# Exploring the photoswitching pathways and efficiency of NO isomerization in ethylenediamine ruthenium nitrosyl complexes

Artem Mikhailov, Appolinaire Tchoutchoua Tiognou, Anastasiya Brovko, Gennadiy Kostin, Dominik Schaniel

► To cite this version:

Artem Mikhailov, Appolinaire Tchoutchoua Tiognou, Anastasiya Brovko, Gennadiy Kostin, Dominik Schaniel. Exploring the photoswitching pathways and efficiency of NO isomerization in ethylenediamine ruthenium nitrosyl complexes. Dalton Transactions, 2025, 10.1039/D5DT00549C. hal-05085964

HAL Id: hal-05085964

https://hal.univ-lorraine.fr/hal-05085964v1

Submitted on 27 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Exploring the photoswitching pathways and efficiency of NO isomerization in
ethylenediamine ruthenium nitrosyl complexes

Artem A. Mikhailov$^{a*}$, Appolinaire Tchoutchoua Tiognou$^{a}$, Anastasiya O. Brovko$^{b}$, Gennadiy A. Kostin$^{b}$,
Dominik Schaniel$^{a}$

**Abstract**

Photo- and thermoswitchable molecular switches are attractive functional blocks, since structural
modification induced by external stimuli can change the optical or ferroic properties of a material. In
this work we report a series of photoswitchable ethylenediamine ruthenium nitrosyl complexes, in
which the ligand environment significantly influences the thermal stability and photoconversion
(population) of photoinduced linkage isomers (PLI) of the NO ligand. In the studied complexes, the
energetically stable ground state (GS) nitrosyl linkage Ru-NO can be reversibly switched to the
metastable isonitrosyl linkage Ru-ON (MS1) or the side-on nitrosyl linkage Ru-η²-(NO) (MS2) under
blue (405-420 nm) or subsequent infrared (940-980 nm) irradiation, respectively. The reverse
transformation back to GS can be induced by 500-700 nm irradiation or by temperature. It was found
that the highest known decay temperature ($T_d$ = 215 K) of the side-on MS2 isomer can be achieved in
[RuNO(en)₂(H₂O)](NO₃)₃ (2) having the H₂O ligand as *trans*-to-NO ligand. Replacing H₂O by OH⁻,
[RuNO(en)₂OH](NO₃)₂ (1), leads to a decrease of $T_d$ down to 207 K, but at the same time to an increase
in the population of the linkage isomers Ru-ON (MS1, 47%) and Ru-η²-(NO) (MS2, 17%).
Photocrystallographic analysis allowed us to unambiguously assign IR- and UV-vis spectroscopic
signatures to the corresponding structural linkage isomer and study the mechanism of isomerization
using ns pulsed excitation. As a result, we found that 410 nm pulsed excitation of the ground state
isomer (Ru-NO, GS) first generates MS2 (GS→MS2) and only then produces isomer MS1 (MS2→MS1)
reaching a photostationary equilibrium $GS \rightleftharpoons MS2 \rightleftharpoons MS1$. According to modelled effective rate
constants ($k_{1-4}$) of all transformations under 410 nm irradiation, the population of MS2 stays very low
(less than 1%) due to the high rate constants of the MS2→GS and MS2→MS1 processes.

**Introduction**

Controlling physical properties of materials by light opens the way to many applications, as it allows
for ultrafast switching of magnetic, electric, ferroic, or (nonlinear) optical properties. ¹⁻³ In this context
small molecule photoswitches have significant potential due to their chemical versatility as well as
ultrafast photoswitching capabilities. ⁴⁻⁶ Metal nitrosyl complexes are one family of such ultrafast
photoswitches,⁷,⁸ where upon photoisomerization of the nitrosyl ligand the physical properties, such
as linear and nonlinear optical or ferroelectric response, can be modified by light. ⁹⁻¹² In order to design
novel complexes with desired switching properties it is essential to understand the underlying
mechanism, in particular since in these metal nitrosyl compounds very often multiple photoisomers
with different properties can be generated ⁶,¹³ and competition between NO photoisomerization and
NO photorelease might occur. ¹⁴,¹⁵

In octahedral metal nitrosyl complexes two PLI can be generated in addition to the nitrogen bound
ground state (GS) with linear M-N-O configuration: an isonitrosyl configuration with linear M-O-N
configuration, labelled MS1 (Metastable State 1), and a side-on bound configuration of NO, labelled
MS2.¹³ These MS1 and MS2 structural configurations are separated by energetic barriers from the GS,

<footnote>a Université de Lorraine, CNRS, CRM2, UMR 7036, Nancy 54000, France b Department of Chemistry</footnote>

<footnote>b Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, 3
Acad. Lavrentiev Avenue, Novosibirsk 630090, Russian Federation</footnote>

<footnote>*Corresponding author: artem.mikhailov.a@gmail.com</footnote>
yielding a lifetime depending on the temperature in an Arrhenius-like manner.¹⁶ In this context, ruthenium nitrosyl complexes are particularly interesting since they offer a broad chemical variety and exhibit a high stability of the PLI, i.e. a high energetic barrier between MS1/MS2 and GS. The highest decay temperature T<sub>d</sub> (temperature for which the lifetime is 1000 seconds, k=10<sup>-3</sup> s<sup>-1</sup>) has indeed been reached for MS1 in a ruthenium nitrosyl complex *trans*-[RuNO(NH<sub>3</sub>)<sub>4</sub>F](ClO<sub>4</sub>)Cl.<sup>17</sup> However, it was noted that the generation of MS1 depends on the properties of MS2, leading to the establishment of a two-step model for the generation of MS1: GS→MS2→MS1, i.e., a first photon drives the system from GS to MS2 and a second photon drives the system from MS2 to MS1.<sup>18</sup> So, in order to generate MS1, MS2 must exhibit a minimum lifetime to catch a photon and ensure efficient MS1 generation. In the search for such efficient PLI compounds, we have studied extensively ruthenium nitrosyls with pyridine and ammine ligands.<sup>19,20</sup> Earlier studies were conducted also on ethylenediamine compounds by Tomizawa, Miki and coworkers.<sup>21-26</sup> They especially detected MS1 states with very high stability,<sup>25,26</sup> but on the other hand they did not report on the MS2 states, and in particular no structure was reported for the MS2 state in these ruthenium nitrosyl ethylenediamine compounds. In order to investigate whether these complexes could offer high MS2 stabilities and present the same type of two-step photoisomerization mechanism, we prepared a series of ruthenium nitrosyl ethylenediamine complexes and studied the structure and properties of the generated PLI.

Experimental

Synthesis

[RuNOen<sub>2</sub>OH]I<sub>2</sub>

Recently reported method was used for the preparation of [RuNOen<sub>2</sub>OH]I<sub>2</sub> precursor.<sup>27</sup> The powders of K<sub>2</sub>[RuNOCl<sub>5</sub>] (414 mg, 1.07 mmol) and en-2HCl (ethylenediamine dihydrochloride, 286 mg, 2.15 mmol) were mixed together in water (15 ml) and gently heated (≈90 °C) to dissolve the solids. After the dissolution, KHCO<sub>3</sub> (534 mg, 5.33 mmol) was added by portions during the heating. After about 5 min of heating the colour of the solution changed from purple to clear yellow-brown. The solution was evaporated to give wet salts of KCl. Then, the mixture was cooled down to room temperature, and KCl was filtered off on a glass filter, washed with 1-2 ml of water. The saturated solution of NaI in water (2.5 g in min volume of H<sub>2</sub>O) was added to the filtrate to give yellow crystalline precipitate of [RuNOen<sub>2</sub>OH]I<sub>2</sub>. The powder of [RuNOen<sub>2</sub>OH]I<sub>2</sub> was filtered off on a glass filter and washed with ethanol, the mass of the complex was 391 mg (yield is 70%). Yellow needle shape single crystals of [RuNOen<sub>2</sub>OH]I<sub>2</sub> suitable for XRD were obtained from a hot water solution of the complex. The asymmetric unit of the structure is shown in Fig. S1.

[RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1)

To obtain the single crystals of [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1), the powder of [RuNOen<sub>2</sub>OH]I<sub>2</sub> (391 mg, 0.75 mmol) was dissolved in min volume of H<sub>2</sub>O and mixed with saturated water solution of AgNO<sub>3</sub> (254 mg, 1.5 mmol). The powder of AgI was filtered off after 10 min of steering. The filtrate was evaporated at room temperature giving yellow square shape crystals of [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1) (235 mg, yield is 80%). The dry single crystals of **1** were used for XRD measurements. <sup>1</sup>H NMR (400 MHz, D<sub>2</sub>O) δ = 5.82 (broad s, 2H, NH<sub>2</sub>), 4.98 (broad s, 2H, NH<sub>2</sub>), 3.26 – 3.12 (m, 4H,H<sub>2</sub>), 3.05 – 2.97 (m, 4H, CH<sub>2</sub>) ppm. <sup>13</sup>C NMR (100.6 MHz, D<sub>2</sub>O) δ = 45.30, 45.17 (CH<sub>2</sub>) ppm. IR bands at room temperature, cm<sup>-1</sup>: 3437 [v(OH)]; 3207, 3071 [v(NH<sub>2</sub>)]; 1878, 1869 [v(NO)]; 1599 [δ(NH<sub>2</sub>)]; 1384 [v(NO<sub>3</sub>)]. Powder XRD patterns for the bulk substance well correspond to the calculated patterns obtained from the SCXRD data.

[RuNOen<sub>2</sub>(H<sub>2</sub>O)](NO<sub>3</sub>)<sub>3</sub> (2) and [(RuNOenCl<sub>2</sub>)<sub>2</sub>(μ-OH)]Cl·2H<sub>2</sub>O (5)

The powders of K₂[RuNOCl₅] (387 mg, 1 mmol) and en-2HCl (ethylenediamine dihydrochloride, 266 mg, 2 mmol) were mixed together in water (15 ml) and gently heated (≈90 °C) to dissolve the solids.
After the dissolution, KHCO₃ (500 mg, 5 mmol) was added by portions during the heating. After about 5 min of heating the colour of the solution changed from purple to clear yellow-brown. The solution was evaporated to give wet salts of KCl. Then, the mixture was cooled down to room temperature, and KCl was filtered off on a glass filter, washed with 1-2 ml of water. To 7-8 ml of the filtrate the same volume of 3 M HNO₃ was added at room temperature. After about 24 h, yellow plate shape crystals of [RuNOen₂(H₂O)](NO₃)₃ (2) together with a few purple needle shape crystals of [(RuNOenCl₂)₂(µ-OH)]Cl·2H₂O (5) were formed. All the crystals were filtered off on a glass filter. The few crystals of [(RuNOenCl₂)₂(µ-OH)]Cl·2H₂O (5) were separated from the water solution of [RuNOen₂(H₂O)](NO₃)₃ (2) by the filtration due to its poor solubility in water. The single crystals of [RuNOen₂(H₂O)](NO₃)₃ (2) were obtained by a slow evaporation of the filtrate solution at room temperature to give 279 g of the product with the yield of 61%. Complex 5 was characterized only by single crystal XRD due to very small yield (few crystals). ¹H NMR of 2 (400 MHz, D₂O) δ = 5.97 (broad s, 2H, NH₂), 5.11 (broad s, 2H, NH₂), 3.22 – 3.10 (m, 4H, CH₂), 3.07 – 2.97 (m, 4H, CH₂) ppm. ¹³C NMR of 2 (100.6 MHz, D₂O) δ = 45.40, 45.28 (CH₂) ppm. IR bands of 2 at room temperature, cm⁻¹: 3434 [v(H₂O)cryst]; 3270 [v(H₂O)coord]; 3147, 3071 [v(NH₂)]; 1932, 1925 [v(NO)]; 1600 [δ(NH₂)]; 1560 [δ(H₂O)coord]; 1384 [v(NO₃)]. Powder XRD patterns for the bulk substance of 2 well correspond to the calculated patterns obtained from the SCXRD data.

