Thermal properties of Zn2(C8H4O4)2•C6H12N2 metal-organic framework compound and mirror symmetry violation of dabco molecules.

Thermal properties of Zn2(C8H4O4)2•C6H12N2 metal-organic framework compound at 8-300 K suggest the possibility of subbarrier tunnelling transitions between left-twisted (S) and right-twisted (R) forms of C6H12N2 dabco molecules with D3 point symmetry. The data agree with those obtained for the temperature behavior of nuclear spin-lattice relaxation times. It is shown that there is a temperature range where the transitions are stopped. Therefore, Zn2(C8H4O4)2•C6H12N2 and related compounds are interesting objects to study the effect of spontaneous mirror-symmetry breaking and stabilization of chiral isomeric molecules in solids at low temperatures.

Introduction

Chirality-related interactions are demonstrated by chiral molecules, i.e. those that can exist in both left- and right-handed forms. According to molecular quantum mechanics, such molecules appear in their ground state which is a symmetrical superposition of these two chiral states. However, biological systems are asymmetric (superselection phenomenon) due to fundamental parity violations[1-3] or the concept of environmental decoherence[4-6]. As it was discussed earlier, it would be of interest to study the stabilization of chiral molecules in solids at low temperatures to simulate the conditions of the cold scenario[7]. However, the expected fundamental conclusions are still not supported by detailed analysis of the interactions within crystal structures where the stabilization effect is not suppressed by other impacts[8, 9]. In this respect, of high interest are metal-organic framework compounds with large pores, open internal channels, and large internal surface areas[10-12].

One such typical example is Zn2(C8H4O4)2•C6H12N2 crystal. It is composed of tetragonal layers of zinc terephthalic acid Zn(C8H4O4) linked by 1,4-diazabicyclo[2.2.2] octane molecules (C6H12N2, or dabco). Dabco molecules have three isomeric forms: one untwisted form with D3h symmetry, one left-twisted (S) and one right-twisted (R) form with D3 symmetry each (Fig. 1). Dabco molecules are dynamically disordered around the axis of Zn2(C8H4O4)2•C6H12N crystal. The distance between them is ~ 7 Å, so they have no direct contacts with each other[11].

Figure 1

Crystal structure of Zn2(C8H4O4)2• C6H12N2, space group P4/mmm; a = 10.93, c = 9.61 Å; Z = 1; T = 223 К[11]. Pillar dabco molecules are shown as dynamically disordered (top). Left- and right-twisted D3 and untwisted D3h conformations of dabco molecules (bottom).

According to our calculations of isolated dabco molecules, their degenerate energy states correspond to twisted D3(S) and D3(R) forms, and the energy barrier (Ea) between these two states can vary between 0 and 0.36 kJ/mol depending on the external conditions[13]. Consequently, D3(S) ↔ D3(R) transforms can happen as: (1) barrier-free transitions; (2) activation transitions to overcome the barrier; (3) subbarrier tunnelling transitions. Low activation barrier Ea between D3(S) and D3(R) forms makes prospective studying tunnelling transitions between these forms, in contrast to those between L- and D-forms of amino acids in solids with Ea ~ 300 kJ/mol barrier[9].

The untwisted D3h state of the dabco molecule corresponds to its transition state and therefore its energy is equal to the value of the energy barrier Ea (Fig. 1)[13]. However, this state can be stable in crystals, and the untwisted molecule can move using both the activation and the tunnelling mechanisms.

As it was discovered earlier, there are three phase transitions in Zn2(C8H4O4)2•C6H12N2 [14-16]. Temperature behavior of spin-lattice relaxation times studied with 1H NMR T1 demonstrates the effects of tunnelling transitions starting between D3(S) and D3(R) forms of dabco molecules at ~165 K, the violation of these transitions at ~60 K, and substantial difference between the values of spin-lattice relaxation data for dabco conformers at <25 K. In this work we analyze thermal energies of dabco molecules in Zn2(C8H4O4)2•C6H12N2 to show that these effects are thermally possible.

