@article{https://doi.org/10.1107/S0108768193008201,
author = {Christy, A. G.},
title = {Multistage diffusionless pathways for reconstructive phase transitions: application to binary compounds and calcium carbonate},
journal = {Acta Crystallographica Section B},
volume = {49},
number = {6},
pages = {987-996},
doi = {https://doi.org/10.1107/S0108768193008201},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1107/S0108768193008201},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1107/S0108768193008201},
year = {1993}
}


@article{doi:10.1021/acs.nanolett.2c01939,
author = {Wang, Kang and Molteni, Carla and Haynes, Peter D.},
title = {Localized Soft Vibrational Modes and Coherent Structural Phase Transformations in Rutile TiO2 Nanoparticles under Negative Pressure},
journal = {Nano Letters},
volume = {22},
number = {14},
pages = {5922-5928},
year = {2022},
doi = {10.1021/acs.nanolett.2c01939},
note ={PMID: 35797495},
URL = {https://doi.org/10.1021/acs.nanolett.2c01939},
eprint = {https://doi.org/10.1021/acs.nanolett.2c01939}
}


@article{sicher,
    author = {Sicher, Michael and Mohr, Stephan and Goedecker, Stefan},
    title = {Efficient moves for global geometry optimization methods and their application to binary systems},
    journal = {The Journal of Chemical Physics},
    volume = {134},
    number = {4},
    pages = {044106},
    year = {2011},
    month = {01},
    abstract = {We show that molecular dynamics based moves in the minima hopping method are more efficient than saddle point crossing moves. For binary systems we incorporate identity exchange moves in a way that allows one to avoid the generation of high energy configurations. Using this modified minima hopping method, we re-examine the binary Lennard-Jones benchmark system with up to 100 atoms and we find a large number of new putative global minima.},
    issn = {0021-9606},
    doi = {10.1063/1.3530590},
    url = {https://doi.org/10.1063/1.3530590},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.3530590/13788474/044106\_1\_online.pdf},
}


@article{doi:10.1021/nl504192u,
author = {Li, Hui and Li, Lei and Pedersen, Andreas and Gao, Yi and Khetrapal, Navneet and Jónsson, Hannes and Zeng, Xiao Cheng},
title = {Magic-Number Gold Nanoclusters with Diameters from 1 to 3.5 nm: Relative Stability and Catalytic Activity for CO Oxidation},
journal = {Nano Letters},
volume = {15},
number = {1},
pages = {682-688},
year = {2015},
doi = {10.1021/nl504192u},
note ={PMID: 25493586},
URL = {https://doi.org/10.1021/nl504192u},
eprint = {https://doi.org/10.1021/nl504192u}
}


@article{bao,
  title = {Structure of large gold clusters obtained by global optimization using the minima hopping method},
  author = {Bao, Kuo and Goedecker, Stefan and Koga, Kenji and Lan\ifmmode \mbox{\c{c}}\else \c{c}\fi{}on, Fr\'ed\'eric and Neelov, Alexey},
  journal = {Phys. Rev. B},
  volume = {79},
  issue = {4},
  pages = {041405},
  numpages = {4},
  year = {2009},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.79.041405},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.79.041405}
}


@Article{Plessow,
author ="Plessow, Philipp N.",
title  ="The transformation of cuboctahedral to icosahedral nanoparticles: atomic structure and dynamics",
journal  ="Phys. Chem. Chem. Phys.",
year  ="2020",
volume  ="22",
issue  ="23",
pages  ="12939-12945",
publisher  ="The Royal Society of Chemistry",
doi  ="10.1039/D0CP01651A",
url  ="http://dx.doi.org/10.1039/D0CP01651A",
abstract  ="The rearrangement of transition metal nanoparticles from cuboctahedral to icosahedral structures is studied for up to 923 atoms. The atomic structure and temperature dependence of the transition are investigated with a well-defined collective variable. This collective variable describes the folding of the square fcc(100) facets into two triangular facets through a linear combination of the diagonals of all fcc(100) facets of all shells of the particle. Activation barriers are determined through harmonic transition state theory and constrained molecular dynamics simulations based on force field potentials. These calculations predict an activation entropy larger than 1 meV K−1{,} leading to strongly temperature dependent activation barriers. Density functional theory calculations were additionally performed both as single point calculations and as full optimizations. Cu{,} Ag{,} Au and Ni clusters show low barriers for concerted{,} symmetric transition up to the 309-atomic clusters. In contrast{,} for Pd{,} Pt{,} Rh and Ir higher barriers are required{,} already for the 147-atomic clusters. With increasing barriers{,} an asymmetric but still concerted rearrangement becomes energetically more favorable than the fully symmetric transformation. The material-dependence of the transition can be correlated with the melting point of the bulk metals."}


