Quantum Rotations and Chiral Polarization of Qubit Prototype

ARTICLE pubs.acs.org/JPCC

Quantum Rotations and Chiral Polarization of Qubit Prototype Molecules in a Highly Porous Metal
Organic Framework: 1H NMR T1 Study Svyatoslav P. Gabuda,* Svetlana G. Kozlova, Denis G. Samsonenko, Danil N. Dybtsev, and Vladimir P. Fedin A. V. Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, 3, Academician Lavrentiev Avenue, Novosibirsk 630090, Russia

bS Supporting Information ABSTRACT: Rotations of bistable diazabicyclooctane (dabco) molecules N2(C2H4)3 in a layered highly porous metal
organic framework [Zn2(C8H4O4)2 3 N2(C2H4)3] have been studied at 310
8 K by the 1H NMR spin
lattice relaxation method. Above 165 K, the relaxation is characterized by a single longitudinal relaxation time, T1, related to the hindered rotation of the dabco molecules. Below 165 K, the quantum tunneling mechanism was found to be responsible for dabco reorientation and spin relaxation. At 165
25 K, the system is characterized by two different spin
lattice relaxation times, T1_1 and T1_2, related to two separate states of dabco in the ratio of ∼1:2. The first state is related to the conformation of point symmetry D3h, and the second to the sum of right- and left-twisted D3 forms. At 25 K, a transition to a low-temperature phase occurs. The transition is characterized by three different spin
lattice relaxation times, T1_1, T1_2, and T1_3, related to three conformation states of dabco in the ratio of ∼2:3:5. The observed relationship of state populations indicates an inequality of right- and left-twisted forms and a chiral polarization of the system because of the break in its right/left symmetry.

1. INTRODUCTION The design of artificial molecular machinery will require a deep understanding of the relationship between different types of framework ordering1,2 and the dynamics of guest molecules in composite media.3
6 Internal dynamics with controlled degrees of freedom includes components with free volume compartments, volume-conserving processes (such as rotation of a cylinder along its principal axis7
10), and correlated motions with two or more components subject to concerted displacements. With these considerations in mind, we have pursued the design, synthesis, and dynamic characterization by NMR spin relaxation of molecular structures that emulate the switch speed function of a nanosize rotor. One such structure is demonstrated in the novel highly porous metal
organic framework (MOF) [Zn2(C8H4O4)2 3 N2(C2H4)3] comprising two-dimensional layers of zinc(II) terephthalate surrounding pillar rotor molecules of diazabicyclooctane N2(C2H4)3 (dabco).11 The crystal structure of the guest-free framework [Zn2(C8H4O4)2 3 N2(C2H4)3] (Figure 1a) is tetragonal [space group P4/mmm; ao = 10.929(2) Å, co = 9.608(1) Å; Z = 1 (T = 223 K)], and its guest-accessible volume is estimated to be ∼62%.11 The trigonal dabco molecules are located at the C4 axis of the crystal structure and are rotationally disordered over 12 orientations. Another disordering mechanism is due to the internal degrees of freedom of the dabco molecules, as they exist in two conformations, one twisted slightly about the symmetry axis [point symmetry D3 (32)] and one untwisted [point symmetry D3h (6m2)]. r 2011 American Chemical Society

Figure 1b shows left-twisted, right-twisted, and untwisted dabco molecules. According to our routine DFT calculations (ref 12 and Supporting Information), the untwisted dabco form (bonding energy Utot =
123.385 eV) and the twisted dabco form (bonding energy Utot =
123.387 eV) are both stable. However, there is still no experimental evidence for possible stabilization of the conformation states of dabco molecules either in liquid or in solids.13,14 Herein, we use 1H NMR spin
lattice measurements of [Zn2(C8H4O4)2 3 N2(C2H4)3] to show that different conformational states of dabco molecules can be stabilized in this composite at low temperatures under conditions of framework quantum confinement. The conformational states potentially can be used as prototypes of memory elements in a hypothetical quantum computer.