### [RuNO(en)₂OH](NO₃)₂·0.5AgNO₃·0.5H₂O (3)

A water solution of AgNO₃ (400 mg, 2.35 mol, min volume of H₂O) was added to a saturated water solution of [RuNOen₂OH]I₂ (1) (235 mg, 0.45 mmol). The powder of AgI was formed immediately and was filtered off after 10 min of steering. The filtrate was evaporated at room temperature to give yellow square shape crystals of [RuNO(en)₂OH](NO₃)₂·0.5AgNO₃·0.5H₂O (3). The crystals were washed on a glass filter with acetonitrile to dissolve a residue of AgNO₃. Then, the single crystals of (3) were recrystallized from the water solution. The yield is 93% (204 mg). ¹H NMR (400 MHz, D₂O) δ = 5.81 (broad s, 2H, NH₂), 4.98 (broad s, 2H, NH₂), 3.22 – 3.12 (m, 4H, CH₂), 3.10 – 2.96 (m, 4H, CH₂) ppm. ¹³C NMR (100.6 MHz, D₂O) δ = 45.17 (CH₂) ppm. IR bands at room temperature, cm⁻¹: 3438 [v(OH)]; 3208, 3072 [v(NH₂)]; 1877, 1869 [v(NO)]; 1599 [δ(NH₂)]; 1384 [v(NO₃)]. Powder XRD patterns for the bulk substance well correspond to the calculated patterns obtained from the SCXRD data.

### [RuNOen₂OH](NO₃)₂·H₂O (4)

The crystals of (4) were obtained by recrystallization of (1) from water solution and picked directly from the solution. The crystals of (4) are not stable outside of the solvent due to a transformation to (1). This complex was characterized only by single crystal XRD due to its instability.

## IR-, UV-Vis- and NMR-Spectroscopy

IR-spectroscopy measurements were performed using a Nicolet 5700 FT-IR spectrometer with a resolution of 2 cm⁻¹ in the range of 400–4000 cm⁻¹. The sample (around 1–2 mg) was mixed with KBr (around 100 mg) and pressed into common pellets for IR measurements. The pellets were bonded onto a cold finger of a closed-cycle cryostat (Oxford Optistat) allowing the control of the temperature in the range of 10–300 K. Thorlabs LEDs (light emitting diodes) with different wavelengths (365–1300 nm) with an optical power of 50–200 mW were used for light irradiation of samples through KBr windows of the cryostat. UV-Vis measurements were performed using a Shimadzu UV-3600 spectrometer with a resolution of 2 nm at 100 K. Polycrystalline samples were prepared as KBr pellets like for IR spectroscopy for measuring solid-state spectra in transmission mode. NMR spectra were recorded at room temperature using a Bruker DRX400 spectrometer (400 MHz for ¹H and 100.6 MHz for ¹³C). Chemical shifts are relative to deuterated solvent residual peaks.

## Density Functional Theory calculations
Density functional theory (DFT) calculations were performed with the ADF 2022 package.²⁸ For the geometry optimization of *trans*-([RuNOen₂OH]²⁺ and *trans*-[RuNOen₂(H₂O)]³⁺ in GS, MS1 and MS2 (closed-shell electron configurations) in the gas phase, the Perdew-Burke-Ernzerhof (PBE) functional²⁹ with triple-ζ-quality with one polarization function all-electron (TZP) basis set was used. Initial geometries for the structure optimization were taken from experimental XRD data of 1.¹⁸ IR spectra were calculated on the same level of theory, which was used for assignment of vibrational bands in the range of 700-400 cm⁻¹.

## Differential scanning calorimetry

Differential scanning calorimetry (DSC) experiments were performed on a Mettler-Toledo DSC1 instrument equipped with a high-sensitivity DSC HSS8 sensor. The sample (about 2 mg of the powder) was homogeneously spread in a standard aluminium crucible (40 ml), such that it formed a thin layer covering the whole surface of the crucible. For MS1 generation, irradiation of GS was performed at 123 K for 15-30 min through a glass window, using the same as in IR measurements Thorlabs LEDs at 405 nm or 420 nm. MS2 was generated under the same conditions by first irradiating at 405 nm or 420 nm for 15-30 min, followed by irradiation at 940 nm for 10-15 min. To detect the enthalpy release during thermal relaxation of the metastable states, the sample was then heated from 123 to 333 K at a heating rate of 6 or 9 K min⁻¹. As a reference measurement the sample was measured using the same protocol but without light irradiation. The experimental data were processed using the Netzsch Proteus analysis software.

## X-ray diffraction

Powder X-ray diffraction (PXRD) patterns were recorded using a PANalytical X'Pert PRO diffractometer equipped with a Cu X-ray tube, a Ge(111) incident-beam monochromator (λ = 1.5406 Å) and an X'Celerator detector. The X-ray data were collected on Rigaku Supernova diffractometer with Excalibur CCD detector using microfocus MoKα X-ray source (λ = 0.71073 Å). CrysAlisPro software package was used both for data collection and reduction. The low temperature during measurements was obtained using liquid nitrogen at 100 K. The crystal structures of ground states (GS) and photoinduced linkage isomers (PLIs) were solved using ShelXT.³⁰ All structures were refined by means of ShelXL³¹ implemented in Olex2.³² The disorder in photoexcited crystals was refined based on Fourier difference map of given structure and photodifference map calculated between respective PLI and GS observed structure factors (F<sub>obsPLI</sub> - F<sub>obsGS</sub>).³³ In all crystal structures all non-hydrogen atoms were refined anisotropically. The hydrogen atoms positions were constrained and treated as riding rotating groups. In disordered crystal structures (1 at 300 K, 1 in MS1, 1 in MS2) a set of restraints on bond lengths (DFIX), and atomic displacement parameters (ADPs) (EADP, ISOR) were applied, adjusted individually for each structure. In the structure of 1 measured at 300 K, DFIXs were applied for one disordered part of ethylenediamine ligand and for N-O bond lengths of disordered NO₃⁻ anion. The bonds N-C and C-C were constrained to 1.44 Å, ISORs were applied to two carbon atoms of the same group in order to avoid appearance of non-positive defined ADPs. All bonds N-O of NO₃⁻ were constrained to 1.25 Å, ISORs were applied to O4, O3A and O5A atoms. In the structure 2, one NO₃⁻ anion (N8) was disordered over two positions (0.85/0.15), the set of constraints was applied only for 0.15 occupancy part (DANG, all angles O-N-O, 2.15 Å; DFIX, all bonds N-O, 1.25 Å; EADPs were applied to all oxygen atoms). In the structure 1 in MS1, the bonds Ru-N and N-O of the Ru-N-O linkage of GS part were constrained by DFIX to 1.745 Å and 1.151 Å, respectively, applying EADP for atoms of NO ligand in GS and MS1. Finally, in the structure 1 in MS2, DFIX constrains were applied to the Ru-N-O linkage of GS, and ISORs were used for N and O atoms of NO group of MS2 to avoid non-positive defined ADPs. To measure structural changes in a single crystal of 1 after light irradiation, first, the structure was measured in GS at 100 K. Irradiations of a single crystal of 1 were performed in-situ on the diffractometer at 100 K by means of 405 nm LED with 140 mW optical power for 90 min for
generation of MS1. To measure the structure of MS2, after the measurement of MS1 structure, the crystal was subsequently irradiated with a cw-laser at 980 nm with 130 mW for 90 min. During irradiation the crystal was rotated around the axis perpendicular to the light beam to ensure a homogenous distribution of the photoproduct in the whole crystal volume. After each irradiation time the XRD experiment was performed and the crystal structure was determined. The measured structures have been deposited with the CCDC with deposition numbers 2402692-2402700 for [RuNOen<sub>2</sub>OH]I<sub>2</sub>, [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (293 K), [RuNOen<sub>2</sub>(H<sub>2</sub>O)](NO<sub>3</sub>)<sub>3</sub>, [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (100 K, GS), [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (100 K, MS1), [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (100 K, MS2), [(RuNOenCl<sub>2</sub>)<sub>2</sub>(μ-OH)]Cl·2H<sub>2</sub>O, [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·0.5AgNO<sub>3</sub>·0.5H<sub>2</sub>O, [RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·H<sub>2</sub>O, respectively. Crystal data and refinement details for reported structures are shown in Table S1.

## Results and discussion

### Structural data of 1-5

The structural fragment of the complex [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1) is shown in Figure 1, a. The structure of the ruthenium fragment represents an octahedron with two ethylenediamine (en) ligands in the equatorial plane, and nitrosyl (NO) and hydroxyl (OH) ligands in a *trans*-position to each other. The octahedron of 1 is similar to that of [RuNO(en)<sub>2</sub>OH]Br<sub>2</sub> reported by Tomizawa, however, in 1, one of the en ligands is disordered over two positions (0.5/0.5).<sup>23</sup> The nitrate anions being counterions of the ruthenium cation(2+) form several intermolecular contacts with the nitrosyl ligand, as shown in Figure 1. The main bond distances of 1 are listed in Table 1 and are in good agreement with this class of compounds.<sup>22,23,27</sup> Particularly, the Ru-N-O coordinate has a linear conformation, where Ru-NO and N-O distances are close to 1.75 and 1.15 Å, respectively. The Ru-N<sub>en</sub> bond lengths are typical for ruthenium complexes containing N-donor ligands, at about 2.1 Å. These distances slightly vary due to involvement of ethylenediamine hydrogen atoms in intermolecular interactions with NO<sub>3</sub><sup>-</sup> anions. It should be noted that 1 exhibits a phase transition (P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>→Pnma) at an onset temperature of 193 K concomitant with an additional disorder of the en ligands and disorder of NO<sub>3</sub><sup>-</sup> anions in the high temperature Pnma phase (see Fig. S2). Since we studied the structure and properties of the PLI at 100 K in the low temperature phase (P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>), this phase will be discussed in more detail.

Two other types of single crystals containing the salt [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> were obtained – the complex [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·H<sub>2</sub>O (4) with crystal water and heterometallic [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·0.5AgNO<sub>3</sub>·0.5H<sub>2</sub>O (3).<sup>34</sup> The bond lengths within the [RuNO(en)<sub>2</sub>OH]<sup>2+</sup> cation are similar for 1, 3 and 4 (see Table 1). A small difference in Ru-OH bond lengths might be related to different intermolecular interactions of the OH ligand. For example, in 4, there is a hydrogen bond between the OH ligand and a molecule of crystalline water H-O-H···O-H of 1.9 Å. While in 3, there are interactions of OH ligands with Ag<sup>+</sup> at distances of 2.3-2.4 Å (see Fig. 1).
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Structural fragments of [RuNO(en)₂OH](NO₃)₂ (1, panel a), [RuNO(en)₂OH](NO₃)₂·H₂O (4, panel b) and [RuNO(en)₂OH](NO₃)₂·0.5AgNO₃·0.5H₂O (3, panel c, H₂O molecule is omitted for clarity) with depicted bond lengths (Å) and intermolecular contacts (Å) of NO ligand. ADPs are given at the 50% probability level.</figcaption></figure>

<table><caption>**Table 1.** Selected interatomic distances (Å) and angles (°) for the structures 1-5 measured at 100 K.</caption><thead><tr><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><td>Ru-NO</td><td>1.745(3)</td><td>1.7360(16)</td><td>1.7447(12)/1.7458(12)</td><td>1.745(3)</td><td>1.721(3)/1.726(2)</td></tr><tr><td>N-O</td><td>1.151(5)</td><td>1.140(2)</td><td>1.1502(16)/1.1485(16)</td><td>1.154(3)</td><td>1.146(3)/1.146(3)</td></tr></tbody></table>
<table><tr><td>Ru-OH</td><td>1.961(3)</td><td>2.0439(13)</td><td>1.9766(10)/1.9694(10)</td><td>1.969(2)</td><td>2.045(2)/2.047(2)</td></tr><tr><td rowspan="4">Ru-N<sub>en</sub></td><td>2.080(4)</td><td>2.0980(16)</td><td>2.1056(12)/2.1136(12)</td><td>2.113(2)</td><td>2.088(2)/2.073(2)</td></tr><tr><td>2.096(4)</td><td>2.1023(17)</td><td>2.1068(12)/2.1144(12)</td><td>2.096(2)</td><td>2.084(2)/2.085(2)</td></tr><tr><td>2.104(4)</td><td>2.1074(16)</td><td>2.1001(11)/2.0997(12)</td><td>2.113(2)</td><td></td></tr><tr><td>2.111(4)</td><td>2.1114(17)</td><td>2.1111(12)/2.0979(12)</td><td>2.109(2)</td><td></td></tr><tr><td>Ru-N-O</td><td>175.8(4)</td><td>179.14(17)</td><td>177.33(12)/176.36(11)</td><td>177.8(2)</td><td>179.8(3)/176.6(2)</td></tr><tr><td rowspan="2">Ru-Cl</td><td rowspan="2">-</td><td rowspan="2">-</td><td rowspan="2">-</td><td rowspan="2">-</td><td>2.3768(8)/2.3806(8)</td></tr><tr><td>2.3778(8)/2.3939(8)</td></tr></table>

The structure of [RuNO(en)₂(H₂O)](NO₃)₃ (2) differs from 1, 3 and 4 due to the charge of the ruthenium cation [RuNO(en)₂(H₂O)]³⁺ resulting from the substitution of the OH⁻ ligand with H₂O. As shown in Table 1, the most significant differences in interatomic distances are observed along the H₂O-Ru-N-O coordinate. Specifically, the Ru-NO and N-O bond lengths are slightly shorter, while the Ru-OH₂ distance increases significantly. A similar bond elongation is observed in the complex [RuNO(en)₂(H₂O)]Cl₃, attributed to the weaker π-donor abilities of the H₂O ligand compared to OH⁻.²³,²⁴ The different *trans*-influence of the H₂O ligand is responsible for the shortening of Ru-N-O distances (see Fig. 2).

