Investigations of Mixed-Valence and Open-Shell Transition-Metal Complexes Employing Modern Density Functional Methods vorgelegt von Diplom-Chemiker Matthias Parthey aus Bad Soden-Salmünster Von der Fakultät II – Mathematik und Naturwissenschaften der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften – Dr. rer. nat. –
genehmigte Dissertation Promotionsausschuss: Vorsitzender:
Prof. Dr. rer. nat. Arne Thomas
Berichter:
Prof. Dr. rer. nat. Martin Kaupp
Berichter:
Prof. Dr. phil. nat. Wolfgang Kaim
Tag der wissenschaftlichen Aussprache:
16.04.2014 Berlin 2014 D83
“No one ever achieved greatness by playing it safe“ Harry J. Gray
Für Hami “Wir werden selber reich, wenn wir Freude schenken“ Brigitte Theilen
ACKNOWLEDGEMENT “It is personalities, not principles, that move the age.” Oscar Wilde First, I want to thank Prof. Martin Kaupp. Martin, words can barely express how grateful I am for the three years of my PhD and the ideas we created and developed together during that time. But not only your support in science but also all the socializing activities like football, skiing, and of course our TV appearance made my PhD an incredibly enjoyable time. I thank Manuel Renz, for introducing me to quantum chemistry, always giving extremely helpful advice, and sticking with me (and my Mac) through more than two years in the office; Anja Greif, my light on gray office days with her dog Sari being my kryptonite, when it comes to working efficiently; Johannes Schraut, amazing football mate, both active and watching; Florian Meier, for being too nice for this world; Hilke Bahmann, coding and social organizing queen; Martin Enke, football and Facebook expert; Toni Maier for filling Manuel’s spot; Kolja Theilacker, Robert Müller, Vladimir Pelmentschikov, Sebastian Gohr, Sascha Klawohn, and the whole Kaupp group for always helping and supporting me. “I left home, but there is one thing that I still know: it’s always summer in my heart and in my soul!” Ryan Key of Yellowcard in “Always Summer” From Durham University, now partly University of Western Australia at Perth, I want to thank the P. J. Low group. Most of all of course Prof. Paul J. Low for all the great work we did together and even more the fun we had while doing it. Sorry for drinking so much coffee and stealing your words for this acknowledgement, Paul! Thanks to my lab mates: Josef Gluyas, the synthetic grandmaster and my English proofreader; Sören Bock, best football and dart partner ever and worst German DJ; “real” thanks to Sam Eaves; Kevin Vincent for the fresh air breaks; Santiago Marquez-Gonzales for his positive attitude; Ross Davidson, the Doughnut provider; Campbell Mackenzie, Marie-Christine Oerthel, and the rest of the group. I also want to thank Prof. Dave J. Tozer and Dr. Mark A. Fox for the quantum-chemical discussions. In this context I also want to thank Prof. D. J. Tozer, Prof. Trygve Helgaker, Dr. Enrico Benassi, and Dr. Christoph Jacob for their excellent lectures, talks, and/or discussion about general concepts and special issues of DFT and quantum-chemistry. Representatively for all people at the TU Berlin, who supported me, I want to thank: Heidi Grauel and Nadine Rechenberger for helping with the enormous amount of formal work,
especially the countless forms for business trips, and the organization of group activities and the homepage; Prof. Christian Limberg, my second supervisor; Dr. Jean-Philippe Lonjaret, the head and heart of the BIG-NSE graduate school; Dr. Norbert Paschedag and Sven Grottke for their IT support; the Schoen group, especially Michael Melle, Tillman Stieger, and Marco Mazza, for being valuable targets for scientific slamming. The same holds true for JeanChristophe Tremblay from the FU Berlin. “They say ‘You don’t grow up, you just grow old’, it seems to say I haven’t done both, I made mistakes, I know, I know, but here I am alive!” Ryan Key of Yellowcard in “Here I Am Alive” I also want to thank my family: My parents, Almuth and Roland, for their endless support, life advice, and that they never pushed me towards any direction; my sister Johanna, my role model when it comes to being persistent, strong, and faithful and thus succeeding in the end; my brother Christian for always helping me with physics, being even more Apple addicted, and for losing the clash of science by working for a chemical company; my grandma Erika “Hami” Goralewski, Godehard and Siegrid Goralewski, my uncle and aunt, and my “uncle” Heinz Löken for their support. I also thank Werner and Christa Parthey, Erika and Josef Jöckel, and Ulrike Selig-Parthey. “That’s what friends are for. They help you to be more of who you are.” Christopher Robin (Disney character) There are a lot of friends I met during different stages of my life, who mainly made my free time enjoyable, every place feel like home, and prevented me from getting to caught up in research, but also gave advice in scientific matters, and thus I want to thank: From Hessen: Augustin Danciu, for broing and awesoming all over the place; Patrick Noll, best wing man (= Goose) ever, proud to be your best man; Sebastian Dietz, oldest friend and like wine our friendship improves with age; Jana Noll, for always being a great observer and of course the famous carnival lasagna; Markus Auhl, hessian philosopher; Natascha Klumpp, forever Troy; Christopher Hämel, doubles partner for life; Andreas Möller, for all the travels and career advice; Theresa and Horst Schmidt, Elke Thesenvitz, Susan Simon, Nina Wallenta, Natalie Alt, Antonia Spielmann, Thomas Hummel, Philipp Roth, Steffen Pfeifer, Till Bergen, and Uta Krammenschneider. From Würzburg: Frank Brunecker, Steffen Kalinna, Marius Silaghi, Klaus Dück, Johannes Landmann, Alexander Mertsch, and Martin Kess, for making even the hard times enjoyable during my studies in Würzburg. I hope, our Christmas market tradition will continue. A
special thanks to Jost Henkel for following or inviting me to all different spots like London, Durham, Berlin, Hannover, … (hopefully this list will continue) From Berlin: My BIG-NSE (Berlin International Graduate School of Natural Science and Engineering) mates Fanni Daruny Sypaseuth, Laura Vieweg, Moritz Baar, Daniel Gallego, Patrick Littlewood, Genwen Tan, Hong Nhan Nong, Jiao Linyu, Setareh Sadjadi, Xunhua Zhao, Heiner Schwarz, Swantje Wiebalck, Xenia Erler, Subhamoy Bhattacharya, María Gracia Colmenares, Inéz Monte Pérez, Laura Pardo Pérez, and all the other nice people from the school. Jakub Stejskal, Igor Anatzki, Marcus Beyerlein, Andreas Podlasly, André Zacher, Benjamin Mietling, Sven Vangermain, Kristen Van Dernoot, and the rest from the Grün-Gold Pankow tennis team. From Durham: Matt Perks, César Segura, Charlie Rozier, Ash Routen, James Koranyi, and the Staff football team. Thanks to the team of the New Inn. I want to thank Reinhold Stein, my former chemistry teacher, for introducing me to chemistry and almost more importantly to Top Gun “It takes a lot more than just fancy flying”. For financial support and the opportunity to work in an exceptional research environment I want to thank the “Unifying Concepts of Catalysis” (UniCat) excellence cluster and the German Academic Exchange Service (DAAD). “I hope you live a life you are proud of; if you are not, I hope you find the strength to start all over again” F. Scott Fitzgerald
I
ABSTRACT
ABSTRACT Mixed-valence multinuclear transition-metal complexes have been in the focus of research since the discovery of the Creutz-Taube ion and related systems in the 1960s. The search for functional (opto-) electronic materials on the molecular scale, such as molecular wires and transistors, has added to the momentum of the field. Successful applications of organic mixed-valence systems as charge carriers - for example in organic light-emitting diodes or dye-sensitized solar cells - are known. Mixed-valence transition-metal complexes are even more versatile in their electronic properties due to the availability of d-orbitals. Hence they are appealing targets for the design of functional materials and additionally of central importance in electron transfer processes in nature - e.g. in metalloenzymes - and in catalysis. A central question in all of these fields is that of the localization of charge on a given redox center (end-cap or bridging ligand) versus delocalization over the molecular framework. In the important model case of two redox centers linked by a bridging ligand, the description of electronic structure is usually made within the Robin-Day scheme, which is based on the extent of electronic coupling. The investigation of the electronic structure is complicated by the lack of information directly extractable from experimental data. Especially challenging is the presence of overlapping absorption bands in UV-vis-NIR spectra and the speculated existence of different thermally accessible conformers. Hence a reliable investigation of the extent of electronic coupling is only possible via combined experimental and quantumchemical studies. The failure of Hartree-Fock and Density Functional Theory - the methods feasible for the system-size of typical mixed-valence systems - in describing the charge localization/delocalization behavior has been overcome in the well balanced global hybrid functional BLYP35, which is employed in combination with solvent models. In this thesis it is shown that the BLYP35/solvent model combination is furthermore capable of describing optoelectronic properties of mixed-valence transition-metal complexes. Even the challenging charge-transfer excitations are reliably reproduced. In addition the longstanding question to which extent the conformation determines the electronic and spectroscopic properties of mixed-valence systems is investigated. Calculations yield rotational motion as explanation for the optical properties of polyynediyl complexes. This prediction is experimentally proven by the Low group. For diethynylphenyl-bridged ruthenium complexes the computations demonstrate that conformational motion may even average to some extent localized and delocalized electronic and molecular structures. These findings lead beyond the traditionally more one-dimensional understanding of the Robin-Day scheme. Additionally the performance of local and range-separated hybrid functionals in describing isotropic transition metal hyperfine coupling constants is validated.
