| 參考文獻 |
[1] Lim C C and Lai S K 2020 Enantiomeric Transitions in the Chiral Cluster Au 15 Studied
by a Reaction Coordinate Deduced from Molecular Dynamics Simulations J. Phys.
Chem. A 124 8679–91
[2] Lai S K and Lim C C 2021 Neutral gold clusters studied by the isothermal Brownian-
type molecular dynamics and metadynamics molecular dynamics simulations J.
Comput. Chem. 42 310–25
[3] Lim C C and Lai S K 2022 Metadynamics molecular dynamics and isothermal
Brownian-type molecular dynamics simulations for the chiralcluster Au 18 J. Phys.:
Condens. Matter 34 325201
[4] Lim C C 2018 Studying Neutral Gold Clusters by the Brownian-type and
Metadynamics Molecular Dynamics Simulations (Zhongli, Taiwan, Republic of China:
National Central University)
[5] Lai S K and Lim C C 2024 Stable structures of copper clusters: from enantiomerism
and quantification of chirality using Hausdorff chirality measure to unraveling the
enantiomeric dynamics bymolecular dynamics simulation
[6] Lim C C and Lai S K 2024 Molecular dynamics simulation of chiral cluster Au 10 and
the use of reaction coordinate to unravel its enantiomeric transition
[7] Lim C C and Lai S K 2024 Structures of neutral gold clusters calculated by the DFTB
theory and insights into the structures of clusters at finite temperatures applying
metadynamics molecular dynamics simulations
[8] Humphrey W, Dalke A and Schulten K 1996 VMD: visual molecular dynamics J. Mol.
Graphics 14 33–8
[9] Anon Jmol: an open-source java viewer for chemical structures in 3D.
[10] Polik W F and Schmidt J R 2022 W EB MO : Web ‐ based computational chemistry
calculations in education and research WIREs Comput Mol Sci 12
[11] Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim Th, Suhai S and
Seifert G 1998 Self-consistent-charge density-functional tight-binding method for
simulations of complex materials properties Phys. Rev. B 58 7260–8
[12] Hohenberg P and Kohn W 1964 Inhomogeneous Electron Gas Phys. Rev. 136 B864–71
[13] Kohn W and Sham L J 1965 Self-Consistent Equations Including Exchange and
Correlation Effects Phys. Rev. 140 A1133–8
[14] Yang Y, Yu H, York D, Cui Q and Elstner M 2007 Extension of the Self-Consistent-
Charge Density-Functional Tight-Binding Method: Third-Order Expansion of the
Density Functional Theory Total Energy and Introduction of a Modified Effective
Coulomb Interaction J. Phys. Chem. A 111 10861–73
[15] Gaus M, Goez A and Elstner M 2013 Parametrization and Benchmark of DFTB3 for
Organic Molecules J. Chem. Theory Comput. 9 338–54
[16] Christensen A S, Kubař T, Cui Q and Elstner M 2016 Semiempirical Quantum
Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical
Applications Chem. Rev. 116 5301–37
[17] Aradi B, Hourahine B and Frauenheim Th 2007 DFTB+, a Sparse Matrix-Based
Implementation of the DFTB Method J. Phys. Chem. A 111 5678–84
[18] Anon AMS DFTB, SCM, Theoretical Chemistry, Vrije Universiteit
[19] Wales D J and Doye J P K 1997 Global Optimization by Basin-Hopping and the
Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms J.
Phys. Chem. A 101 5111–6
[20] Li Z and Scheraga H A 1987 Monte Carlo-minimization approach to the multiple-
minima problem in protein folding. Proc. Natl. Acad. Sci. U.S.A. 84 6611–5
[21] Yen T W and Lai S K 2015 Use of density functional theory method to calculate
structures of neutral carbon clusters C n (3 ≤ n ≤ 24) and study their variability of
structural forms J. Chem. Phys. 142 084313
[22] Liu D C and Nocedal J 1989 On the limited memory BFGS method for large scale
optimization Math. Program. 45 503–28
[23] Lai S K, Lin W D, Wu K L, Li W H and Lee K C 2004 Specific heat and Lindemann-
like parameter of metallic clusters: Mono- and polyvalent metals J. Chem. Phys. 121
1487–98
[24] Bulgac A and Kusnezov D 1990 Canonical ensemble averages from
pseudomicrocanonical dynamics Phys. Rev. A 42 5045–8
[25] Kusnezov D, Bulgac A and Bauer W 1990 Canonical ensembles from chaos I: classical
systems Ann. Phys. 204 155–62
[26] Bulgac A and Kusnezov D 1992 Thermal properties of Na 8 microclusters Phys. Rev.
Lett. 68 1335–8
[27] Bulgac A and Kusnezov D 1992 Phase transitions in Na 7 –Na 9 microclusters Phys. Rev.
B 45 1988–97
[28] Kusnezov D and Bulgac A 1992 Canonical ensembles from chaos II: Constrained
dynamical systems Annals of Physics 214 180–218
[29] Ju N and Bulgac A 1993 Finite-temperature properties of sodium clusters Phys. Rev. B
48 2721–32
[30] Nosé S 1984 A unified formulation of the constant temperature molecular dynamics
methods J. Chem. Phys. 81 511–9
[31] Borgs C and Kotecký R 1995 Surface-induced finite-size effects for first-order phase
transitions J. Stat. Phys. 79 43–115
[32] Ashcroft N W and Mermin N D 1976 Solid State Physics (Cengage Learning)
[33] Santarossa G, Vargas A, Iannuzzi M and Baiker A 2010 Free energy surface of two-
and three-dimensional transitions of Au 12 nanoclusters obtained by ab initio
metadynamics Phys. Rev. B 81 174205
[34] Barducci A, Bussi G and Parrinello M 2008 Well-Tempered Metadynamics: A
Smoothly Converging and Tunable Free-Energy Method Phys. Rev. Lett. 100 020603
[35] Bonomi M, Branduardi D, Bussi G, Camilloni C, Provasi D, Raiteri P, Donadio D,
Marinelli F, Pietrucci F, Broglia R A and Parrinello M 2009 PLUMED: A portable
plugin for free-energy calculations with molecular dynamics Comput. Phys. Commun.
