臺灣博碩士論文加值系統

從奈米級的DNA結構到宏觀的植物卷鬚，自然界存在大量的螺旋構形。而同時包含左旋和右旋螺旋片段的的半螺旋構形（即手性逆轉，或稱為螺旋翻轉）也十分常見，並早在19世紀即在植物卷鬚上被特別研究過。最近，彭旭明和他的實驗團隊在一種特殊類型的分子¬──金屬串分子（EMACs）中發現了半螺旋構形的分子類似物。金屬串分子是一種由一系列金屬構成的中心長鏈和四個左旋或右旋螺旋結構的有機配基連接而成的多核錯合物家族。
在新合成的Mo2NiMo2(tdpa)4X2(X為軸向配基)分子中，顯現出了其配基螺旋性翻轉的可能。我們希望藉由這項工作，發掘此類分子構形的起源與條件，並通過密度泛函理論，證明螺旋配體的形成可歸因於中心金屬-金屬鍵和外圍碳-氮鍵鍵長的不匹配。實驗自三核金屬串(尤其是獨特的非螺旋npo配基金屬串)探討起，並闡述了金屬-金屬鍵長與氮-金屬-金屬-氮二面角之間的關係。此外，我們直接分析Mo2MMo2(tdpa)4(NCS)2 (M=Mn,Fe,Ni)系統以闡明其周圍配基的螺旋翻轉的來由，並說明隨著分子中心處的鉬-鎳鍵長增加，周圍配體中的半螺旋構形能量相對來說逐漸穩定。再者，我們也藉由推廣Su-Schrieffer-Heeger模型，建構與探討中心長鍊中原子的縱向排列與相連配基螺旋性質之間的關係。

Nature abounds with helical conformations in all scales ranging from nanoscale DNA structures to macroscopic tendrils in plants. The related hemihelical conformation that contains left-hand and right-hand helical segments simultaneously, i.e. the reversal of chirality – sometimes also referred to as a helical perversion, in the same chain, also occurs frequently and has been studied particularly in plant tendrils since the 19th century. The molecular analog of helical perversion has only been found recently by Peng and his coworkers in a special type of extended metal atom chains (EMACs), a family of multinuclear coordination complexes consisting of a string of metal atoms connected directly by metal-metal bonding and four surrounding organic ligands in left- or right-handed helical formations. The particular EMACs that show the possibility of helical perversions in its ligands have the general structural formula Mo2MMo2(tpda)4X2, where M=Ni, Co, … and X is the axial ligand. We hope to address the issue on the origin and conditions of their formations in this work. By using the DFT study, we demonstrate that the formation of helical ligands can be attributed to the unbalance of the bond lengths of central metal-metal bonds and peripheral carbon-nitrogen bonds. Starting from trinuclear EMACs, especially the unique nonhelical npo ligand EMACs, we illustrate the relationship between metal-metal bond length and the N-M-M-N dihedral angle, and the effect of ligand helicity on electronic structures. Furthermore, we analyze the Mo2MMo2(tpda)4(NCS)2 system directly to clarify the origin of its helical perversion on the surrounding ligands. Particularly, as the Mo-Ni bond length at the center is increased, the hemihelical conformation in the surrounding ligands is stabilized gradually. Furthermore, we built up a generalized Su-Schreiffer-Heeger model with linked springs representing the surrounding ligands in EMACs so demonstrate the coupling between the central chain longitudinal conformation and the ligand rotational conformation.

誌謝. . .i
摘要 . . . iii
Abstract . . . v
1 Introduction 1
1.1 Helices and Hemihelices . . . 1
1.2 Extended Metal Atom Chains . . . 3
1.2.1 Geometry of EMACs . . . 5
1.2.2 EMACs with Dimolybdenum . . . 8
2 Analysis with Density Functional Calculations on EMACs with Molybdenums . . . 13
2.1 General DFT Computational Details . . . 13
2.2 Tri-nuclear MoNiMo Models . . . 14
2.2.1 Methodology . . . 14
2.2.2 Results and Discussions . . . 16
2.3 Tri-nuclear MoMoM (M=Mn, Fe, Co, Ni) Systems: Comparing dpa and npo Ligands . . . 19
2.3.1 Methodology . . . 19
2.3.2 Results and Discussions . . . 19
2.4 Penta-nuclear MoMoMMoMo (M=Mn, Fe, Ni) system containing two Mo2 units . . . 24
2.4.1 Methodology . . . 24
2.4.2 Results and Discussions . . . 25
2.5 Conclusion . . . 33
3 A Generalized Su-Schrieffer-Heeger Hamiltonian Model for EMACs . . . 35
3.1 A Brief Introduction of Su-Schrieffer-Heeger (SSH) Model in Polyacetylene . . . 36
3.2 Generalizing SSH Model into EMACs chains . . . 40
3.2.1 Building up Generalized SSH Model . . . 40
3.2.2 Results and Discussions . . . 43
3.3 Solitons in Generalized SSH Model: Mimicking EMACs with Helical Perversions . . . 48
3.3.1 Odd-Even Effects . . . 48
3.3.2 Selectivities Between Helical and Hemihelical Ligands: Adding Steric Effects and Nodding Effects . . . 50
4 Conclusions . . . 55
5 Appendix . . . 57
5.1 EMACs Crystals Used in Fig. 1.5 . . . 57
5.2 Atomic coordinates from EMACs Full Optimizations . . . 58
Bibliography . . . 79

[1]James D Watson, Francis HC Crick, et al. Molecular structure of nucleic acids. Nature, 171(4356):737–738, 1953.
