Artem A.
Mikhailov
*a,
Axel
Gansmüller
a,
Krzysztof A.
Konieczny
ab,
Sébastien
Pillet
a,
Gennadiy
Kostin
c,
Peter
Klüfers
d,
Theo
Woike
a and
Dominik
Schaniel
*a
aUniversité de Lorraine, CNRS, CRM2, 54000 Nancy, France. E-mail: artem.mikhailov@univ-lorraine.fr; dominik.schaniel@univ-lorraine.fr
bFaculty of Chemistry, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
cNikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia
dDepartment of Chemistry, Ludwig-Maximilians-Universität, Butenandtstrasse 5–13, München 81377, Germany
First published on 6th May 2024
Photoinduced linkage isomers (PLI) of the NO ligand in transition-metal nitrosyl compounds can be identified by vibrational spectroscopy due to the large shifts of the (NO) stretching vibration. We present a detailed experimental and theoretical study of the prototypical compound K2[RuCl5NO], where (NO) shifts by ≈150 cm−1 when going from the N-bound (κN) ground state (GS) to the oxygen-bound (κO) metastable linkage isomer MS1, and by ≈360 cm−1 when going to the side-on (κ2N,O) metastable linkage isomer MS2. We show that the experimentally observed N–O stretching modes of the GS, MS1, and MS2 exhibit strong coupling with the Ru–N and Ru–O stretching modes, which can be decoupled using the local mode vibrational theory formalism. From the resulting decoupled pure two-atomic harmonic oscillators the local force constants are determined, which all follow the same quadratic behavior on the wavenumber. A Bader charge analysis shows that the total charge on the NO ligand is not correlated to the observed frequency shift of (NO).
In most of the nitrosyl complexes, the ν(NO) stretching vibration shifts to lower wavenumbers when going from GS to MS1 and MS2.2 The only reported exception to this observation for sixfold coordination are the {PtNO}8 complexes [Pt(NH3)4Cl(NO)]Cl2, [Pt(NH3)4(NO3)NO](NO3)2 and [Pt(NH3)4(SO4)NO]HSO4·CH3CN, for which a shift to higher wavenumbers was observed upon generation of PLI.22,23 Note, however, that for these PtNO complexes, the nitrogen-bound GS is already in a bent configuration with Pt–N–O angles of the order of 110–120°, and only one PLI has been detected, an oxygen bound bent configuration with slightly larger (calculated) Pt–O–N angles of the order of 120–130°. In most cases the generation of the PLI is triggered by a metal-to-ligand charge transfer (MLCT) excitation from the occupied metal-d orbitals to the empty antibonding π*(NO) orbitals.18 Therefore, sometimes, the downshift of the ν(NO) stretching vibration has been interpreted as due to an increase of the charge on the NO ligand,24 resulting in a change of the formally NO+ towards NO0 in the MS, an interpretation that would be in line with the known ν(NO) stretching vibrations of free NO, 2387 cm−1 for NO+ and 1876 cm−1 for NO0.25 This simplified picture is sometimes applied as a shortcut to the deduction of the NO angle and its formal charge from the observed frequency of the stretching vibration. This should be however handled with precaution as already Enemark and Feltham pointed out in their seminal 1974 review that “it is very tenuous to infer M–N–O angles from ν(NO)”.26 Fundamental insight into these questions and, especially, also with respect to the oxidation state of the “non-innocent” ligand NO, has been given in the recent work by Klüfers and co-workers.27,28 Through detailed structure analysis combined with DFT calculations and the determination of the charges on the NO, it was shown that the M–N–O angle is not a reliable indicator to derive bond strengths or ligand charges.
In the framework of this fundamental discussion we present a detailed experimental and theoretical study of the PLI in K2[RuCl5NO], which already earlier has served as a prototypical {MNO}6 complex for DFT calculations.29,30 Starting from an accurate single-crystal structure determination of GS we use infrared spectroscopy, including 15N isotope substitution, to unambiguously identify the ν(RuN) and ν(NO) stretching and δ(RuNO) deformation vibrations for GS, MS1 and MS2. A solid-state DFT calculation is performed and its quality is assessed by comparison with the experimental structural, infrared as well as NMR data of the GS. Since MS1 and MS2 populations are too low to allow for experimental structure determination, their structures are calculated and the corresponding calculated vibrational spectra are compared to the experimental results. A Bader31 analysis is performed in order to determine the charges on the relevant atoms and atom groups for GS, MS1, and MS2. Finally, we use the local mode vibrational theory as developed by Konkoli, Cremer and Kraka32 in order to calculate the decoupled ν(RuN) and ν(NO) stretching vibrations and determine the corresponding local force constants. The implications of these results on the interpretation of the downshift of the ν(NO) stretching vibration upon PLI generation are discussed.
