This paper is published as part of a PCCP Themed Issue on: Modern EPR Spectroscopy: Beyond the EPR Spectrum Guest Editor: Daniella Goldfarb

Editorial

Modern EPR spectroscopy: beyond the EPR spectrum Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b913085n

Perspective

Molecular nanomagnets and magnetic nanoparticles: the EMR contribution to a common approach M. Fittipaldi, L. Sorace, A.-L. Barra, C. Sangregorio, R. Sessoli and D. Gatteschi, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905880j

Communication

Radiofrequency polarization effects in zero-field electron paramagnetic resonance Christopher T. Rodgers, C. J. Wedge, Stuart A. Norman, Philipp Kukura, Karen Nelson, Neville Baker, Kiminori Maeda, Kevin B. Henbest, P. J. Hore and C. R. Timmel, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906102a

Papers

Radiofrequency polarization effects in low-field electron paramagnetic resonance C. J. Wedge, Christopher T. Rodgers, Stuart A. Norman, Neville Baker, Kiminori Maeda, Kevin B. Henbest, C. R. Timmel and P. J. Hore, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907915g

Three-spin correlations in double electron–electron resonance Gunnar Jeschke, Muhammad Sajid, Miriam Schulte and Adelheid Godt, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905724b 14N HYSCORE investigation of the H-cluster of [FeFe] hydrogenase: evidence for a nitrogen in the dithiol bridge Alexey Silakov, Brian Wenk, Eduard Reijerse and Wolfgang Lubitz, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905841a

Tyrosyl radicals in proteins: a comparison of empirical and density functional calculated EPR parameters Dimitri A. Svistunenko and Garth A. Jones, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905522c

General and efficient simulation of pulse EPR spectra Stefan Stoll and R. David Britt, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907277b

Dynamic nuclear polarization coupling factors calculated from molecular dynamics simulations of a nitroxide radical in water Deniz Sezer, M. J. Prandolini and Thomas F. Prisner, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905709a

Dynamic nuclear polarization of water by a nitroxide radical: rigorous treatment of the electron spin saturation and comparison with experiments at 9.2 Tesla Deniz Sezer, Marat Gafurov, M. J. Prandolini, Vasyl P. Denysenkov and Thomas F. Prisner, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906719c

Dynamic mixing processes in spin triads of breathing crystals Cu(hfac)2LR: a multifrequency EPR study at 34, 122 and 244 GHz Matvey V. Fedin, Sergey L. Veber, Galina V. Romanenko, Victor I. Ovcharenko, Renad Z. Sagdeev, Gudrun Klihm, Edward Reijerse, Wolfgang Lubitz and Elena G. Bagryanskaya, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906007c

Nitrogen oxide reaction with six-atom silver clusters supported on LTA zeolite Amgalanbaatar Baldansuren, Rüdiger-A. Eichel and Emil Roduner, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b903870a

Multifrequency ESR study of spin-labeled molecules in inclusion compounds with cyclodextrins Boris Dzikovski, Dmitriy Tipikin, Vsevolod Livshits, Keith Earle and Jack Freed, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b903490k

ESR imaging in solid phase down to sub-micron resolution: methodology and applications Aharon Blank, Ekaterina Suhovoy, Revital Halevy, Lazar Shtirberg and Wolfgang Harneit, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905943a

Multifrequency EPR study of the mobility of nitroxides in solid-state calixarene nanocapsules Elena G. Bagryanskaya, Dmitriy N. Polovyanenko, Matvey V. Fedin, Leonid Kulik, Alexander Schnegg, Anton Savitsky, Klaus Möbius, Anthony W. Coleman, Gennady S. Ananchenko and John A. Ripmeester, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906827a

Ferro- and antiferromagnetic exchange coupling constants in PELDOR spectra D. Margraf, P. Cekan, T. F. Prisner, S. Th. Sigurdsson and O. Schiemann, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905524j

Electronic structure of the tyrosine D radical and the water-splitting complex from pulsed ENDOR spectroscopy on photosystem II single crystals Christian Teutloff, Susanne Pudollek, Sven Keßen, Matthias Broser, Athina Zouni and Robert Bittl, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b908093g

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View Article Online / Journal Homepage / Table of Contents for this issue

A W-band pulsed EPR/ENDOR study of CoIIS4 coordination in the Co[(SPPh2)(SPiPr2)N]2 complex Silvia Sottini, Guinevere Mathies, Peter Gast, Dimitrios Maganas, Panayotis Kyritsis and Edgar J.J. Groenen, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905726a

Exchangeable oxygens in the vicinity of the molybdenum center of the high-pH form of sulfite oxidase and sulfite dehydrogenase Andrei V. Astashkin, Eric L. Klein, Dmitry Ganyushin, Kayunta Johnson-Winters, Frank Neese, Ulrike Kappler and John H. Enemark, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907029j

Magnetic quantum tunneling: key insights from multi-dimensional high-field EPR J. Lawrence, E.-C. Yang, D. N. Hendrickson and S. Hill, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b908460f

Spin-dynamics of the spin-correlated radical pair in photosystem I. Pulsed time-resolved EPR at high magnetic field O. G. Poluektov, S. V. Paschenko and L. M. Utschig, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906521k

Enantioselective binding of structural epoxide isomers by a chiral vanadyl salen complex: a pulsed EPR, cw-ENDOR and DFT investigation Damien M. Murphy, Ian A. Fallis, Emma Carter, David J. Willock, James Landon, Sabine Van Doorslaer and Evi Vinck, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907807j

Topology of the amphipathic helices of the colicin A pore-forming domain in E. coli lipid membranes studied by pulse EPR Sabine Böhme, Pulagam V. L. Padmavathi, Julia Holterhues, Fatiha Ouchni, Johann P. Klare and Heinz-Jürgen Steinhoff, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907117m

Structural characterization of a highly active superoxide-dismutase mimic Vimalkumar Balasubramanian, Maria Ezhevskaya, Hans Moons, Markus Neuburger, Carol Cristescu, Sabine Van Doorslaer and Cornelia Palivan, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905593b

Structure of the oxygen-evolving complex of photosystem II: information on the S2 state through quantum chemical calculation of its magnetic properties Dimitrios A. Pantazis, Maylis Orio, Taras Petrenko, Samir Zein, Wolfgang Lubitz, Johannes Messinger and Frank Neese, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907038a

