Quantum chemistry-based interpretations on the lowest triplet state of luminescent lanthanides complexes. Part 1. Relation between the triplet state energy of hydroxamate complexes and their luminescence properties

Article abstract of DOI:10.1039/b316246j

In this paper, we evaluate the potential use of theoretical calculations to obtain an energy scale of the lowest ligand-centred triplet excited state in luminescent terbium(m) complexes. In these complexes, non-radiative deactivation of the terbium emitti

Full text of DOI:10.1039/b316246j

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Quantum chemistry-based interpretations on the lowest triplet
state of luminescent lanthanides complexes. Part 1. Relation
between the triplet state energy of hydroxamate complexes and
their luminescence properties
Fabien Gutierrez,a Christine Tedeschi,b Laurent Maron,a Jean-Pierre Daudey,a Romuald
Poteau,*a Joëlle Azema,b Pierre Tisnèsb and Claude Picard*b
a Laboratoire de Physique Quantique (UMR5626 du CNRS), IRSAMC.
E-mail: romuald.poteau@irsamc.ups-tlse.fr
b Laboratoire de Synthèse et Physico-Chimie de Molécules d’Intérêt Biologique
(UMR5068 du CNRS) Université Paul Sabatier, 118 route de Narbonne,
31062 Toulouse Cedex, France. E-mail: picard@chimie.ups-tlse.fr
Received 12th December 2003, Accepted 17th February 2004
First published as an Advance Article on the web 23rd March 2004
In this paper, we evaluate the potential use of theoretical calculations to obtain an energy scale of the lowest
ligand-centred triplet excited state in luminescent terbium() complexes. In these complexes, non-radiative
deactivation of the terbium emitting state via a back-energy transfer process (T1
Tb(5D4)) is a common
quenching process. Consequently the prediction of the energy gap between these two excited states should be
useful for programming highly luminescent TbIII systems. We report on a strategy based upon experimental and
theoretical investigations of the excited state properties of a series of four simple aromatic hydroxamate ligands
coordinated to TbIII and GdIII ions. By using previously reported crystallographic data, the structural and energies
properties of these systems were investigated in the ground and first excited triplet states at the density functional
theory (DFT) level of calculations. Our theoretical results are consistent with a triplet excited state T1 which is
localised on one ligand only and whose the energy level is independent of the lanthanide ion nature (TbIII, GdIII).
A good agreement between the calculated adiabatic transition energies and experimental data derived from emission
spectra is obtained when a corrective term is considered. These satisfactory results are an indication that this type of
modelling can lead to discriminate in terms of the position of the lowest ligand triplet energy level the best antenna
among a family of chromophoric compounds. In addition this theoretical approach has provided indications that the
difference between the adiabatic transition energies of all the investigated complexes can be mainly explained by
metal–ligand electrostatic interactions. The influence of the number of antennae on the quantum yield and the
luminescence lifetime is discussed.
The lowest excited states of the lanthanide ions involve the
1
Introduction
reorganisation of the electrons within the 4f shell. It is now well
known that the 4f electrons can be considered as core electrons
when dealing with chemical bonding.7 The role of the ligands is
on one hand to collect the photons provided by the light source
in order to allow an energy transfer to the emitting levels of the
LnIII ion, and on the other to shield it against the solvent
in order to avoid non-radiative deactivation processes. In
addition, synergistic ligands can be used in order to completely
remove water from the first solvation shell of the lanthanide
ion.8,9 The intramolecular photochemical pathways which can
be followed are summarized in Fig. 1 in the form of a Jablonski
Trivalent lanthanide ions LnIII are able to form stable com-
plexes with a wide variety of organic ligands. These complexes,
which show interesting magnetic and spectroscopic properties,
are used in many fields. In so far as we are dealing in this paper
with the luminescent properties of lanthanide complexes, it
must be underlined that their long-lived luminescence lifetimes
and the “renaissance of fluorescence energy transfer”1 have
played a significant role in the interest devoted to these systems.
Although most of the systems designed for biomedical tests
essentially involve terbium and europium complexes, recent
developments of multiple fluoroimmunoassays require to con-
sider other lanthanide ions, such as samarium or ytterbium.2,3
Lanthanide complexes are considered as light converter
molecular devices (LCMDs), since they are able to absorb UV
light and to emit a radiation in the near-IR or visible domain.
However, although the involved emitting states are the
electronic levels of the lanthanide ion, free lanthanide ions in
solution do not behave as efficient LCMDs. As a matter of fact,
the absorption of lanthanide ions in water is very inefficient, the
molar absorption coefficient being measured with an order of
magnitude less than 10 dm3 molϪ1 cmϪ1. Thus, the excited states
of the ion must be more efficiently populated. This is achieved
by complexing the LnIII ion by ligands which act as photo-
sensitizers. It was initially reported by Weissman in 19424 and
has been more recently referred to an antenna effect.5 While the
basic mechanism for luminescence has often been reviewed,5,6
a brief recalling is necessary for understanding the purpose of
this work.
Fig. 1 Photochemical pathways.
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
T h i s j o u r n a l i s © T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 4
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diagram. The most probable channel corresponds to (i) the
absorption of UV light by the organic chromophore, (ii) an
intersystem crossing (ISC) from the excited singlet state to a
triplet state of the ligand, (iii) an intramolecular energy transfer
from the triplet state to the closest emitting level of the metal,
(iv) a radiative transition in the visible or near-IR domains,
which is called luminescence in order to be distinguished from
the emission of light of organic fluorophores. It should be
emphasized that transitions between the f states are formally
parity forbidden (Laporte rule), which results in the long
radiative lifetimes (up to the millisecond timescale) and line-
like emission bands which all together make the interest of
lanthanide complexes. Steps (ii), (iii) and (iv) are characterized
by ΦISC, ΦET and ΦLn quantum yields, respectively (see Fig. 1),
the total quantum yield being defined as Φ = ΦISCΦETΦLn.
At this point, some important remarks should be stressed.
From an experimental point of view, it is not clear whether the
energy transfer occurs from an excited singlet or triplet state.
However, Malta and co-workers have shown with a kinetic
model that in several cases the energy transfer channel singlet
complexes. On one hand, the Malta group has provided
theoretical insights, by combining various approaches: ligand
field theory for evaluating the 4f–4f intensities, semi-empirical
methods for the calculation of the ligand excited states, and a
kinetic model for the determination of intramolecular energy
transfer rates. On the other hand, very comprehensive studies
have been reported for excited state levels of An and Ln
complexes, but only in the case of metal-to-metal transitions.17
To our knowledge, this contribution is the first trying to
reproduce, for Ln complexes, the excited electronic spectra
involving LMCT phenomena.
We have considered, experimentally and theoretically, the
excited state properties of hydroxamate ligands coordinated to
TbIII and GdIII ions. Such [CO–N(R)O]Ϫ anionic ligands (LϪ)
behave as bidentate {O,O} ligands. 1-Hydroxypyridin-2-one
(Fig. 2(a)) forms 3 : 1 complexes with lanthanide ions which
have been structurally characterized by X-ray experiments.18,19
Moreover, this ligand acts as a better sensitizer for TbIII with
respect to EuIII. Since such hydroxamate ligands show interest-
ing potential as new types of building blocks for LCMD
devices, we report in this paper new experimental results
concerning three other ligands (Fig. 2(b)–(d)), combined with
theoretical investigations of the structural and energetic
properties of these systems in their ground and first excited
triplet states, S0 and T1. In the present theoretical contribution,
we have applied ab initio and DFT calculations in order to
obtain an energy scale of the lowest triplet state of the ligands,
and also to understand the nature of the lowest triplet state.
(ligand)
emitting level of LnIII is not important.10,11 The
triplet state thus plays a leading role in the intensity of the
luminescence, indirectly confirmed by experimental evidences.
An empirical rule, herafter called the energy-gap rule, states
that the total luminescence quantum yield Φ decreases due
to an energy back-transfer (ETB, see Fig. 1) when the energy
difference between the lowest triplet state of the ligand and the
emitting level of the metal is small. This is in particular
supported by the extensive study of Latva et al.12 which has
clearly shown in the case of terbium complexes a correlation
between the lowest triplet state energy level of the ligand (T1)
and TbIII luminescence quantum yield. The empirical rule states
that a high luminescence quantum yield is unlikely to be
observed if the energy gap between the T1 level of the ligand
and the excited 5D4 level of terbium is less than about
1850 cmϪ1. It should be noticed that in the case of europium
complexes, the correlation between the energy levels of the T1
state and the luminescence quantum yield is less convincing. As
a matter of fact, the presence of other 5Dj resonance levels
higher than the emitting 5D0 level is probably responsible for the
dispersion of the results. More recently, Arnaud and Georges13
have compared the luminescent properties of europium and
terbium complexes with the values reported by Latva et al.
They have shown again that the luminescence lifetimes are
closely related to the energy gap between the ligand triplet and
the resonance energy levels of the metal ion. Archer et al.14 also
found results consistent with the triplet state channel since they
obtained very low quantum yields for europium complexes with
a T1 level below the 5D0 level.
Although we have underlined the important role of the
lowest triplet state of the complexed ligand, other factors can
strongly influence the LnIII luminescence and even overcome the
triplet state factor. Quenching mechanisms induced by the
presence of solvent molecules in the first solvation sphere or by
ligand-to-metal charge transfer (LMCT) states are also known
to be of great importance.5 In this latter case, which is very
likely to occur for europium complexes, the triplet state is very
little populated since there is a competition with the LMCT
states.15,16
The interest generated by the wide range of applications of
luminescent lanthanide complexes explains that the design of
efficient molecular edifices is still an important research goal.
However, the photophysical processes involved in their optical
activity are rather complex and intrinsically tangled, and
chemical intuition may not be sufficient to design efficient
luminescent complexes. There is probably a need for giving a
theoretical point of view in order to understand the mech-
anisms involved, and to provide a “in silico” screening of
lanthanide compounds. To our knowledge, there is very little
theoretical work about the spectroscopic properties of such
Fig. 2 Hydroxamic acids (LH). The hydroxyl group is deprotonated in
hydroxamate ligands (LϪ): (a) 1-hydroxypyridin-2-one, (b) 1-hydroxy-
5,6-dimethylpyrazin-2-one, (c) 1-hydroxyquinolin-2-one, (d) 3-hydroxy-
2-methylquinazolin-4-one.
