Computational studies on the photophysical properties of d8 and d10 organometallic complexes

Dissertations in Forestry and Natural Sciences

DISSERTATIONS | TONI ESKELINEN | COMPUTATIONAL STUDIES ON THE PHOTOPHYSICAL PROPERTIES OF... | No 451

TONI ESKELINEN

Computational studies on the photophysical properties of d ⁸ and d ¹⁰

organometallic complexes

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND

COMPUTATIONAL STUDIES ON THE PHOTOPHYSICAL PROPERTIES OF d

AND d

ORGANOMETALLIC COM-

PLEXES

Toni Eskelinen

COMPUTATIONAL STUDIES ON THE PHOTOPHYSICAL PROPERTIES OF d

AND d

ORGANOMETALLIC COM- PLEXES

Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences

No 451

University of Eastern Finland Joensuu

2021

Academic dissertation

To be presented by permission of the Faculty of Science and Forestry for public examination in the Auditorium F100 in the Futura Building at the University of Eastern Finland, Joensuu, on December 10, 2021, at 12

o’clock noon

PunaMusta Oy Joensuu, 2021 Editor: Nina Hakulinen

Distribution: University of Eastern Finland / Sales of publications www.uef.fi/kirjasto

ISBN: 978-952-61-4402-3 (nid.) ISBN: 978-952-61-4403-0 (PDF)

ISSNL: 1798-5668 ISSN: 1798-5668 ISSN: 1798-5676 (PDF)

Author’s address: Toni Eskelinen

University of Eastern Finland Department of Chemistry P.O. Box 111

80101 JOENSUU, FINLAND email: toni.eskelinen@uef.fi

Supervisors: Docent Pipsa Hirva, Ph.D.

University of Eastern Finland Department of Chemistry P.O. Box 111

80101 JOENSUU, FINLAND email: pipsa.hirva@uef.fi

Professor Igor Koshevoy, Ph.D.

University of Eastern Finland Department of Chemistry P.O. Box 111

80101 JOENSUU, FINLAND email: igor.koshevoy@uef.fi

Reviewers: Associate Professor Toomas Tamm, Ph.D.

Tallinn University of Technology

Department of Chemistry and Biotechnology 19086 TALLINN, ESTONIA

email: toomas.tamm@taltech.ee

Associate Professor Vladimir Sizov, Ph.D.

Saint Petersburg State University Department of Physical Chemistry 199034 SAINT PETERSBURG, RUSSIA email: sizovvv@mail.ru

Opponent: Assistant Professor Antti Karttunen, Ph.D.

Aalto University

Department of Chemistry and Materials Science P.O. Box 16100

00076 AALTO, FINLAND email: antti.karttunen@aalto.fi

5 Eskelinen Toni

Computational studies on the photophysical properties of d⁸ and d¹⁰ organometallic complexes

Joensuu: University of Eastern Finland, 2021 Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences 2021; 451 ISBN: 978-952-61-4402-3 (print)

ISSNL: 1798-5668 ISSN: 1798-5668

ISBN: 978-952-61-4403-0 (PDF) ISSN: 1798-5676 (PDF)

ABSTRACT

Photofunctional metal complexes have attracted considerable amount of research interest due to their various potential applications in fields such as optoelectronic devices, imaging, sensing and photocatalysis. Moreover, computational chemistry has emerged as viable means of studying such systems. Particularly to transition metal complexes, theoretical methods rooted on Density Functional Theory (DFT) can provide a cost-effective and reasonably accurate description of the complex mechanisms involved in these systems.

Light emitting materials based on Pt(II) complexes constitute an intriguing class of compounds, owing to the high spin orbit coupling associated with the heavy metal center. The high spin orbit coupling allows these compounds to overcome the spin selection rule, resulting in an efficient phosphorescence emission from a triplet state. Complexes based on the lighter group 10 metal, namely, palladium are less often luminescent, because of more accessible “dark” ³MC states, which often quench the emission completely. The pronounced tendency of the group 10 d⁸ met- als to form square planar coordination environments allows for intermolecular axial metal-metal interactions to take place, resulting in the formation of aggregates with redshifted emission. This study provides a computational investigation of the pho- tophysical properties of cyclometalated Pd(II) and Pt(II) complexes with accounting of the involved excited state dynamics. The importance of the axial metal-metal interactions in altering the emission and suppressing the non-radiative relaxation is also highlighted.

Furthermore, recently there has been a growing interest towards materials based on Cu(I) and Ag(I) due to their ability to harvest all excitons in electroluminescent devices by means of minimizing the energy gap between the excited singlet and triplet states, which allows a reverse intersystem crossing to take place, followed by

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delayed fluorescence from the singlet state. However, the tetrahedral coordination environment, often adopted by Cu(I) and Ag(I) complexes, makes these com- pounds prone to flattening distortions in the excited state(s). These flattening dis- tortions can promote more efficient non-radiative relaxation, resulting in emission quenching, which makes it crucial to incorporate sterically demanding ligands in order to minimize these structural distortions. This study highlights the importance of using an appropriate model in the computational protocol, which is vital for properly describing the excited state structure modification and eventually the lu- minescence properties.

Universal Decimal Classification: 004.94, 535.37, 544.51, 546.302, 547.113

Library of Congress Subject Headings: Computational chemistry; Computer simulation; Density functionals; Quantum chemistry; Organometallic chemistry;

Transition metal compounds; Complex compounds; Metal complexes;

Organopalladium compounds; Organoplatinum compounds; Organocopper compounds; Organosilver compounds; Organometallic compounds – Optical properties; Luminescence; Fluorescence; Phosphorescence; Excited state chemistry

Yleinen suomalainen ontologia: laskennallinen kemia; simulointi; tiheys- funktionaaliteoria; kvanttikemia; organometalliyhdisteet; kompleksiyhdisteet;

optiset ominaisuudet; luminesenssi; fluoresenssi

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ACKNOWLEDGEMENTS

This work was carried out at the Department of Chemistry, University of Eastern Finland during the years 2017-2021. Financial support from the Faculty of Science and Forestry of University of Eastern Finland (SCITECO program), Finnish Cultural Foundation – North Karelia Regional Fund and Gustaf Komppa Fund is gratefully acknowledged. I also acknowledge CSC – IT Center for Science, Finland, for computational resources.

I would like to express my deepest gratitude to my supervisors Docent Pipsa Hirva and Professor Igor Koshevoy for providing me with the opportunity to work with you. I have learned a lot from you and am forever grateful for your guidance, patience and words of encouragement.

Additionally, I would like to thank the collaborating groups in St. Petersburg, Cologne, Münster and Jyväskylä for their contributions to the publications. I would also like to thank Associate Professor Toomas Tamm and Associate Professor Vladimir Sizov for their careful reading and suggestions for strengthening this thesis. In addition, I am grateful for Assistant Professor Antti Karttunen for accepting the invitation to act as the opponent.

Furthermore, I want to thank all members of the Department of Chemistry. Special thanks to Docent Janne Hirvi, Dr. Sari Suvanto and Professor Mika Suvanto for their assistance during my studies. I also want to thank my in-office colleagues Gomathy, Andrei, Mariia and Iida for interesting discussions and for providing a pleasant working environment.

Finally, I want to thank my friends and family for their continued support throughout the years.

