Download Density functional studies on lanthanide (III) texaphyrins (Ln

MOLECULAR PHYSICS, 10 AUGUST 2003, VOL. 101, NO. 15, 2427–2435
Density functional studies on lanthanide (III) texaphyrins
(Ln-Tex2 þ , Ln ¼ La, Gd, Lu): structure, stability and
electronic excitation spectrum
XIAOYAN CAO1,2 and MICHAEL DOLG1*
1
2
Institut für Theoretische Chemie, Universität zu Köln, D-50939, Germany
Biochemistry Department, Zhongshan University, Guangzhou, 510275, P.R. China
(Received 26 November 2002; revised version accepted 18 February 2003)
Density functional calculations have been performed to study the molecular structure and
chemical properties of selected lanthanide(III) texaphyrins (Ln-Tex2 þ , Ln ¼ La, Gd, Lu). The
lanthanide element is found to reside above the mean N5 texaphyrin plane, and the larger the
cation, the greater the observed out-of-plane displacement. It is concluded that the lanthanide
cation is tightly bound to the macrocyclic skeleton, yielding a stable structure. However, the
chemical properties of Ln-Tex2 þ are found to be only slightly affected by the substitution of
the lanthanide element. A low-energy LUMO is found for the Ln-Tex2 þ (Ln ¼ La, Gd, Lu),
which are therefore easily reduced in an electron-rich environment. Two characteristic bands
are obtained in the calculated electronic excitation spectrum (a high-energy band at
454–462 nm and a low-energy band at 681–686 nm). The intensity of the high-energy band
is much larger than that of the low-energy one, yielding a rather unique spectral feature.
1. Introduction
The texaphyrins are tripyrrolic, penta-aza macrocycles that have a strong but ‘expanded’ resemblance to
the porphyrins and other naturally occurring tetrapyrrolic prosthetic groups [1, 2]. In contrast to porphyrins,
the texaphyrins are ligands that contain five, rather than
four, coordinating nitrogen atoms within their central
core. This central core is roughly 20% larger than that
of the porphyrins, and therefore the texaphyrins have an
ability to form stable 1 : 1 complexes with a range of
larger metal cations, including specifically the trivalent
ions of the lanthanide series (cf. figure 1). The
lanthanide (III) texaphyrins were first synthesized and
structurally characterized by Sessler et al. in 1993 [3].
Using single-crystal X-ray diffraction analysis, they
found that the bound metal cation is situated above
the mean N5 texaphyrin plane and the structures do
reflect the metal employed, i.e., the larger the metal
cation, the greater the out-of-plane displacement [3].
Since then much experimental work has been done to
study the chemical properties of lanthanide (III)
texaphyrins and great progress has been made in recent
years in assessing their physical properties. In analogy to
porphyrins, scientists observed two bands (Soret-type
band and Q-type band) for lanthanide (III) texaphyrins
* Author
uni-bonn.de
for
correspondence.
e-mail:
dolg@thch.
by UV-vis and fluorescence spectroscopy. However, the
texaphyrins display rather unique spectral features since
the intensity of the Soret-type band is much higher than
that of the Q-type band [4, 5]. Compared to typical
porphyrins the Q-type bands are substantially redshifted (by >100 nm) [4]. These water-soluble metallotexaphyrin complexes are known to contain a low-lying
LUMO and were found to react with solvated electrons,
yielding the corresponding one-electron reduced metallotexaphyrins [6, 7]. The most useful discovery for
lanthanide (III) texaphyrins may be that these compounds play an important role in such diverse and
potentially beneficial areas as X-ray radiation therapy
(XRT), photodynamic therapy (PDT) for oncology,
photoangioplasty (PA), and the light-based treatment of
age-related macular degeneration (AMD) [7]. They are
also able to function as tumour-selective magnetic
resonance imaging (MRI) detectable radiation enhancers [8]. Several of these systems, notably motexafin
gadolinium (Gd-Tex, XCYTRINÕ ) and motexafin
lutetium (Lu-Tex, LUTRINÕ ), cf. figure 1b, are
attractive candidates for a range of medically relevant
applications and are at present being evaluated in
advanced clinical trials [9, 10].