180 1961–72
[36] Laio A and Parrinello M 2002 Escaping free-energy minima Proc. Natl. Acad. Sci.
U.S.A. 99 12562–6
[37] Laio A and Gervasio F L 2008 Metadynamics: a method to simulate rare events and
reconstruct the free energy in biophysics, chemistry and material science Rep. Prog.
Phys. 71 126601
[38] Barducci A, Bonomi M and Parrinello M 2011 Metadynamics WIREs Comput Mol Sci
1 826–43
[39] Valsson O, Tiwary P and Parrinello M 2016 Enhancing Important Fluctuations: Rare
Events and Metadynamics from a Conceptual Viewpoint Annu. Rev. Phys. Chem. 67
159–84
[40] Ballester P J and Richards W G 2007 Ultrafast shape recognition to search compound
databases for similar molecular shapes J. Comput. Chem. 28 1711–23
[41] Buda A B, Auf der Heyde T and Mislow K 1992 On Quantifying Chirality Angew.
Chem. Int. Ed. Engl. 31 989–1007
[42] Buda A B and Mislow K 1992 A Hausdorff chirality measure J. Am. Chem. Soc. 114
6006–12
[43] Hausdorff F 1957 Set Theory, translated by J. R. Auman et al. (New York: Chelsea
Publishing Company)
[44] Garzón I L, Beltrán M R, González G, Gutierrez-González I, Michaelian K, Reyes-
Nava J A and Rodríguez-Hernández J I 2003 Chirality, defects, and disorder in gold
clusters Eur. Phys. J. D. 24 105–9
[45] Pelayo J J, Whetten R L and Garzón I L 2015 Geometric Quantification of Chirality in
Ligand-Protected Metal Clusters J. Phys. Chem. C 119 28666–78
[46] Pelayo J J, Valencia I, García A P, Chang L, López M, Toffoli D, Stener M, Fortunelli
A and Garzón I L 2018 Chirality in bare and ligand-protected metal nanoclusters Adv.
Phys.: X 3 1509727
[47] Yen T-W, Lim T-L, Yoon T-L and Lai S K 2017 Studying the varied shapes of gold
clusters by an elegant optimization algorithm that hybridizes the density functional
tight-binding theory and the density functional theory Comput. Phys. Commun. 220
143–9
[48] Rahmani N S 2017 Calculate the lowest energy structures of Au and Ag clusters by the
DFT-based theory and using the Au conformations obtained compare classically and
quantum-mechanically their valence electron charge distributions (Zhongli, Taiwan,
Republic of China: National Central University)
[49] Lai S K and Maftuhin W 2019 An efficient optimization algorithm that hybridizes
DFTB and DFT theories both operated within the modified basin hopping method
Comput. Phys. Commun. 236 164–75
[50] Yen T W and Lai S K 2018 The subtlety of resolving orbital angular momenta in
calculating Hubbard U parameters in the density functional tight-binding theory and its
delicacy is illustrated by the calculated magnetic properties of carbon clusters Theor.
Chem. Acc. 137 134
[51] Lai S K, Setiyawati I, Yen T W and Tang Y H 2017 Studying lowest energy structures
of carbon clusters by bond-order empirical potentials Theor. Chem. Acc. 136 20
[52] Tseng C C 2020 Chirality in Ag clusters by the isothermal Brownian-type molecular
dynamics simulations
[53] Bolhuis P G, Chandler D, Dellago C and Geissler P L 2002 TRANSITION PATH
SAMPLING : Throwing Ropes Over Rough Mountain Passes, in the Dark Annu. Rev.
Phys. Chem. 53 291–318
[54] Fernández E M, Soler J M, Garzón I L and Balbás L C 2004 Trends in the structure
and bonding of noble metal clusters Phys. Rev. B 70 165403
[55] Oliveira L F L, Tarrat N, Cuny J, Morillo J, Lemoine D, Spiegelman F and Rapacioli
M 2016 Benchmarking Density Functional Based Tight-Binding for Silver and Gold
Materials: From Small Clusters to Bulk J. Phys. Chem. A 120 8469–83
[56] Tarrat N, Rapacioli M, Cuny J, Morillo J, Heully J-L and Spiegelman F 2017 Global
optimization of neutral and charged 20- and 55-atom silver and gold clusters at the
DFTB level Comput. Theor. Chem. 1107 102–14
[57] Zhang M, Dong X, Wang Z, Li H, Li S, Zhao X and Zang S 2020 AIE Triggers the
Circularly Polarized Luminescence of Atomically Precise Enantiomeric Copper(I)
Alkynyl Clusters Angew. Chem. 132 10138–44
[58] Zhang C, Li S, Dong X and Zang S 2021 Circularly polarized luminescence of
agglomerate emitters Aggregate 2
[59] Frenzel J, Oliveira A F, Jardillier N, Heine T and Seifert G 2004 Semirelativistic, self-
consistent charge SlaterKoster tables for densityfunctional based tightbinding (DFTB)
for materials science simulations 3
[60] te Velde G, Bickelhaupt F M, Baerends E J, Fonseca Guerra C, van Gisbergen S J A,
Snijders J G and Ziegler T 2001 Chemistry with ADF Journal of Computational
Chemistry 22 931–67
[61] Versluis L and Ziegler T 1988 The determination of molecular structures by density
functional theory. The evaluation of analytical energy gradients by numerical
integration The Journal of Chemical Physics 88 322–8
[62] Fan L and Ziegler T 1991 Optimization of molecular structures by self ‐ consistent and
nonlocal density ‐ functional theory The Journal of Chemical Physics 95 7401–8
[63] Jaque P and Toro-Labbé A 2002 Characterization of copper clusters through the use of
