**Supporting Information **

**Supporting Information**

**A Switchable Molecular Rotator: Neutron Spectroscopy **

**Study on a Polymeric Spin-Crossover Compound **

### J. Alberto Rodríguez-Velamazán,*# Miguel A. González,

&### José A. Real,*† Miguel Castro,#

### M. Carmen Muñoz,‡ Ana B. Gaspar,† Ryo Ohtani,

⊥### Masaaki Ohba,

ξ### Ko Yoneda,

ξ### Yuh

### Hijikata,

⊥### Nobuhiro Yanai,

⊥### Motohiro Mizuno,§ Hideo Ando

∇### and Susumu Kitagawa

⊥# Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC – Universidad de Zaragoza, 50009 Zaragoza, Spain.

& Institut Laue-Langevin, 38042 Grenoble Cedex 9, France.

† Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, 46980 Paterna, Valencia, Spain. ‡ Departamento de Física Aplicada, Universidad Politécnica de Valencia, E-46022, Valencia, Spain. ⊥ Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510, Japan.

ξ Department of Chemistry, Faculty of Science, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan.

§ Department of Chemistry, Graduate School of Natural Science & Technology, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan.

∇_{ Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Katsura, }
Nishikyo-ku, Kyoto 615-8510, Japan.

**Figure S1: Structures of 1 in the HS and LS states at 293 K. The Fe-N(pz) distance changes **

remarkably with the spin transition.

* Figure S2: Temperature dependence of *χM

*T for guest-free {Fe(pz-d*4)[Pt(CN)4

**]} (1d; red) and**

*benzene clathrate {Fe(pz-d*4)[Pt(CN)4

**](benzene)} (1d.bz; blue).**

### χ

M*T*/ em u K m ol -1

*T / K*

### HS state

### LS state

2.21 Å 1.98 Å*a*

*c*

*a*

*c*

*a*

*b*

*a*

*b*Fe Pt Fe Pt

* Q * Γ

**L****(variable)***Γ*

**meV**

**L****(fixed)**

**meV**

**A****L**

**a.u.**

**A****0**

**a.u.**

**Bkg***T=310K 0.5 0.081(3) 0.132(2) 0.0032(2) 0.00538(3) 8.48(90) 0.6 0.138(3) 0.0042(1) 0.00517(3) 5.14(16) 0.7 0.136(3) 0.0050(1) 0.00493(3) 4.95(15) 1 0.125(2) 0.0069(2) 0.00428(3) 6.05(14) 1.1 0.141(3) 0.0075(2) 0.00406(3) 5.68(12) 1.3 0.110(5) 0.0075(2) 0.00380(3) 8.93(10) 1.4 0.100(6) 0.0074(2) 0.00360(2) 9.90(9) 1.5 0.101(6) 0.0073(2) 0.00356(2) 10.44(9) 1.6 0.105(7) 0.0072(2) 0.00335(2) 11.09(9) 1.8 0.152(8) 0.0076(2) 0.00390(2) 13.65(9) 2 0.139(8) 0.0069(2) 0.00310(2) 14.15(10) 2.1 0.130(8) 0.0073(2) 0.00439(2) 14.34(10) T=295K 0.5 0.075(3) 0.123(2) 0.0030(2) 0.00546(3) 8.29(98) 0.6 0.140(3) 0.0041(1) 0.00525(3) 4.84(16) 0.7 0.140(3) 0.0048(2) 0.00505(3) 4.69(15) 1 0.121(2) 0.0067(2) 0.00445(3) 5.61(14) 1.1 0.135(3) 0.0073(2) 0.00424(3) 5.35(13) 1.3 0.103(6) 0.0072(2) 0.00401(3) 8.42(10) 1.4 0.092(7) 0.0071(2) 0.00380(3) 9.44(9) 1.5 0.094(7) 0.0071(2) 0.00376(3) 9.91(9) 1.6 0.097(7) 0.0070(2) 0.00355(3) 10.39(9) 1.8 0.142(9) 0.0066(2) 0.00381(2) 12.95(10) 2 0.124(10) 0.0061(2) 0.00298(2) 13.05(10) 2.1 0.116(10) 0.0070(2) 0.00458(3) 12.88(10)*

**a.u. (x10****-5****)****Table S1: Results of the fit of the S(Q,**ω) spectra at 310 K and 295 K (on cooling) to the sum of a

delta-function and a Lorentzian peak, both convoluted with the resolution function. All spectra that
have contributions from coherent scattering such as Bragg peaks were excluded from the fits. The
fitting parameters are the lorentzian width, Γ*L , and intensity, AL , the elastic intensity, A0 , and a flat *

background. In a first step, all the parameters were adjusted. As explained in the text, the number
of adjustable parameters was reduced in a second step by constraining the fits to adjust Γ*L to the *

**Figure S3: Values of the f parameter at different temperatures resulting from the fit of the EISF to **

the 4-fold-jump modeldescribed in equation (2) in the paper. The solid lines are guides to the eye
displaying the thermal history and showing the hysteretic behavior. The red points correspond to
the system completely in LS state, where the fit is barely meaningful. Nevertheless, the graphics
illustrates the evolution of the fraction of H atoms whose movement can be observed in the time
*window of the instrument, represented by the f parameter, which goes to zero as the LS state is *
approached.