ZUSAMMENFASSUNG
II
ZUSAMMENFASSUNG Gemischtvalente, mehrkernige Übergangsmetallkomplexe sind fester Bestandteil naturwissenschaftlicher Forschung seit der Entdeckung des Creutz-Taube Ions und verwandter Systeme in den 60ern. Auf Grund des Potentials diese als molekulare (opto-) elektronische Bauteile - z.B. als molekulare Drähte oder Transistoren - einzusetzen, rückten diese Untersuchungen weiter in den Fokus. Organische gemischtvalente Systeme werden erfolgreich als Ladungstransportmaterialien - z.B. in organischen Leuchtdioden oder Farbstoffsolarzellen - eingesetzt. Durch die Verfügbarkeit von d-Orbitalen bieten gemischtvalente Übergangsmetallkomplexe noch flexiblere elektronische Eigenschaften. Daher stellen sie attraktive Ziele für die Entwicklung funktioneller Materialien dar. Zudem sind sie von zentraler Bedeutung in Elektrontransferreaktionen in der Natur - z.B. in Metallenzymen - und in der Katalyse. Für alle diese Anwendungen ist vor allem entscheidend, ob die Ladung lokalisiert an einem Redoxzentrum oder delokalisiert vorliegt. Das typische Musterbeispiel eines gemischtvalenten Systems besteht aus zwei Redoxzentren, die über einen Brückenliganden verknüpft sind. In diesem Fall wird das System mit Hilfe des Robin-Day Schemas beschrieben, welches auf der Stärke der elektronischen Kopplung beruht. Die nötigen Informationen können nicht oder nur selten direkt aus experimentellen Daten gewonnen werden. Besonders überlagernde Absorptionsbanden in UV-vis-NIR Spektren sowie der (vermutete) Einfluss verschiedener populierter Konformere erschweren die Analyse. Daher können nur Studien, bei denen experimentelle und quantenchemische Methoden kombiniert werden, Aufschluss über das Ausmaß der elektronischen Kopplung geben. Die quantenchemische Beschreibung gemischtvalenter Systeme beruht auf einem kürzlich entwickelten Protokoll, das geschickt die beiden Methoden Hartree-Fock und Dichtefunktionaltheorie kombiniert. Das Protokoll basiert auf dem BLYP35 Funktional, das üblicherweise in Kombination mit Lösemittelmodellen angewendet wird. In dieser Arbeit wird die Übertragbarkeit dieses Protokolls auf die optoelektronischen Eigenschaften gemischtvalenter Übergangsmetallkomplexe demonstriert. Sogar die anspruchsvolle Beschreibung von Ladungstransferanregungen ist möglich. Zudem kann der Einfluss verschiedener Konformere auf die elektronische Struktur und experimentelle Spektren untersucht werden. Die quantenchemische Vorhersage, dass die optischen Eigenschaften butdiinyl-verbrückter Komplexe auf Rotation zurückzuführen sind, konnte experimentell von der Arbeitsgruppe Low bewiesen werden. Rechnungen zeigen, dass es für diethinphenyl-verbrückte Rutheniumkomplexe von der Konformation abhängt, ob Ladungslokalisierung oder -delokalisierung vorliegt. Dieser Sachverhalt ist nicht mit dem klassischen eindimensionalen Robin-Day Bild zu vereinbaren. Lokale und range-separated Hybridfunktionale wurden zudem für die Beschreibung von Übergangsmetallhyperfeinkopplungskonstanten validiert.
III
LIST OF PUBLICATIONS
LIST OF PUBLICATIONS Journal Articles [8]
Matthias Parthey and Martin Kaupp, “Quantum-chemical insights into mixed-valence systems: within and beyond the Robin/Day scheme”, Chem. Soc. Rev. 2014, DOI: 10.1039/c3cs60481k.
[7]
Kevin B. Vincent, Matthias Parthey, Dmitry S. Yufit, Martin Kaupp, and Paul J. Low, “Synthesis and redox properties of mono-, di- and tri-metallic platinum-ethynyl complexes based on the trans-Pt(C6H4N{C6H4OCH3-4}2)(C≡CR)(PPh3)2 motif ”, Polyhedron, 2014, DOI: 10.1016/j.poly.2014.04.035.
[6]
Matthias Parthey, Josef B.G. Gluyas, Mark A. Fox, Paul J. Low, and Martin Kaupp, “Mixed-Valence Ruthenium Complexes Rotating Through a Conformational RobinDay Continuum”, Chem. Eur. J. 2014, DOI: 10.1002/chem.201304947.
[5]
Matthias Parthey, Kevin B. Vincent, Manuel Renz, Phil A. Schauer, Dmitry S. Yufit, Judith A.K. Howard, Martin Kaupp, and Paul J. Low, “A Combined Computational and Spectroelectrochemical Study of Platinum Bridged Bis-Triarylamine Systems”, Inorg. Chem. 2014, 53, 1544-1554.
[4]
Kevin B. Vincent, Qiang Zeng, Matthias Parthey, Dmitry S. Yufit, Judith A.K. Howard, František Hartl, Martin Kaupp, and Paul J. Low, ”The Syntheses, SpectroElectrochemical Studies, Molecular and Electronic Structures of Ferrocenyl Enediynes”, Organometallics 2013, 32, 6022-6032.
[3]
Matthias Parthey, Josef B.G. Gluyas, Phil A. Schauer, Dmitry S. Yufit, Judith A.K. Howard, Martin Kaupp, and Paul J. Low, “Refining the Interpretation of NIR Band Shapes in a Polyynediyl Molecular Wire”, Chem. Eur. J. 2013, 19, 9780-9784.
[2]
Sören Bock, Samantha G. Eaves, Matthias Parthey, Martin Kaupp, Boris Le Guennic, Jean-François Halet, Dmitry S. Yufit, Judith A.K. Howard, and Paul J. Low, “The preparation, characterisation and electronic structures of 2,4pentadiynylnitrile (cyanobutadiynyl) complexes“ Dalton Trans. 2013, 42, 4240-4243.
[1]
Martin Kaupp, Manuel Renz, Matthias Parthey, Matthias Stolte, Frank Würthner, Christoph Lambert, “Computational and spectroscopic studies of organic mixedvalence compounds: where is the charge?” Phys. Chem. Chem. Phys. 2011, 13, 16973-16986.
LIST OF PUBLICATIONS
IV
Talks and Posters [8]
Talk: “Mixed-Valence Transition-metal complexes: Essential in Catalysis, Challenging for Quantum Chemistry”; BIG-NSE Evaluation Seminar, Berlin (DE), May 2013.
[7]
Talk: “Rotamers of Mixed-Valence Complexes: Spinning Classes for a Better (Band) Shape”; Workshop Modern Methods in Quantum Chemistry in Mariapfarr (A), February 2013.
[6]
Talk: “Mixed-Valence Complexes and Quantum Chemistry – Insights and Challenges”; Group Seminar P.J. Low Group in Durham (UK), October 2012.
[5]
Talk: “Electron Transfer Processes: Crucial for Catalysis, Challenging for Quantum Chemistry”; 2. Berliner Chemie Symposium, Berlin (DE), April 2012.
[4]
Talk: “Investigations of Catalytically Active Open-Shell Systems Using Modern Density Functional Methods”; BIG-NSE Workshop, Berlin (DE), January 2012.
[3]
Poster: “Towards Improved Hyperfine Couplings for Transition-Metal Nuclei with Improved Density Functionals: The Core-Shell vs. Valence-Shell Spin-Polarization Dilemma”; Symposium for Theoretical Chemistry in Sursee (CH), August 2011.
[2]
Talk: “Quantum Chemical Studies of Mixed-Valent Transition-Metal Complexes”; Joint Group Seminar with Schwarz Group, Berlin (DE), April 2011.
[1]
Poster: “A Reliable Quantum-Chemical Protocol for Calculating Mixed-Valence Compounds”; Chem-SyStM in Würzburg (DE), December 2010.
CONTENTS ABSTRACT .......................................................................................................................................... I ZUSAMMENFASSUNG ................................................................................................................... II LIST OF PUBLICATIONS .............................................................................................................. III LIST OF ABBREVIATIONS ........................................................................................................ VII INTRODUCTION ............................................................................................................................... 1 Mixed-Valence Systems in Biocatalysis ...................................................................................... 2 Mixed-Valence Systems in Molecular Electronics ...................................................................... 3 Quantum-Chemical Investigations of Mixed-Valence Systems .................................................. 4 1 THEORETICAL BACKGROUND ................................................................................................ 5 1.1 Mixed-Valence Systems ............................................................................................................ 5 Robin-Day Classes ....................................................................................................................... 5 Marcus-Hush and Mulliken-Hush Theory ................................................................................... 6 Experimental Classification ....................................................................................................... 10 1.2 Density Functional Theory..................................................................................................... 13 Principles .................................................................................................................................... 13 Exchange-Correlation Functionals ............................................................................................. 18 Time-Dependent Density Functional Theory ............................................................................. 24 Spin in Density Functional Theory ............................................................................................ 27 1.3 Quantum-Chemical Description of MV Systems ................................................................. 30 1.4 Computational Details ............................................................................................................ 34 2 THE COMPUTATIONAL STATE OF THE ART ................................................................... 35
3 APPLICATIONS TO MV TRANSITION-METAL COMPLEXES ........................................ 39 3.1 Platinum Bridged Bis-Triarylamine Complexes.................................................................. 39 Introduction ................................................................................................................................ 39 Results and Discussion ............................................................................................................... 44 Conclusions ................................................................................................................................ 50 3.2 Ferrocenyl Ene-diynes ............................................................................................................ 53 Introduction ................................................................................................................................ 53 Results and Discussion ............................................................................................................... 54 Conclusions ................................................................................................................................ 58 4 SPINNING CLASSES: THE IMPORTANCE OF ROTAMERS ............................................. 59 4.1 The Interpretation of NIR Band Shapes in Polyynediyl Molecular Wires ....................... 61 Introduction ................................................................................................................................ 61 The Class III Ruthenium Complex ............................................................................................. 63 The Class III Osmium Complex ................................................................................................. 70 The Class II Molybdenum Complex .......................................................................................... 72 The Class III Rhenium Complex ................................................................................................ 76 4.2 Complexes Rotating Through a Conformational Robin-Day Continuum ........................ 79
Introduction ................................................................................................................................. 79 Results and Discussion................................................................................................................ 84 Conclusions ...............................................................................................................................101
5 THE CORE-SHELL VS. VALENCE-SHELL SPIN POLARIZATION DILEMMA ........... 103 Introduction ...............................................................................................................................103 Computational Details............................................................................................................... 104 Results and Discussion.............................................................................................................. 106 Conclusions and Outlook .......................................................................................................... 109 6 GENERAL CONCLUSIONS AND OUTLOOK ....................................................................... 111 REFERENCES ................................................................................................................................115 APPENDIX ....................................................................................................................................... 128
VII
LIST OF ABBREVIATIONS
LIST OF ABBREVIATIONS AM1
Austin model 1
a.u.
