Determination of the molecular structure of the short-lived light-induced high-spin state in the spin-crossover compound [Fe(6-mepy)₃tren](PF₆)₂

Article

Reference

Determination of the molecular structure of the short-lived light-induced high-spin state in the spin-crossover compound

[Fe(6-mepy)

tren](PF

)

CHAKRABORTY, Pradip, et al .

Abstract

In the spin-crossover compound [Fe(6-mepy)3tren](PF6)2, (6-mepy)3tren = tris{4-[(6-methyl)-2-pyridyl]-3-aza-butenyl}amine, the high-spin state can be populated as metastable state below the thermal transition temperature via irradiation into the metal to ligand charge transfer absorption band of the low-spin species. At 10 K, the lifetime of this metastable state is only 1 s. Despite this, it is possible to determine an accurate excited state structure by following the evolution of relevant structural parameters by synchrotron X-ray diffraction under continuous irradiation with increasing intensity. The difference in metal-ligand bond length between the high-spin and the low-spin state is found to be 0.192 Å obtained from an analysis of the experimental data using the mean-field approximation to model cooperative effects.

CHAKRABORTY, Pradip, et al . Determination of the molecular structure of the short-lived light-induced high-spin state in the spin-crossover compound [Fe(6-mepy)

tren](PF

)

. Physical Review. B, Condensed Matter , 2013, vol. 87, no. 21, p. 214306

DOI : 10.1103/PhysRevB.87.214306

Available at:

http://archive-ouverte.unige.ch/unige:28964

Disclaimer: layout of this document may differ from the published version.

1 / 1

Determination of the molecular structure of the short-lived light-induced high-spin state in the spin-crossover compound [Fe(6-mepy)

tren](PF

)

Pradip Chakraborty,¹Antoine Tissot,¹Lisa Peterhans,¹Laure Gu´en´ee,²C´eline Besnard,² Philip Pattison,³and Andreas Hauser^1,*

1D´epartement de chimie physique, Universit´e de Gen`eve, 30, quai Ernest Ansermet, CH-1211 Gen`eve, Switzerland

2Laboratoire de cristallographie, Universit´e de Gen`eve, 24 Quai Ernest-Ansermet, CH-1211 Gen`eve 4, Switzerland

3Laboratory of Crystallography, EPFL, CH-1015 Lausanne, Switzerland and Swiss-Norwegian Beamline, ESRF, F-38043 Grenoble, France

(Received 3 April 2013; revised manuscript received 29 May 2013; published 26 June 2013)

In the spin-crossover compound [Fe(6-mepy)3tren](PF6)2, (6-mepy)3tren=tris{4-[(6-methyl)-2-pyridyl]-3- aza-butenyl}amine, the high-spin state can be populated as a metastable state below the thermal transition temperature via irradiation into the metal to the ligand charge-transfer absorption band of the low-spin species.

At 10 K, the lifetime of this metastable state is only 1 s. Despite this, it is possible to determine an accurate excited state structure by following the evolution of relevant structural parameters by synchrotron x-ray diffraction under continuous irradiation with increasing intensity. The difference in metal-ligand bond length between the high-spin and the low-spin states is found to be 0.192 ˚A, obtained from an analysis of the experimental data using the mean-field approximation to model cooperative effects.

DOI:10.1103/PhysRevB.87.214306 PACS number(s): 42.70.Gi, 61.50.Ks, 75.30.Wx

I. INTRODUCTION

Molecular iron(II) spin-crossover complexes^1,2 have the ability to change their electronic distribution around the metal ions between the low-spin (LS) and the high-spin (HS) states under the effect of various external stimuli such as temperature, pressure, variation of ligand fields, magnetic field, or light irradiation.^3–9 The potential use of optical switching in data storage and display devices^10,11 has raised a major interest in the LIESST (light-induced excited spin-state trapping) effect in which a metastable HS state is created by optical excitation at temperatures below the thermal spin transition.⁸The lifetime of the metastable HS state can vary over a wide range depend- ing upon the zero-point energy difference between the two spin manifolds of a given system.¹²The dynamics of the HS→LS relaxation have been studied in a number of iron(II) spin- crossover compounds using various techniques.^8,13–19Experi- mental results obtained at ambient temperatures have generally been discussed in terms of classical concepts of thermal acti- vation. For [Fe(6-mepy)3tren](PF6)2, (6-mepy)3tren=tris{4- [(6-methyl)-2-pyridyl]-3-aza-butenyl}amine, Adler et al.

determined the activation energy Ea and the corresponding volume of activation V_HL for the HS→ LS relaxation to be 416(90) cm⁻¹ and −22(3) ˚A³/molecule, respectively, and a volume of reaction, V_HL=V_HS −V_LS, of 25(3) A˚³/molecule.²⁰ In the diluted mixed crystal [Zn₁₋xFex(6- mepy)3tren](PF6)2(x=0.0005), laser flash photolysis exper- iments showed the HS → LS relaxation to be a thermally activated process at temperatures above 100 K in accordance with the above.^21,22 Below 100 K, however, there is strong deviation from classical behavior towards a temperature- independent quantum-mechanical tunneling process at 10 K with a relaxation rate constant of 10⁻¹sec⁻¹.²¹Due to the large volume change,V_HL, [Fe(6-mepy)₃tren](PF₆)₂ and diluted [Zn₁₋xFex(6-mepy)₃tren](PF₆)₂ are particularly interesting with respect to their thermal spin transition as well as the HS→LS relaxation behavior.

With regard to structural aspects of the light-induced metastable HS state, to date, most reports describe either the structure determination of systems with a very long- lived metastable HS state at low temperature by means of conventional x-ray crystallography,^23–25 or recently probing short-lived metastable HS states at higher temperatures by means of ultrafast structural studies,^26–29 where a population of the photoexcited HS state of only a few percents is achieved.