Population transfer for signal enhancement in pulsed EPR experiments on half integer high spin systems Ilia Kaminker, Alexey Potapov, Akiva Feintuch, Shimon Vega and Daniella Goldfarb, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906177k

The reduced [2Fe-2S] clusters in adrenodoxin and Arthrospira platensis ferredoxin share spin density with protein nitrogens, probed using 2D ESEEM Sergei A. Dikanov, Rimma I. Samoilova, Reinhard Kappl, Antony R. Crofts and Jürgen Hüttermann, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b904597j

Frequency domain Fourier transform THz-EPR on single molecule magnets using coherent synchrotron radiation Alexander Schnegg, Jan Behrends, Klaus Lips, Robert Bittl and Karsten Holldack, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905745e

PELDOR study of conformations of double-spin-labeled single- and double-stranded DNA with non-nucleotide inserts Nikita A. Kuznetsov, Alexandr D. Milov, Vladimir V. Koval, Rimma I. Samoilova, Yuri A. Grishin, Dmitry G. Knorre, Yuri D. Tsvetkov, Olga S. Fedorova and Sergei A. Dzuba, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b904873a

Site-specific dynamic nuclear polarization of hydration water as a generally applicable approach to monitor protein aggregation Anna Pavlova, Evan R. McCarney, Dylan W. Peterson, Frederick W. Dahlquist, John Lew and Songi Han, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b906101k

Structural information from orientationally selective DEER spectroscopy J. E. Lovett, A. M. Bowen, C. R. Timmel, M. W. Jones, J. R. Dilworth, D. Caprotti, S. G. Bell, L. L. Wong and J. Harmer, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b907010a

Structure and bonding of [VIVO(acac)2] on the surface of AlF3 as studied by pulsed electron nuclear double resonance and hyperfine sublevel correlation spectroscopy Vijayasarathi Nagarajan, Barbara Müller, Oksana Storcheva, Klaus Köhler and Andreas Pöppl, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b903826b

Local variations in defect polarization and covalent bonding in ferroelectric Cu2+-doped PZT and KNN functional ceramics at themorphotropic phase boundary Rüdiger-A. Eichel, Ebru Erünal, Michael D. Drahus, Donald M. Smyth, Johan van Tol, Jérôme Acker, Hans Kungl and Michael J. Hoffmann, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905642d

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Dynamic mixing processes in spin triads of ‘‘breathing crystals’’

Cu(hfac)2LR: a multifrequency EPR study at 34, 122 and 244 GHzw

Matvey V. Fedin,*a Sergey L. Veber,ab Galina V. Romanenko,a

Victor I. Ovcharenko,aRenad Z. Sagdeev,

aGudrun Klihm,

cEdward Reijerse,

c

Wolfgang Lubitzcand Elena G. Bagryanskaya

a

Received 26th March 2009, Accepted 4th June 2009

First published as an Advance Article on the web 8th July 2009

DOI: 10.1039/b906007c

Spin triads of copper(II) with two nitroxides are responsible for the magnetic anomalies in a new

family of molecular-magnetic compounds called ‘‘breathing crystals’’. We have shown previously

that electron paramagnetic resonance (EPR) spectroscopy allows one to investigate the

peculiarities of these systems and obtain valuable information on exchange interactions governing

the magnetic anomalies. One of the key processes revealed is the dynamic mixing between

different spin multiplets that leads to a coalescence of individual EPR lines at high temperatures.

The rates of the mixing were found to be fast at EPR frequencies between 9 and 94 GHz. In the

present work, we expose the spin triads to higher microwave frequencies of up to 244 GHz in

order to reach the conditions of intermediate or slow mixing rates. Three representatives of the

family of breathing crystals have been studied. Based on the simulations of EPR data at 34, 122

and 244 GHz, the rates of the mixing processes have been estimated and conclusions on their

character and temperature dependence have been drawn. The insights from high-field EPR clarify

previously obtained results and aid in the further development of EPR approaches for studying

these and similar systems. It is suggested that the static and dynamic Jahn–Teller effects may play

an important role in the mechanisms governing the observed spin exchange effects.

Introduction

Exchange-coupled heterospin systems have accumulated

significant interest from researchers during the last few

decades. Such systems of two or more coupled spins are often

found in inorganic and metal–organic complexes, including

those of biological relevance and those used in the design of

advanced magnetic materials.1–7 Three-spin nitroxide–copper(II)–

nitroxide clusters (see structure in Fig. 2a) were found to be

responsible for the magnetic anomalies in a new family of

molecular-magnetic compounds called ‘‘breathing crystals’’.8–16

A key characteristic of breathing crystals is their ability to

undergo reversible, thermally-induced structural rearrangements,

accompanied by changes in magnetic susceptibility similar to a

classical spin crossover. We have found recently that this

magnetic switching can also be induced by light.17 In both

cases of thermal and optical initiation, the switching of the

magnetic properties is attributed to a significant change of

the exchange interaction within the spin triads.16 Therefore,

a detailed understanding of the electronic structure and

dynamics of spin triads in breathing crystals is essential from

both a fundamental and applied point of view.

Electron paramagnetic resonance (EPR) spectroscopy is

widely used in the studies of exchange-coupled systems.18–24

We have shown previously that the EPR of strongly-coupled

spin triads is specific and informative.13–16 First, the ground

multiplet state of a triad (Fig. 1) becomes predominately

populated at relatively high temperatures (ca. 100–200 K for

breathing crystals) due to the large values of the exchange

interaction |J| 4 kT. This results in the observation of

‘‘enhanced’’ signals of the ground state with characteristic

g-values less than 2, whereas the EPR signals of the other

multiplet states are ‘‘suppressed’’ and therefore not observed.13

The effective g-tensors of the spin multiplets are given by

eqn (1), where gCu is the g tensor of the copper ion, and gR is

the isotropic g factor of the nitroxide radical.

gA = (4gR1 � gCu)/3

gB = gCu

gC = (2gR1 + gCu)/3. (1)

