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Density functional study of structural properties and binding energies of dimethylsulfoxide Ru(II) complexes
Journal of Molecular Structure (Theochem) 497 (2000) 91–104 www.elsevier.nl/locate/theochem
Density functional study of structural properties and binding energies of dimethylsulfoxide Ru(II) complexes M. Stener*, M. Calligaris Dipartimento di Scienze Chimiche, Universita` di Trieste, I-34127 Trieste, Italy Received 19 March 1999; received in revised form 5 May 1999; accepted 4 June 1999
Abstract The structures of a series of Ru(II)–dimethylsulfoxide complexes were optimized using a density functional method. The obtained bond lengths reproduce the experimental trends quite well, although a general overestimate is found. The theory is also used to predict the kind of coordination linkage (via O or S) preferred by dmso when different ancillary ligands are present. The results are consistent with the experimental findings and can be explained in terms of s–p contributions in the sulfoxide–metal bond. Insight into the strength of the oxygen/sulfur metal bonds is further given by the calculation of the binding energies of the sulfoxide fragments in different situations. Model molecules with emphasized electronic effects are also considered to confirm the trends and to study special aspects such as preferred conformation structures. The general good performance, combined to computational economy, makes the present method suitable for further applications in this field. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Density functional theory; Binding energies; Dimethylsulfoxide; Ruthenium
1. Introduction Ruthenium sulfoxide complexes display many intriguing stereochemical properties, involving both metric and topographical features, as a consequence of the ambidentate nature of the sulfoxide ligands. This gives rise to linkage isomerism with the formation of S- and O-metal coordinated compounds, depending on the balance of several factors such as the metal oxidation state and mainly, the steric and electronic properties of the sulfoxide and other ancillary ligands [1,2]. Thus, it was observed that in Ru(II) complexes, containing dimethylsulfoxide (dmso) and
* Corresponding author. Tel.: 139-040-6763952; fax: 139-0406763903. E-mail address: [email protected] (M. Stener).
s donor ligands (e.g. NH3), S-bonding is largely preferred, while introduction of strong p acceptor ligands (e.g. CO) favors O-bonding [3–6]. The latter is further favored in Ru(III) complexes, specially in the case of bulkier ligands like diphenyl sulfoxide [7]. The role of the electronic factors was rationalized on the basis of the p acceptor properties of the sulfoxide ligands, and the metal electron charge density either increased or decreased by s donor or p acceptor ligands [1,2]. However, in the first case, p backdonation from metal to sulfoxide molecular orbitals can be strong enough to stabilize S-bonding. In fact, the vast amount of spectroscopic (IR, NMR) and structural (X-ray) data, so far collected, show that O-bonding is largely predominant with “hard” metal ions, while Sbonding is prevalent only with “soft” metal ions of the second and third transition series in group VIII, like ruthenium(II) and, specially, platinum(II) [1,2].
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00200-6
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The aim of the present theoretical study is to substantiate such a rationalization in terms of a general molecular orbital method. The presence of a transition metal and the overall rather large ligand size suggests the use of a computational approach based on the density functional theory (DFT). However, in the transition metal complex, the electron correlation is usually important. Thus, a theoretical study soon becomes intractable by traditional ab initio method, as it is necessary to drastically enlarge the excitation space in a CI formalism, and the use of perturbative schemes may not be very efficient if non-dynamical electron correlation is present [8]. On the contrary, semi-empirical methods are often too approximate to give reliable results in the field of transition metal chemistry. In recent years, the first-principle DFT approaches have become more and more customary [9], as they are much cheaper compared to the traditional ab initio methods, and can describe, with reasonable accuracy, the electronic structure of systems in which the electron correlation plays an important role, like, e.g. transition metal complexes [10] or large transition metal clusters [11]. In order to test the capability of the DFT approach to describe the bonding between Ru(II) and dmso, in the presence of different ancillary ligands, we optimized the geometries of the free ligand itself and those of four significant complexes: cis,fac-RuCl2(CO)3(dmso-O) [5], [Ru(NH3)5(dmso-S)] 21 [12,13], and cis,fac-RuCl2(dmsotrans-RuCl2(dmso-S)4 S)3(dmso-O) [14]. Particular attention has been devoted to the calculation of the dmso binding energy contributions. Further, the protonated dmso, [(dmso)H] 1, and two model complexes, [cis,fac-Ru(NH3)2H3(dmsoS)] 2 and [Ru(CO)5(dmso-S)] 21, representing extreme cases of dmso-S complexes containing strong s donor and p acceptor ancillary ligands, were considered for a thorough investigation of the structural and conformational properties of Ru–dmso complexes.
2. Computational methods The electronic structure of the complexes is
obtained by solving the Kohn–Sham equations [15], in the framework of the DFT, employing the ADF program [16]. During the SCF procedure, the general gradient approximation (GGA) to the exchange correlation energy functional is selfconsistently employed, based on the VWN [17] parametrization corrected by gradient terms for the exchange [18] and the correlation [19], giving the so-called Becke–Perdew (BP) functional. Only for preliminary calculations on the free and protonated dmso the simpler VWN functional, not corrected by gradient terms, is used. In order to choose a basis set which is a good compromise between economy and accuracy, we performed preliminary tests optimizing the free dmso geometry with basis sets of increasing size. A frozen core DZP STO basis set proved to be a good choice for all atoms, with the exceptions of S and Ru. A DZP basis set, with frozen 1s shell for second row elements, and a DZP with frozen 1s, 2s and 2p shells for third row elements were employed. For H, the pure DZP set was chosen, taking the optimized exponents from the database included in the ADF program package [16]. For S, the DZP standard set was modified as regards the polarization functions. We employed two 3d STO with exponents 1.0 and 2.0, and one 4f STO with exponent 2.25. For Ru, the standard TZ basis set included in the ADF program package was employed, keeping the core orbitals frozen up to all the shells with principal quantum number 3. The optimized auxiliary basis set used to fit the electron density was also taken from the same database. During the geometry optimization, all the degrees of freedom were optimized within the imposed symmetry constraints. Unless differently specified, the Cs point group was assumed. The binding energies were calculated with respect to the fragments and not directly as differences of total energies, as a general strategy of ADF [16]. The splitting of energy contributions into steric and electronic terms was performed according to Ref. [20]. The Mulliken charges were used only to give a qualitative description of the electronic structure, as they are very sensitive to the basis set size. These numbers should be considered with caution, focusing more on the trends than on their absolute values.
M. Stener, M. Calligaris / Journal of Molecular Structure (Theochem) 497 (2000) 91–104
(a)
(b)
93
(c)
Fig. 1. Sketch of the molecular structure of (a) dmso; (b) [dmso-OH] 1; and (c) [dmso-SH] 1.
3. Results and discussion 3.1. Dimethylsulfoxide The calculation of the structural parameters of the free dmso ligand is important not only as a test for the choice of the basis set and exchange-correlation functional, but also because the comparison of the dmso structure with those of the protonated and metal coordinated ligand provides fundamental information about its bonding properties. 3.1.1. Free dimethylsulfoxide The optimized internal coordinates and the dipole moment of free dmso (Fig. 1(a)), as obtained with BP and VWN functionals under the Cs point group symmetry, are reported in Table 1 together with the experimental gas phase data [21,22]. We can observe the overall agreement between the observed and the VWN structure, particularly for the bond lengths. It is worth noting that the inclusion of two 3d and one 4f polarization functions in the S basis set is mandatory to obtain converged values in the optimization procedure. If the basis set is further enlarged (on S or on the Table 1 Optimized internal coordinates and dipole moment (with BP and VWN functionals) and experimental data (Exp) of free dmso molecule
˚) S–O (A ˚) S–C (A C–S–O (8) C–S–C (8) m (D) a b
Ref. [21]. Ref. [22].