@Article{D3NH00291H,
author ="Dearg, Malcolm and Roncaglia, Cesare and Nelli, Diana and El Koraychy, El Yakout and Ferrando, Riccardo and Slater, Thomas J. A. and Palmer, Richard E.",
title  ="Frame-by-frame observations of structure fluctuations in single mass-selected Au clusters using aberration-corrected electron microscopy",
journal  ="Nanoscale Horiz.",
year  ="2024",
volume  ="9",
issue  ="1",
pages  ="143-147",
publisher  ="The Royal Society of Chemistry",
doi  ="10.1039/D3NH00291H",
url  ="http://dx.doi.org/10.1039/D3NH00291H",
abstract  ="The multi-dimensional potential energy surface (PES) of a nanoparticle{,} such as a bare cluster of metal atoms{,} controls both the structure and dynamic behaviour of the particle. These properties are the subject of numerous theoretical simulations. However{,} quantitative experimental measurements of critical PES parameters are needed to regulate the models employed in the theoretical work. Experimental measurements of parameters are currently few in number{,} while model parameters taken from bulk systems may not be suitable for nanosystems. Here we describe a new measurement methodology{,} in which the isomer structures of a single deposited nanocluster are obtained frame-by-frame in an aberration-corrected scanning transmission electron microscope (ac-STEM) in high angle annular dark field (HAADF) mode. Several gold clusters containing 309 ± 15 atoms were analysed individually after deposition from a mass-selected cluster source onto an amorphous carbon film. The main isomers identified are icosahedral (Ih){,} decahedral (Dh) and face-centred-cubic (fcc) (the bulk structure){,} alongside many amorphous (glassy) structures. The results{,} which are broadly consistent with static ac-STEM measurements of an ensemble of such clusters{,} open the way to dynamic measurements of many different nanoparticles of diverse sizes{,} shapes and compositions."}