density functional theory reactivity descriptors J. Chem. Phys. 117 3208–18
[64] Jug K, Zimmermann B, Calaminici P and Köster A M 2002 Structure and stability of
small copper clusters J. Chem. Phys. 116 4497
[65] Cao Z, Wang Y, Zhu J, Wu W and Zhang Q 2002 Static Polarizabilities of Copper
Cluster Monocarbonyls Cu n CO (n = 2−13) and Selectivity of CO Adsorption on Copper
Clusters J. Phys. Chem. B 106 9649–54
[66] Guvelioglu G H, Ma P, He X, Forrey R C and Cheng H 2005 Evolution of Small
Copper Clusters and Dissociative Chemisorption of Hydrogen Phys. Rev. Lett. 94
026103
[67] Itoh M, Kumar V and Kawazoe Y 2005 GROWTH BEHAVIORS AND
ELECTRONIC STRUCTURES OF Na AND Cu NANOCLUSTERS: THE ROLE OF
sp–d HYBRIDIZATION Int. J. Mod. Phys. B 19 2421–6
[68] Li S, Alemany M M G and Chelikowsky J R 2006 Real space pseudopotential
calculations for copper clusters J. Chem. Phys. 125 034311
[69] Itoh M, Kumar V, Adschiri T and Kawazoe Y 2009 Comprehensive study of sodium,
copper, and silver clusters over a wide range of sizes 2≤ N ≤75 J. Chem. Phys. 131
174510
[70] Kahnouji H, Najafvandzadeh H, Hashemifar S J, Alaei M and Akbarzadeh H 2015
Density-functional study of the pure and palladium doped small copper and silver
clusters Chem. Phys. Lett. 630 101–5
[71] Li C-G, Shen Z-G, Hu Y-F, Tang Y-N, Chen W-G and Ren B-Z 2017 Insights into the
structures and electronic properties of Cu n+1μ and Cu n S μ (n = 1–12; μ = 0, ±1) clusters
Sci Rep 7 1345
[72] Chaves A S, Piotrowski M J and Da Silva J L F 2017 Evolution of the structural,
energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30
TM n systems for n = 2–15): a density functional theory investigation Phys. Chem.
Chem. Phys. 19 15484–502
[73] Massobrio C, Pasquarello A and Car R 1995 Structural and electronic properties of
small copper clusters: a first principles study Chem. Phys. Lett. 238 215–21
[74] Yang M, Jackson K A, Koehler C, Frauenheim T and Jellinek J 2006 Structure and
shape variations in intermediate-size copper clusters J. Chem. Phys. 124 024308
[75] Lecoultre S, Rydlo A, Félix C, Buttet J, Gilb S and Harbich W 2011 Optical absorption
of small copper clusters in neon: Cu n , (n = 1–9) J. Chem. Phys. 134 074303
[76] Calaminici P, Köster A M and Gómez-Sandoval Z 2007 Density Functional Study of
the Structure and Properties of Cu 9 and Cu 9− J. Chem. Theory Comput. 3 905–13
[77] Guzmán-Ramírez G, Aguilera-Granja F and Robles J 2010 DFT and GEGA genetic
algorithm optimized structures of Cu nν (ν=±1,0,2; n=3-13) clusters Eur. Phys. J. D 57
49–60
[78] Erkoç Ş and Shaltaf R 1999 Monte Carlo computer simulation of copper clusters Phys.
Rev. A 60 3053–7
[79] Darby S, Mortimer-Jones T V, Johnston R L and Roberts C 2002 Theoretical study of
Cu–Au nanoalloy clusters using a genetic algorithm J. Chem. Phys. 116 1536–50
[80] Kabir M, Mookerjee A and Bhattacharya A K 2004 Structure and stability of copper
clusters: A tight-binding molecular dynamics study Phys. Rev. A 69 043203
[81] Kabir M, Mookerjee A and Bhattacharya A K 2004 Copper clusters: electronic effect
dominates over geometric effect Eur. Phys. J. D 31 477–85
[82] Allen R J, Warren P B and ten Wolde P R 2005 Sampling Rare Switching Events in
Biochemical Networks Phys. Rev. Lett. 94 018104
[83] Hussain S and Haji-Akbari A 2020 Studying rare events using forward-flux sampling:
Recent breakthroughs and future outlook J. Chem. Phys. 152 060901
[84] Garzón I L and Jellinek J 1991 Melting of gold microclusters Z. Phys. D. 20 235–8
[85] Jellinek J and Garzón I L 1991 Structural and dynamical properties of transition metal
clusters Z. Phys. D. 20 239–42
[86] Zewail A H 2000 Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond J.
Phys. Chem. A 104 5660–94
[87] Jackson K A 1993 First-principles study of the structural and electronic properties of
Cu clusters Phys. Rev. B 47 9715–22
[88] Calaminici P, Janetzko F, Köster A M, Mejia-Olvera R and Zuniga-Gutierrez B 2007
Density functional theory optimized basis sets for gradient corrected functionals: 3d
transition metal systems J. Chem. Phys. 126 044108
[89] Calaminici P, Köster A M, Russo N and Salahub D R 1996 A density functional study
of small copper clusters: Cu n (n ⩽ 5) J. Chem. Phys. 105 9546–56
[90] Massobrio C, Pasquarello A and Dal Corso A 1998 Structural and electronic properties
of small Cun clusters using generalized-gradient approximations within density
functional theory J. Chem. Phys. 109 6626–30
[91] Poater A, Duran M, Jaque P, Toro-Labbé A and Solà M 2006 Molecular Structure and
Bonding of Copper Cluster Monocarbonyls Cu n CO (n = 1−9) J. Phys. Chem. B 110
6526–36
[92] Assadollahzadeh B and Schwerdtfeger P 2009 A systematic search for minimum
structures of small gold clusters Au n (n = 2–20) and their electronic properties J. Chem.
