Figure 1 is the HOMO for (CpCr)2C8H8, Figure 2 is the HOMO-5, i think the HOMO is antibonding while the HOMO-5 is bonding, or they are both non-bonding?
This can only be unambiguously answered if your orbitals are centred on only two atoms. In this case it is more complex, you will have to ask the question: bonding/antibonding with respect to which atoms?
"Antibonding with respect to atom A and B" of course means that the wavefunction has a node between atom A and B and bonding is when there is no node. So: Your Figure 1 seems to be antibonding with respect to almost everything and certainly with respect to its two main centres (but turn it around and check carefully), while Figure 2 is more mixed, with bonding character between some atoms and antibonding character between others.
As far as I am concern all HOMOs are bonding Orbitals, All LUMOs are antibonding orbitals
Dear Nan,
Bonding and antibonding molecular states have a major difference between them. It is the response to an electric field. If you applied an electric field (with a proper intensity) , then energy of a bonding orbital will be shifted for lower value, while the energy of an antibonding will shifted to a higher value.
So, you need to test this case to indicate bonding and antibonding molecular orbitals.
Dear Björkman, how do you think of this one, pi-bonding or non-bonding?
Dear Karthick Muthusamy, in this case of (CpCr)2C8H8, HOMO seems to be anti-bongding.
Dear Aqeel Ali, since it is the first time for me to calculate metalic multiple bond, I don't know how to applied electric fields. Now I only judge the orbitals by symmetry. It will be very help if you tell me some details about it. OTZ
Dear Aqeel Ali, I optimized the structures using Gaussian09 package and performed NBO analysis at PBEPBE/TZVPP level. In fact, I also calculated the Mayer bond order, the value is about 1.6 for Cr-Cr bond in (CpCr)2C8H8, but it is known to be triple bond in references . I think the small overlap d-d orbitals results in the weak bonding, so that the bond order is only 1.6. Because I haven't enough knowledge of group theory, I hope the molecular orbital would tell me the bond order for briefly.
Hi Nan, Gaussian package use molecular orbital theory which mix all atomic orbitals of a system. Therefore, it do not result high bond order, that need pure atomic orbitals.
An electric field may added to the hamiltonian in Gaussian software, and you can to find this within example test (included within package). If you do not find it just tell me.
Best wishes
Dear Aqeel Ali, thank you very much. I will try it soon and I hope I could find it.
Dear Jonas Wiebke, should I use NBOs to find out the bonding or anti-bonding? Thanks.
Dear Jonas Wiebke, thanks a lot, I do really want to know the bonding or anti-bonding between to metal atoms. The problem is that: the shape of dz2 orbital is apprent, but dxy,dxz, dyz are analogous. Altough the MOs between two metal atoms seems to overlap (bonding), but the symmetry of two atom orbitals might be inconsistent. Two dxy could form σ bonding, two dxz could form π bonding, two dyz could form δ, others are non-bonding. Because of the symmetry of the two orbitals is to distinguish, I really don't know it is π bonding or non bonding between the two atoms. But I guess it is non-bonding.
Since the MOs are made up of atomic orbitals，the shape of MOs could also divided into atomic orbitals，so we could know the type of atomic orbitals。 To compose the MO，atomic orbital should follow three rules：（1）Symmetry （2）Energy （3） Overlap. In this case, the energy of atomic orbitals are near, the overlap seems to indicate the π bonding, but the symmetry seems to indicate non-bonding. I draw a picture to show the σ, π, δ bonding made up of d orbitals.
Dear Jonas Wiebke, thanks for your suggestion. It is indeed a question to think about it.
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