@article{foster2018experimental,
  title={Experimental determination of the energy difference between competing isomers of deposited, size-selected gold nanoclusters},
  author={Foster, DM and Ferrando, R and Palmer, RE},
  journal={Nature communications},
  volume={9},
  number={1},
  pages={1323},
  year={2018},
  publisher={Nature Publishing Group UK London}
}
@article{behler2007generalized,
  title={Generalized neural-network representation of high-dimensional potential-energy surfaces},
  author={Behler, J{\"o}rg and Parrinello, Michele},
  journal={Physical review letters},
  volume={98},
  number={14},
  pages={146401},
  year={2007},
  publisher={APS}
}
@article{deringer2021gaussian,
  title={Gaussian process regression for materials and molecules},
  author={Deringer, Volker L and Bart{\'o}k, Albert P and Bernstein, Noam and Wilkins, David M and Ceriotti, Michele and Cs{\'a}nyi, G{\'a}bor},
  journal={Chemical Reviews},
  volume={121},
  number={16},
  pages={10073--10141},
  year={2021},
  publisher={ACS Publications}
}
@article{behler2011atom,
  title={Atom-centered symmetry functions for constructing high-dimensional neural network potentials},
  author={Behler, J{\"o}rg},
  journal={The Journal of chemical physics},
  volume={134},
  number={7},
  year={2011},
  publisher={AIP Publishing}
}
@article{bartok2013representing,
  title={On representing chemical environments},
  author={Bart{\'o}k, Albert P and Kondor, Risi and Cs{\'a}nyi, G{\'a}bor},
  journal={Physical Review B},
  volume={87},
  number={18},
  pages={184115},
  year={2013},
  publisher={APS}
}
@article{zhu2016fingerprint,
  title={A fingerprint based metric for measuring similarities of crystalline structures},
  author={Zhu, Li and Amsler, Maximilian and Fuhrer, Tobias and Schaefer, Bastian and Faraji, Somayeh and Rostami, Samare and Ghasemi, S Alireza and Sadeghi, Ali and Grauzinyte, Migle and Wolverton, Chris and others},
  journal={The Journal of chemical physics},
  volume={144},
  number={3},
  year={2016},
  publisher={AIP Publishing}
}
@article{drautz2019atomic,
  title={Atomic cluster expansion for accurate and transferable interatomic potentials},
  author={Drautz, Ralf},
  journal={Physical Review B},
  volume={99},
  number={1},
  pages={014104},
  year={2019},
  publisher={APS}
}
@article{wales1997global,
  title={Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms},
  author={Wales, David J and Doye, Jonathan PK},
  journal={The Journal of Physical Chemistry A},
  volume={101},
  number={28},
  pages={5111--5116},
  year={1997},
  publisher={ACS Publications}
}
@article{barkema1996event,
  title={Event-based relaxation of continuous disordered systems},
  author={Barkema, GT and Mousseau, Normand},
  journal={Physical review letters},
  volume={77},
  number={21},
  pages={4358},
  year={1996},
  publisher={APS}
}
@article{mousseau1998traveling,
  title={Traveling through potential energy landscapes of disordered materials: The activation-relaxation technique},
  author={Mousseau, Normand and Barkema, GT},
  journal={Physical Review E},
  volume={57},
  number={2},
  pages={2419},
  year={1998},
  publisher={APS}
}
@article{malek2000dynamics,
  title={Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique},
  author={Malek, Rachid and Mousseau, Normand},
  journal={Physical Review E},
  volume={62},
  number={6},
  pages={7723},
  year={2000},
  publisher={APS}
}
@article{machado2011optimized,
  title={Optimized energy landscape exploration using the ab initio based activation-relaxation technique},
  author={Machado-Charry, Eduardo and B{\'e}land, Laurent Karim and Caliste, Damien and Genovese, Luigi and Deutsch, Thierry and Mousseau, Normand and Pochet, Pascal},
  journal={The Journal of chemical physics},
  volume={135},
  number={3},
  year={2011},
  publisher={AIP Publishing}
}
@article{mousseau2012activation,
  title={The activation-relaxation technique: Art nouveau and kinetic art},
  author={Mousseau, Normand and B{\'e}land, Laurent Karim and Brommer, Peter and Joly, Jean-Fran{\c{c}}ois and El-Mellouhi, Fedwa and Machado-Charry, Eduardo and Marinica, Mihai-Cosmin and Pochet, Pascal},
  journal={Journal of Atomic and Molecular Physics},
  volume={2012},
  year={2012},
  publisher={Hindawi}
}
@article{schonborn2009performance,
  title={The performance of minima hopping and evolutionary algorithms for cluster structure prediction},
  author={Sch{\"o}nborn, Sandro E and Goedecker, Stefan and Roy, Shantanu and Oganov, Artem R},
  journal={The Journal of chemical physics},
  volume={130},
  number={14},
  year={2009},
  publisher={AIP Publishing},
  pages={}
}
@article{goedecker2004minima,
  title={Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems},
  author={Goedecker, Stefan},
  journal={The Journal of chemical physics},
  volume={120},
  number={21},
  pages={9911--9917},
  year={2004},
  publisher={American Institute of Physics}
}
@article{roy2008bell,
  title={Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization},
  author={Roy, Shantanu and Goedecker, Stefan and Hellmann, Vladimir},
  journal={Physical Review E},
  volume={77},
  number={5},
  pages={056707},
  year={2008},
  publisher={APS}
}
@article{amsler2010crystal,
  title={Crystal structure prediction using the minima hopping method},
  author={Amsler, Maximilian and Goedecker, Stefan},
  journal={The Journal of chemical physics},
  volume={133},
  number={22},
  year={2010},
  publisher={AIP Publishing},
  pages={}
}
@article{de2019finding,
  title={Finding reaction pathways with optimal atomic index mappings},
  author={De, Deb Sankar and Krummenacher, Marco and Schaefer, Bastian and Goedecker, Stefan},
  journal={Physical Review Letters},
  volume={123},
  number={20},
  pages={206102},
  year={2019},
  publisher={APS}
}
@article{koga2004size,
  title={Size-and temperature-dependent structural transitions in gold nanoparticles},
  author={Koga, Kenji and Ikeshoji, Tamio and Sugawara, Ko-ichi},
  journal={Physical review letters},
  volume={92},
  number={11},
  pages={115507},
  year={2004},
  publisher={APS}
}
@book{jensen2017introduction,
  title={Introduction to computational chemistry},
  author={Jensen, Frank},
  year={2017},
  publisher={John wiley \& sons}
}
@article{batzner2023,
  title={E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials},
  author={Batzner, Simon and Musaelian, Albert and Sun, Lixin and Geiger, Mario and Mailoa, Jonathan P and Kornbluth, Mordechai and Molinari, Nicola and Smidt, Tess E and Kozinsky, Boris},