Phys. 131 064306
[93] Kumar J, Thomas K G and Liz-Marzán L M 2016 Nanoscale chirality in metal and
semiconductor nanoparticles Chem. Commun. 52 12555–69
[94] Ma W, Xu L, de Moura A F, Wu X, Kuang H, Xu C and Kotov N A 2017 Chiral
Inorganic Nanostructures Chem. Rev. 117 8041–93
[95] Ben-Moshe A, Maoz B M, Govorov A O and Markovich G 2013 Chirality and
chiroptical effects in inorganic nanocrystal systems with plasmon and exciton
resonances Chem. Soc. Rev. 42 7028
[96] Schaaff T G, Knight G, Shafigullin M N, Borkman R F and Whetten R L 1998
Isolation and Selected Properties of a 10.4 kDa Gold:Glutathione Cluster Compound J.
Phys. Chem. B 102 10643–6
[97] Li Y, Yu D, Dai L, Urbas A and Li Q 2011 Organo-Soluble Chiral Thiol-Monolayer-
Protected Gold Nanorods Langmuir 27 98–103
[98] Häkkinen H 2012 The gold–sulfur interface at the nanoscale Nature Chem 4 443–55
[99] Gautier C and Bürgi T 2009 Chiral Gold Nanoparticles ChemPhysChem 10 483–92
[100] Knoppe S and Bürgi T 2014 Chirality in Thiolate-Protected Gold Clusters Acc. Chem.
Res. 47 1318–26
[101] Knoppe, S 2018 Chirality in Ligand-Stabilized Metal Clusters Encyclopedia of
Interfacial Chemistry (Oxford: Elsevier) pp 406–16
[102] Murray R W 2008 Nanoelectrochemistry: Metal Nanoparticles, Nanoelectrodes, and
Nanopores Chem. Rev. 108 2688–720
[103] Han G, Ghosh P and Rotello V M 2007 Functionalized gold nanoparticles for drug
delivery Nanomedicine 2 113–23
[104] Shenhar R and Rotello V M 2003 Nanoparticles: Scaffolds and Building Blocks Acc.
Chem. Res. 36 549–61
[105] Knoppe S, Dolamic I and Bürgi T 2012 Racemization of a Chiral Nanoparticle
Evidences the Flexibility of the Gold–Thiolate Interface J. Am. Chem. Soc. 134 13114–
20
[106] Schaaff T G and Whetten R L 2000 Giant Gold−Glutathione Cluster Compounds:
Intense Optical Activity in Metal-Based Transitions J. Phys. Chem. B 104 2630–41
[107] Wu Z, Gayathri C, Gil R R and Jin R 2009 Probing the Structure and Charge State of
Glutathione-Capped Au 25 (SG) 18 Clusters by NMR and Mass Spectrometry J. Am.
Chem. Soc. 131 6535–42
[108] Zhou M, Tian S, Zeng C, Sfeir M Y, Wu Z and Jin R 2017 Ultrafast Relaxation
Dynamics of Au 38 (SC 2 H 4 Ph) 24 Nanoclusters and Effects of Structural Isomerism J.
Phys. Chem. C 121 10686–93
[109] Senanayake R D, Guidez E B, Neukirch A J, Prezhdo O V and Aikens C M 2018
Theoretical Investigation of Relaxation Dynamics in Au 38 (SH) 24 Thiolate-Protected
Gold Nanoclusters J. Phys. Chem. C 122 16380–8
[110] Yang X, Shi M, Zhou R, Chen X and Chen H 2011 Blending of HAuCl 4 and histidine
in aqueous solution: a simple approach to the Au 10 cluster Nanoscale 3 2596
[111] Trapani M, Castriciano M A, Romeo A, De Luca G, Machado N, Howes B D,
Smulevich G and Scolaro L M 2019 Nanohybrid Assemblies of Porphyrin and Au 10
Cluster Nanoparticles Nanomaterials 9 1026
[112] Lopez N and Nørskov J K 2002 Catalytic CO Oxidation by a Gold Nanoparticle: A
Density Functional Study J. Am. Chem. Soc. 124 11262–3
[113] Lopez N, Janssens T, Clausen B, Xu Y, Mavrikakis M, Bligaard T and Nørskov J 2004
On the origin of the catalytic activity of gold nanoparticles for low-temperature CO
oxidation Journal of Catalysis 223 232–5
[114] Remediakis I N, Lopez N and Nørskov J K 2005 CO Oxidation on Rutile-Supported
Au Nanoparticles Angewandte Chemie International Edition 44 1824–6
[115] Remediakis I N, Lopez N and Nørskov J K 2005 CO oxidation on gold nanoparticles:
Theoretical studies Applied Catalysis A: General 291 13–20
[116] Wang Y-G, Mei D, Glezakou V-A, Li J and Rousseau R 2015 Dynamic formation of
single-atom catalytic active sites on ceria-supported gold nanoparticles Nat Commun 6
6511
[117] Li H, Pei Y and Zeng X C 2010 Two-dimensional to three-dimensional structural
transition of gold cluster Au 10 during soft landing on TiO 2 surface and its effect on CO
oxidation J. Chem. Phys. 133 134707
[118] Johansson M P, Warnke I, Le A and Furche F 2014 At What Size Do Neutral Gold
Clusters Turn Three-Dimensional? J. Phys. Chem. C 118 29370–7
[119] Goldsmith B R, Florian J, Liu J-X, Gruene P, Lyon J T, Rayner D M, Fielicke A,
Scheffler M and Ghiringhelli L M 2019 Two-to-three dimensional transition in neutral
gold clusters: The crucial role of van der Waals interactions and temperature Phys. Rev.
Mater. 3 016002
[120] Kryachko E S and Remacle F 2007 The magic gold cluster Au 20 Int. J. Quantum Chem.
107 2922–34
[121] Molina B, Soto J R and Calles A 2008 DFT normal modes of vibration of the Au 20
cluster Rev. Mex. Fís. 54 314–8
[122] Mullins S-M, Weissker H-Ch, Sinha-Roy R, Pelayo J J, Garzón I L, Whetten R L and
López-Lozano X 2018 Chiral symmetry breaking yields the I-Au 60 perfect golden shell
of singular rigidity Nat Commun 9 3352
[123] Sauceda H E, Salazar F, Pérez L A and Garzón I L 2013 Size and Shape Dependence of
the Vibrational Spectrum and Low-Temperature Specific Heat of Au Nanoparticles J.