Here, we first discuss the thermal spin transition and the light-induced HS→LS relaxation behavior of [Fe(6-mepy)₃tren](PF₆)₂and [Zn₁₋xFex(6-mepy)₃tren](PF₆)₂ with x=0.31 in the tunneling region. We then show that even for a lifetime of the metastable HS state of only a few seconds at 10 K, photocrystallographic studies under continuous irradiation can yield precise structural parameters of the metastable HS state.

II. EXPERIMENTAL

Single-crystals of [Fe(6-mepy)3tren](PF6)2, [Zn(6-mepy)3tren](PF6)2, and mixed [Zn1−xFex(6- mepy)3tren](PF6)2 were synthesized according to previously reported literature procedures.^21,30 The crystals of the zinc compound are colorless; those of the iron-containing systems are bright red at room temperature when predominantly in the HS state and dark red at low temperature when in the LS state. The batch concentration of Fe(II) in the mixed crystals was determined photometrically and found to bex=0.31(3).

For optical investigations, crystals were mounted on copper plates with a small aperture (∼0.1 mm). For this, a small amount of silver contact paste was first administered around the aperture and then a small crystal (∼0.4×0.3×0.17 mm³) was carefully placed so as to cover the aperture completely.

Further silver paste was applied around the crystal so as to establish good thermal contact with the sample holder. The assembly was then fixed to the cold finger of a closed-cycle

PRADIP CHAKRABORTYet al. PHYSICAL REVIEW B87, 214306 (2013) cryostat (Janis Research, SUMITOMO- SHI 4.5) capable

of achieving a base temperature of 4 K and equipped with a programmable temperature controller (Lakeshore Model No. 331). High-quality single-crystal absorption spectra were recorded on a double beam spectrometer (Agilent Cary 5000) between 600–1400 nm during the cooling cycle from room temperature down to 10 K with a sweep rate of 0.5 K/min.

The thermal spin transition was monitored via the evolution of

5T2→⁵E band in the near-IR region (see below). For irradia- tion experiments as a function of laser power and temperature, excitation at 725 nm from a Ti:Sapphire laser (Spectra Physics Model 3900) was used. This wavelength is in the tail of the intense metal-ligand charge transfer (MLCT) band of the LS species and ensures sufficient penetration of the excitation light into the crystal. Given the lifetimes of light-induced HS state of only a few seconds, a system of electronically controlled shutters served to irradiate the samples with the laser light for a given interval and then to monitor the decay at a probe wavelength of 820 nm by using a home-built system consisting of a monochromator (Spex 280M) equipped with a CCD camera (Jobin-Yvon CCD 3500) and a PM (Hamamatsu R928), and a 50-W tungsten-halogen lamp as probe source.

The signal from the PM was monitored by a multichannel scaler (Stanford Research SR400) or a digital oscilloscope (Tektronix TDK2000).

For photocrystallographic experiments, crystals of approx- imately 50×50×50 μm³ were mounted on a cryoloop with silicon grease. Diffraction data at low temperature (10 K) in a helium open flow cryosystem (Oxford Diffraction Helijet) were collected at the Swiss Norwegian Beam Line (SNBL) BM01A at the European Synchrotron Radiation Facility (ESRF), Grenoble, France (synchrotron radiation λ=0.69412 ˚A), using a Pilatus2M pixel area detector from Dectris Ltd. The detector operates in single-photon counting mode. A diode pumped solid-state laser at 728 nm having an external power control and an electronically controlled shutter served to irradiate the samplein situ. A photograph of the setup is shown in Supplemental Material (see Fig. S1).³¹ Diffraction data for [Fe(6-mepy)3tren](PF6)2 at 293 K were collected on an Agilent Supernova diffractometer with mirror- monochromated Cu[Kα] radiation (λ=1.54187 ˚A) and CCD camera. Data were corrected for Lorentz and polarization effects and for absorption. After cell refinement and data reduction were performed using the CrysAlisPro system,³² all structures were solved by direct methods (SIR97)³³ and refined by full-matrix least-squares on F² using theSHELX³⁴

software package.

III. RESULTS AND DISCUSSION A. Optical investigation 1. The thermal spin transition

Figure1 shows the high-quality single-crystal absorption spectra of [Zn₁₋xFex(6-mepy)3tren](PF6)2withx=0.31 and [Fe(6-mepy)3tren](PF6)2, on cooling from room temperature to 10 K with a sweep rate of 0.5 K/min. The spectral evolution of the spin allowed HSd-d (⁵T₂ → ⁵E) band as observed in the near-IR region of the spectrum (∼900 nm) was monitored as a function of temperature. As shown in

1.2 1.0 0.8 0.6 0.4 0.2 0.0 OD

1400 1200

1000 800

600

λ (nm)

10 K 295 K

5T₂ ⁵E

1MLCT 1.4

1.2 1.0 0.8 0.6 0.4 0.2 0.0 OD

295 K

5T₂ ⁵E

1MLCT

10 K (a)

(b)

N2 N1

N3 N4

N5 N6

N7

FIG. 1. (Color online) Single crystal absorption spectra as a function of temperature recorded with a cooling rate of 0.5 K/min of (a) of [Zn1−xFex(6-mepy)3tren](PF6)2 x=0.31; (b) [Fe(6- mepy)3tren](PF6)2. Crystal thicknessd=0.17 mm,εmax=21 M⁻¹ cm⁻¹for⁵T2→⁵E at 900 nm.

Fig.1, upon decreasing temperature, the absorption intensity of thed-dband decreases proportionally to the depopulation of the HS state. At the same time, the rise to the intense

1MLCT band of the LS species moves to higher wavelengths.

Therefore the evolution of the⁵T2→⁵E band can be used to extract thermal spin transition curves, that is, the HS fraction γ_HS as function of T, upon normalization with respect to the d-d band intensity at room temperature. The normalization of the thermal spin transition curves was crosschecked by comparison with magnetic susceptibility measurements (see Fig. S2 in Ref.31). The spectral discontinuity around 850 nm is due to an artifact from the source and detector change in the spectrometer. Additionally, the absence of any baseline shift during the thermal spin transition on cooling from room temperature is attributed to the absence of any crystallographic phase transition. Figure2presents the thermal spin transition curves of the mixed crystals [Zn₁₋xFex(6-mepy)₃tren](PF₆)₂ withx=0.0005, 0.31 and [Fe(6-mepy)₃tren](PF₆)₂. The ther- mal spin transition curve for the highly diluted compound with x=0.0005 from the literature²¹ serves as reference for calculating the thermodynamic parameters within the framework of the mean-field model.

