Unequal torsional rotations driven by normal to modulated phase transition in 4-biphenylcarboxy coupled L-phenylalaninate governed by non-covalent constraints

Amongst the derivatives of 4-biphenylcarboxylic acid and amino acid esters, the crystal structure of 4-biphenylcarboxy-(L)-phenylalaninate is unusual owing to its monoclinic symmetry within a pseudo-orthorhombic lattice. The distortion is described by disparate rotational property around the chiral centers ( ϕ chiral ’ -129 degrees and 58 degrees) of the two molecules in the asymmetric unit. Each of these molecules comprise of planar biphenyl moieties ( ϕ biphenyl = 0 degrees). Using temperature dependent single crystal X-ray diﬀraction experiments we show that the compound undergoes a phase transition below T ∼ 124 K that is characterized by a commensurate modulation wave vector, q = δ (101), δ = 12 . The (3+1) dimensional modulated structure at T = 100 K suggests that the phase transition drives the biphenyl moieties towards non coplanar conformations with signiﬁcant variation of internal torsion ( ϕ maxbiphenyl ≤ 20 degrees). These intramolecular rotations lead to dimerization of the molecular stacks that are described predominantly by intermolecular tilts and small variations in intermolecular distances. Atypical of modulated structures and superstructures of biphenyl and other polyphenyls, ϕ biphenyl of one independent molecule is two to four times larger than the other. We suggest that while the rotations arise from intramolecular steric factors, competing intermolecular H–C ··· C–H contacts and weak C–H ··· O hydrogen bonds govern the distinctively unequal torsional property of the molecules.


I. INTRODUCTION
Molecular biphenyl has been investigated extensively for its stability and conformation in different thermodynamic states. At ambient conditions, the differences in the conjugation states of the π-electrons are governed primarily by the twist about the central C-C single bond in the order: 40 deg -45 deg in gas phase, 20 deg -25 deg in solution and 0 deg (mutually coplanar) in the solid state in centrosymmetric monoclinic space group P 2 1 /a [1][2][3][4].
The planar conformation due to constraints from intermolecular interactions is energetically unfavourable and steric hindrance between the ortho hydrogen atoms is compensated for by out of plane dynamic disorder and in plane displacements of those hydrogens away from each other [4][5][6][7][8][9] A recent study has also suggested the role of intramolecular exchange energy between single bonded carbon atoms in stabilizing the planar conformation [10]. Absorption and fluorescence studies showed additional bands in their spectra at low temperatures (T ) [11,12]. T -dependent Raman spectroscopy and Brillouin scattering experiments have suggested two phase transitions at T c1 = 42 K and T c2 = 17 K respectively [13][14][15][16]. The phase transition at T c1 is continuous and governed by a soft mode associated with the torsion about the central C-C single bond followed by discontinuous changes at T c2 . Inelastic neutron scattering experiments on its deuterated form confirmed the phase transitions with appearance of additional satellite reflections [17]. The modulation wave vector (q) was determined to be q I = δ a a * + 1 2 (1 − δ b )b * and q II = 1 2 (1 − δ b )b * at the intermediate and low temperature phases respectively and were found to vary with temperature, suggesting an incommensurate nature of the modulation [17]. The modulated structure of the low temperature phase II was described within an acentric superspace group symmetry P a(0σ 2 0)0 [18][19][20] and found to be essentially associated with small modulation of translation and rotation (ω) normal to the mean molecular plane, and a significant torsion (ϕ) between the phenyl rings [21][22][23][24]. Theoretical studies have suggested that competition between intramolecular and intermolecular forces drives the phase transition towards the incommensurately modulated states [25][26][27][28].
The fundamental property of flexibility in conformations have made biphenyl an excellent candidate to tune in multifaceted properties in materials. Torsion between the rings has been demonstrated to regulate conductivity of single molecule biphenyl-dithiol junctions [29][30][31][32], tune in thermopower as function of twist angle [31], degeneracy of energy states on substrates [33] and theoretically suggest wide band gap semiconducting properties of its derivatives [34].
On the other hand, biphenyl derivatives have also been reported to influence and increase the efficiency of photophysical properties [35,36]. Planar biphenyl molecule in solid state favours maximum intramolecular conjugation of π electrons as well as increases the probability of interactions between delocalized electrons that could aid in optimal stacking of molecules.