BP
VWN
Exp
1.507 1.834 107.2 95.1 3.65
1.489 1.794 106.8 94.9 3.67
1.485(6) a 1.799(5) a 106.65(3) a 96.57(3) a 3.9 b
other atoms), the results do not change appreciably, while if the smaller standard DZP set (with only one 3d polarization function) is employed for S, the bond ˚. lengths worsen as they increase by about 0.03 A The BP results are definitely worse than the VWN ones: the S–O and S–C bond distances are overesti˚ , respectively, while mated by about 0.02 and 0.04 A the angles show a similar or slightly better agreement. This is not surprising, as it is well known that GGA functionals (like BP) drastically improve the binding energies, while they often give bond lengths that are too long [23]. We have considered here the VWN functional for a comparison between the calculated and experimental structural parameters, in order to assess the basis set requirements for dmso and to test the performances of the method in a stringent way. However, with the exception of the protonated dmso, in the following we will consider only the BP functional, in spite of some deteriorations of the structural parameters, as we are mainly interested in the binding energies and the trends of the bond lengths, rather than their absolute values. Finally, we can observe that the calculated dipole moment is in fairly good agreement with the experimental value with both the functional choices. In fact, the electron density is not very sensitive to the functional. The BP values of the Mulliken charges are: O, 20.64; S, 10.59; C, 20.19, while for H they range from 10.06 to 10.10. These values are consistent with the well known [24] strong polarization of the sulfoxide S–O bond, assessed by ab initio SCF calculations [25,26] and, recently, also evidenced by valence electron density maps, from X-ray diffraction experiments [27]. To complete the description of free dmso, we investigated the nature of its lowest virtual orbitals, as they are involved in the backdonation from the metal to the
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a
O
S
C
S
b
C
Fig. 2. Contour plots relative to the virtual level 8a 00 of dmso: solid, dashed and dot-dashed lines mean positive, negative and zero (nodal line) contributions, respectively. (a) In the plane passing through the S–O bond and orthogonal to the Cs mirror plane; (b) in the plane defined by the ˚ ), isolines: 0, ^ 0.02, ^ 0.05, ^ 0.1, ^ 0.2, ^ 0.5. three atoms C–S–C. Side length: 15 a.u. (7.938 A
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Table 2 Optimized internal coordinates, Mulliken charges (Q) and relative total energies (kJ/mol)(with BP and VWN functional) of free and protonated dmso molecules. [dmso-OH]1 and [dmso-SH] 1 indicate the protonation at O and S atoms, respectively BP
˚) S–O (A ˚) S–C (A C–S–O (8) C–S–C (8) ˚) O–H (A ˚) S–H (A QO (e) QS (e) Relative E
VWN
Dmso
[dmso-OH]
1.507 1.834 107.2 95.1 – – 20.64 10.59 0
1.631 1.792 100.6 101.1 0.993 – 20.55 10.80 2885
1
[dmso-SH] 1.447 1.776 115.7 106.8 – 1.379 20.53 10.98 2793
ligated dmso. Three almost degenerate empty orbitals are found: 8a 00 , 15a 0 and 16a 0 . 8a 00 is the most important because it has mainly p p(S–O) character and should play the major role in back-donation, 15a 0 and 16a 0 have, respectively, mainly S 3d and s p(C– H) character. This attribution was assessed on the grounds of a direct inspection of the wave function shown in Fig. 2, where the plot of the 8a 00 orbital is reported, in the plane through the S–O bond and orthogonal to the symmetry reflection plane (a) and in the C–S–C plane (b). It is apparent that this orbital is delocalized and has p p(S–O) and s p(S–C) character. 3.1.2. (Dmso)H] 1 Table 2 reports the BP and VWN results for the two isomers of the protonated dmso, [dmso-OH] 1 and [dmso-SH] 1 (Fig. 1(b) and (c)), the former being, so far, the only isolated species [1,2]. If we restrict our
1
Dmso
[dmso-OH] 1
1.489 1.794 106.8 94.9 – – 20.61 10.58 0
1.602 1.754 100.6 100.8 0.993 – 20.53 10.82 2865
[dmso-SH] 1 1.432 1.736 115.2 107.4 – 1.384 20.50 10.93 2772
analysis to the BP results, the comparison with the calculated free dmso parameters shows in [dmsoOH] 1 a marked lengthening of the S–O distance ˚ ) and a shortening of the S–C distances (0.124 A ˚ ), accompanied by a narrowing (6.68) of the (0.042 A O–S–C angle and widening (6.08) of the C–S–C angle. This trend is in excellent agreement with the experimental evidence [1,2]. On the contrary, the [dmso-SH] 1 isomer is characterized by a reduction of both the S–O and S–C bond lengths and a widening of all the bond angles, the latter due to the passage from a pyramidal to a tetrahedral structure of the S atom. However, its energy is far greater (92 kJ/mol) than that of the O-protonated species, supporting the observation that with “hard” ions O-bonding is preferred. Further, the present results confirm the suggestion that O-coordination implies a decrease of the S–O bond order, while S-coordination implies its increase, with respect to the free ligand, in which the
Table 3 Optimized distances (with BP functional) and experimental data [5] (Exp) of cis,fac-RuCl2(CO)3(dmso-O) and cis,fac-RuCl2(CO)3(dmso-S) ˚) Distance (A
Exp
Cis,fac-RuCl2(CO)3(dmso-O)
Cis,fac-RuCl2(CO)3(dmso-S)
Ru–O Ru–S S–O S–C Ru–Cl Ru–C a Ru–C b
2.095 – 1.535 1.768 2.393 1.902 1.879
2.169 – 1.557 1.812 2.440 1.929 1.904
– 2.480 1.473 1.805 2.442 1.928 1.954
a b
cis to dmso. trans to dmso.
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M. Stener, M. Calligaris / Journal of Molecular Structure (Theochem) 497 (2000) 91–104
(a)
(b)
Fig. 3. Sketch of the molecular structure of (a) cis,fac-RuCl2(CO)3(dmso-O); and (b) cis,fac-RuCl2(CO)3(dmso-S).
S–O bond has a considerable double bond character [1,2]. The VWN results lead to the same conclusions, as far as only trends are considered. On the contrary, a general shortening of the bonds is observed, as expected after the previous analysis on free dmso. 3.2. Ru(II)–dmso complexes: molecular structures In this section, we will consider four ‘real’ Ru(II)– dmso complexes with different ancillary ligand environments: two limiting situations, one with p acceptor (CO) and the other with s donor (NH3) ligands, and two intermediate cases, with dmso-S and dmso-O as ancillary ligands. In addition, the structures and energies of ‘hypothetical’ (not yet observed) linkage isomers will also be described. 3.2.1. cis,fac-RuCl2(CO)3(dmso-O) The BP geometry optimization results for this complex are reported in Table 3, together with the experimental values and those calculated for its hypothetical isomer, cis,fac-RuCl2(CO)3(dmso-S) (Fig. 3). The comparison between the experimental data and those calculated for the cis,fac-RuCl2 (CO)3(dmso-O) complex is satisfactory as regards the trends in the bond distances, in spite of their general overestimate, caused by the BP functional. It is worth noting that the strong S–O elongation with ˚ ), caused by the coordirespect to free dmso (0.050 A nation to Ru(II), is exactly reproduced by theory. This
trend is in agreement with the more general observation that the S–O distance passes from an average ˚ in free sulfoxides to that of value of 1.492(1) A ˚ in O-coordinated metal complexes [1,2]. 1.529(1) A Further, Table 3 shows that the S–C distance is shor˚ upon coordination, which is again tened by 0.031 A ˚ ), and in correctly predicted by the theory (0.022 A ˚ agreement with the mean reduction of 0.010 A observed while passing from free sulfoxides to Obound complexes [1,2]. The hypothetical linkage isomer, cis,fac-RuCl2(CO)3(dmso-S), displays a very long Ru–S distance ˚ ), far beyond the longest observed value of (2.480 A ˚ , found in cis,cis,trans-RuCl2(CO)2(dmso2.364(1) A S)2 [5]. Of course, the high absolute value is an artifact of the BP functional, in fact a VWN optimization ˚ , still long but in better furnished a value of 2.395 A agreement with the experimental values. The definite Ru–S elongation is consistent with the idea of the marked competition between the two trans p acceptor ligands, CO and dmso-S, with subsequent dramatic weakening of the Ru–S bond. This competition effect between the two trans ligands also results in the ˚ ) of the Ru–C distance, trans lengthening (0.050 A to dmso, passing from the dmso-O to the dmso-S isomer, while the cis Ru–C bond lengths remain practically unaffected. As for [dmso-SH] 1, the BP calcu˚ ) is found to be much lated S–O distance (1.473 A ˚ ), in agreement shorter than that in free dmso (1.507 A with the experimental observation that the S–O ˚ distance passes from an average value of 1.492(1) A
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Table 4 Optimized distances (with BP functional) and experimental data [12] (Exp) of [Ru(NH3)5(dmso-S)] 21 and [Ru(NH3)5(dmso-O)] 21 ˚) Distance (A
Exp
[Ru(NH3)5(dmso-S)] 21
[Ru(NH3)5(dmso-O)] 21
Ru–S Ru–O S–O S–C Ru–N a Ru–N b
2.188 – 1.512 1.815 2.155 2.203
2.272 – 1.504 1.808 2.189 2.247
– 2.236 1.562 1.811 2.178 2.146
a b
cis to dmso. trans to dmso.
˚ in S-coordinated in free sulfoxides to 1.472(1) A metal complexes [1,2]. The Mulliken charges in the dmso-O complex are: O, 20.73; S, 10.79, while in the dmso-S isomer they are: O, 20.58; S, 10.66. It is evident that the improved S–O p overlap, passing from the dmso-O to the dmso-S derivative, reduces the bond polarization. A similar effect, but much weaker, seems to be present for the S–C distances. However, the differences are too small to be reliable at this level of calculation. Interestingly, the calculated energy difference between the O- and S-coordinated isomers of cis,fac-RuCl2(CO)3(dmso), shows that the dmso-S isomer is less stable by 29 kJ/mol with respect to the dmso-O one. This supports the proposal that the Ru–S
(a)
(b)
Fig. 4. Sketch of the molecular structure of (a) [Ru(NH3)5(dmsoS)] 21; and (b) [Ru(NH3)5(dmso-O)] 21. For sake of clarity the ammonia H atoms are not shown.
