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PROOF COVER SHEET
Author(s):
Corneliu I. Oprea, Petre Panait, Boris F. Minaev,
˚ gren, Fanica Cimpoesu, Marilena Ferbinteanu and
Hans A
Mihai A. Gˆırt¸u
Article title:
Comparative computational IR, Raman and phosphorescence
study of Ru- and Rh-based complexes
Article no:
777811
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Corneliu I.
Oprea
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Petre
Panait
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Boris F.
Minaev
4
Hans
˚ gren
A
5
Fanica
Cimpoesu
6
Marilena
Ferbinteanu
7
Gˆırt¸u
Mihai A.
Suffix
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TMPH_A_777811
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Molecular Physics, 2013
Vol. 00, No. 00, 1–13, http://dx.doi.org/10.1080/00268976.2013.777811
Comparative computational IR, Raman and phosphorescence study of Ru- and
Rh-based complexes
˚ grenb , Fanica Cimpoesud , Marilena Ferbinteanue and
Corneliu I. Opreaa , Petre Panaita , Boris F. Minaevb,c,∗ , Hans A
Mihai A. Gˆırt¸ua,∗
5
a
Department of Physics, Ovidius University of Constant¸a, Constant¸a, Romania; b Department of Theoretical Chemistry and Biology,
Royal Institute of Technology, Stockholm, Sweden; c Department of Chemistry, B. Khmelnitsky National University, Cherkassy, Ukraine;
d
Department of Theoretical Chemistry, Institute of Physical Chemistry, Bucharest, Romania; e Department of Inorganic Chemistry,
University of Bucharest, Bucharest, Romania
(Received 16 December 2012; final version received 12 February 2013)
10
We report density functional theory (DFT) calculations providing the infrared and Raman spectra of
[Ru(II)(bpy)3-n (dcbpy)n ]2 + and [Rh(III)(bpy)3-n (dcbpy)n ]3 + complexes, where bpy = 2,2’-bipyridyl, dcbpy = 4,4’dicarboxy-2,2’-bipyridyl, and n = 0, 1, 2, 3, studied in the context of dye-sensitised solar cells. We compare and contrast the
role of the metallic ion and of the COOH groups on the vibration and phosphorescence properties of these complexes. The
vibrational spectra are not very sensitive to the replacement of the metal ion, but the presence of carboxyl groups leads to
a richer spectrum due to the additional bands caused by the COOH groups. Comparison with the limited experimental data
available allowed the assignment of the Raman bands. The calculated phosphorescence lifetimes suffer only modest changes
when the COOH groups are introduced but vary significantly when changing the metal ion, being two orders of magnitude
larger for Rh(III) than for the Ru(II) complexes.
15
Keywords: ruthenium complexes; rhodium complexes; 2,2’-bipyridyl; 4,4’-dicarboxy-2,2’-bipyridyl; density functional
theory; infrared spectra; Raman spectra; phosphorescence
20
1. Introduction
25
30
35
40
Based on its chemical stability, redox properties, excited
state reactivity, luminescence emission, and excited state
lifetime, [Ru(bpy)3 ]2 + (bpy = 2,2’-bipyridine) has provided the natural starting point for numerous studies in inorganic charge-transfer complexes, being one of the most extensively studied species [1]. Research on the larger class of
transition metal-polypyridine complexes has stimulated the
development of photocatalysis [2,3], photo-biochemistry
[4,5], and photovoltaic devices [1,6].
The Gr¨atzel cells [7] are low-cost photovoltaic devices
based on the light absorption in a dye sensitising a wide
bandgap semiconductor, such as TiO2 , in the anatase form.
The electron is transferred from the dye to the semiconductor and, through a transparent conducting oxide, passing
the external load to the counter-electrode, where an electrolyte brings it back to the dye. The Ru(II)-polypyridine
complexes have lead to photovoltaic conversion efficiencies
above 11% [8,9].
Various Ru(II) complexes containing carboxyl groups,
as in 4,4’-dicarboxy-2,2’-bipyridine, dcbpy [10] or 5,5’dicarboxy-2,2’-bipyridine [11], have been studied because
of the need for anchoring groups to ensure the adsorption
of the dye to the oxide. The presence of the carboxyl group
∗
Corresponding author. Email: [email protected]
C 2013 Taylor & Francis
requires special synthesis and leads to modified chemical
properties, dcbpy-based complexes being more difficult to
obtain [10].
Ru(II) polypyridine complexes have been extensively
studied both experimentally [1,12] and theoretically. Density functional theory (DFT) calculations have provided
geometry optimisation and excited-state properties of the
[Ru(bpy)3 ]2 + species [13–15], and allowed the study of ligand substituent effects in [Ru(L)3 ]2 + complexes (L = bpy,
bpm, bpz) [16,17]. Other DFT studies reported the effect of
the ligand substitution in the less symmetric [Ru(bpy)2 L]2 +
family of complexes [18–23], including vibration spectra
analysis and vibronic effects on the charge transfer [24,25].
The theoretical studies have also been extended to other
Ru(II) complexes with various different heterocycles [26–
28], as well as to complexes based on other transition metal
ions, such as Os [29,30], Ir [25,31], Re [32], Pt [33], etc.
Despite this increasing number of theoretical studies
many questions are still waiting for an answer. For instance,
open questions that still need to be addressed relate to (1)
the role of the transition-metal, the Ru(II) complexes outperforming by far other DSSC dyes, (2) the role of the
carboxyl groups, and whether it is limited to just insuring
the anchoring of the dye to the substrate, (3) the influence
45
50
55
60
65
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C.I. Oprea et al.
of the vibronic perturbations on the electron transfer and
(4) the effect of the radiative and non-radiative deexcitation
transitions of the dyes on the device performance.
The vibration spectra have been studied for
[Ru(bpy)3 ]2 + [34–39] and other Ru(II) complexes with
various ligands [40]. Theoretical studies of IR and Raman
75
spectra have addressed in particular the normal modes of the
[Ru(bpy)3 ]2 + [41–44], taking advantage of the symmetry
of the complex. No such studies are available for complexes
with various dicarboxyl groups or with Rh(III) ions.