Distances/angles | XRD | DFT | Δ(exp − calc) |
---|---|---|---|
N–O | 1.140(1) | 1.152 | −0.012 |
Ru–N | 1.740(1) | 1.727 | +0.013 |
Ru–Cl4trans | 2.362(1) | 2.355 | +0.007 |
Ru–Cl1 | 2.374(1) | 2.384 | −0.010 |
Ru–Cl2 | 2.371(1) | 2.380 | −0.009 |
Ru–Cl3 | 2.378(1) | 2.369 | +0.009 |
K–Cl4trans | 3.327(1)/3.455(1) | 3.246/3.478 | +0.081/−0.023 |
K–Cl1 | 3.283(1)/3.527(1) | 3.178/3.562 | +0.105/−0.035 |
K–Cl2 | 3.206(1)/3.240(1) | 3.087/3.133 | +0.119/+0.107 |
3.581(1)/3.666(1) | 3.465/3.572 | +0.116/+0.094 | |
K–Cl3 | 3.307(1)/3.448(1) | 3.253/3.349 | +0.054/+0.099 |
K–O | 4.015(1)/4.279(1) | 3.953/4.385 | +0.062/−0.106 |
K–N | 3.987(1)/4.042(1) | 3.932/4.054 | +0.055/−0.012 |
O–Cl2 | 2.929(1) | 2.890 | +0.039 |
N–Cl1 | 2.929(1) | 2.902 | +0.027 |
∠Ru–N–O | 175.0(1) | 172.5 | +2.5 |
As illustrated in Fig. 1b, the mirror plane m perpendicular to the b-axis contains the Cl4–Ru–N–O axis of the molecule as well as the ligands Cl1 and Cl3, and therefore also the polar angle θ describing the Ru–N–O bending. Notably, we observe a rectangular arrangement of four K+ cations around each Cl ligand (Fig. 2). The corresponding distances are listed in Table 1. This peculiar embedding of the [RuCl5NO]2− anions in the K+ cation lattice, with d(K–Cl) distances of 3.2 to 3.7 Å, and the resulting strong coupling is the reason for the temperature dependence of the bond lengths reported in ref. 53. The excellent quality of our structure determination can be assessed from the residual Fourier-difference maps, where the empty eg and the filled t2g-orbitals of the Ru central atom are clearly visible as electron deficient and enriched zones (see Fig. S1 in ESI†).
Table 1 lists also the bond lengths obtained with geometry optimization in the solid state using the CASTEP DFT code, along with the resulting differences compared to the experimentally obtained values. The intramolecular distances agree very well, the largest difference of 0.013 Å is found for the Ru–N bond. Contrary to that, the cation–anion distances match far less, one of the K–Cl1 distances is overestimated by 0.035 Å and one of the K–Cl2 distances is underestimated by 0.119 Å in the calculation. The Ru–N–O angle is underestimated by 2.5° in the calculation, but the oxygen atom is bent towards the Cl1 atom in the mirror plane, as found experimentally.
In a first step, in order to evaluate the quality of the solid-state DFT calculations based on the XRD structure, we measured the 15N chemical shift tensor and compared the results with our calculations. Table 2 presents the results for GS. Consistently with XRD measurements, only one 15N site is observed with an experimental isotropic chemical shift of δiso = −38.6 ppm with respect to CH3NO2 (see Fig. S2, ESI†). When referencing the DFT calculations to σref = −178.9 ppm, the value used in our precedent NMR study of [Ru(15NO)(py)419F](ClO4)2,48 we find a difference of −5.9 ppm in the range of what was found in our earlier study. These values of the 15N chemical shift are in the range of known values for linear Ru–N–O geometries33,54–56 considering the corresponding reference. Regarding chemical shift anisotropy, the difference between experimental and calculated value are small since the values of the asymmetry parameter η match within experimental error margin, and the reduced anisotropy Δδ (expressed using the Haeberlen convention) shows a deviation of 6%. Due to the polar Ru–N–O angle of θ = 172.5° the calculation yields a small value of η = 0.03, which however could not be detected experimentally, as it is probably too small.