Joensuu, November 2021 Toni Eskelinen

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LIST OF ABBREVIATIONS

DFT Density functional theory

MC Metal-centered

OLED Organic light emitting diode LEEC Light emitting electrochemical cell SOC Spin orbit coupling

IC Internal conversion ISC Intersystem crossing

MLCT Metal-to-ligand charge transfer

TADF Thermally activated delayed fluorescence ILCT Intraligand charge transfer

LC Ligand-centered

HOMO Highest occupied molecular orbital LUMO Lowest unoccupied molecular orbital MMLCT Metal-metal-to-ligand charge transfer

PBE0 Hybrid density functional by Perdew, Burke, Ernzerhof and Adamo C-PCM Conductor-like polarizable continuum model

QM/MM Quantum mechanics/molecular mechanics TD-DFT Time dependent density functional theory ECP Effective core potential

QTAIM Quantum theory of atoms in molecules BCP Bond critical point

DCM Dichloromethane

RMSD Root mean square deviation LLCT Ligand-to-ligand charge transfer

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LIST OF ORIGINAL PUBLICATIONS

This thesis is based on data presented in the following articles, referred to by the Roman Numerals I-IV.

I Belyaev, A.; Eskelinen, T.; Dau, T. M.; Ershova Y. Y.; Tunik, S. P.; Melnikov, A. S.; Hirva, P.; Koshevoy, I. O. Cyanide-Assembled d¹⁰ Coordination Polymers and Cycles: Excited State Metallophilic Modulation of Solid-State Luminescence. Chemistry – A European Journal 2018, 24, 1404-1415.

II Chakkaradhari, G.; Eskelinen, T.; Degbe, C.; Belyaev, A.; Melnikov, A. S.;

Grachova, E. V.; Tunik, S. P.; Hirva, P.; Koshevoy, I. O. Oligophosphine- thiocyanate Copper(I) and Silver(I) Complexes and Their Borane Derivatives Showing Delayed Fluorescence. Inorganic Chemistry 2019, 58, 3646-3660.

III Sivchik, V.; Kochetov, A.; Eskelinen, T.; Kisel, K. S.; Solomatina, A. I.;

Grachova, E. V.; Tunik, S. P.; Hirva, P.; Koshevoy, I. O. Modulation of Metallophilic and π-π Interactions in Platinum Cyclometalated

Luminophores with Halogen Bonding. Chemistry – A European Journal 2021, 27, 1787-1794.

IV Eskelinen, T.; Buss, S.; Petrovskii, S. K.; Grachova, E. V.; Krause, M.; Kletsch, L.; Klein, A.; Strassert, C. A.; Koshevoy, I. O.; Hirva, P. Photophysics and Excited State Dynamics of Cyclometalated [M(Phbpy)(CN)] (M = Ni, Pd, Pt) Complexes: A Theoretical and Experimental Study. Inorganic Chemistry 2021, 60, 8777-8789.

AUTHOR’S CONTRIBUTION

The author is responsible for carrying out all the computational calculations for publications I, II, III and IV. Furthermore, the author has written parts of publications I, II and III and prepared the initial manuscript for publication IV.

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Other related publications by the author during the study not included in this thesis:

i. Kisel, K. S.; Eskelinen, T.; Zafar, W.; Solomatina, A. I.; Hirva, P.;

Grachova, E. V.; Tunik, S. P.; Koshevoy, I. O. Chromophore- Functionalized Phenanthro-Diimine Ligands and Their Re(I) Complexes. Inorganic Chemistry 2018, 57, 6349-6361.

ii. Temerova, D.; Kisel, K. S.; Eskelinen, T.; Melnikov, A. S.; Kinnunen, N.;

Hirva, P.; Shakirova, J. R.; Tunik, S. P.; Grachova, E. V.; Koshevoy, I. O.

Diversifying the luminescence of phenanthro-diimine ligands in zinc complexes. Inorganic Chemistry Frontiers 2021, 8, 2549-2560.

iii. Bulatov, E.; Eskelinen, T.; Ivanov, A. Y.; Tolstoy, P. M.; Kalenius, E.;

Hirva, P.; Haukka, M. Noncovalent axial I···Pt···I interactions in platinum(II) complexes strengthen in the excited state. ChemPhysChem 2021, 22, 2044-2049.

iv. Khistiaeva, V.; Buss, S.; Eskelinen, T.; Hirva, P.; Grachova, E. V.; Klein, A.; Strassert, C.; Koshevoy, I. O. Efficient luminescence and aggregation of cyanide-bridged cyclometalated diplatinum complexes [Manuscript in preparation]

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CONTENTS

ABSTRACT ... 5

ACKNOWLEDGEMENTS ... 7

1 INTRODUCTION ... 13

1.1 Short overview of photophysical processes in metal complexes ... 15

1.2 Luminescent d⁸ complexes based on cyclometalated group 10 metals ... 17

1.3 TADF emitters based on d¹⁰ coinage metals ... 19

1.4 Aims of the study ... 21

2 COMPUTATIONAL DETAILS ... 23

2.1 Models and geometry optimization ... 23

2.2 Properties of the electron density... 26

2.3 Excitation and emission properties ... 26

2.4 Justification for the used methods ... 27

3 RESULTS AND DISCUSSION ... 28

3.1 Cyclometalated palladium and platinum complexes ... 28

3.1.1 Monomeric models ... 28

3.1.2 Dimeric models ... 34

3.2 Copper and silver complexes with multidentate phospholigands ... 42

3.2.1 Isolated models ... 42

3.2.2 Improving the model: QM/MM studies ... 47

4 SUMMARY ... 59

5 REFERENCES ... 61

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13

1 INTRODUCTION

Luminescence is defined as the spontaneous emission of radiation from an excited species not resulting from heat.¹ Although the word “luminescence” was not intro- duced until 1888 by the German physicist Eilhard Wiedemann,² the two cases of radiative decay, namely, fluorescence and phosphorescence were already well doc- umented in the literature even though the difference between the two mechanisms was not fully understood until the emergence of quantum theory in the early 1900s.³

The earliest documented observation for fluorescence was made in 1565 by the Spanish physician Nicolas Monardes.⁴ He reported a blue colour from an infusion of wood from Mexico (later called Lignum nephriticum in Europe), which was used in the treatment of kidney and liver diseases. In his notes, Monardes wrote: “Make sure that the wood renders water bluish, otherwise it is a falsification”. Indeed, observing the blue fluorescence was a method to verify the authenticity of the product.⁵ Later it was shown that the compound responsible for the fluorescence in Lignum nephrit- icum in aqueous media is a four-ring tetrahydromethanobenzofuro[2,3-d]oxacine (matlaline, Figure 1), which is formed as an end product of a very efficient oxida- tion reaction of at least one of the wood’s flavonoids.⁶

Figure 1. Cup made from Lignum nephriticum and the chemical structure of matlanine, the compound responsible for the blue fluorescence.³ Reprinted with permission from ref. 3. Copyright 2011 American Chemical Society

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There are many examples of early known materials which glow in the dark and were thus named phosphors (Greek for “light-bearing”), but one of the more fa- mous examples is the Bolognian phosphor, discovered by a cobbler and alchemist Vincenzo Cascariolo in 1602.³ He discovered this material after reacting stones con- taining barium sulfate with coal, resulting in the reduction of barium sulfate into barium sulfide, a phosphorescent compound. Cascariolo thought that the newly made material would be suitable in “harnessing the golden light of the sun” and thus turning lesser metals into gold.⁷ Sadly, like many other alchemists before and after him, he too was unsuccessful in turning other metals into gold.