We build here on a previous study [45] in
80
which we presented results of DFT calculations providing the structure, electronic properties, and UVVis absorption spectra of [Ru(II)(bpy)3-n (dcbpy)n ]2 +
and [Rh(III)(bpy)3-n (dcbpy)n ]3 + , where dcbpy = 4,4’dicarboxy-2,2’-bipyridyl, bpy = 2,2’-bipyridyl, and n =
85
0, 1, 2, 3 complexes. The comparison with the Rh(III) complexes revealed the better matching with the solar spectrum
of the absorption properties of the Ru(II) complexes. Of
the complexes studied, the most suited as pigments for dyesensitised solar cells are the [Ru(II)(bpy)3-n (dcbpy)n ]2 +
90
complex with n = 1 and 2, based on their intense absorption band in the visible region, the presence of the anchoring
groups allowing the bonding to the TiO2 substrate as well
as the charge transfer, and the good energy level alignment
with the conduction band edge of the semiconducting sub95
strate and the redox level of the electrolyte [45].
Here we report DFT calculations of the infrared (IR)
and Raman spectra as well as phosphorescence studies of
the Ru(II) and Rh(III) complexes mentioned above. We
compare and contrast the role of the metallic ion and of
100 the COOH groups on the vibrational and phosphorescent
properties of these complexes.
Phosphorescence transitions and lifetimes have been
studied from the perspective of new materials for organic
light emitting devices [46], but such studies are also relevant
105 for photovoltaic cells, particularly DSSCs. First principle
theoretical analysis of phosphorescence of organometallic
compounds has recently become a realistic task with the
70
use of the quadratic response (QR) technique in the framework of the time-dependent (TD) DFT approach [47–49].
We report here correlations between the main features of 110
the electronic structures and the phosphorescence lifetimes
and discuss the relevance for hybrid organic–inorganic photovoltaic cells.
2. Computational details
The geometrical structures of the [Ru(II)(bpy)
2+
and [Rh(III)(bpy)3-n (dcbpy)n ]3 + com3-n (dcbpy)n ]
plexes (n = 0, 1, 2, and 3) were reported previously [45],
based on DFT calculations. Correspondingly, the IR and
the Raman spectra were simulated using the same hybrid
B3LYP exchange-correlation functional [50,51]. The Los
Alamos effective core potential (ECP) [52] and double-ζ
quality functions for valence electrons [53] were used by
employing the LANL2DZ basis set.
Optical absorption spectra of all complexes, including
the lowest 50 singlet–singlet excitations and the lowest 6
singlet–triplet excitations, were simulated using the time
dependent-DFT (TD-DFT) method [54], with the same
B3LYP functional and ECP on the metallic ion, but including polarisation functions for the valence region of every
atom via the DZVP basis sets [55]. Calculations were performed both in vacuum and in water solvent by employing
the non-equilibrium conductor-like polarisable continuum
model (C-PCM) [56]. The geometry optimisation, IR and
Raman spectra, electronic structure and transitions in vacuum as well as in water solvent were calculated with the
GAUSSIAN03 package [57], whereas the electronic transitions in vacuum and the phosphorescence lifetime calculations were performed with the Dalton program [58].
3. Results and discussion
3.1. IR and Raman spectra
The optimised geometries for the four Rh-based complexes,
calculated previously [45] are shown in Figure 1. Details
regarding the structures have already been presented [45].
B/w in print, colour online
Figure 1.
Optimised structures of the [Rh(III)(bpy)3-n (dcbpy)n ]3 + complexes, with n equal to a) 0, b) 1, c) 2, and d) 3.
115
120
125
130
135
140
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145
150
155
160
165
170
175
Here we stress that the structures of the corresponding
Ru-based complexes are similar, the role played by the
transition metal ion being most obvious in the distance between the metal ion and the nitrogen atoms of the adjacent
dcbpy or bpy, which is larger for M = Ru by about 0.02
˚ . However, the metal ion does not affect substantially the
A
bpy or dcbpy ligands, as both the carbon–carbon and the
nitrogen–carbon bond lengths are practically identical. For
each metal ion, the difference between r(M–Ndcbpy ) and
˚ , which suggests
r(M–Nbpy ) is very small, less than 0.005 A
that the presence of the carboxyl groups has a negligible
influence on those distances.
The symmetry group of the n = 1 and n = 2 complexes is
C2 , whereas for the n = 0 and n = 3 complexes it is D3 . The
bipyridyl ligands have deviations from planarity of up to
2.15o and are positioned almost reciprocally perpendicular,
the angles taking values in the range 87.73–96.78o .
The simulated IR and Raman spectra of
[Ru(dcbpy)3 ]2 + and [Rh(dcbpy)3 ]3 + , calculated at
DFT/B3LYP/LANL2DZ level, are displayed in Figure
2. The value of the scaling factor used for the vibration
frequencies was 0.9614 [59].
As shown in Figure 2, the IR and Raman spectra of
the complexes with three dcbpy groups have in common
both the high-frequency stretches of the O–H (3511 cm−1 )
and C–H (3130 cm−1 ) groups and the fingerprint region
between 1000 and 1600 cm−1 . Below 1000 cm−1 the Raman
bands are weak, for both metals, whereas the IR spectra
still show intense features. From Figure 2, the effect of
changing the transition metal ion appears stronger in the
Raman spectra, with a significant optical activity drop in
the fingerprint region. In the IR spectra, the extra positive
charge in the Rh-based complex polarises more the system,
enhancing the high-frequency C–H stretch (3511 cm−1 ) but
weakening the metal–nitrogen stretch (1006 cm−1 ). On the
3
B/w in print, colour online
Figure 2. Simulated IR (top) and Raman (bottom) spectra of both
[Ru(dcbpy)3 ]2 + and [Rh(dcbpy)3 ]3 + complexes, calculated at the
DFT/B3LYP/LANL2DZ level. The spectral lines were convoluted
with Lorentzian distributions of 20 cm−1 linewidth.
other hand, as expected, the larger mass of the Rh3 + ion
leads to a shift to lower frequency of the vibration peaks, 180
especially in the high-frequency regime.
