Study On The Mechanism Of Spin-state Transition Based On First-Principles Calculation

Theoretical attempts to explain the intrinsic mechanism of spin-state transition is rather controversial, for distinguishing SCO from complicated phenomena and structure is a difficult challenge. Thus a precise method and better object are necessary, in order to obtain correct theory of the spin-state transition by quantitatively investigation. It is widely proofed that the full-potential First-Principles calculation based on the Density Functional Theory (DFT) is a reliable and precise method. We suppose to investigate in spin-crossover (SCO) complex and the mechanism of this transition via DFT calculation.3D Hofmann-like clathrate compound [Fe(C4H4N2){Pt(CN)4}] provide us an opportunity in the research of SCO phenomenon, for the concise structures and simple phenomenon. It is helpful to separate SCO from complicate aspects, and provide a diagnosis for the intrinsic force.We study the crystallographic structure of this complex with DFT calculation, and find that the XRD measurement is a ideal structure. In fact, it should be monoclinic but not tetragonal. The symmetry of this crystal should be lowered from P4/m into P2/m. The structures of high-temperature form (HT) and low-temperature form (LT) given from our calculations are coincide with the experimental results.The spin-state transition is studied in high precision with full-potential calculation, which shows the structure expansion from LT to HT form. And calculation shows that the expansion are caused by the Fe-N bond lengths, which means the Fe-N lengths should be the main reason in SCO.Fixed-spin-moment method (FSM) calculations are also exerted to find the mechanism of the change in Fe-N bond length. Bistability of this complex is discovered that only a high-spin state (HS) and a low-spin state (LS) existed. The stable and meta-stable states are converted between HS and LS state. And the stable state is decided by the total energy differenceΔEHL between these two states. Calculation shows that the Fe-N lengths lead to the change ofΔEHL,hence the conversion of stable state.In the frame of our d-electrons hopping model, we find a link betweenΔEHL from DFT calculation and the crystal-field splitting energyΔcf. It is found that the reduction ofΔEHL come from the increase of Fe-N lengths which weaken the electric field henceΔcf is reduced. With the reduction ofΔcf,the hopping energyΔfrom t2g orbital into the eg orbital is also reduced. And the complex converts from LS state to HS state due to the Hund exchange energyΔex. It is obvious that the intrinsic force of spin-state transition isΔcf,so that the Fe-N bond lengths can affect the stable state of the complex. It is necessary to considerΔcf as the direct parameter in theory of SCO.In the way analyzing the relationship between Fe-N bond lengths andΔcf,the intrinsic concept of "internal chemical pressure" is revealed, which should be the macroscopic behavior of repulsive force among electrons. Because of the Coulomb interaction, the orbital around iron and the one around nitrogen are attractive and repulsive. In the LT form, the repulsive force is larger than the attractive force because the distance between iron and nitrogen is closed. Thus locative behavior is shown on the electrons of iron. As the temperature changes, iron is excited from t2g orbital into eg orbital. The repulsive force is strengthened for the eg orbital is neared from the orbital of nitrogen, thus the Fe-N lengths increased. As a result, the structure dilation companied with the conversion from LS state to HS state, which is contributed by the Fe-N bond lengths. And it is coincide with the structure analysis.Based on our calculation, we suggest two theoretical models which show the physics image of spin-state transition, and explain the mechanism of SCO in microscopic understanding. The first model is a simplified bistable thermo-excited model, which introduce a temperature dependentΔorΔcf. The theoretical curve consists with the experiment one and this model explains the uncompleted conversion in Light-Induced Excited Spin-State Trapping (LIESST).The other model is a completed one named bistable crystal-field model. This model shows that the temperature has no effect onΔEHL whereas the increase of Fe-N lengths reducesΔEHL linearly in the case that temperature and Fe-N lengths are independent. In this case, HS fraction increases from 0 to 1 with the increase of Fe-N lengths, which corresponds to the spin-state transition. But the parameter of temperature only affects the speed of transition:the lower temperature, the faster the transition; the higher temperature, the slower the transition. In fact, the Fe-N lengths are related with temperature with the action of internal chemical pressure. In the hypothesis of a linear dependence between Fe-N lengths and temperature, the separated parameters are unified together withΔEHL in our model, which clarifies the relationship among these parameters and SCO. Our model consists with the thermo-hysteresis and theλcurves.Our two theoretical models show the reduction ofΔEHL in heating, which is just the key idea of our DFT investigation. Our models descript the SCO phenomenon in detail, and reveal the physic image of competition betweenΔcf andΔex in the spin-state transition.