Second, at higher temperatures, where kT E |J| and kT 4 |J|,

the dynamic mixing processes operate between the three

multiplets of a triad and lead to a coalescence of individual

EPR lines and the actual observation of one averaged signal.14

By their manifestation, these mixing processes are very similar

to the well-known electron spin exchange (or electron

a International Tomography Center SB RAS, 630090, Novosibirsk,Russia. E-mail: mfedin@tomo.nsc.ru

bNovosibirsk State University, 630090, Novosibirsk, RussiacMax-Planck-Institut fur Bioanorganische Chemie, 45470,Mulheim/Ruhr, Germanyw Electronic supplementary information (ESI) available: Calculationsand simulations; crystal data and experimental details forCu(hfac)2L

Bu�0.5C8H10. CCDC reference numbers 725423–725428.For ESI and crystallographic data in CIF or other electronic formatsee DOI: 10.1039/b906007c

6654 | Phys. Chem. Chem. Phys., 2009, 11, 6654–6663 This journal is �c the Owner Societies 2009

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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‘‘hopping’’) processes that might cause a coalescence of

spectral lines in liquid state EPR or NMR.

In our previous work14 we reported the first experimental

evidence for the existence of dynamic mixing processes

between the multiplets of spin triads of breathing crystals.

The observation of a single EPR line of a triad at kT 4 |J|,

instead of three lines of multiplets A, B and C, was explained

by the assumption that the dynamic mixing processes are very

fast at the time scale of the microwave frequencies used in this

work (34 and 94 GHz). The temperature-dependent position

of the EPR line of a triad was then explained by the change of

the relative Boltzman populations of multiplets A, B and C

versus temperature, leading to a shift of the ‘‘gravity center’’ of

the spectrum. As a possible mechanism that induces these

mixing processes, we have proposed a modulation of exchange

interactions between copper and nitroxide spins by lattice

vibrations. The transitions between doublets A 2 B can be

induced by an isotropic exchange interaction, whereas the

other two transitions (A 2 C and B 2 C) are only allowed

if one assumes anisotropy of the exchange interaction

(Fig. 1b). The estimations show that, for large values of |J|

(B100 cm�1), the rates of these transitions can indeed be as

high as 1010–1012 s�1. Model calculations have shown a good

qualitative agreement with the experimental data.

Fast dynamic mixing between multiplets was found to be a

useful characteristic of the processes observed in spin triads of

breathing crystals. It strongly simplifies both analytical

and numerical calculations, as well as the interpretation of

experimental data. The fast mixing condition allows one

to find a clear correlation between EPR and magnetic

susceptibility data.15 Moreover, when the mixing is fast, the

position of a coalesced EPR line of a triad becomes a good

spectroscopic probe of the exchange interaction. This relies on

the fact that we succeeded in developing an elegant approach

for the measurement of the temperature dependence of the

exchange interaction in breathing crystals.16 However, we

have also observed that for some compounds of the family

of breathing crystals the mixing processes at the W-band are

insufficiently fast for this simple theory to apply.14 Because of

that, some compromises between the spectral resolution

and mixing regime must be chosen. This has motivated us in

the present study to expand the EPR frequency range of

investigation to 122 and 244 GHz. It was expected that the

condition of slow or intermediate exchange could be reached

at higher frequencies, yielding the actual rates of the

mixing processes and providing insights into the mechanism.

In the following sections we describe and discuss the obtained

results.

Experimental

Synthesis, magnetic susceptibility and X-ray data of the breathing

crystals of composition Cu(hfac)2LPr, Cu(hfac)2L

Bu�0.5C8H18

(C8H18 = octane) and Cu(hfac)2LBu�0.5C8H10 (C8H10 =

orthoxylene) have been described previously,8–10,12,15 except for

the X-ray data for Cu(hfac)2LBu�0.5C8H10 that is given in the ESI

to this paper (structures in the CIF file are at T = 60, 100, 150,

180, 240 and 295 K).w In all experiments single crystals of these

compounds have been used.

A Bruker ER200D continuous wave Q-band EPR spectro-

meter equipped with a home-built resonator (TE011) and

Oxford CF935 flow cryostat has been used for the experiments

at 34 GHz. A home-built high-field EPR spectrometer25

equipped with an ICE-Oxford cryogenic system has been used

for the experiments at 122 and 244 GHz. These high-field EPR

experiments have been carried out without a resonator and

using induction mode detection.

Fig. 1 (a) Energy levels of a strongly exchange-coupled spin triad

(antiferromagnetic coupling). (b) Transitions induced by the modulation

of isotropic (—) and anisotropic (����) exchange interactions.

Fig. 2 (a) Polymer-chain structure of Cu(hfac)2LPr complexes (spin

triads are circled). (b) Temperature dependence of the effective

magnetic moment meff(T) of the three studied compounds: Cu(hfac)2LPr

(red circles), Cu(hfac)2LBu�0.5C8H10 (blue squares), Cu(hfac)2L

Bu�0.5C8H18 (green triangles). The results are taken from ref. 15.

This journal is �c the Owner Societies 2009 Phys. Chem. Chem. Phys., 2009, 11, 6654–6663 | 6655

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Results and discussion

Choice of the systems

We have selected three compounds of the expanding family of

breathing crystals for the multifrequency EPR study at 34, 122

and 244 GHz. All these compounds—Cu(hfac)2LPr,

Cu(hfac)2LBu�0.5C8H10 and Cu(hfac)2L

Bu�0.5C8H18—have

been previously studied by us using 9, 34 and 94 GHz EPR,

mainly in the form of polycrystalline powders.13–16 In order to

examine the frequency dependence of their EPR spectra at

slow/intermediate rates of the mixing process, we performed a

series of measurements of the temperature-dependent EPR for

each compound at each frequency band. The polycrystalline

powder spectra at high microwave (mw) frequencies (122 and

244 GHz) become very broad, especially at high enough

temperatures, where kT B |J|, where the mixing processes

become efficient, and therefore, are not very informative.

Because of that, single crystals were used in all cases; the

crystal orientation with respect to the magnetic field was

similar in all frequency bands for each compound. The

orientations used were chosen to approximately correspond

to the parallel component of the g-tensor of the one-spin

copper unit. These orientations ensured that no overlap of

the signals of the one-spin copper unit and the spin triad

occurs at high temperatures at any mw band and therefore

were the most convenient.