atomic units
CASSCF
complete active space self-consistent field
CASPT2
complete active space perturbation theory to second order
CC
coupled cluster (theory)
CDFT
constrained density functional theory
CI (SD)
configuration interaction (singles & doubles)
COSMO(-RS)
conductor-like screening model for real solvents
Cp
cyclopentadienyl ligand
(C-)PCM
(conductor-like) polarizable continuum model
CT
charge transfer
dmpe
1,2-bis(dimethylphosphine)ethane
dppe
1,2-bis(diphenylphosphine)ethane
DFT
density functional theory
EPR
electron paramagnetic resonance
ET
electron transfer
Fc
ferrocene
GGA
generalized gradient approximation
HF
Hartree-Fock
HOMO
highest occupied molecular orbital
IC
interconfigurational
INDO
intermediate neglect of differential overlap
IR
infrared (spectral region)
IVCT
intervalence charge transfer
LC
long-range corrected
LDA
local density approximation
LMCT
ligand-metal charge transfer
LMF
local mixing function
LIST OF ABBREVIATIONS LUMO
lowest unoccupied molecular orbital
MAE
mean absolute error
MD
molecular dynamics
MLCT
metal-ligand charge transfer
MO
molecular orbital
MP2
Møller-Plesset perturbation theory to second order
MR
multi-reference
MV
mixed-valence
NIR
near-infrared spectral region
NMR
nuclear magnetic resonance
OEP
optimized effective potential
PES
potential energy surface
QI
quantum-interference
RISM-SCF
reference interaction site model self-consistent field
SCF
self-consistent field
SOMO
singly occupied molecular orbital
STM
scanning tunneling microscopy
SVP
split valence polarization (basis sets)
TAA
triarylamine
TDDFT
time-dependent density functional theory
THF
tetrahydrofuran
UV
ultraviolet spectral region
vis
visible ABBREVIATIONS OF DENSITY FUNCTIONALS
B
Becke
BMK
Boese-Martin for kinetics
LYP
Lee-Yang-Parr
PBE
Perdew-Burke-Ernzerhof
S
Slater-Dirac
TPSS
Tao-Perdew-Staroverov-Scuseria
VWN
Vosko-Wilk-Nusair
VIII
INTRODUCTION
INTRODUCTION A wide range of molecular and solid-state systems is embodied in the mixed-valence (MV) concept, and various models have been devised to classify their electron transfer (ET) characteristics. Generally, one views a MV system as a molecule or solid in which a given redox center appears at least twice, in two different oxidation states, connected by a suitable bridging unit that typically provides for some electronic coupling between the redox centers. The thermal or optically induced ET between the (two or more) redox centers is at the heart of attention, but ET from or to the bridging unit, which is becoming increasingly more widely recognized, also plays a role in the overall ET mechanisms and spectroscopic profiles. The large variety of redox centers and bridge units and the different coupling between them accounts for the multitude of MV systems that can be envisioned or exist, either purposefully or accidentally constructed by synthetic chemists or present in nature. The “classical” MV systems are based on transition-metal redox centers connected by bridging ligands. Examples are Prussian Blue on the “serendipity” branch of the field or the Creutz-Taube ion and its derivatives[1,2] that feature prominently in the purposeful study of ET in transition-metal systems. However, many other molecules have been known that were classified as MV only much later. Examples are the radical anions of aryl compounds with two or more nitro substituents. These have been known and studied spectroscopically since the early 1960s, but they were recognized as MV systems only much later, where the nitro-substituted part of the aryl ring features as redox center, and the remaining aryl part plays the role of bridging unit.[35] This served to introduce organic redox centers to the field, which have received growing attention due to their involvement in organic molecular electronics. Notable examples are
2
INTRODUCTION
those based on triaryl-amine redox-active units (see below). Organic MV systems are usually also based on organic bridges, but ”inverted” MV systems with organic redox centers and transition-metal-based bridges are also known as discussed below. The MV concept may even be widened to such exotic species as the H2+ ion, which may be viewed as the smallest conceivable MV system. In this thesis only MV systems are discussed where the formal redox states differ by one unit, which for two redox centers typically leads to open-shell compounds in the ground and excited states.[6] Of course, MV systems with larger electron-number differences are conceivable. Their closed-shell variants have been classified as donor-acceptor systems.[6] Systems with non-identical redox centers further extend the picture and may call for a looser MV definition.[7] In many cases redox-noninnocence of the bridge or of terminal ligands of transition-metal complexes additionally complicates the redox-center assignment.[8-11] Despite the complications arising from the definition, MV systems have drawn and continue to draw the unabated attention of experimental and theoretical scientists from chemistry, biology, physics, and related natural sciences, which is reflected in a large variety of reviews and special issues.[6,7,12-22] This is due to the fundamental importance of MV systems in ET processes in nature (e.g. in metalloenzymes[23]), in catalysis, and in the design of functional materials.[24] Furthermore these often complex reactions or at least key steps of the reactions can be mimicked and investigated using more readily accessible MV compounds.[25] Additionally the detailed understanding of and the theory behind ET processes is promoted by the investigations of MV systems.[6] MV compounds are versatile in their application, as by varying different factors, like the redox centers, the bridging unit, and/or the enzymatic or solvent environment, the whole range from charge-localized to -delocalized systems can be tuned.
Mixed-Valence Systems in Biocatalysis ET reactions are of tremendous importance in heterogeneous, homogeneous, and enzymatic catalysis. In fact it may be argued that ET is involved the majority of important catalytic processes. Considering biocatalysis in particular, metallo-proteins often contain multinuclear metal sites that feature MV states during catalysis.[23] It is in particular the conversion of small, stable molecules (e.g. H2O, CH4, N2, CO2) that requires a sequence of elementary steps to circumvent high activation barriers.[26] Multinuclear metal sites, sometimes in combination with redox-active ligands, are frequently involved here. The oxygen-evolving complex of the photosystem II, which catalyzes the light-driven water oxidation, represents a typical example for an active site with predominant MV active states.[27,28] The Mn4Ca(µ-On) core features a tetranuclear transition metal cluster, where different (MV) oxidation states are reached as a consequence of light-induced electron removal (i.e. photo-oxidation).[29] Broken-symmetry DFT calculations have clearly
INTRODUCTION
3
demonstrated localized Class II character for the relevant states, and standard functionals like B3LYP have been found to provide a reasonable picture of the electronic structure of these MV clusters, if broken-symmetry approaches are employed. Another type of multinuclear enzyme site is represented by the dinuclear CuA site in various copper enzymes, e.g. cytochrome c oxidase. Here the MV Cu+ICu+II state appears to be a delocalized Class III system, but perturbations due to mutation may alter the protein environment sufficiently to cause partial localization.[23,30-32] In contrast, partial delocalization characterizes many of the important biological iron-sulfur clusters, which renders these systems a challenge for both clear-cut experimental and theoretical descriptions. Charge distribution in FeS clusters depends crucially on coordination number of the metals and the extent of magnetic coupling between them (ferromagnetic coupling favors charge delocalization, whereas antiferromagnetic coupling appears to give rise to charge localization).[23]
Mixed-Valence Systems in Molecular Electronics Class III MV systems are obvious candidates for use as “molecular wires” or “nanojunctions” in the field of molecular electronics.[24] Due to their electronically delocalized character and vanishing thermal ET barriers, fast ET over distances in the nm range is achievable.[14,15,33-36] Good energy matching between the orbitals of the bridge and the redox centers (“end caps”) is essential.[24,37] On the other hand, switching functions or data storage require a certain degree of localization (“trapping”) of charge carriers, pointing to Class II situations with appreciable barriers. Here the currently envisioned targets include the controversially discussed “quantum-dot cellular automata” made up of MV complexes. These may be related to coding information in quantum computers[38-40] and to molecular transistors.[24] Driven by the technological and economic pursuit of “Moore’s Law”, the functional area of a transistor has been halving every eighteen to twenty-four months over the last decades, allowing the number of transistors per chip to double in each technology generation, and thus giving rise to smaller and more powerful electronic devices.[24,41] Although studies suggest another two decades of potential progress in silicon nanoelectronics,[42] a switch from the size-limited traditional materials towards molecular components will be required to continue this process of transistor scaling. Due to their versatile adjustable electronic properties MV systems represent promising targets towards molecule-based electronics. Both organic and inorganic MV compounds are used in photovoltaic devices, where dye-sensitized solar cells represent a highlight. Here MV systems may act as sensitizer, as well as redox shuttle, and remarkable efficiencies have already been achieved.[17,43,44] Specific applications of the MV systems investigated in this thesis are discussed in a small introduction in the respective chapters.
4
INTRODUCTION
Quantum-Chemical Investigations of Mixed-Valence Systems To achieve a proper quantum-chemical description of the ET transitions, it is important to account for effects from both dynamical and non-dynamical correlation, keeping in mind that there is no clear-cut separation between these extremes. With large configuration interaction (CI) or coupled cluster (CC) calculations within an ab initio framework this problem could be addressed in principle. Unfortunately, due to the size of typical MV systems those methods are computationally too demanding. Hartree-Fock (HF) calculations give too localized and standard density-functional calculations too delocalized descriptions. To make things worse, most experimental data are obtained in a polar solvent environment, which inevitably stabilizes a localized charge-separated situation. A recently developed quantum-chemical protocol employing the BLYP35 (global) hybrid functional with 35% exact-exchange, together with continuum solvent models, has been shown to give near optimum results for ground- and excited-state properties of bis-triarylamine radical cations containing two N,Ndi(4-methoxyphenyl)-moieties as redox centers bridged by various organic units[45,46] and a wide variety of other organic MV systems.[47-49] The outstanding feature is that the prediction is made without any assumptions and/or constraints. In this work it is shown that this protocol is also capable of describing the charge localization/delocalization behavior of MV transitionmetal complexes in the ground state. Furthermore an accurate quantum-chemical perspective on the excited-state properties is obtained. As a consequence the quantum-chemical approach facilitates the unique assignment of UV-vis-NIR bands of MV systems near the Class II/Class III borderline, which is very difficult based exclusively on experimental data. Results and parts of this work have already been published in the journals Inorganic Chemistry (Section 3.1), Organometallics (Section 3.2), Chemistry – A European Journal (Chapter 4), and Chemical Society Reviews.