Experiment | DFT | |
---|---|---|
δ iso | −38.6 | −32.7 |
η | 0.00 | 0.03 |
Δ δ | −393 | −368.7 |
Infrared and Raman spectroscopy allow for the detection of changes in bonding due to excitation of PLI even at low populations. Despite the high sensitivity of Raman spectroscopy, only the GS and MS1 configurations were studied by this method since there is no irradiation wavelength for which MS2 is stable with sufficient population (see ref. 57 and Fig. S3, ESI†). Nevertheless, these two methods enable the investigation of local changes both in the molecular ion and the crystal. Using isotopic substitution of 14N for 15N, an unambiguous assignment of the detected vibrational bands is possible. For this reason, IR- and Raman spectroscopy have been applied from the early days for the characterization of NO complexes and their linkage isomers.57–64 Infrared and Raman spectra were collected for GS by Tosi63 and for MS1 and MS2 by Güida et al.64 The latter have also performed DFT calculations for the quasi-free molecule in order to assign the measured vibrational bands. In (idealized) 4m symmetry 18 vibrations are expected for the [RuCl5NO]2− anion, which distribute according to Γ = 5A1 + 2B1 + B2 + 5E. Fig. 3 shows the measured and calculated infrared spectra of GS in the range 1950–1500 cm−1.
In GS, (NO) is split by 11 cm−1 into two bands at 1923 cm−1 and 1912 cm−1. Upon cooling from 296 K to 10 K these two bands shift by 8/9 cm−1 to higher wavenumbers. The first overtone at 3786 cm−1 shows no splitting. Since for the transition 0 → 2 there is only a small concentration in the n = 2 level, this splitting might thus depend on the concentration. For a sample with 96% isotopic substitution of 15N the splitting remains and both (NO) bands shift by 38 cm−1. We note however, that for the remaining 4% of 14N there is no observable splitting. There is no observable splitting either in the 15N band (0.38% natural abundance (NA)) of the original 14N spectrum. The two low-concentration bands without splitting are found at (14N16O) = 1910 cm−1 and (15N16O) = 1867 cm−1, respectively. Upon decreasing concentrations, the bands thus shift by 2 cm−1 and 7 cm−1 to lower wavenumbers, respectively. Hence, the band at 1923 cm−1 appears due to correlation through concentration, and is thus clearly a solid-state effect. Moreover, the vibrations involving 18O (NA of 0.205%) could be detected at (14N18O) = 1863 cm−1 and (15N18O) = 1825 cm−1, their difference being 38 cm−1 as expected, and again, no split can be observed. This type of splitting of the ν(NO) stretching mode into two bands was already measured and discussed by Piro et al.65 in Na2[Fe(CN)5NO]·2H2O (SNP) single crystals using reflectance spectroscopy. As a matter of fact, when considering the vibrational modes in the space group Pnnm of SNP and Pnma for the K2[RuCl5NO] crystal structure, the ν(NO) correlates into the two infrared active optic modes B2u and B3u so that two bands can be expected for a crystalline material.
The anharmonicity of the NO potential with respect to the fundamental 1912 cm−1 is 38 cm−1 for the first and 95 cm−1 for the second overtone. Furthermore, the isotopic substitution with 15N allows to unambiguously assign the ν(RuN) stretching and δ(RuNO) deformation vibrations (see Fig. S3, ESI†). For (RuN) the isotopic shift is only 8 cm−1 (from 609 to 601 cm−1) while for δ(RuNO) it is 16/14 cm−1 (from 590/585 to 574/571 cm−1), so that the larger shift can be used to assign the deformation vibration also for MS1 and MS2. For GS this technique was already used by Miki59–61 through application of a linear three-body model for Ru–N–O. Table 3 summarizes the experimental data and DFT-calculated vibrations for the solid state, along with the differences between experiment and calculation. Overall the agreement between experiment and calculation is good, the largest deviation is found for the (NO) with 41/43 cm−1 for 14N. Note however, that in relative terms the deviation for the (RuN) is with −33/32 cm−1 much higher. The splitting of the deformation mode can be observed also in the first overtone at 1179/1165 cm−1, indicating an influence of the local environment, supported by the fact that the lower energy band is broad.