From the theoretical perspective, to our knowledge
only a simple perimeter model was used to analyze
the magnetic circular dichroism (MCD) spectra of
texaphyrins by Waluk and Michl in 1991 [11], whereas
Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/0026897031000108069
2428
X. Cao and M. Dolg
OH
18
16
19
20
17
15
3
14
N
N4
21
5
Ln
13 12
11
2+
22
1
2
N
10
N
N
23
R
R
6
7
9
lanthanide (III) texaphyrins (Ln-Tex2 þ , Ln ¼ La, Gd,
Lu; cf. figure 1a) using relativistic energy-consistent
ab initio pseudopotentials for the lanthanide metals.
In order to be able to deal with complexes as large as
the lanthanide (III) texaphyrins and to eliminate a large
part of the difficulties associated with the (partially
occupied) lanthanide 4f shell, we adopt a 4f-in-core PP
approach [17, 28]. The main aims are to get the
molecular structure, metal-ligand binding energy, electron affinity, and electron excitation spectrum for LaTex2 þ , Gd-Tex2 þ and Lu-Tex2 þ . The trends in the
lanthanide series will be discussed.
8
OH
Ln=La, Gd, Lu
a) R=O(CH2)3OH, texaphyrin lanthanide
2. Method
The method of relativistic energy-consistent ab initio
pseudopotentials (PPs) is described in detail elsewhere
[17, 18, 28] and will be outlined here only briefly. The
valence-only model Hamiltonian for a system with n
valence electrons and N nuclei with charges Q is given as
Hv ¼ b) R=O(CH2CH2O)3CH3, motexafin lanthanide
Figure 1. Lanthanide (III) texaphyrin
(Ln-Tex2 þ , Ln ¼ La, Gd, Lu) structures.
and
n
n
N
X
X
1X
1
QI QJ
i þ
þ Vav þ
:
2 i
r
rIJ
i<j ij
I<J
motexafin
results of first-principles electronic structure calculations
are not available. The numerous experimental studies for
complexes with different lanthanide centers and different
ligand side chains in varying solvents make a systematic
theoretical study of trends along the lanthanide series
desirable. At present theoretical chemistry investigations
on systems containing f elements are still a considerable
challenge [12–14]. The extremely complex electronic
structure of the f-elements, large relativistic effects and
strong electron correlation pose considerable difficulties
to theoretical work. Despite these difficulties the
relativistic ab initio pseudopotential (PP) method has
been proven to be one of the most successful approaches
for heavy-element chemistry [15], where the explicit
quantum chemical treatment is restricted to the valence
electrons and relativistic effects are only implicitly
accounted for by a proper adjustment of the free
parameters in the valence model Hamiltonian. Several
sets of such effective core potentials (ECPs), both of the
energy-consistent [16–18] and the shape-consistent PP
variety [19–24], have been published for the f elements.
Recently model potentials (MPs) also became available
[25, 26].
In recent years it has become a routine approach to
use pseudopotentials in connection with DFT. Although
most of the pseudopotentials have not been designed for
such calculations, the results are often quite accurate, cf.
e.g. [27]. In this paper, we present a DFT study of
Here i and j are electron indices and I, J are nuclear
indices. In the usual approximation the molecular
pseudopotential Vav is a superposition of atom-centred
potentials
Vav ¼
N
X
I
Vav
:
I
I
Vav
denotes a spin-orbit averaged relativistic PP in
a semilocal form for a core with charge QI
n
n X
X
QI X
I
Vav
¼
þ
AIlk expðaIlk r2iI ÞPIl :
riI
i
i l;k
PlI is the projection operator onto the Hilbert subspace
of angular momentum l with respect to centre I. The free
parameters AIlk and aIlk are adjusted to reproduce
the valence total energies of a multitude of low-lying
electronic states of the neutral atom I and its ions
[29]. Large-core PPs for lanthanides have been used, i.e.,
the 1s–4f shells were included in the PP core, while all
others with a main quantum number larger than 4 were
treated explicitly (11 valence electrons for La, Gd, Lu).
The reference data used to determine Vav have been
taken from relativistic all-electron (AE) calculations
using the so-called Wood-Boring (WB) scalar-relativistic
Hartree–Fock (HF) approach. Both AE WB as well as
PP calculations have been performed with an atomic
finite-difference HF scheme in order to avoid basis set
effects in the determination of the PP parameters.