CHAPTER 1
THEORETICAL BACKGROUND 1 .1 M ixed -V alen ce S ystem s The principles involved in ET processes and models connecting spectroscopic data of MV compounds with their electronic structure have attracted appreciable attention since the discovery of the Creutz-Taube ion, which resulted in the fundamental Marcus-Hush[50,51] and (generalized) Mulliken-Hush theories.[20,52-56] Regardless of the constituents and composition of the system, electronic absorption data are crucial to the characterization of MV complexes.[57,58] Whilst there is a wealth of information contained in the (often overlooked) metal-ligand charge-transfer (MLCT)/ligand-metal charge-transfer (LMCT) transitions that usually fall in the visible region of the spectrum,[55,57,59,60] the lower energy intervalence charge-transfer (IVCT) band typically found in the NIR region is usually the primary source of information concerning the electronic character of a MV system.[12,57,58,61,62] Other important spectroscopic techniques for the investigation of the electronic character of MV complexes, which involve somewhat different energy and time scales, include vibrational spectroscopies (IR, Raman),[63-67] Stark spectroscopy,[68] Mössbauer spectroscopy,[69-71] and electron paramagnetic resonance (EPR) spectroscopy.[5,72,73]
Robin-Day Classes The description of electronic structure of MV systems is usually made within the Robin-Day scheme, which was introduced in 1967.[74] Although in principal, it is applicable to larger and
6
CHAPTER 1: THEORETICAL BACKGROUND
more sophisticated systems, the scheme will be illustrated by the important model case of two redox centers linked by a bridging ligand. It is based on the extent of electronic coupling of two diabatic localized potential energy curves to give adiabatic ground and excited states of the system. The three primary Robin-Day classes are simply denoted Class I, II, and III. Class I corresponds to the situation in which there is no coupling between the diabatic potential energy curves (Figure 1, left). Class II corresponds to partial localization of charge and spin due to the electronic coupling, 2Hab, being smaller than the (internal plus external) Marcus reorganization energy, λ. This leads to a double-well adiabatic ground-state potential curve with an activation barrier for thermal ET. In contrast, in Class III charge and spin are delocalized over both redox centers, and the ground-state barrier has vanished as 2Hab ≥ λ. As optoelectronic properties of a MV system are crucially dependent on the localization/delocalization of charge, the distinction between Class II and III behavior has been investigated in detail, through application of an increasingly wide and sophisticated range of spectroscopic and computational techniques and theoretical treatments. At the borderline between Class II and III, small activation barriers and fast ET processes may give rise to contradictory findings with these different techniques, partly due to the different time scales of internal and solvent reorganization processes. This convolution of internal reorganization and solvent dynamics has led Meyer and coworkers to introduce an intermediate Class II/III.[12] Finally, a Class IV was proposed by Lear and Chisholm by taking the vibronic progression into consideration.[59] The characteristics of Class IV, which may be considered a subclass of Class III, include the absence of (or minimal) vibronic coupling, and the solvent-independence of not only the IVCT but also the MLCT band.
Figure 1. Potential energy curves of the three primary Robin-Day classes: Class I: diabatic states, no coupling, fully localized, no thermal ET (left); adiabatic states, weak coupling, partly localized, ET barrier ∆G* (middle), and Class III adiabatic states, strong coupling, fully delocalized, no ET barrier (right).
Marcus-Hush and Mulliken-Hush Theory Theoretical models to describe MV systems are based on the groundbreaking work on ET reactions based on diabatic potential-energy curves by Marcus, which was awarded with the nobel prize in 1992.[75] The first experimental investigations were performed on “self-
CHAPTER 1: THEORETICAL BACKGROUND
7
exchange reactions”. These correspond to ET between two atoms of the same element in different oxidation states (e.g. FeIII/FeII as found in Prussian Blue) and no chemical bonds are formed or broken. In addition “cross reactions” between different elements in aqueous solution were investigated. In principle, intra-molecular ET processes can be either thermally or optically induced. In the former case, the ET activation barrier ∆G*, also called free activation energy, between two charge-localized states is the rate-determining quantity.[6] Experimentally determined values of ∆G* are available for only few systems, as variabletemperature spectroscopic measurements, typically EPR experiments, have to be performed.[73] This thesis will focus on the investigation of optically induced ET processes and on the factors influencing excited-state parameters. In the case of two diabatic states A and B (Class I), ET proceeds directly via the absorption of a photon. Thus both the ground and excited-state feature charge-localized structures, and the electron is transferred from one redox center to another directly by the excitation. The excitation energy corresponds exactly to the so-called Marcus reorganization energy λ.[6,57] The reorganization energy is normally divided into contribution from slow modes λ0, which account for solvent reorientation after the ET took place, and fast modes λi primarily describing intra-molecular structural changes, e.g bond elongations/contractions associated with oxidation-state changes. For MV complexes exhibiting an ET rate in the frequency range between the solvent (1011-1012 s–1), and the internal modes (1013-1014 s–1) Meyer et al. proposed the intermediate Class II/III.[12]
Etrans = h⌫ = λ = λ0 +
X i
λi
(1.1.1)
The classical Marcus theory is only applicable to MV systems, in which there is no electronic coupling between the redox centers (Class I case). The analysis of systems, which exhibit electronic interaction between the redox moieties, requires an adiabatic treatment, namely Marcus-Hush theory.[50,51,55,76] In this extension to Marcus theory the electronic coupling 2Hab leads to a double-minimum potential in the ground state (Class II, Figure 1), which exhibits an ET activation barrier ∆G*. In the case of a symmetric MV complex, identical redox centers in the neutral complex respectively, ∆G* is given as: G⇤ =
(
2Hab )2 4
(1.1.2)
This equation links thermally and optically induced ET in Class II systems.[77] Remarkably Marcus-Hush theory allows for a detailed analysis of the IVCT transition for Class II systems. It is only valid if the temperature is sufficiently high for the ground-state vibrational modes to be populated following a Boltzmann distribution, and the ET is induced via a vertical excitation following the Franck-Condon principle. Taking the vibronic coupling into account via a harmonic diabatic approach the IVCT band is then nearly symmetrical and Gaussian-
8
CHAPTER 1: THEORETICAL BACKGROUND
shaped in the case of relatively small electronic coupling (Figure 2, top), and the full band width at half maximum ν1/2 is exactly given as: ⌫1/2 =
p 16ln2kB ⌫max
(1.1.3)
Figure 2. NIR band shapes caused by vibronic coupling between ground and excited-state for a MV complex with relatively small electronic coupling Hab resulting in a nearly Gaussian shaped band, (top) and for a complex with relatively strong coupling Hab and small ET activation barrier ∆G* resulting in an asymmetric band (bottom).
CHAPTER 1: THEORETICAL BACKGROUND
9
Unfortunately the comparison of this theoretical value with the experimentally observed band width is often taken as main criterion for the Robin-Day classification: if the Gaussian function fitted to the experimental IVCT band is broader than the value obtained from Equation 1.1.3, the complex is assigned as Class II system. If it is narrower, Class III behavior is assumed. Despite the difficulties to uniquely assign an IVCT band and the problems arising from the Gaussian-deconvolution fitting, which are discussed in the next section, the assumption of a Gaussian-shaped band becomes more and more inaccurate with increasing electronic coupling. This is due to the increasing asymmetry of the IVCT band, which can be illustrated by a simple picture of the vibrational levels of ground and excited-state and the resulting Franck-Condon excitations (Figure 2, bottom). The overlap integral of the groundand excited-state vibrational wave function, corresponding to the Franck-Condon transition probability and intensity, is largest for the areas near the borders of the electronic potential and near the ET barrier. If the barrier is sufficiently small, and vibrational states, which are energetically higher than the barrier, are appreciably populated, an asymmetric IVCT band is observed. In reality the cut-off is not as steep as indicated in the figure, but the band envelope is strongly and continuously decreasing, resulting in a large deviation from of a Gaussianshaped band.[6,57,78] To account for this band asymmetry, more advanced models like the two-mode model have to be applied.[20,79,80] But despite its more complicated form compared to the MarcusHush/Mulliken-Hush models, it is only practical for strongly coupled MV systems. Within the framework of Mulliken-Hush theory the electronic coupling 2Hab can be directly extracted from spectroscopic parameters.[53,54,57,81] Unfortunately the necessary difference in the diabatic dipole moments of the ground and excited states is not directly accessible experimentally. The difference is then typically estimated by the difference of the adiabatic dipole moments, but again the adiabatic dipole moment of the excited states is only rarely determinable by Stark spectroscopy and has to be either calculated by quantum-chemical methods or approximated using the structural estimates such as the redox center distance.[6] The models discussed so far focus on the analysis of the IVCT band. But additionally there is a wealth of information contained in the MLCT/LMCT transitions that usually fall in the visible region of the spectrum.[55,57,59,60] To account for those transitions one has to advance to three-state models and/or generalized Mulliken-Hush theory.[53,54,56] But as these models get more and more sophisticated and several required quantities are not accessible experimentally (sometimes by quantum-chemical calculations), they are not discussed in detail in this thesis, and the focus will be on a purely quantum-chemical description of MV complexes.