Evidently, luminescent materials have been of vast interest to humans ever since the early days, with early applications such as verifying the authenticity of a drug and attempts to produce gold through alchemy. Today, photofunctional com- pounds are widely used in applications such as organic light emitting diodes (OLEDs)^8-12, light emitting electrochemical cells (LEECs)^13-17, sensing^18-22, photocatal- ysis^23-27 and photodynamic therapy.^28-32 Especially the field of OLEDs has seen a dramatic increase in the research interest over the last two decades, which is seen on the number of new publications per year according to a SciFinder search (Figure 2). Materials based on transition metal complexes are of particular interest, owing to their ability to harvest all the generated excitons in electroluminescent devic- es.^33,34

Figure 2. Annual new publications containing the term “organic light emitting di- ode” found using the SciFinder search engine in August 2021.³⁵

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1.1 SHORT OVERVIEW OF PHOTOPHYSICAL PROCESSES IN METAL COMPLEXES

Following photon absorption, the absorbing species is promoted from the ground state S⁰ to an excited electronic state Sⁿ. Because the energy difference between excited states tends to be much lower than the energy difference between the ground state and first excited state, the excitation is followed by very rapid vibrational relaxation, known as internal conversion (IC), to the lowest lying excited singlet state S1.^36-38 From the excited S1 state, the system can relax back to the ground state either non-radiatively by IC or radiatively via prompt fluorescence (Figure 3).

Early emitters in electroluminescent devices (such as OLEDs) were based on materials relying solely on prompt fluorescence, which severely limited the efficiency of these devices due to the fact that only 25 % of the generated excited states were of singlet character and could thus be used in light generation.^39-41 Tris(8-hydroxyquinolinato)aluminium (Alq³, Figure 4a) is one of the early, broadly studied, examples of such emitter compounds.^42-44

Figure 3. Simplified Jablonski diagram showing the important radiative (straight arrows) and non-radiative (curved arrows) transitions between states. Thick lines represent electronic states and thin lines vibrational states.

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Alternatively, population can be transferred from the excited singlet state to an excited triplet state by means of intersystem crossing (ISC), which is a non-radiative transition between states of different multiplicity (Figure 3). Although transitions between states of differenct multiplicity are formally forbidden due to the spin selection rule, spin-orbit coupling can mix the singlet and triplet states, making spin no longer a “good” quantum number and allowing a non-zero ISC rate. Once the T¹ state is populated, either non-radiative relaxation back to the ground state or phosphorescence emission can occur. The strength of SOC is proportional, among other things, to the fourth power of the nuclear charge, making late transition metal complexes highly suitable candidates for phosphorescent emitters.⁴⁵ Indeed, many of the emitters viable for use in second generation OLEDs (or PhOLEDS, phosphorescent OLEDs) are based on complexes of 2^nd and 3^rd row metals such as Ir(III)^46-49, Pt(II)^50-53, Os(II)^54-57, Ru(II)^58-61, Re(I)^62-65 and Au(III).^66-69 Compared to emitters relying on prompt fluorescence, phosphorescent emitters can significantly increase the efficiency of emission in electroluminescent devices since both singlet and triplet excitons can be utilized in light generation, increasing the theoretical maximum of internal quantum yield from 25 % to 100 %. As an example, consider the extensively studied tris(2-phenylpyridine)iridium, [Ir(ppy)³] (Figure 4b). This complex exhibits bright green phosphorescence emission from a ³MLCT (metal-to- ligand charge transfer) state, with near unity internal quantum yield.^70-72

Figure 4. Fluorescent emitter Alq3 (a) and phosphorescent emitter [Ir(ppy)3] (b).

Recently, there has been a growing interest towards materials which exhibit the phenomenon known as thermally activated delayed fluorescence (TADF).^73,74 In these materials, the energy difference between the first excited singlet state S¹ and first excited triplet state T1, ΔE(S1-T1), is minimized.^75-77 This allows a reverse intersystem crossing (rISC) to take place by means of thermal energy at room temperature, which is then followed by delayed fluorescence from the S¹ state (Figure 3). Achieving sufficiently low ΔE(S1-T1) is accomplished by having low-

17 lying CT (charge transfer) states so that the overlap between the frontier molecular orbitals is minimized, resulting in a low quantum mechanical exchange energy. As a result of the minimal energy difference, even compounds with relatively low spin orbit coupling can achieve high rates for rISC. This makes materials based on cheaper and more abundant metals, such as Cu and Ag, highly attractive candidates as emitter compounds. Indeed, TADF emitters based on Cu(I) and Ag(I) are at the forefront of current research for third generation OLEDs.^78-84

1.2 LUMINESCENT d

COMPLEXES BASED ON CYCLOMET- ALATED GROUP 10 METALS

Cyclometalated complexes are organometallic compounds in which a chelating ligand is bound to a metal center with at least one covalent metal-carbon bond, resulting in a cyclic structure in which the metal atom is a part of the cycle.⁸⁵ The denticity of the cyclometalating ligand must be at least two, such as in the C^N cyclometalating 2-phenylpyridine (the ligand used in [Ir(ppy)³], Figure 4b). Bi-, tri- and tetradentate cyclometalating ligands are widely used in combination with the group 10 d⁸ metals Ni(II), Pd(II) and Pt(II), resulting often in highly stable (pseudo)square planar structures.^86-96

While Ni(II) complexes tend to be virtually non-luminescent⁹⁷ and luminescent Pd(II) complexes quite scarce^98-100, cyclometalated Pt(II) complexes can show highly efficient luminescence from wide variety of emissive states, such as MLCT (metal to ligand charge transfer), ILCT (intraligand charge transfer) or LC (ligand-centered) π-π* states, in both solution and solid-state.^101-104 The high spin orbit coupling associated with platinum is also vital in bypassing the restriction imposed by the spin selection rule and achieving efficient T¹ → S⁰ phosphorescence emission. The quenching of emission in the lighter group 10 metals Pd and Ni can be attributed to the lower splitting of the metal d-orbitals resulting in more easily accessible metal centered “dark” d-d* states, which provide an efficient non-radiative relaxation pathway back to the ground state.¹⁰⁵ Moreover, the metal centered d-d* states are also responsible for emission quenching in many Pt(II) complexes.^106,107

A commonly used strategy to destabilize the metal-centered d-d* states is to use ligands with strong σ-donating character. The use of strong-field ligands increases the splitting of the metal d-orbitals and thus destabilizes the d-d* states, making them less accessible. As an example, the platinum complexes with tridentate N^N^N type chelating ligand, 2,2’:6’,2’’-terpyridine (trpy), coupled with halido ancillaries, [Pt(trpy)X]¹⁺ (X = Cl, I), are non-luminescent in fluid medium due to population of low-lying d-d* states.¹⁰⁸ Substituting the tridentate N^N^N ligand to N^C^N type cyclometalating 1,3-di(2-pyridyl)benzene results in phosphorescent

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species, which can be attributed to the high σ-donating strength of the cyclometalating carbanion and thus destabilized metal-centered states.^109,110

The tendency of group 10 d⁸ metals to form complexes with square planar coordination environment results in open coordination sites in the axial positions.