In the neat crystal, the thermal spin transition is complete and quite steep with a transition temperature T_1/2=214 K 214306-2

in line with literature,³⁰ whereas for the diluted mixed crystals the thermal spin transition is also complete, more gradual but still surprisingly steep with transition temperatures T_1/2=210 and 212 K forx=0.0005 and 0.31, respectively.

The steeper thermal spin transition is generally attributed to the cooperative effects due to the large metal-ligand bond length difference,r_HL=r_HS−r_LS, between the two spin manifolds of typically 0.2 ˚A for iron(II) systems.³⁵ This essentially generates elastic stresses inside the lattice. Cooperative effects have been modeled by the superposition of both short-range and long-range interactions. The short-range component is

statistically distributed and depends on the shape and distance between neighboring molecules. The long-range component is proportional to the average number of HS molecules per unit volume and is mediated by the lattice.^18,36–42 In the present case, the shift in the thermal spin transition temperature as a function of Fe(II) concentration is relatively small. Simple thermodynamic considerations, detailed elsewhere,^36,37on the basis of the classical model of Slichter and Drickamer³⁹within the mean-field approximation lead to the expression of Eq.(1) for the equilibrium constant for the mixed crystals of the title compounds and an inert host lattice of Zn(II):

K= γ_HS

1−γ_HS =exp

−H⁰−T S⁰−2x

γ_HS−¹₂

−M(1−x) kBT

, (1)

where H⁰ andS⁰ are the standard enthalpy and entropy variations for the pure compound,is the interaction constant, and the lattice shift_M introduces a correction to the enthalpy change for diluted systems,^42,43 such thatH^x→0=H⁰− M and S^x→0=S⁰ for highly diluted title complex with x=0.0005. Initially, H^x→0 and S^x→0 regarded as temperature independent within the temperature interval of the spin transition, were determined from a numerical least squares fit using Eq.(1)forx=0.0005. Subsequently, those parameters were used to determine andM for the neat compound. Finally, all the numerically fitted parameters were used to calculate the thermal spin transition curve for the intermediate concentration withx=0.31. The best global fit parameters to the data in Fig.2gaveH^x→0=2510(30) K, S^x→0=11.9(2) K,=143(5) K, andM=79(4) K. These

1.0

0.8

0.6

0.4

0.2

0.0 γHS

300 250 200 150 100 50

T (K) x = 0.0005

x = 0.31 x = 1 calculated

FIG. 2. (Color online) Thermal spin transition curve for the mixed-crystals of [Zn_1−xFe_x(6-mepy)₃tren](PF₆)₂,x=0.0005²¹and 0.31 obtained from optical absorption spectroscopy, and for [Fe(6- mepy)3tren](PF6)2 obtained from magnetic measurements. Calcu- lated curves in the framework of mean-field approximation with H^x→0=2510 K,S^x→0=12 K,=143 K, andM=79 K (—).

values are substantially different from the ones found by Adleret al.⁴⁴ based on the line shape analysis of M¨ossbauer spectra under external pressure of the neat compound. The present values, based on the dilute system as reference, are self-consistent and may be regarded as more accurate.

2. Photoinduced HS→LS relaxation

Photoinduced relaxation studies were performed as a function of laser power and temperature for [Fe(6- mepy)3tren](PF6)2 as well as for the mixed system [Zn1−xFex(6-mepy)3tren](PF6)2,x=0.31. The details of the experimental setup and conditions were described above.

Figure3shows photoexcitation curves in the form of a build-up of the HS fraction during excitation and relaxation curves after switching off the laser of both systems at 10 K for different laser powers ranging from nominally 0.7 to 12 mW.

The indicated HS fractions were obtained by normalization of the observed value ofOD with respect to the difference in the optical density of the HS and the LS species at the probe wavelength taken from the absorption spectra at 295 and 10 K, respectively. Three points are to be noted: (i) for the mixed compound, the HS→ LS relaxation is considerably slower than for the neat compound; (ii) for the mixed compound, relaxation curves are close to single exponential, but for the neat compounds deviation from single exponential are evident; (iii) for the mixed compound, the light-induced HS fraction at the steady stateγ_HS^SSincreases much more rapidly with laser power than for the neat compound, and reaches almost quantitative conversion at the highest laser power, whereas for the neat compound, a steady-state HS fraction of only 0.23 is achieved. For the mixed system, γ_HS^SS was determined via the amplitude of the single exponential fit to the buildup. This is quantitatively shown in Fig.4. For the mixed system, this power dependence can be analyzed quantitatively, and this will be detailed in Sec. IIIB. The reason for not achieving higher HS fractions for the neat compound is twofold: in contrast to the mixed system for which the optical density at the irradiation wavelength was quite low, for the neat system, it was substantially larger than 1 for all iron centers in

PRADIP CHAKRABORTYet al. PHYSICAL REVIEW B87, 214306 (2013)

FIG. 3. (Color online) Photoexcitation and HS→LS relax- ation curves at 10 K with irradiation at λex=725 nm, for (a) [Fe(6-mepy)3tren](PF6)2, irradiation time 4.5 s, (b) [Zn1−xFex(6- mepy)3tren](PF6)2,x=0.31, irradiation time 15 s. 10-mW nominal laser power correspond to approximately 5 mW/mm²effective power density for a beam diameter of 1.5 mm and around 15% losses from the reflection of the cryostat windows and the crystal surface.