[2]Zi Chen, Carmel Majidi, David J Srolovitz, and Mikko Haataja. Tunable helical ribbons. Applied Physics Letters, 98(1):011906, 2011.
[3]Shahaf Armon, Efi Efrati, Raz Kupferman, and Eran Sharon. Geometry and mechanics in the opening of chiral seed pods. Science, 333(6050):1726–1730, 2011.
[4]Yoel Forterre and Jacques Dumais. Generating helices in nature. Science, 333(6050):1715–1716, 2011.
[5]Zi Chen. Shape transition and multi-stability of helical ribbons: a finite element method study. Archive of Applied Mechanics, 85(3):331–338, 2015.
[6]Asa Gray. Gray’s Lessons in Botany & Vegetable Physiology. Ivison, Blakemann, Taylor & Company, 1868.
[7]Charles Darwin. The movements and habits of climbing plants. D. Appleton, 1888.
[8]Alain Goriely and Michael Tabor. Spontaneous helix hand reversal and tendril perversion in climbing plants. Physical Review Letters, 80(7):1564, 1998.
[9]Wei-Chieh Hung, Marc Sigrist, Shao-An Hua, Lai-Chin Wu, Tsai-Jung Liu, Bih- Yaw Jin, Gene-Hsiang Lee, and Shie-Ming Peng. A heteropentanuclear metal string complex [Mo2NiMo2 (tpda)4 (NCS)2] with two linearly aligned quadruply bonded Mo2 units connected by a ni ion and a meso configuration of the complex. Chemical Communications, 52(83):12380–12382, 2016.
[10]Wei-Chieh Hung.Heteropentanuclear metal string complex [Mo2NiMo2(tpda)4(NCS)2] with a meso-configuration of the complex. PhD thesis, National Taiwan University Chemistry Department, 2017.
[11]Thomas J Hurley and Martin Alvin Robinson. Nickel (ii)-2, 2’-dipyridylamine system. i. synthesis and stereochemistry of the complexes. Inorganic Chemistry, 7(1):33–38, 1968.
[12]Sujittra Aduldecha and Brian Hathaway. Crystal structure and electronic properties of tetrakis [µ3-bis (2-pyridyl) amido] dichlorotrinickel (ii)–water–acetone (1/0.23/0.5). Journal of the Chemical Society, Dalton Transactions, (4):993–998, 1991.
[13]Wei-Cheng Chang, Che-Wei Chang, Marc Sigrist, Shao-An Hua, Tsai-Jung Liu, Gene-Hsiang Lee, Bih-Yaw Jin, Chun-hsien Chen, and Shie-Ming Peng. Nonhelical heterometallic [Mo2M(npo)4 (NCS)2 ] string complexes (M= Fe, Co, Ni) with high single-molecule conductance. Chemical Communications, 53(63):8886–8889, 2017.
[14]Wei-Cheng Chang. Syntheses and Studies of Nonhelical Trinuclear (Mo2/M) Heterometallic String Complexes with High Single- Molecule Conductance. PhD the- sis, National Taiwan University Chemistry Department, 2017.
[15]David W Brogden, Jonathan H Christian, Naresh S Dalal, and John F Berry. Completing the series of group vi heterotrimetallic M2Cr(dpa)4Cl2(M2= Cr2, Mo2, MoW and W2) compounds and investigating their metal–metal interactions using density functional theory. Inorganica Chimica Acta, 424:241–247, 2015.
[16]Michael Nippe, Eric Victor, and John F Berry. Do metal–metal multiply-bonded “ligands”have a trans influence? structural and magnetic comparisons of het- erometallic Cr-Cr··· Co and Mo-Mo··· Co interactions. European Journal of Inorganic Chemistry, 2008(36):5569–5572, 2008.
[17]Michael Nippe, Jingfang Wang, Eckhard Bill, Håkon Hope, Naresh S Dalal, and John F Berry. Crystals in which some metal atoms are more equal than others: Inequalities from crystal packing and their spectroscopic/magnetic consequences. Journal of the American Chemical Society, 132(40):14261–14272, 2010.
[18]Michael Nippe, Eckhard Bill, and John F Berry. Group 6 complexes with iron and zinc heterometals: Understanding the structural, spectroscopic, and electrochemical properties of a complete series of MM··· M’ compounds. Inorganic chemistry, 50(16):7650–7661, 2011.
[19]David W Brogden and John F Berry. Heterometallic multiple bonding: Delocalized three-center σ and π bonding in chains of 4d and 5d transition metals. Inorganic chemistry, 53(21):11354–11356, 2014.
[20]David W Brogden and John F Berry. Heterometallic second-row transition metal chain compounds in two charge states: Syntheses, properties, and electronic structures of [Mo–Mo–Ru] 6+/7+ chains. Inorganic chemistry, 54(15):7660–7665, 2015.
[21]En-Che Yang, Ming-Chu Cheng, Ming-Shih Tsai, and Shie-Ming Peng. Structure of a linear unsymmetrical trinuclear cobalt (ii) complex with a localized COII– COII bond: dichlorotetrakis [µ3-bis (2-pyridyl) amido] tricobalt (ii). Journal of the Chemical Society, Chemical Communications, (20):2377–2378, 1994.
[22]Jinn-Tsair Sheu, Cheng-Chen Lin, Ito Chao, Chih-Chieh Wang, and Shie-Ming Peng. Linear trinuclear three-centred metal–metal multiple bonds: synthesis and crystal structure of [M3(dpa)4Cl2][M= Ru II or Rh II, dpa= bis (2-pyridyl) amidoan- ion]. Chemical Communications, (3):315–316, 1996.