These open sites in the axial positions can lead to metallophilic M···M and/or π-π stacking interactions in the aggregated state. Metallophilic interactions between Pt(II)^111-113 as well as Au(I)^114-116, Ag(I)^117,118, Cu(I)^119,120 and Pd(II)¹²¹ (and many others) centers are well established in the literature. The metallophilic interactions can be either unsupported or supported. The unsupported interactions can be classified as purely intermolecular interactions, whereas in the supported interactions the ligand essentially acts as a bridge between the interacting metal atoms (Figure 5).

Figure 5. Unsupported (a) and supported (b) metallophilic interactions between two metal centers.

In the unsupported case, interactions between two approaching square planar d⁸ complexes take place via the filled metal dz2 orbitals. This results in the formation of one metal-metal bonding dσ orbital and one antibonding dσ* orbital, which becomes the HOMO (highest occupied molecular orbital) level of the formed dimer, even though the HOMO orbital of the monomer usually is a ligand-centered π-orbital (Figure 6a).¹²² The raised energy-level of the HOMO orbital results in decreased HOMO-LUMO (lowest unoccupied molecular orbital) gap and redshifted emission from a MMLCT (metal-metal to ligand charge transfer) state (Figure 6b).¹²³

19 Figure 6. Simplified molecular orbital diagrams for monomeric and dimeric square planar Pt(II) complexes (a) and emission spectra showing the transition from LC/MLCT emission with vibronic progression (purple and blue curves) to unstructured MMLCT emission (green and red curves).^122,123 Reprinted with permission from refs. 122 and 123. Copyright 2016, 2018 American Chemical Society.

1.3 TADF EMITTERS BASED ON d

COINAGE METALS

Although the first TADF emitters were discovered already in the 60s^124,125, the wide- spread academic and commercial interest over such materials did not become ap- parent until recently.⁷³ Today TADF emitters based on Cu(I) and Ag(I) complexes are extensively studied as cheaper and more abundant alternatives over the phos- phorescent emitters based on 3^rd row transition metal compounds.^126,127

To achieve sufficient reverse ISC rate needed for the TADF process, the energy gap between the excited singlet and triplet states needs to be sufficiently low. This re- sults in small exchange interaction as the energy difference between the singlet and triplet state of same character is defined as twice the exchange energy. Furthermore, as the exchange energy is proportional to the overlap between the involved molecu- lar orbitals, having low-lying excited states with charge transfer character effective- ly results as small values for ΔE(S1-T1).^128,129 In this regard, low-lying MLCT states often encountered for Cu(I) complexes make them viable candidates for TADF ma- terials. Although Ag(I) complexes tend to show low-lying MLCT states less often (due to higher oxidation potential) than their Cu(I) counterparts, TADF lumino- phores based on Ag(I) are still relatively common in the literature.^130-132 As an added

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benefit, the d¹⁰ electronic structure means that there are no low-lying metal- centered d-d* states, which serve as a major non-radiative relaxation pathway in complexes with partially filled d-shell.

Despite Cu(I) and Ag(I) complexes having quite flexible coordination environ- ments, (pseudo)tetrahedral compounds are commonly encountered. The tetrahe- dral geometry coupled with MLCT states results with these complexes being ex- posed to flattening distortions in the excited state, where the tetrahedral geometry is twisted towards a square planar orientation.^133-135 These distortions in the excited state result in decreased optical band gap as well as increased non-radiative decay rate as the overlap of the vibrational states is significantly increased, which in turn results in decreased luminescence quantum yield or even completely quenched emission.^73,136 As an example of the flattening distortions, consider a recent study by Cui et al. where they studied the TADF emission behavior of [Cu(NN)(PP)] (NN = 5-(2-pyridyl)-tetrazolate, PP = bis[(2-diphenylphosphino)-phenyl] ether).¹³⁷ The optimized structures showed that the angles between the planes spanned by N1 – Cu – N2 and P1 – Cu – P2 are severely twisted in the excited states as the geometry is flattened towards a more square planar-like environment (Figure 7).

Figure 7. Simplified effects of the flattening distortions on the potential energy sur- faces and the excited state structures of [Cu(NN)(PP)], as indicated by decreased angle between the planes spanned by N1, Cu and N2 and P1, Cu and P2.^136,137 Re- produced from refs. 136 and 137 with permission from the PCCP Owner Societies.

21 In order to decrease the effect of the flattening distortions on the non-radiative de- cay rate, sterically demanding substituents can be used to increase the rigidity of the complex.^130,132 To demonstrate this, Yersin et al. studied the effects of introduc- ing bulky substituents on the 2,9 and 4,7 positions of 1,10-phenantroline for [Ag(NN)(PP)], where NN = 1,10-phenanthroline and PP = bis(diphenylphosphine)- nido-carborane (Figure 8).¹³¹ The parent complex showed yellow (λ = 575 nm) TADF emission with photoluminescence quantum yield (PLQY) of 36 %. Including methyl substituents on the 4 and 7 positions of the phenanthroline ligand intro- duced a slight blueshift on the emission wavelength (λ = 562 nm) and increased the quantum yield to 45 %. Using the methyl substituents on the 2 and 9 positions in- stead, resulted in further blueshift (λ = 537 nm) and increased in emission efficiency (PLQY = 78 %). Finally, using n-butyl groups at the 2 and 9 positions of the phenan- throline ligand resulted in green emission (λ = 526 nm) with 100 % PLQY.

Figure 8. Structures of four Ag(I) complexes and their photoluminescence quantum yields in powder samples.¹³¹ Reprinted with permission from ref. 131. Copyright 2017 American Chemical Society.

1.4 AIMS OF THE STUDY

The study presented in this thesis aims to provide a computational accounting of the structure-property relationships in a series of d⁸ and d¹⁰ luminophores. In par- ticular, the aims are:

• Describe d⁸ and d¹⁰ luminophores accurately and cost-effectively using methods rooted on density functional theory.

• Highlight the effects of intermolecular interactions in modifying the photo- physical properties of Pd(II) and Pt(II) complexes and to assess the excited state dynamics of such species.

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• Study the effects of structural distortion in the excited states and their im- plications on the photophysical properties of Cu(I) and Ag(I) complexes and to highlight the importance of the used computational model in the prediction of such properties.

• Critically evaluate the used computational methodology.

