# New Materials and Effects in Molecular Nanomagnets
## 6 Theoretical Aspects and Methods  
Besides the aforementioned theoretical aspects in the evaluation of new materials and understanding of the measured phenomena, here, a brief overview is given on the recent theoretical aspects and methods used to model molecular magnets. One of the most interesting problems in molecular magnets is decoherence. [PERSON] et al. investigated environmental decoherence and showed that the theory for  
Figure 7: The supramolecular nanotube formed by [Tb(hfac)\({}_{3}\)NIT-O-Hexyl]\({}_{n}\) chains, showing (**top**) all atoms; (**middle**) one chain; (**bottom**) magnetic backbones only of 11 curled chains forming one nanotube. Reprinted from [129], copyright 2020, with permission from [PERSON]. insulating electronic spin systems could predict environmental decoherence in molecular quantum magnets well, based on phonons, nuclear spins, and intermolecular dipolar interactions [134]. The theory of environmental decoherence was experimentally first verified in the Fe\({}_{5}\) complex by spin-echo measurements and was compared with calculations from the Hamiltonian model used to predict the field splitting [134]. Decoherence is highly important as it modifies the equations describing the time-dependent evolution of a magnetic moment in a varying magnetic field, i.e., the Landau-Zener expression, which allows for calculating the spin reversal probability in a constantly swept magnetic field [135; 136]. The equation is limited to time scales much smaller than the dephasing time, as pointed out for a single-molecule spin transistor containing the single-ion magnetic molecule TbPc\({}_{2}\) (with Pc = phthalocyanine), by comparing the experimental results with calculations based on a Hamiltonion description of the interplay between the time-dependent magnetic field and a constant tunneling term [137]. [PERSON] and [PERSON] used density functional theory (DFT) and time-dependent DFT to calculate decoherence due to spin-phonon coupling in spin \(\frac{1}{2}\) transition molecular qubits based on Cu(II) and V(IV), using the ORCA program to generalize the ligand field theory (LFT) and to enable a comparison of the experimental results with those of LFT, DFT, and time-dependent DFT [138]. A broad overview of such DFT calculations used for SMMs was given by [PERSON] et al., who reported on recent interesting systems based on Ni\({}_{4}\), Co\({}_{4}\), Fe\({}_{4}\), Mn\({}_{10}\) clusters, and V\({}_{15}\), and discussed the anisotropies in different single-molecule magnets [139]. [PERSON] et al. recently showed that a phenomenological Lindblad operator was suitable to model spin-flip probability for small probing currents for different temperatures, cooling times, and sweeping rates in a diluted crystal of TbPc\({}_{2}\) lanthanide single ion molecular magnets [140]. Spin dephasing was studied by propagation of unitary quantum spin dynamics in a reduced Hilbert space to model spin dephasing in vanadyl-based molecular qubits VO(acac)\({}_{2}\) and VO(dmit)\({}_{2}\) (with acac = acetylacetonate and dmit = 1,3-dithiole-2-thione-4,5-dithiolate), applying ORCA to compute some not experimentally available parameters [141]. [PERSON] et al. used the Kubo-Anderson model to connect hyperfine coupling, calculated using DFT, to the coherence time for different vandaryl complexes [142]. It should be mentioned that besides environmental decoherence, there is also an intrinsic decoherence, which is actually a breakdown of quantum mechanics and is much harder to understand [143]. Besides the aforementioned problem of decoherence or coherence time, several more specific questions have risen with respect to molecular magnets and were solved by different theoretical approaches. [PERSON] et al., e.g., used an analytical theory to correlate the tunnel splitting of a single molecular spin with the height of the quantum steps found in the hysteresis loops of the molecular magnets Fe\({}_{5}\), Mn\({}_{12}\), and Mn\({}_{4}\)[144]. [PERSON] et al.