bond trans to CO is destabilized in favor of O-bonding, so that only the dmso-O isomer is formed. 3.2.2. Ru(NH3)5(dmso-S)] 21 This complex represents the opposite limit in the electronic properties of the ancillary ligands, which now are strong s donors. In Table 4, the BP optimized geometry of [Ru(NH3)5(dmso-S)] 21 is reported, together with the experimental data [12] and those calculated for its hypothetical linkage isomer [Ru(NH3)5(dmso-O)] 21 (Fig. 4). The most striking features of the experimental structure are the very short Ru–S bond distance ˚ ) and the very long S–O bond distance (2.188(3) A ˚ ) [12]. In fact, it was shown that the aver(1.512(7) A age values for the Ru–S and S–O bond distances in Ru(II)–sulfoxide complexes are 2.265(3) and ˚ , respectively [1,2]. The dramatic lengthen1.478(1) A ing of the S–O distance, towards the mean value of ˚ found in dmso-O metal complexes, is in 1.529(1) A agreement with the marked decrease of the S–O stretching frequency, from the free to the coordinated sulfoxide [13]. These trends are consistent with the existence of a partial double bond character in the Ru(II)–S bond, attributable to a p back-donation from full d orbitals of the metal to the empty MO’s of the sulfoxide, with mainly S–O antibonding character. Such a bonding scheme is further supported by a considerable amount of crystallographic and spectroscopic (IR) data from a variety of Ru(II) and Ru(III) complexes containing s donor or p acceptor ligands [1,2]. The present calculations are consistent with these considerations if we compare the calculated Ru–S ˚ ) and S–O (1.504 A ˚ ) distances with those (2.272 A
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Table 5 Optimized distances (with BP functional) and experimental data [14] (Exp) of trans-RuCl2(dmso-S)4 and trans,mer-RuCl2(dmsoS)3(dmso-O) Distance ˚) (A
Exp
Trans-RuCl2 (dmso-S)4
Trans,mer-RuCl2 (dmso-S)3(dmso-O)
Ru–S a Ru–S b Ru–O Ru–Cl S–O a S–O b S–O c S–C a S–C b S–C c
2.352 – – 2.402 1.491 – – 1.780 – –
2.402 – – 2.478 1.505 – – 1.808 – –
2.391–2.404 2.252 2.336 2.468 1.488–1.505 1.500 1.518 1.805–1.812 1.809 1.818
a
trans to dmso-S. trans to dmso-O. c dmso-O. b
found in the previous model molecule cis,fac˚ , respecRuCl2(CO)3(dmso-S), of 2.480 and 1.473 A tively. Substitution of CO with NH3 ligands causes a significant shortening of the Ru–S distance and lengthening of the S–O distance as a consequence of the increased metal electron charge density, and hence of its p back-donation ability. Finally, it is of interest to note that the present calculations confirm the experimentally observed trans influence effect of dmso-S on the trans Ru–N ˚ longer than the Ru– distance. This, in fact, is 0.048 A N distances trans to N, in agreement with the ˚ . Interestingly, the calculated difference of 0.058 A
(a)
energy calculated for the linkage isomer, [Ru(NH3)5(dmso-O)] 21, is 13 kJ/mol higher than that of the isolated complex, [Ru(NH3)5(dmso-S)] 21, showing the preference for S-bonding in the presence of s donor ligands. 3.2.3. trans-RuCl2(dmso-S)4 In this case, besides the chlorides, the ancillary ligand is dmso-S itself, hence the situation is intermediate with respect to the two previous cases. In Table 5, the BP optimized geometry of transRuCl2(dmso-S)4 is reported, together with the experimental data [14] and the results for its hypothetical isomer trans,mer-RuCl2(dmso-S)3(dmso-O) (Fig. 5). The Cs point group was employed during the geometry optimization of the first system, while for the second one no symmetry constraint was introduced. The comparison of the experimental structure with respect to the calculated one is only fairly satisfactory, showing the usual overestimate of the bond lengths, ˚ ) for the Ru–Cl distance. particularly large (0.076 A Also in this case we checked the performances of the VWN functional, and obtained the following opti˚ and Ru–Cl, mized distances: Ru–S, 2.330 A ˚ in much better agreement with the experi2.416 A ment, as expected. It is interesting to compare the calculated structure of this tetrakis(dmso) complex with that of the previous dmso-S complex, [Ru(NH3)5(dmso-S)] 21. The experimental Ru–S distance is shorter in the ˚ , and this shortening is well reprolatter by 0.164 A ˚ ). This, on the contrary, duced by the theory (0.130 A
(b)
Fig. 5. Sketch of the molecular structure of (a) trans-RuCl2(dmso-S)4; and (b) trans,mer-RuCl2(dmso-S)3(dmso-O). For sake of clarity the methyl H atoms are not shown.
M. Stener, M. Calligaris / Journal of Molecular Structure (Theochem) 497 (2000) 91–104
c c
a
(a)
(b)
Fig. 6. Sketch of the molecular structure of (a) cis,fac-RuCl2(dmsoS)3(dmso-O); and (b) cis-RuCl2(dmso-S)4. For sake of clarity the methyl H atoms are not shown. With reference to Table 6, some dmso ligands are labeled a, c.
˚ of is not able to reproduce the shortening of 0.021 A the S–O distance in trans-RuCl2(dmso-S)4, giving a ˚ . Probably, the electronic and value of only 0.001 A steric bonding situation is too different in the two compounds to be handled by the present method. The comparison is more reliable between more strictly related complexes, like linkage isomers of the same diastereoisomer. In fact, the comparison between trans-RuCl2(dmso-S)4 and trans,merRuCl2(dmso-S)3(dmso-O), shows that all the bond lengths have the expected trend: (i) the Ru–S distances trans to dmso-S are very close in the two Table 6 Optimized distances (with BP functional) and experimental data [14] (Exp) of cis,fac-RuCl2(dmso-S)3(dmso-O) and cisRuCl2(dmso-S)4 Distance ˚) (A
Exp
Cis,fac-RuCl2(dmso-S)3 (dmso-O)
Cis-RuCl2 (dmso-S)4
Ru–O Ru–S a Ru–S b Ru–S c Ru–Cl S–O b S–O c S–O d S–O a
2.134 – 2.279 2.245 2.424 1.470 1.507 1.537 –
2.246 – 2.312 2.284 2.489 1.499 1.497 1.552 –
– 2.658 2.315 2.339 2.478 1.504 1.496 – 1.483
a
dmso-S a in Fig. 6. dmso-S trans to Cl. c dmso-S c in Fig. 6. d dmso-O. b
99
compounds, while that, in the second one, trans to dmso-O is shorter, as expected from the different trans influence effects of the O and S atoms; (ii) the S–O distance of the dmso-O group is longer than in ˚ is dmso-S; (iii) the Ru–O distance of 2.336 A much longer than the mean experimental value of ˚ found in O-bonded sulfoxide metal 2.131(4) A complexes [1,2]. This suggests that formation of this isomer is unfavored. In fact, trans,merRuCl2(dmso-S)3(dmso-O) has an energy which is 77 kJ/mol higher than the isolated isomer transRuCl2(dmso-S)4.
3.2.4. cis,fac-RuCl2(dmso-S)3(dmso-O) The bond distances calculated for this complex, together with that of its hypothetical isomer, cisRuCl2(dmso-S)4 (Fig. 6), and the experimental data, are given in Table 6. These systems were calculated without any symmetry constraint. As usual, the comparison between the experiment and the calculated results of the actually synthesized complex is satisfactory, making allowance for the overestimate of the bond lengths. As mentioned above, this severe deterioration may be derived from the fact that the overall electronic structure is determined by the combination of many electronic and steric effects, complicated in this case, by the non-equivalence of the four dmso groups. Small inaccuracies may accumulate and worsen the performance of the method. On ˚) the contrary, the experimental difference (0.034 A between the Ru–S distance trans to O and Cl is well ˚ ). Owing to the reproduced by the theory (0.028 A small difference of trans-influence between O and Cl atoms, it seems likely that the longer values for Ru–S bonds cis to dmso-O are due to steric interactions involving these cis dmso ligands. Also, the Ru– ˚ ) is longer than in Cl distance trans to S (2.489 A ˚ ). Finally, the S–O trans-RuCl2(dmso-S)4 (2.478 A distance in the dmso-O moiety is longer than in dmso-S, both in the experiment and theory. The most striking feature of the hypothetical isomer, cis-RuCl2(dmso-S)4, is the exceptionally long distance calculated for one of the two trans ˚ ). This probably results from Ru–S bonds (2.658 A the p competition between the two trans dmso-S ligands and the strong steric repulsions between the cis dmso ligands. As a matter of fact, the total energy
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(a)
(b)
Fig. 7. Sketch of the molecular structure of (a) [cis,fac– Ru(NH3)2H3(dmso-S)] 2; and (b) Ru(CO)5(dmso-S).
of the actually isolated isomer, cis,fac-RuCl2(dmsoS)3(dmso-O), is 56 kJ/mol lower than that of cisRuCl2(dmso-S)4. 3.3. Ru(II)–dmso complexes: binding energies In the previous section, we observed that in all the studied cases, the total energy of the known compounds calculated experimentally were lower than for the model molecules which represent their linkage isomers. This indicates that the present method should be able to give reliable provisions about the preference for S- or O-bonding of dmso in a series of Ru(II) linkage isomers. In order to gain some information about the Ru–S or Ru–O bond strengths, we calculated the binding energy (BE) of the dmso ligand as the energy involved in the following process: RuXn dmso ! RuXn 1 dmso where RuXn(dmso) indicates the whole complex and RuXn the complex obtained by abstraction of the dmso moiety. If we reconsider the two complexes cis,fac-RuCl2(CO)3(dmso) and [Ru(NH3)5(dmso)] 21, for the first one the calculated dmso BEs are 132 and 110 kJ/mol for the dmso-O and dmso-S isomers, respectively. On the contrary, for the second one, the calculated dmso BEs are 200 and 225 kJ/mol for the dmso-O and dmso-S isomers, respectively. Hence, calculations indicate that dmso is more strongly bound to Ru(II) via O in the presence of CO ligands and via S in the presence
of NH3 ligands, corroborating the argument based on the p back-donation. As to the other two complexes, cis,facRuCl2(dmso-S)3(dmso-O) and trans-RuCl2(dmso-S)4, it is of interest to observe that the BE of 161 kJ/mol, calculated for the dmso-S in trans-RuCl2(dmso-S)4, is increased to 172 and 208 kJ/mol in cis,facRuCl2(dmso-S)3(dmso-O), for the dmso-S trans to Cl and O, respectively. This is in agreement with the thermodynamic instability of trans-RuCl2(dmsoS)4 with respect to cis,fac-RuCl2(dmso-S)3(dmso-O), where each dmso-S ligand is trans to Cl or O atoms, namely atoms without p accepting properties [14]. This BE trend parallels the reduction of the mean Ru(II)–S bond length passing from compounds with ˚ ) to that of trans dmso-S ligands (2.330(4) A compounds where dmso-S is trans to N, O, or Cl ˚ ) [1,2]. ligands (2.265(3) A However, in spite of this success it must be observed that the calculated total energy of transRuCl2(dmso-S)4 is lower than that of cis,facRuCl2(dmso-S)3(dmso-O) by 33 kJ/mol, in contrast with its thermodynamic instability. We have already pointed out some inaccuracies in the present method, while describing the electronic structure of different diastereomeric species. The most probable cause can be attributed, as mentioned above, to the difficulty of the method to treat systems where steric repulsions between ligands play a significant role in defining the electronic structure of the complexes. Thus probably, in cis,fac-RuCl2(dmso-S)3(dmso-O) the steric interactions are overestimated with respect to transRuCl2(dmso-S)4, yielding a large total energy. BE calculations were also performed for the hypothetical isomers, trans,mer-RuCl2(dmsoS)3(dmso-O) and cis-RuCl2(dmso-S)4. As already observed, both of them have a total energy larger than that calculated for the corresponding isolated isomers, with an increase of 77 and 56 kJ/mol for the trans- and cis-RuCl2 derivatives, respectively. The dmso BEs in trans,mer-RuCl2(dmso-S)3(dmsoO) of 140 and 230 kJ/mol, for the dmso groups trans to S and O, respectively, indicate a weakening of the Ru–S trans to S, and a strengthening of the Ru–S trans to O bonds. In cis-RuCl2(dmsoS)4, the BE of the dmso-S trans to Cl is 148 kJ/ mol, while the BE’s for the two trans dmso-S ligands are 50 and 190 kJ/mol. The marked
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as [cis,fac–Ru(NH3)2H3(dmso-S)] (Fig. 7(a)) and [Ru(CO)5(dmso-S)] 21 (Fig. 7(b)), able to emphasize, respectively, the different behavior of s donor and p acceptor ligands in dmso-S complexes. These systems were analyzed without imposing any symmetry constraint, but only internal coordinates involving the Ru–dmso moiety were optimized. For the other fragments the average covalent radii were used to build the structures. This choice was suggested by the fact that in the present case we are only interested in the comparison of the internal coordinate of the dmso fragment in the two model systems, hence we can take advantage in the computational economy by reducing the number of degrees of freedom.