10
CHAPTER 1: THEORETICAL BACKGROUND
Experimental Classification Information on the extent of charge localization/delocalization in an MV system can be obtained by various experimental techniques. Most commonly the assignment to a Robin-Day class is based on the analysis of the IVCT band, which typically occurs in the NIR region of the electromagnetic spectrum. The potential for multiple electronic transitions of similar energy but different electronic origin, together with the asymmetric IVCT band-shapes that characterize strongly coupled MV systems, renders derivation of the ET characteristics and electronic structure from NIR spectra alone very difficult in many MV transition-metal complexes, despite the popularity of such analyses. In organic MV systems the IVCT band usually appears as the lowest-energy band in the spectrum, facilitating the assignment.[6] Other important spectroscopic techniques involve somewhat different energy and time scales, e.g. vibrational spectroscopies (IR, Raman), Stark spectroscopy, Mössbauer spectroscopy, and EPR spectroscopy. At the borderline between Class II and III, small activation barriers and fast ET processes may give rise to contradictory findings with different spectroscopic techniques, due to the different time scales of the spectroscopic methods, which can be comparable to the rates of ET, inner-sphere reorganization processes, and solvent dynamics. In some early studies the presence of symmetry-broken crystal structures was used as classification criterion, but of course the solid state may differ significantly from the situation in solution. Despite the fact that crystals are normally grown at low temperatures, at which the ET process is slowed down, crystal structures may be distorted due to packing-, counter ion-, or other crystal-effects.[82] For example salen-type complexes often exhibit symmetry-broken structures in the crystal, but may feature delocalized charge in solution.[83-86] Additionally, for complexes with free coordination sites, direct coordination of Lewis basic solvents may occur. IR and vibrational Raman spectroscopy represent very fast and powerful methods to obtain information on the electronic structure of the ground state of MV systems.[63] They are often used in combination with UV-vis-NIR spectroscopy as part of a spectroelectrochemical approach.[87] Indications of charge localization are easily derived from the IR spectra of complexes, which are symmetric in their non-mixed-valence forms. The splitting of IR bands due to the energy difference in modes, which are degenerate in the delocalized case (e.g. ν(C≡C) vibrations) or the appearance of new IR bands, which do not involve changes of the permanent dipole moment in the case of a symmetrically distributed electron density, point to symmetry-broken structures.[64-66] Satellite groups, such as local auxiliary ligands, may allow monitoring of modes, e.g. ν(NO) or ν(CO), which depend strongly on the oxidation state of the metal center and thus are sensitive to the charge distribution.[67] Analogously, information on electronic structure may be derived from Raman spectra.[63,88]
CHAPTER 1: THEORETICAL BACKGROUND
11
Mössbauer spectroscopy is sensitive to oxidation state and charge distribution and corresponds to short time scales. The technique is limited to the Mössbauer-active nuclei, where 57Fe is the most prominent example.[69-71] The paramagnetic nature of most MV systems complicates the use of NMR spectroscopy due to paramagnetic line broadening. Variable-temperature EPR spectroscopy is widely used to determine ET barriers in organic MV systems.[5,72,73] Applications to MV transition-metal complexes are more limited, due to difficulties in extracting hyperfine coupling constants.[64] In principle the isotropic hyperfine coupling constant of a MV system corresponds to the value obtained for an analogous monometallic complex, if the charge is localized. For a Class III system it is close to half the value of the monometallic analogue. In addition, line broadening effects in the EPR spectrum may reveal ET processes that are slower than or comparable to the EPR time scale (10–9 s).[89] Shortcomings of the State-of-the-Art Experimental Classification A common way to analyze NIR spectra is to fit the spectroscopic data with Gaussian functions. In principle, the population of both ground- and excited-state vibrational levels can to some extent be taken into account assuming that these follow a Boltzmann distribution. Based on the semi-empirical model proposed by Meyer et al., experimental spectra of 3d and 4d complexes are normally fitted with three Gaussian functions.[12] This localized model assumes two interconfigurational (IC) bands, which arise from excitations from orbitals localized at the hole-carrying (more highly oxidized) ruthenium center to orbitals at the same center, and three IVCT bands originating from separate electronic excitations from three dπ orbitals of the other metal center. The IC transitions are normally parity forbidden and only gain intensity, if the system exhibits noticeable spin-orbit coupling. As the latter tends to be significant only for 5d systems, 3d and 4d metal complexes are typically expected to exhibit only the three IVCT excitations. Unfortunately this assumption is only valid for clear-cut Class II or Class III systems in the Robin-Day scheme, as pointed out nicely by Creutz et al. and Lambert and Heckmann.[6,57] For systems close to the Class II/Class III borderline, the NIR band gets more and more asymmetric, as there is a cut-off at the smallest energy possible for an electronic transition (Figure 2). Due to this asymmetry of the band envelope, Gaussian functions are no longer a very suitable approximation. In addition to the vibrational progression, an alternative explanation for the band asymmetry of the Creutz-Taube ion was suggested by Meyer et al.:[12] the asymmetry of the IVCT band of the Creutz-Taube ion is explained by the coupling of two of the proposed IVCT transitions at 6320 cm–1 and 7360 cm–1. The fact that the band shape does not change in low-temperature experiments was used as an argument to rule out vibronic effects. High-level quantum-chemical studies did not reproduce these transitions,[90] and thus caution with Gaussian deconvolutions is advocated, when the investigated system is not a clear-cut Class II or Class III complex. Taking into account the band cut-off, which
12
CHAPTER 1: THEORETICAL BACKGROUND
appears at the low-energy side, one can in principle perform Gaussian deconvolution of the experimental NIR band by fitting only the high-energy part of the curve, which should correspond to a Gaussian shape, if only one transition is present (Figure 3). But a quantumchemical approach, which facilitates assignment of the unique transition and thus of the character of NIR bands, is a clearly preferable method for the explanation of band shapes.
Figure 3. NIR data with Gaussian deconvolutions fitted to only the high-energy half of the curve for a complex with two transitions (left) and for a complex with one transition in this spectral region (right).
CHAPTER 1: THEORETICAL BACKGROUND
13
1 .2 D en sity F u n ction al T h eory Already in 1929 Dirac stated that “the general theory of quantum mechanics is now almost complete ... The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these equations leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.”[91] Density functional theory (DFT) was developed in the 1960s by Kohn, Hohenberg, and Sham as such an applicable approximate practical method.[92,93] But it took until the early 1990s to establish this method widely in applied quantum-chemistry. Ever since then the importance and number of applications of DFT has been growing, and it has become the method of choice for electronic-structure scientists ranging from quantum chemists and solid-state physicists to biophysicists. To explain this success one has to look at the machinery behind the approach and the reasons for its outstanding status among quantum-chemical methods.[94-97] In this section the general quantum-chemical concepts and the specific principles behind DFT as well as it advantages and shortcomings are discussed.
Principles General Quantum-Chemical Principles and Hartree-Fock Theory In the non-relativistic case the energy of any system is given by the time-dependent Schrödinger equation:
i~
@ ˆ t) (r, t) (r, t) = H(r, @t
(1.2.1)
ˆ is the time-dependent Hamiltonoperator, which contains all interactions within the H system and is normally divided into a potential-energy part Vˆ and kinetic-energy part Tˆ . Ψ is
the wave function of the system, which depends on the time t and the particle coordinates r, and ħ represents the reduced Planck constant. In the stationary case the time-dependence can be separated and treated as a phase factor, thus giving the time-independent Schrödinger equation:
ˆ H(r) (r) = E (r)
(1.2.2)
In principle, by solving this Eigenwert equation one obtains the total energy E and all information about the ground-state of any given system can be extracted from the wave
14
CHAPTER 1: THEORETICAL BACKGROUND
function Ψ. Unfortunately, as Dirac stated, this equation (or even more so its relativistic analogues) is much too complicated to be solvable, and approximations have to be made. Typically the first approach is to assume fixed nuclei and to thus obtain the electronic Schrödinger equation. Therefore the kinetic energy of the nuclei is zero and the nuclei-nuclei repulsion is given by a constant. After this so-called Born-Oppenheimer approximation, the electronic Hamiltonian is given by the kinetic energy of the electrons and the two potentialenergy terms, the electron-electron repulsion and the electron-nuclei attraction υ(r), the socalled external potential in DFT. In the case of an atom or molecule in the absence of an external field, υ (r) is simply determined by the nuclear configuration and corresponds to the attractive point-charge Coulomb potential between nuclei and electrons. Thus for a system with N electrons and M nuclei the electronic Hamiltonian is given (in atomic units) by
Hˆe = Tˆe + Vˆee + Vˆne
◆ X N ✓ N N X X 1 2 1 − ri + = − (r) 2 r i β-SOMO transition) and E2 (β-HOMO–3 => β-SOMO transition) and corresponding transition dipole moment µ1 and µ2 from Gaussian09 and TURBOMOLE 6.4 calculations, respectively, for [Ru1´]+ as a function of P-Ru-Ru-P dihedral angle Ω.
