Three-Mode Solvation Comparison

The three-mode comparison estimates how much the solvent environment changes the electronic correlation contribution. It is more expensive than the fixed H2 smoke test and should be run after h2_mc_solvation.py.

Run The Script

uv run python examples/h2_three_mode_comparison.py

Modes

Mode	Formula	Role
fixed	E_QPE(H_vac) + E_MM	Fast baseline; ignores solvent changes in correlation
hf_corrected	E_HF(R) + E_MM	HF-level MM embedding with interval QPE diagnostics
dynamic	E_QPE(H_eff) + E_MM	Runtime MM-embedded QPE coefficients

The comparison delegates analysis to q2m3.solvation.analysis.run_mode_comparison().

Compile-Once Idea

        flowchart LR
    accTitle: Three Mode Execution
    accDescr: Fixed and dynamic modes compile reusable QPE structures while the MC loop updates solvent coordinates and energies.

    mc["MC solvent states"]
    fixed["fixed<br/>vacuum Hamiltonian"]
    hf["hf_corrected<br/>HF energy path"]
    dynamic["dynamic<br/>runtime coefficients"]
    analysis["mode comparison<br/>delta_corr-pol"]

    mc --> fixed
    mc --> hf
    mc --> dynamic
    fixed --> analysis
    hf --> analysis
    dynamic --> analysis
    

Dynamic mode uses runtime-traceable Hamiltonian coefficients so that the circuit structure can be compiled once while coefficients change across MC steps.

Reading The Result

The key scientific quantity is delta_corr-pol, the correlation-polarization coupling term. For small H2 runs, it is a diagnostic of whether the QPE energy changes materially when the MM embedding enters the Hamiltonian rather than only the classical correction.

Optional H3O+ Diagnostics

H3O+ workflows use a larger active space and many more Hamiltonian terms. The public H3O+ scripts are useful for ionic-solvation diagnostics, but they are not the default tutorial path. Use a 16 GB+ RAM machine for h3o_mc_solvation.py and a 30 GB+ RAM machine for 8-bit or dynamic Trotter diagnostics.