The simulated IR and Raman spectra of
[Ru(bpy)3-n (dcbpy)n ]2 + and [Rh(bpy)3-n (dcbpy)n ]3 + ,
n = 0, 1, 2, 3, calculated at DFT/B3LYP/LANL2DZ level,
are displayed in Figures 3 and 4. The calculated frequencies 185
ν, the IR intensities, and the Raman optical activities of
the main transitions in the spectrum are shown in Table 1
(see supplementary material) for the ground state of the
[Ru(dcbpy)3 ]2 + complex, together with the assignment of
the type of vibration. The atom labelling scheme is shown 190
in Figure 5.
B/w in print, colour online
Figure 3. Simulated IR spectra of a) [Ru(II)(bpy)3-n (dcbpy)n ]2 + , b) [Rh(III)(bpy)3-n (dcbpy)n ]3 + for n = 0, 1, 2 and 3, calculated at the
DFT/B3LYP/LANL2DZ level. The spectral lines were convoluted with Lorentzian distributions of 20 cm−1 linewidth.
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C.I. Oprea et al.
Table 1. Frequencies, IR intensities and Raman optical activities of the main transitions in the spectrum for the ground state of the
[Ru(dcbpy)3 ]2 + complex, calculated at DFT/B3LYP/LANL2DZ level. Each mode is described by the corresponding types of vibration.
The atom labelling scheme is shown in Figure 5.
Mode
ν (cm−1 )
49
51
52
54
72
78
82
94
95
109
116
124
125
128
135
136
143
154
162
167
168
173
177
180
181
188
189
191
192
198
205
207
213
226
231
363
373
418
427
544
603
617
720
720
863
883
984
986
992
1006
1035
1062
1143
1254
1274
1275
1322
1326
1387
1411
1454
1455
1524
1525
1593
1639
1640
3130
3511
3512
IR–I (km/mol)
R–AO (A4 /AMU)
Type of vibration
20.6
51.8
36.3
0.0
74.5
81.2
277.7
0.8
11.2
0.7
38.8
18.8
4.1
19.9
0.0
848.9
212.7
186.2
1.4
73.2
0.2
235.9
3.0
253.4
0.1
23.0
1.8
33.2
0.1
1.5
582.7
5.1
5.5
385.9
2.6
3.8
0.0
38.8
21.0
0.1
10.7
5.1
47.0
0.1
45.6
0.1
0.2
104.2
432.2
679.8
0.6
16.2
14.9
428.4
43.6
115.7
25.3
281.4
0.1
314.2
184.9
425.9
75.4
236.9
1004.0
309.0
1060.1
99.4
14.6
785.3
ρ(chelate ring) + τ (OH)
ρ(chelate ring) + τ (OH)
ν(Ru–N) + δ(OCO) + ν(C4–C7); chelate ring breathing
ν(Ru–N) + δ(OCO) + ν(C4–C7); chelate ring breathing
δ(RuNC6) + δ(COH) + δ(CCO)
δ(OCO) + δ(C2NC6) + δ(C3C4C5)
ω(OH)
δ(NRuN) + δ(C2C3C4) + δ(C5C6N) + ν(C2–C2’) + δ(COH)
δ(NruN) + δ(C2C3C4) + δ(C5C6N) + ν(C2–C2’) + δ(COH)
δ(C2NC6) + δ(C3C4C5) + ν(C2–C2’) + ν(C4–C7) + ν(C–O)
ω(CH)
ν(Ru–N) + δ(C2NC6) + δ(C2C3C4) + δ(C4C5C6) + τ (CH)
ν(Ru–N) + δ(C2NC6) + δ(C2C3C4) + δ(C4C5C6) + τ (CH)
ν(Ru–N) + δ(C2NC6) + δ(C2C3C4) + δ(C4C5C6) + τ (CH)
ν(Ru–N) + δ(C2NC6) + δ(C2C3C4) + δ(C4C5C6)
δ(C3C2N) + δ(COH) + ν(C–O) + δ(CCH)
δ(CCH) + δ(COH) + ν(C–O) + δ(C2’C2C3)
δ(COH) + δ(C2C3C4) + ν(C4–C7) + δ(CCH)
δ(C3C2C2’) + δ(CCH) + ν(C2–N)
δ(CCH) + δ(COH) + ν(C2–C2’) + δ(OCO)
δ(CCH) + δ(COH) + ν(C2–C2’) + δ(OCO)
δ(COH) + ν(C4–C7) + δ(CCH) + δ(OCO)
δ(COH) + ν(C4–C7) + δ(CCH) + δ(OCO) + ν(C2–C2’)
δ(CCH) + δ(C2’C2N) + ν(C2–C3) + ν(C5–C6)
δ(C2’C2N) + δ(C4C3C) + ν(C4–C3) + ν(C2–C2’) + δ(CCH)
ν(C2–C2’) + ν(C5–C6) + δ(CCH) + ν(C–N) + δ(C3C2N)
ν(C2–C2’) + ν(C5–C6) + δ(CCH) + ν(C–N) + δ(C3C2N)
ν(C–N) + ν(C4–C5) + δ(C3C4C) + δ(CCH) + δ(NRuN)
ν(C–N) + ν(C4–C5) + δ(C3C4C) + δ(CCH) + δ(NRuN)
ν(C2–C3) + ν(C5–C6) + δ(CCH) + δ(C3C4C5) + δ(C2’C2N)
ν(C–O) + δ(CCO) + δ(COH)
ν(C–O) + δ(CCO) + δ(COH)
ν(C–H)
ν(O–H)
ν(O–H)
B/w in print, colour online
Figure 4. Simulated Raman spectra of a) [Ru(II)(bpy)3-n (dcbpy)n ]2 + , b) [Rh(III)(bpy)3-n (dcbpy)n ]3 + for n = 0, 1, 2 and 3, calculated at
DFT/B3LYP/LANL2DZ level. The spectral lines were convoluted with Lorentzian distributions of 20 cm−1 linewidth.
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Figure 5. Scheme with the atom labelling used to describe the
vibrations of the ligands.