  journal={Nature communications},
  volume={13},
  number={1},
  pages={2453},
  year={2022},
  publisher={Nature Publishing Group UK London}
}
@inproceedings{kozinsky2023scaling,
  title={Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size},
  author={Kozinsky, Boris and Musaelian, Albert and Johansson, Anders and Batzner, Simon},
  booktitle={Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis},
  pages={1--12},
  year={2023}
}
@article{tan2025high,
  title={High-performance training and inference for deep equivariant interatomic potentials},
  author={Tan, Chuin Wei and Descoteaux, Marc L and Kotak, Mit and Nascimento, Gabriel de Miranda and Kavanagh, Se{\'a}n R and Zichi, Laura and Wang, Menghang and Saluja, Aadit and Hu, Yizhong R and Smidt, Tess and others},
  journal={arXiv preprint arXiv:2504.16068},
  year={2025},
  pages={}
}
@article{gupta1981lattice,
  title={Lattice relaxation at a metal surface},
  author={Gupta, Raju P},
  journal={Physical Review B},
  volume={23},
  number={12},
  pages={6265},
  year={1981},
  publisher={APS}
}
@article{o2018grain,
  title={Grain boundary phase transformations in PtAu and relevance to thermal stabilization of bulk nanocrystalline metals},
  author={O’Brien, CJ and Barr, CM and Price, PM and Hattar, K and Foiles, SM},
  journal={Journal of Materials Science},
  volume={53},
  number={4},
  pages={2911--2927},
  year={2018},
  publisher={Springer}
}
@article{daw1984embedded,
  title={Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals},
  author={Daw, Murray S and Baskes, Michael I},
  journal={Physical Review B},
  volume={29},
  number={12},
  pages={6443},
  year={1984},
  publisher={APS}
}
@incollection{jonsson1998nudged,
  title={Nudged elastic band method for finding minimum energy paths of transitions},
  author={J{\'o}nsson, Hannes and Mills, Greg and Jacobsen, Karsten W},
  booktitle={Classical and quantum dynamics in condensed phase simulations},
  pages={385--404},
  year={1998},
  publisher={World Scientific}
}
@article{blochl1994projector,
  title={Projector augmented-wave method},
  author={Bl{\"o}chl, Peter E},
  journal={Physical review B},
  volume={50},
  number={24},
  pages={17953},
  year={1994},
  publisher={APS}
}
@article{kresse1999ultrasoft,
  title={From ultrasoft pseudopotentials to the projector augmented-wave method},
  author={Kresse, Georg and Joubert, Daniel},
  journal={Physical review b},
  volume={59},
  number={3},
  pages={1758},
  year={1999},
  publisher={APS}
}
@article{kresse1996efficient,
  title={Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set},
  author={Kresse, Georg and Furthm{\"u}ller, J{\"u}rgen},
  journal={Physical review B},
  volume={54},
  number={16},
  pages={11169},
  year={1996},
  publisher={APS}
}
@article{kresse1996efficiency,
  title={Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set},
  author={Kresse, Georg and Furthm{\"u}ller, J{\"u}rgen},
  journal={Computational materials science},
  volume={6},
  number={1},
  pages={15--50},
  year={1996},
  publisher={Elsevier}
}
@article{perdew1996generalized,
  title={Generalized gradient approximation made simple},
  author={Perdew, John P and Burke, Kieron and Ernzerhof, Matthias},
  journal={Physical review letters},
  volume={77},
  number={18},
  pages={3865},
  year={1996},
  publisher={APS}
}
@article{larsen2017atomic,
  title={The atomic simulation environment—a Python library for working with atoms},
  author={Larsen, Ask Hjorth and Mortensen, Jens J{\o}rgen and Blomqvist, Jakob and Castelli, Ivano E and Christensen, Rune and Du{\l}ak, Marcin and Friis, Jesper and Groves, Michael N and Hammer, Bj{\o}rk and Hargus, Cory and others},
  journal={Journal of Physics: Condensed Matter},
  volume={29},
  number={27},
  pages={273002},
  year={2017},
  publisher={IOP Publishing}
}
@article{griffiths2017optimal,
  title={Optimal alignment of structures for finite and periodic systems},
  author={Griffiths, Matthew and Niblett, Samuel P and Wales, David J},
  journal={Journal of chemical theory and computation},
  volume={13},
  number={10},
  pages={4914--4931},
  year={2017},
  publisher={ACS Publications}
}
@article{bitzek2006structural,
  title={Structural relaxation made simple},
  author={Bitzek, Erik and Koskinen, Pekka and G{\"a}hler, Franz and Moseler, Michael and Gumbsch, Peter},
  journal={Physical review letters},
  volume={97},
  number={17},
  pages={170201},
  year={2006},
  publisher={APS}
}
@article{schebarchov2018structure,
  title={Structure, thermodynamics, and rearrangement mechanisms in gold clusters—insights from the energy landscapes framework},
  author={Schebarchov, D and Baletto, F and Wales, DJ},
  journal={Nanoscale},
  volume={10},
  number={4},
  pages={2004--2016},
  year={2018},
  publisher={Royal Society of Chemistry}
}
@article{wang2012determination,
  title={Determination of the Ground-State Atomic Structures of Size-Selected Au Nanoclusters<? format?> by Electron-Beam-Induced Transformation},
  author={Wang, ZW and Palmer, RE},
  journal={Physical review letters},
  volume={108},
  number={24},
  pages={245502},
  year={2012},
  publisher={APS}
}
%NANOPartRefs
@article{daniel2004gold,
  title={Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology},
  author={Daniel, Marie-Christine and Astruc, Didier},
  journal={Chemical reviews},
  volume={104},
  number={1},
  pages={293--346},
  year={2004},
  publisher={ACS Publications}
}
@article{rodriguez2025structure,
  title={Structure search for transition metal clusters. Towards a rational understanding of their size-dependent properties},
  author={Rodr{\'\i}guez-Kessler, Peter L and Mu{\~n}oz-Castro, Alvaro},
  journal={Inorganica Chimica Acta},
  volume={574},
  pages={122376},
  year={2025},
  publisher={Elsevier}
}
@article{vidotti2011biosensors,
  title={Biosensors based on gold nanostructures},
  author={Vidotti, Marcio and Carvalhal, Rafaela F and Mendes, Renata K and Ferreira, Danielle and Kubota, Lauro T},
  journal={Journal of the Brazilian Chemical Society},
  volume={22},
  pages={3--20},
  year={2011},
  publisher={SciELO Brasil}
}
@article{portales2008probing,
  title={Probing atomic ordering and multiple twinning in metal nanocrystals through their vibrations},
  author={Portales, H and Goubet, N and Saviot, Lucien and Adichtchev, S and Murray, DB and Mermet, A and Duval, E and Pileni, M-P},
  journal={Proceedings of the National Academy of Sciences},
  volume={105},
  number={39},
  pages={14784--14789},
  year={2008},
  publisher={National Acad Sciences}
}