2
Experimental and computational details
2.1 Experimental
Materials and synthesis. Lanthanide salts were purchased
from Aldrich (GdCl3ؒ6H2O, TbCl3ؒ6H2O) or Strem Chemicals
(Tb2(CO3)3ؒxH2O) and were used without further purification.
1-Hydroxypyridin-2-one, IH. This was purchased from
Aldrich and was purified as previously described.19 Mp 148–
149 ЊC (lit.,20 149–150 ЊC). Found: C, 54.10; H, 4.40; N, 12.52.
C5H5NO2 requires C, 54.06; H, 4.54; N, 12.61%. IR ν/dmϪ1
:
1637 (C᎐O), UV (CH OH) λ/nm (ε/dm3 molϪ1 cmϪ1): 203, 232
᎐
3
(6500), 310 (4500).
1-Hydroxy-5,6-dimethylpyrazin-2-one, IIH. This compound
was prepared in four steps by using procedures described in the
literature.21 N-(tert-Butoxycarbonyl)glycine was coupled with
O-benzylhydroxylamine by using the mixed carbonic anhydride
method with isobutylchlorocarbonate. Deprotection of the Boc
group by trifluoroacetic acid in dichoromethane, followed by
condensation of the resulting salt with 2,3-butanedione gave
compound IIH, O-protected by a benzyl group. Debenzylation
by catalytic hydrogenation on 5% Pd/C and subsequent purifi-
cation on a silica gel column using CHCl3–MeOH–NH4OH
(6 : 3 : 1) as eluent afforded the pure product IIH. Mp 150–
152 ЊC (lit.,21 147–149 ЊC). Found: C, 51.25; H, 5.68; N, 19.76.
C6H8N2O2 requires C, 51.42; H, 5.75; N, 19.99%. IR ν/cmϪ1
3270 (OH), 1729 (C᎐O), 1578 (C᎐N). 1H NMR (CD3OD)
:
᎐
᎐
δ/ppm: 2.36 (s, 3H), 2.43 (s, 3H), 7.71 (s, 1H). UV (CH3OH)
λ/nm (ε/dm3 molϪ1 cmϪ1): 232 (16300), 339 (5300).
1-Hydroxyquinolin-2-one, IIIH. A procedure similar to that
reported by Raban et al.22 was used. To a solution of quinoline
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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N-oxide (1.011 g, 6.97 mmol) in benzene (60 mL) was added
calcium carbonate (0.6 g, 6 mmol) and lead tetraacetate (5 g,
11.28 mmol). The mixture was heated at reflux for 3 h. The
reaction was allowed to cool to room temperature and the
solid was collected and washed with chloroform (50 mL). The
combined filtrates were concentrated under reduced pressure.
The residue was dissolved in 10% hydrochloric acid (30 mL).
The aqueous solution was heated at reflux for 1 h, cooled and
extracted with diethyl ether (2 × 50 mL). The organic phase was
concentrated in vacuo and the solid residue was sublimed
(100 ЊC/26 mbar). Yield 35%. Mp 190–191 ЊC (lit.,22 186–
189 ЊC). Found: C, 66.53; H, 4.32; N, 8.59. C9H7NO2 requires
Terbium complexes. The TbI3ؒ3H2O complex was isolated as
previously described.19 Found: C, 33.26; H, 3.03; N, 7.66.
C15H18N3O9Tb requires C, 33.16; H, 3.34; N, 7.73%. IR ν/cmϪ1
:
1621 (C᎐O).
᎐
The TbIII3ؒ2H2O complex was isolated according to the
following procedure: to solution of Tb2(CO3)3ؒxH2O
a
(25.6 mg) in ethanol (1 mL) was added ligand III (50 mg, 0.31
mmol). The mixture was stirred for 2 h and filtered. The solid
residue was washed with three portions of ethanol (3 × 2 mL),
and then several times with methanol. The combined methanol
extracts were evaporated. The desired product was purified by
recrystallisation from water. Found: C, 47.98; H, 3.38; N, 6.22.
C, 67.08; H, 4.38; N, 8.69%. IR ν/cmϪ1: 2504 (OH), 1636 (C᎐O),
C27H22N3O8Tb requires C, 48.02; H, 3.28; N, 6.22%. IR ν/cmϪ1
:
᎐
1
1581 and 1558 (C᎐C and C᎐N). H NMR (CD OD): δ/ppm
1613 (C᎐O).
᎐
᎐
᎐
3
6.74 (d, J = 9.5 Hz, 1H), 7.28–7.36 (m, 1H), 7.71–7.82 (m, 3H),
7.94 (d, J = 9.5 Hz, 1H). UV (CH3OH) λ/nm (ε/dm3 molϪ1
cmϪ1): 231 (38400), 271 (5200), 331 (5000).
Preparation ‘in situ’ of the terbium complexes. To a solution
of a sample of each bidentate ligands IH–IVH in methanol was
added an equimolar amount of NaOH. Subsequently, a
solution of TbCl3ؒ6H2O (0.33 equivalent) in methanol was
added and the reaction mixture was allowed to stir for 3 h at
room temperature. The concentrations used for photophysical
3-Hydroxy-2-methylquinazolin-4-one, IVH. This compound
was prepared in three steps starting from isatoic anhydride. The
reaction of O-benzylhydroxylamine with isatoic anhydride in
aqueous solution gave the corresponding hydroxamate
(2-amino-N-benzyloxybenzamide). Cyclisation with acetic
anhydride gave compound IVH, O-protected by a benzyl group.
Debenzylation was then performed by catalytic hydrogenation.
2-Amino-N-benzyloxybenzamide. To a solution of O-benzyl-
hydroxylamine hydrochloride (2.160 g, 12.58 mmol) in water
(60 ml) was slowly added 0.935 g of K2CO3. This mixture was
stirred for 0.5 h and then was added isatoic anhydride (2 g, 12.3
mmol). The reaction mixture was kept at room temperature
under stirring for 24 h and was then filtered. The solid was dried
under vacuum and then recrystallized from CH2Cl2. Yield 95%.
Mp 104–105 ЊC (lit.,23 104–106 ЊC). Found: C, 68.84; H, 5.71;
N, 11.41. C14H14N2O2 requires C, 69.41; H, 5.82; N, 11.56%. 1H
NMR (CDCl3) δ/ppm: 5.00 (s, 2H), 5.36 (s, 2H), 6.57 (t, J = 7.5
Hz, 1H), 6.66 (d, J = 7.5 Hz, 1H), 7.13–7.26 (m, 2H), 7.36–7.47
(m, 5H), 8.55 (s, 1H). 13C NMR (CDCl3) δ/ppm: 78.4, 113.0,
116.6, 117.3, 127.1, 128.3, 128.4, 128.7, 133.0, 135.5, 148.8,
168.4.
measurements were between 5 × 10Ϫ6 and 1 × 10Ϫ4 mol dmϪ3
.
TbI3: UV (CH3OH) λ/nm (ε/dm3 molϪ1 cmϪ1): 221, 310
(12000). Luminescence (CH3OH, 295 K, λexc = 310 nm) : λ/nm
491 (relative intensity, 26.5), 548 (100), 588 (14.9), 622 (7.6).
TbII3: UV (CH3OH) λ/nm (ε/dm3 molϪ1 cmϪ1): 227, 333
(12600). Luminescence (CH3OH, 295 K, λexc = 330 nm) : λ/nm
490 (relative intensity, 30.2), 547 (100), 588 (17.5), 622 (10.4).
TbIII3: UV (CH3OH) λ/nm (ε/dm3 molϪ1 cmϪ1): 245
(107100), 347 (10800). Luminescence (CH3OH, 295 K, λexc
=
345 nm) : λ/nm 491 (relative intensity, 40.6), 547 (100), 588
(25.4), 619 (23.8).
TbIV3: UV (CH3OH) λ/nm (ε/dm3 molϪ1 cmϪ1): 220, 255
(70200), 310 (16200). Luminescence (CH3OH, 295 K, λexc = 310
nm): λ/nm 489 (relative intensity, 32.0), 546 (100), 586 (22.3),
620 (21.5).
The gadolinium complexes were prepared ‘in situ’ according
to the procedure described for terbium complexes.
3-Benzyloxy-2-methylquinazolin-4-one.
A
mixture of 2-
Instruments and measurements. Melting points were deter-
1
amino-N-benzyloxybenzamide (2 g, 8.25 mmol) and acetic
anhydride (9.12 mL, 8.3 mmol) was heated under reflux for 2 h.
After cooling, water (3.9 mL) and activated carbon were added
and the mixture was boiled for a further 0.5 h, followed by
filtration through a Celite pad. The Celite pad was washed with
methanol and the combined filtrates were evaporated under
reduced pressure. The residue was subjected to column chrom-
atography on silica gel (CH2Cl2–MeOH, 90 : 10) to give the
desired product. Yield 39%. Mp 111–112 ЊC (lit.,23 110–112 ЊC).
Found: C, 71.93; H, 5.35; N, 10.36. C16H14N2O2 requires C,
mined on a Kofler apparatus. H and 13C magnetic resonance
spectra were recorded on a Bruker 250 spectrometer. IR spectra
were recorded on a Perkin-Elmer spectrometer in potassium
bromide pellets. Elemental analyses were carried out by the
“Service Commun de Microanalyse élémentaire UPS-INP” in
Toulouse.
Electronic spectra in the UV-visible range were recorded at
295 K with a Perkin-Elmer Lambda 17 spectrophotometer
using quartz cells of various path lengths. Time-resolved lumin-
escence spectra and life-times were obtained using a LS-50B
Perkin-Elmer spectrofluorimeter equipped with a Hamamatsu
R928 photomultiplier tube and the low-temperature accessory
No L2250136. For excitation a xenon flash lamp, pulsed at line
frequency (60 Hz) was used. The most highly resolved emission
spectra were obtained using excitation and emission slit widths
of 2.5 nm, following pulsed excitation at the lowest energy
ligand-centered absorption band. Emission spectra were cor-
rected from the wavelength dependence of the photomultiplier
tube, according to the instrument guidebook. Lifetimes τ
(uncertainty ≤5%) are the average values from at least five
separate measurements which were made by monitoring the
decay at 545 nm, following pulsed excitation. The emission
decay curves were fitted by an equation of the form I(t) =
I(0)exp(Ϫt/τ) using a curve-fitting program. Luminescence
quantum yields (uncertainty 15%) were determined by the
method described by Haas and Stein,24 using as standard
quinine sulfate in 1 N sulfuric acid (Φ = 0.54625) and corrected
for the refractive index of the solvent. The absorbance of the
solutions was 0.1 at the excitation wavelength. The lifetimes and
luminescence spectra were recorded in aerated methanol
previously dried over molecular sieves (3Å) and by using freshly
1
72.17; H, 5.30; N, 10.52%. H NMR (CDCl3) δ/ppm: 2.48 (s,
3H), 5.29 (s, 2H), 7.40–7.53 (m, 6H), 7.63 (d, J = 7.5 Hz, 1H),
7.74 (td, J = 7.5, 1.5 Hz, 1H), 8.30 (dd, J = 7.5, 1.5 Hz, 1H). 13
C
NMR (CDCl3) δ/ppm: 20.4, 78.3, 122.6, 126.5, 126.7, 127.1,
128.9, 129.6, 130.0, 133.4, 134.4, 146.5, 153.9, 158.2.