Phys. Chem. C 117 25160–8
[124] Cuny J, Tarrat N, Spiegelman F, Huguenot A and Rapacioli M 2018 Density-functional
tight-binding approach for metal clusters, nanoparticles, surfaces and bulk: application
to silver and gold J. Phys.: Condens. Matter 30 303001
[125] Seifert G and Schmidt R 1992 Molecular dynamics and trajectory calculations : the
application of an LCAO-LDA scheme for simulations of cluster-cluster collisions New
J. Chem. 16 1145–7
[126] Porezag D, Frauenheim Th, Köhler Th, Seifert G and Kaschner R 1995 Construction
of tight-binding-like potentials on the basis of density-functional theory: Application to
carbon Phys. Rev. B 51 12947–57
[127] Frauenheim Th, Seifert G, Elsterner M, Hajnal Z, Jungnickel G, Porezag D, Suhai S
and Scholz R 2000 A Self-Consistent Charge Density-Functional Based Tight-Binding
Method for Predictive Materials Simulations in Physics, Chemistry and Biology Phys.
Stat. Sol. (b) 217 41–62
[128] Frauenheim T, Seifert G, Elstner M, Niehaus T, Köhler C, Amkreutz M, Sternberg M,
Hajnal Z, Di Carlo A and Suhai S 2002 Atomistic simulations of complex materials:
ground-state and excited-state properties J. Phys.: Condens. Matter 14 3015–47
[129] Oliveira A F, Seifert G, Heine T and Duarte H A 2009 Density-functional based tight-
binding: an approximate DFT method J. Braz. Chem. Soc. 20 1193–205
[130] Koskinen P, Häkkinen H, Seifert G, Sanna S, Frauenheim T and Moseler M 2006
Density-functional based tight-binding study of small gold clusters New J. Phys. 8 9
[131] Koskinen P and Mäkinen V 2009 Density-functional tight-binding for beginners
Comput. Mater. Sci. 47 237–53
[132] Mäkinen V, Koskinen P and Häkkinen H 2013 Modeling thiolate-protected gold
clusters with density-functional tight-binding Eur. Phys. J. D 67 38
[133] Spiegelman F, Tarrat N, Cuny J, Dontot L, Posenitskiy E, Martí C, Simon A and
Rapacioli M 2020 Density-functional tight-binding: basic concepts and applications to
molecules and clusters Adv. Phys.: X 5 1710252
[134] Johnston R L 2003 Evolving better nanoparticles: Genetic algorithms for optimising
cluster geometries Dalton Trans. 4193
[135] Mitchel M 1996 An Introduction to Genetic Algorithms (MIT Press: Cambridge, MA)
[136] Vargas A, Santarossa G, Iannuzzi M and Baiker A 2009 Fluxionality of gold
nanoparticles investigated by Born-Oppenheimer molecular dynamics Phys. Rev. B 80
195421
[137] Garzón I L, Reyes-Nava J A, Rodríguez-Hernández J I, Sigal I, Beltrán M R and
Michaelian K 2002 Chirality in bare and passivated gold nanoclusters Phys. Rev. B 66
073403
[138] Lechtken A, Schooss D, Stairs J R, Blom M N, Furche F, Morgner N, Kostko O, von
Issendorff B and Kappes M M 2007 Au 34− : A Chiral Gold Cluster? Angew. Chem. Int.
Ed. 46 2944–8
[139] Santizo I E, Hidalgo F, Pérez L A, Noguez C and Garzón I L 2008 Intrinsic Chirality in
Bare Gold Nanoclusters: The Au 34− Case J. Phys. Chem. C 112 17533–9
[140] Qian H, Eckenhoff W T, Zhu Y, Pintauer T and Jin R 2010 Total Structure
Determination of Thiolate-Protected Au 38 Nanoparticles J. Am. Chem. Soc. 132 8280–1
[141] Tlahuice-Flores A, Whetten R L and Jose-Yacaman M 2013 Vibrational Normal Modes
of Small Thiolate-Protected Gold Clusters J. Phys. Chem. C 117 12191–8
[142] Maioli P, Stoll T, Sauceda H E, Valencia I, Demessence A, Bertorelle F, Crut A, Vallée
F, Garzón I L, Cerullo G and Del Fatti N 2018 Mechanical Vibrations of Atomically
Defined Metal Clusters: From Nano- to Molecular-Size Oscillators Nano Lett. 18
6842–9
[143] Malola S and Häkkinen H 2019 Chiral Inversion of Thiolate-Protected Gold
Nanoclusters via Core Reconstruction without Breaking a Au–S Bond J. Am. Chem.
Soc. 141 6006–12
[144] Fiorin G, Klein M L and Hénin J 2013 Using collective variables to drive molecular
dynamics simulations Mol. Phys. 111 3345–62
[145] Fihey A, Hettich C, Touzeau J, Maurel F, Perrier A, Köhler C, Aradi B and Frauenheim
T 2015 SCC-DFTB parameters for simulating hybrid gold-thiolates compounds J.
Comput. Chem. 36 2075–87
[146] Perdew J P, Burke K and Ernzerhof M 1996 Generalized Gradient Approximation
Made Simple Phys. Rev. Lett. 77 3865–8
[147] Perdew J P, Burke K and Ernzerhof M 1997 Generalized Gradient Approximation
Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] Phys. Rev. Lett. 78 1396–1396
[148] Allen R J, Frenkel D and ten Wolde P R 2006 Simulating rare events in equilibrium or
nonequilibrium stochastic systems J. Chem. Phys. 124 024102
[149] Box G E P, Jenkins G M, Reinsel G C and Ljung G M 2015 Time Series Analysis:
Forecasting and Control, 5th ed (John Wiley & Sons)
[150] Vishwanathan K 2017 Symmetry of Gold Neutral Clusters Au 3-20 and Normal Modes of
Vibrations by using the Numerical Finite Difference Method with Density-Functional
Tight-Binding(DFTB) Approach Arch Chem Res 02
[151] Dong Y and Springborg M 2007 Global structure optimization study on Au 2-20 Eur.
