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Theoretical modeling of electrochemical interactions in bimetallic molybdenum nitrosyl complexes incorporating saturated bridges
Polyhedron 27 (2008) 2819–2824
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Theoretical modeling of electrochemical interactions in bimetallic molybdenum nitrosyl complexes incorporating saturated bridges Klemens Noga a, Piotr P. Roman´czyk b, Andrzej J. Włodarczyk b, Ewa Broclawik c,* a
Department of Theoretical Chemistry, Jagiellonian University, Ingardena Street 3, 30-060 Cracow, Poland Faculty of Chemical Engineering and Technology, Cracow University of Technology, Warszawska Street 24, 31-155 Cracow, Poland c Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek Street 8, 30-239 Cracow, Poland b
a r t i c l e
i n f o
Article history: Received 18 December 2007 Accepted 8 June 2008 Available online 27 July 2008 Keywords: Molybdenum nitrosyl binuclear complex Tris(pyrazolyl)borato ligand Electrochemical interactions Mixed-valence systems DFT modeling
a b s t r a c t Hybrid B3LYP and non-hybrid OLYP DFT formalism has been applied to neutral and reduced forms of bimetallic hydrotris(3-methylpyrazol-1-yl)borato (Tp3-Me) molybdenum nitrosyl complexes incorporating ethane-1,2-diolate bridges. Direct evidence for localization of an extra electron in mixed-valence compounds {16e:17e} is based on the analysis of electron density, energetic stabilization of asymmetric structures with an electron trapped on one Mo and the splitting of both calculated and experimental mNO stretching frequencies. Differences in the first and second electron affinities calculated in PCM solvent model have been successfully related to cyclic voltammetry measurements. Electronic interactions through saturated ethanediolato bridges are evidenced by the extent of spin density delocalization towards the second Mo center. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The design and synthesis of electron donor–acceptor systems, which enable investigation of long-range electronic interactions between redox centers, are important for explaining key processes in biology such as electron transfer in proteins and in the development of potential elements for molecular electronics like molecular wires, diodes, light activated switches [1–3]. In redox-active bimetallic complexes linked by bifunctional bridging ligands a significant measurable indication of the electronic metal–metal interactions is the separation between redox potentials of two chemically identical redox centers, DEf (electrochemical interaction). The change in the electron density in one of the centers could be sensed by the other center and, consequently, two signals are observed in the cyclic voltammetry (CV). The stability of a mixed-valence complex with respect to disproportionation to isovalent forms is expressed by the comproportionation constant, Kc
½Mn -Q-Mn þ ½Mnþ1 -Q -Mnþ1 ¢ 2½Mn -Q -Mnþ1 K c ¼ expðF DEf =RTÞ: In the case of no or negligible interactions, both processes occur as one-electron reductions at virtually the same potential and DEf, and the corresponding Kc can be calculated from the statistical distribu-
* Corresponding author. Tel.: +48 12 6632023; fax: +48 12 6340515. E-mail address: [email protected] (E. Broclawik). 0277-5387/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2008.06.019
tion of products of equal stability with Kc = 4 and DEf = 35.6 mV consequently, where it may no longer be possible to generate the mixed-valence anion free of the isovalent states. The above interaction, dependent on the metal, its environment, the length and the geometry of the bridge and its electronic properties (substitution pattern), as well as the solvent influence, may occur by coulombic through-space and through-bond pathway. The latter could result from a mesomeric effect in the case of delocalized systems or induction effect transmitted through r-bonds. Numerous examples of bimetallic complexes with {MoII/I(d4/5) (NO+)(TpMe2)X}+/0 core containing formally coordinatively unsaturated 16e/17e metal centers (TpMe2 denotes tris(3,5-dimethylpyrazol-1-yl)hydroborate, X is halide) with p-acceptor ligands (e.g. aromatic heterocycles, polyenes) that make the delocalization of the unpaired electron possible have been reported in the literature [1]. The highest values of DEf (recorded in CH2Cl2) were obtained for complexes in which Q = pyrazine (1440 mV, Kc = 2.2 1024) [4], Q = 1,4-HNC6H4NH (920 mV, Kc = 4.0 1015) [5], and Q = 4,40 -bipy (765 mV, Kc = 8.6 1012) [6]. In all these examples, electrochemical interactions were apparently much greater than in the most renowned example of mixed-valence compounds, the Creutz–Taube ion (390 mV, Kc = 3 106; measured in aqueous solution) [7], a simple explanation for such behavior was given in [8]. Electrochemical interactions and significant magnetic interactions were detected in the complex [{Mo(NO)(TpMe2)Cl}2{4,40 -NC5H4(CH@CH)4C5H4N}], in which the Mo Mo distance is ca. 2 nm [9]. The introduction of a saturated
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section into the bridge, which breaks the conjugation, as e.g. in Q = 1,2-bi(4-pyridyl)ethane (105 mV, Kc = 60) [6], considerably decreases DEf, but does not exclude electronic and magnetic through-bridge interactions. However, few examples of complexes containing completely saturated bridges have been described in the literature, e.g. cyclic piperazine-1,4-diyl, Q = NC4H8N (560 mV, Kc = 3 109) [10]. We have shown [11,12] that bimetallic complexes with {Mo(NO)(TpMe2)X}+ (X denotes Cl or Br) core incorporating saturated n-alkanediolate bridges exhibit two chemically reversible one-electron reduction processes. The separations between these processes, being the largest for the complex with a C2 bridge (310 mV, Kc = 1.7 105; Mo Mo distance >6 Å) decrease by ca. 100 mV per CH2 group for C2 to C4 bridges. Starting with C5 bridge the electrochemical interactions could not be detected. The reappearance of a measurable separation between the redox potentials in fluorinated C5 analogue [{Mo(NO)(TpMe2)Cl}2{OCH2(CF2)3CH2O}] (DEf = 70 mV), in spite of both bridges imposing the same Mo Mo distance, is significant and can be explained partly by throughbond interactions enabled by inductive effect of fluorine atoms transmitted through the r-bond framework. This effect also manifested itself in an anodic shift of ca. 300 mV of the first reduction potential, which reflects LUMO stabilization in comparison with a non-fluorinated bimetallic complex. A different solvent reorganization effects cannot be excluded in these two cases. These findings posed a challenge to prospective theoretical research on the nature of electrochemical interactions in bimetallic complexes with saturated bridging ligands. On the other hand, quick development of quantum chemistry methods (especially DFT) in the last few years prompted us to undertake DFT studies on weakly coupled metallic centers in complexes constructed from {M(NO)(TpMe2)}2+ core, one or two saturated bridges and/or Cl ligands. Such modeling has already been used more and more widely to examine mixed-valence compounds [13,14], recently also for nitrosyl complexes containing tris(3,5-dimethylpyrazol1-yl)hydroborate ligand [15], what encouraged us to undertake the research presented in this paper. In this work we focus on the stabilization of reduced mixedvalence species incorporating single and double ethane-1,2-diolate bridges: [{Mo(NO)(TpMe2)Cl}2{O(CH2)2O}] (A) and [Mo(NO)(TpMe2){O(CH2)2O}]2 (B). Monometallic analogue (M) [Mo(NO)(TpMe2)Cl{O(CH2)2OH}] serves for comparative analysis. Calculated geometries, electron affinities and NO stretching frequencies are correlated with experimental X-ray, CV and IR spectral data, where available, in order to as well validate DFT results as draw conclusions regarding localization of additional electron after electrochemical reduction. Electrochemical data for monometallic and singly bridged complex have already been published [11]. Stretching frequencies of NO for monometallic and singly bridged species in solution are given in this work. Unfortunately, doubly bridged bimetallic complex was not soluble in any solvent allowing for electrochemical studies.