@article{settem2024gold,
  title={Gold Clusters on Graphene/Graphite—Structure and Energy Landscape},
  author={Settem, Manoj and Gianetti, Melisa M and Guerra, Roberto and Manini, Nicola and Ferrando, Riccardo and Giacomello, Alberto},
  journal={Small Science},
  volume={4},
  number={9},
  pages={2400078},
  year={2024},
  publisher={Wiley Online Library}
}
@article{baletto2005structural,
  title={Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects},
  author={Baletto, Francesca and Ferrando, Riccardo},
  journal={Reviews of modern physics},
  volume={77},
  number={1},
  pages={371--423},
  year={2005},
  publisher={APS}
}
@article{jindal2020structural,
  title={Structural evolution in gold nanoparticles using artificial neural network based interatomic potentials},
  author={Jindal, Shweta and Bulusu, Satya S},
  journal={The Journal of Chemical Physics},
  volume={152},
  number={15},
  year={2020},
  publisher={AIP Publishing},
  pages = {}
}



@book{bersuker2006jahn,
  title={The Jahn-teller effect},
  author={Bersuker, Isaac B},
  year={2006},
  publisher={Cambridge Cambridge University Press}
}
@article{hakkinen2004symmetry,
  title={Symmetry and electronic structure of noble-metal nanoparticles and the role of relativity},
  author={H{\"a}kkinen, Hannu and Moseler, Michael and Kostko, Oleg and Morgner, Nina and Hoffmann, Margarita Astruc and v. Issendorff, Bernd},
  journal={Physical review letters},
  volume={93},
  number={9},
  pages={093401},
  year={2004},
  publisher={APS}
}