Compound IVH. 10% Pd/C (60 mg) suspended in MeOH
(10 mL) was prehydrogenated with H2 for 0.5 h. To the suspen-
sion was then added a solution of previous O-benzyl protected
compound (0.429 g, 1.61 mmol) in MeOH (15 mL). After
hydrogenation at room temperature with H2 under atmospheric
pressure for 0.25 h, the mixture was filtered through a Celite
pad. The filtrate was evaporated to give a solid residue which
was purified by recrystallisation from a MeOH–water mixture.
Yield 16%. Mp 218–219 ЊC. Found: C, 60.88; H, 4.49; N, 15.78.
C9H8N2O2 requires C, 61.36; H, 4.58; N, 15.90%. IR ν/cmϪ1
:
2561 (OH), 1684 (C᎐O), 1610 and 1564 (C᎐C and C᎐N).
᎐
᎐
᎐
1H NMR (DMSO) δ/ppm: 2.51 (s, 3H), 7.49 (t, J = 7.7 Hz, 1H),
7.61 (d, J = 8.1 Hz, 1H), 7.79 (t, J = 8.1 Hz, 1H), 8.11 (d, J = 7.7
Hz, 1H). 13C NMR (DMSO) δ/ppm: 20.2, 121.3, 125.7, 125.9,
126.6, 133.8, 146.1, 154.2, 157.7. UV (CH3OH) λ/nm (ε/dm3
molϪ1 cmϪ1): 221, 314 (24100).
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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Table 1 Absorption and luminescence properties of the TbIII com-
plexes derived from ligands I–IV in aerated methanol solution at 295 K;
τH and τD are the luminescent lifetimes in CH3OH and CH3OD,
respectively
prepared samples. The phosphorescence spectra of the ligands
and of their Gd() complexes were recorded in an ethanol–
methanol mixture (4 : 1) at 77 K (liquid N2 cooling).
L
λmax/nm
ε/dm3 molϪ1 cmϪ1
τH/ms
τD/ms
Φ
2.2 Computational
All calculations of the molecules in their ground state (S0) and
their three lowest excited triplet states (T i, i = 1, 2, 3) were
carried out with Gaussian 98.26 As usually done in quantum
chemistry calculations, the methyl groups of ligands II and IV
were replaced by hydrogen atoms. These ligands will be here-
after denoted IIЈ and IVЈ. All calculations were done in the gas
phase. The effective core potentials (ECPs) and their associated
basis set developed by the Stuttgart group were used in the case
of terbium, gadolinium and sodium atoms.27,28 In LnL3 com-
pounds, the electronic configuration of the lanthanide() ion is
[Kr]4d105s25p64fnϪ1, and it is now well known that 4f and 4d
electrons do not play any role in the coordination of the ion.7,29
The goal of this work is not to calculate the electronic states of
the metal ion (M), but to get the lowest excited states of the
complex. These states can either be strictly localized on the
ligands (L) or can be ligand-to-metal charge transfer type ones
(LMCT states), involving back-donation towards 5d atomic
orbitals. As a consequence, we used large core ECPs with 11
valence electrons, specifically designed for rare earth atoms with
an oxidation number ϩ3 (LnIII). All the gaussian basis sets are
of double-ζ plus polarization quality. All structures were
optimized in their lowest triplet state (T1) and their ground state
(S0) without symmetry constraints, in order to avoid explor-
ations of potential energy surfaces driven by such constraints.
We systematically explored the potential energy surfaces in the
framework of density functional theory (DFT) methods, using
the B3LYP functional. The lowest triplet state has essentially
been investigated with unrestricted DFT methods. Calculating
energy gaps between the optimized unrestricted DFT triplet
and restricted DFT singlet geometries is the so-called ∆SCF
procedure. However, preliminary geometry optimizations of
some molecules in T1 were also performed by means of the ab
initio CASSCF method,30 in order to check the validity of
single-configuration approaches. Spin contamination is not so
I
312
333
347
310
12000
12600
10800
16200
0.83
0.92
0.93
0.80
1.06
1.16
1.25
0.96
0.20
II
0.001
0.001
0.023
III
IV
complexes, calculation of zero-point-energies were not system-
atically feasible and experimental ν00 wavenumbers will be
compared to theoretical adiabatic wavenumbers νadia unless
otherwise mentioned (Fig. 3).
Fig. 3 Schematic definition of the computed transitions and the
corresponding wavelengths; νadia is calculated as E(T1,GT ) Ϫ E(S0,GS ),
whereas ∆E and T e are calculated as E(S0,GT ) Ϫ E(S0,GS ) and
E(T1,GT ) Ϫ E(S0,GT ), respectively (in the framework of the same
theoretical method, νadia and T e ϩ ∆E are equal).
1
0
1
0
1
1
The molecules and molecular orbitals sketches were drawn
with the MOLEKEL program.37 Finally, in so far as the R
groups defining the four [CO–N(R)OH] acids considered in this
work are different, a comparison between their structures do
not provide relevant information, and we shall only comment
the geometrical parameters and electronic charges of the four
atoms which form a ring with the metal ion in the complexes
(Fig. 4).
severe with unrestricted DFT calculations as in unrestricted
2
ˆ
Hartree–Fock methods, the eigenvalue of S for T1 lying
between 2.00 and 2.06. However, Kohn–Sham molecular
orbitals (MOs) obtained at an unrestricted DFT level of calcu-
lation do not allow a clear analysis of the nature of the triplet
state. Time-dependent DFT (TDDFT) calculations were also
performed to provide an overview of the nature of the T1 state.
TDDFT is currently undergoing a growing interest. Even if
according to some authors this method experiences some
difficulties for the description of Rydberg and charge transfer
states,31 it appears very successful for evaluating vertical
electronic transitions,32–34 and even charge transfer states in
metal complexes.35
Fig. 4 Definition of the labels of the atoms.
3
Experimental results
Finding the optimal geometry of lanthanide complexes is not
a trivial task. However, it will be shown hereafter in section 3
that the four terbium–hydroxamate complexes are very likely
isostructural. We consequently have used the crystallographic
data previously published for terbium18 and gadolinium19
complexes with 1-oxy-2-pyridinonate (ligand IϪ) as a starting
point for geometry optimizations. These data, together with the
Z-matrix editor functionality of the MOLDEN program,36
were also helpful for constructing the geometries of the three
other ligands. For the purpose of comparison with phos-
phorescence spectra, we have also checked in some cases that
relaxing in S0 the optimal structure of the molecule found for T1
leads to the optimal geometry deduced from the terbium and
gadolinium X-ray structures. In other words, in the case of such
simple ligands, when the molecule goes back from T1 to the
ground state it is not trapped into a local minimum that differs
from the optimal geometry in S0. Due to the size of the largest
We first isolated the complexes TbI3 and TbIII3 (See Experi-
mental section) but soon noticed that their emitting properties
in solution are identical with those of mixtures of the ligands
and TbCl3ؒ6H2O in the presence of sodium hydroxide (3 : 1 : 3
equivalents, respectively). The mixtures give absorption and
excitation spectra identical with those of the isolated com-
plexes, we thus employed the latter method for this photo-
physical study. All the photophysical data collected in Table 1
were obtained by using methanol solutions. The absorption
spectra of these complexes are characterized by intense bands
in the UV region. Deprotonation of the ligand and its sub-
sequent bridging to the metal ion has a marked effect on the
absorption profile. For example, free ligand IIIH in methanol
solution exhibits three distinct absorption bands with maxima
around 231, 271 and 331 nm, while the spectrum of the corre-
sponding complex is composed of two absorption bands at 245
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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and 347 nm. On the other hand, it can be noticed that the molar
absorption coefficient at the maximum of the ligand-centered
(LC) band (310 nm < λ < 347 nm) is higher than 104 dm3 molϪ1
cmϪ1 for all these complexes, a favourable condition for an
efficient antenna effect. The Beer-Lambert law is obeyed in the
yield (20%). The TbIII complexes of ligands II, III or IV gave
less satisfactory results, their quantum yields being more than
one or two orders of magnitude lower than that of TbI3.
As mentioned above, numerous factors influence the overall
luminescence quantum yield in photosensitized lanthanide
used range of concentrations (5 × 10Ϫ6 to 1 × 10Ϫ4 mol dmϪ3
)
complexes, e.g. the efficiency of S1
T1 energy conversion, the
which confirms the stability of the complexed species in meth-
anol. Photoexcitation of the complexes from the lowest energy
LC absorption band gives rise to the typical TbIII luminescence
with an intense emission band around 545 nm, and three
weaker bands around 490, 590 and 620 nm. These bands
correspond to the transitions from the 5D4 state to the 7F6, 7F5,
7F4 and 7F3 levels, respectively. The emission spectra and relative
peak heights of terbium emission with all chelates are essen-
tially identical, in agreement with the fact that the terbium
emission bands are not very sensitive to changes outside the
first coordination sphere.38 On the other hand, although these
complexes have similar molar extinction coefficients at λmax, the
total luminescence intensity is chelate dependent. Excitation
spectra of TbIII emission are dominated by broad bands
corresponding to the absorptions of the aromatic hydroxamate
moieties. No transition corresponding to the proper TbIII
absorption levels, especially those located at 485 nm and
between 340 and 380 nm, is observable in the excitation spectra.