[23]Yu-Hua Chen, Chung-Chou Lee, Chih-Chieh Wang, Gene-Hsiang Lee, Shie-Yang Lai, Feng-Yin Li, Chung-Yuan Mou, and Shie-Ming Peng. A linear metal string [Cr7(µ7 teptra)4Cl2] complex with delocalized heptachromium (II) multiple bonds (teptraH3= tetrapyridyltriamine). Chemical Communications, (17):1667–1668, 1999.
[24]Chen-Yu Yeh, Chung-Hsien Chou, Kun-Chih Pan, Chih-Chieh Wang, Gene-Hsiang Lee, Y Oliver Su, and Shie-Ming Peng. Linear pentacobalt complexes: synthesis, structures, and physical properties of neutral and one-electron oxidation com- pounds. Journal of the Chemical Society, Dalton Transactions, (13):2670–2677, 2002.
[25]Ting-Bin Tsao, Gene-Hsiang Lee, Chen-Yu Yeh, and Shie-Ming Peng. Supramolecular assembly of linear trinickel complexes incorporating metalloporphyrins: a novel one-dimensional polymer and oligomer. Dalton Transactions, (8):1465– 1471, 2003.
[26]Ching-Kuo Kuo, Jung-Che Chang, Chen-Yu Yeh, Gene-Hsiang Lee, Chih-Chieh Wang, and Shie-Ming Peng. Synthesis, structures, magnetism and electrochemical properties of triruthenium–acetylide complexes. Dalton Transactions, (22):3696– 3701, 2005.
[27]Chih-Hsien Chien, Jung-Che Chang, Chen-Yu Yeh, Gene-Hsiang Lee, Jim-Min Fang, You Song, and Shie-Ming Peng. Weak antiferromagnetic coupling for novel linear hexanuclear nickel (ii) string complexes (Ni12+) and partial metal– metal bonds in their one-electron reduction products (Ni11+). Dalton Transactions, (26):3249–3256, 2006.
[28]Rayyat H Ismayilov, Wen-Zhen Wang, Rui-Ren Wang, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Four quadruple metal–metal bonds lined up: linear nonachromium (II) metal string complexes. Chemical Communications, (11):1121– 1123, 2007.
[29]Wen-Zhen Wang, Rayyat Huseyn Ismayilov, Gene-Hsiang Lee, Isiah Po-Chun Liu, Chen-Yu Yeh, and Shie-Ming Peng. The nano-scale molecule with the longest delocalized metal–metal bonds: linear heptacobalt (II) metal string complexes [Co7(µ7 − L)4X2]. Dalton Transactions, (8):830–839, 2007.
[30]Marie-Madeleine Rohmer, Isiah Po-Chun Liu, Jheng-Cheng Lin, Mei-Jyun Chiu, Chia-Hwa Lee, Gene-Hsiang Lee, Marc Bénard, Xavier López, and Shie-Ming Peng. Structural, magnetic, and theoretical characterization of a heterometallic polypyridylamide complex. Angewandte Chemie International Edition, 46(19):3533–3536, 2007.
[31]Isiah Po-Chun Liu, Gene-Hsiang Lee, Shie-Ming Peng, Marc Bénard, and Marie- Madeleine Rohmer. Cu- Pd- Cu and Cu- Pt- Cu linear frameworks: Synthesis, magnetic properties, and theoretical analysis of two mixed-metal complexes of dipyridylamide (dpa), isostructural, and isoelectronic with [Cu3(dpa)4Cl2]+. Inorganic Chemistry, 46(23):9602–9608, 2007.
[32]Gin-Chen Huang, Marc Bénard, Marie-Madeleine Rohmer, Long-An Li, Mei-Jyun Chiu, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Ru2M(dpa)4Cl2 (M= Cu, Ni): Synthesis, characterization, and theoretical analysis of asymmetric het- erometal string complexes of the dipyridylamide family. European Journal of Inorganic Chemistry, 2008(11):1767–1777, 2008.
[33]Wen-Zhen Wang, Rayyat Huseyn Ismayilov, Rui-Ren Wang, Yi-Lin Huang, Chen- Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. First stable reduced form of [Co5]+10: fine tuning of linear pentacobalt (ii) complexes containing delocalized metal–metal bonds through ligand modification. Dalton Transactions, (47):6808– 6816, 2008.
[34]Isiah Po-Chun Liu, Chi-Hui Chen, Chi-Fen Chen, Gene-Hsiang Lee, and Shie-Ming Peng. Asymmetric heterometal string complexes: stereochemical control of the unique isomer of (4,0)[CuCuPd(npa)4Cl][PF6] and (4,0) [CuCuPt(npa)4Cl][PF6]. Chemical Communications, (5):577–579, 2009.
[35]Gin-Chen Huang, Isiah Po-Chun Liu, Jau-Huei Kuo, Yi-Lin Huang, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Further investigations of linear trirhodium complexes: experimental and theoretical studies of [Rh3(dpa)4Cl2] and [Rh3(dpa)4Cl2](BF4)[dpa= bis (2-pyridyl) amido anion]. Dalton Transactions, (14):2623–2629, 2009.
[36]Isiah Po-Chun Liu, Chi-Fen Chen, Shao-An Hua, Chi-Hui Chen, Hui-Ting Wang, Gene-Hsiang Lee, and Shie-Ming Peng. Clear evidence of electron delocalization: synthesis, structure, magnetism, EPR and DFT calculation of the asymmetric hexanickel string complex containing a single mixed-valence (Ni2)3+ unit. Dalton Transactions, (18):3571–3573, 2009.