2. EXPERIMENTS The idea for the experiments stems from the fact that the rotation dynamics of guest dabco molecules can differ for twisted and untwisted forms because of the influence of the quantum confinement on the mobility of the rotor molecules in the nearly rigid MOF lattice. Therefore, the 1H NMR longitudinal (spin
lattice) relaxation time T115
17 should be different for the two molecular conformations. Received: July 14, 2011 Revised: September 13, 2011 Published: September 13, 2011 20460

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Figure 1. (a) Crystal structure of [Zn2(C8H4O4)2 3 N2(C2H4)3] at room temperature. The pillar molecules of N2(C2H4)3 (dabco) are shown as dynamically disordered over 12 orientations. (b) Arrangement of rotating pillar molecules N2(C2H4)3 and terephthalate anions [C8H4O4]2
in the metal
organic sorbent [Zn2(C8H4O4)2 3 N2(C2H4)3]. Legend: Zn, white; N, blue, O, red, and H, small balls. Broken lines indicate intermolecular H 3 3 3 O contacts of dabco molecules and terephthalate layers.

The samples were prepared as described in ref 11. According to chemical and X-ray phase analyses, the amount of admixtures in the prepared sample did not exceed 3%. During the NMR experiment, the sample was kept in an evacuated and sealed ampule. The 1H NMR spin
lattice relaxation time T1 was measured with a Bruker SXP 4-100 NMR spectrometer operating at Larmor resonance frequencies νL = ω/2π = 86 and 24.5 MHz at 8
310 K using a flow cryostat from Oxford Instruments. The numerical values of T1 were obtained from analysis of the relaxation of free induction decay after the saturating sequence of eight π/2 pulse sequences with use of the saturation
recovery technique.14
16 The duration of the pulses was 3.5 μs, and the intervals were varied within the range of ∼250
400 μs.

3. RESULTS Generally, the experimental data on the time dependencies of the free induction decay were analyzed using the

function M(t)15
17 ½M0
MðtÞ=M0 ¼

∑i Ci expð
t=T1_iÞ

ð1Þ

where M0 is the equilibrium magnetization of the nuclear spins system; M(t) is the amplitude (proportional to nuclear magnetization) of the signal of the free induction decay; Ci represents the relative contributions to M(t) due to specific mechanisms of 1H spin
lattice relaxation, each of which is characterized by the definite value of time T1_i. The results of the analysis are shown in Figure 2. Above 165 K, the system [Zn2(C8H4O4)2 3 N2(C2H4)3] is characterized by a single value of the spin
lattice relaxation time, T1, and the free induction decay in eq 1 is described by only one term of the exponent function. This means that either all three conformations of the dabco molecule are indistinguishable or that only the most stable of them (i.e., the untwisted one) is realized in the system. 20461

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N2(C2H4)3], with the potential energy V(j) of the rotator N2(C2H4)3 being given by 1 V ðjÞ ¼ Vact ð1
cos nϕÞ 2

ð2Þ

where n = 12 is the multiplicity of V(j) because of the matching between the C3 axis of the molecule and the C4 axis of the sorbent structure, j is the rotation angle about the C4 axis, and Vact is the activation energy of reorientations. Then, the Schr€odinger equation for the system can be written as ! p2 ∂2 Ψ 1
Va ð1
cos njÞ ¼
EΨ ð3Þ 2I ∂j2 2

Figure 2. Temperature dependence of 1H NMR (νL = 86 MHz) spin
lattice relaxation time T1(1H) in [Zn2(C8H4O4)2 3 N2(C2H4)3]: solid line was calculated according to eq 5, (9) experimental data for T1 above T = 165 K, (b,O) experimental data for T1 in the range 165
25 K, (Y,y,O, and solid lines) T1 data below 25 K.