The standard (7s6p5d)/[5s4p3d] valence basis sets
augmented by a (1s1f) set [17] were used for the
Density functional studies on lanthanide (III) texaphyrins
lanthanides. All other atoms were treated at the AE
level. The standard double-zeta (DZ, (8s4p)/[4s2p] for
C, N, O and (4s)/[2s] for H), and double-zeta plus
polarization (DZP, DZ augmented by a (1d) set for C,
N, O or a (1p) set for H) basis sets were used. For
nitrogen, besides DZ and DZP, the polarized valence
tripe-zeta (TZVP, (11s6p)/[5s3p] augmented by a (1d) set)
basis sets were applied too. All basis sets were taken
from the basis set library of the TURBOMOLE program
system [30].
All calculations were carried out with the
TURBOMOLE program package [30]. The computational method was Becke’s semi-empirically parameterized gradient-corrected exchange-correlation hybrid
density functional approach (B3LYP) [31–33]. The
geometry of Ln-Tex2 þ (Ln ¼ La, Gd, Lu) was fully
optimized without any symmetry restriction at the DFT/
B3LYP level. The electron affinity was calculated by
subtracting the energy of Ln-Tex2 þ from Ln-Tex þ .
Similarly, the metal-ligand binding energy was obtained
by subtracting the energy of Ln-Tex2 þ from the possible
dissociation products (Lnn þ , Tex2 n, n ¼ 1, 2, 3).
The electronic excitations were treated within the
adiabatic approximation of time-dependent density
functional theory [34, 35] and the 20 energetically lowest
excitations were calculated. For every calculated spectral line, one Gaussian function (a0 exp [ b(x x0)2])
was used to represent the contribution to the spectrum.
Here a0 is the calculated oscillator strength, x0 is the
calculated wavelength, and b is a broadening parameter
here taken as 0.001. The continuous spectrum in a given
interval was obtained pointwise, as the sum over the 20
Gaussian functions, for each wavelength x.
3. Results and discussion
Before we discuss the results for the structure and
chemical properties in more detail let us first check
the performance of the applied basis sets. Three basis
sets were used, i.e., A: DZ for C, H, O, N; B: DZP for
C, H, O, N; C: DZ for C, H, O, and TZVP for N;
standard (7s6p5d)/[5s4p3d] valence basis sets augmented
by a (1s1f) set for lanthanides in A, B, and C. For bond
lengths and bond angles stable results are obtained for
the three different basis sets, i.e., the differences for
bond lengths and bond angles are at most 0.01 Å, 0.6,
respectively. Similar conclusions are drawn from calculations for the electron affinity and the optical spectrum,
e.g., for the electron excitation spectrum of Lu-Tex2 þ
the highest peak is at 463, 462, and 466 nm for basis sets
A, B, and C, respectively; the corresponding electron
affinities are 7.64, 7.53, and 7.63 eV, respectively.
However the polarization function (d) proved to be
important for N in calculations for the metal-ligand
binding energy, i.e., a very similar metal-ligand binding
2429
energy is obtained for basis sets B and C (the difference
is at most 0.5 eV), whereas for basis A the difference to
B and C mounts up to 1.4 eV. Therefore the average
values for basis B and C are calculated and used for
the discussions below.
3.1. Molecular structures
The most important geometrical parameters of the
fully optimized structures are listed in table 1. For all
Ln-Tex2 þ (Ln ¼ La, Gd, Lu) it is found that the metal
cation is bound above the mean N5 plane, i.e., LaTex2 þ : 0.73 Å, Gd-Tex2 þ : 0.34 Å, Lu-Tex2 þ : 0.02 Å.
The distance of the lanthanide element to the mean N5
plane does reflect the size of the metal cation, i.e., the
larger the ion, the longer the distance obtained. The
smallest lanthanide (III) cation lutetium (III) is found to
almost reside in the mean N5 texaphyrin plane. Our
findings agree with the discovery of experimentalists,
i.e., the single-crystal X-ray diffraction analysis for
lanthanide (III) texaphyrins shows that the cation is
bound 0.91 Å for La, 0.61 Å for Gd, and 0.27 Å for
Lu above the mean N5 texaphyrin plane [3].