2.2. Models All calculations in this paper were conducted on mimetic models in which outer methyl groups of tris(3,5-dimethylpyrazol-1yl)hydroborate ligand were cut off to avoid additional energy inaccuracy due to nearly free rotation of these groups. Secondly it helped to decrease computational problem size. Methyl groups next to nitrosyl ligand were retained since they appeared to be important for keeping proper geometry of NO group and bridging unit. Therefore all compounds presented here contain hydrotris(3-methylpyrazol-1-yl)borato ligand. Starting geometry of bimetallic doubly bridged complex (B) was obtained from crystallographic structure of [Mo(NO)(TpMe2){O(CH2)2O}]2 [11]. This structure is highly symmetric having C2h point group symmetry. Both monometallic complex (M) and bimetallic singly bridged complex (A) starting structures were prepared from computed equilibrium geometry of B. Complex A has Ci symmetry, which was used to prepare the starting structure of this species. Geometries of neutral complexes, monoanions and dianions were optimized independently. Symmetry constraints were used during geometry optimization of non-reduced A and B compounds. On the contrary, computations for singly and doubly reduced complexes of A and B were carried both with and without imposing symmetry. 2.3. DFT calculations Calculations were performed using GAUSSIAN03 [16] within both unrestricted and restricted DFT with hybrid B3LYP functional, widely used in mixed-valence theoretical studies [13,14], and LanL2DZ [17–19] basis set (denoted as BS1), with effective core potential on heavy atoms (molybdenum and chlorine atoms). Additional polarization and diffuse functions were added for chlorine atoms [20]. For BS1 geometries, additional single-point calculations were performed with the extended basis set labeled as BS2 being of triple zeta quality with polarization functions for all atoms. This basis set was constructed using def2TZVPP [21,22] for molybdenum and def2TZVP [21,23] for other atoms. Additionally, for selected properties the performance of non-hybrid OLYP [24] potential was tested in smaller basis BS1. Vacuum equilibrium geometries were used to estimate solvent effects by means of the self-consistent reactions field (SCRF) method called polarizable continuum model (PCM) [25]. Dielectric constant of actual dichloromethane solvent (e = 8.93) and UFF scheme for cavity generation were used for single-point computations. IR spectra were calculated for gas phase models using standard harmonic approximation for equilibrium geometries. Contour plots of spin densities were prepared using GABEDIT [26].
3. Results and discussion 3.1. Experimental results
2. Methodology 2.1. Experimental The complexes [{Mo(NO)(TpMe2)Cl}n{O(CH2)2OH2-n}] (n = 1 or 2) were prepared according to the literature [11]. The reduced forms of these species were prepared by addition of cobaltocene to solutions of the neutral complexes in dichloromethane freshly distilled from CaH2 under argon. Infrared spectra for singly bridged complex with its monometallic analogue reported in this work were recorded using a Bio-Rad FTS 175C spectrophotometer in CH2Cl2 solutions.
The electrochemical results reported for [{Mo(NO)(TpMe2)Cl}2{O(CH2)2O}] (A) (first reduction process at Ef = 1.11 V vs. Fc/ Fc+; separation DEf = 310 mV) [11] indicate that the mixed-valence {16e:17e} form of A is accessible by the reduction of the neutral precursor {16e:16e} using cobaltocene (Ef = 1.34 V vs. Fc/Fc+). We chose the chloride complex, since voltammetric studies of the iodo complexes revealed that the reduction is followed by the dissociation of I, which may disturb the reduction process. The IR spectrum of A in dichloromethane exhibits two NO stretching vibrations, at 1605 and 1542 cm1 (DmNO = 63 cm1) instead of one (1680 cm1) in the neutral precursor or monometallic analogue (Table 10). This shows that this species is valence-trapped
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on the IR timescale (ca. 1013 s) and can be classified as Class I in the Robin-Day scheme (double minimum on the potential-energy curve). 3.2. Equilibrium geometries Optimized geometries of A and B are shown in Fig. 1 and Tables 1 and 2, respectively. Computed geometrical parameters show good agreement with available X-ray crystal structure (Table 2). Even the distance between two molybdenum atoms, which is crucial for electronic interactions investigation but could be very sensitive to any inaccuracies in computed geometry, is reasonably reproduced. In singly bridged complex A this distance is greater by nearly 1.3 Å (25%) than in B. As a result of close packing, the crystal unit cell of B contains two nonequivalent molecules having slightly different geometries; therefore two experimental structure data are shown in Table 2. Addition of an extra electron triggers symmetry breaking in examined compounds. In both complexes A and B molybdenum centers become nonequivalent after first reduction. Values of selected bonds and angles in molybdenum’s neighborhood are given in Tables 3 and 4. The most dramatic difference relates to distances between molybdenum and bridging oxygen (DR 6%) or chlorine (DR 5%), also the distances molybdenum–nitrosyl (DR 0.4%) and nitrogen–oxygen (DR 1.5%) differ between nonequivalent centers; molybdenum–molybdenum separation changes after reduction by nearly 2%. Second reduction leads to triplet dianions with selected geometrical parameters shown in Tables 5 and 6 for A and B, respectively. The inspection of the tables indicates that differences between both molybdenum centers become insignificant in doubly reduced complexes. As mentioned above, computations for singly and doubly reduced complexes were performed both with and without symmetry constraints. The comparison between energies of equilibrium structures of symmetric and asymmetric singly reduced compounds indicates the stabilization of the asymmetric ones (Table 7), with larger effect for singly bridged compound A. Additional single-point BS2 calculations confirm these results. The stabilization of asymmetric structures for singly and doubly bridged species equals to 0.162 eV and 0.037 eV for BS1 and was increased to 0.201 eV and 0.048 eV for BS2, respectively. The energetic stabilization of asymmetric structures and differences in geometries of molybdenum neighborhood confirm nonequivalence of molybdenum atoms in mixed-valence single reduced complexes and, what follows, substantial localization of additional electron. Stabilization of asymmetric structure with extra electron trapped on one molyb-