Coupling reaction mechanism [37] was successfully employed to synthesize 4-biphenylcarboxy protected amino acid esters of L-serine, L-tyrosine, L-alanine, L-leucine and L-phenylalanine [38,39]. In solid state, the compounds crystallize either in acentric orthorhombic space group symmetry P 2 1 2 1 2 1 or the monoclinic subgroup P 2 1 [38,39]. Crystal packing in these systems is determined by π···π stacking between the biphenyl fragments and linear strong hydrogen bonds between the amino acid ester moieties.
We presumed that the biphenyl moieties in these chemically coupled systems could influence the bioactive amino acid esters and vice-versa with respect to evolution or suppression of translational and rotational degrees of freedom in their crystal structures at some thermodynamic condition. Reanalyzing all their crystal structures, the system of 4-biphenylcarboxy-(L)-phenylalaninate attracted our attention because the structure appeared to be similar to the L-tyrosine analogue albeit the monoclinic distortion (Table I, [39]) and two crystallographically independent formula units [Z = 2 [40], Fig. 1(a)] in the crystal structure of the former. The torsion about the chiral center is significantly different for the independent molecules while the rest of the rotations are similar [ Fig. 1(a), [39]]. Each of these molecules consist of coplanar biphenyl moieties which are stacked along a and b respectively while the amide groups are connected by intermolecular N-H···O hydrogen bonds [ Fig. 1(b), [39]].
In the present study, T -dependent phase transition of 4-biphenylcarboxy-(L)-phenylalaninate has been investigated using single crystal X-ray diffraction experiments. The low temperature phase II is found to be a 2a×b×2c superstructure of the high temperature (phase I) structure. The superstructure is described within the (3 + 1)D superspace approach as a commensurately modulated structure [18,[41][42][43][44]. Structural properties of the phase I and the modulated structure have been tabulated and compiled within t-plots (t = phase of the modulation). The origin and stability of phase II is discussed in terms of intra-and intermolecular HC···CH contacts and intermolecular hydrogen bonds and plausible mechanism of the phase transition is suggested.

II. EXPERIMENTAL
A. Temperature dependent single crystal X-ray diffraction Single crystals of the compound used in this study were obtained from those reported by Sasmal et al. [39]. The crystals were protected in oil under mild refrigeration. Single crystal X-ray diffraction (SCXRD) experiments were performed on a Agilent SuperNova, Eos diffractometer employing CuKα radiation. Temperature of the crystal was maintained by a open flow nitrogen cryostat from Oxford Cryosystems. During cooling, visual inspection of diffraction images revealed weaker reflections in addition to strong reflections at low temperatures. Diffraction images collected at T = 150 K, 140 K and 130 K to 114 K in steps of ∆T = 2 K showed that the weaker diffuse features appear at T = 124 K that condense into satellite reflections at T = 122 K (Table I, Fig. S1 in [45]). The transition temperature is significantly higher than that of molecular biphenyl (T c,biphenyl = 42 K).
On the other hand, related polyphenyls p-terphenyl and p-quarterphenyl undergo phase transition towards superstructure phases at much higher critical temperatures (T c,terphenyl ≈ 190 K [46], T c,quarterphenyl ≈ 233 K [47]). Complete diffraction data were collected at T = 160 K and T = 100 K respectively.
Determination of lattice parameters and data reductions were performed using the software suite CrysAlisPro [48] (Table I, Table S1 in [45]). Satellite reflections of first order (m = 1) observed below T c could be indexed with modulation wave-vector q = (σ 1 ,0,σ 3 ), 2 with respect to the basic monoclinic lattice. Here, the q = 1 2 (101) is perpendicular to the b axis consistent with monoclinic symmetry while in molecular biphenyl q I violates monoclinic symmetry and q II is parallel to b [17]. Using the plugin program NADA [49] in CrysAlisPro, deviation of the σ's as function of T from a rational value of 0.5 were found to be within their e.s.ds (Table I), indicating a commensurate nature of the modulation. Reflections at T = 100 K were indexed by four integers (hklm) using a basic monoclinic b-unique lattice (Table I, Table S1 in [45]) and modulation wave vector, q = ( 1 2 ,0, 1 2 ) and data integration was performed. Empirical absorption correction was performed using AbsPack program embedded in CrysAlisPro. The monoclinic lattice as well as the reflection conditions suggest the superspace group P 2 1 (σ 1 0σ 3 )0 with σ 1 = σ 3 = 1 2 [19,20].  Table S1 in [45] for reflections used. The crystal structure of the room temperature phase (phase I hereon) was redetermined at T = 160 K using Superflip [50] and refined using Jana2006 [51] and Jana2020 [52].