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2 COMPUTATIONAL DETAILS

“The underlying physical laws necessary for the mathematical theory of a large part of phys- ics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”

These famous words by Paul Dirac, published in his paper in 1929, highlight the major obstacle in practical quantum chemistry calculations.¹³⁸ Analytic solutions for the Schrödinger (or Dirac) equation can only be obtained for hydrogenic systems (i.e., systems with only one electron).¹³⁹ Therefore, we are forced to using approxi- mate solutions in describing practical chemical systems. Fortunately, advances in theoretical methods and computing hardware have made numerical quantum chemical calculations widely accepted methods to solve chemical problems. Never- theless, the system size remains the limiting factor between the desired accuracy and computational time. In this regard, density functional theory (DFT) has emerged as a cost-effective method to treat transition metal complexes, providing vastly superior results compared to the simple Hartree-Fock (HF) method without being overly time-consuming.^140,141

Based on the early works of Hohenberg, Kohn and Sham,^142,143 DFT aims to solve the total system energy E[ρ(r)] by finding the exact ground state electron density ρ0(r), which minimizes the total system energy. Once the correct density is found, other properties of the system can be obtained by using appropriate operators on the energy functional.^144,145 However, not all components of E[ρ(r)] are known ex- actly and the approximate components are grouped into the so-called exchange- correlation functional E^XC[ρ(r)].¹⁴⁶ There are many proposed formalisms for the ex- change-correlation functional and this is what separates the different DFT methods from one another. Throughout this study, the hybrid density functional PBE0^147,148 was used as it has been shown to yield accurate results for transition metal com- plexes.^149-153

2.1 MODELS AND GEOMETRY OPTIMIZATIONS

In this study, a series of cyclometalated Pd(II) and Pt(II) complexes as well as mono-, di- and tetrametallic Cu(I) and Ag(I) complexes were investigated. All the studied complexes are listed in Figure 9.

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Figure 9. Studied complexes.

The cyclometalated Pd and Pt complexes were modelled in solution and solid phase. For the solution studies, isolated geometries obtained from the experimental

25 crystal structures were used as models, using the C-PCM^154,155 (conductor-like polar- izable continuum model) method to represent the solvent. Experimentally, it was shown that in solid phase the complexes formed dimeric structures with head-to- tail stacking and close metal-metal contacts.^{III, IV} For this reason, a dimeric model was chosen to represent the solid material. In order to provide a more realistic model for the solid-state structure, the dimers were optimized with a hybrid QM/MM (quantum mechanics/molecular mechanics) method within the ONIOM framework.¹⁵⁶ The unit cell was expanded in three dimensions and the central di- meric unit was assigned as the QM part and the surroundings were kept frozen and treated with MM using the UFF force field¹⁵⁷ (Figure 10a).

Figure 10. An example of the used solid-state models for the Pd and Pt complexes (a) and Cu and Ag complexes (b).

The solid-state behaviour of Cu and Ag complexes were modelled with isolated, as well as hybrid QM/MM models (Figure 10b), utilizing the same QM/MM method- ology for the hybrid models as stated above. In particular, the QM/MM method was used to study whether it provides a more realistic description for the excited state structures (compared to the isolated models) since the d¹⁰ complexes are prone to flattening distortions in the excited states.

All models were optimized in the ground state S⁰ as well as the lowest lying S¹ and T1 states within DFT, and its time-dependent extension TD-DFT, level of theory. All geometry optimizations were performed using Gaussian 16 program package.¹⁵⁸ def2-TZVPPD basis set together with the corresponding ECP (effective core poten- tial) was used for all metal atoms.^159-161 In the Pd and Pt complexes, 6-311+G(d,p) basis set was used for the lighter elements. For the mono- and dinuclear Cu and Ag complexes, 6-311+G(d,p) basis set was used for P, N and S atoms, while 6-31G(d) basis set was used for C and H atoms as well as all light atoms in the tetranuclear complexes. All calculations utilized the hybrid PBE0 density functional. Frequency

26

calculations were performed for all optimized structures in order to confirm that the obtained structures corresponded to a minimum in the potential energy surface.

2.2 PROPERTIES OF THE ELECTRON DENSITY

Quantum Theory of Atoms in Molecules (QTAIM) is a population analysis method based on the electron density of the system rather than the basis functions, like some of the simpler population analysis methods, such as the Mulliken or Löwdin methods.¹⁶² Based on the works of Bader and co-workers, QTAIM divides the mo- lecular volume into atomic subspaces (basins) by analysing the gradient vector field of the charge density. In order to be classified as an atomic basin, each attractor (i.e., nucleus) in the molecule must be bound by a surface of zero flux in ∇ρ so that for each point within the subspace, following the gradient vector path will lead to the attractor.¹⁶³

By studying the properties of the electron density at the critical points of ∇ρ (i.e., points in space where the gradient vanishes), valuable information of the chemical properties of the system can be extracted. Of particular interest are the bond critical points (BCPs), located between two nuclear attractors. For example, the electron density at the BCP tends to correlate with the covalency of the interactions, with higher values for ρ indicating higher degree of covalency, the Laplacian of electron density expresses where the electron density is locally concentrated (∇²ρ < 0) or depleted (∇²ρ > 0).¹⁶⁴ The ratio of the potential and kinetic energy densities, |V|/G shows whether the interactions are of shared shell (|V|/G > 2) or closed shell type (|V|/G < 1), with dative bonds typically between the two (1 ≤ |V|/G ≤ 2).¹⁶⁵ Moreo- ver, the delocalization index, δ(A, B), defined as the number of electron pairs shared between atoms A and B, provides yet another quantitative measure for the covalency of the interaction.¹⁶⁶

In this study, QTAIM analyses were carried out for all complexes containing close metal-metal contacts. The calculations were performed with the AIMAll program¹⁶⁷, using the electron densities obtained from the (TD-)DFT calculations.

2.3 EXCITATION AND EMISSION PROPERTIES

To analyse the excitation and emission characteristics as well as the natures of the involved excited states, TD-DFT calculations were performed for all optimized structures. Radiative rates for the excited states were also calculated. Within a non- relativistic or scalar relativistic theory, the radiative rate for phosphorescence is zero. However, spin-orbit coupling can mix the singlet and triplet states, resulting

27 in a “borrowing” of radiation intensity from the spin-allowed singlet-singlet transi- tions and thus a non-zero phosphorescence rate.

In this study, the scalar relativistic ZORA (zeroth order regular approximation) Hamiltonian was used with a perturbative inclusion or SOC effects.^168-171 The excita- tion and emission calculations were performed using the ADF program package.^172-

174 The same functional (PBE0) was used as in the geometry optimizations together with an all-electron TZ2P basis set for all atoms, except for the tetranuclear Cu and Ag complexes, for which a DZP basis was used for lighter atoms in order to keep the total number of basis functions reasonable.¹⁷⁵ The different basis sets used in the ADF calculations are due to the fact that ADF uses Slater type basis functions, as opposed to the Gaussian type basis functions used in Gaussian. For the solvated models, the COSMO solvation model was used in the ADF calculations, as it is closely related to the C-PCM model used in the Gaussian calculations (C-PCM be- ing a re-implementation of COSMO for the family of PCM solvation methods).^154,176

2.4 JUSTIFICATION FOR THE USED METHODS

Although there undoubtetly exist more sophisticated methods for electronic structure calculations than DFT, such as those based on coupled cluster theory, the poor scaling of these highly correlated methods renders them inacclicable for systems as sizeable as studied here. For example, the highly accurate CCSD(T) (coupled cluster with singles, doubles and perturbative triples) method, which is often termed as the gold-standard of computational chemistry^177,178, scales formally as N⁷ with respect to system size, limiting its applicability to fairly small systems.¹³⁹

As stated above, the PBE0 functional was chosen as it has been shown in numerous benchmark studies (as well as in-house testing) to describe transition metal complexes reasonably well. Furthermore, the MN15¹⁷⁹ and CAM-B3LYP¹⁸⁰ functionals were also experimented with, but as the PBE0 functional showed more consistency with respect to the experimental observations,^IV it was thus used throughout the study. Regarding basis set size, the goal was to use a sufficiently flexible basis set, preferrably of triple-zeta quality. Unfortunately, treating all elements with a triple-zeta level of basis turned out to be too expensive for some of the models. In the QM/MM calculations the UFF force field was used because it is the only force field implemented in Gaussian with parameters available for transition metals. Furthermore, as the MM layer is kept frozen and its role is solely to act as a physical obstacle preventing large scale geometric relaxation, the choice of a particular force field is not expected to have a significant impact on the results.