195
200
205
210
215
220
225
230
The vibration spectra of both families of complexes
under study are composed of 61, 67, 73, or 79 atoms, and
have 177, 195, 213, and 231 normal modes of vibration
for n = 0, 1, 2, and 3, respectively. Given the symmetry of
the complexes, the decompositions in normal modes are:
177 = 30a1 + 29a2 + 59e, 195 = 98a + 97b, 213 =
107a + 106b, and 231 = 39a1 + 38a2 + 77e. For the less
symmetric complexes, with n = 1 and 2, all modes are both
IR- and Raman-active. In the case of the more symmetric
n = 0 or 3 complexes, IR-active are the modes transforming
as a2 and e, whereas those transforming as a1 and e are
Raman-active [42]. A careful look at the values reported in
Table 1, however, shows very small but still non-zero IR
intensities for Raman-active modes and the reverse. This
is due to the fact that the software maintained the largest
Abelian group, C2 , instead of the full point group of the
complex, C3 . To better understand the vibration modes and
their symmetry we included in the supplementary materials
animations corresponding to the most intense peaks in both
the IR and Raman spectra.
Figures 3 and 4 allow the analysis of the role played
by the COOH groups. Compared to the prototypical
[Ru(bpy)3 ]2 + the complexes with n = 1, 2, and 3 display
a much richer spectrum due to the additional bands caused
by the COOH groups. The obvious thing to note is the increase with the number of dcbpy ligands, n, of the vibration
intensity of the modes involving COOH groups. The linear dependence with respect to n observed for the intensity
of the IR peaks at 3511, 3130, 1639, 1525, 1387, 1322,
1274, 1143, 1062, 1035, 863, 720, 617, and 544 cm−1 , as
well as the Raman peaks at 3512, 3130, 1640, 1593, 1525,
1455, 1411, 1326, 1275, 1254, 1143, 1062, 1006, 992, and
863 cm−1 , can provide a textbook example for the study of
the vibration spectra.
Also interesting is the inverse correlation, i.e. the decrease of the peak intensity with the number of COOH
groups at 1437 and 775 cm−1 in the IR and at 1305 and
748 cm−1 in the Raman spectra. These bands are diminished when replacing the H atom bound to C4 with COOH.
The bulky carboxyl groups hinder the out-of-plane wagging or twisting of the pyridine rings, shifting the mode to
5
lower frequencies. An increasing number of COOH groups
will shift more and more of the energy available for those
modes, leading to a decrease of the peak activity from n = 0
to 3.
We now proceed for a more systematic analysis of the most important features in the spectra of
[Ru(bpy)3-n (dcbpy)n ]2 + , noting the similarity between the
spectra of the Ru(II) and Rh(III) complexes, as shown in
Figure 2. We focus on the Ru(II) complexes both for their
practical importance and for the availability of some experimental and calculated spectra which allow a more straightforward comparison with our results.
We start with the O–H stretch observed at 3511 cm−1 in
both the IR and Raman spectra. The bands can be attributed
to the O–H in-phase and out-of-phase stretches, as it is well
established [60]. The bands are missing from the spectrum
of the parent, n = 0, compound and have an intensity that
increases proportional to n for the other complexes. The
O–H groups are also present in the scissor modes observed
in the IR fingerprint region, at 1143, 1062, and 1035 cm−1 ,
as well as the wagging modes at 617 cm−1 .
Furthermore, the presence of the carboxyl groups has
a clear mark in the strong C = O stretching mode at
1639 cm−1 in the IR and 1640 cm−1 in the Raman spectra,
which occurs together with the O–C–O and C–O–H bending modes. The scissor modes δ(COH) and δ(OCO) can
also be found in the fingerprint region, at 1322 cm−1 in IR
and 1326 cm−1 in Raman spectra. At lower frequencies, at
601 cm−1 strong O–C–O scissoring modes are present only
in the IR spectra of the n ≥ 1 complexes.
The low-intensity C–H stretches are present in all spectra, regardless of n, at 3130 cm−1 in the IR and Raman
spectra. Bending C–H modes are observed particularly in
the IR spectra at 1143 and 1062 cm−1 as well as in the
Raman spectra, at 1593, 1455, and 1254 cm−1 . However,
the bending modes present in the fingerprint region are not
pure, but mixed with other contributions. For instance, the
vibrations of the entire pyridine ring, as well as the deformations of the chelate ring also contribute to the C–H
bending modes.
The aromatic pyridine rings can withstand vibrations of
the C = C and C = N double bonds. The C = C bonds leave
a clear mark, regardless of n, through the stretching modes
located in the Raman spectra at 1593 (the most intense
band) and 1455 cm−1 and in the IR spectra at 1387 cm−1 .
The C = N bonds display a strong Raman stretching mode
at 1525 cm−1 . At 1524 cm−1 the activity is weaker and the
modes are active also in the IR.
The pyridine rings suffer vibrations as an entity at many
frequencies. Various types of C–C–C scissor modes are
active at frequencies such as 1254, 1143, and 1062 cm−1 .
The former mode is stronger in the Raman whereas the other
two are more intense in the IR spectra. The C–N–C scissor
modes of the pyridine rings occur at lower frequencies, such
as 1006, 992, 986, and 984 cm−1 together with stretches of
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255
260
265
270
275
280
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the metal–nitrogen bonds. The first three are particularly
strong in the Raman spectra.
The C–C σ -bonds connecting the pyridine rings, experience stretching vibrations at various frequencies, the
most important being 1595, 1455, 1411, and 1325 cm−1 ,
the first one being the most important, weaker in the IR but
stronger in the Raman spectra. The C–C interring vibrations
are mixed in the spectrum with δ(CCC) and δ(CCH) modes
of the pyridine rings, which occur together with various
vibration modes of the 5-membered chelate ring.
The metal–nitrogen vibrations are important for the induction of vibronic perturbations in the electron shells of
the excited complexes. The Ru–N stretching modes occur
first in the Raman spectra, with a strong signal at 1006 cm−1
and a weaker optical activity at 992 and 986 cm−1 . As discussed above, the metal–nitrogen stretching comes together
with a C–N–C scissor bending as well as chelate ring deformations. At 984 cm−1 the corresponding IR signal is
stronger. At lower frequencies, the deformation vibrations
of the metallic environment occur together with a bending
of the ligands. At 427 and 418 cm−1 we find chelate ring
breathing bands, the former present only in the Raman,
whereas the later active in both IR and Raman. At lower
frequencies, 373 and 363 cm−1 , the chelate rocking modes
are active mostly in the IR.