Table 7 Optimized internal coordinates (with BP functional) of [cis,fac– Ru(NH3)2H3(dmso-S)] 2 and [Ru(CO)5(dmso-S)] 21 Internal coordinate
[Cis,fac–Ru(NH3)2H3 (dmso-S)] 2
[Ru(CO)5 (dmso-S)] 21
˚) Ru–S (A ˚) S–O (A ˚) S–C (A C–S–C (8) O–S–C (8) Ru–S–O (8)
2.187 1.553 1.875 92.0 100.6 119.0
2.513 1.463 1.810 103.2 110.7 108.8
weakening of one Ru–S bond is related to its ˚. extremely long Ru–S distance of 2.66 A 3.4. Ru(II)–dmso model molecules
3.4.1. Bond length trends The results are reported in Table 7. In agreement with the expectations, the Ru–S bond length in
The effect of p back-bonding on the Ru–S and S–O bond lengths was investigated on model species, such
a E
101 2
b
c
80 70 60 50 40 30 20 10 0 -10 -20 -30 0
30
60
90
120
150
180
φ Fig. 8. Relative energy, E (kJ/mol), as a function of the rotation angle f , around the Ru–S bond in the model system [cis,fac– Ru(NH3)2H3(dmso-S)] 2, shown in three projections down the S–Ru–H axis, (a) f 08, (b) f 908, (c) f 1808. Solid line, total energy; dashed line, partial steric contribution; dotted line, partial electronic contribution.
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Table 8 Optimized internal coordinates (with BP functional) of [Ru(CO)5(dmso-O)] 21 in trans–trans and cis–cis conformations Internal coordinate
Trans–trans
Cis–cis
˚) Ru–O (A ˚) S–O (A ˚) S–C (A Ru–O–S (8)
2.147 1.597 1.806 126.8
2.173 1.559 1.808 149.7
[cis,fac–Ru(NH3)2H3(dmso-S)] 2 is as short as ˚ , while the S–O distance is 1.553 A ˚ . On the 2.187 A contrary, in [Ru(CO)5(dmso-S)] 21, the Ru–S and S– ˚ , respectively. O bond distances are 2.513 and 1.463 A These trends support the assumption that the reduction of the electron charge density on the metal atom, caused by the substitution of s donor ligands (H, NH3) with p acceptors (CO), decreases its p back-donation ability, weakening the metal to sulfur bond. As a consequence, the positive charge on the sulfur atom is increased enhancing the p bonding in the S–O bond. It is worth noting that in [cis,fac– Ru(NH3)2H3(dmso-S)] 2, the S–C bond distances ˚ ) are also longer than in [Ru(CO)5(dmso(1.875 A ˚ ), suggesting that p back-donation S)] 21 (1.810 A involves dmso empty orbitals with S–O and S–C antibonding character, such as the virtual orbital 8a 00 depicted in Fig. 2. Calculations suggest that as the S– O and S–C bond lengths decrease, the C–S–C and O–S–C bond angles increase. 3.4.2. Conformational aspects The presence of a substantial double bond character in the Ru–S bond was related to the necessity of a hindered rotation about the Ru–S bond, yielding a well determined orientation of the sulfoxide ligand with respect to the equatorial coordination plane, in order to achieve an optimum orbital overlap [28]. Thus, in [trans–RuCl4(dmso-S)2] 2, the existence of two orientations of the square arrangement of the chlorides (related by a rotation about the S–Ru–S axis of 17.68) was taken as a proof for the lack of p bonding [28]. In fact, in a Ru(III) complex with two trans dmso-S ligands, little p bonding is expected, as confirmed by the calculation of the total energy as a function of the torsion angle f around the Ru–S bond (08 # f # 3608, step 58) in [Ru(CO)5(dmso-S)] 21 which shows very small energy variations (,1.2 kJ/mol). On the contrary,
the same analysis carried out for [cis,fac– Ru(NH3)2H3(dmso-S)] 2, where considerable p bonding is present, shows that the only significant energy difference upon rotation around the Ru–S bond is due to steric rather than electronic factors. In fact, as shown in Fig. 8, the total energy shows two rather flat energy minima 08 # f # 508 and 1508 # f # 1808, whose energy difference (< 65 kJ/mol) is due to the different orientation of the bulkiest ligands. In fact, when f 08, the S–O bond bisects the N–Ru–N angle and the methyl groups point towards the small equatorial H ligands. However, when f 1808, the S–O bond bisects the H–Ru–H angle and both the methyl groups point towards the bulkier ammonia molecules, causing a marked increase of the steric energy contribution. The steric situation at f between 608 and 1008 is intermediate with one CH3 group close to one NH3 molecule, and the other close to the cis H ligand, as shown by a flat relative energy minimum (35 kJ/mol) (dashed line in Fig. 8). It must be concluded that proper metal d orbital combinations can overlap with proper dmso orbitals to give p back-donation, and that the mutual orientation of the axial and equatorial ligands have only a minor effect on the total energy profile, which is essentially governed by steric factors. The most interesting stereochemical features of Obonded sulfoxide complexes consider the rotation about the metal to oxygen and S–O bonds. Molecular mechanics (MM) calculations on cis,fac-RuCl2(dmsoS)3(dmso-O), have shown in agreement with experimental evidence [1,2], that the most stable conformation of the Ru–O–Sme2 group is characterized by a trans–trans arrangement of the methyl groups, followed by the cis–cis one [29]. Present calculations on [Ru(CO)5(dmso-O)] 21 support this observation, the trans–trans conformer having an energy of 19 kJ/mol lower than the cis–cis one. Interestingly, as shown in Table 8, theory predicts a high strain in the cis–cis conformer with a lengthening of the Ru–O bond distance and a marked widening of the Ru–O–S bond angle, accompanied by a shortening of the S–O bond length. As to rotation about the Ru–O bond, MM calculations showed that in cis,facRuCl2(dmso-S)3(dmso-O) the O-bonded ligand is rather free to rotate around the midpoint defined by the chloride ligands (Df < ^808) [29]. A marked
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energy barrier arises only when the sulfur atom approaches the bulkier dmso-S groups. In the case of the more symmetrical pentacarbonyl derivative [Ru(CO)5(dmso-O)] 21, present calculations show that there is no energy barrier practically, the maximum energy difference being less than 3 kJ/mol in both trans–trans and cis–cis conformers.
4. Conclusions In this work, a series of four complexes of Ru(II) with dmso was studied by means of the DFT method employing the BP exchange-correlation energy functional. The comparison of the calculated results with the experiment is fairly good, the most important trends observed in many different situations are well reproduced by theory, although a general overestimate of the calculated bond lengths is found. The present method was proved to be reliable to decide, on simple energy grounds, which is the preferred bonding mode of dmso in a given environment of ancillary ligands. The results on the Ru–S bonds are consistent with metal–dmso p back-donation arguments, showing a strengthening of the Ru–S bond and a weakening of the S–O bond by increasing the metal electron charge density. When this is markedly reduced, O-bonding is favored. Deterioration of the results are found in special situations, particularly in sterically crowded complexes where the steric repulsion effects seem to be overestimated with respect to the purely electronic ones. The trends of the calculated Ru–dmso binding energies are also consistent with the observed linkage isomer stability. The study of model molecules, with emphasized electronic properties, provided further support to the proposed bonding model, and an insight into the conformational properties of dmso metal complexes. The overall good performance of the method and its computational economy makes it interesting for further applications in this field, where traditional ab initio approaches are impracticable and semi-empirical methods can be too approximate to give reliable results. As a matter of fact, ab initio calculations on [trans–RuCl4(CO)(dmso-O)] 2 provided the correct trends of the bond lengths and the vibrational spectrum characteristics, but the geometry optimization
103
indicated the cis–cis conformation as the most stable [30]. Acknowledgements This work was supported by grants from MURST and CNR of Rome (Italy).
References [1] M. Calligaris, O. Carugo, Coord. Chem. Rev. 153 (1996) 83. [2] M. Calligaris, Croat. Chem. Acta. 72 (1999) in press. [3] M. Henn, E. Alessio, G. Mestroni, M. Calligaris, W.M. Attia, Inorg. Chim. Acta. 187 (1991) 39. [4] E. Alessio, G. Balducci, A. Lutman, G. Mestroni, M. Calligaris, W.M. Attia, Inorg. Chim. Acta. 203 (1993) 205. [5] E. Alessio, B. Milani, M. Bolle, G. Mestroni, P. Faleschini, F. Todone, S. Geremia, M. Calligaris, Inorg. Chem. 34 (1995) 4722. [6] E. Alessio, M. Bolle, B. Milani, G. Mestroni, P. Faleschini, S. Geremia, M. Calligaris, Inorg. Chem. 34 (1995) 4716. [7] M. Calligaris, P. Faleschini, F. Todone, E. Alessio, S. Geremia, J. Chem. Soc., Dalton Trans. (1995) 1653. [8] C.W. Bauschlicher, S.P. Walch, S.R. Langhoff, Quantum Chemistry, in: A. Veillard (Ed.), The Challenge of Transition Metals and Coordination Chemistry, D. Reidel, Dordrecht, 1985, p. 15. [9] D.P. Chong (Ed.), Recent Advances in Density Functional Methods World Scientific, Singapore, 1995. [10] T. Ziegler, V. Tschinke, in: J.K. Labanowsky, J.W. Andzelm (Eds.), Density Functional Methods in Chemistry, Springer, New York, 1991, p. 139. [11] N. Ro¨sch, G. Pacchioni, in: G. Schmid (Ed.), Clusters and Colloids: from Theory to Application, VCH, Weinheim, 1994, p. 5. [12] F.C. March, G. Ferguson, Can. J. Chem. 49 (1971) 3590. [13] C.V. Senoff, E. Maslowsky Jr., R.G. Goel, Can. J. Chem. 49 (1971) 3585. [14] E. Alessio, G. Mestroni, G. Nardin, W.M. Attia, M. Calligaris, G. Sava, S. Zorzet, Inorg. Chem. 27 (1988) 4099. [15] R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. [16] E.J. Baerends, D.E. Ellis, P. Ros, Chem. Phys. 2 (1973) 41. [17] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [18] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [19] J.P. Perdrew, Phys. Rev. B 33 (1986) 8822. [20] T. Ziegler, A. Rauk, Theoret. Chim. Acta 49 (1977) 1. [21] W. Feder, H. Dreizler, H.D. Rudolph, V. Typke, Z. Naturforsch. 24 (1969) 266. [22] A. Bertoluzza, S. Bonora, G. Fini, M.A. Battaglia, P. Monti, J. Raman Spec. 11 (1981) 430. [23] O.D. Ha¨berlen, S.C. Chung, M. Stener, N. Ro¨sch, J. Chem. Phys. 106 (1997) 5189. [24] J.A. Davies, Adv. Inorg. Chem. Radiochem. 24 (1981) 115.