Phys. J. D 43 15–8
[152] Van den Bossche M 2019 DFTB-Assisted Global Structure Optimization of 13- and
55-Atom Late Transition Metal Clusters J. Phys. Chem. A 123 3038–45
[153] Lopez-Acevedo O, Akola J, Whetten R L, Grönbeck H and Häkkinen H 2009 Structure
and Bonding in the Ubiquitous Icosahedral Metallic Gold Cluster Au 144 (SR) 60 J. Phys.
Chem. C 113 5035–8
[154] Yan N, Xia N, Liao L, Zhu M, Jin F, Jin R and Wu Z 2018 Unraveling the long-
pursued Au 144 structure by x-ray crystallography Sci. Adv. 4 eaat7259
[155] Gu X, Bulusu S, Li X, Zeng X C, Li J, Gong X G and Wang L-S 2007 Au 34− : A
Fluxional Core−Shell Cluster J. Phys. Chem. C 111 8228–32
[156] Pyykkö P 2004 Theoretical Chemistry of Gold Angew. Chem. Int. Ed. 43 4412–56
[157] Pyykkö P 2008 Theoretical chemistry of gold. III Chem. Soc. Rev. 37 1967
[158] Gorin D J and Toste F D 2007 Relativistic effects in homogeneous gold catalysis
Nature 446 395–403
[159] Häkkinen H 2008 Atomic and electronic structure of gold clusters: understanding
flakes, cages and superatoms from simple concepts Chem. Soc. Rev. 37 1847
[160] Zhang J, Sasaki K, Sutter E and Adzic R R 2007 Stabilization of Platinum Oxygen-
Reduction Electrocatalysts Using Gold Clusters Science 315 220–2
[161] Turner M, Golovko V B, Vaughan O P H, Abdulkin P, Berenguer-Murcia A, Tikhov M
S, Johnson B F G and Lambert R M 2008 Selective oxidation with dioxygen by gold
nanoparticle catalysts derived from 55-atom clusters Nature 454 981–3
[162] Oliver-Meseguer J, Cabrero-Antonino J R, Domínguez I, Leyva-Pérez A and Corma A
2012 Small Gold Clusters Formed in Solution Give Reaction Turnover Numbers of 10 7
at Room Temperature Science 338 1452–5
[163] Schmidbaur H and Schier A 2012 Aurophilic interactions as a subject of current
research: an up-date Chem. Soc. Rev. 41 370–412
[164] Kepp K P 2016 A Quantitative Scale of Oxophilicity and Thiophilicity Inorg. Chem. 55
9461–70
[165] Wang B, Yin S, Wang G, Buldum A and Zhao J 2001 Novel Structures and Properties
of Gold Nanowires Phys. Rev. Lett. 86 2046–9
[166] Mannini M, Pineider F, Sainctavit P, Danieli C, Otero E, Sciancalepore C, Talarico A
M, Arrio M-A, Cornia A, Gatteschi D and Sessoli R 2009 Magnetic memory of a
single-molecule quantum magnet wired to a gold surface Nature Mater 8 194–7
[167] Gautier C and Bürgi T 2008 Chiral Metal Surfaces and Nanoparticles Chimia 62 465
[168] Baiker A 1997 Progress in asymmetric heterogeneous catalysis: Design of novel
chirally modified platinum metal catalysts J. Mol. Catal. A 115 473–93
[169] Wells P B and Wilkinson A G 1998 Platinum group metals as heterogeneous
enantioselective catalysts Top. Catal. 5 39–50
[170] Liu J, Chen L, Cui H, Zhang J, Zhang L and Su C-Y 2014 Applications of metal–
organic frameworks in heterogeneous supramolecular catalysis Chem. Soc. Rev. 43
6011–61
[171] El-Sepelgy O, Haseloff S, Alamsetti S K and Schneider C 2014 Brønsted Acid
Catalyzed, Conjugate Addition of β-Dicarbonyls to In Situ Generated ortho-Quinone
Methides-Enantioselective Synthesis of 4-Aryl-4 H-Chromenes Angew. Chem. Int. Ed.
53 7923–7
[172] Olesiak-Banska J, Waszkielewicz M and Samoc M 2018 Two-photon chiro-optical
properties of gold Au 25 nanoclusters Phys. Chem. Chem. Phys. 20 24523–6
[173] Swasey S M, Karimova N, Aikens C M, Schultz D E, Simon A J and Gwinn E G 2014
Chiral Electronic Transitions in Fluorescent Silver Clusters Stabilized by DNA ACS
Nano 8 6883–92
[174] Wei J J, Schafmeister C, Bird G, Paul A, Naaman R and Waldeck D H 2006 Molecular
Chirality and Charge Transfer through Self-Assembled Scaffold Monolayers J. Phys.