Table 1 Selected bond distances (Å) and angles (°) for complex A Distance (Å)
Angle (°)
Mo(1)–N(2) Mo(1)–N(1) Mo(1)–O(2) N(1)–O(1) O(2)–C(1) C(1)–C(2) Mo(1)–Cl Mo(1)–Mo(2)
2.26 1.78 1.91 1.23 1.44 1.54 2.44 6.66
N(1)–Mo(1)–N(2) N(1)–Mo(1)–O(2) N(2)–Mo(1)–O(2) Mo(1)–N(1)–O(1) O(2)–Mo(1)–Cl N(1)–Mo(1)–Cl Mo(1)–O(2)–C(1)
177.5 99.2 83.3 179.3 97.5 92.2 144.7
Table 2 Selected bond distances (Å) and angles (°) for complex B (experimental values in parentheses) Distance (Å) Mo(1)–N(2) Mo(1)–N(1) Mo(1)–O(2) N(1)–O(1) O(2)–C(1) C(1)–C(2) Mo(1)–Mo(2)
Angle (°) 2.28 1.78 1.93 1.24 1.44 1.54 5.37
(2.26, (1.77, (1.86, (1.25, (1.46, (1.49, (5.28,
2.26) 1.73) 1.91) 1.24) 1.39) 1.52) 5.28)
N(1)–Mo(1)–N(2) N(1)–Mo(1)–O(2) N(2)–Mo(1)–O(2) Mo(1)–N(1)–O(1) O(2)–Mo(1)–O0 (2) Mo(1)–O(2)–C(1)
175.0 98.9 84.2 176.0 101.0 137.4
(177.6, 177.4) (99.7, 99.0) (81.8, 82.6) (175.0, 175.0) (101.7, 102.2) (137.0, 136.3)
Table 3 Selected bond distances (Å) and angles (°) for singly reduced complex A Distance (Å)
Angle (°)
Mo center
Mo(1)
Mo(2)
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–Cl N(1)–O(1)
1.78 1.88 2.46 1.23
1.78 2.04 2.56 1.26
N(1)–Mo–O(2) O(2)–Mo–Cl N(1)–Mo–Cl Mo–N(1)–O(1)
100.4 99.4 92.7 178.1
99.5 91.8 94.9 177.6
Table 4 Selected bond distances (Å) and angles (°) for singly reduced complex B Distance (Å)
Angle (°) (1)
(2)
Mo center
Mo
Mo
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–O0 (2) N(1)–O(1)
1.78 1.92 1.92 1.25
1.78 2.04 2.04 1.27
N(1)–Mo–O(2) N(1)–Mo–O0 (2) O(2)–Mo–O0 (2) Mo–N(1)–O(1)
99.6 99.6 103.3 174.9
101.0 100.8 92.1 175.0
Fig. 1. Computed equilibrium geometries of complexes A (a) and B (b).
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Table 5 Selected bond distances (Å) and angles (°) for doubly reduced complex A Distance (Å)
Angle (°) (1)
Mo center
Mo
Mo–N(1) Mo–O(2) Mo–Cl N(1)–O(1)
1.78 2.01 2.56 1.26
(2)
Mo
Mo center
Mo(1)
Mo(2)
1.78 2.01 2.56 1.26
N(1)–Mo–O(2) O(2)–Mo–Cl N(1)–Mo–Cl Mo–N(1)–O(1)
101.2 93.3 96.1 174.1
101.2 93.3 96.1 174.1
Table 6 Selected bond distances (Å) and angles (°) for doubly reduced complex B Distance (Å)
Angle (°)
Mo center
Mo(1)
Mo(2)
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–O0 (2) N(1)–O(1)
1.78 2.05 2.05 1.28
1.78 2.05 2.05 1.28
N(1)–Mo–O(2) N(1)–Mo–O0 (2) O(2)–Mo–O0 (2) Mo–N(1)–O(1)
99.5 100.1 95.4 173.1
99.5 100.1 95.4 173.0
Table 7 Stabilization energy of asymmetric structures for singly reduced complexes A and B with respect to symmetric ones (B3LYP calculations) Complex
Stabilization (eV)
A B a
BS1
BS2a
0.162 0.037
0.201 0.048
Single-point for BS1 geometry.
denum site may be rather underestimated here due to known tendency of B3LYP to favor delocalized solutions [27]. 3.3. Analysis of electron affinities The investigations of mixed-valence compounds carried out most commonly by electrochemical experiments provide information about the strength of the electronic metal–metal interactions, measured as the splitting between the redox potentials of metal centers (DEf). The splitting may be well approximated by the difference between the first and second electron affinity, denoted as EA(1) and EA(2) (in the case of reduction) or ionization potentials (in the case of oxidation) of a mixed-valence complex. Electron affinities of A and B shown in Table 8 were calculated as the differences between total energies of neutral and singly reTable 8 Electron affinities for neutral and negatively charged complexes A and B Electron affinity (eV) A
B
duced (EA(1)) or singly reduced and doubly reduced (EA(2)) complexes. Table 8 lists also the differences between computed first and second electron affinities that may be directly compared with experimental DEf listed in the last row of Table 8. Comparison of electron affinities calculated in gas phase and with PCM solvent model indicates that solvent effects play crucial role in stabilization of negatively charged complexes. Calculations with significantly bigger BS2 basis set, in which description of negatively charged species should be of better quality, do not change trends in electron affinities neither in vacuum nor in PCM solvent model. Moreover, even rough solvent model such as PCM provides reasonable agreement with experimental data already at the simplest level. The description of electron affinity differences is improved in extended basis set, the introduction of non-hybrid OLYP functional for solvent model also complies with the experiment. However, one has to be aware that PCM methodology depends on the choice of cavity parameters, which brings additional uncertainty to computed energies thus by no means do we claim quantitative reproduction of the experiment. 3.4. Analysis of spin densities Spin density plots for singly reduced complex A and B are shown on Fig. 2a and 2b, respectively. Localization of an extra electron on one molybdenum center is clearly visible, however, some delocalization (about 10% – see Table 9) occurs in the case of compound B with double bridge, where the distance between molybdenum atoms is nearly 25% smaller than in complex A. The plots indicate also that the additional electron is partly delocalized towards NO ligand, with antiferromagnetic coupling. This phenomenon has already been reported in the literature both for mononuclear and binuclear metal-nitrosyl complexes [28–30], however, here it may be overestimated due to the tendency of UDFT to favor delocalized solutions [23] and to suffer from spin contamination [24,25]. Data collected in Table 9 bring additional evidence that the injected electron is trapped on Mo(1). After second reduction the two molybdenum centers become again equivalent. Spin density on NO ligand may be taken as qualitative fingerprint of metal to ligand p-backdonation enhanced by spurious electron density on Mo center after reduction. Both the increase of the basis set and in particular the use of non-hybrid functional increase delocalization of the extra electron towards the second molybdenum center. Nevertheless, this does not change qualitative picture of an electron predominantly trapped on one molybdenum. In the OLYP case the increase of electron delocalization goes in line with known tendency of non-hybrid potentials, favoring delocalized solutions in comparison to hybrid ones [31]. Smaller values of Mo and NO spin densities in B than in A may be additionally rationalized by to the lack of chlorine ligand in the former case.
