feat(minmode): Davidson subspace as alternative to dimer rotation

[HaoZeke]

Summary

• Adds Davidson minimum-mode finder: FD Hessian-vector products (same class as Lanczos), Ritz projection, residual correction with optional diagonal preconditioner from H*v components.
• Select with [Saddle Search] min_mode_method = davidson (dimer rotation CG and Lanczos unchanged).
• [Davidson] tolerance, max_iterations, diagonal_preconditioner.
• Unit tests: negative eigenvalue; strategy variant; agreement with Lanczos on sign/magnitude band.

Why

Dimer min-mode spends effort on constrained rotational minimization. Davidson expands a Ritz subspace with residual correction — better asymptotic convergence for the lowest curvature mode without the rotational force loop.

Test plan

• CI green
• Local: DimerTest cases tagged [davidson]
• Optional: process_search with min_mode_method=davidson on an LJ/Morse fixture

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Benchmark Results

Tip

1 benchmark(s) improved

	Count
🟢 Improved	1
⚪ Unchanged	7

Improvements

	Benchmark	Before	After	Ratio
🟢	bench_eonclient.TimeMinimizationLJCluster.time_minimization_lbfgs	35.4±0ms	31.8±0ms	0.9x

7 unchanged benchmark(s)

Benchmark	Before	After	Ratio
bench_eonclient.TimeMinimizationLJCluster.peakmem_minimization_lbfgs	41.2M	41.2M	~1x
bench_eonclient.TimeNEBMorsePt.peakmem_neb	41M	41M	~1x
bench_eonclient.TimeNEBMorsePt.time_neb	260±0ms	259±0ms	~1x
bench_eonclient.TimePointMorsePt.peakmem_point_evaluation	41M	41M	~1x
bench_eonclient.TimePointMorsePt.time_point_evaluation	9.92±0ms	10.8±0ms	~1.09x
bench_eonclient.TimeSaddleSearchMorseDimer.peakmem_saddle_search_dimer	41M	41.1M	~1x
bench_eonclient.TimeSaddleSearchMorseDimer.time_saddle_search_dimer	67.2±0ms	67.9±0ms	~1.01x

Details

• Base: 0a40bb30
• Head: 26276a4d
• Runner: ubuntu-22.04

Raw asv-spyglass output

All benchmarks:

| Change   | Before   | After    |   Ratio | Benchmark (Parameter)                                                  |
|----------|----------|----------|---------|------------------------------------------------------------------------|
|          | 41.2M    | 41.2M    |    1    | bench_eonclient.TimeMinimizationLJCluster.peakmem_minimization_lbfgs   |
| -        | 35.4±0ms | 31.8±0ms |    0.9  | bench_eonclient.TimeMinimizationLJCluster.time_minimization_lbfgs      |
|          | 41M      | 41M      |    1    | bench_eonclient.TimeNEBMorsePt.peakmem_neb                             |
|          | 260±0ms  | 259±0ms  |    1    | bench_eonclient.TimeNEBMorsePt.time_neb                                |
|          | 41M      | 41M      |    1    | bench_eonclient.TimePointMorsePt.peakmem_point_evaluation              |
|          | 9.92±0ms | 10.8±0ms |    1.09 | bench_eonclient.TimePointMorsePt.time_point_evaluation                 |
|          | 41M      | 41.1M    |    1    | bench_eonclient.TimeSaddleSearchMorseDimer.peakmem_saddle_search_dimer |
|          | 67.2±0ms | 67.9±0ms |    1.01 | bench_eonclient.TimeSaddleSearchMorseDimer.time_saddle_search_dimer    |