Gaussian09 Ω
∆E
E1
µ1 –1
TURBOMOLE 6.4 E2
µ2 –1
E1
µ1 –1
E2
µ2 –1
[°]
[kJ/mol]
[cm ]
[D]
[cm ]
[D]
[cm ]
[D]
[cm ]
[D]
0
12.6
11572
9.8
14307
0.8
12089
9.2
14736
0.8
10
5.9
11614
9.7
14285
1.2
12102
9.0
14657
1.2
20
2.2
11660
9.6
14154
1.2
12192
8.9
14568
1.2
30
1.0
11729
9.5
14055
1.4
12242
8.8
14438
1.3
40
3.3
11743
9.4
13987
1.6
12337
8.7
14467
1.5
50
6.4
11698
9.3
13974
2.2
12299
8.6
14459
2.0
60
9.8
11587
9.2
13991
2.7
12204
8.5
14497
2.5
70
10.6
11465
9.0
14089
3.1
12072
8.4
14547
3.0
80
11.7
11417
8.7
14137
3.6
12131
8.0
14681
3.4
90
12.2
11616
8.4
14463
3.6
12227
7.8
14882
3.5
100
9.8
11427
8.5
13928
3.8
12136
7.9
14470
3.6
110
6.9
11516
8.7
13924
3.5
12166
8.0
14446
3.2
120
7.3
11547
8.9
14024
3.1
12200
8.2
14564
2.8
130
9.6
11538
9.3
14095
2.4
12231
8.6
14692
2.2
140
6.3
11582
9.5
14120
1.7
12139
8.9
14585
1.6
150
4.1
11601
9.6
14082
1.2
12157
8.9
14551
1.1
160
2.4
one negative-energy excitation
12228
8.9
14554
0.7
170
0.9
11698
9.6
14057
0.5
12301
8.9
14558
0.4
180
0.0
11708
9.5
13961
0.0
12344
8.8
14543
0.0
APPENDIX
131
Table A4. Calculated ground-state properties for different minima of obtained from full structure optimizations of [Os1]+, [Mo1]+, and [Re1]+. Energy difference to the respective most stable conformer ∆E (min-[Os1]+, min[Mo1]+, and min-[Re1]+), total dipole moment µa, spin expectation value 〈S 2 〉 (theoretical value for doublet systems would be 0.75), and calculated C≡C stretching frequencies ν(C≡C). [Os1]+ min ∆E [kJ/mol] 0.0 µa [D] 2.8 0.76 〈S 2 〉 1877 ν(C≡C) [cm–1]
perp 5.9 2.3 0.76 1870
trans 6.5 0.0 0.76 1873
[Mo1]+ min 0.0 12.1 0.81 1971 1913
trans 8.7 9.2 0.80 1930 1897
[Re1]+ trans 0.0 0.1 0.78 1892
cis 2.4 10.0 0.78 1889
132
APPENDIX
Table A5. Calculated excited-state parameters: UV-vis-NIR transition energies Etrans, transition dipole moments µtrans, and contributing orbital transitions for the minima of [Os1]+ obtained from full structure optimizations at the BLYP35/COSMO(CH2Cl2) level. TURBOMOLE 6.4 min-[Os1]+ #
Etrans
µtrans
–1
[cm ]
[D]
1
2415
1.4
2
12652
3
perp-[Os1]+ contributions
Etrans
µtrans
–1
[cm ]
[D]
312 β -> 313 β
1484
1.9
8.4
311 β -> 313 β
12318
14406
0.3
310 β -> 313 β
4
16077
2.2
5
18620
0.2
6
23254
0.4 0.4
Etrans
µtrans
contributions
[cm ]
[D]
312 β -> 313 β
3406
0.0
312 β -> 313 β
8.1
311 β -> 313 β
12875
8.8
311 β -> 313 β
14029
0.3
310 β -> 313 β
15259
0.9
310 β -> 313 β
309 β -> 313 β
15912
3.1
309 β -> 313 β
16436
0.0
309 β -> 313 β
308 β -> 313 β,
17551
0.1
308 β -> 313 β,
19773
0.2
308 β -> 313 β
22970
0.1
23730
0.0
307 β -> 313 β,
307 β -> 313 β
308 β -> 313 β 24071
contributions
–1
307 β -> 313 β
7
trans-[Os1]+
305 β -> 313 β
307 β -> 313 β, 308 β -> 313 β
23571
0.4
305 β -> 313 β
307 β -> 313 β, 303 β -> 313 β
24226
0.6
312 β -> 332 β
Gaussian09 min-[Os1]+ Etrans
µtrans
[cm–1]
[D]
1
2371
1.6
2
11990
3
perp-[Os1]+ Etrans
µtrans
[cm–1]
[D]
312 β -> 313 β
1471
2.2
9.1
311 β -> 313 β
11633
13788
0.4
310 β -> 313 β
4
15439
2.4
5
18183
0.3
#
trans-[Os1]+ Etrans
µtrans
[cm–1]
[D]
312 β -> 313 β
3373
0.0
312 β -> 313 β
8.8
311 β -> 313 β
12102
9.5
311 β -> 313 β
13440
0.4
310 β -> 313 β
14537
1.2
310 β -> 313 β
309 β -> 313 β
15349
3.4
309 β -> 313 β
15679
0.0
309 β -> 313 β
308 β -> 313 β
17155
0.0
307 β -> 313 β,
19210
0.2
308 β -> 313 β
contributions
contributions
contributions
308 β -> 313 β 6
22841
0.4
7
23667
0.1
8
24226
9 10
307 β -> 313 β,
22539
0.1
307 β -> 313 β
23352
0.0
307 β -> 313 β
305 β -> 313 β
23114
0.3
305 β -> 313 β
24019
0.0
305 β -> 313 β
0.5
mixed excitation
24002
0.4
312 β -> 332 β
24303
0.6
312 α -> 333 α
24908
0.2
312 β -> 314 β
24607
0.1
312 β -> 314 β
25242
0.1
312 α -> 314 α
25047
0.1
312 β -> 315 β
24741
0.2
312 β -> 315 β
25249
0.3
312 β -> 315 β
308 β -> 313B
APPENDIX
133
Table A6. Orbital energies (Eorb) and composition from Mulliken population analysis for [Os1]+ ([Os] = Os(dppe)Cp*). Virtual orbitals are marked with a *. min-[Os1]+ Orbital
EOrb [eV]
perp-[Os1]+ EOrb
contributions [%]
trans-[Os1]+ EOrb
contributions [%]
contributions [%]
[Os]
C≡C
C≡C
[Os]
[eV]
[Os]
C≡C
C≡C
[Os]
[eV]
[Os]
C≡C
C≡C
[Os]
/
24
25
25
26
/
25
25
26
25
/
24
25
25
24
β*
-0.65
37
0
0
43
-0.65
0
0
0
83
-0.62
2
0
0
63
α*
-0.67
46
0
0
38
-0.67
0
0
0
85
-0.64
25
0
0
40
β*
-2.75
20
27
27
19
-2.80
18
27
27
21
-2.65
19
26
26
21
α
-5.25
23
22
22
26
-5.23
23
25
24
18
-5.15
22
22
22
25
β
-5.15
20
25
25
20
-5.08
23
24
24
20
-5.20
19
26
26
19
α
-5.29
19
25
25
20
-5.31
23
22
22
24
-5.31
21
26
26
21
β
-5.94
39
10
9
33
-5.93
37
9
8
34
-5.90
33
11
11
37
α
-6.24
36
4
4
42
-6.25
67
5
2
11
-6.25
38
4
4
42
β
-6.18
34
4
4
44
-6.19
40
3
4
39
-6.21
37
4
4
42
α
-6.33
43
4
4
35
-6.29
10
1
6
68
-6.40
35
6
6
39
β
-6.41
40
7
6
35
-6.46
33
8
8
38
-6.34
36
5
5
39
α
-6.68
34
7
6
36
-6.75
35
7
7
35
-6.54
34
5
5
40
β
-6.88
34
8
8
35
-6.78
36
8
9
34
-7.01
39
4
4
38
α
-7.03
37
7
7
35
-6.93
34
8
8
37
-7.11
38
4
4
38
β
-7.13
31
4
5
42
-7.17
44
4
4
30
-7.03
29
8
8
34
α
-7.25
36
4
4
36
-7.28
40
3
4
32
-7.19
30
6
6
34
β
-7.29
44
2
1
29
-7.27
29
2
3
45
-7.31
35
1
1
38
α
-7.46
42
1
3
33
-7.43
34
3
2
43
-7.45
35
2
2
34
β
-7.40
37
3
3
40
-7.42
38
3
3
40
-7.36
36
3
3
36
α
-7.55
36
2
3
44
-7.56
42
3
2
39
-7.54
36
3
3
32
spin density 314
313
312
311
310
309
308
307
306
305
134
APPENDIX Table A7. Calculated excited-state parameters: UV-vis-NIR transition energies Etrans, transition dipole moments µtrans, and contributing orbital transitions for the minima of [Mo1]+ obtained from full structure optimizations at the BLYP35/COSMO(CH2Cl2) level. TURBOMOLE 6.4 min-[Mo1]+ # 1
Etrans
µtrans
[cm–1]
[D]
6073
2.4
trans-[Mo1]+ contributions 284 β -> 285 β,
Etrans
µtrans
[cm–1]
[D]
7301
0.7
281 β -> 285 β 2
10746
5.9
3
12710
0.9
283 β -> 285 β,
7731
9.4
14047
1.7
14701
2.4
280 β -> 285 β,
15133
0.9
6
16276
0.4
284 β -> 286 β,
14589
0.2
15118
0.8
15526
0.2
16582
0.2
285 α -> 292 α
16954
0.8
283 β -> 286 β, 284 α -> 286 α
285 α -> 290 α 7
281 β -> 285 β, 283 β -> 285 β
285 α -> 286 α 285 α -> 291 α,
280 β -> 285 β, 279 β -> 285 β
279 β -> 285 β 5
284 β -> 285 β, 280 β -> 285 β
282 β -> 285 β 4
283 β -> 285 β, 281 β -> 285 β
280 β -> 285 β 281 β -> 285 β,
contributions
284 β -> 286 β, 285 α -> 286 α 285 α -> 289 α
Gaussian09 min-[Mo1]+ # 1
Etrans
µtrans
–1
[cm ]
[D]
6466
2.4
perp-[Mo1]+ contributions 284 β -> 285 β
Etrans
µtrans
–1
[cm ]
[D]
7545
1.0
contributions 281 β ->285 β, 283 β ->285 β
2
10988
5.9
283 β -> 285 β
7959
9.6
284 β ->285 β
3
12702
1.3
281 β -> 285 β
13927
1.9
279 β ->285 β,
4
14729
2.8
280 β -> 285 β
14758
0.2
281 β ->285 β
5
15245
0.9
285 α -> 286 α
15182
0.8
283 β ->286 β
6
16382
0.4
285 α -> 290 α
15540
0.2
284 β ->286 β
7
16682
0.2
mixed excitation
17013
0.8
285 α ->289 α
8
18078
1.7
mixed excitation
17547
0.3
285 α ->286 α,
9
18578
1.8
282 β ->285 β
18181
0.7
282 β ->285 β