the LS state and still non-negligible for a hypothetical HS population of 100%. Thus the excitation light intensity is not homogeneous through the crystal and together with the faster relaxation results in a lower overall HS fraction for the neat compound at a given laser power. The deviations in the HS→ LS relaxation curves from single exponential in the neat compound are due to several factors. First of all, of course, they are due to the cooperative effects, which in principle result in self-accelerated, sigmoidal relaxation curves.¹⁸However, in the present case, the sigmoidal character is outweighed by the above-mentioned light-induced concen- tration gradients, which smear out the sigmoidal character and precluded a quantitative evaluation of the relaxation curves in Fig.3(a). Nevertheless, qualitatively, Fig.3(a) demonstrates the importance of cooperative effects. From the experimental relaxation curves, the initial rate constants att₀ immediately after switching off the laser according to

dγ_HS dt

t₀

= −k^initial_HL γ_HS^SS (2)

1.0

0.8

0.6

0.4

0.2

0.0 γ^ss

12 10 8

6 4 2

0

Laser power (mW) x = 0.31 x = 1

calculated with α = 2.4

HS

FIG. 4. (Color online) The steady-state HS fraction as a function of nominal laser power for [Zn1−xFe_x(6-mepy)3tren](PF6)2at 10 K, x=0.31 ( ) and [Fe(6-mepy)3tren](PF6)2( ). Numerical fit for x=0.31 according to Eq.(10)withαfixed at a value of 2.4 (—).

can be determined numerically. Figure 5 shows k_HL^initial as function of γ_HS^SS for both the neat compound, the mixed system with x=0.31 and for comparison, the very dilute system with x=0.02 (see Figs. S3 and S4 in Ref. 31).

For the very dilute system, k_HL^initial=0.09 s⁻¹ (τ=11 s) is independent of γ_HS^SS. For the mixed system, it is slightly larger and decreases slightly with increasing values ofγ_HS^SS. For the neat system, k_HL^initial=2.7 s⁻¹ for γ_HS^SS=0.015 and decreases rapidly with increasing values ofγ_HS^SS. This is in qualitative agreement with the self-acceleration of the HS→ LS relaxation in concentrated iron(II) spin-crossover systems due to cooperative effects.¹⁸ A quantitative analysis of these data will be presented in Sec.III Btogether with the discussion of the photocrystallographic results.

3 4 5 6

0.1

2 3 4 5 6

1

2 3

kHL (s-1 )

1.0 0.8

0.6 0.4

0.2 0.0

γHS

x = 0.02 x = 0.31 x = 1

ss

initial

FIG. 5. (Color online) Initial relaxation rate constant plotted on a logarithmic scale as a function of initial photo-induced HS fraction for [Zn1−xFex(6-mepy)3tren](PF6)2,x=0.02 ( ), 0.31 ( ), and 1 ( ) at 10 K. Calculated according to Eq.(5)withαfixed at a value of 2.4 (---).

214306-4

TABLE I. Crystallographic data for [Fe(6-mepy)3tren](PF6)2at 295 and 10 K, [Zn(6-mepy)3tren](PF6)2and [Zn1−xFex(6-mepy)3tren](PF6)2

at 10 K.⁴⁵

[Fe(6-mepy)3tren] [Fe(6-mepy)3tren] [Zn1−xFex(6-mepy)3tren] [Zn(6-mepy)3tren]

Empirical formula (PF6)2 (PF6)2 (PF6)2 (PF6)2

Formula weight 801.39 801.39 806.07 810.91

Temperature 293(2) K 10(2) K 10(2) K 10(2) K

Wavelength 1.54184 ˚A 0.69412 ˚A 0.69412 ˚A 0.69412 ˚A

Crystal system Orthorhombic Orthorhombic Orthorhombic Orthorhombic

Space group P 212121 P212121 P 212121 P 212121

a( ˚A) 10.71000(11) 10.51322(12) 10.59320(10) 10.64570(10)

b( ˚A) 17.53208(16) 16.8292(2) 16.9878(2) 17.1150(2)

c( ˚A) 17.64672(16) 17.2609(3) 17.3489(3) 17.43640(10)

α=β=γ 90^◦ 90^◦ 90^◦ 90^◦

Volume ( ˚A³) 3313.50(5) 3053.94(7) 3122.02(7) 3176.93(5)

Z 4 4 4 4

Density (calculated) 1.606 Mg/m³ 1.743 Mg/m³ 1.715 Mg/m³ 1.695 Mg/m³

Absorption coefficient 5.480 mm⁻¹ 0.707 mm⁻¹ 0.843 mm⁻¹ 0.978 mm⁻¹

F(000) 1632 1632 1639.8 1648

Crystal size (mm³) 0.13×0.046×0.036 ∼0.1×0.05×0.05 ∼0.1×0.05×0.05 0.21×0.093×0.050 Theta range for data collection 3.55 to 73.37^◦. 2.22 to 24.40^◦. 2.20 to 24.09^◦. 1.63 to 27.80^◦.

Index ranges –8h13, –12h12, –12h12, –14h14,

–20k21, –20k20, –19k19, –20k20,

–18l21 –18l18 –17l17 –23l23

Reflections collected 11916 12982 12089 14550

Independent reflections 6480 5130 4891 7204

R(int)=0.0223 R(int)=0.0385 R(int)=0.0338 R(int)=0.0641

Completeness 100.0% 94.6% 91.4% 95.9%

Refinement method Full-matrix least-squares on F²

Data/restraints/parameters 6480/0/446 5130/0/446 4891/0/447 7204/0/446

Goodness-of-fit on F² 1.014 1.066 1.038 1.039

R indices [I>2sigma(I)] R1=0.0413, R1=0.0316, R1=0.0312, R1=0.0608,

wR2=0.1173 wR2=0.0823 wR2=0.0816 wR2=0.1588

Rindices (all data) R1=0.0459, R1=0.0342, R1=0.0314, R1=0.0609,

wR2=0.1232 wR2=0.0879 wR2=0.0819 wR2=0.1590

Absolute structure parameter –0.012(4) 0.007(15) 0.040(9) 0.018(8)