These results unequivocally show that an energy transfer
process from the hydroxamate antenna to the metal ion is the
only photophysical pathway leading to observable lumines-
cence in these samples. Representative excitation and emission
spectra are shown in Fig. 5.
quenching mechanism involving ligand-to-LnIII charge transfer,
the energy of the lowest ligand centered triplet state level, the
donor–acceptor distance, and the presence of inner-sphere co-
ordinated hydroxylated molecules. In our opinion, the two lat-
ter factors do not provide an explanation of the differences in
the quantum yield values since the shielding of the metal from
solvent molecules in the four systems is similar, the binding
functions are equivalent, and the geometrical structures of the
complexes are assumed to be analogous. Nor can the experi-
mental results be interpreted by taking into account the
involvement of low lying charge-transfer (LMCT) states, which
may efficiently deactivate the excited states of the ligand to
the ground state. This deactivation pathway, often involved in
the case of europium() complexes,16 is not relevant for
terbium() complexes, as the TbIII ion is very hard to reduce
(Ered = Ϫ3.5 V for the free aqua ion).41 On the contrary, non-
radiative deactivation of the metal emitting state via population
of the lowest ligand triplet excited state is a quenching
mechanism which is commonly observed for TbIII complexes.5
Actually, when taking the heavy atom effect into account,
complexes of LaIII, GdIII, YIII or LuIII have been used in various
papers to obtain the triplet-state energies.14,42–46 These metals
have their lowest excited states located at higher energies than
the emitting states of aromatic ligands. Therefore, ligand-to-
metal energy transfer cannot occur and the consequent metal-
centered emission cannot be observed as happens, in contrast,
for TbIII and EuIII complexes. However, gadolinium() is the
most popular metal used in these studies because GdIII and
TbIII (EuIII) ions are equal in charge, paramagnetic and very
similar in size (eight-coordinated radius: 1.053 Å for GdIII, and
1.040 Å for TbIII 47). Consequently, it is widely accepted that
these three metal ions induce analogous structures and similar
effect on the ligands. So, in order to investigate energy matching
between the triplet state of the ligand and the resonance level of
TbIII, we recorded the phosphorescence spectra of the free
ligands I–IV and their GdIII complexes at 77 K in an EtOH–
MeOH (4 : 1) glass. Time-resolved luminescence measurements
at 77 K showed phosphorescence emission spectra containing
one broad band with its maximum ranging from 408 to 550 nm.
Fig. 6 reports the results obtained for ligand IIIH and the corre-
sponding gadolinium complex. Except for IIH, all the ligands
show a red-shift of the LC phosphorescence maximum upon
complexation of GdIII, as expected because of the influence of
the paramagnetic ion.48 Particularly worth noting is the shift of
about 90 nm (3450 cmϪ1) observed for the III system. From the
Fig.
5
Luminescence emission spectrum showing 5D4
transitions of TbII3 in methanol at 295 K. The inset in this figure is the
7Fj
corresponding excitation spectrum (λem = 545 nm).
Luminescence decays of the complexes were investigated by
direct excitation of the ligand and by recording the intensity of
5
the emitted light of the D4
7F5 transition. In all cases, the
decay profile fits a single-exponential law, as expected for one
discrete [TbL3] solution species. In CH3OH solution at 295 K,
these luminescence lifetimes are in the 0.83–0.93 ms range
(Table 1). The lifetimes are higher in CH3OD, which confirms
the role played by the vibronic deactivation mechanism involv-
ing the O–H oscillators.39 The use of the empirical equation
proposed by Horrocks and Sudnick40 and the experimental life-
times in CH3OH and CH3OD solutions revealed the average
number of methanol molecules (n) in the first coordination
sphere of the metal ion to be n = 2 ( 0.5) for the four complexes.
This is in agreement with the presence of two coordinated
solvent molecules and an eight-coordinated structure as we
observed in the single-crystal X-ray structure of [TbI3(H2O)2]ؒ
H2O19 and suggests that these four complexes are isostructural.
As one can see from Table 1, while the lifetimes are rather simi-
lar for these complexes, the quantum yields are very different.
The TbI3 complex is characterized by a quite high quantum
Fig. 6 Normalized time-resolved phosphorescence spectra in an
EtOH–MeOH (4 : 1) rigid matrix at 77 K of IIIH (plain line) and Gd
complex (dashed line).
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Table 2 Phosphorescence properties of ligands IH–IVH and their gadolinium complexes. The emission maxima (λmax in nm) are reported for these
structures in an EtOH–MeOH (4 : 1) rigid matrix at 77 K. In parentheses are reported the energy range (in cmϪ1) corresponding to the left edge of the
spectrum and λmax
L
I
II
III
IV
LH
465
463
463a
(21650–23800)
550
408b
(24500–26650)
436
(21500–25000)
475
(21600–26300)
463
LGd
(21050–25250)
(21600–26300)
(18200–20800)
(22950–25650)
a ν00 = 23000 cmϪ1
.
b ν00 = 26000 cmϪ1
.
Table 3 Comparison of X-ray data49 and theoretical geometry for the
(IH)2 dimer (bond lengths in Å and angles in Њ)
first peak of the structured phosphorescence profiles of IIIH
and IVH, one can estimate the zero-zero energy of the lowest
ligand centered triplet state, which turns out to be 23000 and
26000 cmϪ1, respectively. Unfortunately, due to the lack of
vibrationally structured phosphorescence emission bands, it
was not possible to determine the ν00 of the triplet level in IH,
IIH and all gadolinium complexes. However, if we inspect the
emission domain ranging from the left edge to the maximum of
the phosphorescence spectra (i.e. an energy range in which lies
the zero–zero energy of the lowest LC triplet state), several key
points can be stressed. These values (Table 2) show that the
triplet state of the complex formed with III lies very close or
slightly below the TbIII 5D4 emitting state (E = 20400 cmϪ1). The
extremely poor luminescence of TbIII3 may be, unambiguously
attributed to a very efficient back-energy transfer process (T1
IH
X-Ray
B3LYP
H–ON
ON–N
OC–C
C–N
1.00
1.018
1.374
1.249
1.401
1.384
1.252
1.380
N–ON–H
C–N–ON
N–C–OC
103
105.2
118.4
121.4
Ϫ67.2
117.7
121.0
Ϫ70
C–N–ON–H
The deprotonated ligand IϪ is complexed as a bidentate
{O,O} donor with terbium. Beyond the purpose of comparing
theoretical and experimental geometries, this case also reveals
that, on the theoretical side of this work, LDA calculations
predict artefactual geometries. The crystal structure which has
been previously reported,18 does not present any particular
symmetry (Fig. 8). However, one can roughly identify a
symmetry plane which contains one of the ligands (L1), the two
other ligands (L2 and L3) being orthogonal to this plane (see
Table 4, θ(L1L2) and θ(L1L3) values).
Tb(5D4)). For the IV system, a ∆ET M (3E00 Ϫ E(5D4)) gap
1
higher than 2500 cmϪ1 may be expected (2500 cmϪ1 < ∆ET M
<
1
5200 cmϪ1). This energy gap is above the threshold value of
1850 cm
,
Ϫ1 12 thus the energy back transfer seems to be of minor
Tb(5D4)
importance in the TbIV3 complex. Since the T1
transfer seems complete, the low quantum yield of TbIV3, by
comparison with that of TbI3, may be probably traced back to a
less efficient S1
T1 energy conversion in the former complex.
As far as the complexes with ligands I and II are concerned, no
definitive conclusion can be drawn from these experimental
data since their ∆ET M gap may lie between 650 and 5900 cmϪ1
.
1
4
Theoretical results
4.1 Geometries
Comparison with crystallographic data. Firstly, we shall focus
on the hydroxamic acid IH. Two tautomeric forms are possible:
the hydroxypyridine N-oxide and the N-hydroxypyridinone
(Fig. 7(a)). Ballesteros et al. have shown that the second tauto-
mer exists in the crystal phase and in solution,49 and have pub-
lished X-ray data for a compound which corresponds to two N-
hydroxypyridinone arranged as a cyclic dimer. We have speci-
fically performed DFT-B3LYP calculations on a dimer for the
purpose of comparison with experimental data. The results,
given in Table 3, show a good agreement between theory and
experiments. Following the suggestion of Ballesteros et al., we
assume that in solution the N-hydroxypyridinone compound
exists as a monomer.
Fig. 8 X-Ray structure for TbI3 in its ground state S0.18
The terbium ion is surrounded by eight oxygen atoms, two of
them belonging to two water molecules in the first coordination
sphere.
A third water molecule, found in the second
coordination sphere of TbIII, is hydrogen-bonded to L2. This
molecule has not been further considered in the theoretical
calculations, since we checked that although its presence does
not significantly alter the geometrical parameters, the adiabatic
transition energy T1
S0 is very much dependent on it. Indeed,
the adiabatic transition energies computed for TbL3(H2O)3 were
not in agreement with the available experimental data, unlike
the results obtained for TbL3(H2O)2, as we shall see in the next
section. The geometrical parameters given in Table 4 indicate
that there is a good overall agreement between theory and
experiment, especially at the B3LYP level of calculation, since
the difference between X-ray and theory is in general within the
experimental error, i.e. 0.04 Å.
The TbI3 complex was also considered. The removal of the
water molecules yields a structure which is almost C3v. While
the Tb–O distances may be significantly different with respect
to the distances calculated for TbI3(H2O)3, no significant differ-
Fig. 7 Optimal geometries of the 1-hydroxypyridin-2-one (IH) in its
planar S0 (a) and T1 (b) state.