Atoms were renamed with suffixes 'a' and 'b' for the two independent molecules 'A' and 'B' [ Fig. 1(a)]. Anisotropic atomic displacement parameters (ADPs) of all non-hydrogens atoms were refined. Hydrogen atoms (H) were added to carbon and nitrogen atoms using riding model in ideal chemical geometry with constraints for isotropic ADPs [U iso (H) = 1.2U eq (N), U iso (H) = 1.2U eq (C aromatic ) and U iso (H) = 1.5U eq (C sp3 )]. Since β is close to 90 • , the integrated data was tested for twinning employing twofold rotation parallel a as twin law. This twin law is a true symmetry element in case of a hypothetical orthorhombic lattice with point group symmetry 222 [53,54]. The fit of the structure model improved (compare R obs F = 0.0463 to 0.0408) and volume of the second component refined to ∼ 2% (Table  S2 in [45]). Finally, positions of the H atoms of NH groups and parameter corresponding to isotropic extinction correction was refined that further improved R obs F values (= 0.0393, Table S2 in [45]). The crystal structure reproduced the values for intramolecular rotations reported those for the structure at T = 200 K [ϕ chiral = ϕ 1 (hereon) and ψ in Fig. 1(a)].
In addition, we also observe that the coplanar biphenyl rings are significantly rotated with respect to the amide groups [at T = 200 K: ϕ 2 = 32.8 deg and 31.2 deg [39], at T = 160 K in Fig. 1(a)] which also remains invariant as function of temperature. The modulated structure of phase II at T = 100 K was refined using Jana2006 and Jana2020. Fractional co-ordinates of all non-hydrogen atoms from the crystal structure at T = 160 K were used as starting model and the average structure was refined against main reflections. In successive steps, an incommensurate (IC) model described by one harmonic wave for displacive modulation describing the atomic modulation functions (AMFs) and basic parameters for anisotropic ADPs for all atoms was refined against main and satellite reflections that resulted in good fit to the diffraction pattern (R obs F = 0.0425). However, ADPs of four non-hydrogen atoms were found to be non-positive definite. Since the components of q, σ 1 and σ 3 are rational, three commensurately modulated structures were pursued by fixing the initial phase of the modulation to values, t 0 = 0, 1 4 and 1 8 respectively. While the former two t 0 values describe monoclinic B2 1 space group symmetry for the equivalent 3D 2a × b × 2c superstructure, the third corresponds to triclinic B1 symmetry. The commensurately modulated structure (C) model corresponding to t 0 = 1 4 resulted in the best fit to the diffraction data (R obs F = 0.0426) including ADPs of all atoms positive definite. As the atomic modulation functions (AMFs) have sinusoidal character, the residual values are similar to the IC model (Fig. 2, Fig. S2-S4 and Table S2 in [45]) However, the C model at t 0 = 1 4 is described with either cosine or sine waves for the AMFs (equal to number of refinable fractional coordinates in the equivalent superstructure) reducing significantly the number of refinable parameters as compared to the IC model (compare N C = 649 to N IC = 811, further tests in [45]). The final C model was further improved by refining the parameter corresponding to isotropic extinction correction and AMFs and positions of hydrogen atoms of NH groups (R obs F = 0.0419, Table S2 in [45]).

A. Structural phase transition and unequal distortion of molecules
In the present case, the monoclinic symmetry is retained below T c unlike monoclinic to triclinic distortion at disorder-order phase transition of p-terphenyl [55] and p-quarterphenyl [56]. In the final commensurately modulated structure model with t 0 = 1 4 , sections corresponding to t = 1 4 and 3  Table S4 in [45]). Notably, the rotations in the present structure are significantly larger than those reported for molecular biphenyl (ϕ ± 5.5 deg in ref. [21,22]) but smaller than those in the low temperature superstructure of p-terphenyl and p-quarterphenyl (Maximum ϕ terphenyl,quarterphenyl 23 deg in ref. [55,56,62]).
Another distinctive property of the modulated structure is the unequal modulation for the two different moieties where u biphenyl > u phenylalaninate (Table S4 in [45]). Therefore, the variation in torsions ϕ 1 and ψ are smaller θ. It could therefore be argued that the dimerization of biphenyl molecular stacks below T c are predominantly governed by distortion described by molecular rotations rather than intermolecular distances. On the other hand, intermolecular distances between aromatic rings of L-phenylalaninate vary similarly to the biphenyls albeit significantly smaller interstack rotations, θ < 3 deg (Fig. S5 in [63]).