28

3 RESULTS AND DISCUSSION

3.1 CYCLOMETALATED PALLADIUM AND PLATINUM COM- PLEXES

3.1.1 Monomeric models

Monomeric models of [M(C^N^N)CN] (C^N^N = pyridinyl-phenylpyridine, M = Pd Pd-1-mono, Pt Pt-1-mono; indazolyl-phenylpyridine, M = Pd Pd-2-mono, Pt Pt- 2-mono; benzyltriazol-phenylpyridine, M = Pt Pt-3-mono; pyrazolyl- phenylpyridine, M = Pt Pt-4-mono) were optimized in the ground state S⁰ and low- est lying singlet and triplet excited states. All calculations were performed using DCM (dichloromethane) as the solvent. The optimized structures are presented in Figures 11 and 12 and the key structural parameters are collected to Table 1. For the palladium monomers, two different minima were found on the triplet potential energy surface. Starting from the optimized ground state, the triplet optimizations lead to a structure corresponding to a ³MLCT/ILCT (Pd-1-mono) or ³(d, π-π*) (Pd-2- mono) state, whereas by manually distorting the starting geometry we were able to locate also the ³MC minimum structures. For the platinum models, attempts to lo- cate the ³MC minima were unsuccessful.

Figure 11. Optimized structures of Pd-1-mono and Pd-2-mono in DCM in the ground state S0 and lowest lying singlet S1 and triplet T1 excited states. * Two differ- ent minima were located for the triplet states, which correspond to ³MLCT/ILCT (Pd-1-mono) or ³(d, π-π*) (Pd-2-mono) and ³MC structures.

29 Figure 12. Optimized structures of Pt-1-mono, Pt-2-mono, Pt-3-mono and Pt-4- mono in DCM in the ground state S⁰ and lowest lying singlet S¹ and triplet T¹ excit- ed states.

In the ground state, all optimized structures feature somewhat distorted square planar coordination environments as the C-M-N and N-M-N bite angles vary from 81.6° to 82.5° and from 76.8° to 78.4°, respectively (Table 1). Worth observing is the distinct difference in the metal-nitrogen bond lengths, the M-Ntrans (trans to the cy-

30

clometalating carbanion) bond being noticeably longer than the M-Ncis bond length.

This can be attributed to the strong trans-influence induced by the cyclometalating carbanion.^181,182

Table 1. Selected structural parameters for the studied monomers in DCM at the optimized ground state.

Pd-1- mono

Pd-2- mono

Pt-1- mono

Pt-2- mono

Pt-3- mono

Pt-4- mono bonds [Å]

M-Ncis 1.992 1.997 1.993 1.997 2.012 2.000

M-N^trans 2.152 2.132 2.132 2.110 2.126 2.129

M-C 1.983 1.978 1.989 1.986 1.987 1.985

M-CCN 1.960 1.960 1.947 1.948 1.946 1.946

angles [°]

C-M-Ncis 82.2 82.5 82.0 82.2 81.6 81.7

N^cis-M-N^trans 78.1 76.8 78.4 77.4 78.0 77.4

For the excited state structures, only very minor geometric alterations are observed, except for the S¹ state structure of Pd-1-mono and the ³MC structures of Pd-1-mono and Pd-2-mono. In the S¹ state structure of Pd-1-mono, the phenyl moiety is dis- torted slightly below the molecular plane. The ³MC state structures, however, fea- ture severely displaced structures as all the metal-ligand bond lengths are elongat- ed by roughly 10 %. Moreover, the central pyridine fragments are being twisted above the plane spanned by the normally planar C^N^N ligand, as well as the MCN fragments being twisted below the plane (Figure 11).

To study the excitation and emission characteristics and resolve the important low lying excited states of the solvated Pd and Pt complexes, TD-DFT calculations were performed. The calculated data for the two lowest lying singlet-singlet and the low- est lying singlet-triplet vertical excitations are collected to Table 2.

31 Table 2. Calculated two lowest lying singlet-singlet and the lowest lying singlet- triplet vertical excitations for the monomeric models in DCM (λ = excitation wavelength, f = oscillator strength).

Complex Transition λ [nm] f Major contributions* Assignment

Pd-1-mono

S₀ → S₁ 381 0.0118 94 % H → L MLCT/ILCT

S₀ → S₂ 359 0.0143 97 % H-1 → L MLCT

S₀ → T₁ 424 - 84 % H → L MLCT/ILCT

Pd-2-mono

S₀ → S₁ 356 0.0614 94 % H → L d, π → π*

S₀ → S₂ 331 0.0218 97 % H-2 → L MLCT

S₀ → T₁ 409 - 65 % H → L, 25 % H → L+1 d, π → π*

Pt-1-mono

S₀ → S₁ 422 0.0042 95 % H → L MLCT/ILCT

S₀ → S₂ 361 0.0166 97 % H-2 → L MLCT

S₀ → T₁ 462 - 83 % H → L MLCT/ILCT

Pt-2-mono

S₀ → S₁ 387 0.0131 96 % H → L d, π → π*

S₀ → S₂ 335 0.4160 81 % H-1 → L, 15 % H → L+1 d, π → π*

S₀ → T₁ 432 - 76 % H → L, 14 % H → L+1 d, π → π*

Pt-3-mono

S₀ → S₁ 392 0.0082 98 % H → L d, π → π*

S₀ → S₂ 335 0.0262 99 % H-2 → L MLCT

S₀ → T₁ 437 - 87 % H → L d, π → π*

Pt-4-mono

S₀ → S₁ 385 0.0155 98 % H → L d, π → π*

S₀ → S₂ 329 0.0257 99 % H-2 → L MLCT

S₀ → T₁ 432 - 83 % H → L d, π → π*

[*] H = HOMO, L = LUMO

For the complexes incorporating the pyridinyl-phenylpyridine ligand (i.e., Pd-1- mono and Pt-1-mono), the lowest lying S⁰ → S¹ transitions (estimated at 381 nm and 422 nm) can be assigned as a mixed MLCT/ILCT transitions with the electron density shifting from the metal and phenyl moieties over to the bipyridine system (Figures 13 and 14). The S⁰ → T¹ excitations have virtually the same character with ca. 40 nm higher excitation wavelength (Figures 13 and 14). For every other Pd and Pt monomer, the S⁰ → S¹ and S⁰ → T¹ transitions have a distinct π-π* character and are assigned as metal perturbed local excitations within the cyclometalating C^N^N ligand (Figures 13 and 14). The second lowest singlet-singlet transition, S0 → S², is assigned as a pure MLCT transition for each studied monomer, except for Pt-2- mono, for which it has a distinct metal perturbed π-π* character (Figures 13 and 14).

32

Figure 13. Natural transition orbital hole-particle pairs for the low-lying vertical excitations for the monomeric Pd models in DCM.

Figure 14. Natural transition orbital hole-particle pairs for the low-lying vertical excitations for the monomeric Pt models in DCM.