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Table 4 Comparison of X-ray data and DFT geometry for TbI3 (bond
Table 5 Comparison of X-ray data19 and theoretical geometry for the
gadolinium complex (bond lengths in Å and angles in Њ). The values for
the four ligands were averaged; θ(LiLj) is the angle between two ligands
Li and Lj; αOGdO is the average bite angle of the ligand
lengths in Å and angles in Њ; Tb–XY refers to a distance between the Tb
i
atom and the XY atom which belongs to ligand Li). Except for TbI3,
ligands L2 and L3 are approximately in the same plane, while ligand L1
is orthogonal to this plane (see Fig. 8). Labels w1 and w2 refer to the two
water molecules within the first coordination sphere of the metal ion;
θ(LiLj) is the angle between two ligands Li and Lj; αOTbO is the average
bite angle of the ligands
GdI4Na
X-Ray
B3LYP
TbI3(H2O)2
Gd–ON
Gd–OC
ON–N
OC–C
C–N
2.384
2.383
1.330
1.300
1.382
2.437
2.514
1.332
1.273
1.395
TbI3
X-Raya
LDA
B3LYP
B3LYP
Tb–ON
Tb–OC
2.366
2.370
2.366
2.376
2.411
2.315
1.353
1.329
1.316
1.268
1.288
1.313
1.374
1.366
1.361
2.434
2.350
2.291
2.361
2.398
2.334
2.382
2.370
1.319
1.319
1.321
1.279
1.283
1.274
1.386
1.385
1.391
2.486
2.431
2.322
2.413
2.411
2.377
2.426
2.428
1.339
1.343
1.342
1.274
1.271
1.275
1.392
1.393
1.392
2.610
2.518
2.322
2.340
2.322
2.340
2.322
2.340
1.339
1.339
1.339
1.276
1.276
1.276
1.393
1.393
1.393
–
1
2
3
1
Tb–ON
Tb–OC
θ(L1L2)
θ(L1L3)
θ(L4L2)
θ(L4L3)
αOGdO
105.0
101.6
78.4
85.9
66.0
90.1
112.5
103.2
80.4
2
Tb–ON
Tb–OC
ON –N13
63.6
1
ON –N2
2
ON –N3
3
OC –C1
1
OC –C2
2
OC –C3
3
C1–N1
C2–N2
C3–N3
Tb–Ow1
Tb–Ow2
–
θ(L1L2)
θ(L1L3)
αOTbO
91.9
81.9
65.6
27.7
133.0
66.7
86.3
89.3
67.1
119.9
120.1
67.4
a X-Ray data report the presence of a third water molecule in the second
coordination sphere of the terbium ion.18
ences are observed for the ON–N, OC–C and C–N bond lengths.
The differences can be justified by the existence of hydrogen
bonds observed in our calculations between the hydrogen atoms
of the water molecules and the oxygen atoms of the ligands
(w1 with L1 and L2 and w2 with L2 and L3). When only distances
are considered, LDA performs as well as B3LYP. However, it
can be seen in Table 4 that LDA dramatically fails to suitably
describe the π interactions between the rings. As a matter of
fact, geometry optimization yields an artifactual π-stacking
of two ligands, L1 and L2, which are not orthogonal, unlike the
X-ray and B3LYP structures. This attractive behavior was also
observed in the case of the geometry optimization of the com-
plex in its triplet state. Although LDA is usually known to
provide accurate geometries, these statements cast suspicion on
the ability of LDA to give reasonable geometries and energies
for such complexes. From now on, only the B3LYP functional
will be used in the framework of DFT calculations. Moreover,
since one purpose of this work is to give theoretical insights
into the triplet state, we have considered the terbium complex
without water molecules in the first and second solvation shells.
As a matter of fact, the interactions of water molecules with the
ligands by hydrogen bonding make the latter non-equivalent,
which may lead to biased conclusions on the nature of the
Fig. 9 X-Ray structure for GdI4Na in its ground state S0, after ref. 19.
with the experimental data. Two neighbouring ligands are
approximately orthogonal. The largest discrepancy is observed
for the B3LYP Gd–OC bond length, too long by 0.126 Å with
respect to the experimental value. In so far as the theoretical
results obtained for the terbium complex are within the experi-
mental error, a justification for this discrepancy probably lies
in the reduction of the [Na2Gd2I8(H2O)3]ؒ6H2O unit to the
GdI4Na subunit. In particular, since water molecules interact
with the ligands, their absence in the calculation is partly
responsible for this disagreement. The origin of this apparent
lack of accuracy of theory may also depend on the fact that
crystal packing forces shrink bond lengths. However, we assume
that there is no prejudicial consequences on the evaluation of
the triplet state energy.
Hydroxamic acids LH. The geometries obtained at the
DFT-B3LYP level of calculation show that the four hydroxamic
acids are planar in their ground state S0. Selected geometrical
parameters and Mulliken atomic charges are given in Table 6.
The H–ON bond length does not depend much on the ligand,
the maximum difference, observed between protonated ligands
IH and IVЈH, is 0.009 Å. The largest difference between the
acids concerns the C–N bond length, which varies from 1.411 to
1.392 Å between molecules IH and IIIH.
When dealing with the geometries of the ligands in their
lowest triplet state T1, the most striking feature is the pyr-
amidalization of the nitrogen atom in molecules IH and IIЈH,
while IIIH and IVЈH remain planar. As a matter of fact, for
L = I (see Fig. 7(b)) and L = IIЈ, the ON and H atoms are no
longer in the plane of the ring, the dihedral angle defined by ON
and three atoms of the ring (ωO) being 23.0 and 27.5Њ for L = I
and IIЈ, respectively. In the case of ligands III and IVЈ, the
extent of the conjugated system is more important and may
explain that there is no out-of-plane distortion. As can be seen
from Table 6, another feature is the rather important lengthen-
triplet state and the factors influencing the adiabatic T1
transition energy. Besides, it will be shown in the section dealing
with adiabatic T1 S0 transitions that the corresponding
S0
wavenumbers do not depend on the presence of water mole-
cules in the first coordination shell of the lanthanide ion.
As concerns ligand IϪ complexed with gadolinium, its
crystallographic structure consists of [Na2Gd2I8(H2O)3]ؒ6H2O
units.19 The sodium counterion links two complex anions
via the oxygen atoms of IϪ ligands, and it is six-coordinated.
Considering the handicap for theory to tackle such large
molecules, we have performed geometry optimization at the
DFT-B3LYP level of calculation for the GdI4Na subunit
(Fig. 9). The results, reported in Table 5, are in good agreement
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Table 6 Geometrical parameters and Mulliken charges of the central ligand in the S0 and T1 optimal geometries of LH. The labels of the atoms are
defined in Fig. 4; ωN and ωO are dihedral angles, defined by atoms N–Cα–Xβ–Cγ and ON–Cα–Xβ–Cγ, respectively (X–N or C according to L)
I
IIЈ
III
IVЈ
L
S0
T1
0.978
2.043
1.410
1.240
1.442
S0
T1
0.979
2.080
1.400
1.238
1.454
S0
T1
1.018
1.665
1.340
1.252
1.524
S0
T1
0.990
1.882
1.375
1.244
1.389
H–ON
H–OC
N–ON
C–OC
N–C
0.997
1.803
1.376
1.243
1.411
0.995
0.993
0.988
1.850
1.371
1.239
1.403
1.832
1.383
1.241
1.392
1.911
1.382
1.235
1.395
ωN
ωO
0.0
0.0
2.9
Ϫ23.0
0.0
0.0
Ϫ0.6
Ϫ27.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
qH
0.35
0.34
Ϫ0.42
Ϫ0.44
Ϫ0.20
0.52
0.36
Ϫ0.42
Ϫ0.52
Ϫ0.14
0.52
0.35
Ϫ0.40
Ϫ0.43
Ϫ0.17
0.50
0.35
Ϫ0.43
Ϫ0.53
Ϫ0.26
0.53
0.37
Ϫ0.38
Ϫ0.52
Ϫ0.23
0.51
0.35
Ϫ0.43
Ϫ0.50
Ϫ0.17
0.51
0.36
Ϫ0.41
Ϫ0.50
Ϫ0.13
0.49
qO
Ϫ0.43
Ϫ0.54
Ϫ0.16
0.54
N
qO
C
qN
qC
Table 7 Geometrical parameters and Mulliken population analysis in the S0 and T1 optimal geometries of TbL3; S0: average values for the three
ligands; T1: the left column corresponds to the excited ligand, the average value for the two non-excited ligands is given in the right column
I
IIЈ
III
IVЈ
S0
T1
2.445
2.298
1.312
1.283
1.499
S0
T1
2.385
2.340
1.318
1.274
1.491
S0
T1
2.418
2.291
1.298
1.282
1.498
S0
T1
2.411
2.289
1.303
1.288
1.488
Tb–ON
Tb–OC
N–ON
C–OC
N–C
2.322
2.312
2.321
1.340
1.279
1.391
2.335
2.325
2.320
1.331
1.278
1.385
2.309
2.303
2.333
1.346
1.277
1.370
2.295
2.377
1.346
1.267
1.373
2.295
2.362
1.346
1.269
1.372
2.340
1.339
1.276
1.393
2.333
1.331
1.276
1.387
2.351
1.346
1.275
1.371
αOTbO
ωN
ωO
67.4
0.0
Ϫ0.1
67.8
2.9
31.1
67.9
0.0
Ϫ0.3
67.8
0.0
Ϫ0.3
68.0
2.0
25.0
67.9
0.0
0.2
67.5
0.0
0.3
66.7
0.1
0.8
67.7
0.0
0.4
67.9
0.0
0.4
67.8
0.0
Ϫ0.8
68.0
0.0
0.5
qTb
1.40
Ϫ0.59
Ϫ0.61
Ϫ0.05
0.56
1.41
Ϫ0.42
Ϫ0.62
Ϫ0.11
0.53
1.43
Ϫ0.59
Ϫ0.62
Ϫ0.05
0.57
1.44
Ϫ0.58
Ϫ0.62
Ϫ0.02
0.56
1.42
Ϫ0.47
Ϫ0.58
Ϫ0.07
0.52
1.44
Ϫ0.58
Ϫ0.62
Ϫ0.02
0.56
1.43
Ϫ0.61
Ϫ0.61
Ϫ0.14
0.56
1.44
Ϫ0.48
Ϫ0.63
Ϫ0.15
0.56
qO
Ϫ0.61
Ϫ0.61
Ϫ0.13
0.56
Ϫ0.60
Ϫ0.59
Ϫ0.07
0.55
Ϫ0.49
Ϫ0.63
Ϫ0.04
0.46
Ϫ0.60
Ϫ0.60
Ϫ0.06
0.55
N
qO
C
qN
qC
ing of the N–C distance in T1 with respect to S0 for L = I, IIЈ
and III, which reaches 0.132 Å for IIIH. Another point which
must be stressed, although the variations are less important,
concerns the H–ON bond length. It decreases for L = I (0.019 Å)
and L = IIЈ (0.016 Å), while it increases for L = III (0.025 Å) and
almost remains constant for L = IVЈ (0.002 Å). As concerns the
Mulliken charges, no significant variations in T1 with respect to
S0 are observed, with the exception of the OC atom, whose
negative charge decreases by approximately 0.1 a.u. for IH
and IIЈH.
