why irrep is negative, why direct product of irreps not associative? #2680
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The symmetry of one molecule is 'Coov' Why irreps[1] × irreps[2] × irreps[2]=-12? Why （irreps[1] × irreps[2] )×irreps[2] =-12 not equal to irreps[1]× (irreps[2] × irreps[2])= irreps[1] ×Ag= irreps[1]=10? |
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Replies: 4 comments
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'the code is as follows' basis = {'C': [[0, geom = [['C',(0, 0, 0)],['H',(0, 0, 2.26184115)]] 'irreps~~~' mf = pyscf.scf.RHF(mol) print('mo_energy',mf.mo_energy) ' calculate irreps[1] × irreps[2] × irreps[2]' |
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Hello, can someone help me? Can we use pyscf to calculates the direct product of irreps under ‘Coov’ symmetry? |
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The direct product in your case involves is the product of 2D irreps. It can be decomposed to 2 1D irreps and 1 2D irreps. The To accurately handle the symmetry of cylindrical symmetry, the orbitals should be linearly transformed to (+) and (-) complex orbitals from the real orbitals in x, y representations. Then you can obtain the momentum of the orbitals and use the momentum to derive the direct product. In fci module, the cylindrical symmetry is treated this way, e.g. pyscf/pyscf/lib/mcscf/fci_contract.c Line 983 in 231da24 |
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Hi @yuhanzheng1 , thanks for asking. Has your question been answered? |
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The direct product in your case involves is the product of 2D irreps. It can be decomposed to 2 1D irreps and 1 2D irreps. The
direct_prodfunction only outputs one of the three irreps. You cannot use this function to find the accurate direct products for cylindrical symmetry.To accurately handle the symmetry of cylindrical symmetry, the orbitals should be linearly transformed to (+) and (-) complex orbitals from the real orbitals in x, y representations. Then you can obtain the momentum of the orbitals and use the momentum to derive the direct product. In fci module, the cylindrical symmetry is treated this way, e.g.
pyscf/pyscf/lib/mcscf/fci_contract.c
Line 983 in 231da24