Bibliography#

The method references are stored in docs/source/references.bib.

[Bak86]

Jon Baker. An algorithm for the location of transition states. Journal of Computational Chemistry, 7:385, 1986. doi:10.1002/jcc.540070402.

[CTW05]

Joanne M. Carr, Semen A. Trygubenko, and David J. Wales. Finding pathways between distant local minima. The Journal of Chemical Physics, 122:234903, 2005. doi:10.1063/1.1931587.

[CWT+14]

Samuel T. Chill, Matthew Welborn, Rye Terrell, Liang Zhang, Jean-Claude Berthet, Andreas Pedersen, Hannes Jónsson, and Graeme Henkelman. Benchmarks for characterization of minima, transition states, and pathways in atomic systems. Modelling and Simulation in Materials Science and Engineering, 22:055002, 2014. doi:10.1088/0965-0393/22/5/055002.

[CPR74]

A. R. Curtis, M. J. D. Powell, and J. K. Reid. On the estimation of sparse Jacobian matrices. IMA Journal of Applied Mathematics, 13:117, 1974. doi:10.1093/imamat/13.1.117.

[dMBjorner08]

Leonardo de Moura and Nikolaj Bjørner. Z3: an efficient SMT solver. In Tools and Algorithms for the Construction and Analysis of Systems, 337. 2008. doi:10.1007/978-3-540-78800-3_24.

[Fuk70]

Kenichi Fukui. Formulation of the reaction coordinate. The Journal of Physical Chemistry, 1970. doi:10.1021/j100717a029.

[Fuk81]

Kenichi Fukui. The path of chemical reactions - the irc approach. Accounts of Chemical Research, 1981. doi:10.1021/ar00072a001.

[GMP05]

Assefaw Hadish Gebremedhin, Fredrik Manne, and Alex Pothen. What color is your Jacobian? graph coloring for computing derivatives. SIAM Review, 47:629, 2005. doi:10.1137/S0036144504444711.

[GS89]

Carlos Gonzalez and H. Bernhard Schlegel. An improved algorithm for reaction path following. The Journal of Chemical Physics, 1989. doi:10.1063/1.456010.

[Gos26a]

Rohit Goswami. Reproducible orchestration of best practices for reaction path optimization with the nudged elastic band. 2026. arXiv:2603.14737, doi:10.48550/arXiv.2603.14737.

[Gos26b]

Rohit Goswami. Truncated chains and the dimer. 2026. Cited after doi:10.3389/fchem.2026.1807063. arXiv:2603.10992.

[GCH26]

Rohit Goswami, Samuel T. Chill, and Graeme Henkelman. eOn. 2026. doi:10.5281/zenodo.18529495.

[GGJonsson26]

Rohit Goswami, Miha Gunde, and Hannes Jónsson. Enhanced climbing image nudged elastic band method with Hessian eigenmode alignment. Frontiers in Chemistry, 2026. doi:10.3389/fchem.2026.1807063.

[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, 111:7010, 1999. doi:10.1063/1.480097.

[HJonsson00]

Graeme Henkelman and Hannes Jónsson. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. The Journal of Chemical Physics, 113:9978, 2000. doi:10.1063/1.1323224.

[HUJonsson00]

Graeme Henkelman, Blas P. Uberuaga, and Hannes Jónsson. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. The Journal of Chemical Physics, 113:9901, 2000. doi:10.1063/1.1329672.

[HSZ22]

Eric D. Hermes, Khachik Sarsfield, and Judit Zador. Sella, an open-source automation-friendly molecular saddle point optimizer. Journal of Chemical Theory and Computation, 2022. doi:10.1021/acs.jctc.2c00395.

[Hig02]

Nicholas J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, 2 edition, 2002. doi:10.1137/1.9780898718027.

[IMK77]

Kazuhiro Ishida, Keiji Morokuma, and Andrew Komornicki. The intrinsic reaction coordinate. an ab initio calculation for hnc to hcn. The Journal of Chemical Physics, 1977. doi:10.1063/1.434152.

[KGH16]

Esben L. Kolsbjerg, Michael N. Groves, and Bjørk Hammer. An automated nudged elastic band method. The Journal of Chemical Physics, 145:094107, 2016. doi:10.1063/1.4961868.

[LN89]

Dong C. Liu and Jorge Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45:503, 1989. doi:10.1007/BF01589116.

[MM00]

Rachid Malek and Normand Mousseau. Finding saddle points using the activation-relaxation technique. Physical Review E, 62:7723, 2000. doi:10.1103/PhysRevE.62.7723.

[MBJ+14]

A. Marek, V. Blum, R. Johanni, V. Havu, B. Lang, T. Auckenthaler, A. Heinecke, H.-J. Bungartz, and H. Lederer. The elpa library: scalable parallel eigenvalue solutions for electronic structure theory and computational science. Journal of Physics: Condensed Matter, 2014. doi:10.1088/0953-8984/26/21/213201.

[mC20]

The mathlib Community. The Lean mathematical library. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, 367. 2020. doi:10.1145/3372885.3373824.

[OKH+04]

R. A. Olsen, G. J. Kroes, Graeme Henkelman, Andri Arnaldsson, and Hannes Jónsson. Comparison of methods for finding saddle points without knowledge of the final states. The Journal of Chemical Physics, 121:9776, 2004. doi:10.1063/1.1809574.

[PM88]

Michael Page and James W. McIver. On evaluating the reaction path hamiltonian. The Journal of Chemical Physics, 1988. doi:10.1063/1.454172.

[PT79]

M. J. D. Powell and Ph. L. Toint. On the estimation of sparse Hessian matrices. SIAM Journal on Numerical Analysis, 16:1060, 1979. doi:10.1137/0716078.

[SGRG15]

Bastian Schaefer, S. Alireza Ghasemi, Shantanu Roy, and Stefan Goedecker. Stabilized quasi-Newton optimization of noisy potential energy surfaces. The Journal of Chemical Physics, 142:034112, 2015. doi:10.1063/1.4905665.

[SPSJonsson14]

Søren Smidstrup, Andreas Pedersen, Kurt Stokbro, and Hannes Jónsson. Improved initial guess for minimum energy path calculations. The Journal of Chemical Physics, 140:214106, 2014. doi:10.1063/1.4878664.

[SJorgensenG24]

Martin Sommer-Jörgensen and Stefan Goedecker. COMPASS: double-ended saddle point search as a constrained optimization problem. The Journal of Chemical Physics, 160:064110, 2024. doi:10.1063/5.0186903.

[AsgeirssonBB+21]

Vilhjálmur Ásgeirsson, Benedikt Orri Birgisson, Ragnar Bjornsson, Ute Becker, Frank Neese, Christoph Riplinger, and Hannes Jónsson. Nudged elastic band method for finding minimum energy paths of transitions. Journal of Chemical Theory and Computation, 17:4929, 2021. doi:10.1021/acs.jctc.1c00462.