In vacuum
In solvent
In vacuum
In solvent
3.5. Analysis of IR spectra
EA(1) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
2.40 2.10 1.91
3.78 3.52 3.29
1.39 1.24 1.14
2.77 2.68 2.43
EA(2) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
0.19 0.05 0.20
3.66 3.32 3.16
0.92 1.13 1.56
2.64 2.34 1.94
2.30 2.37 2.73
0.14 0.34 0.49
In experimental IR spectra after first reduction, both nitrosyl stretching frequencies are shifted towards red, but the splitting of 63 cm1 is registered. Theoretical computations go in line with the experiment, however, the shift of nitrosyl stretching frequency for non-reduced center in A and B is underestimated. Therefore computed splitting of nitrosyl stretching frequencies in singly reduced compound A is bigger by 30 cm1 than the experimental value. Nevertheless, both experiment and theory nicely corroborate the issue of electron trapping on IR time scale. Similar situation occurs in singly reduced complex B – calculated nitrosyl vibrational bands are split, but due to partial delocalization of the extra electron the splitting is smaller than in A. Unfortunately, experimental IR spectra for B are not available thus only
EA(2) EA(1) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a DEexp f a b
2.20 2.14 2.11
0.12 0.19 0.13 0.31b
Single-point calculations for geometries optimized with B3LYP/BS1. From Ref. [11].
K. Noga et al. / Polyhedron 27 (2008) 2819–2824
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Fig. 2. Spin density plots for singly reduced complexes A (a) and B (b) (contour value 0.002).
Table 9 Spin densities on Mo atoms and NO ligands in singly reduced complexes A and B Complex
Functional/basis
Mo(1)
Mo(2)
NO(1)
NO(2)
B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
1.26 1.10 1.00
0.00 0.07 0.14
0.37 0.21 0.20
0.00 0.04 0.04
B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
1.14 0.96 0.74
0.10 0.04 0.29
0.35 0.15 0.15
0.04 0.00 0.06
A
only in vacuum whereas experiment was done in solution. Nevertheless, both experiment and theory properly describe qualitative features of IR spectra for neutral and reduced bimetallic complexes; the dependence of NO stretching frequencies on the degree of electron density localization is properly described and helps to understand the nature of mixed-valence compounds.
B
a
Single-point calculations for geometries optimized with B3LYP/BS1.
Table 10 Experimental and calculated IR frequencies for neutral and one-electron reduction products for monometallic (M) or singly (A) and doubly (B) bridged bimetallic complexes
DmNOa (cm1)
mNO (cm1)
Complex
Neutral
Singly reduced
M
Exp Calc
1680 1652
1600 1549
–
A
Exp Calc
1680 1645
1605, 1542 1640, 1547
63 93
B
Exp Calc
1642b 1603
–c 1575, 1489
–c 86
a DmNO denotes the difference between reduced and non-reduced molybdenum center in bimetallic complexes. b Data from Ref. [11], obtained in KBr disc. c Complex B was insoluble in solvents other than CHCl3, which is unsuitable for
theoretical analysis is possible here. On the contrary, the two nitrosyl stretching vibrations calculated for doubly reduced complexes have the same frequency (1545 cm1 in the case of A and 1476 cm1 for B), slightly lower than the frequency of nitrosyl bound to reduced Mo in singly reduced species, due to additional electrostatic interaction with the second reduced metal center. Calculated shifts of NO stretching frequencies are consistent with the increase of NO bond distances (Tables 1–6) and metal to ligand p-backdonation ability estimated from spin density transfer towards NO. Nearly linear geometry of NO ligand in neutral complexes would comply with classification of diamagnetic (S = 0) and nearly linear MoNO moieties into nitrosonium category [32]. Neither NO bond length nor low IR frequency, however, do correspond to the assumption of NO+ ligand. Reduction of Mo centers yields more radical character on NO; linearity of Mo–NO fragment is retained what may be attributed to geometrical constraints imposed by surrounding CH3 groups from hydrotris(3-methylpyrazol-1-yl)borate ligand. In summary, no quantitative agreement of calculated and measured IR spectra could be expected here since theoretical NO frequencies could be calculated
4. Conclusions Electronic structure of mixed-valence states of two bimetallic hydrotris(3-methylpyrazol-1-yl)borato molybdenum nitrosyl complexes and their reduced forms has been theoretically investigated. Computed IR spectra, geometrical and energetic parameters show good agreement with experimental results, which allows for the validation of our computational scheme for such large molecules. DFT modeling showed to be capable of describing symmetry-broken structures with the electron trapped on one reduced Mo center in mixed-valence complexes; however, some electron delocalization through the saturated bridge may be also directly evidenced here. DFT calculations have shown that the nonequivalence of molybdenum centers in mixed-valence compound is energetically favorable and in both investigated bimetallic complexes an extra electron is localized on one of the molybdenum centers. Therefore both compounds should be considered as Class I complexes according to Robin-Day classification. However, in the doubly bridged complex (B) partial electron delocalization occurs, which may suggest that saturated bridging ligands could play a role in the strengthening of electronic interactions and, what follows, shifting the complex into Class II category. In addition, calculating and experimental infrared spectra confirm the assumption of electron localization yielding Class I labeling, stemming from geometry, energetic and spin density discussions. As could be expected, stretching vibrations of NO bound to two molybdenum centers in singly reduced complexes are diversified. After addition of the second electron this difference vanishes. This reasoning corroborates electron localization in mixed-valence compounds prepared from A and B. Again, in the case of doubly bridged complex (B) partial delocalization occurs, while in singly bridged compound (A) it is much less significant. Present work may be regarded as a first part (concentrating on short bridging ligands) of a bigger project that concerns the study of possible mechanisms of electron transfer trough saturated bridges in {Mo(NO)Tp}2+/1+ complexes, undertaken in our group.
Acknowledgments The computations were performed at the Academic Computer Centre CYFRONET AGH (Grant Nos. MNiSW/SGI2800/UJ/133/2006 and MNiSW/SGI3700/UJ/133/2006).