The experimental values are slightly larger than our
calculated values since in the real systems some solvent
molecules are bound to the metal, i.e., 10-coordinate
lanthanum (III), 9-coordinate gadolinium (III), and
8-coordinate lutetium (III) were observed, exhibiting a
somewhat larger displacement of the metal from the
mean N5 plane. The calculated Ln-N bond lengths
decrease with the increase of the nuclear charge, i.e., LaTex2 þ : 2.432–2.613 Å, Gd-Tex2 þ : 2.339–2.513 Å, LuTex2 þ : 2.285–2.462 Å, whereas the average N–Ln–N
angles become larger, i.e., for Gd-Tex2 þ and Lu-Tex2 þ
the average N–Ln–N angle is at least 2.5 and 3.1 larger
2þ
than that for La-Tex . On the other hand, bond
distances and bond angles which exclude the metal are
only slightly affected by the substitution of different
lanthanide (III) cations, e.g., the change of the average
internal angle about C (or N) and its next-adjacent atom
within the ring is at most 1.5 .
3.2. Charge distribution and frontier orbitals
The Mulliken orbital populations (cf. table 2) show
only small charge populations in the f symmetry for La
(0.04) and Gd (0.01), whereas no charge population in
the f symmetry is found for Lu (0.00). We note that the
f-in-core PPs applied for the lanthanides in this work
attribute 0(La), 7(Gd), and 14(Lu) 4f electrons to the
core, but allow for higher non-integral 4f occupations for
La and Gd by means of a modified f projector [17, 28].
Therefore our findings may imply the weak participation
in chemical bonding of the 4f shell of La. A relatively
constant 5d occupation of 0.8 electrons is observed for
all complexes indicating covalent metal–ligand bonding
2430
Table 1.
X. Cao and M. Dolg
Selected five bond lengths (Å) and angles (deg) for lanthanide (III) texaphyrin complexes (Ln ¼ La, Gd, Lu) calculated
at the B3LYP level.a
La
N3
N2
N4
N5
N1
D(N5)c
C16,C11d
C21,C6d
N5,N1d
Npe
Np,ie
Nie
Gd
Lu
Ab
Bb
Cb
Ab
Bb
Cb
Ab
Bb
Cb
2.520
2.428
2.429
2.613
2.612
0.69
129.3
118.8
125.0
75.2
65.8
62.1
2.526
2.433
2.434
2.613
2.614
0.75
129.3
118.7
124.7
74.7
65.3
61.5
2.525
2.434
2.436
2.613
2.614
0.74
129.1
118.5
124.3
74.8
65.4
61.6
2.429
2.336
2.338
2.513
2.513
0.28
128.9
118.6
124.6
78.0
68.3
64.5
2.437
2.342
2.342
2.513
2.513
0.39
129.0
118.5
124.4
77.5
67.9
64.0
2.436
2.340
2.341
2.513
2.512
0.35
128.9
118.4
124.0
77.7
68.1
64.1
2.385
2.284
2.284
2.471
2.468
0.02
128.0
118.0
123.3
78.6
69.0
64.7
2.385
2.285
2.284
2.460
2.456
0.03
128.3
118.0
123.3
78.6
69.0
64.9
2.389
2.286
2.286
2.465
2.462
0.02
128.1
117.9
122.9
78.6
69.1
64.7
a
Unless otherwise noted, the distance (Å) given is for the separation between the indicated atom and the trivalent lanthanide
cation. 46-, 53-, and 60-electron core PPs selected for La, Gd, and Lu, respectively. Standard (7s6p5d)/[5s4p3d] valence basis sets
augmented by (1s1f) sets used for lanthanides.
b
A:DZ basis sets for C, H, O; N; B: DZP basis sets for C, H, O; N; C: DZ basis sets for C, H, O and TZVP for N.
c
The distance (Å) to the lanthanide (III) cation from the average plane through the five nitrogen atoms.
d
Refers to the average internal angle about this atom and its next-adjacent atom within the ring; i.e., C16,C11 denotes the average
angle about these two mesolike methine carbons, namely C17–C16–C15 and C12–C11–C10, respectively.
e
Np refers to the average N–Ln–N angle involving adjacent pyrrole nitrogens, i.e., N3–Ln–N4; Np,i refers to the average
N–Ln–N angle involving a pyrrole nitrogen and that of its adjacent imine; Ni is the N–Ln–N angle defined by the two imine
nitrogens.
Table 2.
