Add output files

[jonmarks12]

Summary

This PR adds QChem inspired output files to the ML-FSM, closing #35. There is still some room for improvement beyond the files that are generated here, and we may want to consider convenience outputs (ex. ts_guess.xyz and/or the final string).

The major changes are an output writer, and changes to the optimizer return signature such that the file can report accurate per-node optimization stats. Other changes are largely adding calls to the output writer.

Changes

1. New module src/mlfsm/output.py

The FSMOutput class owns a single file handle and writes sections incrementally such that the output is useable mid-run, preserving information in partially completed runs.

Setup phase: called once before the growth loop.

• write_header banner, credit block, timestamp, maybe a fun place to add ascii art of the tiger hawk?
• write_parameters parameter dump
• write_system_info formula, atoms, charge, multiple, 1-indexed fixed atoms
• write_calculator_info uses the get_calculator_info() that pulls various calculator specific parameters. This system could be improved but this is a working first version.
• write_initial_structures coordinate blocks
• write_path_init writes a summary of the internal coordinates types when RIC is used

Per-iteration changes

• _ensure_iteration_header writes header
• write_current_frontier_node pre-interpolation geometry
• write_forntier_node interpolated structure selected with actual step size
• write_optimized_nodew energy + geometry, also should report nfev, nit, and nls where nls = nfev - nit
• write_iteration_summary a Claude suggestion to write the full energy table with absolute + relative to min columns

Final summary

• write_final)_summary total iterations, total grad calls, TS guess, full string, citation block

2. Optimizer return signature changes src/mlfsm/opt.py

Changed the return tuple of both CartesianOptimizer.optimize and InternalsOptimizer.optimize.

• Before: (atoms, energy, njev)
• New: (Atoms, energy, nfev, nit)
  nfev should be njev for our use case.

Wiring src/mlfsm/cos.py

• FreezingString.__init__ has an additional output kwarg output: Optional[FSMOutput] = None, later we can shift this to be the default but given that some infastructure may rely on the vfile setup we currently have I think this should be optional for a while
• Store the initial interpolation object used to compute path length such that it can be exposed as self.init?coordsobj. Non RIC methods get init_coordsobj = None
• grow() wiring of above per-iteration functions
• optimize() correctly unpacks the new function and accumulates self.ngrad += nfev

Net

There should be no changes to actual behavioral effects here, if anything the counting of gradient evaluations could be affected.

[joegomes]

I'm guessing first author inverted is stylistic choice? I am fine if this was intentional

[jonmarks12]

That is the MLA format that I copy and pasted from the google scholar cite button

[joegomes]

Sorry I missed this review request! LGTM!