The increased distortions are also accompanied by suppression of dynamic disorder below T c . For example, the carbon atoms at ortho (C14, C16, C19, C23) and meta (C13, C17, C20, C22) positions are strongly displaced (Fig. 5, Table S4 and S5 in [45]). Subsequently, the ADPs are significantly reduced as compared to phase I (Fig. 5, Table S5 in [45]). Notably, decrease of the ADPs (U eq ) from T = 160 K to T = 100 K is larger for those of molecule

B. Competitive forces governing modulations
Structural studies in the 3D phase of molecular biphenyl have suggested that the orthohydrogen atoms are displaced away in the plane of the rings to minimize steric hindrance [3,4,6]. On the other hand, dynamic disorder predominantly governed by torsional vibrations around the long molecular axis [22] is predicted to balance the planar conformation of biphenyl favourable for crystal packing [9]. As short as 1.98Å in phase I (Table II), these contacts are shorter than the predicted values for twice van der Waals radius for hydrogen (r = 1.1-1.2Å [64,65]). In the modulated structure, we observe that the distances between the ortho-hydrogen atoms are marginally but consistently larger than those in phase I (Table II) that could suggest that the torsional modulations aid in minimization of the presumed steric hindrance below T c [63,66].
A peculiar property of the modulated structure under discussion is the significant difference in the torsional amplitude ϕ 3 of the independent molecules. This aspect cannot be explained solely based on the intramolecular steric factors. Analysis of the crystal packing shows that each of these independent biphenyl moieties maintains close intermolecular CH···HC contacts with the phenyl rings of L-phenylalaninate in AB and BA fashion (Fig. 4). These distances are significantly longer (intermolecular d H···H ≥ 2.4Å, Table II) compared to the intramolecular H···H distances. On the other hand, the aromatic rings of  Table S5 in [45].
L-phenylalaninate interact with adjacent oxygen atoms of -COOCH 3 via C-H···O hydrogen bonds ( Fig. 4 and Table II). These hydrogen bonds are weaker [67] but highly directional ( (C-H···O) = 159-164 deg) with very little variation in the distances. Interestingly, those H···H distances involving biphenyl moieties of 'B' are consistently smaller than those of 'A' in both phases (Table II). We argue that in the presence of both the van der Waals interactions and weak C-H···O bonds, the larger distortions of 'A' is favored by weaker CH···HC interactions while that is suppressed in 'B'. The four different values of intramolecular torsion ϕ 3 within the biphenyl moieties is distinctively governed by intra-and intermolecular non-bonded H···H contacts as well as weak hydrogen bonds. involved in hydrogen bonds and steric factors in phase I (T 1 ) and phase II (T 2 ; t = 1 4 ; 3 4 ) respectively. Symmetry codes: Phase I-(i) x−1, y, z; (ii) x+1, y, z; (iii) −x+1,

IV. CONCLUSIONS
The single crystal to single crystal phase transition of 4-biphenylcarboxy-(L)-phenylalaninate below T = 124 K drives the 3D structure directly to a locked-in twofold superstructure. The

Supplemental material
Unequal torsional rotations driven by normal to modulated phase transition in 4-biphenylcarboxy coupled L-phenylalaninate governed by non-covalent constraints Details of structure refinements of different modulated structure models Structure refinements have been performed using Jana2006 1 and Jana2020 2 . Structural model at T = 160 K has been used as an initial model for the basic structure of the modulated structure at T = 100 K. All atoms were set to isotropic for displacement parameters and the model was refined against main reflections [R obs F (m=0) = 0.0723]. In the next step, first order harmonic for displacive modulation was described for all atoms and an incommensurate (IC) model was refined against main and satellite reflections. Refinement led to improved fit to the main reflections [R obs F (m=0) = 0.0586, R obs F (m=1) = 0.1215]. Refinement of the anisotropic atomic displacement parameters (ADPs) of all non-hydrogen atoms resulted in significant improvement to the residual values [IC model A: R obs F (m=0) = 0.0374, R obs F (m=1) = 0.0771] and residual features (∆ρ min /∆ρ max ) decreased from -0.68/1.23 eÅ −3 to -0.33/0.31 eÅ −3 . However, ADPs of four non-hydrogen atoms were found to be non-positive definite. Further test by describing first order harmonic for ADP modulation for all non-hydrogen atoms model led to improvement of the residual values [IC model A: R obs F (m=0) = 0.0363, R obs F (m=1) = 0.0677] but ADPs of 11 non-hydrogen atoms were found to be non-positive definite along certain t-sections. This model was discarded for further analysis.