Mulliken orbital populations and atomic charges (Q) on Ln (Ln ¼ La, Gd, Lu) and nitrogens (TZVP basis sets were used
for metal and nitrogen) in lanthanide (III) texaphyrinsa.
s
p
d
f
Q
La
N3
N2
N1
N5
N4
2.04
3.59
3.59
3.62
3.62
3.59
5.82
3.78
3.86
3.87
3.87
3.87
0.82
0.03
0.03
0.03
0.03
0.03
0.04
–
–
–
–
–
2.27
0.39
0.48
0.52
0.52
0.49
Gd
N3
N2
N1
N5
N4
2.08
3.55
3.55
3.61
3.61
3.56
5.90
3.78
3.91
3.89
3.89
3.92
0.77
0.03
0.03
0.03
0.03
0.03
0.01
–
–
–
–
–
2.24
0.36
0.49
0.52
0.52
0.50
Lu
N3
N2
N1
N5
N4
2.34
3.53
3.52
3.60
3.60
3.52
6.05
3.66
3.84
3.83
3.84
3.84
0.78
0.03
0.03
0.03
0.03
0.03
0.00
–
–
–
–
–
1.83
0.22
0.38
0.46
0.47
0.39
a
A 5s25p65d16s2 ground-state valence subconfiguration is considered for the lanthanide elements; 0, 7 and 14 electrons in the 4f
shell are attributed to the PP core for La, Gd and Lu, respectively.
2431
Density functional studies on lanthanide (III) texaphyrins
Table 3.
Calculated Ln-Tex2 þ (Ln ¼ La, Gd, Lu) bond energies (Ebond), electron affinities (EA), HOMO and LUMO energies,
all in units of eV.
La
Ebondb
Ebondc
Ebondd
EA
EHOMO
ELUMO
Gd
Lu
Aa
Ba
Ca
Aa
Ba
Ca
Aa
Ba
Ca
33.32
17.11
17.11
11.59
11.59
7.60
10.43
8.65
32.39
15.98
15.98
10.36
10.36
7.49
10.52
8.54
31.98
15.80
15.80
10.24
10.24
7.59
10.44
8.65
35.74
18.60
18.60
12.40
13.11
7.61
10.44
8.67
34.76
17.42
17.42
11.02
11.84
7.51
10.54
8.57
34.33
17.24
17.24
10.90
11.72
7.61
10.44
8.67
37.70
19.79
20.21
11.77
14.87
7.64
10.45
8.70
36.72
18.61
19.03
10.49
13.59
7.53
10.54
8.59
36.29
18.42
18.84
10.36
13.46
7.63
10.45
8.69
a
A, B, C: basis sets cf. table 1.
Ebond ¼ E(Ln-Tex2 þ ) E(Ln3 þ ) E(Tex ) the ground state configuration of La3 þ , Gd3 þ and Lu3 þ are d0 1S0, f7d0 8S7/2
and f14d0 1S0, respectively.
c
Ebond ¼ E(Ln-Tex2 þ ) E(Ln2 þ ) E(Tex), first line: the ground state configurations of La2 þ , Gd2 þ and Lu2 þ are d1 2D3/2,
7 19
f d D2, and f14s1 2S1/2, respectively; second line: the configurations of La2 þ , Gd2 þ and Lu2 þ are d1 2D3/2, f7d1 9D2 and f14d1 2D3/2,
respectively.
d
Ebond ¼ E(Ln-Tex2 þ ) E(Ln þ ) E(Tex þ ), first line: the ground state configurations of La þ , Gd þ , and Lu þ are d2 3F2,
f7d1s1 10D5/2, and f14s2 1S0, respectively; second line: the configurations of La þ , Gd þ and Lu þ are d2 3F2, f7d2 10F3/2 and f14d2 3F2,
respectively.
b
contributions from this shell, i.e., substantial deviations
from a purely ionic complex between Ln3 þ [4fn] 5s25p6
and Tex1 ions. It is also noteworthy that the 6s
occupation increases from 0.04 for La-Tex2 þ to 0.34 for
Lu-Tex2 þ . We attribute both the constant 5d and
increasing 6s occupations to increasing relativistic effects
along the lanthanide series as well as to shell structure
effects due to the filling of the 4f shell, i.e. the lanthanide
contraction (cf., e.g., [36] for hri-expectation values and
orbital energies): the 6s orbital contracts significantly
(Dhri6s ¼ 0.34 Å) and gets energetically stabilized
(D6s ¼ 1.15 eV), when going from La to Lu. In
contrast the 5d orbital contracts only slightly
(Dhri5d ¼ 0.08 Å) but becomes significantly less stable
(D5d ¼ 1.31 eV). Whereas the orbital contraction makes
the cation smaller and allows the formation of nearly
planar complexes with higher stability, the orbital
stabilization/destabilization clearly favors a charge
transfer from the ligand to the metal 6s orbital. As a
result an increasing ligand oxidation is found to
accompany the insertion of the lanthanide element, i.e.,
the N5 carry decreasing negative charges (La-Tex2 þ :
2.40, Gd-Tex2 þ : 2.39, Lu-Tex2 þ : 1.92, cf., table 2)
and the metals carry decreasing positive charges
(La-Tex2 þ : 2.27, Gd-Tex2 þ : 2.24, Lu-Tex2 þ : 1.83, cf.