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[25] N.S. Panina, Yu.N. Kukushkin, Zh. Neorganich. Khimii 42 (1997) 466. [26] S. Ianelli, A. Musatti, M. Nardelli, R. Benassi, U. Folli, F. Taddei, J. Chem. Soc. Perkin Trans. 2 (1992) 49. [27] S. Geremia, G. Desogus, M. Calligaris, Acta Chim. Slov. 43 (1996) 207.
[28] J.S. Jaswal, S.J. Rettig, B.R. James, Can. J. Chem. 68 (1990) 1808. [29] S. Geremia, M. Calligaris, J. Chem. Soc. Dalton Trans. (1997) 1541. [30] N.S. Panina, Yu.N. Kukushkin, M. Calligaris, Russian J. Inorg. Chem. (1999) in press.
Density functional study of structural properties and binding energies of dimethylsulfoxide Ru(II) complexes M. Stener*, M. Calligaris Dipartimento di Scienze Chimiche, Universita` di Trieste, I-34127 Trieste, Italy Received 19 March 1999; received in revised form 5 May 1999; accepted 4 June 1999
Abstract The structures of a series of Ru(II)–dimethylsulfoxide complexes were optimized using a density functional method. The obtained bond lengths reproduce the experimental trends quite well, although a general overestimate is found. The theory is also used to predict the kind of coordination linkage (via O or S) preferred by dmso when different ancillary ligands are present. The results are consistent with the experimental findings and can be explained in terms of s–p contributions in the sulfoxide–metal bond. Insight into the strength of the oxygen/sulfur metal bonds is further given by the calculation of the binding energies of the sulfoxide fragments in different situations. Model molecules with emphasized electronic effects are also considered to confirm the trends and to study special aspects such as preferred conformation structures. The general good performance, combined to computational economy, makes the present method suitable for further applications in this field. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Density functional theory; Binding energies; Dimethylsulfoxide; Ruthenium
1. Introduction Ruthenium sulfoxide complexes display many intriguing stereochemical properties, involving both metric and topographical features, as a consequence of the ambidentate nature of the sulfoxide ligands. This gives rise to linkage isomerism with the formation of S- and O-metal coordinated compounds, depending on the balance of several factors such as the metal oxidation state and mainly, the steric and electronic properties of the sulfoxide and other ancillary ligands [1,2]. Thus, it was observed that in Ru(II) complexes, containing dimethylsulfoxide (dmso) and
* Corresponding author. Tel.: 139-040-6763952; fax: 139-0406763903. E-mail address: [email protected] (M. Stener).
s donor ligands (e.g. NH3), S-bonding is largely preferred, while introduction of strong p acceptor ligands (e.g. CO) favors O-bonding [3–6]. The latter is further favored in Ru(III) complexes, specially in the case of bulkier ligands like diphenyl sulfoxide [7]. The role of the electronic factors was rationalized on the basis of the p acceptor properties of the sulfoxide ligands, and the metal electron charge density either increased or decreased by s donor or p acceptor ligands [1,2]. However, in the first case, p backdonation from metal to sulfoxide molecular orbitals can be strong enough to stabilize S-bonding. In fact, the vast amount of spectroscopic (IR, NMR) and structural (X-ray) data, so far collected, show that O-bonding is largely predominant with “hard” metal ions, while Sbonding is prevalent only with “soft” metal ions of the second and third transition series in group VIII, like ruthenium(II) and, specially, platinum(II) [1,2].
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00200-6
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The aim of the present theoretical study is to substantiate such a rationalization in terms of a general molecular orbital method. The presence of a transition metal and the overall rather large ligand size suggests the use of a computational approach based on the density functional theory (DFT). However, in the transition metal complex, the electron correlation is usually important. Thus, a theoretical study soon becomes intractable by traditional ab initio method, as it is necessary to drastically enlarge the excitation space in a CI formalism, and the use of perturbative schemes may not be very efficient if non-dynamical electron correlation is present [8]. On the contrary, semi-empirical methods are often too approximate to give reliable results in the field of transition metal chemistry. In recent years, the first-principle DFT approaches have become more and more customary [9], as they are much cheaper compared to the traditional ab initio methods, and can describe, with reasonable accuracy, the electronic structure of systems in which the electron correlation plays an important role, like, e.g. transition metal complexes [10] or large transition metal clusters [11]. In order to test the capability of the DFT approach to describe the bonding between Ru(II) and dmso, in the presence of different ancillary ligands, we optimized the geometries of the free ligand itself and those of four significant complexes: cis,fac-RuCl2(CO)3(dmso-O) [5], [Ru(NH3)5(dmso-S)] 21 [12,13], and cis,fac-RuCl2(dmsotrans-RuCl2(dmso-S)4 S)3(dmso-O) [14]. Particular attention has been devoted to the calculation of the dmso binding energy contributions. Further, the protonated dmso, [(dmso)H] 1, and two model complexes, [cis,fac-Ru(NH3)2H3(dmsoS)] 2 and [Ru(CO)5(dmso-S)] 21, representing extreme cases of dmso-S complexes containing strong s donor and p acceptor ancillary ligands, were considered for a thorough investigation of the structural and conformational properties of Ru–dmso complexes.
2. Computational methods The electronic structure of the complexes is
obtained by solving the Kohn–Sham equations [15], in the framework of the DFT, employing the ADF program [16]. During the SCF procedure, the general gradient approximation (GGA) to the exchange correlation energy functional is selfconsistently employed, based on the VWN [17] parametrization corrected by gradient terms for the exchange [18] and the correlation [19], giving the so-called Becke–Perdew (BP) functional. Only for preliminary calculations on the free and protonated dmso the simpler VWN functional, not corrected by gradient terms, is used. In order to choose a basis set which is a good compromise between economy and accuracy, we performed preliminary tests optimizing the free dmso geometry with basis sets of increasing size. A frozen core DZP STO basis set proved to be a good choice for all atoms, with the exceptions of S and Ru. A DZP basis set, with frozen 1s shell for second row elements, and a DZP with frozen 1s, 2s and 2p shells for third row elements were employed. For H, the pure DZP set was chosen, taking the optimized exponents from the database included in the ADF program package [16]. For S, the DZP standard set was modified as regards the polarization functions. We employed two 3d STO with exponents 1.0 and 2.0, and one 4f STO with exponent 2.25. For Ru, the standard TZ basis set included in the ADF program package was employed, keeping the core orbitals frozen up to all the shells with principal quantum number 3. The optimized auxiliary basis set used to fit the electron density was also taken from the same database. During the geometry optimization, all the degrees of freedom were optimized within the imposed symmetry constraints. Unless differently specified, the Cs point group was assumed. The binding energies were calculated with respect to the fragments and not directly as differences of total energies, as a general strategy of ADF [16]. The splitting of energy contributions into steric and electronic terms was performed according to Ref. [20]. The Mulliken charges were used only to give a qualitative description of the electronic structure, as they are very sensitive to the basis set size. These numbers should be considered with caution, focusing more on the trends than on their absolute values.
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(a)
(b)
93
(c)
Fig. 1. Sketch of the molecular structure of (a) dmso; (b) [dmso-OH] 1; and (c) [dmso-SH] 1.
3. Results and discussion 3.1. Dimethylsulfoxide The calculation of the structural parameters of the free dmso ligand is important not only as a test for the choice of the basis set and exchange-correlation functional, but also because the comparison of the dmso structure with those of the protonated and metal coordinated ligand provides fundamental information about its bonding properties. 3.1.1. Free dimethylsulfoxide The optimized internal coordinates and the dipole moment of free dmso (Fig. 1(a)), as obtained with BP and VWN functionals under the Cs point group symmetry, are reported in Table 1 together with the experimental gas phase data [21,22]. We can observe the overall agreement between the observed and the VWN structure, particularly for the bond lengths. It is worth noting that the inclusion of two 3d and one 4f polarization functions in the S basis set is mandatory to obtain converged values in the optimization procedure. If the basis set is further enlarged (on S or on the Table 1 Optimized internal coordinates and dipole moment (with BP and VWN functionals) and experimental data (Exp) of free dmso molecule
˚) S–O (A ˚) S–C (A C–S–O (8) C–S–C (8) m (D) a b
Ref. [21]. Ref. [22].