Chem. B 110 1301–8
[175] Gansel J K, Thiel M, Rill M S, Decker M, Bade K, Saile V, von Freymann G, Linden S
and Wegener M 2009 Gold Helix Photonic Metamaterial as Broadband Circular
Polarizer Science 325 1513–5
[176] Dreaden E C, Alkilany A M, Huang X, Murphy C J and El-Sayed M A 2012 The
golden age: gold nanoparticles for biomedicine Chem. Soc. Rev. 41 2740–79
[177] Das M, Shim K H, An S S A and Yi D K 2011 Review on gold nanoparticles and their
applications Toxicol. Environ. Health Sci. 3 193–205
[178] Lim C C and Lai S K Molecular dynamics simulation of chiral cluster Au 10 and the use
of reaction coordinate to unravel its enantiomeric transition
[179] Goldsmith M-R, George C B, Zuber G, Naaman R, Waldeck D H, Wipf P and Beratan
D N 2006 The chiroptical signature of achiral metal clusters induced by dissymmetric
adsorbates Phys. Chem. Chem. Phys. 8 63–7
[180] Humblot V, Haq S, Muryn C, Hofer W A and Raval R 2002 From Local Adsorption
Stresses to Chiral Surfaces: (R,R)-Tartaric Acid on Ni(110) J. Am. Chem. Soc. 124 503–
10
[181] Yao H, Fukui T and Kimura K 2007 Chiroptical Responses of D -/ L -Penicillamine-
Capped Gold Clusters under Perturbations of Temperature Change and Phase Transfer
J. Phys. Chem. C 111 14968–76
[182] Gautier C and Bürgi T 2006 Chiral N -Isobutyryl-cysteine Protected Gold
Nanoparticles: Preparation, Size Selection, and Optical Activity in the UV−vis and
Infrared J. Am. Chem. Soc. 128 11079–87
[183] Gautier C and Bürgi T 2008 Chiral Inversion of Gold Nanoparticles J. Am. Chem. Soc.
130 7077–84
[184] Noguez C and Garzón I L 2009 Optically active metal nanoparticles Chem. Soc. Rev.
38 757
[185] Bussi G and Laio A 2020 Using metadynamics to explore complex free-energy
landscapes Nat Rev Phys 2 200–12
[186] E W, Ren W and Vanden-Eijnden E 2005 Finite Temperature String Method for the
Study of Rare Events J. Phys. Chem. B 109 6688–93
[187] Chandler D 1978 Statistical mechanics of isomerization dynamics in liquids and the
transition state approximation J. Chem. Phys. 68 2959
[188] van Erp T S, Moroni D and Bolhuis P G 2003 A novel path sampling method for the
calculation of rate constants J. Chem. Phys. 118 7762–74
[189] Barnett R N and Landman U 1993 Born-Oppenheimer molecular-dynamics
simulations of finite systems: Structure and dynamics of (H 2 O) 2 Phys. Rev. B 48 2081–
97
[190] Kühne T D 2014 Second generation Car-Parrinello molecular dynamics WIREs
Comput. Mol. Sci. 4 391–406
[191] Ashcroft N W and Stroud D 1978 Theory of the Thermodynamics of Simple Liquid
Metals Solid State Physics vol 33, ed H Ehrenreich, F Seitz and D Turnbull (Academic
Press) pp 1–81
[192] Evans R 1978 Microscopic Structure and Dynamics of Liquids ed J Dupuy and AJ
Dianoux
[193] Lai S K 1988 Accurate calculation of the Helmholtz free energy for simple liquid
metals Phys. Rev. A 38 5707–13
[194] Schwerdtfeger P 2003 Gold Goes Nano—From Small Clusters to Low-Dimensional
Assemblies Angew. Chem. Int. Ed. 42 1892–5
[195] Daniel M-C and Astruc D 2004 Gold Nanoparticles: Assembly, Supramolecular
Chemistry, Quantum-Size-Related Properties, and Applications toward Biology,
Catalysis, and Nanotechnology Chem. Rev. 104 293–346
[196] Saha K, Agasti S S, Kim C, Li X and Rotello V M 2012 Gold Nanoparticles in
Chemical and Biological Sensing Chem. Rev. 112 2739–79
[197] Teles J H, Brode S and Chabanas M 1998 Cationic Gold(I) Complexes: Highly
Efficient Catalysts for the Addition of Alcohols to Alkynes Angew. Chem. Int. Ed. 37
1415–8
[198] Veenboer R M P, Dupuy S and Nolan S P 2015 Stereoselective Gold(I)-Catalyzed
Intermolecular Hydroalkoxlation of Alkynes ACS Catal. 5 1330–4
[199] Rudolph M and Hashmi A S K 2011 Heterocycles from gold catalysis Chem. Commun.
47 6536–44
[200] Ma Z and Dai S 2011 Development of novel supported gold catalysts: A materials
perspective Nano Res. 4 3–32
[201] Austin L A, Mackey M A, Dreaden E C and El-Sayed M A 2014 The optical,
photothermal, and facile surface chemical properties of gold and silver nanoparticles in
biodiagnostics, therapy, and drug delivery Arch. Toxicol. 88 1391–417
[202] Jiang W, Gao Y, Xu D, Liu F and Wang Z 2017 Structural Influence on Superatomic
Orbitals of Typical Gold Nanostructure Building Blocks J. Electron. Mater. 46 3938–41
[203] Fa W, Luo C and Dong J 2005 Bulk fragment and tubelike structures of Au N (N =
2−26) Phys. Rev. B 72 205428
[204] Walker A V 2005 Structure and energetics of small gold nanoclusters and their positive
ions J. Chem. Phys. 122 094310
[205] Xiao L, Tollberg B, Hu X and Wang L 2006 Structural study of gold clusters J. Chem.
Phys. 124 114309
[206] Li X-B, Wang H-Y, Yang X-D, Zhu Z-H and Tang Y-J 2007 Size dependence of the
structures and energetic and electronic properties of gold clusters J. Chem. Phys. 126
084505
[207] Idrobo J C, Walkosz W, Yip S F, Öğüt S, Wang J and Jellinek J 2007 Static
polarizabilities and optical absorption spectra of gold clusters (Au n , n = 2–14 and 20)
from first principles Phys. Rev. B 76 205422
[208] Zanti G and Peeters D 2010 DFT Study of Bimetallic Palladium−Gold Clusters Pd n
Au m of Low Nuclearities (n + m ≤ 14) J. Phys. Chem. A 114 10345–56
[209] Fernández E M and Balbás L C 2011 GGA versus van der Waals density functional
results for mixed gold/mercury molecules and pure Au and Hg cluster properties Phys.
Chem. Chem. Phys. 13 20863–70
[210] Götz D A, Schäfer R and Schwerdtfeger P 2013 The performance of density functional
and wavefunction-based methods for 2D and 3D structures of Au 10 J. Comput. Chem.
