Hi Rick,
On Thu, May 4, 2017 at 8:51 AM, Rick Muller <rpmul...@gmail.com> 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?
Can you give an example of an equation that contains it?
I.e., are you interested in symbolically calculating the two-particle
integrals of, say, Gaussians? Or rather just representing the
two-particle integral, and let SymPy take care of the freedom due to
the symmetries, as in the example you posted:
>>> SymmetricTensor('I2',(a,b),(c,d))
I2([a,b],[c,d])
>>> SymmetricTensor('I2',(c,d),(a,b))
I2([a,b],[c,d])
So you already have some proof-of-concept solution. How do you
actually want to use it? What is the application?
Ondrej
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