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All figures of the molecular models were created using xyzviewer software by Sven de Marothy (from Stockholm University). References [1] [2] [3] [4] [5] [6] [7] [8] [9]
[10] [11] [12] [13] [14] [15] [16]
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Theoretical modeling of electrochemical interactions in bimetallic molybdenum nitrosyl complexes incorporating saturated bridges Klemens Noga a, Piotr P. Roman´czyk b, Andrzej J. Włodarczyk b, Ewa Broclawik c,* a
Department of Theoretical Chemistry, Jagiellonian University, Ingardena Street 3, 30-060 Cracow, Poland Faculty of Chemical Engineering and Technology, Cracow University of Technology, Warszawska Street 24, 31-155 Cracow, Poland c Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek Street 8, 30-239 Cracow, Poland b
a r t i c l e
i n f o
Article history: Received 18 December 2007 Accepted 8 June 2008 Available online 27 July 2008 Keywords: Molybdenum nitrosyl binuclear complex Tris(pyrazolyl)borato ligand Electrochemical interactions Mixed-valence systems DFT modeling
a b s t r a c t Hybrid B3LYP and non-hybrid OLYP DFT formalism has been applied to neutral and reduced forms of bimetallic hydrotris(3-methylpyrazol-1-yl)borato (Tp3-Me) molybdenum nitrosyl complexes incorporating ethane-1,2-diolate bridges. Direct evidence for localization of an extra electron in mixed-valence compounds {16e:17e} is based on the analysis of electron density, energetic stabilization of asymmetric structures with an electron trapped on one Mo and the splitting of both calculated and experimental mNO stretching frequencies. Differences in the first and second electron affinities calculated in PCM solvent model have been successfully related to cyclic voltammetry measurements. Electronic interactions through saturated ethanediolato bridges are evidenced by the extent of spin density delocalization towards the second Mo center. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The design and synthesis of electron donor–acceptor systems, which enable investigation of long-range electronic interactions between redox centers, are important for explaining key processes in biology such as electron transfer in proteins and in the development of potential elements for molecular electronics like molecular wires, diodes, light activated switches [1–3]. In redox-active bimetallic complexes linked by bifunctional bridging ligands a significant measurable indication of the electronic metal–metal interactions is the separation between redox potentials of two chemically identical redox centers, DEf (electrochemical interaction). The change in the electron density in one of the centers could be sensed by the other center and, consequently, two signals are observed in the cyclic voltammetry (CV). The stability of a mixed-valence complex with respect to disproportionation to isovalent forms is expressed by the comproportionation constant, Kc
½Mn -Q-Mn þ ½Mnþ1 -Q -Mnþ1 ¢ 2½Mn -Q -Mnþ1 K c ¼ expðF DEf =RTÞ: In the case of no or negligible interactions, both processes occur as one-electron reductions at virtually the same potential and DEf, and the corresponding Kc can be calculated from the statistical distribu-
* Corresponding author. Tel.: +48 12 6632023; fax: +48 12 6340515. E-mail address: [email protected] (E. Broclawik). 0277-5387/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2008.06.019
tion of products of equal stability with Kc = 4 and DEf = 35.6 mV consequently, where it may no longer be possible to generate the mixed-valence anion free of the isovalent states. The above interaction, dependent on the metal, its environment, the length and the geometry of the bridge and its electronic properties (substitution pattern), as well as the solvent influence, may occur by coulombic through-space and through-bond pathway. The latter could result from a mesomeric effect in the case of delocalized systems or induction effect transmitted through r-bonds. Numerous examples of bimetallic complexes with {MoII/I(d4/5) (NO+)(TpMe2)X}+/0 core containing formally coordinatively unsaturated 16e/17e metal centers (TpMe2 denotes tris(3,5-dimethylpyrazol-1-yl)hydroborate, X is halide) with p-acceptor ligands (e.g. aromatic heterocycles, polyenes) that make the delocalization of the unpaired electron possible have been reported in the literature [1]. The highest values of DEf (recorded in CH2Cl2) were obtained for complexes in which Q = pyrazine (1440 mV, Kc = 2.2 1024) [4], Q = 1,4-HNC6H4NH (920 mV, Kc = 4.0 1015) [5], and Q = 4,40 -bipy (765 mV, Kc = 8.6 1012) [6]. In all these examples, electrochemical interactions were apparently much greater than in the most renowned example of mixed-valence compounds, the Creutz–Taube ion (390 mV, Kc = 3 106; measured in aqueous solution) [7], a simple explanation for such behavior was given in [8]. Electrochemical interactions and significant magnetic interactions were detected in the complex [{Mo(NO)(TpMe2)Cl}2{4,40 -NC5H4(CH@CH)4C5H4N}], in which the Mo Mo distance is ca. 2 nm [9]. The introduction of a saturated
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section into the bridge, which breaks the conjugation, as e.g. in Q = 1,2-bi(4-pyridyl)ethane (105 mV, Kc = 60) [6], considerably decreases DEf, but does not exclude electronic and magnetic through-bridge interactions. However, few examples of complexes containing completely saturated bridges have been described in the literature, e.g. cyclic piperazine-1,4-diyl, Q = NC4H8N (560 mV, Kc = 3 109) [10]. We have shown [11,12] that bimetallic complexes with {Mo(NO)(TpMe2)X}+ (X denotes Cl or Br) core incorporating saturated n-alkanediolate bridges exhibit two chemically reversible one-electron reduction processes. The separations between these processes, being the largest for the complex with a C2 bridge (310 mV, Kc = 1.7 105; Mo Mo distance >6 Å) decrease by ca. 100 mV per CH2 group for C2 to C4 bridges. Starting with C5 bridge the electrochemical interactions could not be detected. The reappearance of a measurable separation between the redox potentials in fluorinated C5 analogue [{Mo(NO)(TpMe2)Cl}2{OCH2(CF2)3CH2O}] (DEf = 70 mV), in spite of both bridges imposing the same Mo Mo distance, is significant and can be explained partly by throughbond interactions enabled by inductive effect of fluorine atoms transmitted through the r-bond framework. This effect also manifested itself in an anodic shift of ca. 300 mV of the first reduction potential, which reflects LUMO stabilization in comparison with a non-fluorinated bimetallic complex. A different solvent reorganization effects cannot be excluded in these two cases. These findings posed a challenge to prospective theoretical research on the nature of electrochemical interactions in bimetallic complexes with saturated bridging ligands. On the other hand, quick development of quantum chemistry methods (especially DFT) in the last few years prompted us to undertake DFT studies on weakly coupled metallic centers in complexes constructed from {M(NO)(TpMe2)}2+ core, one or two saturated bridges and/or Cl ligands. Such modeling has already been used more and more widely to examine mixed-valence compounds [13,14], recently also for nitrosyl complexes containing tris(3,5-dimethylpyrazol1-yl)hydroborate ligand [15], what encouraged us to undertake the research presented in this paper. In this work we focus on the stabilization of reduced mixedvalence species incorporating single and double ethane-1,2-diolate bridges: [{Mo(NO)(TpMe2)Cl}2{O(CH2)2O}] (A) and [Mo(NO)(TpMe2){O(CH2)2O}]2 (B). Monometallic analogue (M) [Mo(NO)(TpMe2)Cl{O(CH2)2OH}] serves for comparative analysis. Calculated geometries, electron affinities and NO stretching frequencies are correlated with experimental X-ray, CV and IR spectral data, where available, in order to as well validate DFT results as draw conclusions regarding localization of additional electron after electrochemical reduction. Electrochemical data for monometallic and singly bridged complex have already been published [11]. Stretching frequencies of NO for monometallic and singly bridged species in solution are given in this work. Unfortunately, doubly bridged bimetallic complex was not soluble in any solvent allowing for electrochemical studies.