[37]Isiah Po-Chun Liu, Wen-Zhen Wang, and Shie-Ming Peng. New generation of metal string complexes: strengthening metal–metal interaction via naphthyridyl group modulated oligo-α-pyridylamido ligands. Chemical Communications, (29):4323–4331, 2009.
[38]Shao-An Hua, Isiah Po-Chun Liu, Hasan Hasanov, Gin-Chen Huang, Rayyat Huseyn Ismayilov, Chien-Lan Chiu, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Probing the electronic communication of linear heptanickel and nonanickel string complexes by utilizing two redox-active [Ni2(napy)4]3+ moieties. Dalton Transactions, 39(16):3890–3896, 2010.
[39]Kai-Neng Shih, Min-Jie Huang, Hao-Cheng Lu, Ming-Dung Fu, Ching-Kuo Kuo, Gin-Chen Huang, Gene-Hsiang Lee, Chun-hsien Chen, and Shie-Ming Peng. On the tuning of electric conductance of extended metal atom chains via axial ligands for [Ru3(µ3 − dpa)4(X)2]0/+(X = NCS−, CN−). Chemical Communications, 46(8):1338–1340, 2010.
[40]Shao-An Hua, Gin-Chen Huang, Isiah Po-Chun Liu, Jau-Huei Kuo, Ching-Hong Jiang, Chien-Lan Chiu, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Manipulation of electronic structure via supporting ligands: a charge disproportionate model within the linear metal framework of asymmetric nickel string [Ni7(phdptrany)4Cl](PF6). Chemical Communications, 46(27):5018–5020, 2010.
[41]Ming-Chuan Cheng, Isiah Po-Chun Liu, Chan-Hsiang Hsu, Gene-Hsiang Lee, Chun-hsien Chen, and Shie-Ming Peng. New trinuclear metal string complexes containing rigid Hdzp ligands: synthesis, structure, magnetism and DFT calculation (Hdzp= 1, 9-diazaphenoxazine). Dalton Transactions, 41(11):3166–3173, 2012.
[42]Isiah Po-Chun Liu, Chun-hsien Chen, and Shie-Ming Peng. The road to molecular metal wires: The past and recent advances of metal string complexes. Bulletin of Japan Society of Coordination Chemistry, 59:3–10, 2012.
[43]Wen-Zhen Wang, Rayyat Huseyn Ismayilov, Gene-Hsiang Lee, Yi-Lin Huang, Chen-Yu Yeh, Ming-Dung Fu, Chun-hsien Chen, and Shie-Ming Peng. Fine tuning of pentachromium (II) metal string complexes through elaborate design of ligand. New Journal of Chemistry, 36(3):632–637, 2012.
[44]Ming-Chuan Cheng, Chi-Lun Mai, Chen-Yu Yeh, Gene-Hsiang Lee, and Shie-Ming Peng. Facile synthesis of heterotrimetallic metal–string complex [N iCoRh(dpa)4Cl2] through direct metal replacement. Chemical Communica- tions, 49(72):7938–7940, 2013.
[45]Shao-An Hua, Yi-Chou Tsai, and Shie-Ming Peng. A journey of metal-metal bonding beyond cotton’s quadruple bonds. Journal of the Chinese Chemical Society, 61(1):9–26, 2014.
[46]Min-Jie Huang, Shao-An Hua, Ming-Dung Fu, Gin-Chen Huang, Caixia Yin, Chih- Hung Ko, Ching-Kuo Kuo, Chia-Hung Hsu, Gene-Hsiang Lee, Kuan-Yi Ho, et al. The first heteropentanuclear extended metal-atom chain:[Ni+ − Ru25+ − Ni2+ − Ni2+(tripyridyldiamido)4 (NCS)2]. Chemistry–A European Journal, 20(16):4526– 4531, 2014.
[47]Chung-Han Yu, Min-Shiang Kuo, Ching-Yi Chuang, Gene-Hsiang Lee, Shao- An Hua, Bih-Yaw Jin, and Shie-Ming Peng. Chirality control of quadruple helixes of metal strings by peripheral chiral ligands. Chemistry–An Asian Journal, 9(11):3111–3115, 2014.
[48]Wen-Zhen Wang, Yang Wu, Rayyat H Ismayilov, Juao-Hui Kuo, Chen-Yu Yeh, Hsuan-Wei Lee, Ming-Dung Fu, Chun-hsien Chen, Gene-Hsiang Lee, and Shie-Ming Peng. A magnetic and conductive study on a stable defective extended cobalt atom chain. Dalton Transactions, 43(16):6229–6235, 2014.
[49]Wen-Zhen Wang, Dan Zhao, Ting-Bin Tsao, Rayyat Ismayilov, Gene-Hsiang Lee, and Shie-Ming Peng. A very stable nickel broken-chain complex with isolated Ni– Ni interactions. European Journal of Inorganic Chemistry, 2015(26):4329–4334, 2015.
[50]Shao-An Hua, Ming-Chuan Cheng, Chun-hsien Chen, and Shie-Ming Peng. From homonuclear metal string complexes to heteronuclear metal string complexes. European Journal of Inorganic Chemistry, 2015(15):2510–2523, 2015.
[51]Lien-Hung Tsou, Marc Sigrist, Ming-Hsi Chiang, Er-Chien Horng, Chun-hsien Chen, Shou-Ling Huang, Gene-Hsiang Lee, and Shie-Ming Peng. Asymmetric tetranuclear nickel chains with unidirectionally ordered 2-(α-(5-phenyl) pyridylamino)-1, 8-naphthyridine ligands. Dalton Transactions, 45(43):17281– 17289, 2016.