table 2). Therefore the nitrogens tighten up the metal and
high metal-ligand binding energies for all lanthanide
(III) texaphyrins are expected.
A quite low LUMO energy is obtained for Ln-Tex2 þ ,
i.e., the LUMO is only 1.87 eV higher than the
HOMO (table 3). Therefore one can expect that the
Ln-Tex2 þ easily absorb electrons in an electron-rich
environment. It is worthwhile to mention that the
energies of the HOMO and LUMO for Ln-Tex2 þ are
almost unaffected by the substitution of metal cation,
i.e., for La-Tex2 þ , Gd-Tex2 þ , and Lu-Tex2 þ the difference is at the most 0.01 eV for the HOMO and 0.06 eV
for the LUMO. Therefore very similar chemical properties are expected for all Ln-Tex2 þ (Ln ¼ La, Gd, Lu)
complexes.
3.3. Electron Affinity and Electronic Spectrum
The electron affinity is an important chemical
property related to the LUMO, and crucial for the
role of Gd-Tex2 þ as an in vivo X-ray radiation enhancer
(XCYTRINÕ , motexafin gadolinium, figure 1b) [7].
MRI can be used to visualize that the highly paramagnetic Gd-Tex2 þ localizes in cancerous lesions. It is
believed that it captures electrons formed as a result of
the interaction of X-rays with water at nearly diffusion
control rates and, in the absence of oxygen, thus leads
to an augmented concentration of hydroxyl radicals,
which are important and known cytotoxins in XRT.
On the other hand, in the presence of oxygen, the
electron capture product Gd-Tex þ reacts with oxygen
to form superoxide anion as a reactive oxygen species
(ROS) via a fast equilibrium. It is hypothesized that GdTex2 þ in combination with X-rays leads in vivo to a
cascade-like cell killing process. The in vitro experiments
have also proven that Ln-Tex2 þ is very easily and
quasi-reversibly reduced to Ln-Tex þ (E1/2 0.27 V
X. Cao and M. Dolg
1
a
0.8
Intensity (AU)
versus Ag/AgCl) and Ln-Tex (E1/2 0.75 V vs. Ag/
AgCl) [6]. High electron affinities were obtained for
these complexes in the present DFT calculations, i.e.,
La-Tex2 þ : 7.54, Gd-Tex2 þ : 7.56, Lu-Tex2 þ : 7.58 eV.
The main contributions for the LUMO are from atomic
orbitals of the main group elements, i.e., N1, N3, N5,
C7, C9, C11, C16, C18, C20, C22, and C23. Therefore
the added electron is most likely going to the ligand
rather than going to the metal, thus explaining the
nearly metal-independent electron affinity and reduction
potentials.
It is fair to note that 4f-in-core PPs cannot model an
accommodation of the additional electron in the 4f shell
of La and Gd. Such a possibility is however very
unlikely, since the La 4f shell is quite unstable with
respect to explicit occupation and the Gd 4f shell is
stabilized by half filling, each added electron causing
a large unfavorable 4f intrashell electron repulsion.
Moreover, addition of an electron to the 4f shell
increases the ionic radii and would result in less planar
and less strongly bound complexes. From the experimental point of view the unfavorably high reduction
potentials of the Ln(III)/Ln(II) couples rule out a
reduction of the metal [37].
In analogy to porphyrins the measured and calculated
electron excitation spectra of lanthanide (III) texaphyrins
exhibit two dominant bands. The texaphyrin bands are
red-shifted by 60–80 nm compared to the porphyrin
bands, most likely as a consequence of the larger
p-electron system (22p-electrons versus 18p-electrons).