2.2. Models All calculations in this paper were conducted on mimetic models in which outer methyl groups of tris(3,5-dimethylpyrazol-1yl)hydroborate ligand were cut off to avoid additional energy inaccuracy due to nearly free rotation of these groups. Secondly it helped to decrease computational problem size. Methyl groups next to nitrosyl ligand were retained since they appeared to be important for keeping proper geometry of NO group and bridging unit. Therefore all compounds presented here contain hydrotris(3-methylpyrazol-1-yl)borato ligand. Starting geometry of bimetallic doubly bridged complex (B) was obtained from crystallographic structure of [Mo(NO)(TpMe2){O(CH2)2O}]2 [11]. This structure is highly symmetric having C2h point group symmetry. Both monometallic complex (M) and bimetallic singly bridged complex (A) starting structures were prepared from computed equilibrium geometry of B. Complex A has Ci symmetry, which was used to prepare the starting structure of this species. Geometries of neutral complexes, monoanions and dianions were optimized independently. Symmetry constraints were used during geometry optimization of non-reduced A and B compounds. On the contrary, computations for singly and doubly reduced complexes of A and B were carried both with and without imposing symmetry. 2.3. DFT calculations Calculations were performed using GAUSSIAN03 [16] within both unrestricted and restricted DFT with hybrid B3LYP functional, widely used in mixed-valence theoretical studies [13,14], and LanL2DZ [17–19] basis set (denoted as BS1), with effective core potential on heavy atoms (molybdenum and chlorine atoms). Additional polarization and diffuse functions were added for chlorine atoms [20]. For BS1 geometries, additional single-point calculations were performed with the extended basis set labeled as BS2 being of triple zeta quality with polarization functions for all atoms. This basis set was constructed using def2TZVPP [21,22] for molybdenum and def2TZVP [21,23] for other atoms. Additionally, for selected properties the performance of non-hybrid OLYP [24] potential was tested in smaller basis BS1. Vacuum equilibrium geometries were used to estimate solvent effects by means of the self-consistent reactions field (SCRF) method called polarizable continuum model (PCM) [25]. Dielectric constant of actual dichloromethane solvent (e = 8.93) and UFF scheme for cavity generation were used for single-point computations. IR spectra were calculated for gas phase models using standard harmonic approximation for equilibrium geometries. Contour plots of spin densities were prepared using GABEDIT [26].
3. Results and discussion 3.1. Experimental results
2. Methodology 2.1. Experimental The complexes [{Mo(NO)(TpMe2)Cl}n{O(CH2)2OH2-n}] (n = 1 or 2) were prepared according to the literature [11]. The reduced forms of these species were prepared by addition of cobaltocene to solutions of the neutral complexes in dichloromethane freshly distilled from CaH2 under argon. Infrared spectra for singly bridged complex with its monometallic analogue reported in this work were recorded using a Bio-Rad FTS 175C spectrophotometer in CH2Cl2 solutions.
The electrochemical results reported for [{Mo(NO)(TpMe2)Cl}2{O(CH2)2O}] (A) (first reduction process at Ef = 1.11 V vs. Fc/ Fc+; separation DEf = 310 mV) [11] indicate that the mixed-valence {16e:17e} form of A is accessible by the reduction of the neutral precursor {16e:16e} using cobaltocene (Ef = 1.34 V vs. Fc/Fc+). We chose the chloride complex, since voltammetric studies of the iodo complexes revealed that the reduction is followed by the dissociation of I, which may disturb the reduction process. The IR spectrum of A in dichloromethane exhibits two NO stretching vibrations, at 1605 and 1542 cm1 (DmNO = 63 cm1) instead of one (1680 cm1) in the neutral precursor or monometallic analogue (Table 10). This shows that this species is valence-trapped
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on the IR timescale (ca. 1013 s) and can be classified as Class I in the Robin-Day scheme (double minimum on the potential-energy curve). 3.2. Equilibrium geometries Optimized geometries of A and B are shown in Fig. 1 and Tables 1 and 2, respectively. Computed geometrical parameters show good agreement with available X-ray crystal structure (Table 2). Even the distance between two molybdenum atoms, which is crucial for electronic interactions investigation but could be very sensitive to any inaccuracies in computed geometry, is reasonably reproduced. In singly bridged complex A this distance is greater by nearly 1.3 Å (25%) than in B. As a result of close packing, the crystal unit cell of B contains two nonequivalent molecules having slightly different geometries; therefore two experimental structure data are shown in Table 2. Addition of an extra electron triggers symmetry breaking in examined compounds. In both complexes A and B molybdenum centers become nonequivalent after first reduction. Values of selected bonds and angles in molybdenum’s neighborhood are given in Tables 3 and 4. The most dramatic difference relates to distances between molybdenum and bridging oxygen (DR 6%) or chlorine (DR 5%), also the distances molybdenum–nitrosyl (DR 0.4%) and nitrogen–oxygen (DR 1.5%) differ between nonequivalent centers; molybdenum–molybdenum separation changes after reduction by nearly 2%. Second reduction leads to triplet dianions with selected geometrical parameters shown in Tables 5 and 6 for A and B, respectively. The inspection of the tables indicates that differences between both molybdenum centers become insignificant in doubly reduced complexes. As mentioned above, computations for singly and doubly reduced complexes were performed both with and without symmetry constraints. The comparison between energies of equilibrium structures of symmetric and asymmetric singly reduced compounds indicates the stabilization of the asymmetric ones (Table 7), with larger effect for singly bridged compound A. Additional single-point BS2 calculations confirm these results. The stabilization of asymmetric structures for singly and doubly bridged species equals to 0.162 eV and 0.037 eV for BS1 and was increased to 0.201 eV and 0.048 eV for BS2, respectively. The energetic stabilization of asymmetric structures and differences in geometries of molybdenum neighborhood confirm nonequivalence of molybdenum atoms in mixed-valence single reduced complexes and, what follows, substantial localization of additional electron. Stabilization of asymmetric structure with extra electron trapped on one molyb-