In the next step, IC model A was used as a starting model to describe three commensurate (C) models by fixing the initial phase of the modulation, t 0 = 0, 1 4 and 1 8 respectively. The former two t 0 values correspond to 2a × b × 2c superstructure in 3D with monoclinic symmetry B2 1 while the later correspond to a superstructure with triclinic B1 symmetry. Restrictions on t 0 values also impose constraints on the refinable variables corresponding to atomic modulation functions (AMFs). These restrictions follow the argument that the total number of refinable parameters in the equivalent 3D superstructure and their (3+1)D commensurately modulated structural models must be equal. In the present case, either sin or cos waves can be refined for structural models with t 0 = 0 and 1 4 because the point group symmetry is same in their corresponding 3D superstructure models. On the other hand, assumed monoclinic to triclinic distortion in the 3D superstructure (space group B1)corresponding to (3+1)D C model with t 0 = 1 8 can be derived by using both components of the Fourier series. It must be noted that such restrictions on sin and cos waves cannot be formally imposed on the AMFs of hydrogen atoms in Jana2006 and Jana2020 as their modulations are fully determined by geometrical conditions of the riding model. t 0 = 1 4 yielded the best fit to the diffraction data (Table S3) with reduced number of parameters as compared to the IC model A (compare N C,t 0 =0.25 = 649 to N IC,model A = 811). Most importantly, ADPs of all non-hydrogen atoms are positive definite.
Notably, the residual values of the IC model as well as the C model at t 0 = 1 8 is marginally smaller than for the C model at t 0 = 1 4 . Assuming all the three models should fit similarly to the diffraction data for equivalent descriptions of structural models further tests included attempts to refine the IC model and C model at t 0 = 1 8 with reduced number of parameters (= 649) similar to t 0 = 1 4 . Refinements led to worse fit with large R-values (Table S3). In the final step, all reflections were averaged in monoclinic symmetry corresponding to t 0 = 0. One parameter corresponding to isotropic extinction correction was refined. Finally, fractional co-ordinates and AMFs for hydrogen atoms belonging to N-H groups involved in strong hydrogen bonds improved the fit to the diffraction data marginally (R obs F = 0.0419 in Table S2).
Additional refinement was performed including first order harmonic for anisotropic ADPs of all non-hydrogen atoms. Refinement of this model with additional 324 parameters converged with marginal improvement of R obs F (= 0.0406) values. However, the residual density ∆ρ min /∆ρ max remained unchanged [compare -0.26/0.28 e/Å 3 to -0.25/0.29 e/Å 3 ] and 306 parameters refined to values within three times their standard uncertainties. The model was therefore discarded. Thus the superspace approach reduced the total numbers of refinable parameters by ∼ 33 %.

Additional X-ray diffraction experiments
Powder X-ray diffraction experiments were performed on thoroughly ground powder of the compound at ambient conditions using a Rigaku SmartLab with a CuKα radiation. JANA2006 was used to index the diffraction patterns. For reference, lattice parameters at ambient conditions were obtained from single crystal X-ray diffraction (SCXRD) experiment at ambient conditions (Table S7). The PXRD pattern could not be indexed using the lattice parameters as obtained from the SCXRD data [ Fig. S7(a)] that suggest that the compound undergoes phase transition upon grinding. Lattice parameters were calculated employing the singular value decomposition (SVD)-Index algorithm in TOPAS 3;4 . The PXRD pattern could be indexed using a primitve triclinic cell (Cell 1) with unit cell volume comparable to that of single crystal [ Table S7, Fig S7(b)]. Another triclinic cell (Cell 2) could also describe the pattern [Fig. S7(c)]. Le Baile refinements of the patterns against both the cells resulted in similar residual values (Table S7). However, Cell 1 fits better to the PXRD than Cell 2 [compare inset plots of Fig  S7(b) and Fig S7(c)]. In addition, the unit cell volume of Cell 2 is larger than 7.5 % to that of the single crystal that implies different density of the ground material.
Based on this difference of phases between single crystals (monoclinic structure) and pulverised material (triclinic structure), T -dependent PXRD experiments to complement the single crystal to single crystal phase transition in this material was not pursued.        Table S4: Components of the amplitude of atomic modulation functions (|u x |, |u y | and |u z |) along the three basis vectors a, b and c respectively for molecules A and B. Atom 0  Table S5: Equivalent value of the ADP tensors, (U eq ) of atoms of the biphenyl moieties at T = 160 K (phase I) and T = 100 K (phase II); and the sum of the square of the amplitudes of their atomic modulation functions along three basis vectors (u 2 ) for molecules A and B . u 2 = (u x ) 2 + (u y ) 2 +(u z ) 2 .