In the remaining of this section we will compare our
results to the experimental data available. For a proper
comparison, we represent in Figure 6 the Raman intensity, calculated keeping in mind not just the part intrinsic
to the scattering molecule (Gaussian’s Raman optical activity), but also the factor that depends on temperature (which
affects the population of the scattering vibrational state),
B/w in print, colour online
Figure
6. Simulated
Raman
intensity
of
[Ru(II)(bpy)3-n (dcbpy)n ]2 + , for n = 1 and 3, calculated
[61] at DFT/B3LYP/LANL2DZ level, at room temperature and
a laser excitation wavelength of 532 nm [39]. The spectral
lines were convoluted with Lorentzian distributions of 20 cm−1
linewidth.
and the factor that is dependent on the exciting laser frequency [61]. The relative height of the peaks is different in
Figure 6 with respect to Figure 4a mainly because of the
factor depending on the excitation frequency, which tends
to increase the low-frequency bands.
As mentioned in the introduction, except for the case of
[Ru(bpy)3 ]2 + [34–44] and a paper on [Ru(dcbpy)3 ]2 + [39]
there are no published experimental spectra or theoretical
results for the IR and Raman spectra of the complexes
calculated in this study. Therefore, for comparison, we will
also use some other data available for similar bipyridyl
complexes [40,62–64].
The key bands in the experimental Raman spectra available of [Ru(dcbpy)3 ]2 + [39] are located at 1618, 1546,
1480, 1433, 1373, 1298, and 1276 cm−1 . Similarly, for
[Ru(bpy)2 (dcbpy)]2 + [39], the main peaks observed experimentally are situated at 1542, 1375, and 1272 cm−1 . Our
calculations make possible the assignment of these bands
as shown below.
The 1618 cm−1 experimental peak likely corresponds
to the very intense 1593 cm−1 mode attributed to the ν(C2–
C3) and ν(C5–C6) stretches with some contributions from
δ(CCH) and δ(C3C4C5) scissoring vibrations. Correspondingly, in the Raman spectrum of the [Ru(bpy)3]2 + complex
[41,62], the bands of the ν(C2–C3) stretching vibrations of
pyridine are observed at lower frequencies, of 1608 cm−1 ,
whereas using the same scaling factor of 0.9614 [59] for the
entire frequency range, we obtain 1578 cm−1 . The presence
of the COOH groups in the [Ru(dcbpy)3]2 + complex shifts
that band to higher frequencies both in the experimental and
the calculated spectra.
The bands at 1546 cm−1 for [Ru(dcbpy)3]2 + ,
at 1542 cm−1 for [Ru(bpy)2 (dcbpy)]2 + [39], and at
1563 cm−1 for [Ru(bpy)3]2 + [41], may correspond to the
vibrations of the aromatic C = C and C = N bonds of the
pyridine rings, ν(C–N) and ν(C4–C5). Our results follow
a similar trend: 1525 cm−1 , 1522 cm−1 , and 1533 cm−1 ,
respectively.
Further, the peaks at 1480 cm−1 for the complex with
n = 3 [39] and at 1491 cm−1 for the one with n = 0 [41]
can be correlated with the vibrations of the interring C–C
σ -bond. Our calculations reflect the same trend, providing
frequencies of 1455 and 1467 cm−1 , respectively.
The next main experimental band for [Ru(dcbpy)3]2 + ,
located at 1433 cm−1 [39], may be attributed to the pyridine
ring deformations, particularly the δ(C2’C2N), δ(C4C3C),
and δ(CCH) scissor modes together with the ν(C4–C3),
ν(C4–C7), and ν(C2–C2’) stretches, with a calculated maximum at 1411 cm−1 . We note that the corresponding band
of [Ru(bpy)3]2 + , is very weak in the Raman spectrum.
Further down in the frequencies, the bands of the complex with the n = 3, situated at 1373 cm−1 , or for the one
with n = 1 at 1375 cm−1 [39], again have no clear correspondent in the experimental spectrum of n = 0 [41].
This band is more difficult to assign, as the modes that are
320
325
330
335
340
345
350
355
360
365
370
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380
385
390
395
400
405
410
415
420
relatively close in frequency are strongly active in the IR
and only very weak in the Raman spectra. A mode with a
high Raman intensity is found at 1326 and 1325 cm−1 for
the two complexes, respectively, and it consists of vibrations involving the COOH groups, such as the δ(COH) and
δ(OCO) scissoring modes and the ν(C4–C7) stretches.
We also note a reversed situation, where an intense
Raman band of [Ru(bpy)3]2 + [41], located at 1320 cm−1 ,
has no clear assignment in the [Ru(dcbpy)3]2 + spectra [39].
The intense band due to both the interring C–C σ -bond
stretch and the in-plane bending of the CH group which
is peaked at 1305 cm−1 in our calculated spectra. Similar
interring vibrations with a pronounced contribution from
δ(CCH) vibrations, have been observed at 1317 cm−1 in
the spectrum of the [Ru(bpy)2(BIK)]2 + complex [62].
The band at 1298 cm−1 in the experimental spectrum of the n = 3 complex [39] can be assigned to
the 1275 cm−1 theoretical mode, consisting of various
scissor modes, δ(CCH), δ(COH), and δ(OCO), together
with an interring stretch, ν(C2–C2’). The last main peaks
in the experimental Raman spectra of [Ru(dcbpy)3]2 +
and [Ru(bpy)2 (dcbpy)]2 + [39] are found at 1276 and
1272 cm−1 , respectively. The calculated spectra show intense maxima at 1254 and 1248 cm−1 , respectively, attributed mainly to the δ(C3C2C2’) and δ(CCH) bending
modes, together with a C–N stretch.
Unfortunately, the range of the experimental spectra
available does not extend below 1200 cm−1 , missing some
important features, particularly at 1006 cm−1 where we
calculated that the Ru–N stretching vibrations occur. Other
such calculated stretching modes can be found at 992, 986,
and 418 cm−1 . These vibrations are the most important for
the induction of vibronic perturbations in the electron shells
of the excited complexes. The Ru–N stretching vibrations
in the experimental spectra of [Ru(bpy)3]2 + are located at
371 cm−1 and correspond to the 353 cm−1 in our results,
occurring together with a chelate ring breathing [65].
