Return to Answer

1. The traditional "orbitals" that introductory chemistry teaches resemble what theoreticians would call spatial orbitals. These are distinct from spin orbitals, i.e. one-electron wavefunctions which describe both the spatial and spin orientations of the electron. The spatial orbitals only describe the spatial component.

For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent an "orbital" being filled with two electrons is by taking the product of the two spin orbitals, i.e. the product of two one-electron wavefunctions. So, the "two-electron orbitals" from introductory chemistry still have a mathematical form in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).

The reason why you don't see "two-electron wavefunctions" being discussed is because they have no real meaning in electronic structure theory. The N-electron wavefunction is useful because that is the way we choose to describe the entire molecule, and we can use it to extract information such as the energy of the system. The one-electron wavefunctions are useful because (1) they are used to construct the N-electron wavefunction (most simply by direct multiplication, or more properly using Slater determinants), and (2) we have developed methods to obtain the best possible forms of these. Two-electron wavefunctions are somewhere in the middle: they're not useful for describing the molecule as a whole, but at the same time there's no mathematical motivation for using them.

2. As for basis sets, it's a different ball game: we are no longer talking about what orbitals theoretically are ("theoretical chemistry"), but rather what is the best way to model them for a computer to get accurate results ("computational chemistry"). AOs themselves have no intrinsic physical meaning in a molecule, they merely serve as useful building blocks for MOs. Also, we don't even use the actual AOs as basis functions: we use things that resemble AOs as basis functions, to increase computational efficiency. So it is not too much of a stretch to add "unphysical" functions such as 1p, 2d, ... all for the purposes of getting better and/or faster results.

   Also, orbitals in DFT have an entirely different meaning from orbitals in HF, but that's a story I'm not qualified to tell.

1. The traditional "orbitals" that introductory chemistry teaches resemble what theoreticians would call spatial orbitals. These are distinct from spin orbitals, i.e. one-electron wavefunctions which describe both the spatial and spin orientations of the electron. The spatial orbitals only describe the spatial component.

   For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent an "orbital" being filled with two electrons is by taking the product of the two spin orbitals, i.e. the product of two one-electron wavefunctions. So, the "two-electron orbitals" from introductory chemistry still have a mathematical form in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).

   The reason why you don't see "two-electron wavefunctions" being discussed is because they have no real meaning in electronic structure theory. The N-electron wavefunction is useful because that is the way we choose to describe the entire molecule, and we can use it to extract information such as the energy of the system. The one-electron wavefunctions are useful because (1) they are used to construct the N-electron wavefunction (most simply by direct multiplication, or more properly using Slater determinants), and (2) we have developed methods to obtain the best possible forms of these. Two-electron wavefunctions are somewhere in the middle: they're not useful for describing the molecule as a whole, but at the same time there's no mathematical motivation for using them.

2. As for basis sets, it's a different ball game: we are no longer talking about what orbitals theoretically are ("theoretical chemistry"), but rather what is the best way to model them for a computer to get accurate results ("computational chemistry"). AOs themselves have no intrinsic physical meaning in a molecule, they merely serve as useful building blocks for MOs. Also, we don't even use the actual AOs as basis functions: we use things that resemble AOs as basis functions, to increase computational efficiency. So it is not too much of a stretch to add "unphysical" functions such as 1p, 2d, ... all for the purposes of getting better and/or faster results.

   Also, orbitals in DFT have an entirely different meaning from orbitals in HF, but that's a story I'm not qualified to tell.

For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent an "orbital" being filled with two electrons is by taking the product of the two spin orbitals. So, the "two-electron orbitals" from introductory chemistry are still a thing in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).

The reason why you don't see "two-electron wavefunctions" is because it has no real meaning in electronic structure theory. The N-electron wavefunction is useful because that is the way we choose to describe the entire molecule. The one-electron wavefunction is useful because (1) they are used to construct the N-electron wavefunction (most simply by direct multiplication, or more properly using Slater determinants), and (2) we have developed methods to obtain the best possible forms of these. Two-electron wavefunctions are somewhere in the middle: they're not useful for describing the molecule as a whole, but at the same time there's no mathematical motivation for using them.

For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent an "orbital" being filled with two electrons is by taking the product of the two spin orbitals, i.e. the product of two one-electron wavefunctions. So, the "two-electron orbitals" from introductory chemistry still have a mathematical form in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).

The reason why you don't see "two-electron wavefunctions" being discussed is because they have no real meaning in electronic structure theory. The N-electron wavefunction is useful because that is the way we choose to describe the entire molecule, and we can use it to extract information such as the energy of the system. The one-electron wavefunctions are useful because (1) they are used to construct the N-electron wavefunction (most simply by direct multiplication, or more properly using Slater determinants), and (2) we have developed methods to obtain the best possible forms of these. Two-electron wavefunctions are somewhere in the middle: they're not useful for describing the molecule as a whole, but at the same time there's no mathematical motivation for using them.

1. The traditional "orbitals" that introductory chemistry teaches are what theoreticians would call spatial orbitals. These are distinct from the one-electron orbitals in theoretical chemistry, which are spin orbitals, i.e. one-electron wavefunctions which describe both the spatial and spin orientations of the electron.

For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent a spatial orbital being filled with two electrons is by taking the product of the two spin orbitals. So, the "two-electron orbitals" from introductory chemistry are still a thing in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).

1. The traditional "orbitals" that introductory chemistry teaches resemble what theoreticians would call spatial orbitals. These are distinct from spin orbitals, i.e. one-electron wavefunctions which describe both the spatial and spin orientations of the electron. The spatial orbitals only describe the spatial component.

For every spatial orbital, there are two possible spin orbitals, because you can have one electron with up spin and one with down spin. The simplest possible way to represent an "orbital" being filled with two electrons is by taking the product of the two spin orbitals. So, the "two-electron orbitals" from introductory chemistry are still a thing in theoretical chemistry, although it does depend on exactly what theory you are looking at (there are cases where the notion of a two-electron spatial orbital breaks down).