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本帖最后由 Uus/pMeC6H4-/キ 于 2025-4-19 13:35 编辑
zako 发表于 2025-4-19 04:05
Thank you very much for your reply.
this is the my first time i work with cluster, and what i und ...
No, you are not getting my point. Perhaps I should get in line with avatar *clears throat* and try explaining details in plain words, but then it will be a lengthy post.
Remember the introductory course for general chemistry about atomic orbitals and energy levels? (If not, at least pick it up by reading wikipedia...) It is usually said that for a single Fe atom at ground state, the valence electron configuration is 3d6 4s2, with the five 3d orbitals partially occupied by six electrons and the one 4s orbital filled. But this pretty simplified picture only tells about one configuration and does not say anything about other possibilities. The five 3d orbitals are basically on the same energy level due to bearing the same principal quantum number (3) and azimuthal quantum number (denoted by d) (well, technically occupation patterns matter but there is little effect); while the 4s (and even 4p and 4d) orbitals are higher in energy, the differences with respect to 3d are not that large. Therefore, even if electrons are excited and the configuration change to something like 3d7 4s1 or another 3d6 4s2 with all 3d electrons spin-paired, the resulting total energy would be similar to the original 3d6 4s2 configuration. Consequently, the states are mixing and a realistic wavefunction description of any one of them, be it ground or excited, should take different configurations into account and express the overall wavefunction as a combination of several wavefunctions corresponding to different configurations. This is what the word "multiconfigurational" encompasses. To tell the energies of configurations apart, the static correlation between electrons must be described accurately, which is beyond capability of conventional single-reference HF and DFT methods; "single-reference" means that they can describe the wavefunction with just one single Slater determinant. This manifests as unreachable convergence and wavefunction instability in simple-minded DFT calculation attempts.
The argument above concerns a single Fe atom, but now you have a whopping six of them bonding as a cluster. The molecular orbital of such cluster forms by combining individual atomic orbitals according to symmetry. Even limiting to 3d and 4s atomic orbitals, there is a total of 6x(5+1)=36 molecular orbitals available for 6x(6+2)=48 electrons; incorporating virtual 4p and 4d orbitals would only make it worse. How are they ranked in energy and how are electrons arranged on top of their interactions? Definitely not trivial to answer! The frontier molecular orbitals are expected to be severely degenerate and the HOMO-LUMO gap are small; even in a tiny range of allowed energy there would be a variety of potential electron configurations coexisting, each with distinct spin multiplicities. None of these can represent the actual state alone, ruling out the meaningfulness of "find[ing] a suitable 'spin multiplicity'" by looking one of them. In other words, the cluster is much, much more horribly "multiconfigurational" and constitutes a significant challenge, if not an outright impossible mission, for simple DFT methods.
tl;dr: owing to the weird Fe6 cluster, the "whole issue" is way more complicated than what you anticipated.
I have no idea why your first time working with a cluster is faced with such a hardcore system, and whether you really have an idea how researches on electronic structure of transition metal clusters are met with theoretical difficulties. Before jumping into such a rabbit hole and investing computational resources, it is far easier to simply question oneself: is this model a correct and sensible representation of the actual chemistry? For example, if you are in fact looking into adsorption of organic molecules onto the surface of bulk iron, then since the Fe6 cluster cannot reproduce the enviroment of solid surface, it is suggested to go and find a package for periodic calculation (refer to the subforum labelled "First Principle" in this kein forum) instead of continue with programs for individual isolated systems (labelled "Quantum Chemistry" in this kein forum; this topic is covered in http://sobereva.com/540 in which pros and cons are discussed).
Edit: for clarification, there are still "multiconfigurational" issues for solid surface when it comes to ferromagnetic materials, and wavefunction convergence may also be hard to reach in a periodic calculation. Yet it seems to be partially addressed with some techniques such as Fermi smearing and DFT+U. |
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发表于 Post on 2025-4-17 21:09:16
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