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standard-method

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Fetch the Birkholz & Schlegel 2016 paper and its supporting information — the "standard method" (SM) that PyBerny's optimization algorithm follows — plus the papers it cites. Use when the user references the SM, asks about algorithm details/equations/convergence criteria, asks for test structures, asks about any of the SM's cited references (RFO, BFGS/SR1/PSB/Bofill, trust region, redundant internal coordinates, etc.), or asks anything that would be answered by reading [BirkholzTCA16] (cited in `doc/algorithm.rst`).

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Standard method paper (Birkholz & Schlegel 2016) and supporting literature

doc/algorithm.rst notes that PyBerny "loosely follows" the standard method (SM) described in the appendix of:

Birkholz, A. B. & Schlegel, H. B. Exploration of some refinements to geometry optimization methods. Theor. Chem. Acc. 135, (2016). DOI: 10.1007/s00214-016-1847-3

The SM appendix is self-contained for headline formulas but defers several pieces to other papers (RFO derivation, trust-region details, Bofill MSP, pRFO/EF for TS) or omits them entirely (initial Hessian, bond detection, B-matrix derivatives, coordinate formulas). The bundle therefore also includes those cited / canonical sources.

None of these papers are checked into the repo (copyright). They are downloaded from PAPERS_URL.

How to access

The container is ephemeral, so re-download as needed:

wget -q "$PAPERS_URL" -O /tmp/standard-method.zip
unzip -o /tmp/standard-method.zip -d /tmp/

The Read tool renders PDFs visually (via poppler-utils) — equations, bold matrices, subscripts and fractions all come through cleanly. Always pass a pages range for multi-page PDFs.

Bundle contents (under /tmp/standard-method/)

Primary

  • 390.pdf — Birkholz & Schlegel 2016, 12 pp. Appendix "Standard method" (pp. 8–12) is what PyBerny implements. Numbered Eqs. 14–33 cover B-matrix, generalised inverse, back-transformation, RFO, trust region, BFGS/SR1/PSB/MSP, convergence.
  • 214_2016_1847_MOESM1_ESM.txt — SI. Plain-text XYZ coordinates (Å) for the 20 test molecules (Artemisinin, Aspartame, …), each preceded by name and charge multiplicity.

SM appendix's explicit deferrals (see Ref. [X])

  • Banerjee, Adams, Simons - 1985 - Search for Stationary Points on Surfaces.pdf — SM ref [26]. RFO derivation and pRFO for transition states. The Banerjee article begins a few pages into the PDF (the journal-issue layout puts a different article first).
  • baker1996.pdf — SM ref [17]. Baker & Chan 1996, eigenvector-following for TS optimization (referenced alongside [26] for pRFO).
  • Dennis, Numerical Methods for Unconstrained Optimization and Nonlinear Equations.pdf — SM ref [27]. Dennis & Schnabel textbook, 395 pp. Adaptive trust-region material is in chapter 6.
  • bofill1994.pdf — SM ref [14]. Bofill 1994, J. Comput. Chem. 15(1):1. Source of the MSP / "Bofill" Hessian update (Eqs. 8–13 of that paper define the φ-mixed family that the SM cites as Eqs. 32–33).

SM appendix's implicit / canonical-source references

  • peng1996.pdf — SM ref [16]. Peng, Ayala, Schlegel & Frisch 1996. The RIC machinery PyBerny implements (bond-detection rule, recursive dihedrals through linear atoms, projector + α(1−P) penalty in Eq. 9 with α = 1000 au — this is the source of PyBerny's hard-coded 1000·(I − proj) in berny.py:191, not an ad-hoc constant). Iterative back-transformation is Eq. 11.
  • 1992_Pulay_2856.pdf — SM ref [3]. Pulay & Fogarasi 1992, J. Chem. Phys. 96:2856. Generalised inverse, projector approach (basis for SM Eqs. 18–21).
  • Schlegel - 1984 - Estimating the Hessian for gradient-type geometry optimizations.pdf — SM ref [7]. Analytic B-matrix derivatives for stretch/bend/torsion coordinates (the SM doesn't write these out; PyBerny's coord.eval(..., grad=True) implements them).
  • Schlegel11_Geometry_optimization.pdf — SM ref [1]. Schlegel 2011 WIREs Comput. Mol. Sci. review. Useful overview context, especially for line searches (not in the SM but used by PyBerny).
  • Swart, Bickelhaupt - 2006 - Optimization of Strong and Weak Coordinates.pdf — [SwartIJQC06] from doc/algorithm.rst. The Lindh-style diagonal initial Hessian PyBerny uses; fills the gap the SM leaves silent.

When to consult which paper

NeedFile
Exact SM convergence criteria, sketch of full algorithm390.pdf appendix
Test geometries to reproduce results / build test cases214_…_MOESM1_ESM.txt
Why the augmented-Hessian eigenvector gives the RFO stepBanerjee 1985
pRFO / eigenvector-following for TSBanerjee 1985, Baker 1996
Trust-region update theory & convergence guaranteesDennis & Schnabel, ch. 6
Bofill / MSP update derivationBofill 1994
RIC construction details (bonds, dihedrals through linears, α(1−P) penalty, iterative back-transformation)Peng 1996
Generalised inverse + projector formulationPulay-Fogarasi 1992
Analytic B-matrix derivativesSchlegel 1984
Background, line-search rationale, overall contextSchlegel 2011
Initial Hessian modelSwart-Bickelhaupt 2006

Notes for reviewing / extending PyBerny against the SM

  • PyBerny's 1000·(I − proj) penalty in berny.py:191 comes from Peng 1996 Eq. 9 (α = 1000 au) — not ad-hoc.
  • The SM omits the initial Hessian, bond detection, and B-matrix derivatives — those are PyBerny's own choices, sourced from Swart-Bickelhaupt, Peng et al., and Schlegel 1984 respectively.
  • Issue #29 ("fully conform to the SM") and issue #30 (linear bends with dummy atoms) are the open TODOs.

If PAPERS_URL is unset, ask the user — do not invent a URL.