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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. 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