We note that although our results describe accurately
the experimental data available, the exact position of the
peaks is systematically shifted towards lower frequencies
by a factor of roughly 0.984 compared to the experimental
data available [39]. The use of a standard scaling factor
of 0.9614 [59] over the entire range of frequencies leads
to an underestimation of the peak values. Based on our
results, a scaling factor of 0.9771 would have described
more accurately the actual positions of the vibration bands.
For comparisons of various scaling factors for different IR
regions see references [66–69].
3.2. Phosphorescence study
Spectral properties of the dye complexes are studied in
425 the framework of time-dependent density functional theory (TD DFT) [47]. In this scheme the excitation energies
∇ω can be determined from the poles of the ground state
7
linear polarisation propagator,
det E [2] − ωS [2] = 0,
(1)
where E[2] and S[2] are the electronic Hessian and overlap matrices, respectively. The transition moments can 430
be calculated from the residues of Equation (1) for the
singlet–triplet transitions. In the case of singlet–triplet transitions the zeroth-order contribution vanishes due to spinorthogonality. The first contribution to the transition moment then comes from the first-order perturbation theory 435
when the spin-orbit (SO) coupling operator is treated as
a perturbation. The sublevels of the triplet state are considered to be energy degenerate in the first order, so the
singlet–triplet transition moment reduces to:
∞
S0 |μˆ α |Sn Sn |Hˆ SO |T1k S0 |μˆ α |T1k = Mαk =
E(Sn ) − E(T1 )
n=0
+
∞
S0 |Hˆ SO |Tn Tn |μˆ α |T k 1
n=1
E(Tn ) − E(S0 )
,
(2)
where the summation over intermediate triplet states Tn 440
includes all three sublevels of each triplet state.
The radiative rate constant Ak and the phosphorescence
lifetime from one of the three sublevels
(indexed by k = x,
y, z) of the lowest triplet state T1k is given by
Ak =
3 k 2
1
4 3
M ,
=
αo E k
α
τk
3t0
α∈{x,y,z}
(3)
where t0 = (4π ε0 )2 3 /me e4 , α 0 is the fine-structure con- 445
stant, Ek is the transition energy, and Mα k is the α-axis
projection of the electric dipole transition moment between
the ground state and the k-spin level of the triplet state. The
radiative lifetime of the triplet state in the high-temperature
450
limit is estimated by [70]
1 1
1
=
.
τ
3 α∈{x,y,z} τk
(4)
It corresponds to averaging over all three sublevels when
they are in thermal equilibrium. We note that Equation (4)
is not strictly valid for the triplet states with high zero-field
splitting (ZFS) [71] but is applicable [72] tothe complexes Q1
discussed here, for which the six d electrons are paired. In 455
the present work the SOC operator in Equation (2) is used
in a semi-empirical effective single-electron approximation
[73], in which the number of electrons is reduced and the
two-electron part of SO coupling is removed, which greatly
460
simplifies the calculations.
The electronic transitions in vacuum and the phosphorescence lifetime calculations performed in the gas phase
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Table 2. Radiative phosphorescence lifetimes, τ (μs), of [Ru(II)(bpy)3-n (dcbpy)n ]2 + and [Rh(III)(bpy)3-n (dcbpy)n ]3 + complexes (n = 0,
1, 2, and 3), calculated with quadratic response DFT. ES-T (eV) is the S0 –T1 transition energy. Calculations are performed at the S0
optimised geometry in gas phase. The experimental values are from reference [1] and reference [76] for the Ru(II) and Rh(III) complexes,
respectively. RT = room temperature.
M
N
ES-T calc.
ES-T exp.
77 K
Ru(II)
Rh(III)
465
470
475
480
485
490
τ exp.
RT
77 K
Principal configuration
RT
0
2.38
2.04
13.9
0.60
1
2.19
2.02
10.5
0.46
2
2.23
14.0
3
2.28
11.5
0
2.91
1
2.84
4.99 103
2
2.83
4.53 103
3
2.83
5.10 103
2.77
2.70
5.93 103
with Dalton [58], with linear and quadratic response functions, respectively [74,75], are reported in Table 2 for all
six complexes. The values of the triplet–singlet transition
energies are compared, where data are available for experimental values obtained at 77 K and/or at room temperature.
The calculated S0 –T1 transition energies are systematically
larger than the experimental ones especially those measured at room temperature, by at most 14%. The values
determined at liquid nitrogen temperatures are much closer
to the calculated ones, within 5%. Such differences occur when computing vertical transitions. Calculations of
the transition energies were also performed using GAUSSIAN03 [57] with the same DFT functional and basis sets
and we found that the energy differences are smaller than
0.15%.
We note that in the case of the Rh(III) ion the transition energies are systematically larger than those for the
Ru(II) complexes. The composition of the S–T transitions
reveals a ligand-to-metal charge-transfer nature in the case
of Ru(II) and a ligand-to-ligand charge-transfer character
for the Rh(III) species, which is consistent with our previous
work regarding UV-Vis absorption based on singlet–singlet
transitions [45].
The calculated phosphorescence lifetimes are very different from Rh(III) to Ru(II) complexes, variations of two
orders of magnitude being observed. A probable explanation is related to the nature of the states involved in the
transitions from the perspective of the spin–orbit interaction. In the case of the Rh(III) complexes the metal ion has
only a small contribution to only one of the two states (less
2.0 103
0.015
Expansion of the special part of
the triplet state wave function
LUMO + 1 (dt2g π ∗ bpy ) →
HOMO (dz2 )
LUMO (dt2g π ∗ dcbpy ) → HOMO
(dz2 )
LUMO + 1 (dt2g π ∗ dcbpy ) →
HOMO (dz2 )
LUMO + 1 (dt2g π ∗ dcbpy ) →
HOMO (dz2 )
LUMO (dt2g π ∗ bpy ) → HOMO-2
(π bpy )
LUMO (dt2g π ∗ dcbpy ) →
HOMO-2 (π bpy )
LUMO + 1 (ddz2 π ∗ dcbpy ) →
HOMO-4 (π bpy )
LUMO (dt2g π ∗ dcbpy ) →
HOMO-7 (π dcbpy )
Coeff.