Table 1 Selected bond distances (Å) and angles (°) for complex A Distance (Å)
Angle (°)
Mo(1)–N(2) Mo(1)–N(1) Mo(1)–O(2) N(1)–O(1) O(2)–C(1) C(1)–C(2) Mo(1)–Cl Mo(1)–Mo(2)
2.26 1.78 1.91 1.23 1.44 1.54 2.44 6.66
N(1)–Mo(1)–N(2) N(1)–Mo(1)–O(2) N(2)–Mo(1)–O(2) Mo(1)–N(1)–O(1) O(2)–Mo(1)–Cl N(1)–Mo(1)–Cl Mo(1)–O(2)–C(1)
177.5 99.2 83.3 179.3 97.5 92.2 144.7
Table 2 Selected bond distances (Å) and angles (°) for complex B (experimental values in parentheses) Distance (Å) Mo(1)–N(2) Mo(1)–N(1) Mo(1)–O(2) N(1)–O(1) O(2)–C(1) C(1)–C(2) Mo(1)–Mo(2)
Angle (°) 2.28 1.78 1.93 1.24 1.44 1.54 5.37
(2.26, (1.77, (1.86, (1.25, (1.46, (1.49, (5.28,
2.26) 1.73) 1.91) 1.24) 1.39) 1.52) 5.28)
N(1)–Mo(1)–N(2) N(1)–Mo(1)–O(2) N(2)–Mo(1)–O(2) Mo(1)–N(1)–O(1) O(2)–Mo(1)–O0 (2) Mo(1)–O(2)–C(1)
175.0 98.9 84.2 176.0 101.0 137.4
(177.6, 177.4) (99.7, 99.0) (81.8, 82.6) (175.0, 175.0) (101.7, 102.2) (137.0, 136.3)
Table 3 Selected bond distances (Å) and angles (°) for singly reduced complex A Distance (Å)
Angle (°)
Mo center
Mo(1)
Mo(2)
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–Cl N(1)–O(1)
1.78 1.88 2.46 1.23
1.78 2.04 2.56 1.26
N(1)–Mo–O(2) O(2)–Mo–Cl N(1)–Mo–Cl Mo–N(1)–O(1)
100.4 99.4 92.7 178.1
99.5 91.8 94.9 177.6
Table 4 Selected bond distances (Å) and angles (°) for singly reduced complex B Distance (Å)
Angle (°) (1)
(2)
Mo center
Mo
Mo
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–O0 (2) N(1)–O(1)
1.78 1.92 1.92 1.25
1.78 2.04 2.04 1.27
N(1)–Mo–O(2) N(1)–Mo–O0 (2) O(2)–Mo–O0 (2) Mo–N(1)–O(1)
99.6 99.6 103.3 174.9
101.0 100.8 92.1 175.0
Fig. 1. Computed equilibrium geometries of complexes A (a) and B (b).
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Table 5 Selected bond distances (Å) and angles (°) for doubly reduced complex A Distance (Å)
Angle (°) (1)
Mo center
Mo
Mo–N(1) Mo–O(2) Mo–Cl N(1)–O(1)
1.78 2.01 2.56 1.26
(2)
Mo
Mo center
Mo(1)
Mo(2)
1.78 2.01 2.56 1.26
N(1)–Mo–O(2) O(2)–Mo–Cl N(1)–Mo–Cl Mo–N(1)–O(1)
101.2 93.3 96.1 174.1
101.2 93.3 96.1 174.1
Table 6 Selected bond distances (Å) and angles (°) for doubly reduced complex B Distance (Å)
Angle (°)
Mo center
Mo(1)
Mo(2)
Mo center
Mo(1)
Mo(2)
Mo–N(1) Mo–O(2) Mo–O0 (2) N(1)–O(1)
1.78 2.05 2.05 1.28
1.78 2.05 2.05 1.28
N(1)–Mo–O(2) N(1)–Mo–O0 (2) O(2)–Mo–O0 (2) Mo–N(1)–O(1)
99.5 100.1 95.4 173.1
99.5 100.1 95.4 173.0
Table 7 Stabilization energy of asymmetric structures for singly reduced complexes A and B with respect to symmetric ones (B3LYP calculations) Complex
Stabilization (eV)
A B a
BS1
BS2a
0.162 0.037
0.201 0.048
Single-point for BS1 geometry.
denum site may be rather underestimated here due to known tendency of B3LYP to favor delocalized solutions [27]. 3.3. Analysis of electron affinities The investigations of mixed-valence compounds carried out most commonly by electrochemical experiments provide information about the strength of the electronic metal–metal interactions, measured as the splitting between the redox potentials of metal centers (DEf). The splitting may be well approximated by the difference between the first and second electron affinity, denoted as EA(1) and EA(2) (in the case of reduction) or ionization potentials (in the case of oxidation) of a mixed-valence complex. Electron affinities of A and B shown in Table 8 were calculated as the differences between total energies of neutral and singly reTable 8 Electron affinities for neutral and negatively charged complexes A and B Electron affinity (eV) A
B
duced (EA(1)) or singly reduced and doubly reduced (EA(2)) complexes. Table 8 lists also the differences between computed first and second electron affinities that may be directly compared with experimental DEf listed in the last row of Table 8. Comparison of electron affinities calculated in gas phase and with PCM solvent model indicates that solvent effects play crucial role in stabilization of negatively charged complexes. Calculations with significantly bigger BS2 basis set, in which description of negatively charged species should be of better quality, do not change trends in electron affinities neither in vacuum nor in PCM solvent model. Moreover, even rough solvent model such as PCM provides reasonable agreement with experimental data already at the simplest level. The description of electron affinity differences is improved in extended basis set, the introduction of non-hybrid OLYP functional for solvent model also complies with the experiment. However, one has to be aware that PCM methodology depends on the choice of cavity parameters, which brings additional uncertainty to computed energies thus by no means do we claim quantitative reproduction of the experiment. 3.4. Analysis of spin densities Spin density plots for singly reduced complex A and B are shown on Fig. 2a and 2b, respectively. Localization of an extra electron on one molybdenum center is clearly visible, however, some delocalization (about 10% – see Table 9) occurs in the case of compound B with double bridge, where the distance between molybdenum atoms is nearly 25% smaller than in complex A. The plots indicate also that the additional electron is partly delocalized towards NO ligand, with antiferromagnetic coupling. This phenomenon has already been reported in the literature both for mononuclear and binuclear metal-nitrosyl complexes [28–30], however, here it may be overestimated due to the tendency of UDFT to favor delocalized solutions [23] and to suffer from spin contamination [24,25]. Data collected in Table 9 bring additional evidence that the injected electron is trapped on Mo(1). After second reduction the two molybdenum centers become again equivalent. Spin density on NO ligand may be taken as qualitative fingerprint of metal to ligand p-backdonation enhanced by spurious electron density on Mo center after reduction. Both the increase of the basis set and in particular the use of non-hybrid functional increase delocalization of the extra electron towards the second molybdenum center. Nevertheless, this does not change qualitative picture of an electron predominantly trapped on one molybdenum. In the OLYP case the increase of electron delocalization goes in line with known tendency of non-hybrid potentials, favoring delocalized solutions in comparison to hybrid ones [31]. Smaller values of Mo and NO spin densities in B than in A may be additionally rationalized by to the lack of chlorine ligand in the former case.
