Ondrej, The best source is some course notes I wrote up while a staff member at Caltech. I just put them on github in http://github.com/rpmuller/PracticalQuantumChemistry. The PDF is at: https://github.com/rpmuller/PracticalQuantumChemistry/blob/master/PracticalQuantumChemistry.pdf
Still embarrassingly incomplete, but Sect 2.6-2.7, and Ch 9 have some of what you want. I can expand at length anytime. In fact, it's sometimes hard to stop me from talking about it ;-). I'm talking about something along the lines of eq 2.33. Given an energy expression made of one- and two-electron terms that depend upon orbitals constructed of linear combinations of atomic basis functions, we can write a general expression for varying an orbital by some small amount \delta. These result in a set of orbital optimization equations that you can solve to find the optimal orbitals. For closed-shell HF, this results in the well-known Fock equations, and they're pretty simple, by which I mean they can be derived in a lot of different ways. General MC-SCF energy expressions like eq 9.12 are a little more complicated, but it's the same idea. However, rather than just diagonalizing a set of fock equations, you also have to do some occupied orbital rotations, and solve a CI equation. I think this is well within the capabilities of sympy. Apologies if this isn't clear. Again, this is one of my loves, so I'm happy to go into exhaustive detail on this. I'm only not doing so to spare you a lot of stuff, in case you're not interested. On Thursday, May 4, 2017 at 8:51:42 AM UTC-6, Rick Muller wrote: > > I was hoping that someone could give me some help getting started with the > sympy tensor objects. I'd like to define symbolic objects to represent one- > and two-electron integrals in quantum chemistry with the proper index > permutation symmetries. These are real-valued integrals, so commutation > relations aren't a problem (and, when they are, can be handled by the > physics.secondquant module. > > The one-electron integrals are symmetric, i.e. I1[i,j] = I1[j,i], which I > assume should be straightforward. > > The two-electron integrals are a little trickier, for I2[i,j,k,l] the > integral is symmetric when i,j are permuted, and/or k,l are permuted, > and/or i,j is permuted with k,l. I've never been able to derive a symbolic > object that captures this, and it would be really convenient, for example, > to derive equations for orbital optimization for different MC-SCF wave > functions. > > I'm familiar with techniques to compute the orbitals numerically, e.g., > https://github.com/rpmuller/pyquante2. What I'm interested here is to > derive and simplify equations for the symbolic manipulations of equations > containing these terms. Has anyone done any work on this? > > Thanks in advance, > > Rick > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/264669fb-fc76-4c35-911b-af8b2b139e33%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
