CCL上关于分子轨道的意义的讨论

sobereva

CCL上有人提到HOMO-LUMO gap，然后有个人这么回复。感觉此人太偏激了，对于“轨道”这个重要的概念在化学研究中的价值了解得太少了。纵使由于存在电子相关，导致轨道这个概念不是物理上严格定义的，但它毕竟在电子相关特别是静态相关不重要情形下近似描述和认识体系电子波函数的重要且合理的手段，是不可缺少的概念，也有重要的实际价值，诸如前线轨道理论。此人举了两篇文献，第一篇全是空洞的废话（可以供吐槽，作为附件贴上来了），第二篇没仔细看，感觉有点跑题了。
至于他提到的HOMO->LUMO这种方式描述不正确，强调CIS形式才能基本正确描述激发态波函数，这就有点那种中鸟“知道一点东西也要说出来显摆”的感觉。其实这根本不重要，比如一个跃迁CIS计算HOMO->LUMO贡献是100%，那么直接用LUMO密度与HOMO密度求差就能得出和CIS一致的激发态和基态的密度差，而此人非要强调激发态波函数不能用单行列式描述，这已经主次不分了。何况，CIS波函数和HOMO->LUMO跃迁这个说法实际上也毫不矛盾嘛。


Can I try to exaggerate this discussion a bit?

It is well known that a concept of 'orbital' has historically originated from Hartree-Fock approximation, and that in fact molecular orbital
is no more than a mathematical tool for building an approximate wavefunction.
Some authors have advocated the viewpoint that in reality orbitals simply do not exist! For example:
* Martín Labarca, Olimpia Lombardi "Why orbitals do not exist?" [Foundations of Chemistry, 2010, Volume 12, Issue 2, pp 149-157, DOI 10.1007/s10698-010-9086-5 ]
* J. F. Ogilvie, "The nature of the chemical bond—1990: There are no such things as orbitals!" [J. Chem. Educ., 1990, 67 (4), p 280, DOI: 10.1021/ed067p280 ]

With that in mind, do HOMO and LUMO have any importance, - except for adding another 'beautiful picture' to some paper with HOMO and/or LUMO
isosurfaces and withOUT any discussion of what consequences does their shapes imply , - for understanding physical properties and chemical reactivity ?

Similar doubts about an importance apply to the HOMO-LUMO gap, but here I'd like to recall that, ofr example, replacing ONE (filled) orbital (HOMO) in
a Slatter determinant with ONE unfilled orbital (e.g., LUMO) does NOT produce even approximate wavefunction of an excited state, since the
crudest approximation to that wavefunction comes with CIS method, where a linear combination of (many!) singly substituted determinants is used
in order to get (a not so good) wavefunction of an excited state. So, there seems to be no physical ground for associating the HOMO-LUMO gap with
characteristic wavelengths in a UV-Vis-like spectra.

So, why to care about HOMO / LUMO unless we are not dealing with solids ?...

Best regards,
Tymofii,
a physicist ;)

sobereva

这个回复还成

Dear all,


I agree, of course, that eigenvalues are not at all that best values to be used for gap calculations from the formal (and, frequently, also from the practical point of view), but, nevertheless, they DO provide SOME approximation. Eigenvalues, naturally, look like 'approximation for everything', as we are talking both about MO-to-MO transitions when considering UV-Vis spectra and about electron removal from some orbital / electron addition to some orbital, talking about ionization or electron capture. Of course, in reality one and the same quantity cannot describe both. However, it is well known that, for example, Koopmans' theorem often provides quite good results (okay, it's due to error compensation). Eigenvalue differences are also the first approximation in TD methods.
I want also to emphasize that the person asking was dealing with HOMO-LUMO gap in a TRANSITION STATE. From more physical point of view, Mr. van Sittert should compute ionization potential of electron donor in his reaction and electron affinity of the acceptor, according to Δ (or ΔSCF) methodology (energy difference). However, I do not know if this would be easy task to perform in transition state, correctly including the polarization of other molecules in the reaction center. Eigenvalues, on the contrary, are ready available from every optimization run; that's why I did not comment anything in my first answer.

We are now, actually, concerned with something similar, currently reconciling ourselves with Mulliken charges of surrounding molecules for the polarization field (but we are not dealing with the transition state). Is it correct enough to consider reactants as separate electronic systems in the transition state at all?



With best wishes,

Igors Mihailovs

Institute of Solid State Physics

University of Latvia

jiangning198511

不要和一个学物理的人讨论非物理量

卡开发发

附件的参考文献颇有民科的味道，orbital只是个沿用词，看起来就在批判量子论了？最后也没根据他的观点在量子化学发展的层面上给出什么好的提议，实在失望至极，我还以为作者会搞出来个什么《无轨道量子力学》呢，一点都不好玩。看了一下这篇文章当中睡着了好几次（也许最近睡眠不太好）。