At temperatures below 165 K, the function M(t) becomes more complicated and can be matched with an accuracy of ∼5% if two relaxation parameters, T1_1 and T1_2, along with two constituents, C1 = 1/3 and C2 = 2/3, are included in eq 1. Figure 2 shows the results of the analysis: the smaller and greater relaxation times T1_1 and T1_2 correspond to ∼30% and ∼70% of the magnetization amplitude M(t), respectively. The first constituent characterized by relaxation time T1_1 can be related to the untwisted (D3h) form, in accordance with the nearly equal probabilities of the three conformations. This fact makes it possible to relate the second constituent to the sum of left- and right-twisted conformations (D3) of dabco molecules characterized by the same relaxation time T1_2. This breakdown of the 1H spin system into two subsystems definitely shows that conformation transitions of dabco molecules between twisted and untwisted forms are hindered in the low-temperature phase (below 165 K). A sharp change of the free induction decay function M(t) was found also at temperatures below 25 K (Figure 2). In this region, the experimental data for M(t) can be matched with an accuracy of up to ∼7% if at least three terms are used in the sum of eq 1. These terms can correspond to three different sources of spin
lattice relaxation characterized by the times T1_1, T1_2, and T1_3 with relative contributions to M(t) of C1 = 0.2, C2 = 0.3, and C3 = 0.5. It is reasonable to relate these contributions to spin relaxation for various conformations of dabco molecules, i = 1
3, each characterized by a time T1_i. The inequality of these contributions shows the inequality of the concentrations of right and left dabco conformations and, hence, the chiral polarization of the system at the lowest temperatures.

4. DISCUSSION Rotation Dynamics in the High-Temperature Phase. Generally, 1H spin
lattice relaxation in solid-state systems is related to rotational dynamics represented by hindered reorientations and quantum tunneling of definite molecules. In the studied composite, the dynamics can be represented by uniaxial rotations of dabco molecules localized at the C4 axis of [Zn2(C8H4O4)2 3

where E denotes the energy eigenvalues of the rotor. In solids, molecular reorientation freedom is usually considered15
17 to consist of random independent jumps between two sets of allowed orientations determined by the symmetry elements of the lattice and the molecule. These orientations correspond to minima, or wells, in the orientation potential energy surface, V(j), of the molecule; in these wells, the molecules undergo libration motion. The molecules are excited by thermal vibrations of the crystal lattice to libration states above the barrier, where they rotate classically before being de-excited into a libration state within an adjacent well. The activation energy, Vact, can therefore be considered as the energy a dabco molecule needs to overcome the potential barrier between these potential wells, and the correlation time, τ, is the average time that separates reorientation jumps between allowed orientations. According to the Arrhenius equation, the mean lifetime τ (or correlation time) of a molecule in the ground state is given as   1=2     2π 2I Vact Vact ð4Þ exp ¼ τ0 exp τ¼ n Vact RT RT where τ0 = (2π/n)(2I/Vact)1/2 is the libration period of the molecules in their ground state, I is the moment of inertia of the molecule, R is the gas constant, and T is the temperature. If the spin
lattice NMR relaxation is caused by reorientation jumps of such molecules, then T1 is described by the classical equation15
17 ðT1 Þ
1 ¼

2 2 γ ΔS½τ=ð1 þ τ2 ω2 Þ 3 þ 4τ=ð1 þ 4τ2 ω2 Þ

ð5Þ

where γ is the gyromagnetic ratio of the 1H nuclei and ΔS is the fluctuating part of the root-mean-square width of the 1H NMR spectral line. A value of ΔS = 10.7 G2 was calculated previously in ref 13. Figure 2 shows a comparison of the experimental temperature dependency, T1(T), with the theoretical expression in eq 5. As can be seen, between 310 and 165 K, the theoretical model is in good accordance with the experimental data for T1(T). The values obtained for the adjustable parameters are τ0 =1.1  10
14 s and Vact = 4.0 ( 0.5 kJ/mol. It is interesting to compare the above values with the reorientation parameters τ0 = 10
12 s and Vact = 30 ( 3 kJ/mol found for dabco molecules in bulk solid N2(C2H4)3.18 The difference in Vact can be related to the absence of direct intermolecular contacts of dabco molecules at 10.92 Å in the MOF, whereas the distance in bulk solid N2(C2H4)3 is only ∼2.4 Å. The minor complication is with the values of τ0. According to eq 4, a 1-order-of-magnitude 20462

