fe (3d64s2), Se (4s2 4p4) electrons are treated explicitly, while the remaining electrons of the cores are taken into account by using pseudopotentials [20]. The cutoff energy for the plane-wave basis set was selected 300 eV. Integration over the Brillouin zone had been done on a Monkhorst-Pack k-point mesh \(3\times 2\times 3\) which corresponds to the actual spacing of \(0.300\times 0.259\times 0.202\) per A [21]. Equilibrium geometry was obtained after the several stages of full structural relaxation that include atomic positions, cell shape and cell volume. The phonon dispersion and density of states (PDOS) were obtained within harmonic approximation making use of the Medea-Phonon software [6]. The approach to the lattice dynamics is based on the ab initio evaluation of forces acting on all atoms by a set of finite displacements of a few atoms within an otherwise perfect crystal. The lattice parameters obtained after the lattice relaxation are given by \(a\) = 7.520 A, \(b\) = 12.153 A, \(c\) = 5.574 A, and the angle \(\beta\) = 111.83\({}^{\circ}\). There is a slight deviation of the calculated lattice parameters from the experimental ones [5] of about 1-2 percent, which is typical for DFT calculations [2]. All calculations accounted for the spin polarization due to the antiferromagnetic ordering of RbFeSe\({}_{2}\). The antiferromagnetic spin pattern was set in accordance with the magnetic structure obtained previously by neutron diffraction data [22]. The best agreement between the calculated (\(m\)(Fe) = 2.80 uB) and the experimental (\(m\)(Fe) = 2.66 uB [22; 23]) values of the magnetic moment per iron ion was obtained for choosing the Hubbard \(U\) parameter equal to zero. Figure 1: \({}^{57}\)Fe nuclear inelastic scattering spectrum of RbFeSe\({}_{2}\) (red dots) and instrumental function (blue dots). The inset displays a fragment of the RbFeSe\({}_{2}\) crystal structure showing quasi-one-dimensional structure of edge-sharing (FeSe\({}_{4}\)) tetrahedra. The red colored histogram in Figure 2A shows PDOS which is output of ab initio calculations [3] with the calibrated frequency scale (see below). The solid red line in Figure 2B shows the calibrated (cf. Section 3) partial PDOS for the iron atoms obtained from the previously calculated ab initio one, Figure 2A. The calculated PDOS is a discrete set of contributions from phonon modes, while the experimental one is a quasi-continuous sequence determined by the settings of the beamline setup, but to the greatest extent by the monochromator energy (frequency) resolution of 0.9 meV.