Theoretical background

Over-barrier transitions (activation) are characterized by the correlation timewhere kB is the Boltzmann constant, τa0 is the pre-exponential factor for the Arrhenius law, T is the temperature.

Subbarrier tunnelling is described by the Shrödinger equation and is characterized by the correlation timewhere m is the mass of the tunnelling particle, τt0 is the pre-exponential factor for tunnelling transitions (inverse vibrational frequency of the particle in the potential well), E is the kinetic (thermal) energy of the particle, L is the width of the activation barrier, ħ is the Planck constant.

As is well known, thermal energy of atoms and molecules is determined by the temperature of the solid and can be calculated as E = Cp·T, where Cp is the thermal capacity of the solid at constant pressure.

In solids, thermal energy is unevenly distributed between atoms and molecules, and at each moment the amplitude and the energy of thermal vibrations for some part of particles can be higher or lower than their average values. To make the transitions possible, some thermal energy is needed. Activation transitions require that some part of particles have E > Ea, while tunnelling transitions proceed at E < Ea.

We assume that tunneling and activation transitions have the same reaction coordinate. Then for tunnelling transitions with reaction coordinate coinciding with that of reorientational motion (maintaining D3h and D3 symmetries), the minimum distances between the atoms are DH = 1.08 Å (for hydrogen atoms) and DC = 0.65 Å (for carbon atoms). For tunnelling transitions between D3(S) and D3(R) these distances are DH = 0.66 Å and DC = 0.15 Å[13]. Both DC values are smaller than the covalent radius of the carbon atom (rC ~ 0.70 Å). Hence, we can assume that carbon atoms change their positions during tunnelling without having to overcome a barrier. DH values exceed the covalent radius of the hydrogen atom (rH ~ 0.30 Å). In this case, the barrier has finite width L and reaches its minimum of ~0.06 Å for tunnelling transitions between D3(S) and D3(R) dabco forms. The comparison of distances between hydrogen and carbon atoms for both types of tunnelling transitions suggests that the tunneling between twisted forms has the highest probability.

The activation barrier between these two forms in Zn2(C8H4O4)2•C6H12N2 crystal is unknown. Moreover, the width and the height of the activation barrier fluctuate due to thermal vibrations. They can change when the temperature decreases and consequently affect the tunneling processes. Nonetheless, the value of the parabolic barrier can be estimated as[7]:where Tc is the onset temperature of the tunnelling processes (in our case, 165 K)[14-16], L = 0.06 Å, and m is the particle mass. In our case, m is the sum of masses of 12 hydrogen atoms. Carbon atoms can be excluded because of their barrier-free motion, and nitrogen atoms are not involved in tunnelling transitions because they are located along C3 axis of the dabco molecule.

Results and Discussion

Figure 2 presents temperature dependence Cp·T, where Cp is the thermal capacity of Zn2(C8H4O4)2•C6H12N2 obtained in ref. 17. The same figure shows E a values for dabco molecules. Values E a = 0.22 kJ/gr_at and E a = 0.37 kJ/gr_at correspond to experimental values Ea = 4.0 kJ/mol and Ea = 6.6 kJ/mol, and E a = 0.43 kJ/gr_at corresponds to the calculated Ea = 7.7 kJ/mol, respectively. E a values are assumed to correspond to activation energies only of hydrogen and carbon atoms of the dabco molecule, and nitrogen atoms are not involved in the reorientation. All values of Cp·T and Ea were normalized to one gram-atom to make easier comparison of the results obtained from different methods.

Figure 2

Left: temperature dependence of the thermal energy Cp·T in Zn2(C8H4O4)2•C6H12N2 (о). Red horizontal line corresponds to the activation barrier (E a) between energy minima of D3(S) and D3(R) forms of dabco molecules. Blue horizontal lines correspond to the experimental activation barriers (E a) obtained for the reorientation of dabco molecules in Phases I and II. Right: temperature dependence of 1H NMR T1 in Zn2(C8H4O4)2•C6H12N2 presented in the double logarithmic scale. C, Ci and ci (i = 1, 2, 3) are the fractions of the components in the FID. Ea are experimental activation barriers for the reorientation of dabco molecules. Vertical dashed arrows indicate the position of phase transition temperatures according to NMR data[14–16].