TbL3 Complexes. Excited states wavefunctions are often very
complex. Various electronic configurations can mix, and the
electronic structure of excited states is consequently multi-
configurational. In this context, density functional theory can
be suspected to yield a poor description of the lowest triplet
state. We have thus previously performed CASSCF calcu-
lations, in order to check whether the wavefunction of the low-
est triplet state is multiconfigurational or can be described by a
single configuration. This calculation involves six electrons in
seven orbitals. The active space is defined by one π and one π*
orbitals localized on each ligand. The last orbital, selected for
allowing the obtaining of a LMCT state, is a d atomic orbital of
the metal. The geometry of the TbI3 complex has been fully
optimized without constraints at the CASSCF level of calcu-
lation, both for its ground and lowest triplet states. It appears
that when the molecule adopts its stable geometry in the lowest
triplet state, T1 can be mainly described by one configuration,
which corresponds to a π, π* excitation strictly localized on one
ligand only. According to the density matrix, the occupancy of
each of the π and π* MOs involved in the excitation is close to
1. This ligand does not remain planar, contrary to the two
others. As was observed for 1-hydroxypyridin-2-one (IH), there
is a pyramidalization of the bonds around the nitrogen atom.
These results strongly suggest that the excitation is localized on
one ligand only. This is also supported by the analysis of the
interaction distances between the ion and the ligands. As a
matter of fact, while the Tb–ON and Tb–OC distances are iden-
tical for the three ligands in the ground state of the complex
(2.321 and 2.359 Å, respectively) the distance between the
excited ligand and the ion significantly changes when the com-
plex is in its T1 optimal geometry (2.493 Å for Tb–ON and 2.274
Å for Tb–OC). It should be noticed that no dramatic change of
the interaction distances between the metal and the two other
ligands in T1 with respect to S0 is observed (2.317 Å for Tb–ON
and 2.340 Å for Tb–OC). Although these calculations are rather
time-consuming, geometry optimizations of the complex in its
second triplet state have been performed. The exploration of
the T2 potential energy surface yields a triplet state almost
degenerate with T1. The optimal geometry corresponds to the
distortion of another ligand with respect to T1, while the excited
ligand in T1 adopts its S0 geometry. Again, T2 is described by
a single π, π* configuration strictly localized on the distorted
ligand. Thus DFT, which is formally a single reference method,
is expected to be appropriate for describing the lowest triplet
state of lanthanide complexes LnLn. Selected geometrical
parameters, obtained in the framework of DFT-B3LYP calcu-
lations, which characterize the optimal geometries of TbL3
complexes in their ground state S0 and their first triplet state T1
are given in Table 7, together with Mulliken charges. As
concerns TbI3 in its triplet state T1, the main comment is that
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
1341

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Table 8 Geometrical parameters and Mulliken charges in the S0 and T1 optimal geometries of GdL4Na; S0: average values for the four ligands; T1:
the left column corresponds to the excited ligand, the average value for the three non-excited ligands is given in the right column
I
IIЈ
III
IVЈ
a
a
a
a
S0
T1
2.629
2.478
1.311
1.261
1.503
S0
T1
2.571
2.502
1.320
1.259
1.482
S0
T1
2.506
2.384
1.292
1.273
1.496
S0
T1
2.521
2.358
1.297
1.280
1.494
Gd–ON
Gd–OC
N–ON
C–OC
N–C
2.437
2.514
1.332
1.273
1.395
2.392
2.512
1.329
1.278
1.393
2.450
2.401
2.503
1.319
1.278
1.387
2.423
2.421
2.537
1.339
1.274
1.372
2.459
2.490
1.342
1.260
1.377
2.48
2.50
1.343
1.261
1.376
2.501
1.322
1.273
1.389
2.532
1.338
1.271
1.373
αOGdO
ωN
ωO
63.6
0.3
0.7
62.5
1.2
29.0
64.2
0.1
0.4
64.0
0.1
0.5
63.4
2.0
26.0
63.6
0.1
0.3
63.5
0.2
0.2
64.2
1.4
0.4
63.8
0.2
0.3
64.3
0.2
0.4
65.5
0.1
0.6
64.2
0.1
0.4
qGd
1.43
Ϫ0.60
Ϫ0.68
Ϫ0.10
0.64
1.47
Ϫ0.51
Ϫ0.58
Ϫ0.11
0.58
1.37
Ϫ0.57
Ϫ0.63
Ϫ0.02
0.56
1.40
Ϫ0.54
Ϫ0.50
Ϫ0.05
0.52
1.37
Ϫ0.60
Ϫ0.62
Ϫ0.13
0.56
1.39
Ϫ0.45
Ϫ0.59
Ϫ0.15
0.56
1.38
Ϫ0.62
Ϫ0.58
Ϫ0.06
0.55
1.40
Ϫ0.46
Ϫ0.60
Ϫ0.04
0.46
qO
Ϫ0.58
Ϫ0.70
Ϫ0.10
0.64
Ϫ0.55
Ϫ0.66
Ϫ0.02
0.56
Ϫ0.61
0.67
Ϫ0.13
0.57
Ϫ0.63
Ϫ0.58
Ϫ0.06
0.55
N
qO
C
qN
qC
a The metal–oxygen distances for the ligand which is considered as excited in T1 are (in Å): 2.536, 2.542, 2.379, 2.379 for Gd–ON and 2.461, 2.452,
2.431, 2.441 for Gd–OC).
it experiences a distortion of one ligand with respect to the
optimal geometry in S0, and a variation of the distance between
that ligand and the TbIII ion, analogous to the CASSCF results.
This is also the case for L = IIЈ, III and IVЈ: the geometry of a
single ligand significantly changes in T1 with respect to S0.
Moreover, as previously found for hydroxamic acids, there is a
pyramidalization of the nitrogen atom which results in an
out-of-plane motion of ON for L = I and L = IIЈ (ωO = 31.1 and
25.0Њ, respectively), while for L = III and L = IVЈ the excited
ligand remains planar. This ligand, which can be considered as
excited in the triplet state, will hereafter been denoted L*. The
variations of Tb–O distances in T1 with respect to S0 for the two
non-excited ligands do not exceed 0.02 Å for all the series. This
is rather negligible, considering the variations for L*: the
Tb–ON distance increases by 0.123, 0.050, 0.109 and 0.116 Å for
L = I, IIЈ, III and IVЈ, respectively, whereas the Tb–OC distance
decreases by 0.042, 0.060 and 0.088 Å for L = I, III, and IVЈ,
respectively. Among the series, only the excited ligand IIЈ* does
not exhibit a significant variation of the Tb–OC distance (0.007
Å). Considering now all the atoms which form a ring with the
terbium ion, the N–ON, C–OC and N–C bond lengths do not
noticeably vary for the two non-excited ligands. Although the
Fig. 10 Variation of the metal–oxygen distances in the T1 state with
N–ON and C–OC bond lengths more significantly change for
L*, the largest variation is observed for the N–C bond length: it
increases by more than 0.1 Å, whatever the ligand. It can also
be seen in Table 7 that the bite angle αOTbO remains constant.
Considering now the Mulliken charges, the terbium ion is, as
expected, positively charged, and its electronic population does
not change in the triplet state. The obtained value of 1.4 a.u.
can be considered as a large positive charge. Although it is quite
far from the formal charge value of ϩ3, such values are usually
found in such Mulliken analysis on lanthanides. It should be
noticed that other charge analysis methods such as NBO yield
electronic charges around 2.4 a.u for lanthanide ions LnIII.50
Considering the present Mulliken charge analysis, it is interest-
ing to notice that, similarly to the bond lengths, variations are
observed for the excited ligands L*, and mainly concern the two
oxygen atoms.
GdL4Na Complexes. The geometrical parameters given in
Table 8 are presented in a similar way as for TbL3 complexes.
While the three ligands in TbL3 complexes are equivalent in S0,
the four ligands of GdL4Na are not, due to the presence of the
sodium counterion. Although the situation seems less clear-cut,
similar trends can be drawn: only one ligand can be considered
as excited, whereas the three others remain in their ground state.
This can be in particular stated from the variation of the
Gd–ON and Gd–OC bond lengths, as can be seen in Fig. 10. The
respect to the S0 state for TbL3 and GdL4Na. Only the excited ligand L*
is considered.
variations of the metal–oxygen bond lengths in T1 with respect
to S0 for the whole series of the ligands clearly show a parallel-
ism between the Tb and Gd curves, although they are not
exactly superimposable. Similarly to TbL3, the positive charge
on GdIII remains constant in T1 with respect to S0, and the only
significant variation concerns the charge of the oxygen atoms.
These statements can be summarized by considering the excited
terbium and gadolinium complexes as TbL*L2 and GdL*L3Na,
respectively.
4.2 Adiabatic transition energies
The principal aim of this study is to compare experimental
spectroscopic data with theoretical values. It was shown in the
previous sections, that geometries obtained at the CASSCF and
B3LYP levels of theory compare well, both in the ground state
S0 and in the lowest triplet state T1. Thus, the calculations were
carried out using the computationally economical methods,
i.e. restricted and unrestricted B3LYP calculations for S0 and
T1, respectively. Since full geometry optimization was achieved,
theoretical wavenumbers calculated as νtahdeioa = [E(T1) Ϫ E(S0)]/hc
can be compared with the experimental 0–0 transitions (νe0x0p),
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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Table 9 Theoretical and experimental T1
S0 transition wave-
[ν Ϫ νelxwp] (where ν and ν correspond to the maximum intensity
Table 10 Theoretical T1
S0 transition wavenumbers νadia (in cmϪ1
)
numbers (in cmϪ1) of the protonated free ligands LH. An energy range
of the terbium TbL3(H2O)2, TbL3 and gadolinium GdL4Na complexes.
An energy range is given for the experimental emission spectra (see
caption of Table 9)
exp
max
exp
max
exp
lw
and the left wing of the experimental spectrum, respectively) is given for
molecules IH and IIH since the vibrational structure is not observable
exp
(in emission spectra, νelxwp > νe0x0p ≥ ν
)
Tb (theo.)
Gd
max
νadia
ν00
L
TbL3(H2O)2
TbL3
Theo.
Exp.
L
Theo.
Theo.
Exp.
