Talk:Localized molecular orbitals

Exclusive Orbitals
From "Molecular Orbitals in Chemistry, Physics, and Biology: A Tribute to R. S. Mulliken" pp 416

' Boys and Foster (1960) define "exclusive orbitals" by maximizing all centroids of electronic charge, i.e., by maximizing the functional:

B = Product_(i<j) [r_ii - r_jj]^2  : r_ij := \INT \Conj[psi_i]*r*\psi_j DX

on the Hartree-Fock manifold subject to orthonormality constraints. The functional derivatives are ..... Brydustin (talk) 20:04, 9 February 2012 (UTC)

Error in equation for Boys method
The new equation (with the Σ) inserted this week for the Boys method is dimensionally inconsistent, because the first term has dimensions of r and the second term has dimensions of r2. I presume there is either an exponent 2 missing or a parenthesis missing somewhere, but I do not have the source to check the original version. Could someone please correct this equation?

Also the source in the edit history should be placed in the article. I will do this. Dirac66 (talk) 13:09, 30 June 2011 (UTC)


 * OK, I have now fixed the equation as per a 1974 paper by Lipscomb's group which compares the ER and Boys methods. The difference between the two terms is squared, not just the second term.Dirac66 (talk) 19:28, 8 July 2011 (UTC)

LMOs, hybrids and VSEPR
This:
 * Similarly, molecular orbital calculations show two nonbonding valence-shell orbitals: a roughly sp2 hybrid orbital in the plane of the molecule and a pure p orbital perpendicular to this plane. The tetrahedral sp3 hybrids of valence bond theory and the electron pairs of VSEPR theory can be compared to the sum and the difference of these nonbonding orbitals.

has recently been removed as incorrect. In general it is not incorrect. It correctly describes the non-bonding MOs of water. The sum and difference of these gives two lone pairs, which can be used in VB theory. They are not exactly sp3. However VSEPR should not be confused with VB theory. Gillespie is quite clear about that. I therefore put that text back wth two changes. -- Bduke   (Discussion)  23:11, 4 December 2012 (UTC)


 * Although this view is not mainstream, I was thinking of the Pipek-Mezey picture of lone pairs for water. This is the same picture as the one originally proposed by Pauling which includes differentiated lone pairs. This is also the view taken by Weinhold and Landis (see ).--Officer781 (talk) 00:41, 23 June 2013 (UTC)
 * What is the reference to that manuscript? Is it published? -- Bduke   (Discussion)  02:16, 23 June 2013 (UTC)

There are several points that are worth mentioning here. First, The Pipek-Mezey localisation scheme does indeed give a different picture than do the other two common schemes of Boys and of Ruedenberg. However all are unitary transformations of the MOs and thus a Salter determinant of doubly occupied LMOs is identical to one of doubly occupied MOs. Each has its own uses. I have used all three in the last year. Second, Weinhold and Landis do have a specific view on this matter, but it is disputed. I draw your attention to three articles in "Chemistry Education Research and Practice"  The second and third are advance articles available over the internet. I do not have an opinion on this argument between experts. -- Bduke   (Discussion)  05:20, 25 May 2015 (UTC)