Largest diff. peak 0.552 and 0.291 and 0.251 and 0.590 and

and hole –0.302 e. ˚A⁻³ –0.428 e. ˚A⁻³ –0.427 e. ˚A⁻³ –1.086 e. ˚A⁻³

B. Photocrystallographic study

As described in the experimental section, the photocrystal- lographic study was performed using the synchrotron based x-ray single crystal diffraction technique, allowing rapid collection of full data sets under continuous irradiation at 728 nm for different laser powers. Table Igives the data of the structure determination for [Fe(6-mepy)3tren](PF6)2at 295 and 10 K without irradiation, and TableIIlists corresponding relevant structural parameters as reference (see Fig. 1 inset for structure of the complex and atom labeling). In addition, TablesIandII contain the data for [Zn(6-mepy)₃tren](PF₆)₂ and [Zn₁₋xFex(6-mepy)3tren](PF6)2, also at 10 K. For the latter, x was calculated from the average M-N (M=Zn or Fe) bond lengths at 10 K without irradiation and a value of x=0.37(1) for the crystal investigated was obtained. This is somewhat larger than the value of 0.31 obtained on a bulk sample from a photometric determination, and may reflect some sample variability. In the following, the value of 0.37, which is specific for the crystal studied, will be used. All com- pounds crystallize in the orthorhombic space groupP212121

with Z=4, without any crystallographic phase transition

between 295 and 10 K even for the neat spin-crossover system [Fe(6-mepy)3tren](PF6)2. For this compound, the bond length

TABLE II. Relevant structural parameters of [Zn_1−xFex(6- mepy)3tren](PF6)2.

x=0, x=0.37, x=1, x=1,

10 K 10 K 10 K 295 K

r(M-N2) ( ˚A) 2.118(2) 2.056(2) 1.948(2) 2.142(3) r(M-N5) ( ˚A) 2.141(3) 2.070(2) 1.951(3) 2.160(3) r(M-N4) ( ˚A) 2.148(3) 2.071(2) 1.955(2) 2.160(3) r(M-N3) ( ˚A) 2.249(2) 2.185(2) 2.064(2) 2.273(3) r(M-N6) ( ˚A) 2.266(2) 2.191(2) 2.078(2) 2.286(3) r(M-N1) ( ˚A) 2.294(3) 2.214(2) 2.082(2) 2.292(3) r(M-N)( ˚A) 2.203(1) 2.131(1) 2.012(1) 2.218(1) d(M-N7) ( ˚A) 3.329(4) 3.406(4) 3.557(4) 3.314(4) _dis(deg)^a 94.5(4) 89.8(4) 79.5(4) 99.9(4)

Mis either Zn or Fe depending on the structure.

adis=12

i=1|90−φi|.

PRADIP CHAKRABORTYet al. PHYSICAL REVIEW B87, 214306 (2013)

100 95 90 85 80 Σdis (deg)

50 40 30 20 10 0

Laser power (mW)

experimental numerical fit fit parameters α = 2.40 ΔΣdis = 21.7˚

2.19 2.16 2.13 2.10 2.07 2.04 2.01

<r(Fe-N)> (Å)

experimental numerical fit fit parameters α = 2.40

Δr(Fe-N)= 0.192 Å

3160 3140 3120 3100 3080 3060 Vc (Å3 )

experimental numerical fit fit parameters α = 2.43

ΔV_c= ZΔV_HL = 115.5 ų 3.55

3.50 3.45 3.40 3.35 d(Fe-N7) (Å)

50 40 30 20 10 0

Laser power (mW) experimental numerical fit fit parameters α = 2.34

Δd(Fe-N7) = 0.23 Å

FIG. 6. (Color online) Variation of the different structural parameters as a function of nominal laser power for [Fe(6-mepy)₃tren](PF₆)₂at 10 K and the numerical fit (—).

changes with an average value ofr_HL=0.206 ˚A on cooling from 295 to 10 K, which is in line with a complete thermal spin transition.

Full data sets for the neat compound as well as the mixed system withx=0.37 were likewise collected under continuous irradiation. The diffractograms even of the neat compound showed no evidence for phase separation. All diffraction peaks just reflect the continuous expansion of the unit cell due to the light-induced population of the HS state, with only

marginal broadening of the individual peaks (see Fig. S5, Ref.31).

Figures6 and7 show the variation of selected crystallo- graphic parameters, namely the unit cell volumeVc=ZV_HL, the average Fe-N bond lengths of the six directly coordinated nitrogen atoms r(Fe-N), the distance between Fe and the apical nitrogen atom d(Fe-N₇), and, as a measure for the overall distortion of the coordination octahedron, the sum of all cis N-Fe-N angles_dis as a function of nominal laser

2.19 2.18 2.17 2.16 2.15 2.14 2.13

<r(Fe- N)> (Å)

experimental numerical fit fit parameters

α = 2.4

Δr(Fe-N)= 0.065 Å

3160 3150 3140 3130 3120 Vc (Å3 )

experimental numerical fit fit parameters α = 2.4

ΔVc= ZΔVHL= 40.18 ų 95

94 93 92 91 90 89 Σdis (deg)

50 40 30 20 10 0

Laser power (mW)

experimental numerical fit fit parameters α = 2.4 ΔΣdis = 5.97˚

3.40 3.39 3.38 3.37 3.36 3.35 3.34 3.33 d(Fe - N7) (Å)

50 40 30 20 10

0 Laser power (mW) experimental numerical fit fit parameters α = 2.40

Δd(Fe-N7)= 0.075 Å

FIG. 7. (Color online) Variation of the different structural parameters as a function of nominal laser power for [Zn1−xFex(6- mepy)3tren](PF6)2, with an effective dilution ofx=0.37 at 10 K and the numerical fit (—).

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power (for additional structural parameters such as the lattice parameters see Figs. S6 and S7 in Ref.31).