@article{garzon1998lowest,
  title={Lowest energy structures of gold nanoclusters},
  author={Garz{\'o}n, IL and Michaelian, K and Beltr{\'a}n, MR and Posada-Amarillas, A and Ordej{\'o}n, P and Artacho, E and S{\'a}nchez-Portal, D and Soler, JM},
  journal={Physical review letters},
  volume={81},
  number={8},
  pages={1600},
  year={1998},
  publisher={APS}
}

@article{PhysRevLett.81.1600,
  title = {Lowest Energy Structures of Gold Nanoclusters},
  author = {Garz\'on, I. L. and Michaelian, K. and Beltr\'an, M. R. and Posada-Amarillas, A. and Ordej\'on, P. and Artacho, E. and S\'anchez-Portal, D. and Soler, J. M.},
  journal = {Phys. Rev. Lett.},
  volume = {81},
  issue = {8},
  pages = {1600--1603},
  numpages = {0},
  year = {1998},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.81.1600},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.81.1600}
}

@article{sommer2024compass,
  title={COMPASS: Double-ended saddle point search as a constrained optimization problem},
  author={Sommer-J{\"o}rgensen, Martin and Goedecker, Stefan},
  journal={The Journal of Chemical Physics},
  volume={160},
  number={6},
  year={2024},
  publisher={AIP Publishing},
  pages={}
}
@article{jahn1937stability,
  title={Stability of polyatomic molecules in degenerate electronic states-I—Orbital degeneracy},
  author={Jahn, Hermann Arthur and Teller, Edward},
  journal={Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences},
  volume={161},
  number={905},
  pages={220--235},
  year={1937},
  publisher={The Royal Society London}
}


@article{BEP,
author = {Bell, Ronald Percy },
title = {The theory of reactions involving proton transfers},
journal = {Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences},
volume = {154},
number = {882},
pages = {414-429},
year = {1936},
doi = {10.1098/rspa.1936.0060},