The dimeric complex [(RuNOenCl₂)₂(μ-OH)]Cl·2H₂O (5) is a product of the partial substitution of the K₂[RuNOCl₅] precursor by en, which was obtained as a side product during the synthesis of 2. The bond distances along the (μ-OH)-Ru-N-O axis resemble those of complex 2, likely, due to the similar π-donor strength of the bridging OH⁻ ligand. The Ru-Cl bond distances are much longer compared to Ru-Nₐₙ reaching about 2.38 Å, characteristic of ruthenium chloride complexes.²¹,²² The *trans*-influence of Cl⁻ ligands leads to a shortening of Ru-Nₐₙ distances (see Table 1), which are notably shorter compared to those in 1-4. It is worth noting, that 5 is a relatively rare example of a nitrosyl complex with a bridging μ-OH⁻ ligand, only four examples of complexes containing the {ON-Ru-(μ-OH)-Ru-NO} fragment were found in the Cambridge Structural Database (CSD).³⁵⁻³⁸
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Structural fragments of [RuNO(en)₂(H₂O)](NO₃)₃ (2, panel a, disorder (0.85/0.15) of N8 NO₃⁻ anion is not shown for clarity) and [(RuNOenCl₂)₂(µ-OH)]Cl·2H₂O (5, panel b) with depicted bond lengths (Å) and intermolecular contacts (Å) of NO ligand. ADPs are given at the 50% probability level.</figcaption></figure>

### Photocrystallographic studies of [RuNO(en)₂OH](NO₃)₂ (1)

Due to the fact that the highest population of metastable states MS1 and MS2 was achieved for complex 1 (see IR-spectroscopy section), this complex was selected for photo-crystallographic studies. The procedures to generate MS1 and MS2 in a single crystal of 1 are described in the Experimental section. To assess the photoinduced changes, so-called photodifference maps (PD maps) were initially generated.³³ These maps enable a model free analysis of changes in electron density distribution before and after light excitation. The PD maps obtained after generation of MS1 and MS2 are shown in Fig. 3 c, and d, respectively. Blue circles indicate electron density that appears in the structure after light-excitation, while red circles show a depletion in electron density compared to the GS structure. As shown in the PD map of MS1 (Fig. 3, c), a significant increase in electron density is observed at the
nitrogen atom position N1 of GS after irradiation, suggesting an electron density enrichment at this location. A slight depletion in electron density is observed at the oxygen atom position O1. The contour around O1 is broader compared to the positive density around N1, possibly due to the terminal position of the O1 atom (N1A in the case of MS1). Therefore, the increase in electron density at N1 and the corresponding decrease at O1 can be explained by the 180° rotation of NO from Ru-N-O (GS) to Ru-O-N (MS1) linkage. The PD map obtained after the MS2 generation is shown in Fig. 3, d. In this case, a depletion in electron density is observed at both N1 and O1 positions, with corresponding appearance of electron densities at positions perpendicular to the Ru-N-O coordinate (atoms N1A and O1A in Fig. 3, d). Thus, the 90° rotation of nitrosyl ligand is observed, which is characteristic of the MS2 configuration.<sup>19,39,40</sup> The resulting photodifference maps give clear evidence for a displacement of the nitrosyl group after light excitation.

Based on this qualitative analysis of electron density changes after light excitation, particular structural models of MS1 and MS2 were proposed (see Fig. 3, a, b, and Table 2). The structure of MS1 was refined with a disordered NO ligand in two positions – GS and MS1 with populations of 51(4)% and 49(4)%, respectively. The disordered model was also applied to the MS2 structure resulting in 7(1)% of MS2 and 93(1)% of GS, which is consistent with IR-spectroscopy data. The Ru-ON bond length of MS1 became notably longer (1.835(10) Å) than the Ru-NO length of GS (1.745(3) Å). The bonds Ru-N1A and Ru-O1A of MS2 become even longer reaching 2.01(4) Å and 2.13(4) Å, respectively. According to the obtained structural models, the N-O bond distance changes after isomerization, become longer in MS1 and shorter in MS2 (see Table 2). The *trans*-ligand $OH^-$ is sensitive to the Ru-ON bond length elongation, thus the Ru-OH distance changes from 1.961(3) Å in GS, to 1.947(3) Å in MS1. It should be noted, that the position of the $OH^-$ ligand was not refined as a disordered model over two positions, meaning that the $Ru-OH_{MS1}$ bond length corresponds to the average of Ru-OH distances of GS(49(4)% and MS1(51(4)%). Overall, care must be taken not to overinterpret bond length changes, given that we deal with disordered structures, with sometimes low population like for MS2 or some structural configurations that heavily overlap like in the case of MS1 (see <sup>41</sup> for a discussion of this aspect).
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

**Fig. 3.** Structural models of MS1, MS2 and photodifference (PD) maps of **1**: panels a, b show structural models of MS1 and MS2, respectively; panel c shows the photodifference map after generation of MS1; panel d represents the photodifference map after generation of MS2. Positive electron density is shown by blue, negative contours – by red colour. The contours are at 0.4 e·Å⁻³ level.

<table><caption>**Table 2.** Selected interatomic distances (Å) and angles (°) for the GS, MS1 and MS2 structures of [RuNO(en)₂OH](NO₃)₂ (1) measured at 100 K.</caption><thead><tr><th colspan="4">[RuNO(en)₂OH](NO₃)₂ (1)</th></tr><tr><th></th><th>GS</th><th>MS1</th><th>MS2</th></tr></thead><tbody><tr><td>Ru-NO</td><td>1.745(3)</td><td>-</td><td>2.01(4)</td></tr><tr><td>Ru-ON</td><td>-</td><td>1.835(10)</td><td>2.13(4)</td></tr><tr><td>N-O</td><td>1.151(5)</td><td>1.20(2)</td><td>1.06(5)</td></tr><tr><td>Ru-OH</td><td>1.961(3)</td><td>1.947(3)</td><td>1.957(2)</td></tr><tr><td rowspan="4">Ru-N<sub>en</sub></td><td>2.080(4)</td><td>2.080(4)</td><td>2.088(3)</td></tr><tr><td>2.096(4)</td><td>2.097(4)</td><td>2.099(3)</td></tr><tr><td>2.104(4)</td><td>2.101(5)</td><td>2.103(3)</td></tr><tr><td>2.111(4)</td><td>2.104(4)</td><td>2.112(3)</td></tr><tr><td>Ru-N-O</td><td>175.8(4)</td><td>-</td><td>82(3)</td></tr><tr><td>Ru-O-N</td><td>-</td><td>173(4)</td><td>69(3)</td></tr></tbody></table>

## IR- and UV-vis spectroscopic properties of 1-3

IR-spectroscopy allowed us to determine optimal parameters, such as excitation wavelength and population of metastable states necessary for successful photocrystallographic experiments. Specifically, the band of v(NO) is highly sensitive to changes in the Ru-NO linkage, enabling
measurement of the area under the v(NO) band after light excitation to evaluate the population of each linkage isomer. The spectra of **1** before and after light excitation at 100 K are shown in Fig. 4. Irradiation of **1** in GS with 405 nm (115 mW) light results in a significant decrease in the v(NO)GS band at 1881/1873 cm⁻¹ accompanied by the emergence of the v(NO)MS1 band at 1747 cm⁻¹ with a 47% population (see Table 3). The isomerization of Ru-NOGS to Ru-ONMS1 also impacts other bands, such as v/δ(OH), v/δ(Ru-N-O) and v(Ru-OH) as shown in Fig. 4, S3 and Table S2. For instance, the v(OH) band shifts to lower energy, while δ(OH) and v(Ru-OH) shift to higher energy after isomerization to MS1. The highest population of MS1 in **2** and **3** was achieved with excitation at 420 nm (100) resulting in similar spectral changes shown in Fig. S4. Irradiation of MS1 with 980 or 940 nm (120 mW) light leads to the transformation of MS1 to MS2, evident in the formation of v(NO)MS2 bands in the range of 1500-1600 cm⁻¹ (see Table 3). Therefore, due to the highest populations of MS1 (47%) and MS2 (17%) in **1**, this complex was selected for crystallographic studies. Both MS1 and MS2 can be reversibly transferred to the GS by irradiation in the 500-700 nm range.

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Changes in IR-spectra of **1** after generation of MS1 (405 nm, 30 min) and MS2 (405 nm, 30 min + 980 nm, 110 min) at 100 K.</figcaption></figure>

<table><caption>**Table 3.** Frequencies of v(NO) stretching bands (v [cm⁻¹]) and maximum populations (Pop. [%]) at excitation wavelengths (λ [nm]) of MS1 and MS2 in **1-3**.</caption><thead><tr><th rowspan="2"></th><th colspan="1">GS</th><th colspan="2">MS1</th><th colspan="2">MS2</th></tr><tr><th>v [cm<sup>-1</sup>]</th><th>v [cm<sup>-1</sup>]</th><th>Pop. [%], λ [nm]</th><th>v [cm<sup>-1</sup>]</th><th>Pop. [%], λ [nm]</th></tr></thead><tbody><tr><td>1</td><td>1881, 1873</td><td>1747</td><td><b>47, 405</b></td><td>1512</td><td><b>17, 980</b></td></tr><tr><td>2</td><td>1937, 1927</td><td>1800, 1788</td><td><b>13, 420</b></td><td>1567</td><td><b>6, 940</b></td></tr><tr><td>3</td><td>1882, 1872, 1850, 1840</td><td>1746, 1723, 1713, 1704</td><td><b>20, 420</b></td><td>1514</td><td><b>7, 940</b></td></tr></tbody></table>

In order to explain the photoinduced population-depopulation dynamics of metastable states, UV-vis-spectra of **1-3** were investigated after light irradiation at 100 K. MS1 and MS2 were produced using the same excitation wavelengths listed in Table 3. In GS, all the complexes exhibit absorption bands starting from about 500 nm up to the deeper UV-range (see Figs. 5 and S5). Thus, irradiation at 405 or
420 nm leads to an efficient excitation of metal-to-ligand charge transfer (MLCT) bands resulting in the population of MS.⁴² The broad MS1 bands in **1-3** show maxima around 600 nm, absorbing from 1000 nm up to the UV-range. The high absorbance of MS1 at 500-700 nm explains the possibility of the photoinduced reaction MS1→GS after excitation in this range, while its irradiation at 405 or 420 leads to steady-state equilibrium GS ↔ MS1 and partial population of GS and MS1. A low-intensity absorption of MS1 in the range of 900-1000 nm is responsible for its excitation towards MS2. Considering the low population of MS2 in **1-3**, the absorption coefficient of MS2 in these complexes is the highest compared to those of GS and MS1 in the range of 400-1000 nm. UV-vis-spectra of MS2 show broad maxima at 500 and 800 nm, the latter is much less intense in the case of **2**. Taking into account the hypothesis of a two-step mechanism of MS1 formation (GS→MS1→MS2),¹⁶ the high absorbance of MS2 at 405 or 420 nm favours efficient excitation of MS2 right after GS excitation, leading to MS1 formation. Since the absorption coefficient of MS2 is very high at 405-420 nm, the steady-state population of MS2 after irradiation in this range is negligible. Similar to the MS1 case, irradiation of MS2 in the range of 500-700 nm induces the MS2→GS (or MS2→MS1→GS) reaction. The fact that MS2 absorbs relatively less at 900-1000 nm allows its population via MS1→MS2 transfer, however, prolonged irradiation in this range also leads to its depopulation.