BP
VWN
Exp
1.507 1.834 107.2 95.1 3.65
1.489 1.794 106.8 94.9 3.67
1.485(6) a 1.799(5) a 106.65(3) a 96.57(3) a 3.9 b
other atoms), the results do not change appreciably, while if the smaller standard DZP set (with only one 3d polarization function) is employed for S, the bond ˚. lengths worsen as they increase by about 0.03 A The BP results are definitely worse than the VWN ones: the S–O and S–C bond distances are overesti˚ , respectively, while mated by about 0.02 and 0.04 A the angles show a similar or slightly better agreement. This is not surprising, as it is well known that GGA functionals (like BP) drastically improve the binding energies, while they often give bond lengths that are too long [23]. We have considered here the VWN functional for a comparison between the calculated and experimental structural parameters, in order to assess the basis set requirements for dmso and to test the performances of the method in a stringent way. However, with the exception of the protonated dmso, in the following we will consider only the BP functional, in spite of some deteriorations of the structural parameters, as we are mainly interested in the binding energies and the trends of the bond lengths, rather than their absolute values. Finally, we can observe that the calculated dipole moment is in fairly good agreement with the experimental value with both the functional choices. In fact, the electron density is not very sensitive to the functional. The BP values of the Mulliken charges are: O, 20.64; S, 10.59; C, 20.19, while for H they range from 10.06 to 10.10. These values are consistent with the well known [24] strong polarization of the sulfoxide S–O bond, assessed by ab initio SCF calculations [25,26] and, recently, also evidenced by valence electron density maps, from X-ray diffraction experiments [27]. To complete the description of free dmso, we investigated the nature of its lowest virtual orbitals, as they are involved in the backdonation from the metal to the
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a
O
S
C
S
b
C
Fig. 2. Contour plots relative to the virtual level 8a 00 of dmso: solid, dashed and dot-dashed lines mean positive, negative and zero (nodal line) contributions, respectively. (a) In the plane passing through the S–O bond and orthogonal to the Cs mirror plane; (b) in the plane defined by the ˚ ), isolines: 0, ^ 0.02, ^ 0.05, ^ 0.1, ^ 0.2, ^ 0.5. three atoms C–S–C. Side length: 15 a.u. (7.938 A
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95
Table 2 Optimized internal coordinates, Mulliken charges (Q) and relative total energies (kJ/mol)(with BP and VWN functional) of free and protonated dmso molecules. [dmso-OH]1 and [dmso-SH] 1 indicate the protonation at O and S atoms, respectively BP
˚) S–O (A ˚) S–C (A C–S–O (8) C–S–C (8) ˚) O–H (A ˚) S–H (A QO (e) QS (e) Relative E
VWN
Dmso
[dmso-OH]
1.507 1.834 107.2 95.1 – – 20.64 10.59 0
1.631 1.792 100.6 101.1 0.993 – 20.55 10.80 2885
1
[dmso-SH] 1.447 1.776 115.7 106.8 – 1.379 20.53 10.98 2793
ligated dmso. Three almost degenerate empty orbitals are found: 8a 00 , 15a 0 and 16a 0 . 8a 00 is the most important because it has mainly p p(S–O) character and should play the major role in back-donation, 15a 0 and 16a 0 have, respectively, mainly S 3d and s p(C– H) character. This attribution was assessed on the grounds of a direct inspection of the wave function shown in Fig. 2, where the plot of the 8a 00 orbital is reported, in the plane through the S–O bond and orthogonal to the symmetry reflection plane (a) and in the C–S–C plane (b). It is apparent that this orbital is delocalized and has p p(S–O) and s p(S–C) character. 3.1.2. (Dmso)H] 1 Table 2 reports the BP and VWN results for the two isomers of the protonated dmso, [dmso-OH] 1 and [dmso-SH] 1 (Fig. 1(b) and (c)), the former being, so far, the only isolated species [1,2]. If we restrict our
1
Dmso
[dmso-OH] 1
1.489 1.794 106.8 94.9 – – 20.61 10.58 0
1.602 1.754 100.6 100.8 0.993 – 20.53 10.82 2865
[dmso-SH] 1 1.432 1.736 115.2 107.4 – 1.384 20.50 10.93 2772
analysis to the BP results, the comparison with the calculated free dmso parameters shows in [dmsoOH] 1 a marked lengthening of the S–O distance ˚ ) and a shortening of the S–C distances (0.124 A ˚ ), accompanied by a narrowing (6.68) of the (0.042 A O–S–C angle and widening (6.08) of the C–S–C angle. This trend is in excellent agreement with the experimental evidence [1,2]. On the contrary, the [dmso-SH] 1 isomer is characterized by a reduction of both the S–O and S–C bond lengths and a widening of all the bond angles, the latter due to the passage from a pyramidal to a tetrahedral structure of the S atom. However, its energy is far greater (92 kJ/mol) than that of the O-protonated species, supporting the observation that with “hard” ions O-bonding is preferred. Further, the present results confirm the suggestion that O-coordination implies a decrease of the S–O bond order, while S-coordination implies its increase, with respect to the free ligand, in which the
Table 3 Optimized distances (with BP functional) and experimental data [5] (Exp) of cis,fac-RuCl2(CO)3(dmso-O) and cis,fac-RuCl2(CO)3(dmso-S) ˚) Distance (A
Exp
Cis,fac-RuCl2(CO)3(dmso-O)
Cis,fac-RuCl2(CO)3(dmso-S)
Ru–O Ru–S S–O S–C Ru–Cl Ru–C a Ru–C b
2.095 – 1.535 1.768 2.393 1.902 1.879
2.169 – 1.557 1.812 2.440 1.929 1.904
– 2.480 1.473 1.805 2.442 1.928 1.954
a b
cis to dmso. trans to dmso.
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(a)
(b)
Fig. 3. Sketch of the molecular structure of (a) cis,fac-RuCl2(CO)3(dmso-O); and (b) cis,fac-RuCl2(CO)3(dmso-S).
S–O bond has a considerable double bond character [1,2]. The VWN results lead to the same conclusions, as far as only trends are considered. On the contrary, a general shortening of the bonds is observed, as expected after the previous analysis on free dmso. 3.2. Ru(II)–dmso complexes: molecular structures In this section, we will consider four ‘real’ Ru(II)– dmso complexes with different ancillary ligand environments: two limiting situations, one with p acceptor (CO) and the other with s donor (NH3) ligands, and two intermediate cases, with dmso-S and dmso-O as ancillary ligands. In addition, the structures and energies of ‘hypothetical’ (not yet observed) linkage isomers will also be described. 3.2.1. cis,fac-RuCl2(CO)3(dmso-O) The BP geometry optimization results for this complex are reported in Table 3, together with the experimental values and those calculated for its hypothetical isomer, cis,fac-RuCl2(CO)3(dmso-S) (Fig. 3). The comparison between the experimental data and those calculated for the cis,fac-RuCl2 (CO)3(dmso-O) complex is satisfactory as regards the trends in the bond distances, in spite of their general overestimate, caused by the BP functional. It is worth noting that the strong S–O elongation with ˚ ), caused by the coordirespect to free dmso (0.050 A nation to Ru(II), is exactly reproduced by theory. This
trend is in agreement with the more general observation that the S–O distance passes from an average ˚ in free sulfoxides to that of value of 1.492(1) A ˚ in O-coordinated metal complexes [1,2]. 1.529(1) A Further, Table 3 shows that the S–C distance is shor˚ upon coordination, which is again tened by 0.031 A ˚ ), and in correctly predicted by the theory (0.022 A ˚ agreement with the mean reduction of 0.010 A observed while passing from free sulfoxides to Obound complexes [1,2]. The hypothetical linkage isomer, cis,fac-RuCl2(CO)3(dmso-S), displays a very long Ru–S distance ˚ ), far beyond the longest observed value of (2.480 A ˚ , found in cis,cis,trans-RuCl2(CO)2(dmso2.364(1) A S)2 [5]. Of course, the high absolute value is an artifact of the BP functional, in fact a VWN optimization ˚ , still long but in better furnished a value of 2.395 A agreement with the experimental values. The definite Ru–S elongation is consistent with the idea of the marked competition between the two trans p acceptor ligands, CO and dmso-S, with subsequent dramatic weakening of the Ru–S bond. This competition effect between the two trans ligands also results in the ˚ ) of the Ru–C distance, trans lengthening (0.050 A to dmso, passing from the dmso-O to the dmso-S isomer, while the cis Ru–C bond lengths remain practically unaffected. As for [dmso-SH] 1, the BP calcu˚ ) is found to be much lated S–O distance (1.473 A ˚ ), in agreement shorter than that in free dmso (1.507 A with the experimental observation that the S–O ˚ distance passes from an average value of 1.492(1) A
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97
Table 4 Optimized distances (with BP functional) and experimental data [12] (Exp) of [Ru(NH3)5(dmso-S)] 21 and [Ru(NH3)5(dmso-O)] 21 ˚) Distance (A
Exp
[Ru(NH3)5(dmso-S)] 21
[Ru(NH3)5(dmso-O)] 21
Ru–S Ru–O S–O S–C Ru–N a Ru–N b
2.188 – 1.512 1.815 2.155 2.203
2.272 – 1.504 1.808 2.189 2.247
– 2.236 1.562 1.811 2.178 2.146
a b
cis to dmso. trans to dmso.
˚ in S-coordinated in free sulfoxides to 1.472(1) A metal complexes [1,2]. The Mulliken charges in the dmso-O complex are: O, 20.73; S, 10.79, while in the dmso-S isomer they are: O, 20.58; S, 10.66. It is evident that the improved S–O p overlap, passing from the dmso-O to the dmso-S derivative, reduces the bond polarization. A similar effect, but much weaker, seems to be present for the S–C distances. However, the differences are too small to be reliable at this level of calculation. Interestingly, the calculated energy difference between the O- and S-coordinated isomers of cis,fac-RuCl2(CO)3(dmso), shows that the dmso-S isomer is less stable by 29 kJ/mol with respect to the dmso-O one. This supports the proposal that the Ru–S
(a)
(b)
Fig. 4. Sketch of the molecular structure of (a) [Ru(NH3)5(dmsoS)] 21; and (b) [Ru(NH3)5(dmso-O)] 21. For sake of clarity the ammonia H atoms are not shown.
