Abstract: Sodium-cooled fast reactor (SFR) is one of the major the Generation Ⅳ nuclear reactors, which utilizes the liquid sodium as the coolant. Despite of the excellent heat-transfer characteristic and low neutron absorption cross-section, the liquid sodium suffers the serious accident risks due to the high chemical reactivity of sodium atoms, especially when liquid sodium contacts with water or steam during the break accident. Recently, the liquid sodium nanofluid, obtained by dispersing the transition metal nanoparticles in liquid sodium (Nano-LS), have been gained wide consideration due to the enhancement to the coolant performance, especially the suppression of the reactivity of sodium atoms. However, the reported experimental or theoretical works mainly focused on the Nano-LS doped with titanium nanoparticles. The influence of transition metal type and the suppression mechanism is still ambiguous from the atomic scale. Theoretical chemistry is an effective tool to reveal the special natures of the Nano-LS. Hence, detailed theoretical computations based on the density functional theory and electronic structure analysis were performed to reveal the stability of three representative 3d transition metal clusters, TM_n (namely, Ti, Fe and Cu, with atom number n from 2 to 13), and clarify the interaction characteristic between TM_n and sodium atoms. The TM_n representative structures were accessed according to the artificial bee colony algorithm for cluster global optimization using ABCluster code. Structures and energies of TM_n and Na-TM_n with different multiplicities were further calculated to obtain the most energy stable isomers based on TPSS functionals with the double zeta basis sets def2-SVP and triple zeta basis sets def2-TZVPP, respectively. The D3 Becke-Johnson damping correction was used to consider the dispersion interaction. The structure, electronic energy, electron affinity, ionization potential, and electronegativity of TM_n were calculated to compare the cluster stability. And the adsorption sites on the TM_n for sodium atom were predicted by the electrostatic potential mapped molecular van der Waals surface. Furthermore, the chemical stability, intra-molecular interaction (namely, independent gradient model based on Hirshfeld partition analysis), and charge transfer analysis were combined to illustrate the strength and nature of the interaction between sodium atom and TM_n. All the DFT calculations were performed using the ORCA 5.0.4 program, and the wavefunction analysis were realized utilizing the Multiwfn 3.8 code. The results indicate that with the increase of atom numbers n, the average binding energies E_A(n) for Ti_n, Fe_n and Cu_n increase. Meanwhile, the vertical electron affinity and vertical ionization potential tend to increase and decrease when the size of TM_n becomes larger. The values of Mulliken electronegativity of different TM_n shows size-independent. The electrostatic potential mapped molecular surface show that the Electrostatic potential minimum point always tends to located over the center of three transition metal atoms, which is considered as the interaction site to adsorb Na atoms. Overall, the Ti_n is more stable compared with Fe_n and Cu_n, while are less attractive for sodium atom. Mulliken electronegativity and electrostatic potential analysis are effective tools to predict the interaction strength and sites for Na-TM_n complexes. The sodium atom is absorbed on the TM_n mainly through van der Waals interaction, and has no significant effects on the structure of TM_n clusters. The obtained atomic dipole moment corrected Hirshfeld population charges for Na-TM_n indicate that the electron transfers from sodium atom to TM_n. Hence, TM_n are always carry the negative charge, which contributes to the suspension stability of TM_n in liquid sodium.