34 1975–81
[211] Shayeghi A, Götz D, Davis J B A, Schäfer R and Johnston R L 2015 Pool-BCGA: a
parallelised generation-free genetic algorithm for the ab initio global optimisation of
nanoalloy clusters Phys. Chem. Chem. Phys. 17 2104–12
[212] Kinaci A, Narayanan B, Sen F G, Davis M J, Gray S K, Sankaranarayanan S K R S
and Chan M K Y 2016 Unraveling the Planar-Globular Transition in Gold Nanoclusters
through Evolutionary Search Sci. Rep. 6 34974
[213] Nhat P V, Si N T, Leszczynski J and Nguyen M T 2017 Another look at structure of
gold clusters Aun from perspective of phenomenological shell model Chem. Phys. 493
140–8
[214] Wu P, Liu Q and Chen G 2019 Nonlocal effects on the structural transition of gold
clusters from planar to three-dimensional geometries RSC Adv. 9 20989–99
[215] Khatun M, Majumdar R S and Anoop A 2019 A Global Optimizer for Nanoclusters
Front. Chem. 7 644
[216] Persaud R R, Chen M and Dixon D A 2020 Prediction of Structures and Atomization
Energies of Coinage Metals, (M) n , n < 20: Extrapolation of Normalized Clustering
Energies to Predict the Cohesive Energy J. Phys. Chem. A 124 1775–86
[217] Nhat P V, Si N T, Anh N N K, Duong L V and Nguyen M T 2022 The Au 12 Gold
Cluster: Preference for a Non-Planar Structure Symmetry 14 1665
[218] Nhat P V, Si N T, Hang N T N and Nguyen M T 2022 The lowest-energy structure of
the gold cluster Au 10 : planar vs. nonplanar? Phys. Chem. Chem. Phys. 24 42–7
[219] Pyykko P 1988 Relativistic effects in structural chemistry Chem. Rev. 88 563–94
[220] Häkkinen H, Moseler M and Landman U 2002 Bonding in Cu, Ag, and Au Clusters:
Relativistic Effects, Trends, and Surprises Phys. Rev. Lett. 89 033401
[221] Gruene P, Rayner D M, Redlich B, van der Meer A F G, Lyon J T, Meijer G and
Fielicke A 2008 Structures of Neutral Au 7 , Au 19 , and Au 20 Clusters in the Gas Phase
Science 321 674–6
[222] Ghiringhelli L M, Gruene P, Lyon J T, Rayner D M, Meijer G, Fielicke A and Scheffler
M 2013 Not so loosely bound rare gas atoms: finite-temperature vibrational fingerprints
of neutral gold-cluster complexes New J. Phys. 15 083003
[223] Gruene P, Butschke B, Lyon J T, Rayner D M and Fielicke A 2014 Far-IR Spectra of
Small Neutral Gold Clusters in the Gas Phase Z. Phys. Chem. 228 337–50
[224] Lecoultre S, Rydlo A, Félix C, Buttet J, Gilb S and Harbich W 2011 UV–visible
absorption of small gold clusters in neon: Au n (n = 1–5 and 7–9) J. Chem. Phys. 134
074302
[225] Li X-T, Xu S-G, Yang X-B and Zhao Y-J 2020 Energy landscape of Au 13 : a global view
of structure transformation Phys. Chem. Chem. Phys. 22 4402–6
[226] Henkelman G and Jónsson H 2000 Improved tangent estimate in the nudged elastic
band method for finding minimum energy paths and saddle points J. Chem. Phys. 113
9978–85
[227] Beret E C, Ghiringhelli L M and Scheffler M 2011 Free gold clusters: beyond the
static, monostructure description Faraday Discuss. 152 153–67
[228] Rapacioli M, Schön J C and Tarrat N 2021 Exploring energy landscapes at the DFTB
quantum level using the threshold algorithm: the case of the anionic metal cluster Au 20–
Theor. Chem. Acc. 140 85
[229] Gaus M, Cui Q and Elstner M 2011 DFTB3: Extension of the Self-Consistent-Charge
Density-Functional Tight-Binding Method (SCC-DFTB) J. Chem. Theory Comput. 7
931–48
[230] Mitchell I, Aradi B and Page A J 2018 Density functional tight binding ‐ based free
energy simulations in the DFTB+ program J. Comput. Chem. 39 2452–8
[231] Rincon L, Hasmy A, Marquez M and Gonzalez C 2011 A perturbatively corrected
tight-binding method with hybridization: Application to gold nanoparticles Chem. Phys.
Lett. 503 171–5
[232] Idrobo J C, Walkosz W, Yip S F, Öğüt S, Wang J and Jellinek J 2008 Erratum: Static
polarizabilities and optical absorption spectra of gold clusters ( Au n , n = 2 − 14 and
20) from first principles [Phys. Rev. B 76 , 205422 (2007)] Phys. Rev. B 77 249903
[233] Zanti G and Peeters D 2013 Electronic structure analysis of small gold clusters Au m (m
≤ 16) by density functional theory Theor. Chem. Acc. 132 1300
[234] Tao J, Perdew J P, Staroverov V N and Scuseria G E 2003 Climbing the Density
Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed
for Molecules and Solids Phys. Rev. Lett. 91 146401
[235] David J, Guerra D and Restrepo A 2012 Structure, stability and bonding in the 1 Au 10
clusters Chem. Phys. Lett. 539–540 64–9
[236] Lee H M, Ge M, Sahu B R, Tarakeshwar P and Kim K S 2003 Geometrical and
Electronic Structures of Gold, Silver, and Gold−Silver Binary Clusters: Origins of
Ductility of Gold and Gold−Silver Alloy Formation J. Phys. Chem. B 107 9994–10005
[237] Shirts M R and Chodera J D 2008 Statistically optimal analysis of samples from
multiple equilibrium states J. Chem. Phys. 129 124105 |
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