The intensity of the high-energy band is much higher than
that of the low-energy band, showing a rather unique
spectral feature, cf., figures 2–4. The spectrum is slightly
affected by the substitution of the metal cation, e.g., the
highest peak is at 457, 454, and 462 nm for La-Tex2 þ ,
Gd-Tex2 þ , and Lu-Tex2 þ , respectively. Our results agree
well with the experimental findings, e.g., for Lu-Tex2 þ
(figure 1a) the calculated stronger band is at 462 nm and
the weaker one at 681 nm, whereas the experimental
optical spectrum of the PDT photosensitizer Lu-Tex
(LUTRINÕ , motexafin lutetium, figure 1b) in aqueous
5% mannitol [4, 5] exhibits a stronger band at 475 nm and
a weaker band at 732 nm. The light absorption in the farred portion of the visible spectrum (>700 nm) where
blood and bodily tissues are most transparent is ideal for
an effective photosensitizer. This part of the spectrum is
especially sensitive to the additional ligation of the
lanthanide (III) cation by solvent molecules or counter
ions as well as to variations in the Tex anion side
chains. Since the actual ligation of Ln-Tex2 þ localized in
cancerous tissue is not known, we performed model DFT
calculations using DZ basis sets on Gd-Tex2 þ complexes
with one bidentate NO
counter ions,
3 and two CH3O
yielding the experimentally observed 9-fold coordination
0.6
0.4
0.2
0
350
450
550
Wavelength (nm)
650
750
Figure 2. The electronic spectrum of La-Tex2 þ in arbitrary
units (AU) from time-dependent DFT/B3LYP calculations (H, C, N, O: DZP, La: TZVP); a: simulated
spectrum by superposition of Gaussian functions, cf.
text, section 2.
a
1
0.8
Intensity (AU)
2432
0.6
0.4
0.2
0
350
Figure 3.
450
550
Wavelength (nm)
650
750
Same as figure 2 but for Gd-Tex2 þ .
of Gd(III) (complex 37 in Ref. 7). Several low-energy
absorption peaks (>900 nm) arise essentially from
transitions on the ligating negative ions. The most intense
low-energy transition of Gd-Tex2 þ shifts from 695 to 856
nm upon complexation with three one-fold negative
counter ions. Taking into account that the in vivo
situation of texaphyrin gadolinium (III) is intermediate
to the limiting situations Gd-Tex2 þ and (Gd-Tex)L
3
considered here, a far-red absorption appears plausible.
3.4. Stability
In order to study the stability of the metal–nitrogen
bond in lanthanide (III) texaphyrins, metal-ligand binding energies were calculated according to three possible
2433
Density functional studies on lanthanide (III) texaphyrins
40
1
a
a
30
∆E (eV)
Intensity (AU)
0.8
0.6
20
b
0.4
c
10
0.2
0
350
Figure 4.
450
550
Wavelength (nm)
650
Same as figure 2 but for Lu-Tex
750
2þ
.
dissociationpaths(a: Ebond ¼ E(Ln-Tex2 þ ) E(Ln3 þ )
E(Tex ); b: Ebond ¼ E(Ln-Tex2 þ ) E(Ln2 þ ) E(Tex);
c: Ebond ¼ E(Ln-Tex2 þ ) E(Ln þ ) E(Tex þ )). The
results are summarized in table 3. The analysis of the
Mulliken orbital populations on Ln (Ln ¼ La, Gd, Lu,
cf., table 2) shows a high positive charge on the metal, the
atomic charges on La, Gd, Lu being 2.27, 2.24, and 1.83,
respectively. Therefore only dissociation products with
metal cations were considered. It is found that the path
choice for metal dissociation mainly depends on the
cationic metal produced, e.g., La3 þ is about 30.48 eV
(exp. 30.24 eV) higher than La þ , whereas Tex is only
about 8.44 eV lower than Tex þ . Therefore a lower metalligand binding energy was obtained for path (c)
(10.30 eV) than for path (a) (32.19 eV). However, for all
three metal dissociation paths considered, the calculated
binding energies are higher than 10 eV, proving that the
Ln-Tex2 þ complexes are very stable. The calculated
binding energies for path (a) (La 32.19, Gd 34.55, Lu
36.53 eV), which would be preferred in aqueous solution,
are almost as large as the experimentally observed Ln3 þ
hydration energies (La 33.6, Gd 37.0, Lu 39.0 eV) in
agreement with the existence of water-soluble stable
Ln-Tex2 þ complexes [3].