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Figure 3. Experimental dependence of the 1H NMR (νL = 86 MHz) spin
lattice relaxation times T1 on reciprocal temperature showing the √ ∼ 2 change of Vact in the case of untwisted D3h dabco molecules at 165
125 K. (Y,y) T1 values measured at νL = 24.5 MHz.

smaller value of Vact in the sorbent should be accompanied by ∼3times-greater value of τ0, whereas the experiment demonstrates an opposite effect of τ0 diminishing by 2 orders of magnitude. The diminishing can be explained by influence of the so-named “compensation” effect, first described in ref 19. Low-Temperature Phase I. According to Figures 2 and 3, the temperature dependence of the 1H NMR spin
lattice relaxation in [Zn2(C8H4O4)2 3 N2(C2H4)3] terminates abruptly at 165 K. This change correlates well with the heat anomaly in the composite discovered previously at this temperature.18 The thermal effect and the structural phase transition in the compound [Zn2(C8H4O4)2 3 N2(C2H4)3] were related to the second-order Jahn
Teller effect in the [ZnO4]2 cluster and to a reduction of the local symmetry of Zn2+ ions from C4 to C2.18 The symmetry reduction causes a change of the multiplicity order of the potential V(j) from n = 12 to n = 6. If we assume the libration period τ0 = (2π/n)(2I/Vact)1/2 of the molecules in their ground state to be nearly constant, then the 2-fold decrease of n will √ entail an increase of the hindering barrier Vact by a factor of 2. This means that the hindering barrier Vact for reorientation of dabco molecules in the composite [Zn2(C8H4O4)2 3 N2(C2H4)3] is expected to increase from Vact = 4.0 kJ/mol in the hightemperature phase (above 165 K) to Vact ≈ 5.7 kJ/mol in the low-temperature phase (below 165 K). This consideration correlates well with the value of the activation energy Vact(D3h) = 6.6 kJ/mol found from T1(T)_1 experimental data of untwisted dabco molecules between 165 and ∼125 K (Figure 3). However, at lower temperatures, the experimental dependence T1(T)_1 is no longer parallel to the expected dependence represented by the continuous line in Figure 2. As a result, the minimum value of the 1H NMR spinrelaxation time, T1_1 ≈ 20 ms, is ∼250 times longer than the expected value of T1min ≈ 0.08 ms calculated according to eq 5 for the model of activation mechanism of dabco rotations (Figure 2). It is also surprising that the T1_1 values are temperature-independent between ∼80 and ∼30 K. These facts definitely show that classical over-barrier jumps of untwisted dabco molecules are not responsible for the mechanisms of