Since in Phase I thermal energy Cp·T > 0.43 > 0.22 kJ/gr_at, above Tc all dabco conformers can overcome barriers E a = 0.43 kJ/gr_at and E a = 0.22 kJ/gr_at through the activation mechanism, which agrees with T1 NMR data (Fig. 2). The temperature dependence of 1Н NMR T1 in Zn2(C8H4O4)2•C6H12N2 at 310–165 K obeys the classical theory of nuclear spin-lattice relaxation and is characterized by a single-exponential recovery of the free induction decay (FID)[18, 19]. The activation mobility of dabco molecules is characterized by one barrier Ea = 4 kJ/mol and τa0 = 1.1·10−14 s. It means that in Phase I either two twisted forms and one untwisted form of dabco molecules are indistinguishable in their energies, or that the system has only one of three conformations (e.g., untwisted) as energetically excited[14, 16].

Thermal energy Cp·T varies in Phase II from 1.0 to 0.2 kJ/gr_at. These thermal energies make it impossible for all particles to overcome the barrier with E a = 0.43 kJ/gr_at by the activation mechanism, as well as the barrier E a = 0.37 kJ/gr_at. Hence, this phase suggests tunnelling transitions. Indeed, at 165–60 K the activation mobility of particles is violated. Firstly, the double-exponential recovery of FID is observed[14, 16]. The contribution of FIDs characterized by longer time T1 L and shorter time T1 S to the total magnetization are С1 = 2/3 and С2 = 1/3, respectively. This double-exponential recovery of FID may indicate that activation mobility of dabco molecules is hindered and that energy states of their conformers become different. From the obtained С1 and С2 values we can conclude that the energy states were equally stabilized for each conformer. Since D3(S) and D3(R) forms are characterized by the same time T1 L, they are indistinguishable in energy. These dabco molecules can make tunnelling transitions under the barrier Ea = 7.7 kJ/mol. Their states are energetically more favorable than those of the untwisted form. This follows from the fact that if molecules are distributed over their energy states in crystals according to the Boltzmann statistics, then the energy population for the untwisted form (C2) in Zn2(C8H4O4)2•C6H12N2 turns out to be lower than that of two twisted forms (C1). The conclusion correlates with quantum chemical calculations which show that the untwisted form of a free dabco molecule (D3h symmetry) is its transition state[13]. Secondly, in the range 165–120 K T1 L is virtually temperature independent, which indicates tunnelling transitions[14, 16]. The T1 S behavior at these temperatures corresponds to the activation process with Ea = 6.6 kJ/mol and τa0 = 0.3·10−14 s. Therefore, untwisted molecules continue to participate in activation transitions. Below 100 K dabco molecules are capable mostly of tunnelling transitions, since Cp·T < 0.37 kJ/gr_at. Therefore, the structure of untwisted dabco molecules cannot correspond to the stable state and must get its symmetry lower.

As follows from Fig. 2, in Phase III tunnelling transitions are possible. On the other hand, due to possible asymmetry of the double-well potential for D3(S) and D3(R) forms the transitions can be stopped. This is indicated by the behavior of anomalous part of the heat capacity of Zn2(C8H4O4)2•C6H12N2 at the second order phase transitions ~60 K[20]. Below ~60 K, the anomalous part of the specific heat demonstrates exponential behavior, which suggests tunnelling of less stable right-enantiomers into more stable left-enantiomers (Salam model)[2, 3, 20].