0.668
0.649
0.679
0.672
0.422
0.592
0.415
0.308
than 6% of the electron density), which leads to a weak SO
coupling, a small transition rate and a long lifetime (see
Table 3). In contrast, in the case of the Ru(II) complexes
the states participating in the transition have a more significant electron density on the metal ion (∼60%), leading
to stronger SO interactions and shorter phosphorescence
lifetimes.
The presence of the carboxyl groups within each family
of complexes leads to differences in the lifetimes within
25%, with no apparent systematic trend when considering
the COOH content.
The agreement between the calculated and experimental phosphorescence lifetimes is worsening with increasing
temperature. The data available for the [Rh(III)(bpy)3 ]3 +
complex show that our calculations are much closer to the
77 K value than that at the room temperature one [76]. This
is because the phosphorescence lifetime measured at the
room temperature includes a large contribution from the
non-radiative quenching [67]. We also note that the calculated transition energy is in better agreement with the value
measured at the lower temperature.
As no 77 K data is known to us for the case of Ru(II)
complexes, in order to check the reliability of our results
we note that both at 77 and ∼300 K experimental phosphorescence lifetimes values are available for similar systems.
For instance, for [Ru(II)(dmbpy)3 ]2 + the lifetimes are 4.6
and 0.95 μs, whereas for [Ru(II)(bpy)2 (dmbpy)]2 + , 5.2 and
0.44 μs, at 77 K and RT, respectively [77,78]. Moreover,
more recently, another complex, [Ru(II)(bpy)2 (L1)]2 + , was
reported with 5.23 and 0.22 μs, correspondingly [79]. The
495
500
505
510
515
520
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Table 3. Electron density (in %) on the various building blocks of [Ru(II)(bpy)3-n (dcbpy)n ]2 + and [Rh(III)(bpy)3-n (dcbpy)n ]3 +
complexes (n = 0, 1, 2, and 3), calculated by DFT/B3LYP/LANL2-DZVP for the key molecular orbitals.
[Ru(II)(bpy)3-n (dcbpy)n ]2 +
n=0
M
bpy
–COOH
n=1
n=2
n=3
HOMO
LUMO + 1
HOMO
LUMO
HOMO
LUMO + 1
HOMO
LUMO + 1
62.41
37.59
–
8.19
91.81
–
61.44
38.26
0.30
5.75
86.98
7.28
60.44
38.96
0.60
9.98
83.35
6.67
59.57
39.53
0.90
9.64
83.77
6.59
[Rh(III)(bpy)3-n (dcbpy)n ]3 +
n=0
M
bpy
–COOH
n=1
n=2
n=3
HOMO-2
LUMO
HOMO-2
LUMO
HOMO-2
LUMO
HOMO-2
LUMO
3.18
96.82
–
5.25
94.75
–
0.43
99.51
0.06
4.49
95.45
0.06
0.37
89.43
10.20
3.32
90.73
5.95
0.35
89.29
10.36
5.49
88.92
5.59
room temperature values of these systems are comparable to
the ones reported for [Ru(II)(bpy)3 ]2 + [1,76] which leads
525 us to speculate that the 77 K values might also be similar.
If that was true the measured values are still lower than the
ones we calculated for [Ru(II)(bpy)3-n (dcbpy)n ]2 + but in
reasonable agreement, especially considering the fact that
our DFT approach does not take into account the influence
530 of the temperature.
It is of interest that a comparative analysis of all complexes with respect to the requirements for the dyes in order
to be used in dye-sensitised solar cells. From this perspective, the energy level alignment between the substrate, the
dye, and the electrolyte is crucial for a good photovoltaic 535
conversion [80,81]. Figure 7 displays an energy diagram
with the conduction and valence band edges of the TiO2
[80], the energy levels of the singlet ground states, the lowest triplet excited state, and the sixth triplet excited state
of all the eight complexes under study, calculated for con- 540
sistency in water solvent, as well as the redox level of the
I3− /I− electrolyte [81].
B/w in print, colour online
Figure 7. Energy diagram showing the HOMO level (blue) which is taken as an origin for the singlet ground states energy levels,
the lowest triplet excited state (red) and the sixth triplet excited state (orange) levels of the various [Ru(II)(bpy)3-n (dcbpy)n ]2 + and
[Rh(III)(bpy)3-n (dcbpy)n ]3 + complexes for n = 0, 1, 2 and 3, calculated in solution by TD-DFT/B3LYP/LANL2-DZVP methods. The
conduction (red) and valence band (blue) edges of the TiO2 [80], as well as the redox level of the I3− /I− electrolyte [81] are also shown.
Next to the transition line is stated, in eV, the energy of the first (sixth) singlet–triplet transition for each complex.
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Figure 8. Isodensity surfaces (0.03 e/bohr3 ) of selected molecular orbitals of the [Ru(II)(bpy)2 (dcbpy)]2 + complex: a) singlet ground
state, S0 , b) triplet excited state, T3 , c) triplet excited state, T5 , and of the [Rh(III)(bpy)2 (dcbpy)]3 + complex: d) singlet ground state, S0 ,
e) triplet excited state, T3 , f) triplet excited state, T5 .
We find that, except for the n = 0 and 1 Ru(II) complexes, all dyes having the first six triplet excited states
545 lie below the CB edge of the semiconductor. Therefore, for
[Ru(II)(bpy)3 ]2 + and [Ru(II)(bpy)2 (dcbpy)]2 + some of the
triplet excited states may contribute to the electron injection into the TiO2 conduction band. In the other cases, the
low-lying triplet states cannot participate in charge injec550 tion, the photoelectron being lost by radiative deexcitation
to the ground state. Such phosphorescence processes are
detrimental to the efficiency of photovoltaic devices [82].