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reorientation and NMR spin
lattice relaxation in the lowtemperature phase of composite [Zn2(C8H4O4)2 3 N2(C2H4)3]. The explanation is instead based on the solution of the Schr€odinger equation (eq 3) for the case when the energy eigenvalues E correspond to the libration motion of the rotor. In this case, the main mechanism of spin relaxation can be associated with quantum tunneling of the hydrogen atoms in dabco through the potential barrier V(j). According to the quantum theories of rotation dynamics and NMR spin
lattice relaxation developed in refs 20
24, the apparent activation energy Vtun = 1.0 kJ/mol determined from the low-temperature slope of the T1(T)_1 dependence (between 125 and ∼60 K, Figure 3) can be identified as the energy difference between the ground and first excited states of the untwisted D3h dabco rotator, or the ground-state tunneling splitting. The temperature independence of the spin
lattice relaxation time observed below 60 K (Figure 2) indicates that only the ground state is occupied. Judging from Figures 2 and 3, the hindering barrier Vact(D3) for reorientation of twisted dabco molecules exceeds the value of Vact = of 6.6 kJ/mol found for untwisted molecules. Such a conclusion follows from the fact that the spin
lattice relaxation time T1_2 of twisted (D3) dabco molecules is several times longer than T1_1 of untwisted (D3h) dabco molecules. The above consideration explains why the starting 1H spin system characterized by a solitary high-temperature spin
lattice relaxation T1(T) splits, in the low-temperature phase I, into two subsystems characterized by relaxation times T1_1 and T1_2. According to the crystal structure data of [Zn2(C8H4O4)2 3 N2(C2H4)3] and DFT calculations of dabco molecules, the shortest distance, D(H 3 3 3 O) = 2.518 Å, in the case of the untwisted configuration is ∼0.1 Å longer than the value of D(H 3 3 3 O) = 2.432 Å calculated for the twisted configuration. The difference in D(H 3 3 3 O) unequivocally indicates that the hindering barrier for rotational mobility of the twisted dabco rotator, Vact(D3), should be increased relative to the barrier for rotational mobility of the untwisted dabco molecules, Vact(D3h). However, the real Vact(D3) value in this case cannot be determined directly because the spin
lattice relaxation time T1_2 of the twisted (D3) dabco molecules is almost temperature-independent between 165 and ∼130 K. In parallel with the above consideration of the spin
lattice relaxation time T1_1 of the untwisted (D3h) dabco molecules, the similar behavior of T1_2 definitely indicates the quantum tunneling mechanism of rotations of the twisted (D3) dabco molecules. Such a conclusion is independently supported by the fact that the spin
lattice relaxation times T1_1 and T1_2 do not depend on the Larmor frequency νL (Figure 3), as expected according to the quantum theory of NMR spin
lattice relaxation.20
24 The noticeable difference in the temperature dependences of the spin
lattice relaxation times T1_1 and T1_2 can be related to the increased hindering barrier Vact(D3) for rotations of the twisted dabco molecules, resulting in a more complicated spectrum of tunnelling states for the twisted (D3) dabco molecules with respect to the untwisted ones. Phase Transition and Chiral Polarization at 25 K. The sharp change in T1 of [Zn2(C8H4O4)2 3 N2(C2H4)3] at ∼25 K can be supposed to be an analogue of the previously observed T1 change in the metal
organic framework [CH3)2NH2]Zn(HCOO)3 at ∼65 K, where the transition to the low-temperature glassy state has been confirmed.1 However, there is a noticeable feature of the low-temperature spin
lattice relaxation in [Zn2(C8H4O4)2 3 N2(C2H4)3]: Below 25 K, three different 20463

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times, T1_1, T1_2, and T1_3, are observed, and the amplitudes, C1 = 0.2, C2 = 0.3, and C3 = 0.5, are unequal. Such a distribution might indicate a structural phase transformation related to some ordering of dabco conformers playing the role of pseudospins in standard molecular field theories of phase transitions.25,26 The interaction of the dabco pseudospins at distances of ∼10 Å in the MOF can be mediated by the layers of zinc terephthalate. The key elements in this interaction are the above-mentioned N
C
H 3 3 3 O bridges between the dabco molecules and the carboxyl groups [
COO
] of terephthalate anions mediating such indirect (or “supramolecular”) interactions along the [001] axis (Scheme 1). The terephthalate anions, [C8H4O4]2
, can also mediate the ordering of dabco pseudospins within (001) layers because the anion librations should be correlated with the ligand rotation.27 The combination of uniaxial ordering along the [001] axis and two-dimensional ordering within (001) layers can lead to a threedimensionally ordered structure with left-twisted, right-twisted, and untwisted dabco molecules that can be arranged in any one of 17807 roto space groups of symmetry recently derived in ref 28. In this case, the inequality of concentrations (i.e., C2 = 0.2 and C3 = 0.5)—and, hence, the chiral polarization of the system— can result from causal factors similar to those responsible for the precipitation of right and left forms of optically active crystals from the racemate. However, it is striking that there are different spin
lattice relaxation times T1_2 and T1_3, which are the microscopic parameters of the right-twisted and left-twisted forms of dabco molecules in the studied composite system. The detected difference can be considered as an analogy of the previously discovered effect of doubling the fine structure of an NMR spectrum when changing from an optically inactive (racemic) mixture to an optically active mixture of handed, or chiral, isomers. The effect was first discovered for solutions of racemic and optically active dihydroquinine in an achiral solvent29 for which the 13C NMR chemical shifts of the enantiomers appeared to be different and the difference was nearly proportional to the value of the optical activity of the system. Later, similar results were also obtained for 31P NMR data for mirror antipodes of a great number of organophosphorous compounds.30 The phenomenon has been attributed to the influence of the so-called “chiral polarization” of the studied