In Phase IV, thermal energy is Cp·T ≤ 0.02 kJ/gr_at. In this case, only tunnelling transitions are possible, and, according to equation (2), time τt must reach its highest value here. However, the behavior of T1 (Fig. 2) does not correspond to classical views on tunnelling processes[7, 21, 22]. T1 grows when the temperature decreases (like T1 during activation transitions). But there is no consistent activation mobility of the particles neither. Experimental data on time dependences of FID for these temperatures makes it possible to distinguish at least three components (c1, c2, c3) characterized by three different T1 values (Fig. 2). This can mean that D3(S) and D3(R) energies are not equal at the lowest temperatures and that the system as a whole must be characterized by chiral polarization[14-16]. The discovered difference between Т1 times can be considered as an analogue of the previously discovered effect when the multiplicity of the NMR spectrum is doubled when passing from a optically inactive (racemic) to optically active mixtures of chiral isomers[23, 24].

As was shown earlier, the mechanism of phase transition from Phase III to Phase IV in our model can be associated with the ordered packing of untunnelling and non-reorienting D3(S) and D3(R) dabco molecules[14-16]. In this case, violation of D3(S) ↔ D3(R) symmetry can be due to random factors similar to those affecting the precipitation of R- and S-forms of optically active crystals from racemates[25]. However, the fact that there are three values c1, c2, and c3 (Fig. 2) obtained from the analysis of FID suggests some ambiguity of the proposed model. We can assume that further temperature decrease should lead to further phase transitions and molecular ordering. Also, some additional mechanism to cause non-exponential FID and nuclear spin-lattice relaxations is also possible[16].

Note that we do not consider here the mobility of C8H4O4 2− anions, because their high activation barrier (>36 kJ/mol) makes them perform only slow reorientations about the second-order axis. There are no fluctuations of intramolecular dipole-dipole interactions, the fluctuations of intermolecular dipole-dipole interactions are small, and reorientation of C8H4O4 2− anions is not evidenced by 1Н NMR T1 measurements[14, 26–28].

Conclusions

Thermal properties of Zn2(C8H4O4)2•C6H12N2 crystals suggest that there is a possibility that mirror symmetry can be violated between D3(S) and D3(R) forms of dabco molecules. Most interesting are the lowest temperatures where all conformers can be stabilized in their local positions.

Structural transformations associated with the ordering of dynamically disordered dabco molecules in Zn2(C8H4O4)2•C6H12N2 during phase transitions can, in principle, be characterized using the approaches described in refs 29 and 30. Here we can only describe the structures expected in different phases. In the high-temperature Phase I, twisted and untwisted dabco molecules are fully disordered. In the Phase II, the crystal structure is built of the chains of dabco molecules, some of which are composed only of untwisted forms and other only of twisted forms. In Phase III, the twisting of dabco enantiomers is expected to be hindered. Finally, when the interaction between the chains becomes prevailing, the crystal structure is supposed to be chirally ordered in Phase IV.

Note that according to a recent study of [Zn2(C8H4O4)2•C6H12N2] properties, the Phase II → Phase I transition can be interpreted as an order-disorder phase transition associated with some structural disorder of C8H4O4 2− anions[12]. However, dabco molecules remain dynamically disordered and their role in the phase transition is not defined.

Thus, in our opinion, metal-organic framework compound [Zn2(C8H4O4)2•C6H12N2] and related crystals[10–12, 31] containing racemic mixtures of chiral molecules are convenient systems to develop the approaches aimed at controlling molecular transitions from racemic to chirally polarized states. A special feature of these systems is the absence of direct contacts between chiral molecules in crystals. Such systems are interesting in terms of studying the stabilization of chiral molecules in solids at low temperatures and can serve as models for the conditions of the cold scenario of life origin on the Earth[7].

Methods

Heat capacity was measured at 8.98–299.57 K using a computerized vacuum adiabatic calorimeter well tested by measurements of various compounds including sorbents metal-organic framework compound [Zn2(C8H4O4)2•C6H12N2]. The details of the synthesis, experimental conditions, and heat capacity values can be found in work[17]. The 1H NMR spin-lattice relaxation time T1 of [Zn2(C8H4O4)2•C6H12N2] was measured with a Bruker SXP 4-100 device at 8–300 K and was previously analyzed in a number of works[14-16].