bond trans to CO is destabilized in favor of O-bonding, so that only the dmso-O isomer is formed. 3.2.2. Ru(NH3)5(dmso-S)] 21 This complex represents the opposite limit in the electronic properties of the ancillary ligands, which now are strong s donors. In Table 4, the BP optimized geometry of [Ru(NH3)5(dmso-S)] 21 is reported, together with the experimental data [12] and those calculated for its hypothetical linkage isomer [Ru(NH3)5(dmso-O)] 21 (Fig. 4). The most striking features of the experimental structure are the very short Ru–S bond distance ˚ ) and the very long S–O bond distance (2.188(3) A ˚ ) [12]. In fact, it was shown that the aver(1.512(7) A age values for the Ru–S and S–O bond distances in Ru(II)–sulfoxide complexes are 2.265(3) and ˚ , respectively [1,2]. The dramatic lengthen1.478(1) A ing of the S–O distance, towards the mean value of ˚ found in dmso-O metal complexes, is in 1.529(1) A agreement with the marked decrease of the S–O stretching frequency, from the free to the coordinated sulfoxide [13]. These trends are consistent with the existence of a partial double bond character in the Ru(II)–S bond, attributable to a p back-donation from full d orbitals of the metal to the empty MO’s of the sulfoxide, with mainly S–O antibonding character. Such a bonding scheme is further supported by a considerable amount of crystallographic and spectroscopic (IR) data from a variety of Ru(II) and Ru(III) complexes containing s donor or p acceptor ligands [1,2]. The present calculations are consistent with these considerations if we compare the calculated Ru–S ˚ ) and S–O (1.504 A ˚ ) distances with those (2.272 A
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Table 5 Optimized distances (with BP functional) and experimental data [14] (Exp) of trans-RuCl2(dmso-S)4 and trans,mer-RuCl2(dmsoS)3(dmso-O) Distance ˚) (A
Exp
Trans-RuCl2 (dmso-S)4
Trans,mer-RuCl2 (dmso-S)3(dmso-O)
Ru–S a Ru–S b Ru–O Ru–Cl S–O a S–O b S–O c S–C a S–C b S–C c
2.352 – – 2.402 1.491 – – 1.780 – –
2.402 – – 2.478 1.505 – – 1.808 – –
2.391–2.404 2.252 2.336 2.468 1.488–1.505 1.500 1.518 1.805–1.812 1.809 1.818
a
trans to dmso-S. trans to dmso-O. c dmso-O. b
found in the previous model molecule cis,fac˚ , respecRuCl2(CO)3(dmso-S), of 2.480 and 1.473 A tively. Substitution of CO with NH3 ligands causes a significant shortening of the Ru–S distance and lengthening of the S–O distance as a consequence of the increased metal electron charge density, and hence of its p back-donation ability. Finally, it is of interest to note that the present calculations confirm the experimentally observed trans influence effect of dmso-S on the trans Ru–N ˚ longer than the Ru– distance. This, in fact, is 0.048 A N distances trans to N, in agreement with the ˚ . Interestingly, the calculated difference of 0.058 A
(a)
energy calculated for the linkage isomer, [Ru(NH3)5(dmso-O)] 21, is 13 kJ/mol higher than that of the isolated complex, [Ru(NH3)5(dmso-S)] 21, showing the preference for S-bonding in the presence of s donor ligands. 3.2.3. trans-RuCl2(dmso-S)4 In this case, besides the chlorides, the ancillary ligand is dmso-S itself, hence the situation is intermediate with respect to the two previous cases. In Table 5, the BP optimized geometry of transRuCl2(dmso-S)4 is reported, together with the experimental data [14] and the results for its hypothetical isomer trans,mer-RuCl2(dmso-S)3(dmso-O) (Fig. 5). The Cs point group was employed during the geometry optimization of the first system, while for the second one no symmetry constraint was introduced. The comparison of the experimental structure with respect to the calculated one is only fairly satisfactory, showing the usual overestimate of the bond lengths, ˚ ) for the Ru–Cl distance. particularly large (0.076 A Also in this case we checked the performances of the VWN functional, and obtained the following opti˚ and Ru–Cl, mized distances: Ru–S, 2.330 A ˚ in much better agreement with the experi2.416 A ment, as expected. It is interesting to compare the calculated structure of this tetrakis(dmso) complex with that of the previous dmso-S complex, [Ru(NH3)5(dmso-S)] 21. The experimental Ru–S distance is shorter in the ˚ , and this shortening is well reprolatter by 0.164 A ˚ ). This, on the contrary, duced by the theory (0.130 A
(b)
Fig. 5. Sketch of the molecular structure of (a) trans-RuCl2(dmso-S)4; and (b) trans,mer-RuCl2(dmso-S)3(dmso-O). For sake of clarity the methyl H atoms are not shown.
M. Stener, M. Calligaris / Journal of Molecular Structure (Theochem) 497 (2000) 91–104
c c
a
(a)
(b)
Fig. 6. Sketch of the molecular structure of (a) cis,fac-RuCl2(dmsoS)3(dmso-O); and (b) cis-RuCl2(dmso-S)4. For sake of clarity the methyl H atoms are not shown. With reference to Table 6, some dmso ligands are labeled a, c.
˚ of is not able to reproduce the shortening of 0.021 A the S–O distance in trans-RuCl2(dmso-S)4, giving a ˚ . Probably, the electronic and value of only 0.001 A steric bonding situation is too different in the two compounds to be handled by the present method. The comparison is more reliable between more strictly related complexes, like linkage isomers of the same diastereoisomer. In fact, the comparison between trans-RuCl2(dmso-S)4 and trans,merRuCl2(dmso-S)3(dmso-O), shows that all the bond lengths have the expected trend: (i) the Ru–S distances trans to dmso-S are very close in the two Table 6 Optimized distances (with BP functional) and experimental data [14] (Exp) of cis,fac-RuCl2(dmso-S)3(dmso-O) and cisRuCl2(dmso-S)4 Distance ˚) (A
Exp
Cis,fac-RuCl2(dmso-S)3 (dmso-O)
Cis-RuCl2 (dmso-S)4
Ru–O Ru–S a Ru–S b Ru–S c Ru–Cl S–O b S–O c S–O d S–O a
2.134 – 2.279 2.245 2.424 1.470 1.507 1.537 –
2.246 – 2.312 2.284 2.489 1.499 1.497 1.552 –
– 2.658 2.315 2.339 2.478 1.504 1.496 – 1.483
a
dmso-S a in Fig. 6. dmso-S trans to Cl. c dmso-S c in Fig. 6. d dmso-O. b
99
compounds, while that, in the second one, trans to dmso-O is shorter, as expected from the different trans influence effects of the O and S atoms; (ii) the S–O distance of the dmso-O group is longer than in ˚ is dmso-S; (iii) the Ru–O distance of 2.336 A much longer than the mean experimental value of ˚ found in O-bonded sulfoxide metal 2.131(4) A complexes [1,2]. This suggests that formation of this isomer is unfavored. In fact, trans,merRuCl2(dmso-S)3(dmso-O) has an energy which is 77 kJ/mol higher than the isolated isomer transRuCl2(dmso-S)4.
3.2.4. cis,fac-RuCl2(dmso-S)3(dmso-O) The bond distances calculated for this complex, together with that of its hypothetical isomer, cisRuCl2(dmso-S)4 (Fig. 6), and the experimental data, are given in Table 6. These systems were calculated without any symmetry constraint. As usual, the comparison between the experiment and the calculated results of the actually synthesized complex is satisfactory, making allowance for the overestimate of the bond lengths. As mentioned above, this severe deterioration may be derived from the fact that the overall electronic structure is determined by the combination of many electronic and steric effects, complicated in this case, by the non-equivalence of the four dmso groups. Small inaccuracies may accumulate and worsen the performance of the method. On ˚) the contrary, the experimental difference (0.034 A between the Ru–S distance trans to O and Cl is well ˚ ). Owing to the reproduced by the theory (0.028 A small difference of trans-influence between O and Cl atoms, it seems likely that the longer values for Ru–S bonds cis to dmso-O are due to steric interactions involving these cis dmso ligands. Also, the Ru– ˚ ) is longer than in Cl distance trans to S (2.489 A ˚ ). Finally, the S–O trans-RuCl2(dmso-S)4 (2.478 A distance in the dmso-O moiety is longer than in dmso-S, both in the experiment and theory. The most striking feature of the hypothetical isomer, cis-RuCl2(dmso-S)4, is the exceptionally long distance calculated for one of the two trans ˚ ). This probably results from Ru–S bonds (2.658 A the p competition between the two trans dmso-S ligands and the strong steric repulsions between the cis dmso ligands. As a matter of fact, the total energy
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(a)
(b)
Fig. 7. Sketch of the molecular structure of (a) [cis,fac– Ru(NH3)2H3(dmso-S)] 2; and (b) Ru(CO)5(dmso-S).