All three compounds under study experience gradual spin

transitions, i.e. the magnetic susceptibility changes smoothly

with temperature (Fig. 2b). The steepest dependence, meff(T), isobserved for Cu(hfac)2L

Bu�0.5C8H18. The curves of meff(T) forCu(hfac)2L

Pr and Cu(hfac)2LBu�0.5C8H10 are very close.

However, their shapes are somewhat different and the

maximum inclination (dmeff/dT) for Cu(hfac)2LBu�0.5C8H10 is

shifted by ca. 60 K to lower temperatures. We have chosen

these three cases of gradual dependences, meff(T), in order to be

able to trace the dynamics of spin transitions in detail, which

would hardly be possible for abrupt spin transitions occurring

within a few Kelvin.

Overview of the experimental results and general trends

Fig. 3 shows the 34, 122 and 244 GHz EPR data for the

breathing crystal Cu(hfac)2LPr. This compound has been most

Fig. 3 Temperature-dependent EPR spectra of Cu(hfac)2LPr. (a) nmw E 33.97 GHz; (b) nmw E 121.46 GHz; (c) nmw E 243.10 GHz. The spectra

in (a) and spectra on the left in (b) and (c) are normalized to the signal of the one-spin copper ion (low-field part of the spectrum). Plots on the right

in (b) and (c) represent the magnified signals of spin triads normalized to their maxima. Red lines show the simulations.

6656 | Phys. Chem. Chem. Phys., 2009, 11, 6654–6663 This journal is �c the Owner Societies 2009

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exhaustively studied by us previously (but never in single

crystal form, nor at microwave frequencies of nmw 4 95 GHz),

therefore it is an appropriate compound to start with. X-Ray

data show that this crystal consists of alternating planes in

which the polymer chains are not collinear with respect to each

other; however, in the direction of the principal axis of

symmetry, both the spin triads and one-spin copper(II) units

belonging to different chains are magnetically equivalent.

Therefore, the crystal was oriented with this principal axis

along the magnetic field. The spectrum of the spin triad at

Q-band shows a single EPR line at all temperatures. Its width

increases monotonically with T, and its position shifts from

the effective g-values of geff o 2 at low T to geff 4 2 at high T.

These observations at 34 GHz are characteristic for the case

of a fast mixing process between the spin multiplets of the

triad. However, at higher frequencies of 122 and 244 GHz, a

principally different behavior was observed. At intermediate

temperatures (T= 130–180 K), two lines corresponding to the

spin triad are readily detected, and a transfer of the intensity of

one line into the other occurs with increasing temperature.

This implies that the mixing processes at 122 and 244 GHz

become comparable to or slower than the frequency difference

between the two observed lines. One also observes that the

mixing process is generally slower at 244 GHz compared to

122 GHz, because, e.g. at T = 170 K, the two lines are nearly

coalesced at 122 GHz, whereas at 244 GHz they never do but

just transfer intensity from one to the other. Thus, a clear

qualitative conclusion can be drawn that the mixing processes

in spin triads of Cu(hfac)2LPr pass from fast to intermediate to

slow rates when the mw frequency is changed from 34 to 122

to 244 GHz.

The rates of the dynamic mixing processes are expected to

depend on temperature; therefore the above conclusion is only

valid for the temperature range where two resolved lines

of a triad are observed, i.e. at T = 130–180 K. At higher

temperatures, the observation of a single EPR line of the triad

shows that the mixing processes are fast at all mw bands. At

low temperatures (T o 100–120 K), one also observes a single

EPR line of the triad, although not necessarily due to fast

mixing, but rather because of a predominant population of the

ground state multiplet A and negligible populations of the two

higher multiplets.

Fig. 4 shows the 34, 122 and 244 GHz EPR data for the

breathing crystal Cu(hfac)2LBu�0.5C8H10.

In general, all the trends observed for this compound are

very similar to the case of the breathing crystal Cu(hfac)2LPr.

Again, the low-frequency (34 GHz, Fig. 4a) data show that the

EPR spectrum of the spin triad consists of a single line in the

temperature range of 50–250 K. The shape and the width of

this line does not change dramatically with temperature (as

compared to 122 and 244 GHz), with the exception of the

range of 100–130 K, where the line broadens and becomes

asymmetric. Thus, at 34 GHz the rate of the mixing process is

always fast as compared to the frequency difference between

the EPR lines of multiplets A, B and C. At the same time, it is

not as fast at T = 100–130 K, otherwise the averaged

(coalesced) line would have been symmetric. In contrast, at

higher frequencies (122 and 244 GHz) two resolved lines of the

spin triad are observed, and the intensity of one line is

gradually transferred to the other with increasing temperature.

Therefore, a similar qualitative conclusion can be drawn for

the breathing crystal Cu(hfac)2LBu�0.5C8H10, as was done for

Cu(hfac)2LPr above: the mixing process rates pass from the

situation of moderately fast mixing at 34 GHz to the situation

of slow mixing at 244 GHz.

Our third example, the compound of composition

Cu(hfac)2LBu�0.5C8H18, represents the other extreme case.

The EPR spectra of the triad show a single line at all frequency

bands (34, 122 and 244 GHz), which implies the slow mixing

regime cannot be reached even at 244 GHz (Fig. 5).

However, the evolution of the linewidth with temperature is

different at each frequency band, as shown in Fig. 6a.

The linewidth at 34 GHz increases monotonically with

temperature, which can be attributed to the increase of the

electron spin relaxation rate. The dependence of the linewidth

(half width at half maximum) on temperature, G(T), at 122 GHz,

however, has a pronounced maximum at ca. 110 K; then the

line narrows with increasing temperature until 170 K, where

relaxation takes over and the line starts to broaden again.

The G(T) dependence at 244 GHz displays an even more

pronounced maximum at ca. 110 K. All these observations

imply that the rates of the mixing processes are not extremely

fast at 122 and 244 GHz, but are still fast enough to lead to a

complete coalescence of the individual EPR lines of different

multiplets and an observation of a single line from the

spin triad. The shapes of the G(T) curves at 34, 122, and

244 GHz can be understood uniformly as superpositions of a

monotonically increasing function related to the homogeneous

linewidth with a ‘‘bell’’-like function arising from spin

exchange. The amplitudes of the ‘‘bell curves’’ for G(T) at

122 and 244 GHz differ roughly by a factor of 4. This is

consistent with the theoretical expectation that the linewidth in

the fast exchange limit is proportional to (oi � oj)2, where oi,j

are the frequencies of the exchanged lines that differ by a

factor of two between 122 and 244 GHz.