For the neat [Fe(6-mepy)3tren](PF6)2crystal, the variation of the crystallographic parameters as a function of laser power (see Fig.6) is sigmoidal in shape, which is attributed to the aforementioned cooperative effects. As the photocrystallo- graphic study was performed on a very small and thin crystal such that the optical density at the irradiation wavelength was less than 0.15, and as it was placed in the He-cryostream for very efficient cooling, light-induced concentration gradients as well as temperature gradients are minimal. As mentioned above, no phase separation, no increase in diffuse scattering and only marginal broadening of the diffraction peaks were observed under irradiation. Therefore the cooperative effects can be modeled on the basis of the mean-field approximation, which is particularly justified in the present case because they are not too large and the continuous irradiation and relaxation actually establishes a random distribution of the HS and LS complexes in the steady-state type situation. The following differential equation is considered for the photoexcitation and relaxation processes:

dγ_HS

dt =k_exγ_LS−k_HLγ_HS = −dγ_LS

dt , (3) where k_ex andk_HL are the excitation and the relaxation rate constant, respectively. At the steady-state, dγ_HS/dt=0, and accordingly,

γ_HS^SS= k_ex

k_ex+k_HL = 1

1+k_HL/k_ex = 1

1+k_HL/cP, (4) whereγ_HS^SSis the steady-state HS fraction,cis a proportionality constant, and P is the laser power such that k_ex=cP. In dilute systems, k_HL would just be a constant, but for neat and concentrated crystals, where cooperative effects are significant, the HS → LS relaxation rate constant in the mean-field approximation is given by^8,18

k_HL=k⁰e^αγLS=k⁰e^α(1−γHS), (5) whereαis the self-acceleration factor andk⁰is the rate constant atγ_LS=0.

Combining Eqs.(4)and(5)yields γ_HS^SS= 1

1+k⁰e^α(1−γ_HS^SS)/cP. (6)

For the neat compound, the experimentally determined average structural parameters under continuous irradiation are given according to Vegard’s law:⁴⁶

X_obs=γ_HS^SSX_HS+

1−γ_HS^SS

X_LS (7a) or X_obs=X_obs−X_LS=γ_HS^SS(XHS−X_LS)

=γ_HS^SSX_HL, (7b) where X_HS andX_LS are the values of the structural param- eter under consideration for full HS and LS populations, respectively, and X_HL is the corresponding difference for full conversion extrapolated to infinite laser power.X_obsis the difference between the observed value of the structural parameter and the value of the LS state from the structure determination without irradiation. Introducing Eq. (7) into Eq.(6)yields

X_obs= X_HL

1+k⁰e^{α(1−Xobs/XHL)}/cP. (8) Numerical least-squares fits of the implicit Eq.(8)to the four experimental curves of Fig.6 yield the three fit parameters X_HL,α, and the scaling factork⁰/c, withX_LS fixed at the corresponding value taken from the structure determination without irradiation. The global fit to the four curves of Fig.6 is excellent, and the corresponding values of the variation of the structural parametersVc,r(Fe-N),d(Fe-N7), and _dis, as well as the value of the self-acceleration parameterα are given in TableIII. The structural parameters can be directly compared to those obtained for the iron complex crystallized with PF6− as anion and the incorporation of toluene and acetonitrile as crystal solvent, for which the light-induced state is sufficiently long-lived to allow a determination of the crystal structure of the fully converted metastable HS state.⁴⁷In particular, the agreement forr(Fe-N) =0.192 ˚A is excellent. For the other relevant parameters, the agree- ment is still very good, showing significant increases in V_HL=V_c/Z,d(Fe-N7) and _dis. Whereas the value of r(Fe-N) is a hard value not much influenced by crystal packing effects, the others are much more susceptible to these effects. This is particular evident in d(Fe-N7), which increases significantly more in the more loosely packed reference compound with incorporated solvent molecules.

TABLE III. Summary of the selected structural parameters for [Fe(6-mepy)3tren](PF6)2, the mixed crystal of [Zn1−xFex(6- mepy)₃tren](PF₆)₂, x=0.37 extracted from the mean-field fit and comparison with [Zn(6-mepy)₃tren](PF₆)₂, and the long-lived reference [Fe(6-mepy)3tren](PF6)2·C7H8·CH3CN.^d

Neat crystal Mixed crystal^b Zn-reference^c Long-lived reference^d

α 2.4(3) 2.4 – –

x 1 0.37(3) 0 –

VHL( ˚A³)^a 29(2) 26.8(2) 30.7(1) 24.3(1)

r(Fe-N)( ˚A) 0.192(6) 0.173(3) 0.190(1) 0.192(1)

d(Fe-N7) ( ˚A) 0.233(6) 0.200(4) 0.231(4) 0.317(4)

dis(deg) 21.7(4) 15.9(3) 15.69(3) 25.55(4)

aThe volume change calculated for one Fe atom.

bAll the values are extrapolated to one Fe by taking into account the value ofx.

cIt is the difference in the structure of [Zn(6-mepy)3tren](PF6)2and [Fe(6-mepy)3tren](PF6)2at 10 K.

dFor [Fe(6-mepy)3tren](PF6)2·C7H8·CH3CN from Ref.47.

PRADIP CHAKRABORTYet al. PHYSICAL REVIEW B87, 214306 (2013) A further point to discuss is the value of the self-acceleration

factor α of 2.4, which is directly related to the value of interaction constant of 143 K extracted from the thermal spin transition curves. In the quantum-mechanical tunneling regime,⁸

α= 2

¯ hωln

S n₀

forn₀>1, (9) where S is the Huang-Rhys factor describing the relative horizontal displacement of the HS and the LS potential wells, ¯hωis the average vibrational frequency of the totally symmetric stretch vibration, and n0 is the zero-point energy difference,E⁰_HL, between the two states expressed in units of ¯hω. For S and ¯hω, the standard model values of 45 and 250 cm⁻¹ may be employed.^21,48 An estimate of n₀ is more delicate. In principle, E_HL⁰ =H⁰(T→0), but as H⁰decreases rapidly towards low temperatures,^8,42it is not advisable to just take the value from the thermal spin transition.