[52]Po-Jung Chen, Marc Sigrist, Er-Chien Horng, Geng-Min Lin, Gene-Hsiang Lee, Chun-hsien Chen, and Shie-Ming Peng. A ligand design with a modified naphthyridylamide for achieving the longest EMACs: the 1st single-molecule conductance of an undeca-nickel metal string. Chemical Communications, 53(34):4673– 4676, 2017.
[53]Ming-Chuan Cheng, Shao-An Hua, Qiying Lv, Marc Sigrist, Gene-Hsiang Lee, Yu-Chiao Liu, Ming-Hsi Chiang, and Shie-Ming Peng. Stepwise synthesis of the heterotrimetallic chains [MRu2(dpa)4X2]0/1+ using group 7 to group 12 transition metal ions and [Ru2(dpa)4Cl]. Dalton Transactions, 2018.
[54]Bo-Han Wu, Li-Yen Hung, Jheng-Yang Chung, Shie-Ming Peng, and I-Chia Chen. Determination of the Ni–Ni bonding strength in metal-string complexes using head- to-head nanorods and electrochemical surface-enhanced raman spectroscopy. The Journal of Physical Chemistry C, 122(11):6332–6339, 2018.
[55]Liang-Yan Hsu, Qian-Rui Huang, and Bih-Yaw Jin. Charge transport through a single molecular wire based on linear multimetal complexes: A non-equilibrium green’s function approach. The Journal of Physical Chemistry C, 112(28):10538– 10541, 2008.
[56]Te-Wei Tsai, Qian-Rui Huang, Shie-Ming Peng, and Bih-Yaw Jin. Smallest electrical wire based on extended metal-atom chains. The Journal of Physical Chemistry C, 114(8):3641–3644, 2010.
[57]Chung-Jen Hsiao, Szu-Hsueh Lai, I-Chia Chen, Wen-Zhen Wang, and Shie-Ming Peng. Metal- metal bonding and structures of metal string complexes Cr3(dpa)4Cl2, Cr3(dpa)4(NCS)2, and [Cr3(dpa)4Cl2](PF6) from IR, Raman, and surface-enhanced raman spectra. The Journal of Physical Chemistry A, 112(51):13528–13534, 2008.
[58]Szu-Hsueh Lai, Chung-Jen Hsiao, Jung-Wei Ling, Wen-Zhen Wang, Shie-Ming Peng, and I-Chia Chen. Metal–metal bonding in metal–string complexes M3(dpa)4X2 (M= Ni, Co, dpa= di (2-pyridyl) amido, and X= Cl, NCS) from reso nance Raman and infrared spectroscopy. Chemical Physics Letters, 456(4-6):181– 185, 2008.
[59]Chao-Han Cheng, Ruei-Ding Hung, Wen-Zhen Wang, Shie-Ming Peng, and I-Chia Chen. Excited-state dynamics of the metal string complex Co3(dpa)4(NCS)2 from femtosecond transient absorption spectra. ChemPhysChem, 11(2):466–473, 2010.
[60]Chao-Han Cheng, Ruei-Ding Hung, Wen-Zhen Wang, Shie-Ming Peng, and I-Chia Chen. Excited-state dynamics of metal string complex Ni3(dpa)4X2 from femtosecond transient absorption spectra. ChemPhysChem, 11(2):517–524, 2010.
[61]Szu-Hsueh Lai, Chung-Jen Hsiao, Yu-Min Huang, I-Chia Chen, Wen-Zhen Wang, and Shie-Ming Peng. Metal–metal bonding and structures of trinickel and tricobalt dipyridylamido complexes from surface-enhanced raman spectra. Journal of Ra- man Spectroscopy, 41(12):1694–1699, 2010.
[62]Yu-Min Huang, Szu-Hsueh Lai, Sheng Jui Lee, I-Chia Chen, Cheng Liang Huang, Shie-Ming Peng, and Wen-Zhen Wang. Metal- metal bonding and structures of metal- string complexes: Tripyridyldiamido pentanickel and pentacobalt from IR, Raman, and surface-enhanced raman scattering spectra. The Journal of Physical Chemistry C, 115(5):2454–2461, 2011.
[63]Yu-Min Huang, Huei-Ru Tsai, Szu-Hsueh Lai, Sheng Jui Lee, I-Chia Chen, Cheng Liang Huang, Shie-Ming Peng, and Wen-Zhen Wang. Bonding between chromium atoms in metal-string complexes from Raman spectra and surface- enhanced raman scattering: Vibrational frequency of the chromium quadruple bond. The Journal of Physical Chemistry C, 115(28):13919–13926, 2011.
[64]Bo-Han Wu, Jyun-You Lin, Kuan-Yi Ho, Min-Jie Huang, Shao-An Hua, Ming- Chuan Cheng, Yaw-Wen Yang, Shie-Ming Peng, Chun-hsien Chen, and I-Chia Chen. Determination of the valence state of diruthenium moiety using redox reactions and surface-enhanced raman scattering: Application in heterometal extended metal-atom chain diruthenium nickel complexes. The Journal of Physical Chem- istry C, 120(36):20297–20302, 2016.
[65]F Albert Cotton, Carlos A Murillo, and Richard A Walton. Multiple bonds between metal atoms. Springer Science & Business Media, 2005.
[66]F Albert Cotton, Lee M Daniels, Carlos A Murillo, and Isabel Pascual. Compounds with linear, bonded trichromium chains. Journal of the American Chemical Society, 119(42):10223–10224, 1997.
[67]F Albert Cotton, Lee M Daniels, Carlos A Murillo, and Xiaoping Wang. Getting the right answer to a key question concerning molecular wires. Chemical Communications, (24):2461–2462, 1999.