Mode | GS-14N | GS-15N | Δ(Iso) | DFT-14N | DFT-15N | Δ(Isoto) | Δ 14N(exp − calc) |
---|---|---|---|---|---|---|---|
3 × (NO) | 5641 | 5527 | 114 | — | — | — | — |
2 × (NO) | 3786 | 3711 | 75 | — | — | — | — |
(NO) | 1923 | 1885 | 38 | 1882 | 1844 | 38 | 41 |
1912 | 1874 | 38 | 1869 | 1831 | 38 | 43 | |
2 × (RuN) | 1213 | 1196 | 17 | — | — | — | — |
2 × δ(RuNO) | 1179 | 1147 | 32 | — | — | — | — |
2 × δ(RuNO) | 1165 | 1139 | 26 | — | — | — | — |
(RuN) | 609 | 601 | 8 | 642/641 | 635/633 | 7/8 | −33/−32 |
δ(RuNO) | 590 | 574 | 16 | 577 | 561 | 16 | 13 |
585 br | 571 br | 14 | 573/569 | 558/554 | 15/15 | 12/16 | |
(RuCl) | 349 | 349 | 0 | 339 | 339 | 0 | 10 |
(RuCl) | 343 | 343 | 0 | 335/334 | 335/333 | 0/1 | 8/9 |
(RuCl) | 332 | 332 | 0 | 330 | 330 | 0 | 2 |
(RuCl) | 324 | 324 | 0 | 328 | 328 | 0 | −4 |
In order to verify the azimuthal position of the NO in MS2, we performed calculations with several starting geometries of the NO group, choosing the azimuthal position of φ = 45°, i.e. the NO ligand is oriented along the direction between Ru–Cl1 and Ru–Cl2 bonds, the so-called staggered geometry of MS2 (Fig. 4b, top). For the latter, the converged position of the O atom is pointing towards the Cl3 ligand (see Fig. 4b, top). The energy of the NO position where O is closer to Cl3 is 0.12 eV higher than that for the direction towards Cl1, so that the latter corresponds to the global minimum of MS2 (Fig. 4a). In GS the symmetry related distances Ru–Cl2 and Ru–Cl2′ are identical with 2.371(1) Å. According to the calculations the NO remains in the mirror plane and the Ru–Cl2 and Ru–Cl2′ distances are identical (see Fig. 4), independent whether the final position of the O atom is towards Cl1 or Cl3. These two configurations lead to different Ru–Cl1 distances. When the oxygen atom of NO is in the direction of Cl1, the bond lengths of Ru–Cl1 is shorter than that of Ru–Cl3. The calculations were performed in space groups with lower symmetry (P21/c and P1) in order to avoid symmetry-induced preferential orientations for NO, especially due to the mentioned mirror plane. Table 4 summarizes the calculated structural data for GS and MS2 and the corresponding differences. The pairs of values correspond to the two configurations where the O atom is in direction of Ru–Cl3/Ru–Cl1.
Distances/angles | MS2 (DFT) | GS (DFT) | Δ(MS2-GS) |
---|---|---|---|
Ru–N | 1.900/1.908 | 1.727 | +0.173/+0.181 |
Ru–O | 2.137/2.131 | — | — |
N–O | 1.207/1.210 | 1.152 | +0.055/+0.058 |
Ru–Cl4trans | 2.324/2.327 | 2.355 | −0.031/−0.028 |
Ru–Cl1 | 2.446/2.356 | 2.384 | +0.062/−0.028 |
Ru–Cl2 | 2.376/2.373 | 2.380 | −0.004/−0.007 |
Ru–Cl3 | 2.342/2.425 | 2.369 | −0.027/+0.056 |
∠Ru–N–O | 83.8/83.0 | 172.5 | −88.7/−89.5 |
Due to the fact that experimentally achievable populations of MS2 and MS1 in K2[RuCl5NO] are rather low, infrared spectroscopy is the best tool to obtain structural information on these linkage isomers. The side-on geometry of MS2 leads to a pronounced downshift of (NO) by 369/362 cm−1 with respect to GS. The observed splitting in MS2 is three times smaller than the one observed in GS. Since the population of MS2 is very low (only 2–3%), the origin of the splitting in MS2 is most probably due to the local environment and not a consequence of a coupling to the lattice.