A qualitative comparison of the mixing rates of all three

studied compounds can be done using the G(T) dependenciesat low mw frequency (34 GHz) where a single line of the triad

is always observed for all compounds (Fig. 6b). The G(T)dependence of Cu(hfac)2L

Bu�0.5C8H18 shows virtually no

observable bell-like shape, meaning that the mixing rates lay

always in the fast exchange limit, as discussed above. The G(T)dependence of Cu(hfac)2L

Pr shows a quite shallow, but still

clearly detectable, bell-like shape, meaning that the mixing

rate for this compound is slower. Finally, the G(T) dependenceof Cu(hfac)2L

Bu�0.5C8H10 clearly shows a pronounced

bell-like shape indicating that the mixing processes are slowest

for this compound among the three studied. Consequently, the

mixing rate increases in the series of the three compounds as

Cu(hfac)2LBu�0.5C8H10 - Cu(hfac)2L

Pr - Cu(hfac)2LBu�

0.5C8H18.

In the case of the slow mixing process, which seems to occur

for the compounds of composition Cu(hfac)2LBu�0.5C8H10

and Cu(hfac)2LPr at 244 GHz, we observe a spectrum of the

spin triad, consisting of two lines that pass the intensity from

one to the other with increasing temperature. The question is

why can only these two EPR lines be detected, even though

there are three multiplets, A, B and C, with their three

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individual (and clearly different) g-tensors [see eqn (1)]? In our

previous work we proposed that the dynamic mixing process

could be caused by the modulation of the exchange interaction

through lattice vibrations.14 We have remarked that the

transitions between the multiplets A and B are much faster

than all other transitions involving multiplet C, because the

A2 B mixing is induced by the isotropic part of the exchange

interaction, whereas the other transitions are only weakly

allowed due to the anisotropic exchange and other smaller

contributions. Therefore, the rates of mixing between

multiplets A and B should be much faster than the ones for

A,B 2 C. It seems that our high-field study confirms these

expectations. First, the region where the signal of multiplet B

should be observed, with g= gCu, is absolutely ‘‘clean’’ within

our experimental accuracy at all temperatures. Note that the

g-tensors of the magnetically isolated copper ion and the

copper ion within a spin triad are not collinear, and that no

overlap of their signals is expected for the chosen orientations.

Second, the position of the high-field line of the triad shifts

slightly towards higher g-factors even before and during the

transfer of its intensity to the low-field line (Fig. 3c and 4c).

These two observations are fully consistent with the assumption

of fast mixing between multiplets A and B for all studied

systems at all mw bands. The lower limit for the A 2 B

exchange rate at high temperatures can be estimated from the

difference of g-factors, gA and gB, and the mw frequency,

244 GHz, as kexA2B 4 3 � 1010 s�1.

Now, having understood the basic trends and differences of

the EPR spectra of these three selected compounds, we would

like to investigate the mixing processes in more detail, with the

aim of understanding what quantitative information can be

obtained using simulations, as well as what information on the

mechanism and character of the mixing processes can be

derived.

Simulations and quantitative study

In order to verify the agreement of the experimental data with

our theoretical model, we have performed ‘‘2-D’’ simulations

Fig. 4 Temperature-dependent EPR spectra of Cu(hfac)2LBu�0.5C8H10. (a) nmw E 33.97 GHz; (b) nmw E 121.48 GHz; (c) nmw E 243.07 GHz.

The spectra in (a) and the spectra on the left in (b) and (c) are normalized to the signal of the one-spin copper ion (low-field part of the spectrum).

Plots on the right in (b) and (c) represent the magnified signals of spin triads normalized to their maxima. Red lines show the simulations.

At T = 130–160 K, an agreement between experiment and simulation cannot be found, as exemplified by red dotted lines in (c).

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of the experimental spectra vs. temperature and vs. mw

frequency. The theoretical approach was described in our

previous work.14 Briefly, (i) the multiplets, A, B and C, of a

spin triad are modeled by three paramagnetic centers, with the

corresponding g-tensors given by eqn (1); (ii) the intensities

of their lines take into account the probabilities of the

corresponding EPR transitions and the Boltzmann population

factors corresponding to the exchange interaction J; (iii) the

dynamic mixing process between given multiplets, M and N, is

introduced as a reversible, monomolecular reaction, M 2 N,

with the rate constants coupled by an expression, kM-N =

kN-Mexp[(EM � EN)/kT], where EM,N are the energies of the

corresponding multiplets. The characteristic rate of the mixing

(exchange) process is then defined as kexMN = kM-N + kN-M,

as is usual for exchange rates. The solution of the modified

Bloch equations is numerically performed and the arrays of

the resulting spectra are simultaneously calculated for the

three mw bands at each temperature. The input parameters

of the spin triad at a certain temperature are: g-factors of the

copper ion, gCu, and nitroxide, gR; the exchange coupling

constant, J; the transverse relaxation times, TA,B,C2 , of each

multiplet, A, B and C, associated with the widths of

corresponding lines; and the mixing process rate constants,

kexMN = kM-N + kN-M. The exchange coupling constant is a

function of temperature, J = J(T), and was estimated by

fitting the magnetic susceptibility data of Cu(hfac)2LBu�

0.5C8H10 and Cu(hfac)2LPr, or taken directly as obtained

previously by EPR16 of Cu(hfac)2LBu�0.5C8H18 (details in

the ESIw). The g-tensor of the nitroxide was taken to be

isotropic, with gR = 2.007. The relaxation times, TA,B,C2 ,

influence mainly the linewidth of the signals and were adjusted

for each spectrum. The main difficulty in the interpretation of

the temperature dependence of the single crystal EPR of the

breathing crystals is the fact that the g-tensor of the copper ion

also evolves with temperature [gCu = gCu(T)], and thus the

Fig. 5 Temperature-dependent EPR spectra of Cu(hfac)2LBu�0.5C8H18. (a) nmw E 33.96 GHz; (b) nmw E 122.00 GHz; (c) nmw E 243.80 GHz. All

spectra are normalized to the signal of the one-spin copper ion (low-field part of the spectrum). Red lines show the simulations.