10
18973
2.4
282 β ->285 β
18844
0.5
282 β -> 285 β
280 β ->285 β
284 β ->286 β
APPENDIX
135
Table A8. Orbital energies (Eorb) and composition from Mulliken population analysis for [Mo1]+ ([Mo] = Mo(η-C7H7)(dppe)). Virtual orbitals are marked with a *. min-[Mo]+ Orbital
EOrb
trans-[Mo]+ EOrb
contributions [%]
[eV]
[Mo]
/
73
7
10
5
/
66
8
11
11
β*
-1.24
67
10
6
3
-1.36
55
12
9
11
α*
-1.39
75
9
5
2
-1.45
65
10
7
8
β*
-2.75
58
14
10
2
-2.79
53
15
12
8
α
-5.00
5
12
16
56
-5.19
4
12
18
56
β
-4.98
8
11
14
56
-5.11
14
6
9
59
α
-5.36
4
13
20
56
-5.37
10
15
19
50
β
-5.50
8
10
15
58
-5.34
17
15
18
45
α
-6.05
2
4
6
79
-6.17
2
3
4
83
β
-6.03
11
6
6
68
-6.16
2
2
5
84
α
-6.36
30
15
8
36
-6.45
41
12
6
33
β
-6.24
32
9
5
47
-6.29
45
9
4
34
α
-6.64
25
20
14
31
-6.61
26
18
11
32
β
-6.67
55
13
9
15
-6.64
48
15
12
11
α
-7.13
89
3
0
0
-7.12
91
2
0
0
β
-7.00
44
14
17
10
-7.02
54
12
15
5
α
-7.41
7
0
3
77
-7.46
6
2
5
75
spin density
C≡C
C≡C
[Mo]
[eV]
contributions [%] [Mo]
C≡C
C≡C
[Mo]
286
285
284
283
282
281
280
279
136
APPENDIX
Table A9. Computed energy difference to the most stable rotamer (Ω =180 °), ∆E, two lowest excitation energies E1 and E2 and corresponding transition dipole moment µ1 and µ2 from TURBOMOLE 6.4 calculations, respectively, for [Mo1]+ as a function of P-Mo-Mo-P dihedral angle Ω. Ω
∆E
E1
µ1 –1
E2
µ2 –1
[°]
[kJ/mol]
[cm ]
[D]
[cm ]
[D]
0
18.3
7349
1.1
7938
9.1
10
16.6
7033
4.2
8170
8.1
20
13.7
6557
4.9
8498
7.6
30
7.6
6291
4.4
9115
7.2
40
3.0
6089
3.7
9682
6.8
50
0.6
6035
2.9
10285
6.3
60
0.0
6056
2.3
10833
5.9
70
1.0
6056
1.5
11127
5.3
80
2.3
6060
0.7
11327
5.1
90
3.5
6123
0.1
11318
4.9
100
4.6
6033
0.6
11050
5.2
110
5.0
6109
1.3
10781
5.5
120
5.6
6161
2.1
10239
5.9
130
6.3
6277
3.0
9773
6.4
140
6.5
6411
3.6
9363
6.9
150
7.3
6505
4.6
8694
7.3
160
10.7
6709
4.6
8415
7.9
170
9.6
7034
4.6
7864
8.3
180
9.1
7260
1.6
7655
9.4
APPENDIX
137
Table A10. Calculated excited-state parameters: UV-vis-NIR transition energies Etrans, transition dipole moments µtrans, and contributing orbital transitions for the minima of [Re1]+ obtained from full structure optimizations at the BLYP35/COSMO(CH2Cl2) level. TURBOMOLE 6.4 trans-[Re1]+ Etrans
µtrans
[cm–1]
[D]
1
10238
0.8
2
10346
10.0
3
14237
3.0
#
cis-[Re1]+ Etrans
µtrans
[cm–1]
[D]
253 β -> 255 β
10269
0.2
253 β -> 255 β 96.7
254 β -> 255 β,
10287
10.0
254 β -> 255 β,
14232
3.0
contributions
254 β -> 256 β 254 α -> 256 α,
253 β -> 256 β
253 β -> 256 β 4
16722
0.0
254 α -> 263 α,
18423
1.0
6
19731
0.0
255 α -> 256 α,
16686
0.1
18464
1.0
19817
0.3
19894
0.4
251 β -> 255 β
19910
0.4
255 α -> 256 α, 251 β -> 255
249 β -> 255 β 7
254 α -> 263 α, 253 β -> 263 β
251 β -> 255 β 252 β -> 255 β,
254 α -> 256 α, 253 β -> 256 β
253 β -> 263 β 5
contributions
252 β -> 255 β, 249 β -> 255 β 251 β -> 255 β
138
APPENDIX Table A11. Orbital energies (Eorb) and composition from Mulliken population analysis for [Re1]+ ([Re] = ReCp(PPh3)(NO)). Virtual orbitals are marked with a *. trans-[Re]+ Orbital
EOrb [eV]
spin density
cis-[Re]+ EOrb
contributions [%] [Re]
C≡C
C≡C
[Re]
[eV]
contributions [%] [Re]
C≡C
C≡C
[Re]
/
28
20
20
28
/
28
20
20
28
β*
-1.65
32
15
15
32
-1.66
31
15
15
31
α*
-1.59
32
15
15
32
-1.60
32
15
15
32
β*
-3.27
24
23
23
24
-3.28
24
23
23
24
α
-5.72
26
20
20
26
-5.73
26
20
20
26
β
-6.17
34
10
10
34
-6.17
34
10
10
34
α
-6.45
22
26
26
22
-6.46
22
26
26
22
β
-6.42
22
26
26
22
-6.43
22
26
26
22
α
-6.97
38
5
5
38
-6.98
38
6
6
38
β
-7.08
37
5
5
37
-7.10
38
5
5
37
α
-7.13
38
5
5
37
-7.15
39
4
4
37
β
-7.11
39
2
2
39
-7.13
38
3
3
39
α
-7.15
38
4
4
39
-7.17
38
4
4
39
β
-7.68
39
2
2
39
-7.68
39
2
2
39
α
-7.76
43
2
2
43
-7.77
42
2
2
42
β
-7.71
30
9
9
30
-7.71
34
8
8
34
α
-7.79
42
2
2
41
-7.79
43
2
2
43
β
-7.81
44
0
0
42
-7.82
44
0
0
44
α
-7.84
43
0
0
43
-7.86
43
0
0
44
256
255
254
253
252
251
250
249
248
APPENDIX
139
Table A12. Computed energy difference to the most stable rotamer (Ω =180 °), ∆E, three lowest excitation energies E1, E2, and E3 and corresponding transition dipole moment µ1, µ2, and µ3 from TURBOMOLE 6.4 calculations, respectively, for [Re1]+ as a function of P-Re-Re-P dihedral angle Ω. Ω
∆E
E1
µ1 –1
E2
µ2 –1
E3
µ3 –1
[°]
[kJ/mol]
[cm ]
[D]
[cm ]
[D]
[cm ]
[D]
0
2.5
10267
0.2
10288
10.0
14230
3.0
10
2.5
9298
6.8
11160
7.3
14249
2.9
20
3.7
8244
6.7
11884
7.5
14293
2.5
30
5.2
7074
6.6
12394
7.6
14317
1.7
40
8.2
5775
6.5
12707
7.7
14358
0.7
50
11.7
4418
6.5
12868
7.6
14384
0.5
60
15.7
3072
6.8
12882
7.3
14181
1.4
70
19.9
3484
4.2
13185
5.9
13852
2.7
80
22.0
4077
1.7
13214
5.1
14380
2.9
90
23.1
4300
0.3
13236
5.0
14652
2.6
100
22.1
4220
1.5
13256
5.0
14436
3.0
110
19.9
3622
3.9
13200
5.9
13913
2.9
120
15.3
3115
6.7
12891
7.4
14245
1.6
130
10.2
4404
6.6
12851
7.7
14401
0.6
140
6.5
5765
6.5
12671
7.8
14340
0.7
150
3.7
7033
6.6
12310
7.7
14288
1.7
160
1.3
8205
6.7
11807
7.5
14244
2.4
170
0.0
9315
6.7
11132
7.4
14234
2.9
180
0.1
10250
1.1
10343
9.9
14240
3.0
140
APPENDIX
Figure A2. Cut through the PES of [Ru2-Me]+ for Ω = 180° and spin-density isosurface plots (± 0.002 a.u.) for all structures of the relaxed scan of Θeff (BLYP35/def2-SVP/COSMO(CH2Cl2) level).
APPENDIX
Figure A3. Properties (BLYP35/def2-SVP/COSMO(DCM) level) as function of conformational phase space of [Ru2-Me]+. a) TDDFT transition dipole moment µtrans of the third excitation at around 10000 cm–1 (9500-11500 cm–1) (top), and b) TDDFT transition dipole moment µtrans of the fourth excitation (bottom) of [Ru2-Me]+. For two structures (Ω = 50°, Θeff = 91.7° and Ω = 100°, Θeff = 101.6°) on the PES the excited-state is unstable and thus the transition dipole moment is set to zero. BLYP35/def2-SVP/COSMO(CH2Cl2) level.
141
142
APPENDIX
Figure A4. Potential energy surface of [Ru3-Me]+ (BLYP35/def2-SVP/COSMO(CH2Cl2) level) using different color scales.
APPENDIX
143
Figure A5. Surface of the difference, ∆SD, of the Mulliken spin density contributions of the two Cl(dmpe)2Ru-C≡C units for [Ru3-Me]+ (near 0% for delocalized structures and close to 100% for fully localized charge distributions). BLYP35/def2-SVP/COSMO(CH2Cl2) level.
β-SOMO
β-HOMO
β-HOMO–1
β-HOMO–2
Figure A6. Isosurface plots (± 0.03 a.u.) of β-SOMO (top left), β-HOMO (top right), β-HOMO–1 (bottom,
left)
and
β-HOMO–2
SVP/COSMO(CH2Cl2) level).
(bottom,
right)
of
sb-[
Ru3-Me]+
(BLYP35/def2-
144
APPENDIX
Figure A7. Conformational potential-energy surface of [CTI]5+ (BLYP35/def2-SVP/COSMO(CH2Cl2) level).
Figure A8. Surface of the difference, ∆SD, of the Mulliken spin density contributions of the two (NH3)5Ru units in [CTI]5+ (0% for delocalized structures, close to 100% for localized charge distributions (BLYP35/def2-SVP/COSMO(CH2Cl2) level).
APPENDIX
Figure A9. Computed Boltzmann-weighted TDDFT stick spectra of [CTI]5+ (BLYP35/def2SVP/COSMO(CH2Cl2) level).