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** UV-vis spectra of **1** (panel a) and **2** (panel b) in GS, MS1 and MS2 at 100 K. The spectra of MS1 and MS2 are shown as difference spectra MS1-GS and MS2-GS. In GS the increased absorption in the range of 500-800 nm is related to a diffusion of light caused by the KBr matrix.</figcaption></figure>

## Thermal stability of linkage isomers in **1-3**

The thermal stability of MS1 and MS2 in **1-3** was assessed using DSC, since the thermal decay of both states is accompanied by an exothermic effect (see Table 4 and Fig. S6). The thermal effects of MS-GS transitions were treated with first-order kinetics to determine activation energies (Ea) and frequency factors (k0), followed by calculating decay temperatures Td.²⁵,⁴³ Td is a convenient parameter that allows for comparing thermal stability of different states in different complexes, since it comprises both Ea and k0 (see caption of Table 4). The thermal stability of MS2 is lower compared to MS1 by 50-100 K, depending on the complex. For example, Td(MS2) increases in the row **3-1-2**, with the highest in complex **2** bearing the H2O ligand. Moreover, this Td(MS2) = 215(1) K is the highest MS2 decay temperature in this class of nitrosyl compounds.⁴⁴ A similar pattern of thermal stability is observed for MS1 isomers showing an even larger difference between complexes with OH⁻ (**1,3**) and H2O (**2**). According to previous studies,⁴⁵⁻⁴⁷ the thermal stability of metastable states depends on the electronegativity of the *trans*-ligand to NO and the charge of the complex – higher electronegativity and a higher positive charge favour the thermal stability of both metastable states. Indeed, the higher stability of MS1 and MS2 in **2** is attributed to the increased charge of the complex (3+) compared to
1, 3 (2+). The order of the charge effect is slightly less than the electronegativity of the *trans*-ligand, as the T<sub>d</sub> of the related fluoride complex [RuNO(en)<sub>2</sub>F](ClO<sub>4</sub>)<sub>2</sub> is higher (300(3) K).<sup>27</sup> For better understanding the influence of the equatorial ligands on the thermal stability of PLI complexes with coordinates ON-Ru-OH(H<sub>2</sub>O), the parameters obtained for different equatorial ligands (en, NH<sub>3</sub> and pyridine (Py)) were gathered in Table 5. As shown in the table, T<sub>d</sub> of pyridine complexes are the smallest for both MS1 and MS2. The change in the intermolecular environment also significantly influences the T<sub>d</sub> (see T<sub>d</sub>(MS2) of **1** and **3**),<sup>48</sup> however, pyridine complexes show an even bigger decrease in T<sub>d</sub>. This effect might be connected with higher charge delocalization in Py than in NH<sub>3</sub> and en ligands. However, it is important to mention that pyridine complexes exhibit the highest populations of MS1.<sup>41,49</sup>

<table><caption>**Table 4.** Activation energies (E<sub>a</sub>), frequency factors (k<sub>0</sub>) and decay temperatures (T<sub>d</sub>) of MS→GS transitions in **1-3** obtained from DSC data. T<sub>d</sub> is the temperature (T) at k = 10<sup>-3</sup> s<sup>-1</sup> from Arrhenius law (k=k<sub>0</sub>·exp(-E<sub>a</sub>·R<sup>-1</sup>·T<sup>-1</sup>), where R is the gas constant).<sup>25</sup></caption><thead><tr><th rowspan="2"></th><th colspan="3">MS1</th><th colspan="3">MS2</th></tr><tr><th>E<sub>a</sub> [kJ/mol]</th><th>k<sub>0</sub> [lg]</th><th>T<sub>d</sub> [K]</th><th>E<sub>a</sub> [kJ/mol]</th><th>k<sub>0</sub> [lg]</th><th>T<sub>d</sub> [K]</th></tr></thead><tbody><tr><td><b>3</b></td><td>80.836(0.701)</td><td>13.712(0.137)</td><td>253(2)</td><td>53.459(1.048)</td><td>12.199(0.280)</td><td>184(4)</td></tr><tr><td><b>1</b></td><td>88.417(0.261)</td><td>14.867(0.050)</td><td>259(1)</td><td>63.780(1.991)</td><td>13.107(0.476)</td><td>207(6)</td></tr><tr><td><b>2</b></td><td>99.474(0.268)</td><td>14.951(0.046)</td><td>290(1)</td><td>64.680(0.147)</td><td>12.704(0.034)</td><td>215(1)</td></tr><tr><td>*</td><td>107.1(6.8)</td><td>15.7(1.1)</td><td>300(3)</td><td>-</td><td></td><td></td></tr></tbody><tfoot><tr><td colspan="7">* Data on [RuNO(en)<sub>2</sub>F](ClO<sub>4</sub>)<sub>2</sub> complex with *trans*-coordinate F-Ru-NO.<sup>27</sup></td></tr></tfoot></table>

<table><caption>**Table 5.** Comparison of T<sub>d</sub> of OH<sup>-</sup> and H<sub>2</sub>O complexes with different equatorial ligands: en, NH<sub>3</sub>, pyridine (Py).</caption><thead><tr><th>Equatorial ligands</th><th>Trans-ligand: OH<sup>-</sup></th><th>T<sub>d</sub>MS1 [K]</th><th>T<sub>d</sub>MS2 [K]</th><th>Trans-ligand: H<sub>2</sub>O</th><th>T<sub>d</sub>MS1 [K]</th><th>T<sub>d</sub>MS2 [K]</th></tr></thead><tbody><tr><td rowspan="2">en</td><td>[RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1)</td><td>259</td><td>207</td><td>[RuNO(en)<sub>2</sub>(H<sub>2</sub>O)](NO<sub>3</sub>)<sub>3</sub> (2)</td><td>290</td><td>215</td></tr><tr><td>[RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·0.5Ag NO<sub>3</sub>·0.5H<sub>2</sub>O (3)</td><td>253</td><td>184</td><td></td><td></td><td></td></tr><tr><td>NH<sub>3</sub></td><td>[RuNO(NH<sub>3</sub>)<sub>4</sub>(OH)]Cl<sub>2</sub><sup>20</sup></td><td>258</td><td>189</td><td>[RuNO(NH<sub>3</sub>)<sub>4</sub>(H<sub>2</sub>O)]Cl<sub>3</sub>·H<sub>2</sub>O<sup>20</sup></td><td>277</td><td>211</td></tr><tr><td rowspan="2">Py</td><td>[RuNOPy<sub>4</sub>OH](PF<sub>6</sub>)<sub>2</sub><sup>45</sup></td><td>222</td><td>143</td><td>[RuNOPy<sub>4</sub>(H<sub>2</sub>O)](ClO<sub>4</sub>)<sub>3</sub>·2H<sub>2</sub>O<sup>47</sup></td><td>261</td><td>-</td></tr><tr><td>[RuNOPy<sub>4</sub>OH](ClO<sub>4</sub>)<sub>2</sub>·H<sub>2</sub>O<sup>47</sup></td><td>211</td><td>-</td><td></td><td></td><td></td></tr></tbody></table>

Photoinduced dynamics in [RuNO(en)<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1) under pulsed irradiation

The equilibrium GS ⇌ MS2 ⇌ MS1 between linkage isomers can be of photochemical or thermal nature. In the temperature range used in the pulsed experiment (10 K) the thermal transformations of MS1 and MS2 to GS (MS2 → MS1 → GS) are extremely slow, thus in the present experiment the equilibrium between linkage isomers is only photochemical. Since activation energy (E<sub>a</sub>) and frequency factor (k<sub>0</sub>) determine thermal stability of MS1 and MS2 at a chosen temperature, the lifetimes (k<sup>-1</sup>) of both states can be calculated using Arrhenius law (k = k<sub>0</sub>·exp(-E<sub>a</sub>·R<sup>-1</sup>·T<sup>-1</sup>), where R is the gas constant). At 10 K the lifetimes of MS1 and MS2 are more than 10<sup>283</sup> and 10<sup>298</sup> years, respectively. Thus, we can consider MS1 and MS2 as thermally stable species at 10 K, and therefore we can investigate the transformations GS ⇌ MS2 ⇌ MS1 at 10 K which can be considered as purely photoinduced.

In order to investigate the isomerization mechanism, the sample of **1** was irradiated with pulsed laser at 10 K and probed with IR-spectroscopy. The sample was exposed to 5 ns of 410 nm (2.68 mJ/pulse,
10 Hz) pulsed irradiation and IR-spectra were registered after each excitation sequence. The qualitative description of dependencies between IR bands intensities and irradiation energy corresponds to sequential transformation GS ↔ MS2 ↔ MS1 with the MS2 isomer as the intermediate state before MS1 formation. Indeed, the first observable linkage isomer was MS2 with the characteristic v(NO)MS2 band at 1513 cm⁻¹ detectable after 20 pulses (0.05 J, see Fig. 6, a). The MS2 band continued to grow with further excitation, and the v(ON)MS1 band at 1749 cm⁻¹ appeared only after 40 pulses (0.11 J). The quasi-stationary conditions were achieved when E > 0.3-0.7 J, in that time the MS2 band intensity became approximately constant (see Fig. 6, b). And finally, after irradiation energy more than 120 J (50000 pulses) the system is approached the photochemical equilibrium (see Fig. 6, c). Thus, based on the current experimental evidence, the MS1 generation mechanism in studied complexes should be considered as reversible set of GS ↔ MS2 ↔ MS1 transformations, as found for the pyridine, amine ruthenium and iron nitrosyls reported in previous studies.<sup>7,19,50</sup>

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** IR-spectra after pulsed laser excitation with 410 nm at 10 K. Panel a shows difference spectra before irradiation and after excitation with given number of pulses. Panels b and c represent evolution of integral intensities of v(NO)GS, v(ON)MS1 and v(NO)MS2 bands after pulsed excitation in different ranges. Pulse energy [J] is the total integrated pulsed energy that arrived on the sample.</figcaption></figure>

Thus, the general view of experimental curves is similar to the two-step reversible first-order kinetic GS ↔ MS2 ↔ MS1 with the absorbed energy instead of time with the corresponding effective constants (k, J⁻¹) of four single stages: GS →<sub>k₁</sub>MS2, MS2 →<sub>k₂</sub>GS, MS2 →<sub>k₃</sub>MS1, MS1 →<sub>k₄</sub>MS2. The set of three differential equations dXᵢ/dE for the variation of the molar fractions Xᵢ (i=GS, MS1, MS2) can then be
solved using the boundary condition $X_{GS}+X_{MS2}+X_{MS1} = 1$, as well as the initial condition $X_{GS}=1$. The quantitative description of dependencies was carried out by minimizing the total discrepancy $\Sigma(I_{GS}^{exp} - I_{GS}^{calc})^2 + (I_{MS1}^{exp} - I_{MS1}^{calc})^2 + (I_{MS2}^{exp} - I_{MS2}^{calc})^2$ for all experimental points varying the effective constants ($k_i$) and integral absorption coefficients $\varepsilon_{GS}$, $\varepsilon_{MS1}$, $\varepsilon_{MS2}$, based on the formula $\varepsilon = I/X$, where I denotes the integral absorbance of the corresponding band in the IR spectra (see Supporting Information for the details). Experimental and calculated curves are shown in Fig. 7.

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** The experimental and calculated integral intensities of $v(\text{NO})_{\text{GS}}$, $v(\text{ON})_{\text{MS1}}$ and $v(\text{NO})_{\text{MS2}}$ (panels a, b). The first derivatives of the molar fractions for GS and MS1 indicating appearance of quasi-stationary state after E=0.5 J (panel c). Panel c represents the rates of $X_{\text{GS}}$ consumption (d$X_{\text{GS}}$/dE<0) and $X_{\text{MS1}}$ accumulation (d$X_{\text{MS1}}$/dE>0), both curves are monotone.</figcaption></figure>

Calculated curves describe well the experimental data with good correlation coefficients ($R^2 = 0.967-0.998$). The lower correlation for MS2 is due to its low population throughout the experiment which results in the higher uncertainness. Still, the calculated MS2 curve well fits the main features in the beginning of the experiment, namely the energy required for the stationary state and MS2 stationary molar fraction (Fig. 7 b, c). The obtained values of k and ε are given in Table 6.