Fig. 6 Linewidth (HWHM) analysis for the studied compounds

vs. temperature and mw frequency. (a) Temperature dependence of

the linewidth of the compound Cu(hfac)2LBu�0.5C8H18 in three mw

bands (corresponding frequencies are indicated on the plot). (b)

Comparison of the temperature dependence of the linewidth for the

three studied compounds in the Q-band (34 GHz): Cu(hfac)2LPr

(red circles), Cu(hfac)2LBu�0.5C8H10 (blue squares), Cu(hfac)2L

Bu�0.5C8H18 (green triangles). The points are connected using spline

functions.

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g-value at each temperature has to be adjusted experimentally.

Finally, the last variables are the exchange rates between

corresponding multiplets (kexMN), which, of course, are constant,

vs. mw frequency at each particular temperature. This, despite

many variable parameters in the simulation, allowed us to

obtain rather strict estimates for the mixing rate constants. As

was discussed above, we assume that the mixing rates of

A,B 2 C are much slower than A 2 B because the former

two transitions are only weakly allowed due to the small

anisotropy of the exchange coupling. Therefore, following

our previous work,14 the mixing rates depend on the energy

splitting between corresponding multiplets and temperature

according to:

kexMN ¼ KMNcothEM � ENj j

2kT

� �; ð2Þ

and KA2C E KB2C = aKA2B, with ao 1 being the measure

of exchange anisotropy in the system. Because there are too

many unknown adjustable variables, our main focus was to

test the agreement of experiment and theory for a reasonable

set of parameters and to obtain estimates for the mixing rate

constants.

For the compound Cu(hfac)2LPr, we succeeded in obtaining

a satisfactory agreement with the experimental data for all mw

bands and temperatures (Fig. 3) using a reasonable set of

parameters (given in the ESIw). Indeed, with a couple

of exceptions, the relative line intensities and shapes are

fairly well described; both of them are very sensitive to the

mixing process rates, kexMN. The obtained values vary in the

temperature range from T = 90 to T = 250 K as follows:

kexAB= (2� 1010)–(2� 1012) s�1, kexAC= (1� 109)–(8� 1010) s�1,

kexBC = (1 � 109)–(2 � 1011) s�1.

Good agreement with the experiment was also obtained for

the compound of composition Cu(hfac)2LBu�0.5C8H18. For

this compound the condition of fast exchange is met and a

single EPR line has to be simulated without a resolved

structure. The dependence of the linewidth on temperature

allowed us to obtain a good estimate for the lower limit of the

mixing rate constants that vary in a temperature range from

T=50 toT=220K as follows: kexAB4 (2� 1011)–(1� 1013) s�1,

kexAC4 (1� 1010)–(4� 1011) s�1, kexBC4 (1� 1010)–(1� 1012) s�1.

However, for the compound Cu(hfac)2LBu�0.5C8H10, we did

not succeed in obtaining a reasonable agreement between

experiment and model calculations at 122 and 244 GHz at

intermediate temperatures. We have found that, although

qualitatively all the trends are very similar for Cu(hfac)2LPr

and Cu(hfac)2LBu�0.5C8H10, the positions of the two observed

lines can be well simulated in the former case, but cannot in

the latter (exemplified in Fig. 4c for T = 130–160 K). In fact,

this is a fundamental disagreement, because, theoretically, the

positions of EPR lines of multiplets A and C are inter-

connected by the relations in eqn (1). Therefore the adjustment

of the position of one line should automatically result in the

correct position of the second line. The zero-field splitting

could possibly result in a shift of the line of multiplet C

(S = 3/2 state). However, the separation of two EPR lines

of a triad is virtually the same in the units of g-factor at 122

and 244 GHz, and the effective g-values corresponding to the

observed signals are very close in both bands. This excludes a

contribution from the zero-field splitting to the positions of the

lines of the spin triad. A closer consideration shows that the

assignment of the low-field line of the triad to the line of

multiplet C is even more problematic. On the one hand, the

observation of two lines that pass the intensity from one to

the other implies the slow mixing (exchange) limit, and thus

the low-field line should be observed at gC = (2gR + gCu)/3.

However, the observed g-factor was equal to 2.007, which

would lead to an unrealistic value of gCu E gR E 2.007, which

is unusual for copper(II) ions in general, and outside the range

of the g-tensor of copper for these compounds, whose powders

were studied by us previously (principal values of

gCu = [2.063, 2.078, 2.314] were found at T = 80 K).14,15

Thus, the low-field line of the triad cannot be assigned to the

multiplet C (nor B, for the same reason, nor their mixture).

The evolution of this line at higher temperatures of T4 160 K

resembles the evolution of the fast dynamically-averaged line

of the spin triad that, finally at kT c |J|, should coincide with

the EPR line of multiplet C. Indeed, a single line is observed

that shifts with the temperature towards higher g-values. The

simulations of low temperature and high temperature spectra

allowed us to set the limits for the values of the mixing

rates that vary in a temperature range from T = 70 and

T = 250 K as follows: kexAB = 2 � 1010–3 � 1011 s�1,

kexAC = 1 � 109–1 � 1010 s�1, kexBC = 1 � 109–4 � 1010 s�1,

respectively. The questions still to be answered are (i) what is

happening at intermediate temperatures when the two resolved

lines are clearly observed, and (ii) what difference between the

two compounds Cu(hfac)2LPr and Cu(hfac)2L

Bu�0.5C8H10

could be the reason for the agreement or disagreement of

the experiment with theory?

As was mentioned above, the single crystal EPR spectra of

the spin triads and their temperature dependence are affected

by the evolution of the g-tensor of the copper ion. At high

temperatures, the elongated axis of the octahedron (and thus gCu8 )

is oriented along the OL–Cu–OL bond, where OL is the

oxygen atom of the nitroxide. At low temperatures,

the elongated axis of the octahedron (and gCu8 ) is flipped to

the perpendicular plane along the Ohfac–Cu–Ohfac bond, where

Ohfac is the oxygen atom of hexafluoroacetylacetonate.