### 0

### 50

### 100

### 150

### 200

### 250

### 300

### 350

### 0.0

### 0.2

### 0.6

### 0.8

*f*

## T / K

* Figure S4: Experimental (black) and simulated (red) *2

**H-NMR spectra of 1d with magnetic behavior.**(the cooling process, 1) 320 K, 2) 300 K, 3) 290 K and 4) 240 K, and the heating process, 4) 240 K, 5) 260 K, 6) 280 K, 7) 290 K and 8) 300 K)

### -100

### 0

### 100

### kHz

### (c) 4-site

### (a) 2-site (90 deg.)

### (b) 2-site (180 deg.)

### ν

### / kHz

* Figure S5: Simulated *2

**H-NMR spectra of 1d using (a) 2-site flip model (flip angle of 90°), (b) 2-site**

* Figure S6: *2

*H-NMR spectrum of {Fe(pz-d*4)[Pt(CN)4

**](benzene)} (1d.bz) at 290 K.**100 0 –100 ν/ kHz 100 0 –100 100 0 –100 ν/ kHz

*In*

*te*

*n*

*s*

*it*

*y*/ a .u .

*v / kHz*

**Simulation of the **

**Simulation of the**

**2****H-NMR spectra **

**H-NMR spectra**

### For the four site flip motion,

2*H NMR frequency at site i was calculated as in Ref. 19 *

## ∑

### −

### ±

### =

*j*

*Pij*

*Qi*

*i*

### ω

### ω

### ω

### ,

### where

### ω

_{Qi}### and

### ω

_{Pij}### are the contributions of the quadrupole interaction and the dipolar

### interaction between

2*H nucleus at site i and the jth paramagnetic ion, which are written by *

### the second-order Wigner rotation matrix

*D*(2)*(Ω)

_{nm}### as

) 2 ( )* 2 ( 2 2 , )* 2 ( 0

### (

### ,

### ,

### )

### (

### ,

### ,

### )

### 2

### 3

*mQ*

*i*

*i*

*i*

*nm*

*m*

*n*

*n*

*Qi*

*D*

### ψ

### θ

### φ

*D*

### α

### β

### γ

*T*

### ω

## ∑

=### =

### ,

*Dij*

*ij*

*ij*

*ij*

*n*

*n*

*n*

*Pij*

*D*

### ψ

### θ

### φ

*D*

### α

### β

### γ

### ω

### ω

### (

### ,

### ,

### )

### (

### ,

### ,

### )

### 2

### 3

(2)* 0 2 2 )* 2 ( 0## ∑

=### =

### ,

###

*qQ*

*e*

*T*

*2 ) 2 ( 0*

_{Q}### 8

### 3

### =

### ,

###

*qQ*

*e*

*T*

*2 ) 2 ( 2*

_{Q}### 4

### η

### =

±### ,

3 0### 2

*ij*

*A*

*M*

*D*

*ij*

*D*

*r*

*N*

*B*

### χ

### γ

### ω

### =

### ,

### where

(### α

*,*

_{i}### β

*,*

_{i}### γ

*)*

_{i}### ,

(### α

*,*

_{ij}### β

*,*

_{ij}### γ

*)*

_{ij}### and

(### ψ

,### θ

,### φ

)### are the Euler angles for transformation from

### the molecular axes to the principal axes of the electric field gradient (EFG) tensor, from

### the molecular axes to the principal axes of the dipolar interaction between the

2### H nucleus

*and the jth paramagnetic ion and from the laboratory axes to the molecular axes, *