of the actually isolated isomer, cis,fac-RuCl2(dmsoS)3(dmso-O), is 56 kJ/mol lower than that of cisRuCl2(dmso-S)4. 3.3. Ru(II)–dmso complexes: binding energies In the previous section, we observed that in all the studied cases, the total energy of the known compounds calculated experimentally were lower than for the model molecules which represent their linkage isomers. This indicates that the present method should be able to give reliable provisions about the preference for S- or O-bonding of dmso in a series of Ru(II) linkage isomers. In order to gain some information about the Ru–S or Ru–O bond strengths, we calculated the binding energy (BE) of the dmso ligand as the energy involved in the following process: RuXn dmso ! RuXn 1 dmso where RuXn(dmso) indicates the whole complex and RuXn the complex obtained by abstraction of the dmso moiety. If we reconsider the two complexes cis,fac-RuCl2(CO)3(dmso) and [Ru(NH3)5(dmso)] 21, for the first one the calculated dmso BEs are 132 and 110 kJ/mol for the dmso-O and dmso-S isomers, respectively. On the contrary, for the second one, the calculated dmso BEs are 200 and 225 kJ/mol for the dmso-O and dmso-S isomers, respectively. Hence, calculations indicate that dmso is more strongly bound to Ru(II) via O in the presence of CO ligands and via S in the presence
of NH3 ligands, corroborating the argument based on the p back-donation. As to the other two complexes, cis,facRuCl2(dmso-S)3(dmso-O) and trans-RuCl2(dmso-S)4, it is of interest to observe that the BE of 161 kJ/mol, calculated for the dmso-S in trans-RuCl2(dmso-S)4, is increased to 172 and 208 kJ/mol in cis,facRuCl2(dmso-S)3(dmso-O), for the dmso-S trans to Cl and O, respectively. This is in agreement with the thermodynamic instability of trans-RuCl2(dmsoS)4 with respect to cis,fac-RuCl2(dmso-S)3(dmso-O), where each dmso-S ligand is trans to Cl or O atoms, namely atoms without p accepting properties [14]. This BE trend parallels the reduction of the mean Ru(II)–S bond length passing from compounds with ˚ ) to that of trans dmso-S ligands (2.330(4) A compounds where dmso-S is trans to N, O, or Cl ˚ ) [1,2]. ligands (2.265(3) A However, in spite of this success it must be observed that the calculated total energy of transRuCl2(dmso-S)4 is lower than that of cis,facRuCl2(dmso-S)3(dmso-O) by 33 kJ/mol, in contrast with its thermodynamic instability. We have already pointed out some inaccuracies in the present method, while describing the electronic structure of different diastereomeric species. The most probable cause can be attributed, as mentioned above, to the difficulty of the method to treat systems where steric repulsions between ligands play a significant role in defining the electronic structure of the complexes. Thus probably, in cis,fac-RuCl2(dmso-S)3(dmso-O) the steric interactions are overestimated with respect to transRuCl2(dmso-S)4, yielding a large total energy. BE calculations were also performed for the hypothetical isomers, trans,mer-RuCl2(dmsoS)3(dmso-O) and cis-RuCl2(dmso-S)4. As already observed, both of them have a total energy larger than that calculated for the corresponding isolated isomers, with an increase of 77 and 56 kJ/mol for the trans- and cis-RuCl2 derivatives, respectively. The dmso BEs in trans,mer-RuCl2(dmso-S)3(dmsoO) of 140 and 230 kJ/mol, for the dmso groups trans to S and O, respectively, indicate a weakening of the Ru–S trans to S, and a strengthening of the Ru–S trans to O bonds. In cis-RuCl2(dmsoS)4, the BE of the dmso-S trans to Cl is 148 kJ/ mol, while the BE’s for the two trans dmso-S ligands are 50 and 190 kJ/mol. The marked
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as [cis,fac–Ru(NH3)2H3(dmso-S)] (Fig. 7(a)) and [Ru(CO)5(dmso-S)] 21 (Fig. 7(b)), able to emphasize, respectively, the different behavior of s donor and p acceptor ligands in dmso-S complexes. These systems were analyzed without imposing any symmetry constraint, but only internal coordinates involving the Ru–dmso moiety were optimized. For the other fragments the average covalent radii were used to build the structures. This choice was suggested by the fact that in the present case we are only interested in the comparison of the internal coordinate of the dmso fragment in the two model systems, hence we can take advantage in the computational economy by reducing the number of degrees of freedom.
Table 7 Optimized internal coordinates (with BP functional) of [cis,fac– Ru(NH3)2H3(dmso-S)] 2 and [Ru(CO)5(dmso-S)] 21 Internal coordinate
[Cis,fac–Ru(NH3)2H3 (dmso-S)] 2
[Ru(CO)5 (dmso-S)] 21
˚) Ru–S (A ˚) S–O (A ˚) S–C (A C–S–C (8) O–S–C (8) Ru–S–O (8)
2.187 1.553 1.875 92.0 100.6 119.0
2.513 1.463 1.810 103.2 110.7 108.8
weakening of one Ru–S bond is related to its ˚. extremely long Ru–S distance of 2.66 A 3.4. Ru(II)–dmso model molecules
3.4.1. Bond length trends The results are reported in Table 7. In agreement with the expectations, the Ru–S bond length in
The effect of p back-bonding on the Ru–S and S–O bond lengths was investigated on model species, such
a E
101 2
b
c
80 70 60 50 40 30 20 10 0 -10 -20 -30 0
30
60
90
120
150
180
φ Fig. 8. Relative energy, E (kJ/mol), as a function of the rotation angle f , around the Ru–S bond in the model system [cis,fac– Ru(NH3)2H3(dmso-S)] 2, shown in three projections down the S–Ru–H axis, (a) f 08, (b) f 908, (c) f 1808. Solid line, total energy; dashed line, partial steric contribution; dotted line, partial electronic contribution.
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Table 8 Optimized internal coordinates (with BP functional) of [Ru(CO)5(dmso-O)] 21 in trans–trans and cis–cis conformations Internal coordinate
Trans–trans
Cis–cis
˚) Ru–O (A ˚) S–O (A ˚) S–C (A Ru–O–S (8)
2.147 1.597 1.806 126.8
2.173 1.559 1.808 149.7
[cis,fac–Ru(NH3)2H3(dmso-S)] 2 is as short as ˚ , while the S–O distance is 1.553 A ˚ . On the 2.187 A contrary, in [Ru(CO)5(dmso-S)] 21, the Ru–S and S– ˚ , respectively. O bond distances are 2.513 and 1.463 A These trends support the assumption that the reduction of the electron charge density on the metal atom, caused by the substitution of s donor ligands (H, NH3) with p acceptors (CO), decreases its p back-donation ability, weakening the metal to sulfur bond. As a consequence, the positive charge on the sulfur atom is increased enhancing the p bonding in the S–O bond. It is worth noting that in [cis,fac– Ru(NH3)2H3(dmso-S)] 2, the S–C bond distances ˚ ) are also longer than in [Ru(CO)5(dmso(1.875 A ˚ ), suggesting that p back-donation S)] 21 (1.810 A involves dmso empty orbitals with S–O and S–C antibonding character, such as the virtual orbital 8a 00 depicted in Fig. 2. Calculations suggest that as the S– O and S–C bond lengths decrease, the C–S–C and O–S–C bond angles increase. 3.4.2. Conformational aspects The presence of a substantial double bond character in the Ru–S bond was related to the necessity of a hindered rotation about the Ru–S bond, yielding a well determined orientation of the sulfoxide ligand with respect to the equatorial coordination plane, in order to achieve an optimum orbital overlap [28]. Thus, in [trans–RuCl4(dmso-S)2] 2, the existence of two orientations of the square arrangement of the chlorides (related by a rotation about the S–Ru–S axis of 17.68) was taken as a proof for the lack of p bonding [28]. In fact, in a Ru(III) complex with two trans dmso-S ligands, little p bonding is expected, as confirmed by the calculation of the total energy as a function of the torsion angle f around the Ru–S bond (08 # f # 3608, step 58) in [Ru(CO)5(dmso-S)] 21 which shows very small energy variations (,1.2 kJ/mol). On the contrary,
the same analysis carried out for [cis,fac– Ru(NH3)2H3(dmso-S)] 2, where considerable p bonding is present, shows that the only significant energy difference upon rotation around the Ru–S bond is due to steric rather than electronic factors. In fact, as shown in Fig. 8, the total energy shows two rather flat energy minima 08 # f # 508 and 1508 # f # 1808, whose energy difference (< 65 kJ/mol) is due to the different orientation of the bulkiest ligands. In fact, when f 08, the S–O bond bisects the N–Ru–N angle and the methyl groups point towards the small equatorial H ligands. However, when f 1808, the S–O bond bisects the H–Ru–H angle and both the methyl groups point towards the bulkier ammonia molecules, causing a marked increase of the steric energy contribution. The steric situation at f between 608 and 1008 is intermediate with one CH3 group close to one NH3 molecule, and the other close to the cis H ligand, as shown by a flat relative energy minimum (35 kJ/mol) (dashed line in Fig. 8). It must be concluded that proper metal d orbital combinations can overlap with proper dmso orbitals to give p back-donation, and that the mutual orientation of the axial and equatorial ligands have only a minor effect on the total energy profile, which is essentially governed by steric factors. The most interesting stereochemical features of Obonded sulfoxide complexes consider the rotation about the metal to oxygen and S–O bonds. Molecular mechanics (MM) calculations on cis,fac-RuCl2(dmsoS)3(dmso-O), have shown in agreement with experimental evidence [1,2], that the most stable conformation of the Ru–O–Sme2 group is characterized by a trans–trans arrangement of the methyl groups, followed by the cis–cis one [29]. Present calculations on [Ru(CO)5(dmso-O)] 21 support this observation, the trans–trans conformer having an energy of 19 kJ/mol lower than the cis–cis one. Interestingly, as shown in Table 8, theory predicts a high strain in the cis–cis conformer with a lengthening of the Ru–O bond distance and a marked widening of the Ru–O–S bond angle, accompanied by a shortening of the S–O bond length. As to rotation about the Ru–O bond, MM calculations showed that in cis,facRuCl2(dmso-S)3(dmso-O) the O-bonded ligand is rather free to rotate around the midpoint defined by the chloride ligands (Df < ^808) [29]. A marked
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energy barrier arises only when the sulfur atom approaches the bulkier dmso-S groups. In the case of the more symmetrical pentacarbonyl derivative [Ru(CO)5(dmso-O)] 21, present calculations show that there is no energy barrier practically, the maximum energy difference being less than 3 kJ/mol in both trans–trans and cis–cis conformers.
4. Conclusions In this work, a series of four complexes of Ru(II) with dmso was studied by means of the DFT method employing the BP exchange-correlation energy functional. The comparison of the calculated results with the experiment is fairly good, the most important trends observed in many different situations are well reproduced by theory, although a general overestimate of the calculated bond lengths is found. The present method was proved to be reliable to decide, on simple energy grounds, which is the preferred bonding mode of dmso in a given environment of ancillary ligands. The results on the Ru–S bonds are consistent with metal–dmso p back-donation arguments, showing a strengthening of the Ru–S bond and a weakening of the S–O bond by increasing the metal electron charge density. When this is markedly reduced, O-bonding is favored. Deterioration of the results are found in special situations, particularly in sterically crowded complexes where the steric repulsion effects seem to be overestimated with respect to the purely electronic ones. The trends of the calculated Ru–dmso binding energies are also consistent with the observed linkage isomer stability. The study of model molecules, with emphasized electronic properties, provided further support to the proposed bonding model, and an insight into the conformational properties of dmso metal complexes. The overall good performance of the method and its computational economy makes it interesting for further applications in this field, where traditional ab initio approaches are impracticable and semi-empirical methods can be too approximate to give reliable results. As a matter of fact, ab initio calculations on [trans–RuCl4(CO)(dmso-O)] 2 provided the correct trends of the bond lengths and the vibrational spectrum characteristics, but the geometry optimization
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indicated the cis–cis conformation as the most stable [30]. Acknowledgements This work was supported by grants from MURST and CNR of Rome (Italy).
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