Dimer method¶

The dimer method of Henkelman and Jónsson [DM_HJonsson99] with improvements by Heyden et al. [DM_HBK05] and Kästner and Sherwood [DM_KastnerS08] for estimating the lowest Eigenmode using only first derivatives.

An overview may be found in Olsen et al. [DM_OKH+04].

The dimer separation is set in the [Main] section with the finiteDifference parameter.

The method of Melander et al. [DM_MLJonsson15] is also implemented for use with gas phase systems.

Note

There is no point removing rotations for an extended system. Rotation removal may be more detrimental as noted in Goswami [DM_Gos25].

Added in version 2.5: The Gaussian Process Regression accelerated dimer in C++ from Goswami et al. [DM_GMK+25].

Rotation backends¶

The softest-mode estimate used in the dimer rotation step can be chosen with rotation_backend under [Dimer] (default classical). Min-mode-following translation along that mode is unchanged; only how τ / the lowest curvature is obtained differs.

Value	Mode estimation	Notes
`classical`	Constrained dimer rotation (Heyden / Kästner–Sherwood style)	Default; uses `opt_method`, torque limits, and rotation budgets as before
`lanczos`	Finite-difference Lanczos min-mode	Shares the client Lanczos implementation; see Lanczos
`davidson`	Finite-difference Davidson min-mode	Same role as Lanczos with a different iterative subspace
`lor`	Locally optimal rotation (LOR), Algorithm I	Leng et al. [DM_LGSL13]; at most one new FD force per rotation iteration via Hessian–vector products and force translation of prior H·N / H·F⊥ products

Added in version TBD: rotation_backend (classical | lanczos | davidson | lor). The LOR path implements Leng et al. [DM_LGSL13]: 2×2 then 3×3 Ritz problems in the rotation subspace, force translation for H·P₃ (linear action of H on the unit Gram–Schmidt residual of the trial direction, not Gram–Schmidt on H·P in ambient space), residual / rotations_max / stall stops, and a best-mode restore when the Ritz sequence is non-monotonic under FD noise.

LOR stops when the relative residual ‖F_⊥‖ / (|C_N| + 1) < max(1e-3, lor_residual_tol) (default lor_residual_tol = 0.1). That parameter is not classical torque_min (angular torque for the constrained rotation loop); it only applies when rotation_backend = lor. Budget is rotations_max (default 10; values <= 0 fall back to 10). Exhausting the budget without meeting the residual stop sets rotationDidConverge false on ImprovedDimer.

Example:

[Dimer]
improved = True
rotation_backend = lor
lor_residual_tol = 0.1
rotations_max = 20

improved = True (default) uses ImprovedDimer; non-classical backends skip the classical IDimerRot loop and call the selected min-mode backend through a shared dispatch helper. Rotation iteration budgets for LOR follow rotations_max (not geometry max_iterations).

Configuration¶

[Dimer]

References¶

[DM_Gos25]

Rohit Goswami. Bayesian hierarchical models for quantitative estimates for performance metrics applied to saddle search algorithms. AIP Advances, 15(8):85210, August 2025. doi:10.1063/5.0283639.

[DM_GMK+25]

Rohit Goswami, Maxim Masterov, Satish Kamath, Alejandro Peña-Torres, and Hannes Jónsson. Efficient implementation of gaussian process regression accelerated saddle point searches with application to molecular reactions. May 2025. arXiv:2505.12519, doi:10.48550/arXiv.2505.12519.

[DM_HJonsson99]

Graeme Henkelman and Hannes Jónsson. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. The Journal of Chemical Physics, 111(15):7010–7022, October 1999. doi:10.1063/1.480097.

[DM_HBK05]

Andreas Heyden, Alexis T. Bell, and Frerich J. Keil. Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method. The Journal of Chemical Physics, 123(22):224101, December 2005. doi:10.1063/1.2104507.

[DM_KastnerS08]

Johannes Kästner and Paul Sherwood. Superlinearly converging dimer method for transition state search. The Journal of Chemical Physics, 128(1):014106, January 2008. doi:10.1063/1.2815812.

[DM_LGSL13] (1,2)

Jing Leng, Weiguo Gao, Cheng Shang, and Zhi-Pan Liu. Efficient softest mode finding in transition states calculations. The Journal of Chemical Physics, 138(9):094110, March 2013. doi:10.1063/1.4792644.

[DM_MLJonsson15]

Marko Melander, Kari Laasonen, and Hannes Jónsson. Removing External Degrees of Freedom from Transition-State Search Methods using Quaternions. Journal of Chemical Theory and Computation, 11(3):1055–1062, March 2015. doi:10.1021/ct501155k.

[DM_OKH+04]

R. A. Olsen, G. J. Kroes, G. Henkelman, A. Arnaldsson, and H. Jónsson. Comparison of methods for finding saddle points without knowledge of the final states. The Journal of Chemical Physics, 121(20):9776–9792, November 2004. doi:10.1063/1.1809574.