<table><caption>**Table 6.** The values of effective constants of different transformations and integral absorption coefficients in IR spectra for GS, MS1 and MS2.</caption><thead><tr><th colspan="4">The effective constants k, J<sup>-1</sup></th></tr><tr><th>k<sub>1</sub></th><th>k<sub>2</sub></th><th>k<sub>3</sub></th><th>k<sub>4</sub></th></tr></thead><tbody><tr><td>0.1</td><td>5.6</td><td>0.6</td><td>1.5&middot;10<sup>-2</sup></td></tr><tr><th colspan="4">IR integral absorption coefficients</th></tr><tr><th>&epsilon;<sub>GS</sub></th><th>&epsilon;<sub>MS1</sub></th><th>&epsilon;<sub>MS2</sub></th><th>-</th></tr><tr><td>19.5</td><td>13.1</td><td>5.7</td><td>-</td></tr></tbody></table>
First of all, one can see that k₂, k₃ >> k₁, k₄, that means that photochemical equilibrium (k₁/k₂ = XMS2∞/XGS∞, k₄/k₃ = XMS2∞/XMS1∞) is significantly shifted to GS and MS1, thus, one cannot achieve a high population of MS2 with blue light irradiation (410 nm). The ratio of k₂/k₃ describes the probability of MS2 to GS or MS1 transformation after MS2 excitation. For the investigated complex the reverse MS2→GS process is more efficient than MS2→MS1 transition. The final equilibrium ratio XGS∞/XMS1∞ is determined by the combination k₄k₂/k₁k₃ = 1.4, which is close enough to the value (IGS/εGS)/(IMS1/εMS1) = 1.3 of the last experimental point (E = 180 J). Also, the IR absorption coefficients for GS and MS1 differ only by a factor of 1.5, while for MS2 the value is 2-3 times lower. That can be explained by different dipole moment of NO in each isomer due to different coordination modes.¹⁰ Finally, we estimated quantum yield (Φ) of the first transformation GS→MS2 considering only initial linear part of dXGS/dE slope giving Φ = 11% (see Supporting information for the details). Earlier we estimated switching efficiency (different than Φ) of GS→MS1 reaction in [RuNOPy₄F](ClO₄)₂ without consideration of the optical absorption coefficient of GS at excitation wavelength about 0.1%.¹⁹ Obtained Φ = 11% for GS→MS2 in **1** agrees with previous data, since total quantum yield of GS→MS1 should decrease when convoluting with the second stage MS2→MS1.

## Conclusions

In conclusion we have reported new ruthenium nitrosyl complexes with ethylenediamine ligands for which PLI of NO with high stability can be generated. In this context the very high decay temperature of MS2 in [RuNO(en)₂(H₂O)](NO₃)₃ (**2**) is interesting as it offers the possibility to generate MS1 at higher temperatures. The highest Td(MS2) in **2** can be explained by the high charge of the complex (3+) due to the neutral H₂O ligand in *trans*-position to NO, and by en ligands (also neutrally charged) having localized electron density at nitrogen atoms. During the studies of mechanism of NO isomerization we found that the photoisomerization involves a two-step process for MS1 formation via MS2 (GS ↔ MS2 ↔ MS1) as known from the ruthenium nitrosyl compounds with pyridine or amine ligands. Effective constants k₂ and k₃ representing MS2→GS and MS2→MS1 processes are much higher than constant k₁ (GS→MS2), which explains low population of MS2 during the excitation with 410 nm. Since absorption coefficients of GS, MS1 and MS2 at 410 nm are quite similar (187.52, 188.59 and 214.63 L·mol⁻¹·cm⁻¹, respectively), we can assume that quantum yields of photoinduced reactions will be proportional to k₄<k₁<k₃<k₂.

## Author contributions

A.A.M. writing – original draft, writing – review & editing, investigation, formal analysis, conceptualization; A.T.T. investigation; A.O.B. investigation, writing – review & editing; G.A.K. formal analysis, writing – review & editing; D.S. supervision, conceptualization, writing – review & editing.

## Conflicts of interest

There are no conflicts to declare

## Data availability

The data supporting this article have been included as part of the ESI. Spectroscopic and calorimetric data are available from the repository Recherche Data Gouv, under the link https://doi-org.bases-doc.univ-lorraine.fr/10.57745/QPLP1U. Crystallographic data for [RuNOen₂OH]I₂, [RuNOen₂OH](NO₃)₂ (293 K), [RuNOen₂(H₂O)](NO₃)₃, [RuNOen₂OH](NO₃)₂ (100 K, GS), [RuNOen₂OH](NO₃)₂ (100 K, MS1), [RuNOen₂OH](NO₃)₂ (100 K, MS2), [(RuNOenCl₂)₂(µ-OH)]Cl·2H₂O, [RuNO(en)₂OH](NO₃)₂·0.5AgNO₃·0.5H₂O, [RuNOen₂OH](NO₃)₂·H₂O have been deposited at the CCDC
under deposition numbers 2402692-2402700 and can be obtained from
https://www.ccdc.cam.ac.uk/.

Acknowledgements

The work has been financially supported by ANR (grant no. ANR-21-CE30-0045-01 and LUE-ANR-15-
IDEX-0004). We thank the PMD2X platform of Université de Lorraine for granting access to XRD
diffractometers.

References

(1) Ohkoshi, S.; Imoto, K.; Tsunobuchi, Y.; Takano, S.; Tokoro, H. Light-Induced Spin-Crossover Magnet. *Nat. Chem.* **2011**, *3* (7), 564–569. https://doi.org/10.1038/nchem.1067.

(2) Ohkoshi, S.; Takano, S.; Imoto, K.; Yoshikiyo, M.; Namai, A.; Tokoro, H. 90-Degree Optical Switching of Output Second-Harmonic Light in Chiral Photomagnet. *Nat. Photonics* **2014**, *8* (1), 65–71. https://doi.org/10.1038/nphoton.2013.310.

(3) Kimel, A. V.; Kalashnikova, A. M.; Pogrebna, A.; Zvezdin, A. K. Fundamentals and Perspectives of Ultrafast Photoferroic Recording. *Phys. Rep.* **2020**, *852*, 1–46.
https://doi.org/10.1016/j.physrep.2020.01.004.

(4) Thaggard, G. C.; Haimerl, J.; Park, K. C.; Lim, J.; Fischer, R. A.; Maldeni Kankanamalage, B. K. P.; Yarbrough, B. J.; Wilson, G. R.; Shustova, N. B. Metal–Photoswitch Friendship: From Photochromic Complexes to Functional Materials. *J. Am. Chem. Soc.* **2022**, *144* (51), 23249–23263. https://doi.org/10.1021/jacs.2c09879.

(5) Grommet, A. B.; Lee, L. M.; Klajn, R. Molecular Photoswitching in Confined Spaces. *Acc. Chem. Res.* **2020**, *53* (11), 2600–2610. https://doi.org/10.1021/acs.accounts.0c00434.

(6) Gütlich, P.; Garcia, Y.; Woike, T. Photoswitchable Coordination Compounds. *Coord. Chem. Rev.* **2001**, *219–221*, 839–879. https://doi.org/10.1016/S0010-8545(01)00381-2.

(7) Schaniel, D.; Nicoul, M.; Woike, T. Ultrafast Reversible Ligand Isomerisation in Na2[Fe(CN)5NO]·2H2O Single Crystals. *Phys. Chem. Chem. Phys.* **2010**, *12* (31), 9029.
https://doi.org/10.1039/b924528f.

(8) Gallé, G.; Nicoul, M.; Woike, T.; Schaniel, D.; Freysz, E. Unraveling the Mechanism of NO Ligand Photoisomerism by Time-Resolved Infrared Spectroscopy. *Chem. Phys. Lett.* **2012**, *552*, 64–68. https://doi.org/10.1016/j.cplett.2012.09.071.

(9) Schaniel, D.; Imlau, M.; Weisemoeller, T.; Woike, T.; Krämer, K. W.; Güdel, H.-U. Photoinduced Nitrosyl Linkage Isomers Uncover a Variety of Unconventional Photorefractive Media. *Adv. Mater.* **2007**, *19* (5), 723–726. https://doi.org/10.1002/adma.200601378.

(10) Xu, W.-J.; Li, M.-F.; Garcia, A. R.; Romanyuk, K.; Martinho, J. M. G.; Zelenovskii, P.; Tselev, A.; Verissimo, L.; Zhang, W.-X.; Chen, X.-M.; Kholkin, A.; Rocha, J. Molecular Design of a Metal-Nitrosyl Ferroelectric with Reversible Photoisomerization. *J. Am. Chem. Soc.* **2023**, *145* (25), 13663–13673. https://doi.org/10.1021/jacs.3c01530.

(11) Komine, M.; Imoto, K.; Namai, A.; Yoshikiyo, M.; Ohkoshi, S. Photoswitchable Nonlinear-Optical Crystal Based on a Dysprosium–Iron Nitrosyl Metal Assembly. *Inorg. Chem.* **2021**, *60* (4), 2097–2104. https://doi.org/10.1021/acs.inorgchem.0c03493.

(12) Goulkov, M.; Schaniel, D.; Woike, T. Pulse Recording of Thermal and Linkage Isomer Gratings in Nitrosyl Compounds. *J. Opt. Soc. Am. B* **2010**, *27* (5), 927. https://doi.org/10.1364/josab.27.000927.

(13) Coppens, P.; Novozhilova, I.; Kovalevsky, A. Photoinduced Linkage Isomers of Transition-
Metal Nitrosyl Compounds and Related Complexes. *Chem. Rev.* **2002**, *102* (4), 861–884.
https://doi.org/10.1021/cr000031c.

(14) Stepanenko, I.; Zalibera, M.; Schaniel, D.; Telser, J.; Arion, V. B. Ruthenium-Nitrosyl Complexes as NO-Releasing Molecules, Potential Anticancer Drugs, and Photoswitches Based on Linkage Isomerism. *Dalt. Trans.* **2022**, *51* (14), 5367–5393.
https://doi.org/10.1039/D2DT00290F.

(15) García, J. S.; Alary, F.; Boggio-Pasqua, M.; Dixon, I. M.; Heully, J.-L. Is Photoisomerization Required for NO Photorelease in Ruthenium Nitrosyl Complexes? *J. Mol. Model.* **2016**, *22* (11), 284. https://doi.org/10.1007/s00894-016-3138-2.

(16) Schaniel, D.; Woike, T. Necessary Conditions for the Photogeneration of Nitrosyl Linkage Isomers. *Phys. Chem. Chem. Phys.* **2009**, *11* (21), 4391. https://doi.org/10.1039/b900546c.

(17) Mikhailov, A. A.; Sukhikh, T. S.; Kuratieva, N. V.; Pishchur, D. P.; Kostin, G. A. Remarkable Thermal Stability of Light-Induced Ru-ON Linkage Isomers in Mixed Salts of a Ruthenium Amine Complex with a Trans -ON-Ru-F Coordinate. *Dalt. Trans.* **2021**, *50* (8), 2864–2871.
https://doi.org/10.1039/D0DT04323K.

(18) Mikhailov, A. A.; Wenger, E.; Kostin, G. A.; Schaniel, D. Room-Temperature Photogeneration of Nitrosyl Linkage Isomers in Ruthenium Nitrosyl Complexes. *Chem. – A Eur. J.* **2019**, *25* (31), 7569–7574. https://doi.org/10.1002/chem.201901205.

(19) Hasil, A.; Konieczny, K. A.; Mikhailov, A.; Pillet, S.; Schaniel, D. CW or Pulsed Laser – That Is the Question: Comparative Steady-state Photocrystallographic Analysis of Metal Nitrosyl Linkage Isomers. *ChemPhotoChem* **2024**, *8* (3), e202300149.
https://doi.org/10.1002/cptc.202300149.

(20) Schaniel, D.; Woike, T.; Delley, B.; Boskovic, C.; Biner, D.; Krämer, K. W.; Güdel, H.-U. Long-Lived Light-Induced Metastable States in Trans-[Ru(NH 3 ) 4 (H 2 O)NO]Cl 3 ·H 2 O and Related Compounds. *Phys. Chem. Chem. Phys.* **2005**, *7* (6), 1164–1170.
https://doi.org/10.1039/B415435E.

(21) Tomizawa, H.; Harada, K.; Miki, E.; Mizumachi, K.; Ishimori, T.; Urushiyama, A.; Nakahara, M. Preparation and Characterization of Ethylenediaminetrihalogenonitrosylruthenium(III) Complexes. *Bull. Chem. Soc. Jpn.* **1993**, *66* (6), 1658–1663.
https://doi.org/10.1246/bcsj.66.1658.