[68]Rodolphe Clerac, F Albert Cotton, Kim R Dunbar, Carlos A Murillo, Isabel Pascual, and Xiaoping Wang. Further study of the linear trinickel (II) complex of dipyridylamide. Inorganic chemistry, 38(11):2655–2657, 1999.
[69]F Albert Cotton, Carlos A Murillo, and Xiaoping Wang. Can crystal structure determine molecular structure? For Co3(dpa)4Cl2, yes. Journal of the Chemical Society, Dalton Transactions, (19):3327–3328, 1999.

[70]Rodolphe Clérac, F Albert Cotton, Stephen P Jeffery, Carlos A Murillo, and Xiaoping Wang. Compounds with symmetrical tricobalt chains wrapped by dipyridy- lamide ligands and cyanide or isothiocyanate ions as terminal ligands. Inorganic Chemistry, 40(6):1265–1270, 2001.

[71]Rodolphe Clérac, F Albert Cotton, Lee M Daniels, Kim R Dunbar, Carlos A Murillo, and Xiaoping Wang. Structural and magnetic properties of Co3(dpa)4Br2. Journal of the Chemical Society, Dalton Transactions, (4):386–391, 2001.

[72]John F Berry, F Albert Cotton, Lee M Daniels, and Carlos A Murillo. A trinickel dipyridylamido complex with metal- metal bonding interaction: prelude to polynickel molecular wires and devices? Journal of the American Chemical Society, 124(13):3212–3213, 2002.

[73]John F Berry, F Albert Cotton, Peng Lei, and Carlos A Murillo. Further structural and magnetic studies of tricopper dipyridylamido complexes. Inorganic chemistry, 42(2):377–382, 2003.

[74]John F Berry, F Albert Cotton, and Carlos A Murillo. Making connections with molecular wires: extending tri-nickel chains with axial cyanide, dicyanamide, and phenylacetylide ligands. Dalton Transactions, (15):3015–3021, 2003.

[75]John F Berry, F Albert Cotton, Lee M Daniels, Carlos A Murillo, and Xiaoping Wang. Oxidation of Ni3(dpa)4Cl2 and Cu3(dpa)4Cl2: Nickel- nickel bonding interaction, but no copper- copper bonds. Inorganic chemistry, 42(7):2418–2427, 2003.
[76]John F Berry, F Albert Cotton, Tongbu Lu, Carlos A Murillo, and Xiaoping Wang. Enhancing the stability of trinickel molecular wires and switches: Ni6+/Ni7+. Inorganic chemistry, 42(11):3595–3601, 2003.
[77]John F Berry, F Albert Cotton, Tongbu Lu, Carlos A Murillo, Brian K Roberts, and Xiaoping Wang. Molecular and electronic structures by design: Tuning symmetrical and unsymmetrical linear trichromium chains. Journal of the American Chemical Society, 126(22):7082–7096, 2004.
[78]John F Berry, F Albert Cotton, and Carlos A Murillo. A trinuclear EMAC-type molecular wire with redox-active ferrocenylacetylide “alligator clips”attached. Organometallics, 23(10):2503–2506, 2004.
[79]John F Berry, F Albert Cotton, Christopher S Fewox, Tongbu Lu, Carlos A Murillo, and Xiaoping Wang. Extended metal atom chains (EMACs) of five chromium or cobalt atoms: Symmetrical or unsymmetrical? Dalton Transactions, (15):2297– 2302, 2004.
[80]John F Berry, F Albert Cotton, and Carlos A Murillo. Mono-, di-, and tri-ruthenium complexes with the ligand 2, 2’-dipyridylamide (dpa): insights into the formation of extended metal atom chains. Inorganica chimica acta, 357(13):3847–3853, 2004.
[81]John F Berry, F Albert Cotton, Carlos A Murillo, and Brian K Roberts. An ef- ficient synthesis of acetylide/trimetal/acetylide molecular wires. Inorganic chemistry, 43(7):2277–2283, 2004.
[82]Dong-Hun Chae, John F Berry, Suyong Jung, F Albert Cotton, Carlos A Murillo, and Zhen Yao. Vibrational excitations in single trimetal-molecule transistors. Nano letters, 6(2):165–168, 2006.
[83]Daniel W Armstrong, F Albert Cotton, Ana G Petrovic, Prasad L Polavarapu, and Molly M Warnke. Resolution of enantiomers in solution and determination of the chirality of extended metal atom chains. Inorganic chemistry, 46(5):1535–1537, 2007.
[84]Michael Nippe and John F Berry. Introducing a metal- metal multiply bonded group as an “axial ligand”to iron: Synthetic design of a linear Cr- Cr··· Fe framework. Journal of the American Chemical Society, 129(42):12684–12685, 2007.
[85]Michael Nippe, Eric Victor, and John F Berry. Oxidation chemistry of axially protected Mo2 and W2 quadruply bonded compounds. Inorganic chemistry, 48(24):11889–11895, 2009.
[86]Michael Nippe, George H Timmer, and John F Berry. Remarkable regioselectivity in the preparation of the first heterotrimetallic Mo –W··· Cr chain. Chemical Communications, (29):4357–4359, 2009.
[87]Michael Nippe, Yevgeniya Turov, and John F Berry. Remote effects of axial ligand substitution in heterometallic Cr-Cr··· M chains. Inorganic chemistry, 50(21):10592–10599, 2011.
[88]Giovanni Li Manni, Allison L Dzubak, Abbas Mulla, David W Brogden, John F Berry, and Laura Gagliardi. Assessing metal–metal multiple bonds in Cr-Cr, Mo- Mo, and W-W compounds and a hypothetical U-U compound: A quantum chemical study comparing DFT and multireference methods. Chemistry-A European Jour- nal, 18(6):1737–1749, 2012.