As stated above, for Pd-1-mono and Pd-2-mono, two different minima were located on the triplet potential energy surface. Unrestricted DFT as well as TD-DFT calcula- tions at the optimized minimum structures suggest that the ³MC structure is about 120 meV more stable than the ³MLCT/ILCT structure for Pd-1-mono and 235 meV more stable than the ³(d, π-π*) structure for Pd-2-mono. Thus, the ³MC state is ex- pected to represent the global minimum within the triplet manifold for both palla- dium monomers, providing an efficient non-radiative pathway back to the ground state, resulting in completely quenched emission.

33 As for the monomeric platinum complexes, the S1 and T1 states are separated by an energy difference of 0.36 eV, 0.58 eV, 0.53 eV and 0.58 eV for Pt-1-mono, Pt-2-mono, Pt-3-mono and Pt-4-mono, respectively. The smaller ΔE(S1-T1) value for Pt-1-mono is explained by the increased charge transfer character, and thus smaller quantum mechanical exchange energy. The small energy differences, combined with calcu- lated spin-orbit coupling matrix elements of 34.1 cm^-1, 63.2 cm^-1, 49.8 cm^-1 and 44.1 cm^-1 between the S¹ and T¹ states should result in fast ISC rate and efficient popula- tion of the T1 states. The energy difference is, however, far too great to be overcome by thermal energy, rendering any reverse ISC implausible. Phosphorescence emis- sion stemming from a ³MLCT/ILCT (Pt-1-mono) or ³(d, π-π*) (Pt-2-mono, Pt-3- mono and Pt-4-mono) is thus predicted by the TD-DFT calculations (Figure 15).

Calculated estimates for the radiative rate range from 3.8 · 10⁴ s^-1 to 7.5 · 10⁴ s^-1, cor- responding to radiative lifetimes between 26 and 13 microseconds (Table 3), with the predicted emission wavelengths falling into the green-yellow region. The pre- dicted rates are in line with previously reported radiative rates for other Pt(II) com- plexes.10,106,183-185

Table 3. Calculated radiative rates, lifetimes, emission wavelengths and emissive state characters for the phosphorescence emission in monomeric Pt complexes in DCM.

Complex kr [s^-1] τ [μs] λ [nm] Assignment

Pt-1-mono 4.4 · 10⁴ 23 578 MLCT/ILCT

Pt-2-mono 3.8 · 10⁴ 26 542 d, π → π*

Pt-3-mono 6.2 · 10⁴ 16 537 d, π → π*

Pt-4-mono 7.5 · 10⁴ 13 537 d, π → π*

Figure 15. Natural transition orbital hole-particle pairs for the phosphorescence emission for the monomeric Pt models in DCM obtained at the optimized T¹ state geometries.

34

3.1.2 Dimeric models

The solid-state behavior of the Pd and Pt complexes were studied computationally using dimeric models because experimentally it was shown that all complexes, except Pt-4, form dimeric structures with close metal-metal contacts in the solid state.^{III, IV} Bond lengths for the (TD-)DFT optimized dimers in the ground state and lowest lying singlet and triplet excited states are given in Tables 4 and 5.

Table 4. Selected structural parameters for Pd-1-dim and Pd-2-dim.

Pd-1-dim Pd-2-dim S⁰ S¹ T¹ S⁰ S¹ T¹ bonds [Å]

M-M’ 3.353 2.907 2.862 3.511 2.919 3.523 M-N^cis 1.981 1.988 1.963 1.992 1.991 1.976 1.981 1.968 1.986 1.993 1.979 1.994 M-Ntrans 2.135 2.149 2.102 2.127 2.153 2.131 2.135 2.107 2.145 2.132 2.124 2.133 M-C 1.976 1.982 1.994 1.965 1.971 1.948 1.976 1.996 1.982 1.966 1.976 1.966 M-C^CN 1.950 1.953 1.962 1.953 1.953 1.958 1.950 1.961 1.953 1.953 1.959 1.953

Table 5. Selected structural parameters for Pt-1-dim, Pt-2-dim, Pt-3-dim and Pt- 4-dim.

Pt-1-dim Pt-2-dim Pt-3-dim Pt-4-dim

S⁰ S¹ T¹ S⁰ S¹ T¹ S⁰ S¹ T¹ S⁰ S¹ T¹ bonds [Å]

M-M’ 3.458 2.925 2.861 3.508 2.905 2.858 3.423 2.875 2.816 - - - M-Ncis 1.984 1.983 1.981 1.992 1.993 1.988 2.012 2.002 2.001 1.994 1.994 1.994

1.984 1.992 1.982 1.993 1.992 1.988 2.011 2.013 2.002 1.999 1.974 1.978 M-N^trans 2.110 2.104 2.110 2.102 2.126 2.121 2.132 2.137 2.139 2.118 2.120 2.118 2.110 2.130 2.111 2.104 2.117 2.112 2.120 2130 2.123 2.129 2.091 2.137 M-C 1.980 2.005 1.994 1.973 1.981 1.980 1.973 1.990 1.985 1.981 1.980 1.981 1.980 1.989 1.993 1.973 1.980 1.979 1.973 1.983 1.984 1.979 1.933 1.953 M-CCN 1.945 1.957 1.955 1.946 1.954 1.954 1.946 1.958 1.958 1.947 1.946 1.946 1.945 1.951 1.955 1.946 1.953 1.954 1.944 1.952 1.956 1.950 1.966 1.958 In the optimized ground state structures, metal-metal distances between 3.353 Å and 3.511 Å are predicted for M-1-dim, M-2-dim and Pt-3-dim. These predictions

35 are close to the experimental values, obtained with X-Ray diffraction measure- ments.^{III, IV} All metal-ligand bond lengths are similar to the corresponding values obtained for the monomeric models and correlate well with the experimental data.

The M-N^cis bond length is again distinctly smaller than the M-N^trans, due to the trans- influence induced by the cyclometalating carbanion. The M-C^CN bond length is also slightly smaller than the M-C bond length, which can be attributed to π- backdonation from the metal ion to the cyanide moiety.

In the lowest lying singlet and triplet excited states, severe contractions in the met- al-metal distances are predicted by the TD-DFT optimizations for all dimers except the T¹ structure for Pd-2-dim. Whereas the M-M bond length is virtually unaffected by the S⁰ → T¹ excitation in Pd-2-dim, metal-metal distances ranging from 2.925 Å to 2.816 Å are predicted for the rest of the excited state structures in M-1-dim, M-2- dim and Pt-3-dim as an electron is excited from a metal centered d-d* orbital. For the metal-ligand bond lengths only very minor alterations are predicted upon exci- tation. To study the metal-metal interactions in the dimeric models, QTAIM anal- yses were performed for M-1-dim, M-2-dim and Pt-3-dim at the optimized S⁰, S¹ and T1 state structures and the data is collected to Table 6.

36

Table 6. Properties of the electron density at the M-M BCPs in the dimeric mod- els. The properties are: ρ = the electron density at the BCP; ∇²ρ = the Laplacian of the electron density; |V|/G = the ratio between potential and kinetic energy den- sities; E^int = the interaction energy between the two atoms¹⁸⁶ and δ(A, B) = elec- tron delocalization index between atoms A and B.