(22) Tomizawa, H.; Miki, E.; Mizumachi, K.; Ishimori, T. Preparation and Characterization of Trans - and Cis -Anionobis(Ethylenediamine)Nitrosylruthenium(II) Complexes. *Bull. Chem. Soc. Jpn.* **1994**, *67* (7), 1809–1815. https://doi.org/10.1246/bcsj.67.1809.

(23) Tomizawa, H.; Miki, E.; Mizumachi, K.; Ishimori, T. Crystal Structures of Trans - and Cis - Anionobis(Ethylenediamine)Nitrosylruthenium(II) Complexes. *Bull. Chem. Soc. Jpn.* **1994**, *67* (7), 1816–1824. https://doi.org/10.1246/bcsj.67.1816.

(24) Kawano, M.; Ishikawa, A.; Morioka, Y.; Tomizawa, H.; Miki, E.; Ohashi, Y. X-Ray Diffraction and Spectroscopic Studies of the Light-Induced Metastable State of a Ethylenediamine Nitrosyl Ruthenium Complex. *J. Chem. Soc. Dalt. Trans.* **2000**, No. 14, 2425–2431.
https://doi.org/10.1039/b001132k.

(25) Morioka, Y.; Ishikawa, A.; Tomizawa, H.; Miki, E. Light-Induced Metastable States in Nitrosyl- Ruthenium Complexes Containing Ethylenediamine and Oxalate Ion Ligands. *J. Chem. Soc. Dalt. Trans.* **2000**, *54* (5), 781–786. https://doi.org/10.1039/a906429j.

(26) Ookubo, K.; Morioka, Y.; Tomizawa, H.; Miki, E. Vibrational Spectroscopic Study of Light-Induced Metastable States of Ethylenediaminetitrosylruthenium(II) Complexes. *J. Mol. Struct.*
1996, 379 (1-3), 241-247. https://doi.org/10.1016/0022-2860(95)09197-1.

(27) Brovko, A. O.; Kuratieva, N. V; Emelyanov, V. A.; Pishchur, D. P.; Kostin, G. A. A New Heteroleptic Complex of Nitrosyl Ruthenium with Ethylenediamine and the NO–Ru–F Trans-Coordinate: Synthesis, Structure, and Photoinduced Linkage Isomerization. *J. Struct. Chem.* **2024**, *65* (7), 1404–1411. https://doi.org/10.1134/S0022476624070114.

(28) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. *J. Comput. Chem.* **2001**, *22* (9), 931–967.
https://doi.org/10.1002/jcc.1056.

(29) Ernzerhof, M.; Scuseria, G. E. Assessment of the Perdew–Burke–Ernzerhof Exchange-Correlation Functional. *J. Chem. Phys.* **1999**, *110* (11), 5029–5036.
https://doi.org/10.1063/1.478401.

(30) Sheldrick, G. M. SHELXT – Integrated Space-Group and Crystal-Structure Determination. *Acta Crystallogr. Sect. A Found. Adv.* **2015**, *71* (1), 3–8.
https://doi.org/10.1107/S2053273314026370.

(31) Sheldrick, G. M. Crystal Structure Refinement with SHELXL. *Acta Crystallogr. Sect. C Struct. Chem.* **2015**, *71* (1), 3–8. https://doi.org/10.1107/S2053229614024218.

(32) Dolomanov, O. V.; Bourhis, L. J.; Gildea, R. J.; Howard, J. A. K.; Puschmann, H. OLEX2: A Complete Structure Solution, Refinement and Analysis Program. *J. Appl. Crystallogr.* **2009**, *42* (2), 339–341. https://doi.org/10.1107/S0021889808042726.

(33) Pillet, S. Time-Resolved Structural Analysis: Probing Condensed Matter in Motion. In *Structures on Different Time Scales*; De Gruyter, 2018; pp 143–220.
https://doi.org/10.1515/9783110433920-005.

(34) Stepanenko, I.; Mizetskyi, P.; Orlowska, E.; Bučinský, L.; Zalibera, M.; Vénosová, B.; Clémancey, M.; Blondin, G.; Rapta, P.; Novitchi, G.; Schrader, W.; Schaniel, D.; Chen, Y.-S.; Lutz, M.; Kožíšek, J.; Telser, J.; Arion, V. B. The Ruthenium Nitrosyl Moiety in Clusters: Trinuclear Linear µ-Hydroxido Magnesium(II)-Diruthenium(II), µ 3 -Oxido Trinuclear Diiron(III)-Ruthenium(II), and Tetranuclear µ 4 -Oxido Trigallium(III)-Ruthenium(II) Complexes. *Inorg. Chem.* **2022**, *61* (2), 950–967.
https://doi.org/10.1021/acs.inorgchem.1c03011.

(35) M.Gembicky, M.Pearsal, A.Larsen, P. C. No Title. *CSD Commun.* **2009**, CCDC 648020.
https://doi.org/10.5517/ccpr9wl.

(36) Chan, W.-L.; Hsieh, C.-M.; Yang, L.; Hsu, C.-C.; Lin, S.-T. A Critical Evaluation on the Performance of COSMO-SAC Models for Vapor–Liquid and Liquid–Liquid Equilibrium Predictions Based on Different Quantum Chemical Calculations. *Ind. Eng. Chem. Res.* **2016**, *55* (34), 9312–9322. https://doi.org/10.1021/acs.iecr.6b02345.

(37) Sridevi, V. S.; Leong, W. K. Catalytic Reductive Homocoupling of 9-Bromofluorene. *Tetrahedron Lett.* **2007**, *48* (38), 6669–6670. https://doi.org/10.1016/j.tetlet.2007.07.120.

(38) Svetlanova-Larsen, A.; Zoch, C. R.; Hubbard, J. L. Aqueous Organometallic Chemistry of the Electrophilic [(η-C 5 (CH 3 ) 5 )Ru(NO)] 2+ Fragment. *Organometallics* **1996**, *15* (13), 3076–3087. https://doi.org/10.1021/om960257z.

(39) Carducci, M. D.; Pressprich, M. R.; Coppens, P. Diffraction Studies of Photoexcited Crystals: Metastable Nitrosyl-Linkage Isomers of Sodium Nitroprusside. *J. Am. Chem. Soc.* **1997**, *119* (11), 2669–2678. https://doi.org/10.1021/ja9625743.

(40) Mikhailov, A. A.; Gansmüller, A.; Konieczny, K. A.; Pillet, S.; Kostin, G.; Klüfers, P.; Woike, T.; Schaniel, D. Local Force Constants and Charges of the Nitrosyl Ligand in Photoinduced NO
Linkage Isomers in a Prototypical Ruthenium Nitrosyl Complex. *Phys. Chem. Chem. Phys.* **2024**, *26* (21), 15255–15267. https://doi.org/10.1039/D4CP01374C.

(41) Cormary, B.; Malfant, I.; Buron-Le Cointe, M.; Toupet, L.; Delley, B.; Schaniel, D.; Mockus, N.; Woike, T.; Fejfarová, K.; Petříček, V.; Dušek, M. [Ru(Py) 4 Cl(NO)](PF 6 ) 2 ·0.5H 2 O: A Model System for Structural Determination and Ab Initio Calculations of Photo-Induced Linkage NO Isomers. *Acta Crystallogr. Sect. B Struct. Sci.* **2009**, *65* (5), 612–623.
https://doi.org/10.1107/S0108768109027207.

(42) Mikhailov, A.; Deresz, K.; Tiognou, A. T.; Kostin, G.; Lassalle-Kaiser, B.; Schaniel, D. Electronic Structure of Light-Induced Nitrosyl Linkage Isomers Revealed by X-Ray Absorption Spectroscopy at Ru L3,2-Edges. *Spectrochim. Acta Part A Mol. Biomol. Spectrosc.* **2025**, 325 (June 2024), 125053. https://doi.org/10.1016/j.saa.2024.125053.

(43) Schaniel, D.; Woike, T.; Kushch, L.; Yagubskii, E. Photoinduced Nitrosyl Linkage Isomers in Complexes Based on the Photochromic Cation [RuNO(NH3)5]3+ with the Paramagnetic Anion [Cr(CN)6]3- and the Diamagnetic Anions [Co(CN)6]3- and [ZrF6]2-. *Chem. Phys.* **2007**, *340* (1-3), 211–216. https://doi.org/10.1016/j.chemphys.2007.08.023.

(44) Mikhailov, A. A.; Komarov, V. Y.; Pishchur, D. P.; Schaniel, D.; Kostin, G. A. Nitrosyl Linkage Photoisomerization in Heteroleptic Fluoride Ruthenium Complexes Derived from Labile Nitrate Precursors. *New J. Chem.* **2021**, *45* (18), 8192–8202.
https://doi.org/10.1039/D1NJ01038G.

(45) Mikhailov, A. A.; Kostin, G. A.; Schaniel, D. The Influence of the Trans -Ligand to NO on the Thermal Stability of the Photoinduced Side-Bond Coordinated Linkage Isomer. *New J. Chem.* **2022**, *46* (26), 12641–12650. https://doi.org/10.1039/D2NJ01388F.

(46) Yamaletdinov, R. D.; Zilberberg, I. L. The Effect of Trans Ligands in the NO-Linkage Reverse Isomerization for Ruthenium-Nitrosyl-Tetraammine Complexes: A DFT Study. *Eur. J. Inorg. Chem.* **2017**, *2017* (23), 2951–2954. https://doi.org/10.1002/ejic.201700138.

(47) Vorobeyev, V.; Mikhailov, A. A.; Komarov, V. Y.; Makhinya, A. N.; Kostin, G. A. Tuning the Structure and Photoinduced Linkage Isomerism of Tetrapyridine Nitrosyl Ruthenium(<scp>ii</scp>) Complexes by Changing the *Trans*-to-NO Coordinated Ligand. *New J. Chem.* **2020**, *44* (12), 4762–4771. https://doi.org/10.1039/C9NJ05862A.

(48) Zöllner, H.; Krasser, W.; Woike, T.; Haussühl, S. The Existence of Light-Induced Long-Lived Metastable States in Different Xn[Fe(CN)5NO]·yH2O Crystals, Powders and Solutions. *Chem. Phys. Lett.* **1989**, *161* (6), 497–501. https://doi.org/10.1016/0009-2614(89)87027-7.

(49) Cormary, B.; Ladeira, S.; Jacob, K.; Lacroix, P. G.; Woike, T.; Schaniel, D.; Malfant, I. Structural Influence on the Photochromic Response of a Series of Ruthenium Mononitrosyl Complexes. *Inorg. Chem.* **2012**, *51* (14), 7492–7501. https://doi.org/10.1021/ic202702r.