As for GS, we performed solid-state DFT calculations of the IR vibrations on the structural model obtained in 4a, which corresponds to the minimum-energy configuration. As listed in Table 5, the difference between calculated and experimental (NO) values are 63/66 cm−1 and thus about 20 cm−1 larger than in GS. Fig. 5 and Fig. S4, S5 (ESI†) illustrate the experimental and solid-state DFT-calculated infrared spectra, respectively. Surprisingly, we observe a shift by 18 cm−1 to higher wavenumbers for the δ(Ru–O–N) deformation mode, even though atomic distances increase in MS2 with respect to GS. The assignment of the band to the deformation mode is based on the larger isotopic shift compared to the (Ru–N) stretching mode. The latter is hidden by the Ru–Cl vibrational modes, and the calculation shows that it has a small cross section. Possibly, the detected intensity changes in the band at 349 cm−1 after transferring MS1 to MS2 through 1310 nm irradiation, are due to the appearance of the ν(Ru–N) stretching mode of MS2, but the change is too small to unambiguously assign it. For all the other bands, the agreement between calculated and experimentally observed isotope shift is excellent, so that their assignment is unambiguous, even though the absolute value of the upshift of the δ(Ru–O–N) deformation mode is largely overestimated by the calculation (+99 cm−1) compared to the observed +18 cm−1. The calculated downshift of (Ru–N) is -219 cm−1, possibly much to large. However, the direction of the shift of these two bands is opposite and in agreement with experiment. Similar trends were reported earlier.29,30
Mode | MS2-14N | MS2-15N | Δ(Iso) | DFT-14N | DFT-15N | Δ(Iso) | Δ(14N) |
---|---|---|---|---|---|---|---|
(NO) | 1554/1550 | 1527/1522 | 27/28 | 1491/1484 | 1464/1457 | 27/27 | +63/+66 |
δ(RuNO) | 608/603 | 593/588 | 15/15 | 676/673 | 658/654 | 18/19 | −68/−70 |
(RuN) | — | — | — | 423/422 | 421/419 | 2/3 | — |
(RuCl) | 349 | 349 | 0 | 342 | 342 | 0 | 7 |
(RuCl) | 343 | 343 | 0 | 340 | 340 | 0 | 3 |
(RuCl) | 338 | 338 | 0 | 328 | 328 | 0 | 10 |
(RuCl) | 332 | 332 | 0 | 325/324 | 325/324 | 0 | 7 |
Table 6 summarizes the most important structural changes between GS and MS1, notably the increased Ru–O distance of 1.837 Å compared to GS Ru–N distance of 1.727 Å and the significantly shortened Ru–Cl4 bond (Cl4 = trans to NO) of 2.298 Å compared to 2.355 Å in GS. The N–O distance remains almost the same in the inverted MS1 geometry and the polar Ru–O–N angle points again toward Cl1. The Ru–Cl1 distance decreases by 0.02 Å.
Distances/angles | MS1(DFT) | GS(DFT) | Δ(MS1-GS) |
---|---|---|---|
Ru–O/N | 1.837 | 1.727 | +0.110 |
N–O | 1.154 | 1.152 | +0.002 |
Ru–Cl4trans | 2.298 | 2.355 | −0.057 |
Ru–Cl1 | 2.364 | 2.384 | −0.020 |
Ru–Cl2 | 2.380 | 2.380 | 0 |
Ru–Cl3 | 2.378 | 2.369 | +0.009 |
∠Ru–O–N/Ru–N–O | 172.8 | 172.5 | +0.3 |
With respect to the vibrational bands, the increase or decrease of atomic distances is expected to lead to a corresponding decrease or increase of the vibrational frequency. We note immediately that especially for the case of the (NO) stretching vibration the large downshift of 153/146 cm−1 in MS1 with respect to GS cannot be explained in this manner.