I
22740
21616
21427
18634
–
23195
22790
22110
19096
–
22464
–
20956
17853
–
21050–25250
21600–26300
–
18200–20800
22950–25650
–
II
I
II
IIЈ
III
IV
IVЈ
23000
19813
20300
21410
24661
24907
21905
19001
19411
20463
23196
23555
21500–25000
21600–26300
–
23000
26000
–
IIЈ
III
IV
IVЈ
22654
22805
22309
transition wavenumber of molecule IVH cannot directly be
compared with the others.
although zero-point energy (ZPE) corrections to the theoretical
energies should be taken into account for a relevant com-
parison. Unfortunately, such ZPE corrections could only be
systematically computed for the protonated ligands LH, due to
the high computational cost for the largest systems.
TbL3(H2O)2, TbL3 and GdL4Na complexes. As it was
previously recalled, the energy of the lowest triplet state of
the ligands complexed with LnIII ions can be probed by
phosphorescence experiments on gadolinium complexes, since
the lowest electronic level of the gadolinium ion (6P7/2) lies
Hydroxamic acids LH. The theoretical adiabatic transition
above 31000 cmϪ1 51
i.e. at higher energy than the emitting
,
theo
adia
wavenumbers ν
for acids IH–IVH ranged from 19813 to
triplet state of the complexed ligands. Contrarily to experi-
ments, the theoretical determination of the position of the
triplet state for terbium complexes is as straightforward as in
the case of gadolinium complexes. The triplet state energy of
TbL3 and TbL3(H2O)2 complexes is almost the same, the triplet
state of TbL3 lying at most 700 cmϪ1 above the triplet level of
terbium complexes with water in the first coordination shell
(Table 10). This small difference confirms that water molecules
present in the first coordination sphere do not play a significant
role in the position of the triplet state of the complex, although
they have a significant role when considering their ability to
quench luminescence via vibrational deactivation. As can be
noticed according to the results given in Table 10, the replace-
ment of terbium by gadolinium does not affect the triplet state
energy level. For instance, T1 for the Gd(IIЈ)4Na complex lies
471 cmϪ1 below the triplet state of Tb(IIЈ)3(H2O)2. The theoret-
ical values for L = I and L = III, augmented with a shift
analogous to the δ value introduced for LH hydroxamic acids,
are within the experimental energy range. Again, the agreement
between theory and experiments confirms the validity of the
theoretical method employed in this work.
24907 cmϪ1 (Table 9). ZPE corrections systematically lower the
theoretical wavenumbers by approximately 1000 cmϪ1, which
means that the potential energy surface is more flat in T1 than in
S0. The substitution of methyl groups with hydrogen atoms
only slightly increases the energy of molecules IIЈH and IVЈH
with respect to molecules IIH and IVH, and therefore confirms
the validity of this simplification. Among all molecules, the
lowest triplet state of IVH is the less stable with respect to the
ground state. All theoretical results are supported by the avail-
able experimental work, when available. Similarly, the direct
comparison of theoretical and experimental ν00 wavenumbers
for molecules IIIH and IVH indicates that the stability of the
triplet state with respect to S0 is overestimated by approximately
δ00 = 2700 cmϪ1 for both molecules. To be more precise, the
exp
theo
difference ∆ν = ν Ϫ ν is 2537 and 2804 cmϪ1 for IIIH and
00
00
IVH, respectively. This can be considered as a constant shift of
theoretical values with respect to experiments. This is a good
result, considering the nature of the ∆SCF method, and in so
far as the best ab initio methods for the calculation of electronic
excited states such as CASPT2 claim an accuracy of 800–2000
cmϪ1 on transition energies.30 Considering the adiabatic trans-
ition wavenumbers, the difference between theory and experi-
4.3 Nature of the lowest triplet state
ments is artificially reduced to approximately δ = 1700 cmϪ1
.
The broadening on the vibrational structure of the experi-
On one hand, α- and β-Kohn–Sham MOs provided by
unrestricted DFT calculations do not allow to describe the
triplet state T1 with respect to the ground state S0 in terms of
one or several transitions between MOs. On the other hand, we
experienced for the TbI3 complex that CASSCF calculations
performed for the ground state and the first triplet states are
very time-consuming, and cannot be handled for exhaustive
studies on a wide range of complexes. These CASSCF calcu-
lations revealed that the lowest triplet state is described with
respect to the ground state by a single excitation between two
π MOs localized on the distorted ligand. Since CASSCF
calculations are very expensive, we have performed TDDFT
calculations in order to get an analysis of T1 wavefunctions in
terms of transitions between MOs. It should be recalled that,
although TDDFT deals with the electronic density ρ, the
wavefunctions are usually analyzed as linear combinations of
single-excited determinants, i.e. ψ = ΣΣCa,b(ꢀa,ꢀb), where ꢀa and
ꢀb are MOs. We have considered hydroxamic acids LH and
terbium complexes TbL3 (L = I, IIЈ, III, IVЈ) in their T1 optimal
geometry. TD-B3LYP calculations show that in all cases, the
mental emission spectra of IH and IIH due to solvent effects
does not allow the measurement of νe0x0p for these two molecules,
theo
00
and accordingly we shall only compare ν
with an experi-
mental energy range. The theoretical value, augmented or not
with δ00, lies within νmax and the left wing of the spectrum.
theo
00
Concerning IIH, ν corrected by the amount δ yields 21700
cmϪ1. It is not clear whether in that case the theoretical value is
exp
very underestimated or ν coincides with νmexapx. However, no
00
special reason can be put forward for favouring the former
explanation.
Analysis of the theoretical results yields some general trends
concerning the link between the extent of conjugation and the
position of T1 with respect to S0. As a matter of fact, molecules
IIH and IVH differ with respect to IIЈH and IVЈH, respectively,
by the substitution of methyl ligands by hydrogen atoms. In
other words, the hyperconjugation extends the delocalization of
the π electrons of the ring. We have checked that hyperconju-
theo
adia
theo
adia
gation more stabilizes T than S and thus ν
(LH) < ν
1
0
(LЈH). The same conclusion also holds for molecule IIIH,
which, relative to IH is a large conjugated system. As a matter
wavefunction ψT is mainly described as C1 (HOMO, LUMO),
with C1 ≥ 0.78 (see Table 11). The vertical transition energies T e
are also indicated in this table. For LH acids as well as TbL3
1
theo
of fact, the ν value calculated for IIIH is low relative to IH.
00
Finally, due to its different chemical structure, the adiabatic
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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Table 11 Analysis of the TDDFT wavefunction ψT of the lowest
towards the lanthanide ion energy levels. TDDFT calculations
show that lanthanide complexes LnL3 in their ground state have
three almost degenerate triplet states. Since triplet states usually
have long lifetimes, it can be reasonably assumed that the initial
1
triplet state of LH and TbL3 in the T1 geometry, optimized at the
UB3LYP level of calculation; T e is the vertical transition energy, in eV
(see Fig. 3)
geometry GS of the lanthanide complex relaxes in T1, leading
L
I
IIЈ
III
IVЈ
0
to a new optimal geometry GT (see Fig. 3). We have thus per-
1
formed CASSCF geometry optimizations in T1 and T2 in order
to understand the grounds of the phenomena. The calculations
LH
C1
T e
C1
T e
0.82
2.02
0.85
1.63
0.86
1.67
0.81
1.86
0.79
2.03
0.84
1.57
0.80
2.33
0.78
2.10
TbL3
clearly show that each triplet state Ti in its optimal geometry GT
i
can be considered as typical of a single ligand (Li) which thus
behaves as a chromophore. As a matter of fact, the two singly
complexes, the HOMO and LUMO are π MOs, as can be seen
in the case of L = I in Figs. 11 and 12. However the HOMOs
and LUMOs involved in the transition are not necessarily the
same in LH and TbL3 compounds. It can be seen on the figures
that this is the case for L = I, for which the HOMOs are differ-
ent. However, for both molecules the HOMO has a bonding
character between C and N, whereas the LUMO presents an
antibonding character. This is consistent with the unrestricted
DFT results, which yield larger N–C bond lengths in the T1
state with respect to the ground state S0. Concerning the TbIII
occupied MOs describing T1 with respect to S0 are π orbitals
L1
strictly localized on the L1 ligand (πL and π* ). The atomic
1
orbitals of the lanthanide which could cast a bridge between
two ligands orbitals, are not involved, and no mixing of two πL
i
and πL MOs occurs. As a consequence, TbL3 complexes with-
j
out solvent molecules are symmetrical in S0, exhibiting roughly
a three-fold axis, whereas GT is unsymmetrical. TDDFT calcu-
1
lations provide an estimation of the energy difference between
the symmetrical and unsymmetrical geometries in the lowest
triplet state. From the results given in Table 12, we deduce that
this energy difference lies within 6500 cmϪ1 (18 kcal molϪ1) and
12000 cmϪ1 (34 kcal molϪ1) according to the ligand. These
results can be related to the work of Amouyal et al., which has
experimentally characterized the lowest singlet excited MLCT
state of phenylterpyridine–Ru() complexes.52 This work, also
supported by extended Hückel calculations, shows a similarity
of the excited-state absorptions to those of the ligand radical
anion, and was interpreted as a localization of the excited elec-
tron on a single ligand. How can these statements can be useful
in the framework of experimental works? Consider a lan-
thanide complex, with three or four identical ligands which are
not directly linked together by covalent bonding. Each ligand
acts as an individual antenna, which functions in the frame-
work of the whole complex, but which is characterized by a
triplet state energy independent of the other antennae. As a
consequence, each antenna may provide energy to the lan-
thanide ion. In so far as the lanthanide complex is surrounded
by solvent molecules which dynamically perturb the complex,
energy transfer from each of the ligands can alternatively be
favored (see also the discussion in ref. 52). The ligands, submit-
ted to a continuous beam of photons, are excited, and the sensi-
tization of the LnIII ion is thus achieved in a very efficient way,
the lanthanide complexes considered in this work being multi-
chromophoric systems. If we consider now a lanthanide ion
surrounded by one antenna only, the energy transfer to LnIII is
now ensured by a single collector of photons. Since we propose
that the triplet state energy does not significantly change with
respect to the multi-chromophoric complex, and considering
the energy gap rule, no variation of the luminescence quantum
yield should be observed. Our analysis is grounded on the hypo-
thesis (i) that the triplet states are not in equilibrium due to a
high energy barrier between them and (ii) that interligand
energy transfer does not occur. If that latter point is taken into
account, it could mean that the number of antennae may influ-
complexes, the π MOs which describe the T1
S0 transition are
localized on the ligand which is distorted and for which the
interaction distance with the metal significantly changes.