At some intermediate temperature, the octahedrons pass

the situation of equal bond lengths between l(OL–Cu)

and l(Ohfac–Cu), where l indicates bond length. Perhaps,

due to the Jahn–Teller nature of copper, this situation

corresponds to an instability point of the octahedron,

and two vibronically-coupled states with slightly different

bond lengths, l(OL–Cu) o l(Ohfac–Cu) and l(OL–Cu) 4l(Ohfac–Cu), may coexist. Because the exchange interaction

is a function of bond length, the positions of these two states

(effective g-factors) will be different. The temperature change

will affect the probability of the system being found in one of

the vibronically-coupled states, and thus will lead to the

passing of intensity from one EPR line to the other. Following

this hypothesis, we should assign the high-field EPR line

of the triad of Cu(hfac)2LBu�0.5C8H10 to the structural state

where l(OL–Cu) o l(Ohfac–Cu), and the low-field line to the

structural state where l(OL–Cu) 4 l(Ohfac–Cu). This dualism

is clearly observed only in a relatively narrow range of

temperatures (T = 120–160 K). Outside this region, the

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behavior of the EPR spectrum is consistent with the

expectations of our previously developed model. When

discussing the rates of the mixing process in this situation,

we should discriminate between the mixing between multiplets

A, B and C of each triad (kexMN), and the mixing between two

geometrically different structural states of each triad. The

former mixing should be fast enough to average the individual

lines of multiplets A, B and C. The latter mixing between two

geometrically different states, on the other hand, should be

slow at 122 and 244 GHz for two separate (not coalesced) lines

to be detected.

The questions arise: why should the same concept not be

used for the interpretation of the very similar behavior of

Cu(hfac)2LPr? For Cu(hfac)2L

Pr, are we really observing the

lines of the different multiplets of the triad in the slow

exchange limit, or, alternatively, could the two lines result

from two geometrically different vibronically-coupled states,

like in case of Cu(hfac)2LBu�0.5C8H10? At the moment we

cannot confidently distinguish between these two alternative

explanations; however, the following arguments support the

assignments made. In case of Cu(hfac)2LPr, the simpler model

(without any dualism around the instability point) allows for a

good agreement with the experiment and provides the correct

positions of the EPR lines. The temperature-induced shift of

the dynamically-averaged line at temperatures above the range

where two lines are observed (T = 180 - 260 K for

Cu(hfac)2LPr and T = 150 - 280 K for Cu(hfac)2L

Bu�0.5C8H10) is much larger in case of Cu(hfac)2L

Bu�0.5C8H10

(ca. 0.15 T; cf. 0.06 T for Cu(hfac)2LPr). This implies that the

low-field line of the triad in the case of Cu(hfac)2LBu�0.5C8H10

is more likely to be assigned to the fast dynamically averaged

state of the triad, rather than to the line of multiplet C in the

slow exchange regime. It also makes sense to compare the

structural data on bond lengths for all three investigated

compounds. Fig. 7 shows the dependences of l(OL–Cu) and

l(Ohfac–Cu) on temperature. For Cu(hfac)2LBu�0.5C8H18, the

instability point [l(OL–Cu) = l(Ohfac–Cu)] is located at the

lower temperature end of the spin transition (T E 120 K),

where the multiplet A is still predominately populated. For

Cu(hfac)2LPr, it is, on the other hand, located at the upper

temperature end (T E 205 K), where |J| o kT and all three

spin multiplets are populated. For our complicated case of

Cu(hfac)2LBu�0.5C8H10, the instability point is located closer

to the center of the spin transition (T E 175 K), i.e. the

pronounced redistribution of populations between spin

multiplets occurs more or less around the instability point.

We suppose that this might be the reason for the peculiar

dualism observed for Cu(hfac)2LBu�0.5C8H10. Apparently, the

following conditions must be fulfilled for the dualism to be

observed: (i) the temperature evolution of the bond lengths in

the octahedrons must allow for the slow passing through of

the instability point, and (ii) the temperature of the instability

point must be close to the center of the spin transition.

Discussion of the dynamic mixing mechanism

Finally, we would like to discuss some novel aspects of the

mixing process mechanism arising from our present and some

other recent studies. In our first report on the observation of

the dynamic mixing processes we proposed that the mixing

could be induced by a modulation of the exchange interaction

due to lattice vibrations.14 We showed that for large enough

values of J the rate of mixing due to this mechanism can be

fast enough to average the lines of individual multiplets at mw

frequencies up to 94 GHz. An estimated value of the mixing

rate constant, kexMN, of up to 1012 s�1 was obtained assuming

|J|B 100 cm�1. However, in our later work,16 we showed that

the exchange interaction in breathing crystals is strongly

temperature-dependent: the J value decreases by one order

of magnitude (as for Cu(hfac)2LBu�0.5C8H18) at high T. The

expected dependence, kexMN(J), due to the modulation

of the exchange interaction is very steep (approximately,

kexMN p J4 for kT c J), and thus kexMN(J) is expected to drop

down to B108 s�1 at high T. Hence, the modulation of the

exchange interaction does not provide for sufficiently high

mixing rates at high temperatures and we have to look for an

additional mechanism.

It is well known that many octahedral complexes of Cu(II)

exhibit a static and/or dynamic Jahn–Teller effect. The static

effect results in the distortion of regular octahedrons and

observation of elongated or compressed geometries. The

dynamic Jahn–Teller effect is a more complicated phenomenon

and usually shows interesting manifestations in single-crystal

EPR spectra. For example, if several orientations of the

elongated octahedral axis are allowed by the structure, the

low temperature EPR spectrum would show a superposition

of signals corresponding to each orientation. At higher

temperatures, however, the fast jumps (exchanges) between

these orientations average these signals and a coalesced line

with an average g-value is observed instead. The transition

temperature from a ‘‘static’’ to a ‘‘dynamic’’ spectrum

(often called the ‘‘anisotropic’’ - ‘‘isotropic’’ transition) is

determined by the magnitudes of potential barriers between

the local energy minima in each orientation. The structure of

Fig. 7 Temperature-dependent bond length changes for the three

studied compounds as observed by X-ray crystallography (ESIw and

ref. 15): Cu(hfac)2LPr (blue), Cu(hfac)2L

Bu�0.5C8H10 (red),

Cu(hfac)2LBu�0.5C8H18 (green). For each compound, Cu–Ohfac and

Cu–OL bond lengths, that ‘‘cross’’ with temperature, are shown. Note

that the Cu–OL bond lengths increase with temperature, whereas the

Cu–Ohfac bond lengths decrease with increasing temperature.