Complex State ρ [eÅ^-3] ∇²ρ [eÅ^-5] |V|/G E^int [kJ/mol] δ(A, B)

Pd-1-dim

S₀ 0.093 0.814 1.02 -11.4 0.14

S₁ 0.212 1.238 1.28 -29.8 0.28

T₁ 0.233 1.330 1.30 -33.6 0.30

Pd-2-dim

S₀ 0.072 0.630 0.94 -7.7 0.10

S₁ 0.210 1.233 1.27 -29.5 0.27

T₁ 0.070 0.617 0.94 -7.4 0.10

Pt-1-dim

S₀ 0.106 0.852 1.04 -12.7 0.17

S₁ 0.278 1.533 1.28 -37.4 0.37

T₁ 0.316 1.672 1.32 -44.5 0.41

Pt-2-dim

S₀ 0.097 0.793 1.02 -11.3 0.16

S₁ 0.287 1.628 1.28 -39.8 0.38

T₁ 0.319 1.707 1.32 -45.4 0.41

Pt-3-dim

S₀ 0.112 0.897 1.06 -13.7 0.18

S₁ 0.304 1.704 1.30 -43.3 0.39

T₁ 0.346 1.814 1.35 -51.2 0.44

In the ground state structures the metal-metal interactions are almost pure closed- shell interactions, indicated by the small electron densities at the BCPs and |V|/G ratios close to unity, with interaction energies being comparable to weak hydrogen bonds.^187,188 Upon excitation, distinct strengthening in the metal-metal interactions is predicted for nearly all dimers as the interactions gain partial covalent character as indicated by the 2-3-fold increases in the electron densities, interaction energies and delocalization indices. In the T¹ structure of Pd-2-dim, however, no such strength- ening in the metal-metal interactions is observed, which is to be expected, given the structural similarity between the S⁰ and T¹ states of Pd-2-dim. In the isostructural M-1-dim and M-2-dim, the metal-metal interactions are slightly stronger in case of the platinum containing congeners, both in the ground and excited states.

The metal-metal interactions also drastically alter the photophysical behavior of the complexes. As predicted by the TD-DFT calculations, virtually all low-lying vertical excitations can be characterized as MMLCT transitions for every dimeric model containing metal-metal contacts (Table 7, Figure 16). Compared to the monomeric

37 models, the low-lying excitations for M-1-dim, M-2-dim and Pt-3-dim are also sig- nificantly redshifted with the change in the S⁰ → S¹ excitation wavelength between 53 nm and 95 nm. For Pt-4-dim, the lack of metal-metal interactions results in no changes in the nature of the low-lying vertical excitations, as the transitions can be characterized as metal-perturbed π-π* transitions, just like in the monomeric model (Figures 14 and 16). The estimated excitation wavelengths are in close agreement with the experimental solid-state excitation data.^{III, IV}

Table 7. Two lowest lying singlet-singlet and the lowest lying singlet-triplet ver- tical excitation for the dimeric Pd and Pt models. (λ = excitation wavelength, f = oscillator strength).

Complex Transition λ [nm] f Major contributions* Assignment

Pd-1-dim

S₀ → S₁ 476 0.0331 97 % H → L MMLCT

S₀ → S₂ 460 0.0000 97 % H → L+1 MMLCT

S₀ → T₁ 497 - 95 % H → L MMLCT

Pd-2-dim

S₀ → S₁ 409 0.0428 94 % H → L MMLCT

S₀ → S₂ 395 0.0001 92 % H → L+1 MMLCT

S₀ → T₁ 428 - 89 % H → L MMLCT

Pt-1-dim

S₀ → S₁ 511 0.0358 97 % H → L MMLCT

S₀ → S₂ 499 0.0000 98 % H → L+1 MMLCT

S₀ → T₁ 542 - 96 % H → L MMLCT

Pt-2-dim

S₀ → S₁ 440 0.0514 95 % H → L MMLCT

S₀ → S₂ 424 0.0001 94 % H → L+1 MMLCT

S₀ → T₁ 468 - 92 % H → L MMLCT

Pt-3-dim

S₀ → S₁ 448 0.0586 97 % H → L MMLCT

S₀ → S₂ 425 0.0005 95 % H → L+1 MMLCT

S₀ → T₁ 482 - 95 % H → L MMLCT

Pt-4-dim

S₀ → S₁ 399 0.0012 79 % H-1 → L d, π → π*

S₀ → S₂ 398 0.0039 50 % H → L+1, 38 % H → L d, π → π*

S₀ → T₁ 443 - 70 % H-1 → L d, π → π*

[*] H = HOMO, L = LUMO

38

Figure 16. Natural transition orbital hole-particle pairs for the low-lying vertical excitations in the dimeric Pd and Pt models.

Because of the highly distorted structures of the ³MC states for Pd-1-mono and Pd- 2-mono, it is argued that the solid-state packing severely restricts the formation of the metal-centered states in the aggregated state and thus gives rise to potentially emissive species. To estimate the solid-state emission behavior of the studied di- meric species, the energy differences between the lowest lying singlet and triplet states were first compared (Table 8).

39 Table 8. Energy differences between the lowest lying singlet and triplet excited states for the studied dimeric models.

Complex ΔE(S₁-T₁) [eV]

Pd-1-dim 0.12 Pd-2-dim 0.29 Pt-1-dim 0.18 Pt-2-dim 0.25 Pt-3-dim 0.22 Pt-4-dim 0.56

Pd-1-dim and Pt-1-dim are characterized with a ΔE(S1-T1) values of 0.12 eV and 0.18 eV, respectively. Such low energy differences could mean the possibility of TADF emission. For M-2-dim, Pt-3-dim and Pt-4-dim, the energy differences are some- what higher with calculated estimates between 0.22 eV and 0.56 eV. The increased energy differences and the relatively large Stokes shifts observed in the experi- mental emission spectra hint that these complexes decay with phosphorescence emission. The calculated phosphorescence data for M-2-dim, Pt-3-dim and Pt-4- dim is collected to Table 9.

Table 9. Calculated radiative rates, lifetimes, emission wavelengths and emissive state characters for the phosphorescence emission in M-2-dim, Pt-3-dim and Pt- 4-dim.

Complex kr [s^-1] τ [μs] λ [nm] Assignment Pd-2-dim 7.25 · 10³ 138 523 d, π → π*

Pt-2-dim 1.38 · 10⁴ 73 698 MMLCT Pt-3-dim 1.37 · 10³ 728 717 MMLCT Pt-4-dim 5.96 · 10³ 168 543 d, π → π*

For Pd-2-dim, the T1 state is characterized as a metal perturbed π-π* state (Table 9, Figure 17) even though the lowest lying singlet-triplet vertical excitation from the ground state was of MMLCT character. The estimated emission wavelength is 523 nm and the radiative lifetime 138 μs. The experimental emission spectrum shows vibronic progression in the region between 550 nm and 660 nm, agreeing closely with the TD-DFT results.^III The low radiative rate also explains the poor quantum yield (< 0.01) observed experimentally. The phosphorescence in Pt-2-dim and Pt-3- dim is assigned to ³MMLCT state with estimated emission wavelengths of 698 nm and 717 nm, respectively. Experimentally, these complexes show broad unstruc- tured bands at 618 nm and 660 nm, although it should be noted that Pt-3 is sensitive to mechanical stimuli, showing a mechanochemical transitioning from vibronic fine