[89]Brian S Dolinar and John F Berry. Electronic tuning of Mo2(thioamidate)4 complexes through π-system substituents and cis/trans isomerism. Dalton Transactions, 43(16):6165–6176, 2014.
[90]David W Brogden, Yevgeniya Turov, Michael Nippe, Giovanni Li Manni, Elizabeth A Hillard, Rodolphe Clérac, Laura Gagliardi, and John F Berry. Oxidative stretching of metal–metal bonds to their limits. Inorganic chemistry, 53(9):4777– 4790, 2014.
[91]Jonathan H Christian, David W Brogden, Jasleen K Bindra, Jared S Kinyon, Johan van Tol, Jingfang Wang, John F Berry, and Naresh S Dalal. Enhancing the magnetic anisotropy of linear Cr (II) chain compounds using heavy metal substitutions. Inorganic chemistry, 55(13):6376–6383, 2016.
[92]David W Brogden and John F Berry.Coordination chemistry of 2, 2’-dipyridylamine: The gift that keeps on giving. Comments on Inorganic Chemistry, 36(1):17–37, 2016.
[93]Jill A Chipman and John F Berry. Extraordinarily large ferromagnetic coupling (j“ 150 cm−1) by electron delocalization in a heterometallic Mo-Mo-Ni chain complex. Chemistry–A European Journal, 24(7):1494–1499, 2018.
[94]Dimitrios A Pantazis and John E McGrady. A three-state model for the polymorphism in linear tricobalt compounds. Journal of the American Chemical Society, 128(12):4128–4135, 2006.
[95]Dimitrios A Pantazis, Carlos A Murillo, and John E McGrady. A re-evaluation of the two-step spin crossover in the trinuclear cation [Co3(dipyridylamido)4Cl2]+. Dalton Transactions, (5):608–614, 2008.
[96]Vihar P Georgiev and John E McGrady. Efficient spin filtering through cobalt-based extended metal atom chains. Inorganic chemistry, 49(12):5591–5597, 2010.
[97]Vihar P Georgiev and John E McGrady. Influence of low-symmetry distortions on electron transport through metal atom chains: when is a molecular wire really “broken”? Journal of the American Chemical Society, 133(32):12590–12599, 2011.
[98]Vihar P Georgiev, WMC Sameera, and John E McGrady. Attenuation of conductance in cobalt extended metal atom chains. The Journal of Physical Chemistry C, 116(38):20163–20172, 2012.
[99]PJ Mohan, Vihar P Georgiev, and John E McGrady. Periodic trends in electron transport through extended metal atom chains: comparison of Ru3(dpa)4(NCS)2 with its first-row analogues. Chemical Science, 3(4):1319–1329, 2012.
[100]Vihar P Georgiev, PJ Mohan, Daniel DeBrincat, and John E McGrady. Lowsymmetry distortions in extended metal atom chains (EMACs): Origins and conse- quences for electron transport. Coordination Chemistry Reviews, 257(1):290–298, 2013.
[101]Daniel DeBrincat, Oliver Keers, and John E McGrady. Can heterometallic 1- dimensional chains support current rectification? Chemical Communications, 49(80):9116–9118, 2013.
[102]Tingting Weng, Daniel DeBrincat, Vaida Arcisauskaite, and John E McGrady. In search of structure–function relationships in transition-metal based rectifiers. Inorganic Chemistry Frontiers, 1(6):468–477, 2014.
[103]Vaida Arcisauskaite, Mariano Spivak, and John E McGrady. Structure and bonding in trimetallic arrays containing a Cr–Cr quadruple bond: A challenge to density functional theory. Inorganica Chimica Acta, 424:293–299, 2015.
[104]M Spivak, V Arcisauskaite, X López, JE McGrady, and C de Graaf. A multiconfigurational approach to the electronic structure of trichromium extended metal atom chains. Dalton Transactions, 46(19):6202–6211, 2017.
[105]Marie-Madeleine Rohmer and Marc Bénard. Bond stretch isomerism still elusive in linear trimetallic complexes. DFT calculations on Co3(dipyridylamine)4Cl2. Journal of the American Chemical Society, 120(36):9372–9373, 1998.
[106]Marie-Madeleine Rohmer and Marc Bénard. Structural versatility in polyoxometalates and in some linear trimetallic complexes: An electronic interpretation. Journal of Cluster Science, 13(3):333–353, 2002.
[107]Pascal Kiehl, Marie-Madeleine Rohmer, and Marc Bénard. Electron delocalization in nickel metallic wires: A DFT investigation of Ni3(dpa)4Cl2 and [Ni3(dpa)4]3+(dpa= dipyridylamide) and extension to higher nuclearity chains. In- organic chemistry, 43(10):3151–3158, 2004.
[108]Xavier López, Ming-Yi Huang, Gin-Chen Huang, Shie-Ming Peng, Feng- Yin Li, Marc Bénard, and Marie-Madeleine Rohmer. Even-numbered metal chain complexes: Synthesis, characterization, and dft analysis of [Ni4(µ4-Tsdpda)4(H2O)2](Tsdpda2−= n-(p-toluenesulfonyl) dipyridyl-diamido),[Ni4(µ4-Tsdpda)4]+, and related Ni4 string complexes. Inorganic chemistry, 45(22):9075–9084, 2006.
