A Switchable Molecular Rotator: Neutron Spectroscopy. Study on a Polymeric Spin-Crossover Compound

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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.

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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 χMT for guest-free {Fe(pz-d4)[Pt(CN)4]} (1d; red) and benzene clathrate {Fe(pz-d4)[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

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Q ΓL (variable) meV ΓL (fixed) meV AL a.u. A0 a.u. Bkg a.u. (x10-5) 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)

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, ΓL , 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 ΓL to the

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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

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Figure S4: Experimental (black) and simulated (red) 2H-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 2H-NMR spectra of 1d using (a) 2-site flip model (flip angle of 90°), (b) 2-site

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Figure S6: 2H-NMR spectrum of {Fe(pz-d4)[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

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Simulation of the

2

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

Dnm(2)*(Ω)

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

Q 2 ) 2 ( 0

8

3

=

,

qQ

e

T

Q 2 ) 2 ( 2

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

=

.

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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

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Pyrazine rotational entropy difference (ΔS

rot

) between the HS and the LS state:

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.

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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

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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

(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.

Figure

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