145
146
APPENDIX
Table A13. Isotropic hyperfine coupling constants Aiso, spin expectation value 〈S 2 〉, and difference between experimental and calculated isotropic hyperfine coupling constant values ∆Aiso for different functionals implemented in TURBOMOLE. Complex
ScO
BVWN
BLYP
B3LYP
1919
1979
1999
1981
1938
1955
1940
1948
〈S 〉
0.752
0.751
0.751
0.751
0.751
0.753
0.753
0.750
∆Aiso [MHz]
-29
32
52
33
-9
7
-8
Aiso [MHz]
-558
-572
-580
-576
-562
-565
-562
-559
〈S 〉
0.755
0.753
0.752
0.753
0.756
0.757
0.757
0.750
∆Aiso [MHz]
1
-13
-21
-17
-3
-6
-3
Aiso [MHz]
-246
-256
-256
-250
-238
-253
-257
-241
〈S 〉
2.013
2.010
2.008
2.012
2.017
2.023
2.023
2.000
∆Aiso [MHz]
-5
-15
-14
-9
3
-12
-15
Aiso [MHz]
1352
1407
1408
1352
1144
1343
1385
1314
〈S 〉
2.046
2.036
2.034
2.085
2.409
2.134
2.111
2.000
∆Aiso [MHz]
38
93
94
38
-170
29
70
Aiso [MHz]
804
843
841
818
779
835
872
780
〈S 2 〉
3.796
3.785
3.782
3.800
3.824
3.835
3.832
3.750
∆Aiso [MHz]
24
63
62
38
-1
55
93
Aiso [MHz]
528
548
550
528
535
531
597
481
〈S 2 〉
8.791
8.783
8.782
8.829
9.036
8.842
8.838
8.750
∆Aiso [MHz]
47
67
69
47
54
50
116
Aiso [MHz]
299
318
325
251
157
233
318
105
〈S 2 〉
8.760
8.759
8.758
8.760
8.760
8.761
8.762
8.750
∆Aiso [MHz]
194
213
219
146
52
128
212
Aiso [MHz]
486
513
514
479
429
474
537
443
〈S 〉
12.003
12.002
12.002
12.003
12.003
12.003
12.003
12.000
∆Aiso [MHz]
44
71
72
36
-13
31
94
Aiso [MHz]
386
415
397
343
284
362
425
280
〈S 〉
12.004
12.004
12.003
12.003
12.002
12.003
12.004
12.000
∆Aiso [MHz]
106
135
116
63
4
82
145
Aiso [MHz] 2
TiN
2
TiO
2
VN
2
VO
MnO
MnF2
MnF
2
MnH
2
BHH LYP
t-LMFt-ρVWN LMFVWN
BP86
Exp.
APPENDIX Complex
TiF3
BVWN
BLYP
B3LYP
-218
-216
-222
-196
-161
-200
-213
-185
〈S 〉
0.753
0.752
0.752
0.752
0.752
0.753
0.754
0.750
∆Aiso [MHz]
-33
-31
-37
-11
24
-15
-28
Aiso [MHz]
1979
2020
2031
1731
1275
1774
1902
1617
〈S 〉
0.769
0.765
0.764
0.871
1.857
0.871
0.835
0.750
∆Aiso [MHz]
362
402
414
114
-342
157
285
Aiso [MHz]
-642
-571
-609
-715
-666
-806
-811
-490
〈S 〉
0.761
0.759
0.761
0.766
0.766
0.767
0.768
0.750
∆Aiso [MHz]
-152
-81
-119
-224
-176
-315
-321
Aiso [MHz]
-95
-78
-82
-110
-147
-121
-48
-198
〈S 〉
8.765
8.762
8.761
8.762
8.762
8.765
8.766
8.750
∆Aiso [MHz]
103
120
116
88
51
77
150
Aiso [MHz]
24
20
20
25
33
25
13
41
〈S 2 〉
8.762
8.759
8.757
8.760
8.761
8.764
8.765
8.750
∆Aiso [MHz]
-18
-21
-21
-16
-8
-16
-29
Aiso [MHz]
-8
-13
-20
4
39
29
22
71
〈S 2 〉
0.752
0.752
0.751
0.753
0.757
0.754
0.754
0.750
∆Aiso [MHz]
-79
-83
-90
-66
-31
-42
-48
Aiso [MHz]
14
12
12
29
53
35
17
14
〈S 2 〉
0.759
0.759
0.759
0.796
0.992
0.776
0.781
0.750
∆Aiso [MHz]
0
-2
-2
15
39
21
3
Aiso [MHz]
-4
10
7
-48
-182
-75
34
-57
〈S 〉
0.762
0.761
0.761
0.787
1.012
0.775
0.773
0.750
∆Aiso [MHz]
53
67
64
9
-124
-18
91
Aiso [MHz]
-169
-143
-152
-240
-480
-268
-140
-271
〈S 〉
0.775
0.771
0.772
0.873
1.723
0.871
0.840
0.750
∆Aiso [MHz]
101
127
119
31
-210
3
130
Aiso [MHz]
2
CuO
2
[Mn(CN)4]2-
2
[Cr(CO)4]+
[Cu(CO)3]
[Ni(CO)3H]
Co(CO)4
2
Mn(CN)4N-
2
BHH LYP
t-LMFt-ρVWN LMFVWN
BP86
2
MnO3
147 Exp.
148
APPENDIX
Complex
Mn(CN)5NO2-
BVWN
BLYP
B3LYP
-147
-116
-123
-212
-290
-254
-91
-218
〈S 〉
0.866
0.854
0.860
1.434
2.093
1.363
1.269
0.750
∆Aiso [MHz]
72
102
95
6
-72
-36
127
Aiso [MHz]
5
16
12
4
3
0
50
-4
〈S 〉
0.754
0.753
0.753
0.757
0.766
0.756
0.755
0.750
∆Aiso [MHz]
9
20
16
8
7
4
54
Aiso [MHz]
0
3
2
-2
-8
-5
7
-3
〈S 〉
0.757
0.756
0.757
0.762
0.768
0.761
0.760
0.750
∆Aiso [MHz]
3
5
5
0
-5
-2
10
Aiso [MHz] 2
Mn(CO)5
2
Fe(CO)5+
2
BHH LYP
t-LMFt-ρVWN LMFVWN
BP86
Exp.
APPENDIX
149
Table A14. Isotropic hyperfine coupling constants Aiso, spin expectation value 〈S 2 〉, and difference between experimental and calculated isotropic hyperfine coupling constant values ∆Aiso for different functionals implemented in Gaussian. Complex ScO
TiN
CAMB3LYP
MnO
MnF2
MnF
Exp.
2022
2205
2115
1948
〈S 2 〉
0.751
0.752
0.751
0.751
0.752
0.750
∆Aiso [MHz]
152
-16
75
257
168
Aiso [MHz]
-610
-568
-592
-644
-618
-559
〈S 〉
0.752
0.755
0.752
0.751
0.754
0.750
∆Aiso [MHz]
-51
-10
-33
-86
-59
Aiso [MHz]
-264
-256
-259
-280
-271
-241
〈S 〉
2.013
2.016
2.014
2.012
2.016
2.000
∆Aiso [MHz]
-22
-15
-17
-38
-29
Aiso [MHz]
1369
920
1355
1424
1363
1314
〈S 〉
2.127
2.144
2.105
2.176
2.198
2.000
∆Aiso [MHz]
55
-394
41
110
48
Aiso [MHz]
858
863
-222
915
883
780
〈S 2 〉
3.804
3.807
3.781
3.797
3.807
3.750
∆Aiso [MHz]
78
83
-1002
135
104
Aiso [MHz]
535
541
523
533
517
481
〈S 2 〉
8.833
8.806
8.832
8.802
8.809
8.750
∆Aiso [MHz]
54
60
42
52
36
Aiso [MHz]
230
245
216
228
207
105
〈S 2 〉
8.759
8.758
8.758
8.756
8.757
8.750
∆Aiso [MHz]
125
140
111
123
102
Aiso [MHz]
490
498
471
516
489
443
〈S 〉
12.002
12.002
12.002
12.001
12.001
12.000
∆Aiso [MHz]
47
55
29
73
47
Aiso [MHz]
341
381
470
360
356
280
〈S 〉
12.002
12.002
12.006
12.001
12.001
12.000
∆Aiso [MHz]
61
101
189
80
76
2
MnH
LCBP86
1931
2
VO
LCBLYP
2100
2
VN
ωB97 XD
Aiso [MHz]
2
TiO
LCωPBE
2
150
APPENDIX Complex TiF3
MnO3
CAMB3LYP
[Cu(CO)3]
[Ni(CO)3H]
Co(CO)4
Exp.
-186
-174
-172
-185
〈S 2 〉
0.752
0.752
0.752
0.752
0.752
0.750
∆Aiso [MHz]
2
6
0
12
13
Aiso [MHz]
1634
1738
1665
1637
1600
1617
〈S 〉
1.007
0.900
0.927
1.052
1.055
0.750
∆Aiso [MHz]
17
121
48
20
-17
Aiso [MHz]
-747
-535
-728
-561
-527
-490
〈S 〉
0.766
0.760
0.765
0.760
0.759
0.750
∆Aiso [MHz]
-257
-45
-238
-70
-37
Aiso [MHz]
-114
-87
-127
-108
-122
-198
〈S 〉
8.760
8.762
8.759
8.758
8.761
8.750
∆Aiso [MHz]
84
111
71
90
76
Aiso [MHz]
25
21
26
23
27
41
〈S 2 〉
8.760
8.763
8.758
8.758
8.762
8.750
∆Aiso [MHz]
-16
-20
-15
-18
-14
Aiso [MHz]
22
48
17
38
52
71
〈S 2 〉
0.756
0.762
0.755
0.760
0.761
0.750
∆Aiso [MHz]
-49
-22
-53
-33
-19
Aiso [MHz]
-2
-16
12
-5
-6
14
〈S 2 〉
0.758
0.757
0.759
0.757
0.757
0.750
∆Aiso [MHz]
-16
-30
-2
-19
-20
Aiso [MHz]
-63
-16
-117
-43
-55
-57
〈S 〉
0.802
0.778
0.805
0.783
0.780
0.750
∆Aiso [MHz]
-6
42
-60
14
2
Aiso [MHz]
-284
-204
-299
-289
-307
-271
〈S 〉
1.031
0.969
0.984
1.136
1.112
0.750
∆Aiso [MHz]
-13
67
-28
-18
-36
2
Mn(CN)4N-
LCBP86
-179
2
[Cr(CO)4]+
LCBLYP
-183
2
[Mn(CN)4]2-
ωB97 XD
Aiso [MHz]
2
CuO
LCωPBE
2
APPENDIX Complex Mn(CN)5NO2-
Mn(CO)5
CAMB3LYP
ωB97 XD
LCBLYP
LCBP86
Exp.
ωPBE
Aiso [MHz]
-67
-51
-56
-73
-81
-218
〈S 2 〉
0.884
0.841
0.962
0.804
0.808
0.750
∆Aiso [MHz]
151
168
163
145
137
Aiso [MHz]
3
26
-4
15
7
-4
〈S 〉
0.758
0.760
0.758
0.760
0.761
0.750
∆Aiso [MHz]
7
30
0
19
11
Aiso [MHz]
-4
1
-8
-2
-4
-3
〈S 〉
0.761
0.757
0.762
0.757
0.757
0.750
∆Aiso [MHz]
-1
3
-5
1
-1
2
Fe(CO)5+
2
LC-
151