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systems, but the intrinsic mechanism of the physical difference of right-handed and left-handed molecules in the chiral-polarized solutions is still unclear.31
33

5. CONCLUSIONS According to 1H NMR spin
lattice relaxation data for the metal
organic framework [Zn2(C8H4O4)2 3 N2(C2H4)3], the conformational states of N2(C2H4)3 (dabco) molecular rotors are mixed in the high-temperature phase stable above 165 K. The fast transitions between the chiral (twisted) and achiral (untwisted) dabco forms are induced by the dynamic pseudoJahn
Teller effect in the zinc terephthalate framework. In the low-temperature phase I, the twisted and untwisted conformation states of dabco are observed separately. The stabilization of the conformation states of dabco molecules is related to the influence of conditions of quantum confinement in the framework distorted by the static pseudo-Jahn
Teller effect. At the lowest temperatures (below 25 K, phase II), the chiral polarization of the composite [Zn2(C8H4O4)2 3 N2(C2H4)3] is revealed with different spin
lattice relaxation times, T1_1, T1_2, and T1_3, related to the untwisted, right-twisted, and left-twisted conformation states of dabco. The chiral ordering can be related to the indirect (supramolecular) interaction of N2(C2H4)3 (dabco) conformers mediated by terephthalate [C8H4O4]2
anions in the structure of the composite. The resulting lowsymmetry structure probably belongs to one of recently derived roto space groups of symmetry.28 It can be expected that, in the case of the thin-film form of [Zn2(C8H4O4)2 3 N2(C2H4)3], the distribution of states of dabco molecules can be controlled by an external impact,2 and the chiral conformations of N2(C2H4)3 can be regarded as a novel type of memory element for a hypothetical quantum (“chiratronic”) computer. ’ ASSOCIATED CONTENT

bS

Supporting Information. DFT calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the SB RAS (Grant 100). The article is devoted to Prof. Renad Z. Sagdeev in honor of his 70th birthday. ’ REFERENCES (1) Besara, T.; Jain, P.; Dalal, N.S.; Kuhns, P. L.; Reyes, A. P.; Kroto, H.W.; Cheetham, A. K. Proc. Natl. Acad. Sci. U.S.A. 2011, 108 (17), 6828–6832. (2) Stroppa, A.; Jain, P.; Barone, P.; Marsman, M.; Perez-Mato, J. M.; Cheetham, A. K.; Kroto, H. W.; Picozzi, S. Angew. Chem., Int. Ed. 2011, 50 (26), 5847–5850. (3) Balzani, V.; Credi, A.; Raymo, F.; Stoddart, F. Angew. Chem., Int. Ed. 2000, 39, 3348–3391. (4) Kottas, G. S.; Clarke, L. I.; Horinek, D.; Michl, J. J. Chem. Rev . 2005, 105, 1281–1376. 20464

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