The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and interaction of nuclei and electrons in the framework of the theory of the electron density functional are presented. Common approximations and approaches in the methods of quantum mechanics are presented, including the Born–Oppenheimer approximation, the Hartree–Fock approximation, the Thomas–Fermi theory, the Hohenberg–Kohn theorems, and the Kohn–Sham formalism. Various options for describing the exchange–correlation energy in the theory of the electron density functional are considered, such as the local density approximation, generalized and meta-generalized gradient approximations, and hybridization of the generalized gradient method. The development of methods of quantum mechanics to quantum molecular dynamics or the dynamics of Car–Parrinello is shown. The basic idea of combining classical molecular modeling with calculations of the electronic structure, which is reflected in the potentials of the embedded atom, is described.
The present paper considers a mathematical model describing the time evolution of spin states and magnetic properties of a nanomaterial. We present the results of two variants of nanosystem simulations. In the first variant, cobalt with a structure close to the hexagonal close-packed crystal lattice was considered. In the second case, a cobalt nanofilm formed in the previously obtained numerical experiment of multilayer niobium–cobalt nanocomposite deposition was investigated. The sizes of the systems were the same in both cases. For both simulations, after pre-correction in the initial time stages, the value of spin temperature stabilized and tended to the average value. Also, the change in spin temperature occurred near the average value. The system with a real structure had a variable spin temperature compared to that of a system with an ideal structure. In all cases of calculations for cobalt, the ferromagnetic behavior was preserved. Defects in the structure and local arrangement of the atoms cause a deterioration in the magnetic macroscopic parameters, such as a decrease in the magnetization modulus.
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