*respectively. e*

*2*

*qQ/ħ and η are the quadrupole-coupling parameters. r*

*ij*

### is the distance

### between the

2*H nucleus at site i and the jth paramagnetic ion. *

*γ*

D*, B*

0### ,

*χ*

*M*

* and N*

A### are the

### gyromagnetic ratio of deuteron, the strength of the external field, the magnetic

### susceptibility and the Avogadro constant, respectively. The experimental value of

*χ*

*M was*

### used for the calculation of

*ω*

*Dij.*

### The quadrupole echo signal

*G*

### (

*t*

### ,

### θ

### ,

### φ

### )

### is written as

### (

*t*

### ,

### θ

### ,

### φ

### )

### =

**P**

### ⋅

**B**

### ˆ

3### exp(

**A**

### ˆ

*t*

### )

### exp(

**A**

### ˆ

### τ

### )

### exp(

**A**

### ˆ

*### τ

### )

### ⋅

**1**

*G*

### ,

### where

**A**

### ˆ

### is the matrix with the elements i

*ω*

*i - kii on the diagonal and kij off the diagonal. kij*

*is the jumping rate between site i and j. *

**B**

### ˆ

### and

**P**

### are the matrix for finite pulse width

### and a vector of site populations, respectively.

**1**

### is a vector written as

**1**

### =

### (

### 1

### ,

### 1

### ,

### 1

### )

### .

### The signal of a powder sample was calculated by

### ( )

*t*

π π*G*

### (

*t*

### θ

### φ

### )

### θ

*d*

### θ

*d*

### φ

*G*

2 ### ,

### ,

### sin

0 2 0## ∫

## ∫

### =

### .

*Figure S6 shows the molecular axes (x*

M*, y*

M*, z*

M### ), the principal axes of the electric field

*gradient (EFG) tensor (x*

Q*, y*

Q*, z*

Q### ) and the principal axes of the dipolar interaction between

### the

2*H nucleus and the jth paramagnetic ion (x*

*Dj*

*, y*

*Dj*

*, z*

*Dj*

*) in {Fe(pz-d*

4### )[Pt(CN)

4### ]}. The z

*axis of the molecular axes was set to the C*

4### axis for the 4-hold jump of pyrazine ring. The

### z axis of the electric field gradient (EFG) tensor was assumed to be parallel to the C-

2### H

*bond. e*

*2*

*qQ/ħ = 165 kHz, η = 0 were used for the *

2### H NMR spectral simulation. The

### distances between the

2### H nucleus and the first-, second-, third-nearest Fe(II) are 3.17, 5.39,

### 5.78 Å, respectively (Figure S7). The paramagnetic effects from these three Fe(II) were

### calculated for the

2### H NMR spectral simulation in the paramagnetic HS state.

* Figure S7: Scheme showing the different sets of axes and the distances between the *2H nucleus

**and the nearest Fe(II) atoms.****Reference **

**Reference**

**Pyrazine rotational entropy difference (ΔS**

**Pyrazine rotational entropy difference (ΔS**

**rot****) between the HS and the LS state: **

**) between the HS and the LS state:**

**Theoretical estimation from experimental activation barriers **

**Theoretical estimation from experimental activation barriers**

### We prepared an potential energy function which is appropriate for the pz rotation in

### {Fe(pz)[Pt(CN)

4*]} as follows:. *

*V (*

*θ) = E*

*a*

*/2 (1 *

*− cos 4θ) *

### where

*θ and E*

*a*

* are the rotation angle (see Figure S1 in our previous Letter*

15### ) and the

### potential energy barrier height for the pz rotation, respectively. Herein, considering a barrier

*height Ea*

* of 7.8 kcal/mol in the LS state and 1.7 kcal/mol in the HS state, we obtained the *

### potential energy curves shown in Figure S8. The other conditions for the Fourier grid

### Hamiltonian method and the entropy calculations are the same as our Letter.

15**Figure S8: Potential energy curves of the pz rotation in the LS and the HS states **

### In Figure S9

*, the difference (ΔSrot) between pz rotational entropy in the HS state and that in *

### the LS state is plotted with respect to temperature. The

*ΔSrot*

* value is positive at all *

### temperatures. In high temperature region from 200 to 400 K, the temperature dependence of

*ΔSrot*

* is small and the averaged *

*ΔSrot*

* value is 1.88 cal mol*

*−1*

### K

*−1*

### (cf. 1.84 cal mol

*−1*

### K

*−1*

### in

### the corresponding theoretical result

15### ). At

*298.15 K, the ΔSrot*

* value is 1.90 cal mol*

*−1*

### K

*−1*

### ,

### which is as large as 9.4

*% of total ΔS value for single crystal {Fe(pz)[Pt(CN)*

4### ]}.

4d### This

### points out that the pz rotation provides a significant entropy difference and is an important

### factor for the thermal spin transition from the LS to the HS state.

**Figure S9: ***Difference (ΔSrot*) between hindered rotational entropy of pz ligands in the HS

framework and that in the LS framework

**References **

**References**

**(15) H. Ando, Y. Nakao, H. Sato, M. Ohba, S. Kitagawa, S. Sakaki, Chem. Phys. Lett., 2011, 511, 399–404 **
and references therein

(4d) T. Tayagaki, A. Galet, G. Molnár, M. C. Muñoz, A. Zwick, K. Tanaka, J. A. Real, A. Bousseksou, J.
**Phys. Chem. B, 2005, 109, 14859. **