(50) Schaniel, D.; Woike, T.; Boskovic, C.; Güdel, H. U. Evidence for Two Light-Induced Metastable States in Cl 3[Ru(NH3)5NO]H2O. *Chem. Phys. Lett.* **2004**, *390* (4–6), 347–351.
https://doi.org/10.1016/j.cplett.2004.04.038.
Supporting Information

Exploring the photoswitching pathways and efficiency of NO isomerization in ethylenediamine ruthenium nitrosyl complexes

Artem A. Mikhailov<sup>a*</sup>, Appolinaire Tchoutchoua Tiognou<sup>a</sup>, Anastasiya O. Brovko<sup>b</sup>, Gennadiy A. Kostin<sup>b</sup>, Dominik Schaniel<sup>a</sup>

<figure><img src="image_12.png" /><figcaption>Fig. S1. Asymmetric unit of [RuNO(en)<sub>2</sub>OH]I<sub>2</sub> structure measured at 150 K.</figcaption></figure>

<table><caption>**Table S1.** Crystal data and refinement details of studied structures.</caption><thead><tr><th>Identification code</th><th>[RuNOen<sub>2</sub>OH]I<sub>2</sub></th><th>[RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1, RT)</th></tr></thead><tbody><tr><td>Empirical formula</td><td>C<sub>4</sub>H<sub>17</sub>I<sub>2</sub>N<sub>5</sub>O<sub>2</sub>Ru</td><td>C<sub>4</sub>H<sub>17</sub>N<sub>7</sub>O<sub>8</sub>Ru</td></tr><tr><td>Formula weight</td><td>522.09</td><td>392.32</td></tr><tr><td>Temperature/K</td><td>150(2)</td><td>293(2)</td></tr><tr><td>Crystal system</td><td>monoclinic</td><td>orthorhombic</td></tr><tr><td>Space group</td><td>P2<sub>1</sub></td><td>Pnma</td></tr><tr><td>a/Å</td><td>8.3577(7)</td><td>9.2856(5)</td></tr><tr><td>b/Å</td><td>9.1809(7)</td><td>16.8095(6)</td></tr><tr><td>c/Å</td><td>9.5836(8)</td><td>8.8220(4)</td></tr></tbody></table>

<footnote><sup>a</sup> Université de Lorraine, CNRS, CRM2, UMR 7036, Nancy 54000, France <sup>b</sup> Department of Chemistry</footnote>

<footnote><sup>b</sup> Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, 3 Acad. Lavrentiev Avenue, Novosibirsk 630090, Russian Federation</footnote>

<footnote>*Corresponding author: artem.mikhailov.a@gmail.com</footnote>
<table><tr><td>α/°</td><td>90</td><td>90</td></tr><tr><td>β/°</td><td>110.233(2)</td><td>90</td></tr><tr><td>γ/°</td><td>90</td><td>90</td></tr><tr><td>Volume/Å³</td><td>689.98(10)</td><td>1376.99(11)</td></tr><tr><td>Z</td><td>2</td><td>4</td></tr><tr><td>ρ<sub>calc</sub>g/cm³</td><td>2.513</td><td>1.892</td></tr><tr><td>μ/mm⁻¹</td><td>5.600</td><td>9.735</td></tr><tr><td>F(000)</td><td>484.0</td><td>792.0</td></tr><tr><td>Crystal size/mm³</td><td>0.11 × 0.03 × 0.02</td><td>0.2 × 0.1 × 0.05</td></tr><tr><td>Radiation</td><td>MoKα (λ = 0.71073)</td><td>Cu Kα (λ = 1.54184)</td></tr><tr><td>2θ range for data collection/°</td><td>5.194 to 55.034</td><td>10.526 to 152.856</td></tr><tr><td>Index ranges</td><td>-10 ≤ h ≤ 10, -11 ≤ k ≤ 11, 0 ≤ l ≤ 12</td><td>-9 ≤ h ≤ 10, -20 ≤ k ≤ 21, -11 ≤ l ≤ 11</td></tr><tr><td>Reflections collected</td><td>2971</td><td>11078</td></tr><tr><td>Independent reflections</td><td>2895 [R<sub>int</sub> = 0.0316, R<sub>sigma</sub> = 0.0282]</td><td>1431 [R<sub>int</sub> = 0.0461, R<sub>sigma</sub> = 0.0323]</td></tr><tr><td>Data/restraints/parameters</td><td>2895/1/128</td><td>1431/15/144</td></tr><tr><td>Goodness-of-fit on F²</td><td>1.074</td><td>1.052</td></tr><tr><td>Final R indexes [I>=2σ (I)]</td><td>R₁ = 0.0355, wR₂ = 0.0903</td><td>R₁ = 0.0385, wR₂ = 0.0910</td></tr><tr><td>Final R indexes [all data]</td><td>R₁ = 0.0480, wR₂ = 0.0945</td><td>R₁ = 0.0494, wR₂ = 0.0995</td></tr><tr><td>Largest diff. peak/hole / e Å⁻³</td><td>1.35/-1.88</td><td>0.63/-0.75</td></tr></table>

<table><tr><td>Identification code</td><td>[RuNO(en)<sub>2</sub>H<sub>2</sub>O](NO<sub>3</sub>)<sub>3</sub> (2)</td><td>[RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub> (1, GS, 100 K)</td></tr><tr><td>Empirical formula</td><td>C<sub>4</sub>H<sub>18</sub>N<sub>8</sub>O<sub>11</sub>Ru</td><td>C<sub>4</sub>H<sub>15</sub>N<sub>7</sub>O<sub>8</sub>Ru</td></tr><tr><td>Formula weight</td><td>455.33</td><td>390.30</td></tr><tr><td>Temperature/K</td><td>100(1)</td><td>100(1)</td></tr><tr><td>Crystal system</td><td>orthorhombic</td><td>orthorhombic</td></tr><tr><td>Space group</td><td>P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub></td><td>P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub></td></tr><tr><td>a/Å</td><td>9.3314(2)</td><td>8.7729(2)</td></tr><tr><td>b/Å</td><td>11.8505(3)</td><td>9.1051(2)</td></tr><tr><td>c/Å</td><td>13.4342(3)</td><td>16.5461(3)</td></tr></table>
<table><tr><td>α/°</td><td>90</td><td>90</td></tr><tr><td>β/°</td><td>90</td><td>90</td></tr><tr><td>γ/°</td><td>90</td><td>90</td></tr><tr><td>Volume/Å³</td><td>1485.58(6)</td><td>1321.67(5)</td></tr><tr><td>Z</td><td>4</td><td>4</td></tr><tr><td>ρ<sub>calc</sub>g/cm³</td><td>2.036</td><td>1.961</td></tr><tr><td>μ/mm⁻¹</td><td>1.134</td><td>1.239</td></tr><tr><td>F(000)</td><td>920.0</td><td>784.0</td></tr><tr><td>Crystal size/mm³</td><td>0.2 × 0.1 × 0.1</td><td>0.2 × 0.1 × 0.05</td></tr><tr><td>Radiation</td><td>Mo Kα (λ = 0.71073)</td><td>Mo Kα (λ = 0.71073)</td></tr><tr><td>2θ range for data collection/°</td><td>4.584 to 65.79</td><td>4.924 to 59.562</td></tr><tr><td>Index ranges</td><td>-14 ≤ h ≤ 13, -18 ≤ k ≤ 16, -19 ≤ l ≤ 20</td><td>-12 ≤ h ≤ 12, -12 ≤ k ≤ 12, -22 ≤ l ≤ 22</td></tr><tr><td>Reflections collected</td><td>28532</td><td>99184</td></tr><tr><td>Independent reflections</td><td>5212 [R<sub>int</sub> = 0.0318, R<sub>sigma</sub> = 0.0217]</td><td>3620 [R<sub>int</sub> = 0.0702, R<sub>sigma</sub> = 0.0211]</td></tr><tr><td>Data/restraints/parameters</td><td>5212/7/230</td><td>3620/0/201</td></tr><tr><td>Goodness-of-fit on F²</td><td>1.069</td><td>1.038</td></tr><tr><td>Final R indexes [I>=2σ (I)]</td><td>R₁ = 0.0190, wR₂ = 0.0440</td><td>R₁ = 0.0309, wR₂ = 0.0687</td></tr><tr><td>Final R indexes [all data]</td><td>R₁ = 0.0200, wR₂ = 0.0448</td><td>R₁ = 0.0346, wR₂ = 0.0711</td></tr><tr><td>Largest diff. peak/hole / e Å⁻³</td><td>0.75/-0.87</td><td>1.06/-0.69</td></tr><tr><td>Identification code</td><td>[RuNOen₂OH](NO₃)₂ (1, MS1, 100 K)</td><td>[RuNOen₂OH](NO₃)₂ (1, MS2, 100 K)</td></tr><tr><td>Empirical formula</td><td>C₄H₁₇N₇O₈Ru</td><td>C₄H₁₇N₇O₈Ru</td></tr><tr><td>Formula weight</td><td>392.32</td><td>392.32</td></tr><tr><td>Temperature/K</td><td>100(1)</td><td>100(1)</td></tr><tr><td>Crystal system</td><td>orthorhombic</td><td>orthorhombic</td></tr><tr><td>Space group</td><td>P2₁2₁2₁</td><td>P2₁2₁2₁</td></tr><tr><td>a/Å</td><td>8.8117(4)</td><td>8.7896(2)</td></tr><tr><td>b/Å</td><td>9.1391(4)</td><td>9.1067(2)</td></tr></table>
<table><tr><td>c/Å</td><td>16.4948(9)</td><td>16.5846(4)</td></tr><tr><td>α/°</td><td>90</td><td>90</td></tr><tr><td>β/°</td><td>90</td><td>90</td></tr><tr><td>γ/°</td><td>90</td><td>90</td></tr><tr><td>Volume/Å³</td><td>1328.34(12)</td><td>1327.50(5)</td></tr><tr><td>Z</td><td>4</td><td>4</td></tr><tr><td>ρ<sub>calc</sub>g/cm³</td><td>1.962</td><td>1.963</td></tr><tr><td>μ/mm⁻¹</td><td>1.233</td><td>1.234</td></tr><tr><td>F(000)</td><td>792.0</td><td>792.0</td></tr><tr><td>Crystal size/mm³</td><td>0.2 × 0.1 × 0.05</td><td>0.2 × 0.1 × 0.05</td></tr><tr><td>Radiation</td><td>MoKα (λ = 0.71073)</td><td>MoKα (λ = 0.71073)</td></tr><tr><td>2Θ range for data collection/°</td><td>4.94 to 62.202</td><td>4.912 to 62.246</td></tr><tr><td>Index ranges</td><td>-12 ≤ h ≤ 12, -12 ≤ k ≤ 12, -22 ≤ l ≤ 23</td><td>-12 ≤ h ≤ 12, -13 ≤ k ≤ 13, -23 ≤ l ≤ 22</td></tr><tr><td>Reflections collected</td><td>10892</td><td>56294</td></tr><tr><td>Independent reflections</td><td>3779 [R<sub>int</sub> = 0.0419, R<sub>sigma</sub> = 0.0564]</td><td>4156 [R<sub>int</sub> = 0.0514, R<sub>sigma</sub> = 0.0225]</td></tr><tr><td>Data/restraints/parameters</td><td>3779/2/208</td><td>4156/14/220</td></tr><tr><td>Goodness-of-fit on F²</td><td>1.082</td><td>1.077</td></tr><tr><td>Final R indexes [I≥=2σ (I)]</td><td>R₁ = 0.0369, wR₂ = 0.0753</td><td>R₁ = 0.0286, wR₂ = 0.0662</td></tr><tr><td>Final R indexes [all data]</td><td>R₁ = 0.0463, wR₂ = 0.0823</td><td>R₁ = 0.0324, wR₂ = 0.0689</td></tr><tr><td>Largest diff. peak/hole / e Å⁻³</td><td>1.31/-0.85</td><td>1.34/-0.84</td></tr><tr><td>Identification code</td><td>[(RuNOenCl₂)₂(μ-OH)]Cl·2H₂O (5)</td><td>[RuNO(en)₂OH](NO₃)₂·0.5AgNO₃·0.5H₂O (3)</td></tr><tr><td>Empirical formula</td><td>C₄H₂₁Cl₅N₆O₅Ru₂</td><td>C₄H₁₈Ag₀.₅N₇.₅O₁₀Ru</td></tr><tr><td>Formula weight</td><td>612.66</td><td>486.26</td></tr><tr><td>Temperature/K</td><td>100(1)</td><td>100(1)</td></tr><tr><td>Crystal system</td><td>monoclinic</td><td>triclinic</td></tr><tr><td>Space group</td><td>P2₁/c</td><td>P-1</td></tr><tr><td>a/Å</td><td>7.9938(5)</td><td>8.8973(2)</td></tr></table>
<table><tr><td>b/Å</td><td>10.5289(5)</td><td>12.8520(3)</td></tr><tr><td>c/Å</td><td>21.7413(12)</td><td>14.2720(3)</td></tr><tr><td>α/°</td><td>90</td><td>88.821(2)</td></tr><tr><td>β/°</td><td>90.649(5)</td><td>72.312(2)</td></tr><tr><td>γ/°</td><td>90</td><td>71.523(2)</td></tr><tr><td>Volume/Å<sup>3</sup></td><td>1829.76(18)</td><td>1469.49(6)</td></tr><tr><td>Z</td><td>4</td><td>4</td></tr><tr><td>ρ<sub>calc</sub>g/cm<sup>3</sup></td><td>2.224</td><td>2.198</td></tr><tr><td>μ/mm<sup>-1</sup></td><td>2.407</td><td>1.783</td></tr><tr><td>F(000)</td><td>1200.0</td><td>968.0</td></tr><tr><td>Crystal size/mm<sup>3</sup></td><td>0.2 × 0.05 × 0.03</td><td>0.2 × 0.15 × 0.15</td></tr><tr><td>Radiation</td><td>Mo Kα (λ = 0.71073)</td><td>Mo Kα (λ = 0.71073)</td></tr><tr><td>2θ range for data collection/°</td><td>3.746 to 61.876</td><td>3.354 to 65.87</td></tr><tr><td>Index ranges</td><td>-10 ≤ h ≤ 11, -14 ≤ k ≤ 9, -31 ≤ l ≤ 16</td><td>-13 ≤ h ≤ 13, -19 ≤ k ≤ 19, -21 ≤ l ≤ 21</td></tr><tr><td>Reflections collected</td><td>10593</td><td>46567</td></tr><tr><td>Independent reflections</td><td>5091 [R<sub>int</sub> = 0.0384, R<sub>sigma</sub> = 0.0580]</td><td>10218 [R<sub>int</sub> = 0.0340, R<sub>sigma</sub> = 0.0241]</td></tr><tr><td>Data/restraints/parameters</td><td>5091/5/225</td><td>10218/0/426</td></tr><tr><td>Goodness-of-fit on F<sup>2</sup></td><td>0.992</td><td>1.080</td></tr><tr><td>Final R indexes [I>=2σ (I)]</td><td>R<sub>1</sub> = 0.0322, wR<sub>2</sub> = 0.0518</td><td>R<sub>1</sub> = 0.0199, wR<sub>2</sub> = 0.0474</td></tr><tr><td>Final R indexes [all data]</td><td>R<sub>1</sub> = 0.0453, wR<sub>2</sub> = 0.0563</td><td>R<sub>1</sub> = 0.0225, wR<sub>2</sub> = 0.0488</td></tr><tr><td>Largest diff. peak/hole / e Å<sup>-3</sup></td><td>0.99/-1.05</td><td>0.67/-1.02</td></tr><tr><td>Identification code</td><td>[RuNOen<sub>2</sub>OH](NO<sub>3</sub>)<sub>2</sub>·H<sub>2</sub>O (4)</td><td></td></tr><tr><td>Empirical formula</td><td>C<sub>4</sub>H<sub>19</sub>N<sub>7</sub>O<sub>9</sub>Ru</td><td></td></tr><tr><td>Formula weight</td><td>410.33</td><td></td></tr><tr><td>Temperature/K</td><td>100(1)</td><td></td></tr><tr><td>Crystal system</td><td>monoclinic</td><td></td></tr><tr><td>Space group</td><td>P2<sub>1</sub>/n</td><td></td></tr><tr><td>a/Å</td><td>8.4249(3)</td><td></td></tr></table>
<table><tr><td>b/Å</td><td>17.5864(5)</td></tr><tr><td>c/Å</td><td>9.3788(2)</td></tr><tr><td>α/°</td><td>90</td></tr><tr><td>β/°</td><td>90.997(3)</td></tr><tr><td>γ/°</td><td>90</td></tr><tr><td>Volume/Å³</td><td>1389.39(7)</td></tr><tr><td>Z</td><td>4</td></tr><tr><td>ρ<sub>calc</sub>g/cm³</td><td>1.962</td></tr><tr><td>μ/mm<sup>-1</sup></td><td>1.188</td></tr><tr><td>F(000)</td><td>832.0</td></tr><tr><td>Crystal size/mm³</td><td>0.2 × 0.1 × 0.05</td></tr><tr><td>Radiation</td><td>Mo Kα (λ = 0.71073)</td></tr><tr><td>2θ range for data collection/°</td><td>4.632 to 52.742</td></tr><tr><td>Index ranges</td><td>-10 ≤ h ≤ 10, -21 ≤ k ≤ 21, -11 ≤ l ≤ 11</td></tr><tr><td>Reflections collected</td><td>43223</td></tr><tr><td>Independent reflections</td><td>2838 [R<sub>int</sub> = 0.0941, R<sub>sigma</sub> = 0.0319]</td></tr><tr><td>Data/restraints/parameters</td><td>2838/0/194</td></tr><tr><td>Goodness-of-fit on F²</td><td>1.081</td></tr><tr><td>Final R indexes [I≥=2σ (I)]</td><td>R<sub>1</sub> = 0.0271, wR<sub>2</sub> = 0.0590</td></tr><tr><td>Final R indexes [all data]</td><td>R<sub>1</sub> = 0.0354, wR<sub>2</sub> = 0.0633</td></tr><tr><td>Largest diff. peak/hole / e Å<sup>-3</sup></td><td>1.08/-0.58</td></tr></table>
<figure><img src="image_13.png" /><figcaption>Fig. S2. Asymmetric unit of [RuNO(en)₂OH](NO₃)₂ (1 RT) structure measured at 300 K.</figcaption></figure>