[109]Yasutaka Kitagawa, Toru Matsui, Yasuyuki Nakanishi, Yasuteru Shigeta, Takashi Kawakami, Mitsutaka Okumura, and Kizashi Yamaguchi. Theoretical studies of electronic structures, magnetic properties and electron conductivities of one- dimensional Nin (n= 3, 5, 7) complexes. Dalton Transactions, 42(45):16200– 16208, 2013.
[110]Yasutaka Kitagawa, Mizuki Asaoka, Yoshiki Natori, Koji Miyagi, Rena Teramoto, Toru Matsui, Yasuteru Shigeta, Mitsutaka Okumura, and Masayoshi Nakano. Theoretical study on relationship between spin structure and electron conductivity of one-dimensional tri-nickel (II) complex. Polyhedron, 136:125–131, 2017.
[111]Marie-Madeleine Rohmer, Alain Strich, Marc Bénard, and Jean-Paul Malrieu. Metal- metal bond length variability in Co3(dipyridylamide)4Cl2: Bond-stretch isomerism, crystal field effects, or spin transition process? A DFT study. Journal of the American Chemical Society, 123(37):9126–9134, 2001.
[112]Dilahan Aydin-Cantürk and Hanne Nuss Max-Planck. Synthesis, structure determination, and magnetic properties of [Cr3(dpa)4Cl2][CuCl2], a compound comprising a trinuclear chain cation. Zeitschrift für Naturforschung B, 67(8):759–764, 2012.
[113]Zahra Tabookht, Coen de Graaf, and Xavier López. Towards a low-spin configuration in extended metal atom chains. theoretical study of trimetallic systems with 22 metal electrons. Dalton Transactions, 41(2):498–504, 2012.
[114]Andrea Cornia, Luca Rigamonti, S Boccedi, R Clérac, M Rouzières, and L Sorace. Magnetic blocking in extended metal atom chains: a pentachromium (II) complex behaving as a single-molecule magnet. Chemical Communications, 50(96):15191– 15194, 2014.
[115]P Szarek and W Grochala. Fine-tuning of magnetic properties in nickel (II) trinuclear EMACs via modifications of equatorial ligands. The Journal of Physical Chemistry A, 119(35):9363–9372, 2015.
[116]Paweł Szarek, Wojciech Wegner, and Wojciech Grochala. Ferromagnetic ground state for a hypothetical iron-based extended metal atom chain. Journal of molecular modeling, 22(3):63, 2016.
[117]M Spivak, V Arcisauskaite, X López, and C de Graaf. Backbone flexibility of extended metal atom chains. ab initio molecular dynamics for Cr3(dpa)4X2 (X= NCS, CN, NO3) in gas and crystalline phases. Dalton Transactions, 46(44):15487–15493, 2017.
[118]Aivaras Dirvanauskas, Rita Galavotti, Alessandro Lunghi, Alessio Nicolini, Fabrizio Roncaglia, Federico Totti, and Andrea Cornia. Solution structure of a pentachromium (II) single molecule magnet from DFT calculations, isotopic labelling and multinuclear NMR spectroscopy. Dalton Transactions, 47(2):585–595, 2018.
[119]Anandi Srinivasan, Miguel Cortijo, Vladimir Bulicanu, Ahmad Naim, Rodolphe Clérac, Philippe Sainctavit, Andrei Rogalev, Fabrice Wilhelm, Patrick Rosa, and Elizabeth A Hillard. Enantiomeric resolution and X-ray optical activity of a tri- cobalt extended metal atom chain. Chemical Science, 2018.
[120]Frank Neese. The ORCA program system. Wiley Interdisciplinary Reviews: Computational Molecular Science, 2(1):73–78, 2012.
[121]John P Perdew. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Physical Review B, 33(12):8822, 1986.
[122]John P Perdew. Erratum: Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Physical Review B, 34(10):7406, 1986.
[123]Axel D Becke. Density-functional exchange-energy approximation with correct asymptotic behavior. Physical review A, 38(6):3098, 1988.
[124]Ansgar Schäfer, Hans Horn, and Reinhart Ahlrichs. Fully optimized contracted gaussian basis sets for atoms Li to Kr. The Journal of Chemical Physics, 97(4):2571–2577, 1992.
[125]Karin Eichkorn, Oliver Treutler, Holger Öhm, Marco Häser, and Reinhart Ahlrichs. Auxiliary basis sets to approximate coulomb potentials. Chemical Physics Letters, 240(4):283–290, 1995.
[126]Karin Eichkorn, Florian Weigend, Oliver Treutler, and Reinhart Ahlrichs. Auxiliary basis sets for main row atoms and transition metals and their use to approximate coulomb potentials. Theoretical Chemistry Accounts, 97(1-4):119–124, 1997.
[127]Florian Weigend and Reinhart Ahlrichs. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Physical Chemistry Chemical Physics, 7(18):3297–3305, 2005.
[128]Dimitrios A Pantazis, Xian-Yang Chen, Clark R Landis, and Frank Neese. All- electron scalar relativistic basis sets for third-row transition metal atoms. Journal of Chemical Theory and Computation, 4(6):908–919, 2008.
[129]WP Su, JR Schrieffer, and AJ Heeger. Solitons in polyacetylene. Physical Review Letters, 42(25):1698, 1979.
[130]WP Su, JR Schrieffer, and AJ Heeger. Soliton excitations in polyacetylene. Physical Review B, 22(4):2099–2111, 1980.
[131]WP Su, JR Schrieffer, and AJ Heeger. Erratum: Soliton excitations in polyacetylene. Physical Review B, 28(2):1138, 1983.
[132]Alan J Heeger, S Kivelson, JR Schrieffer, and W-P Su. Solitons in conducting polymers. Reviews of Modern Physics, 60(3):781, 1988.