In vacuum
In solvent
In vacuum
In solvent
3.5. Analysis of IR spectra
EA(1) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
2.40 2.10 1.91
3.78 3.52 3.29
1.39 1.24 1.14
2.77 2.68 2.43
EA(2) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
0.19 0.05 0.20
3.66 3.32 3.16
0.92 1.13 1.56
2.64 2.34 1.94
2.30 2.37 2.73
0.14 0.34 0.49
In experimental IR spectra after first reduction, both nitrosyl stretching frequencies are shifted towards red, but the splitting of 63 cm1 is registered. Theoretical computations go in line with the experiment, however, the shift of nitrosyl stretching frequency for non-reduced center in A and B is underestimated. Therefore computed splitting of nitrosyl stretching frequencies in singly reduced compound A is bigger by 30 cm1 than the experimental value. Nevertheless, both experiment and theory nicely corroborate the issue of electron trapping on IR time scale. Similar situation occurs in singly reduced complex B – calculated nitrosyl vibrational bands are split, but due to partial delocalization of the extra electron the splitting is smaller than in A. Unfortunately, experimental IR spectra for B are not available thus only
EA(2) EA(1) B3LYP/BS1 B3LYP/BS2a OLYP/BS1a DEexp f a b
2.20 2.14 2.11
0.12 0.19 0.13 0.31b
Single-point calculations for geometries optimized with B3LYP/BS1. From Ref. [11].
K. Noga et al. / Polyhedron 27 (2008) 2819–2824
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Fig. 2. Spin density plots for singly reduced complexes A (a) and B (b) (contour value 0.002).
Table 9 Spin densities on Mo atoms and NO ligands in singly reduced complexes A and B Complex
Functional/basis
Mo(1)
Mo(2)
NO(1)
NO(2)
B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
1.26 1.10 1.00
0.00 0.07 0.14
0.37 0.21 0.20
0.00 0.04 0.04
B3LYP/BS1 B3LYP/BS2a OLYP/BS1a
1.14 0.96 0.74
0.10 0.04 0.29
0.35 0.15 0.15
0.04 0.00 0.06
A
only in vacuum whereas experiment was done in solution. Nevertheless, both experiment and theory properly describe qualitative features of IR spectra for neutral and reduced bimetallic complexes; the dependence of NO stretching frequencies on the degree of electron density localization is properly described and helps to understand the nature of mixed-valence compounds.
B
a
Single-point calculations for geometries optimized with B3LYP/BS1.
Table 10 Experimental and calculated IR frequencies for neutral and one-electron reduction products for monometallic (M) or singly (A) and doubly (B) bridged bimetallic complexes
DmNOa (cm1)
mNO (cm1)
Complex
Neutral
Singly reduced
M
Exp Calc
1680 1652
1600 1549
–
A
Exp Calc
1680 1645
1605, 1542 1640, 1547
63 93
B
Exp Calc
1642b 1603
–c 1575, 1489
–c 86
a DmNO denotes the difference between reduced and non-reduced molybdenum center in bimetallic complexes. b Data from Ref. [11], obtained in KBr disc. c Complex B was insoluble in solvents other than CHCl3, which is unsuitable for
theoretical analysis is possible here. On the contrary, the two nitrosyl stretching vibrations calculated for doubly reduced complexes have the same frequency (1545 cm1 in the case of A and 1476 cm1 for B), slightly lower than the frequency of nitrosyl bound to reduced Mo in singly reduced species, due to additional electrostatic interaction with the second reduced metal center. Calculated shifts of NO stretching frequencies are consistent with the increase of NO bond distances (Tables 1–6) and metal to ligand p-backdonation ability estimated from spin density transfer towards NO. Nearly linear geometry of NO ligand in neutral complexes would comply with classification of diamagnetic (S = 0) and nearly linear MoNO moieties into nitrosonium category [32]. Neither NO bond length nor low IR frequency, however, do correspond to the assumption of NO+ ligand. Reduction of Mo centers yields more radical character on NO; linearity of Mo–NO fragment is retained what may be attributed to geometrical constraints imposed by surrounding CH3 groups from hydrotris(3-methylpyrazol-1-yl)borate ligand. In summary, no quantitative agreement of calculated and measured IR spectra could be expected here since theoretical NO frequencies could be calculated
4. Conclusions Electronic structure of mixed-valence states of two bimetallic hydrotris(3-methylpyrazol-1-yl)borato molybdenum nitrosyl complexes and their reduced forms has been theoretically investigated. Computed IR spectra, geometrical and energetic parameters show good agreement with experimental results, which allows for the validation of our computational scheme for such large molecules. DFT modeling showed to be capable of describing symmetry-broken structures with the electron trapped on one reduced Mo center in mixed-valence complexes; however, some electron delocalization through the saturated bridge may be also directly evidenced here. DFT calculations have shown that the nonequivalence of molybdenum centers in mixed-valence compound is energetically favorable and in both investigated bimetallic complexes an extra electron is localized on one of the molybdenum centers. Therefore both compounds should be considered as Class I complexes according to Robin-Day classification. However, in the doubly bridged complex (B) partial electron delocalization occurs, which may suggest that saturated bridging ligands could play a role in the strengthening of electronic interactions and, what follows, shifting the complex into Class II category. In addition, calculating and experimental infrared spectra confirm the assumption of electron localization yielding Class I labeling, stemming from geometry, energetic and spin density discussions. As could be expected, stretching vibrations of NO bound to two molybdenum centers in singly reduced complexes are diversified. After addition of the second electron this difference vanishes. This reasoning corroborates electron localization in mixed-valence compounds prepared from A and B. Again, in the case of doubly bridged complex (B) partial delocalization occurs, while in singly bridged compound (A) it is much less significant. Present work may be regarded as a first part (concentrating on short bridging ligands) of a bigger project that concerns the study of possible mechanisms of electron transfer trough saturated bridges in {Mo(NO)Tp}2+/1+ complexes, undertaken in our group.
Acknowledgments The computations were performed at the Academic Computer Centre CYFRONET AGH (Grant Nos. MNiSW/SGI2800/UJ/133/2006 and MNiSW/SGI3700/UJ/133/2006).
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