In the gas phase path (c) is preferable, i.e., it has a
binding energy at least 5.6 and 21.9 eV lower than those
for path (b) and path (a), respectively. For the most
favourable dissociation path (c), the Lu-Tex2 þ (10.45 eV)
has almost the same metal-ligand binding energy as LaTex2 þ (10.32 eV), whereas for Gd-Tex2 þ the calculated
value is 0.63 eV larger than for La-Tex2 þ . It should be
noted that the ground states for Lan þ , Gdn þ and Lun þ
(n ¼ 1, 2) are different. However the metal-ligand
binding energy for Gd, and Lu will be increased if the
same configuration for Gdn þ and Lun þ is chosen as for
Lan þ (n ¼ 1, 2), e.g., for dissociation path (c) the energy
0
La
Gd
Lu
2þ
Figure 5. Ln-Tex
binding energies for all lanthanide
elements from the calculated data for La, Gd, and Lu
by linear regression and interpolation (curves a and b
empty circles; curve c empty squares). Corrected binding
energies for Ln-Tex2 þ with corrections taken from
the lanthanide ion substate considered in the interpolation to the experimentally observed ground state with
the experimental energy difference [39] (curve b filled
circles; curve c filled squares). Curves a, b, and c refer
to three different metal dissociation paths, see text
section 3.
will be 0.80 and 3.10 eV higher if the configurations f7d2
and f14d2 are chosen for Gd þ and Lu þ , respectively.
In previous work it was observed that for a fixed
valence substate of the lanthanide atoms/ions and
compounds as well as a fixed electronic state of the
non-lanthanide fragment the binding energy is nearly
linear in the lanthanide nuclear charge [38]. This allows
an interpolation of the Ln-Tex2 þ binding energies for
all lanthanide elements from the data for La, Gd and Lu
by linear regression. The correlation coefficients for
paths (a), (b), and (c) were 0.9986, 0.9995, and 0.9998,
respectively. Correcting from the lanthanide ion substate considered in the interpolation to the experimentally observed ground state with the experimental energy
difference [39] yields the typical saw-tooth behavior of
the binding energy also observed for other lanthanide
compounds [38], cf. figure 5. Considering the most
favourable dissociation path (c) we conclude that
without solvent effects Gd-Tex2 þ appears to be the
most stable lanthanide (III) texaphyrin complex,
closely followed by the Tb, Ce, La and Lu systems.
The corresponding Eu and Yb compounds should be
the least stable systems.
4. Conclusions
The molecular structures and chemical/physical properties (stability, electron affinity and optical spectrum)
2434
X. Cao and M. Dolg
of lanthanide (III) texaphyrins (Ln-Tex2 þ , Ln ¼ La,
Gd, Lu) were calculated using a DFT/B3LYP method
in connection with scalar-relativistic energy-consistent
4f-in-core lanthanide pseudopotentials. The d polarization function for nitrogen was found to be necessary to
calculate a reliable metal-ligand binding energy. The
structures of Ln-Tex2 þ do reflect the cation employed,
i.e., the larger the cation, the greater the out-of plane
displacement of the metal from the mean N5 plane.
The stability of the metal-nitrogen bond was studied for
three possible metal-ligand dissociation paths. In all
cases the metal binding energy has relatively high values
(>10 eV), indicating agreement with experimental findings that the metal is tightly bound to the macrocyclic
skeleton, yielding very stable complexes especially for
Gd, Tb, Ce, La and Lu. It was found that Ln-Tex2 þ
(Ln ¼ La, Gd, Lu) has a relatively low LUMO located
mainly on the macrocycle, i.e., the LUMO is only about
1.9 eV higher than the HOMO, resulting in a high,
nearly metal-independent electron affinity of 7.6 eV
for Ln-Tex2 þ . The related easy absorption of an electron
from the environment is used in Ln-Tex2 þ -based X-ray
radiation enhancers in cancer therapy. Two main bands
are obtained in the calculated visible electron excitation
spectrum for Ln-Tex2 þ : a strong band at ca. 454–462
nm, and a weaker band at ca. 681-686 nm. Model
calculations indicate that additional complexation of
Ln-Tex2 þ shifts the weaker band to the region >700 nm,
which is especially interesting for medical applications
as photosensitizers.
The authors are grateful to Prof. J. L. Sessler
for helpful correspondence on the subject and to
Dr. A. Kämper for providing experimental data of
crystal structures for texaphyrin lanthanide (III) complexes. The financial support of Fonds der Chemischen
Industrie is acknowledged.
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