We display in Figure 8 the singlet ground state and two
triplet excited states of [Ru(II)(bpy)2 (dcbpy)]2 + , to illus555 trate the likelihood of charge transfer to the TiO2 nanoparticle. The singlet ground state is fairly localised on the metal
ion, whereas the triplet excited states are delocalised over
the bipyridyl ligand, with a modest contribution from the
t2g -like orbitals. The electron transfer to the semiconducting oxide is more likely from the orbital with high electron 560
density on the dcbpy ligand, due to the likely binding to
titanium through the anchoring COO- groups.
For contrast, we also display in Figure 8
the electron density of the corresponding MOs of
[Rh(III)(bpy)2 (dcbpy)]3 + . The electron transfer is highly 565
unlikely because of the poor alignment with the conduction band edge of the oxide (see Figure 7). The very weak
electron density on the Rh(III) ion illustrates the data presented in Table 3, for explaining the long phosphorescence
570
lifetimes.
To strengthen this argument, we provide in Table 3 the
Mulliken charge for the closed shell ground state of all
Table 4. Mulliken charge on the various building blocks of [Ru(II)(bpy)3-n (dcbpy)n ]2 + and [Rh(III)(bpy)3-n (dcbpy)n ]3 + complexes
(n = 0, 1, 2, and 3), calculated by DFT/B3LYP/LANL2-DZVP for the singlet ground state.
Ru
Q2
M
bpy
dcbpy
2 COOH
Rh
n=0
n=1
n=2
n=3
n=0
n=1
n=2
n=3
0.892
0.370
–
–
0.889
0.387
0.522
−0.184
0.890
0.400
0.533
−0.178
0.886
–
0.543
−0.172
0.780
0.740
–
–
0.774
0.745
0.779
−0.044
0.771
0.750
0.783
−0.043
0.764
–
0.787
−0.042
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complexes. In the case of Ru(II) complexes, the charge is almost equally distributed between the metal ion (∼0.89) and
575 the three ligands (∼3∗ 0.37), whereas for the Rh(III) complexes the charge is located mostly on the ligands (∼3∗ 0.74
compared to ∼0.78 on the metal). As expected, the extra
electron leaving the Rh(III) ion is distributed on the ligands.
It is worthwhile to note in Table 4 the charge density on
580 the COOH groups. The highest negative charge density on
carboxyl groups occurs in the case of the Ru(II) systems,
particularly for the n = 1 complex. This result is relevant
to DSSCs, showing that the charge transfer is optimised in
the case of [Ru(II)(bpy)2 (dcbpy)]2 + .
585
590
595
600
605
610
615
620
625
4. Conclusions
Based on DFT calculations we simulated the IR
and Raman spectra of [Ru(bpy)3-n (dcbpy)n ]2 + and
[Rh(bpy)3-n (dcbpy)n ]3 + complexes. We found that the
spectra are not very sensitive to the replacement of the metal
ion, the overall qualitative behaviour being similar. The effect of changing the transition metal ion appears stronger
in the Raman spectra, with a significant optical activity
drop in the fingerprint region. The replacement of Ru(II)
with Rh(III) leads in the IR spectra to the enhancement
of the high-frequency C–H stretch and a weakening of the
metal–nitrogen stretch. Also, as expected, the larger mass
of the Rh(III) ion leads to a shift to lower frequency of the
vibration peaks, especially in the high-frequency regime.
The presence of carboxyl groups leads to a richer spectrum due to the additional bands caused by the COOH
groups. The vibration intensity of the modes involving
COOH groups increases proportionally with the number
of dcbpy ligands, n, providing a textbook example for the
study of vibration spectra. Also, some bands are inhibited,
as the replacement of the H atom bound to C4 with bulky
carboxyl groups hinder the out-of-plane wagging or twisting of the pyridine rings.
The comparison with the limited experimental data
available allowed the assignment of the Raman bands for
[Ru(dcbpy)3 ]2 + and [Ru(bpy)2 (dcbpy)]2 + . Moreover, our
results are compatible with previous experimental and theoretical studies of [Ru(bpy)3 ]2 + as well as various other
complexes with substituted ligands. Although our results
describe accurately the experimental data available, the exact position of the peaks is systematically shifted towards
lower frequencies compared to the experimental data available. The use of a standard scaling factor of 0.9614 over the
entire range of frequencies leads to an underestimation of
the peak values, whereas a scaling factor of 0.9771 would
have described more accurately the actual positions of the
vibration bands.
The composition of the transitions between the triplet
excited states and the singlet ground state reveals a ligandto-metal charge-transfer in the case of Ru(II) and a ligandto-ligand charge-transfer for Rh(III), consistent with our
11
previous work regarding absorption singlet-to-singlet transitions. The calculated phosphorescence lifetimes are two
orders of magnitude larger for Rh(III) than for Ru(II) complexes, likely due to the nature of the states involved in
the transitions. In the case of the Ru(II) complexes the 630
states participating in the transition have a more significant electron density on the metal ion, leading to a stronger
SO interaction and shorter phosphorescence lifetimes. For
[Ru(II)(bpy)3 ]2 + and [Ru(II)(bpy)2 (dcbpy)]2 + some of the
triplet excited states may have some contribution to the elec- 635
tron injection into the TiO2 conduction band, whereas in the
other cases the photoelectron is, likely, lost by radiative deexcitation to the ground state. Our present study strengthens
our previous conclusion that, of the eight dyes studied, the
Ru(II) complexes with n = 1 or 2, [Ru(II)(bpy)2 (dcbpy)]2 + 640
in particular, are most suited for being used in DSSCs.
Acknowledgements
The authors acknowledge partial financial support as follows:
M.F., F.C., and M.A.G from ANCS, grant PN2-Capacitati-M3
contract 517/2011, C.I.O. from CNCS, grant PN2-RU-PD contract 172/2010 and B.F.M from the Ministry of Education and
Science of Ukraine. The authors thank Professor Ionel Humelnicu, for useful discussions.
645
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Supplementary information
See the supplementary materials for tables of the frequencies, IR
and Raman intensities and assignment of the vibration modes,
13
tables of the triplet–singlet transition energies and phosphorescence lifetimes in vacuum, and tables of the triplet–singlet
transition energies in water solvent for all eight complexes:
[Ru(bpy)3-n(dcbpy)n]2 + and [Rh(bpy)3-n(dcbpy)n]3 + , with n
= 0, 1, 2, and 3.
820