As for the other isomers, we performed solid-state DFT calculations of the IR vibrations. Table 7 lists the experimental and calculated vibrations for 14N and 15N in MS1, and the corresponding spectra are shown in Fig. 5. The (Ru–Cl) vibrations do not exhibit any change when going from GS to MS1. For (NO) we observe again a splitting as in GS, for the NA sample the two 14N bands are found at 1770/1766 cm−1 and for the 96% 15N the two bands at 1741/1737 cm−1, thus an isotopic shift of 29 cm−1. The 14N band (4%) in the 15N sample is found as a single band at 1766 cm−1, analogous to the GS case we interpret thus the splitting as due to coupling to the lattice, and the correlation-free band is the one found for low concentrations at 1766 cm−1. The assignment of the (RuO) band at 467 (465) cm−1 and δ(RuON) band at 454 (449) cm−1 can be made by the smaller/larger isotope shift. We note that the (RuO) band remains the higher frequency band in MS1 as in GS, even after rotation of the NO ligand. The rather important downshift for (RuO) and δ(RuON) of 142 and 136 cm−1, respectively, is compatible with the significant change in Ru–O bond length of +0.11 Å compared to the Ru–N GS configuration, which is in line with the previous report.42 While the (NO) in MS1 are well reproduced by the calculations, the (RuO) and δ(RuON) are overestimated and hence the downshift with respect to GS is underestimated. Moreover, the calculation indicates a splitting of 1 cm−1 for the δ(RuON), which was not detected experimentally (resolution of 1 cm−1), since these bands are weak and broad.
Mode | MS1-14N | MS1-15N | Δ(Iso) | DFT-14N | DFT-15N | Δ(Iso) | Δ(14N) |
---|---|---|---|---|---|---|---|
2 × (NO) | 3499 | 3443 | 56 | — | — | — | — |
(NO) | 1770/1766 | 1741/1737 | 29/29 | 1778/1772 | 1749/1743 | 29/29 | 8/6 |
(RuO) | 467 | 465 | 2 | 486/484/482 | 485/480/479 | 1/4/3 | −19/−17/−15 |
δ(RuON) | 454 | 449 | 5 | 506/505 | 500/499 | 6/6 | −52/−45 |
(RuCl) | 349 | 349 | 0 | 346 | 346 | 0 | 3 |
(RuCl) | 343 | 343 | 0 | 344 | 344 | 0 | 1 |
(RuCl) | 332 | 332 | 0 | 325 | 325 | 0 | 7 |
(RuCl) | 324 | 324 | 0 | 318/316 | 318/316 | 0 | 6/8 |
GS | MS2 | MS1 | ||||||
---|---|---|---|---|---|---|---|---|
Total | charge q | Total | charge q | Δq | Total | charge q | Δq | |
O | 6.32 | −0.32 | 6.37 | −0.37 | +0.05 | 6.46 | −0.46 | +0.14 |
N | 4.83 | +0.17 | 4.88 | +0.12 | +0.05 | 4.62 | +0.38 | −0.21 |
Ru | 14.73 | +1.27 | 14.78 | +1.22 | +0.05 | 14.78 | +1.22 | +0.05 |
Cl1 | 7.55 | −0.55 | 7.55 | −0.55 | ±0.00 | 7.56 | −0.56 | +0.01 |
Cl2 | 7.57 | −0.57 | 7.56 | −0.56 | −0.01 | 7.59 | −0.59 | +0.02 |
Cl3 | 7.56 | −0.56 | 7.50 | −0.50 | −0.06 | 7.57 | −0.57 | +0.01 |
Cl4trans | 7.57 | −0.57 | 7.50 | −0.50 | −0.07 | 7.52 | −0.52 | −0.05 |
K | 8.15 | +0.85 | 8.15 | +0.85 | ±0.00 | 8.15 | +0.85 | ±0.00 |
∑(RuNO) | 25.88 | +1.12 | 26.03 | +0.97 | +0.15 | 25.86 | +1.14 | −0.02 |
∑(Cl) | 37.82 | −2.82 | 37.67 | −2.67 | −0.15 | 37.83 | −2.83 | +0.01 |
[RuCl5NO] | −1.70 | −1.70 | −1.69 |
The total charges on the atoms are calculated with respect to the charge enclosed in the Bader volume defined by the surface of minimal charge density between atoms; the resulting charge q on the atom is given by the difference with respect to the neutral atom. In GS the NO is negative (−0.15e), in MS2 it gets even more negative (−0.25e) while in MS1 it is almost neutral (−0.08e). Hence, the downshift of (NO) cannot be explained by a pure charge redistribution effect. The simple rule that the more negative the NO the lower the ν(NO) stretching vibration, does not apply to the present case, and we have to search for further mechanisms.