<table><caption>Table S2. Selected vibrational bands of 1-3 in GS, MS1 and MS2.</caption><thead><tr><th>v [cm<sup>-1</sup>]</th><th>GS</th><th>MS1</th><th>MS2</th></tr></thead><tbody><tr><td rowspan="4">1</td><td>3447 (νOH)</td><td>3410 (νOH)</td><td>3358 (νOH)</td></tr><tr><td>978 (δOH)</td><td>996 (δOH)</td><td>1051 (δOH)</td></tr><tr><td>578 (δ(Ru-N-O)/(ν(Ru-OH)))</td><td>611 (ν(Ru-OH))</td><td>665 (δ(Ru-N-O)/(ρ(CH<sub>2</sub>,NH<sub>2</sub>)))</td></tr><tr><td>518 (ν(Ru-NO))</td><td>500 (δ(Ru-O-N))</td><td>600 (ν(Ru-OH))</td></tr><tr><td rowspan="2">2</td><td>563 (ν(Ru-NO))</td><td>586 (ρ(H<sub>2</sub>O))</td><td rowspan="2">607 (δ(Ru-N-O))</td></tr><tr><td>552;516 (δ(Ru-N-O))</td><td>491 (δ(Ru-O-N))</td></tr><tr><td rowspan="4">3</td><td>3451 (νOH)</td><td>3411 (νOH)</td><td>3353 (νOH)</td></tr><tr><td>977 (δOH)</td><td>1001 (δOH)</td><td>1047 (δOH)</td></tr><tr><td>578;571 (δ(Ru-N-O)/(ν(Ru-OH)))</td><td>624;610 (ν(Ru-OH))</td><td>668 (δ(Ru-N-O)/(ρ(CH<sub>2</sub>,NH<sub>2</sub>)))</td></tr><tr><td>517 (ν(Ru-NO))</td><td>484 (δ(Ru-O-N))</td><td>605 (ν(Ru-OH))</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>Fig. S3. Difference spectrum MS2-GS in the range of 1075-950 cm⁻¹.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. S4.** IR-spectra of **2** (panel a) and **3** (panel b) in the range of 2000-1450 cm⁻¹ in GS, MS1 and MS2 measured at 100 K. MS1 were generated with 420 nm light for 30 min, MS2 were produced by the subsequent irradiation of MS1 with 940 nm light for 95 and 8 min for **2** and **3**, respectively. It is important to mention that IR-spectrum of **2** comprises low intense bands of [RuNOen₂OH]²⁺ complex due to partial deprotonation of H₂O ligand of **2** during the synthesis.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. S5.** UV-vis spectra of **3** in GS, MS1 and MS2 at 100 K. The spectra of MS1 and MS2 are shown as difference spectra MS1/MS2-GS. In GS the increased absorption in the range of 500-1100 nm is related to a diffusion of light caused by the KBr matrix.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. S6. DSC curves of MS1 and MS2 decay in 1 (panels a, b), 2 (panels c, d) and 3 (panels e, f).</figcaption></figure>

## The kinetic model details

The dependencies of IR integral absorbances for each state were described by the following scheme:

$$GS \rightleftharpoons MS2 \rightleftharpoons MS1,$$

with the corresponding efficient constants (J⁻¹):

$$GS \xrightarrow{k_1} MS2, \quad MS2 \xrightarrow{k_2} GS, \quad MS2 \xrightarrow{k_3} MS1, \quad MS1 \xrightarrow{k_4} MS2,$$

$$\frac{dX_{GS}}{dE} = -k_1X_{GS} + k_2X_{MS2};$$

$$\frac{dX_{MS2}}{dE} = k_1X_{GS} - (k_2 + k_3)X_{MS2} + k_4X_{MS1};$$

$$\frac{dX_{MS1}}{dE} = k_3X_{MS2} - k_4X_{MS1}.$$

The analytical solution of the system results in the following equations for the molar fraction (X) of each state versus the irradiation energy (E).

$$X_{GS} = A_{11}C_{1} + A_{21}C_{2}\exp(r_{2}E) + A_{31}C_{3}\exp(r_{3}E);$$

$$X_{MS2} = A_{12}C_{1} + A_{22}C_{2}\exp(r_{2}E) + A_{32}C_{3}\exp(r_{3}E);$$

$$X_{MS1} = A_{13}C_{1} + A_{23}C_{2}\exp(r_{2}E) + A_{33}C_{3}\exp(r_{3}E),$$
where r₂ and r₃ – non-zero eigenvalues of matrix:

$$ \begin{pmatrix} -k_1 & k_2 & 0 \\ k_1 & -k_2 - k_3 & k_4 \\ 0 & k_3 & -k_4 \end{pmatrix}. $$

r₂ = $\frac{-a+\sqrt{a^2-4b}}{2}$, r₃ = $\frac{-a-\sqrt{a^2-4b}}{2}$, a = k₁+k₂+k₃+k₄, b = k₁k₃+k₁k₄+k₂k₄. The first eigenvalue for the matrix r₁ = 0.

Eigenvectors of matrix, corresponding to eigenvalues r₁-r₃:

$$ \begin{pmatrix} A_{11} & A_{21} & A_{31} \\ A_{12} & A_{22} & A_{32} \\ A_{13} & A_{23} & A_{33} \end{pmatrix}. $$

C₁-C₃ – are coefficients determined by the initial conditions before irradiation (E = 0): XGS = 1, XMS1 = 0, XMS2 = 0.

The integral absorbance of IR band is determined as I = εX, where ε - integral absorption coefficient for the IR band of each isomer.

Thus, the solution of kinetic model was performed by the minimizing square deviation sum (SDS):

$$ \Sigma(I_{GS}^{exp} - I_{GS}^{calc})^2 + (I_{MS1}^{exp} - I_{MS1}^{calc})^2 + (I_{MS2}^{exp} - I_{MS2}^{calc})^2 = f(k_1, k_2, k_3, k_4, \epsilon_{GS}, \epsilon_{MS1}, \epsilon_{MS2}), $$

varying the set of k₁ and εᵢ.

Elimination of any reverse processes (k₂ = 0 or k₄ = 0) results in the strong fit deviation (the SDS increases for 30 times).

## Quantum yield calculation

Quantum yield (Φ) of GS→MS2 transformation was estimated using the formula considering only initial linear part of XGS kinetics (XGS is molar fraction of GS):

$$ \Phi = \frac{k_{fit}N(GS)_0}{I_0(1-10^{-Aex})}, $$

where k_{fit} [J⁻¹] is the slope dXGS/dE_{laser} of the initial linear part of the graph (E_{laser} - total pulsed energy arrived on the sample [J]), N(GS)₀ [mol] initial quantity of GS molecules, I₀ [mol·J⁻¹] is energy of 1 mol of 410 nm photons calculated by formula:

$$ I_0 = \frac{\lambda_{ex}}{hcN_a}, $$

where λ_{ex} [m] is wavelength of pulsed laser, h is Plank constant [J·s], c [m·s⁻¹] – speed of light, N_a [mol⁻¹] is Avogadro number. A_{ex} is absorbance of the sample at excitation wavelength:

$$ A_{ex} = \varepsilon_{ex} C_0 l_{ex}, $$

where ε_{ex} [L·mol⁻¹·cm⁻¹] is absorption coefficient of GS at 410 nm, C₀ [mol·L⁻¹] is initial concentration of GS molecules, l_{ex} [cm] – length of the light of the laser path through the sample (thickness of the sample).

Thus,
$$A_{ex} = 187.52 \cdot 0.02 \cdot 0.04 = 0.15,$$

$$I_0 = \frac{410 \cdot 10^{-9}}{6.62 \cdot 10^{-34} \cdot 3 \cdot 10^{8} \cdot 6.02 \cdot 10^{23}} = 3.46 \cdot 10^{-6} \, \text{mol} \cdot \text{J}^{-1},$$

$$\Phi = \frac{0.1 \cdot 1.07 \cdot 10^{-6}}{3.46 \cdot 10^{-6} \cdot (1 - 10^{-0.15})} = 0.11 \text{ or } 11\%.$$