Fig. 11 According to TDDFT calculations the T1 state of IH is mainly
described by the HOMO and LUMO orbitals.
Fig. 12 According to TDDFT calculations the T1 state of TbI3 is
mainly described by the HOMO and LUMO orbitals.
TDDFT calculations on the three lowest triplet states were
done both in the ground state and in the triplet state optimal
geometries. The three lowest triplet states are almost degenerate
in the S0 geometry, while T1 is significantly stabilized in its
optimal geometry with respect to T2 and T3 which remain
degenerate (Table 12). These results suggest that the three trip-
lets are uncoupled.
ence the luminescence lifetime. The ligand
ligand energy
transfer would introduce a delay in the energy transfer towards
the emitting level of the lanthanide ion, and consequently the
luminescence lifetime should increase. Results recently obtained
by Ferrand et al.53 are not in contradiction with our conclu-
sions. Finally, it should be noticed that such an “energy reser-
voir” effect has already been discussed in the case of a
bichromophoric system based on a ruthenium–ligand complex
linked to an energy reservoir unit.54 Our crude models for
energy transfer processes in TbL3 very partially address the
more general problem of four-center energy transfer, and the
effects of geometry and symmetry on the resonance energy
transfer mechanisms, which have been recently studied by
means of molecular quantum electrodynamics.55 Moreover, we
do not know whether the energy transfer is concerted or step-
From a more methodological point of view, it is interesting to
compare the adiabatic transition wavenumber calculated in the
framework of the ∆SCF method with the value obtained by
considering the addition of ∆E obtained at the DFT level and
the TDDFT transition energy T e between S0 and T1 (see Fig. 3).
This latter quantity, is obtained at different levels of calculation
which are formally not consistent, and the νadia value computed
in this manner (i.e. ∆E ϩ T e) appears to be significantly under-
estimated for all ligands.
5
Discussion
We shall now propose a rough picture of the energy transfer
process which occurs from the triplet states of the ligands
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
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Table 12 Vertical transition energies T e of TbL3 complexes, L–I, IIЈ, III, IVЈ in the S0 and T1 geometries obtained at the TDB3LYP level of theory;
∆E = E(S0,GT ) Ϫ E(S0,GS ) (see Fig. 3)
1
0
I
IIЈ
III
IVЈ
L
S0
T1
S0
T1
S0
T1
S0
T1
T 1
T 2
T 3
∆E
25424
25440
25539
7589
20736
23195
13147
25414
25584
23384
23386
23405
5384
20366
22110
14982
23502
23521
20724
20733
20752
3952
16915
19096
12963
20601
20623
23579
22583
22592
3599
20554
22805
16955
23425
23437
∆E ϩ T e
theo
adia
ν
wise. A corresponding pictorial representation could be streams
(the energy provided by the ligands) which feed a river (the
energy emitted by the lanthanide ion): do the streams simul-
taneously or alternately feed the river? We believe that our
interpretations and interrogations, undoubtedly controversial
and speculative, could participate to the debate between theore-
ticians and experimentalists.
consequence it also depends on the variation of electrostatic
interactions induced by the variation of the negative charge of
the oxygen atoms.
The adiabatic transition energies, compared to data derived
from emission spectra, are summarized in Fig. 14. Theoretical
results are in general not in disagreement with experimental
ones, although the triplet state position is systematically under-
estimated, in the order of δ00 = 2700 cmϪ1. The purpose of the
theoretical part of this work being to understanding key issues
in order to validate a method for designing good luminescent
lanthanide complexes in the context of the energy-gap rule, it
is very positive that the energy scale provided by the ∆SCF
procedure is very similar to the experimental energy scale. Simi-
larly, theory indicates that the triplet state level of molecule
IIIH lies 2733 cmϪ1 below the triplet state of IVH, whereas the
difference between the experimental 0–0 transition wave-
numbers is 3000 cmϪ1. The only discrepancy between theory
and experiments concerns ligand II. As a matter of fact, while
the experimental energy range is exactly the same for molecules
IIH and GdII4, theory finds that the triplet state of the
The results obtained for GdL4Na complexes do not seem to
raise doubts on the previous analysis. Again, one ligand
appears excited in the triplet state, the other ones still remaining
in their ground state. We have previously shown in Fig. 10 that
the variation of the main geometrical parameters which char-
acterize the distortion of the ligand in T1 with respect to S0,
that is to say the variation of the metal–oxygen distance, is
analogous in TbL3 and GdL4Na complexes. However we did
not discuss about the factors influencing the triplet state energy.
For that purpose, the difference of the Mulliken charges of the
oxygen of L* in T1 according to the values in S0 are plotted in
Fig. 13. There is a striking parallelism between the curves of
Figs. 10 and 13, which strongly suggests that metal-ligand
interactions in the triplet state are dominated by the electro-
static interactions between the metal and the surrounding
atoms. This is not very surprising, since it is well known that
bonding between LnIII ions and anionic ligands in S0 has mainly
a ionic character, even if a charge transfer mechanism may also
play a role for weaker ligands.29 It has also been shown that
a predominant electrostatic effect is responsible of some
geometrical features of lanthanide complexes.56 Considering
the triplet state, the (πLi, π*Li) transition changes the electronic
density on the oxygen atoms of Li, yielding different ligand–
metal electrostatic interactions. The triplet state energy thus
depends on the nature of the (πLi, π*Li) transition, and as a
Fig. 14 Comparison of theoretical adiabatic transition wavenumbers
adia
theo
Fig. 13 Variation of the Mulliken charge in the T1 state with respect to
the S0 state for TbL3 and GdL4Na. Only the excited ligand L* is
considered.
ν
(plain lines) and experimental wavenumbers obtained by
phosphorescence (dashed lines); ligand labels are indicated in bold
italic.
D a l t o n T r a n s . , 2 0 0 4 , 1 3 3 4 – 1 3 4 7
1345

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chromophore is destabilized in the complex with respect to the
hydroxamate free ligand. No special reason can be put forward
for explaining this disagreement.
lanthanide complexes, ligands (antennae) should cautiously be
designed in order to have a triplet state energy slightly above the
emitting level of the lanthanide ion. Although this is not a
sufficient condition, it is a necessary condition for obtaining
efficient luminescent lanthanide complexes. Recently, in a
combined experimental/theoretical work on nine-coordinated
Concerning ligand IIIϪ coordinated with gadolinium, it is
not possible to strictly assign the νe0x0p wavenumber, although the
phosphorescence emission spectrum presents a vibrational
structure at 19300 cmϪ1. Consequently, the shift between theory
lanthanide podates published by the Bünzli group, arguments
theo
adia
1
and experiments agrees with the energy shift δ, since ν
lies
on the ππ*
3ππ* ISC have been given by considering the
1450 cmϪ1 below the estimated value for νe0x0p. It is interesting to
note that the effect of complexation is very strong for ligand
IIIϪ. As a matter of fact, theoretical as well as experimental
results agree for locating the triplet state level of the gadolinium
complex stabilized by approximately 3000 cmϪ1 with respect to
the protonated ligand IIIH. The interpretation does not lie in a
different description of the nature of the triplet state of IIIH
and GdIII4Na, since we have checked that, contrarily to ligand I
(see Figs. 11 and 12), the triplet state of the two molecules
correspond to an excitation between the same orbitals. This
means that, although the two MOs involved in the excitation do
not spread on the metal, the LnIII ion has a strong effect on T1.
Finally, the effect of the complexation is not the same along
the series of hydroxamate ligands. Ligand IVϪ also shows a
spectacular stabilization of its triplet state due to complexation.
In contrast, the lowest triplet state of ligand IIϪ is strongly
destabilized. As for ligand IϪ, its triplet state energy is only
slightly lowered.
Coming back to the correlation between triplet state energy
and luminescence quantum yield, it is noteworthy that the pos-
ition of the triplet state, experimentally probed on gadolinium
complexes, is implicitly assumed to be the same for other
lanthanide complexes. We have shown the transferability of
triplet state energy found for gadolinium complexes to terbium
complexes. Moreover, we have also performed preliminary
calculations on europium complexes which confirm this trans-
ferability in the case of ligand IϪ. Thus, we have theoretically
validated the experimentally implicit hypothesis, on which the
energy-gap rule is grounded.
vertical energy gap calculated in the ground state geometry.57 As
a matter of fact, it is assumed that a large energy gap of 5000
cmϪ1 is required for an efficient ISC.58 While this may possibly
provide a first estimation of the ISC efficiency, we believe that
an exhaustive theoretical investigation of the spectroscopic
properties of these compounds is desirable. However, this
would require explorations of excited potential energy surfaces
in order to find crossings between surfaces and even conical
intersections.59–61 Considering the size of these complexes and
the difficulty for calculating their electronic structure, this is far
beyond the possibilities of ab initio theoretical methods. The
∆SCF method, applied in the framework of DFT calculations,
has shown its ability to provide reliable results on the lowest
triplet state, in agreement with experimental data. It thus seems
possible to theoretically provide an energy scale of triplet states
of several lanthanide compounds, with a low cost compared to
the experimental approach. We also suggest that the number of
antennae, while not influencing the triplet state energy, may
nevertheless have an influence on the luminescence lifetime: our
prescription is to saturate the lanthanide ion with antennae in
order to enhance this property. We have also discussed the
strong involvement of electrostatic factors in the ligand–metal
bonding in the lowest triplet state T1.
Finally, a more detailed discussion about electrostatic
interactions as well as screening of functional groups R in
hydroxamate ligands [CO–N(R)O]Ϫ will be given in the second
paper of this series.
Acknowledgements
Although the theoretical energy levels for gadolinium
complexes reported in Fig. 14 should be shifted for the purpose
of quantitative comparison with the experimental energy of the
F. G., L. M., J.-P. D. and R. P. thank the CALcul en
MIdi-Pyrénées (CALMIP) and the Centre Informatique
National de l’Enseignement Supérieur (CINES) for allocations
of computational resources.
emitting level of the TbIII ion (5D4), it is possible to correlate, in
theo
adia
the framework of the energy-gap rule, ν
with the lumines-
cence properties of the terbium complexes. The energy of the T1
5
state of ligands IIϪ and IIIϪ is very close to the D4 state, thus
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