In MS1 we observe a charge redistribution between N, O and Ru upon NO inversion. The negative charge on the oxygen atom increases by 0.14e, that on the nitrogen decreases by 0.21e and that of the ruthenium atom increases by 0.05e. Moreover, 0.05e are redistributed from the trans-to-NO ligand Cl4trans to the equatorial Cl-ligands, which also receive the minimal excess charge from RuNO. The decisive charge redistribution occurs thus, as might be expected, on the N and O atoms. In MS2 the negative charge on the Ru, N, O atoms is equally increased by 0.05e. This charge stems from the Cl ligands, in particular from Cl4trans and Cl3, so that in MS2 the Cl-ligands contribute much more charge for the stabilization of this structural configuration.
Such a charge redistribution when going from GS to MS1 was also calculated for the complex trans-[Ru(py)4(NO)F](ClO4)2,48 for which the NO has a Bader charge of −0.13e in the GS, which reduces to -0.03e in the MS1. The frequency of the (NO) stretching vibration changes from GS(NO) = 1909 cm−1 to MS1(NO) = 1761 cm−1, i.e. by 148 cm−1, which compares well with the observations of the shift of 146/153 cm−1 in K2[RuCl5NO]. Hence, also for this second ruthenium-nitrosyl complex (cation instead of anion) the downshift of (NO) cannot be explained by a simple increase of the total charge on the NO.
Overall one could thus potentially explain the downshift of the ν(NO) stretching vibration, and hence the reduced force constant, for MS2 by the increase in charge of 0.10e and in bond length of 0.058 Å (in case of O–Cl1 geometry). But for MS1 this argument no longer holds, since the charge on the NO ligand is reduced by 0.07e with respect to GS and the change in bond length amounts to only 0.002 Å. Already Sizova and co-workers30 discussed this discrepancy between the calculated and experimental results for the vibrational frequencies, which occur especially for MS1. They investigated the influence of the environment by applying a polarizable continuum model (PCM), which nevertheless did not resolve the issue for MS1. In such a simple picture, the contribution of the coupling between (RuN) and (NO) to the experimentally observed values is neglected. As a matter of fact, Sizova et al.30 indicated the contributions of the internal coordinates to the NO and RuNO vibrations for the [RuCl5NO]2− complex, which amounts up to 11% of (RuN) to 89% (NO) in GS using a valence force model, but without proceeding to a detailed analysis including further calculations of local force constants. Such a complete decoupling for the solid state by the transformation of all vibrations into a pure two-atomic behavior can be obtained by using the local vibrational mode theory formalism.32 Using the PyMol plugin, named LModeA-nano, implementing the local vibrational mode theory for periodic systems,46 we obtain the decoupled wavenumbers and force constants kdc. The coupled force constants kc, which are given in Table 9, can then be obtained from the equation kc/kdc = (c/dc)2 with the calculated wavenumbers.
, k | Decoupled (dc, kdc) | Coupled (c, kc) | Δ(coupled–decoupled) | ||||||
---|---|---|---|---|---|---|---|---|---|
cm−1, N cm−1 | GS | MS2 | MS1 | GS | MS2 | MS1 | GS | MS2 | MS1 |
(NO) calc. | 1799 | 1408 | 1741 | 1869 | 1484 | 1772 | +70 | +76 | +31 |
(NO) exp. | 1912 | 1550 | 1766 | +113 | +142 | +25 | |||
(RuN,O) calc. | 884 | 636 | 643 | 641 | 422 | 482 | −243 | −214 | −161 |
(RuN,O) exp. | 609 | — | 467 | −275 | — | −176 | |||
k(NO) | 14.239 | 8.72 | 13.334 | 15.369 | 9.687 | 13.813 | 1.130 | 0.967 | 0.479 |
k(RuN,O) | 5.658 | 2.930 | 3.368 | 2.975 | 1.290 | 1.893 | −2.683 | −1.640 | −1.475 |
The most important result of the decoupling is the blueshift of the dc(RuN), dc(RuO) vibrations and the redshift of dc(NO) with respect to the coupled c values, which demonstrates together with the resulting force constants the strong coupling of the corresponding atomic movements. Since the transformation into local modes is a linear operation, the resulting decoupled parameters still reflect the same physical properties. So, if there would be an unusual behavior of the vibrations in the metastable states it should remain visible in the uncoupled parameters. Due to the fact that these local modes are harmonic oscillators, the force constants depend on the wavenumbers as k = 4π2c2μ2 in which c is the light velocity, μ is the reduced mass of the corresponding atoms and is the wavenumber. The pre-factor 4π2c2μ is then exactly the same for GS, MS2 and MS1, so that the decoupled wavenumbers of these three states need all follow the same quadratic dependence k ∼ 2. Additionally, the fitted pre-factor must be identical with the calculated one, which is indeed the case for the NO, since the calculated pre-factor is 4.399096 × 10−4 cm2 kg s−2 and the fitted one is 4.3992(4) × 10−4 cm2 kg s−2 (Fig. 7). This quadratic dependence of the local force constants on the calculated decoupled vibrations shows the pure functional dependence of the harmonic oscillator, e.g., the two-atomic system NO, which then should be true, independent of the system in which the NO is integrated. This can be clearly seen when inserting the calculated decoupled values from the study of Popp & Kluefers28 for different metal-nitrosyl complexes, as shown in Fig. 7.