URL = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1936.0060},
eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1936.0060}
,
    abstract = { The majority of reactions catalysed by acids or bases have been found to be catalysed not only by hydrogen ions (or hydroxyl ions), but by all molecular species which are acids or bases in the sense of modern definitions of these terms. In all such reactions which have been investigated quantitatively, the relative efficiencies of different catalysts have been found to conform to the following relation, due to Brönsted, kc = GK1x, (1) where kc is the catalytic constant of a given acid (or base), and K1 is its electrolytic dissociation constant. G and x are constants for the same substrate at the same temperature. This relation holds accurately for a series of acids or bases of the same type (e. g., carboxylic acids, or amino bases), and roughly for different types. Equation (1) is essentially empirical, and it is the object of the present paper to provide it with some theoretical basis. }
}


@article{PhysRevLett.123.206102,
  title = {Finding Reaction Pathways with Optimal Atomic Index Mappings},
  author = {De, Deb Sankar and Krummenacher, Marco and Schaefer, Bastian and Goedecker, Stefan},
  journal = {Phys. Rev. Lett.},
  volume = {123},
  issue = {20},
  pages = {206102},
  numpages = {6},
  year = {2019},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.123.206102},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.206102}
}

@article{krummenacher2024performing,
  title={Performing highly efficient Minima Hopping structure predictions using the Atomic Simulation Environment (ASE)},
  author={Krummenacher, Marco and Gubler, Moritz and Finkler, Jonas A and Huber, Hannes and Sommer-J{\"o}rgensen, Martin and Goedecker, Stefan},
  journal={SoftwareX},
  volume={25},
  pages={101632},
  year={2024},
  publisher={Elsevier}
}

@Article{D2MA01088G,
author ="Fisicaro, Giuseppe and Schaefer, Bastian and Finkler, Jonas A. and Goedecker, Stefan",
title  ="Principles of isomer stability in small clusters",
journal  ="Mater. Adv.",
year  ="2023",
volume  ="4",
issue  ="7",
pages  ="1746-1768",
publisher  ="RSC",
doi  ="10.1039/D2MA01088G",
url  ="http://dx.doi.org/10.1039/D2MA01088G",
abstract  ="In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral{,} anionic and cationic isomers{,} moving left to right across the third period of the periodic table and varying the number of atoms n and the cluster charge state q (Xqn{,} with X = {Na{,} Mg{,} Al{,} Si{,} Ge}{,} q = −1{,} 0{,} 1{,} 2). We use structural descriptors such as bond lengths and atomic coordination numbers{,} the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures{,} that frequently have a high degree of symmetry{,} the Kohn–Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells{,} a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster{,} since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers{,} whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters."}


@article{gong2010first,
  title={First-principles study of metal--graphene interfaces},
  author={Gong, Cheng and Lee, Geunsik and Shan, Bin and Vogel, Eric M and Wallace, Robert M and Cho, Kyeongjae},
  journal={Journal of Applied Physics},
  volume={108},
  number={12},
  year={2010},
   pages={123711},
  publisher={AIP Publishing}
}
@article{giovannetti2008doping,
  title={Doping graphene with metal contacts},
  author={Giovannetti, GAKPA and Khomyakov, Petr A and Brocks, Geert and Karpan, VM vd and van den Brink, Jeroen and Kelly, Paul J},
  journal={Physical review letters},
  volume={101},
  number={2},
  pages={026803},
  year={2008},
  publisher={APS}
}

@article{blum2009ab,
  title={Ab initio molecular simulations with numeric atom-centered orbitals},
  author={Blum, Volker and Gehrke, Ralf and Hanke, Felix and Havu, Paula and Havu, Ville and Ren, Xinguo and Reuter, Karsten and Scheffler, Matthias},
  journal={Computer Physics Communications},
  volume={180},
  number={11},
  pages={2175--2196},
  year={2009},
  publisher={Elsevier}
}
@article{marek2014elpa,
  title={The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science},
  author={Marek, Andreas and Blum, Volker and Johanni, Rainer and Havu, Ville and Lang, Bruno and Auckenthaler, Thomas and Heinecke, Alexander and Bungartz, Hans-Joachim and Lederer, Hermann},
  journal={Journal of Physics: Condensed Matter},
  volume={26},
  number={21},
  pages={213201},
  year={2014},
  publisher={IOP Publishing}
}