Following Spieringet al.,^42,43 H⁰(T→0) can be estimated to be around 1000 K for the present system, and thus the expected value of αlies between 2 and 3. This is in perfect agreement with the experimental value of 2.4. Even though the quality of the experimental data from optical spectroscopy shown in Fig. 5 for the neat iron(II) compound does not allow an independent determination ofα,k^initial_HL calculated as a function ofγ_HS^SSaccording to Eq.(5)supports the value of 2.4.

Taken together, the analysis of the power dependent structural data based on the mean-field approximation gives an accurate picture of the molecular geometry of the comparatively short-lived metastable HS state in neat [Fe(6-mepy)₃tren]

(PF6)2.

For the mixed system [Zn₁₋xFex(6-mepy)3tren](PF6)2, x=0.37, cooperative effects are less pronounced and the evolution of the steady-state HS fraction γ_HS^SS as a function of laser power (see Fig.4) follows the more conventional form given by Eq.(4) with a constant value ofk_HL. Despite this, cooperative effects cannot be fully neglected and Eq.(6)can be modified with a reduced value for the acceleration factor fixed atαx=xαsuch that

γ_HS^SS= 1

1+k⁰e^xα(¹−γ_HS^SS)/cP. (10) A least squares fit of Eq.(10)to the experimental data in Fig.4 with only the scaling factork⁰/cas fit parameter while keeping x=0.37 andα=2.4 fixed, as determined for the neat system, results in a perfect reproduction of the experimental data. For the observed structural parameters,

X_obs=(1−x)XZn+x γ_HS^SSX_HS+

1−γ_HS^SS X_LS

=(1−x)X_Zn+xX_LS+xγ_HS^SSX_HL (11a) orX_obs=X_obs−(1−x)XZn+xX_LS=xγ_HS^SSX_HL,

(11b) and Eq.(8)thus becomes

X_obs= xX_HL

1+k⁰e^{xα(1−Xobs/xXHL)}/cP. (12)

A numerical least-squares fit of Eq.(12)to the experimental data of Fig.7with onlyX_HLand the scaling factork⁰/cas fit parameters, while keeping x=0.37 and α=2.4 fixed as above, gives the values for the different structural parameters listed in TableIII.

TableIIIsummarizes the structural parameters extrapolated to infinite laser power extracted from the mean-field model in case of neat [Fe(6-mepy)3tren](PF6)2 as well as for the diluted [Zn1−xFex(6-mepy)3tren](PF6)2, along with the reference Zn analogue and the long-lived solvated complex of [Fe(6-mepy)₃tren](PF₆)₂·C₇H₈·CH₃CN. As the structure of [Zn(6-mepy)3tren](PF6)2 is similar to the HS [Fe(6- mepy)3tren](PF6)2 structure, the Zn-complex was chosen as the reference. All values are mutually compatible and indicate that the dynamic structure determination of the light-induced HS state for the neat as well as the mixed system is very accurate.

IV. CONCLUSIONS

As detailed in the introduction, crystal structures of light- induced metastable HS states in spin-crossover compounds have been reported before. The key aspect of the present study is the determination of the light-induced HS structure of a system for which the lifetime of the metastable state is only few seconds. Despite this, a judicious choice of the irradiation wavelength in the tail of the absorption band in order to avoid light-induced concentration gradient, efficient cooling in a He gas jet in order to avoid temperature gradients, and a rigorous protocol to measure the evolution of the steady-state structure under continuous irradiation as a function of irradiation intensity, resulted in high-quality data sets. The evaluation of the power dependence using a mean-field approach allowed extrapolation of the light- induced structure to an HS fraction of 100%. The extrapolated structural parameters are in very good agreement with those of the analogous zinc compound as well as with the related system having a lifetime of several hours at 10 K. The mean- field model parameters for the cooperative effects extracted from the dynamic photocrystallographic study and from the thermodynamic treatment of the thermal spin transition are in mutual agreement. The same protocol together with the corresponding reference structures also allowed an accurate determination of the molecular structure of the short-lived HS state in a mixed crystal. Thus by making use of the rapid collection of full data sets at synchrotron facilities, we have developed a general protocol for the accurate determination of comparatively short-lived light-induced molecular structures, with the potential to be applied to a variety of reversible photoactive systems.

ACKNOWLEDGMENTS

This work was financially supported by the Swiss National Science Foundation (Grant No. 200020_137567). We thank Nahid Amstutz for sample preparation and crystal growth, and the Swiss Norwegian Beamlines for the provision of synchrotron beam time.

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*Corresponding author: [email protected]

1Spin Crossover in Transition Metal Compounds I-III, edited by P. G¨utlich and H. A. Goodwin, Topics in Current Chemistry (Springer, Heidelberg, 2004), pp. 233–235.

2A. Bousseksou, G. Moln´ar, L. Salmon, and W. Nicolazzi,Chem.

Soc. Rev.40, 3313 (2011).

3J. Jeftic and A. Hauser,J. Phys. Chem. B101, 10262 (1997).

4P. G¨utlich, V. Ksenofontov, and A. B. Gaspar,Coord. Chem. Rev.

249, 1811 (2005).

5A. Bousseksou, N. Negre, M. Goiran, L. Salmon, J.-P. Tuchagues, M.-L. Boillot, K. Boukheddaden, and F. Varret, Eur. Phys. J. B13, 451 (2000).

6S. Bonhommeau, G. Moln´ar, M. Goiran, K. Boukheddaden, and A. Bousseksou,Phys. Rev. B74, 064424 (2006).

7M. Ohba, K. Yoneda, G. Agusti, M. C. Munoz, A. B. Gaspar, J. A.

Real, M. Yamasaki, H. Ando, Y. Nakao, S. Skaki, and S. Kitagawa, Angew. Chem., Int. Ed.48, 4767 (2009).

8P. G¨utlich, A. Hauser, and H. Spiering, Angew. Chem.106, 2971 (1994); A. Hauser,Top. Curr. Chem.234, 155 (2004).

9P. G¨utlich, P. J. van Koningsbruggen, and F. Renz,Struct. Bond.

107, 27 (2004).

10J.-F. L´etard,Top. Curr. Chem.235, 221 (2004).

