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What is the purpose of calculating other orbitals than HOMO and LUMO?
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Keith Johnson
What is the purpose of calculating other orbitals than HOMO and LUMO?
A practical answer: in most of molecular quantum chemistry, the cost of obtaining unoccupied ("virtual") orbitals is next to nothing because of the algorithms involved. In short, one diagonalizes some matrix (i.e. finding eigenvalues and eigenfunctions, which are the orbital energies and orbitals) and the virtual orbitals are usually delivered anyway.
A more theoretical answer: While a lot of chemistry involves only the ground state, there is UV/vis spectroscopy and photochemistry. For those fields, virtual orbitals are immensely useful, because they will be used for the description of the electronic transitions that happen in those fields. These transitions are not necessarily between HOMO and LUMO because of symmetry, energy scales involved etc.
A practical answer: in most of molecular quantum chemistry, the cost of obtaining unoccupied ("virtual") orbitals is next to nothing because of the algorithms involved. In short, one diagonalizes some matrix (i.e. finding eigenvalues and eigenfunctions, which are the orbital energies and orbitals) and the virtual orbitals are usually delivered anyway.
A more theoretical answer: While a lot of chemistry involves only the ground state, there is UV/vis spectroscopy and photochemistry. For those fields, virtual orbitals are immensely useful, because they will be used for the description of the electronic transitions that happen in those fields. These transitions are not necessarily between HOMO and LUMO because of symmetry, energy scales involved etc.
@pH13-YetanotherPhilipp There are useful algorithms that do not yield all eigenpairs, but merely give you all of them up to a set threshold (the case in solid state QC). I have applied them in molecular QC. For UV/vis, some DFT fanatics will tell you about approaches that are not reliant on virtual orbitals per se.More
. For UV-vis, virtual orbitals are not only "immensly useful" but they are absolutely necessary in almost all cases. The HOMO-LUMO transition is usually only one peak but might not be the most interesting one in photophysics/-chemistry.More
In general, Id say you are right, but I think your phrasing is not to the point. You dont get virtual orbitals at "next to nothing" cost, that sounds as if youd make some extra calculation to get them, but because they are part of the solution. They are not "usually delivered anyway" but they are delivered More
A practical answer: in most of molecular quantum chemistry, the cost of obtaining unoccupied ("virtual") orbitals is next to nothing because of the algorithms involved. In short, one diagonalizes some matrix (i.e. finding eigenvalues and eigenfunctions, which are the orbital energies and orbitals) and the virtual orbitals are usually delivered anyway.
A more theoretical answer: While a lot of chemistry involves only the ground state, there is UV/vis spectroscopy and photochemistry. For those fields, virtual orbitals are immensely useful, because they will be used for the description of the electronic transitions that happen in those fields. These transitions are not necessarily between HOMO and LUMO because of symmetry, energy scales involved etc.
A practical answer: in most of molecular quantum chemistry, the cost of obtaining unoccupied ("virtual") orbitals is next to nothing because of the algorithms involved. In short, one diagonalizes some matrix (i.e. finding eigenvalues and eigenfunctions, which are the orbital energies and orbitals) and the virtual orbitals are usually delivered anyway.
A more theoretical answer: While a lot of chemistry involves only the ground state, there is UV/vis spectroscopy and photochemistry. For those fields, virtual orbitals are immensely useful, because they will be used for the description of the electronic transitions that happen in those fields. These transitions are not necessarily between HOMO and LUMO because of symmetry, energy scales involved etc.
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