An immediate consequence of these findings is that the experimentally measured red- or blueshifts for the vibrations of an atomic group (pair) cannot be used as a direct measure of possible underlying distance changes or charge redistributions, since the experimentally observed vibrations are always the result of coupled motions. However, the calculated decoupled force constants, being local force constants, confirm the softening of the N–O and Ru–N, Ru–O bonds, which is more pronounced for the side-on geometry. In order to properly interpret the observations, we might estimate the coupling of the modes, in particular between the (NO) and (RuN) and (RuO). Comparing the coupled and uncoupled values, we can see from Table 9 that for NO all coupled force constants, kc, are higher than their uncoupled counterparts, kdc. For Ru–N/O the coupled force constants are lower than the uncoupled ones. Thus, there is transfer of bond strength from the Ru–N/O to the N–O. This transfer varies significantly between the three states as we can estimate using the ratios Δ(coupled–decoupled)/kc for the gain in NO bond strength and Δ(coupled–decoupled)/kdc for the loss in Ru–N and Ru–O bond strength. While for GS the N–O receives 7.35% bond strength at a cost of 47.42% loss of bond strength in Ru–N, for MS1 the N–O receives only 3.47% with a loss of 43.79% for the Ru–O. Thus, the seemingly unusually large redshift of (NO) observed in MS1 is actually largely due to the fact that there is less transfer from the Ru–O bond to the N–O bond than in the GS (Ru–N to N–O). For MS2, the N–O receives 9.98% at a loss of 55.97% for Ru-N. Note that these are all calculated values as we have no means to access experimentally the uncoupled parameters. Furthermore, we have to keep in mind that the calculated coupled vibrational frequencies are underestimated compared to the experimental values (Table 9) except for MS1.
Still, one problem remains unresolved by the local vibrational mode transformation: the anharmonicity of the measured values. The strong change of the dipole moment allows to measure the first and second overtones, which show the anharmonicity of the NO potential. This is not considered in the local mode calculation. Nevertheless, the quadratic dependence k ∼ 2 of all vibrations after the local mode transformation clearly shows that all photoinduced linkage isomers behave as expected and that the observed, seemingly atypical, large shift of the (NO) stretching vibration is due to a significant change in the coupling of the N–O and Ru–N/O modes, and thus does not properly reflect the intrinsic changes in bond strength. One should therefore refrain from interpreting this observed shift directly into changes of bond length or even redistribution of charge on the NO group. In view of the fact that we can now treat the decoupled vibrations of NO in the framework of a two-atomic harmonic oscillator, the observed redshift of the (NO) vibration when going from GS to MS1 and MS2 might be explained by the influence of an external lateral charge-ligand interaction, as proposed by Popp & Klufers28 for diatomic ligands like NO or CO. Additionally, an internal contribution due to modified occupations of the N(2s), N(2p), O(2s), O(2p) and Ru(4d) orbitals, as can be seen from a Mulliken population analysis (see discussion in Supplementary material and Table S6), might also contribute to this shift. Further calculations are necessary to shine light on these potential external and internal contributions.
Footnote |
† Electronic supplementary information (ESI) available. CCDC 2336093. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4cp01374c |
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