11M. Matsuda and H. Tajima, Patent No. JP2009212164-A, 2009.

12A. Hauser, Chem. Phys. Lett. 173, 507 (1990); S. Schenker, A. Hauser, W. Wang, and I. Y. Chan,ibid.297, 281 (1998).

13E. K¨onig, Struct. Bond.76, 53 (1991).

14J. K. Beattie,Adv. Inorg. Chem.32, 1 (1988).

15E. K¨onig,Prog. Inorg. Chem.35, 527 (1987).

16C.-L. Xie and D. N. Hendrickson,J. Am. Chem. Soc.109, 6981 (1987).

17E. Buhks, G. Navon, M. Bixon, and J. Jortner,J. Am. Chem. Soc.

102, 2918 (1980).

18A. Hauser, J. Jeftic, H. Romstedt, R. Hinek, and H. Spiering,Coord.

Chem. Rev.190–192, 471 (1999).

19A. Hauser, P. G¨utlich, and H. Spiering, Inorg. Chem. 25, 4245 (1986).

20P. Adler, A. Hauser, A. Vef, H. Spiering, and P. G¨utlich,Hyperfine Interact.47, 343 (1989).

21A. Hauser, A. Vef, and P. Adler, J. Chem. Phys. 95, 8710 (1991).

22A. Hauser, P. Adler, S. Deisenroth, P. G¨utlich, C. Hennen, H. Spiering, and A. Vef,Hyperfine Interact.90, 77 (1994).

23S. Pillet, E.-E. Bendeif, S. Bonnet, H. J. Shepherd, and P. Guionneau,Phys. Rev. B86, 064106 (2012).

24M. B.-L. Cointe, J. H´ebert, C. Bald´e, N. Moisan, L. Toupet, P. Guionneau, J. F. L´etard, E. Freysz, H. Cailleau, and E. Collet, Phys. Rev. B85, 064114 (2012).

25H. Cailleau, M. Lorenc, L. Gu´erin, M. Servol, E. Collet, and M. B.-L. Cointe, Acta Crystallogr. Sect. A 66, 189 (2010).

26E. Collet,Acta Crystallogr. Sect. A66, 133 (2010).

27E. Collet, M. Lorenc, M. Cammarata, L. Gu´erin, M. Servol, A. Tissot, M.-L. Boillot, H. Cailleau, and M. B.-L. Cointe,Chem.

Eur. J.18, 2051 (2012).

28E. Collet, N. Moisan, C. Bald´e, R. Bertoni, E. Trzop, C. Laulh´e, M. Lorenc, M. Servol, H. Cailleau, A. Tissot, M.-L. Boillot, T. Graber, R. Henning, P. Coppens, and M. Buron,Phys. Chem.

Chem. Phys.14, 6192 (2012).

29M. Lorenc, J. H´ebert, N. Moisan, E. Trzop, M. Servol, M. Buron, H. Cailleau, M.-L. Boillot, E. Ponte, M. Wulff, S. Koshihara, and E. Collet,Phys. Rev. Lett.103, 028301 (2009).

30M. A. Hoselton, L. J. Wilson, and R. S. Drago,J. Am. Chem. Soc.

97, 1722 (1975).

31See Supplemental Material at http://link.aps.org/supplemental/

10.1103/PhysRevB.87.214306and Refs.1–7therein for additional figures and discussions of data evaluation and the temperature dependence of relaxation rates.

32CRYSALISPRO, Agilent Technologies, Version 1.171.35.21 (release 20-01-2012CRYSALIS171.NET, compiled Jan 23 2012,18:06:46).

33A. Altomare, M. C. Burla, M. Camalli, G. Cascarano, C. Giacovazzo, A. Guagliardi, G. Moliterni, G. Polidori, and R. Spagna,J. Appl. Cryst.32, 115 (1999).

34SHELX [Includes SHELXL97, CIFTAB] - G. M. Sheldrick, Acta Crystallogr. Sect. A64, 112 (2008).

35P. Guionneau, M. Marchivie, G. Bravic, J.-F. L´etard, and D. Chasseau,Top. Curr. Chem.234, 97 (2004);J. Kusz, P. G¨utlich, and H. Spiering,ibid.234, 129 (2004).

36J.-P. Martin, J. Zarembowitch, A. Dworkin, J. G. Haasnoot, and E. Codjovi, Inorg. Chem. 33, 2617 (1994); J.-P. Martin, J. Zarembowitch, A. Bousseksou, A. Dworkin, J. G. Haasnoot, and F. Varret,ibid.33, 6325 (1994).

37R. Jakobi, H. Spiering, L. Wiehl, E. Gmelin, and P. G¨utlich,Inorg.

Chem.27, 1823 (1988).

38M. A. Halcrow,Chem. Soc. Rev.40, 4119 (2011).

39C. P. Slichter and H. G. Drickamer,J. Chem. Phys.56, 2142 (1972).

40F. Varret, K. Boukheddaden, E. Codjovi, C. Enachescu, and J. Linares,Top. Curr. Chem.234, 199 (2004).

41S. I. Klokishner, M. A. Roman, and O. S. Reu,Inorg. Chem.50, 11394 (2011).

42H. Spiering,Top. Curr. Chem.235, 171 (2004).

43H. Spiering, E. Meissner, H. K¨oppen, E. W. M¨uller, and P. G¨utlich, Chem. Phys.68, 65 (1982).

44P. Adler, H. Spiering, and P. G¨utlich,J. Phys. Chem. Solids50, 587 (1989); Inorg. Chem.26, 3840 (1987).

45CCDC 931008 to 931011 contain the supplementary crystallo- graphic data for this paper. These data can be obtained free of charge from the Cambridge crystallographic data centre via www.ccdc.cam.ac.uk/data_request/cif.

46L. Vegard, Z. Cryst.67, 239 (1928).

47A. Tissot, Ph.D thesis, University Paris Sud 11, France, 2011.

48S. Schenker, A. Hauser, W. Wang, and I. Y. Chan,J. Chem. Phys.

109, 9870 (1998).