Mass weight Gaussian energy derivative datatypes

[ericchansen]

Is the Gaussian Hessian already mass weighted? For the option -gh, there currently isn't any additional mass weighting going on after reading the Hessian from the archive, which may be a big problem.

For -geigz, we simply read the eigenvalues and convert them to a diagonal matrix. Again, does any mass weighting have to occur here? Currently, I only have methods for mass weighting Hessians and eigenvectors, not eigenvalues. I'm not sure how I would do this.

For -mgeig, we use the Gaussian eigenvectors and the MM Hessian to form the diagonal eigenvalue matrix. Again, do we need to mass weight the eigenvectors after reading them?

[peonor]

I think I answered mopst of this in another issue. If you get a Hessina from archive or formchk, or jaguar .01.in, do mass weighting of the Hessian. If you pick the eigensystem from the log files, no need. Only Hessians are ever mass-weighted, but the eigen-vectors and -values from the mass-weighted are different.

For the MM Hessian, it must be mass-weighted before we use it with the eigenvectors. Since we get it from RRHO-files, it will be mass-weighted in the log file, which is why we must use mass-weighting with the QM Hessians. Note that the mass from atom.typ is used, it must be correct! Change for Z0 if you use it.

[ericchansen]

So it sounds like the Gaussian Hessian for -gh needs mass weighting. On the other hand, -geigz doesn't need eigenvalues modified. Similarly, -mgeig doesn't need the eigenvectors modified. The bit about -mgeig surpirses me because the eigenvectors are mass weighted in -mjeig (see line 1137 of calculate).

For future reference, the masses used are in constants.MASSES.

[peonor]

I don't remember, and don't have time to check right now, but I think there was a difference between Jaguar and Gaussian eigenvectors, maybe the former needed mass-weighting... It rings a bell. Strange if so, but yes, I think that was the only way I could rationalize differences between Gaussian and Jaguar output. Needs checking.

[ericchansen]

Closing as superseded by #64 (Port Hessian eigenmatrix training data with TS coordinate inversion).

Key insights preserved for #64:

1. Gaussian Hessian from .fchk/archive needs mass-weighting before use with eigenvectors (per @peonor)
2. Eigenvalues from log files do NOT need additional mass-weighting -- they're already from the mass-weighted Hessian
3. Jaguar vs Gaussian eigenvectors may differ in whether mass-weighting is applied -- PO noted this needed checking and suspected Jaguar eigenvectors required mass-weighting while Gaussian's did not
4. MM Hessian from RRHO files is already mass-weighted in the log, so QM Hessians must match

These details are critical for correct Hessian comparison in the objective function and have been noted in #64 for the new implementation. The modern SDK will initially focus on Gaussian/Psi4 (not Jaguar, which is Schrodinger-proprietary), simplifying the mass-weighting logic.