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breathing crystals (and thus the potential energy surface) are

temperature dependent, thus the dynamic Jahn–Teller effect

may not simply lead to a collapse of the ‘‘static’’ spectrum into

a single line at high temperatures, but may also lead

to additional peculiarities at intermediate temperatures.

Moreover, because we studied the spin triad and not a single

copper ion, the manifestations of the dynamic Jahn–Teller

effect in the EPR should also be different. In fact, they should

be very similar to the manifestations of mixing due to the

modulation of J, as discussed by us in ref. 14 and also in this

work. Both mechanisms—the modulation of J coupling and

the dynamic Jahn–Teller effect—may cause the mixing of spin

multiplets of a triad. In the first case it is a direct process

induced by magnetic interactions; in the second case it might

occur due to the relaxation-assisted redistribution of thermal

populations of multiplets following the sudden changes in J

coupling. It is noteworthy that our recent studies also witness

that the excited state, characterized by a different Jahn–Teller

axis, is not structurally forbidden and can be accessed and

trapped using light excitation at low temperatures.17

To estimate the magnitudes of the mixing rates due to the

dynamic Jahn–Teller effect, we can employ the literature data

for copper(II) ions. Of course, this approach is not fully correct

since we have an additional magnetic (exchange) interaction in

the spin triad, but, for a rough order-of-magnitude estimate, it

should be valid. In many known cases of copper(II) ions, the

transition from an anisotropic to an isotropic spectrum begins

at around 100 K, and then, as the temperature increases, the

spectrum is continuously transformed into the isotropic shape.

Ref. 26 reports the Q-band (34 GHz) spectra of

[(HC(Ph2PO)3)2Cu](ClO4)2�2H2O powder, which are not

influenced by the dynamic Jahn–Teller effect at T = 9.1 K,

but display the averaged components of the g-tensor at 292 K.

According to a theoretical extrapolation, the complete aver-

aging occurs at ca. 340 K. Ref. 27 reports an extensive

reinvestigation of complex Cu(im)6 in Zn(im)6Cl2�4H2O,

which exhibits a strong Jahn–Teller effect, which is static

below 100 K. At higher temperatures the dynamic Jahn–Teller

effect operates, leading to a transition to an isotropic

(liquid-like) spectrum; however, up to room temperature the

transformation remains incomplete. The detailed study of the

vibronic dynamics of Cu(H2O)6 complexes allowed the same

authors to estimate the rate of jumps between the two sites of

Cu2+ complexes, yielding values as high as 109 s�1 at room

temperature.28 Typically, for copper(II) ions doped in a

diamagnetic lattice, the energy gap between the ground state

and the first excited vibronic level corresponds to kT at a

temperature of a few hundred Kelvin (which determines that

the transition from the anisotropic to the isotropic spectrum

shape usually occurs at ca. 100 K). In the breathing crystals

studied by us, the bond lengths change gradually with

temperature, passing slowly through the ‘‘instability’’ point

of two equal bond lengths. Therefore, it is reasonable to expect

a significant lowering of the potential energy barrier at

temperatures around this point and significantly higher jump

rates than B109 s�1 (obtained for a barrier of B100 cm�1)

between the ground and low-lying excited states.

Thus, both the modulation of the exchange interaction

and the dynamic Jahn–Teller effect may contribute to the

mechanism of dynamic mixing processes in breathing crystals.

In fact, these two processes are coupled in an exchange-

coupled spin triad. Indeed, in the presence of exchange inter-

actions between copper and oxygen spins, the jumps between

situations with different Cu–O bond lengths are conjugated

with the changes in the exchange interaction. Therefore, the

dynamic Jahn–Teller jumps can be considered as some kind of

large-amplitude modulation of the exchange interaction, i.e.

our previously proposed mechanism.14 From the other point

of view, when discussing the jump rates due to the dynamic

Jahn–Teller effect in breathing crystals, we must account for

the perturbations induced by sudden changes of J and their

influence on the spin system. Thus, these two mechanisms are

interdependent. Of course, a detailed theoretical description of

the Jahn–Teller effect coupled to the exchange interaction in

spin triads has yet to be developed. Our experimental data

could then be analyzed on the basis of such a treatment, and

definite conclusions on the mechanism could be drawn.

Conclusions

In this work, we have studied the dynamic mixing processes in

strongly-coupled spin triads of breathing crystals, Cu(hfac)2LR,

using high-field multifrequency EPR at 34, 122, and 244 GHz.

We could, for the first time, observe the resolved structure of the

multiplets of the spin triad at 122 and 244 GHz by reaching the

limit of slow mixing rates compared to the frequency difference

between the EPR lines. The multifrequency EPR study and

simulations allowed us to estimate the characteristic rates of the

exchange processes: they typically range from 109 to 1012 s�1

and higher. Based on these values and the comparison

of simulation and experiment, we have proposed that the

contribution of the dynamic Jahn–Teller effect in breathing

crystals is important and should be studied theoretically in the

future. As one of the consequences of the present study, the

applicability of the previously developed method of measuring

the temperature dependence of the exchange interaction, J(T),

has been substantiated.16 The first high-frequency (122 and

244 GHz) EPR study of breathing crystals has confirmed our

previously developed theoretical model, but has also revealed

new characteristics to be addressed in the future.

Acknowledgements

We thank Dr Ksenia Yu. Maryunina (ITC Novosibirsk) for

providing us with the compounds. This work was supported

by the Alexander von Humboldt Foundation (M.F.), the Max

Planck Society; the RFBR (08-03-00326); the Council at the

RF president (MK-60.2008.3); the Grant for the Leading

Scientific Schools (NSh-3604.2008.3); the Russian Science

Support Foundation; and the Program of Presidium RAS

No. 18.13.

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