Accepted Article Title: Integrated Computational Protocol for Analyzing Quadrupolar Splittings from Natural Abundance Deuterium NMR Spectra in (Chiral) Oriented Media Authors: Armando Navarro-Vazquez, Philippe Berdagué, and Philippe Georges Julien Lesot This manuscript has been accepted after peer review and appears as an Accepted Article online prior to editing, proofing, and formal publication of the final Version of Record (VoR). This work is currently citable by using the Digital Object Identifier (DOI) given below. The VoR will be published online in Early View as soon as possible and may be different to this Accepted Article as a result of editing. Readers should obtain the VoR from the journal website shown below when it is published to ensure accuracy of information. The authors are responsible for the content of this Accepted Article. To be cited as: ChemPhysChem 10.1002/cphc.201601423 Link to VoR: http://dx.doi.org/10.1002/cphc.201601423

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Integrated Computational Protocol for Analyzing Quadrupolar Splittings from Natural Abundance Deuterium NMR Spectra in (Chiral) Oriented Media Armando Navarro-Vazqueza, Philippe Berdaguéb and Philippe Lesot b,* a

Departamento de Química Fundamental, Universidade Federal de Pernambuco Cidade Universitária, CEP: 50.740-540 Recife, PE, Brazil. b RMN en Milieu Orienté, ICMMO, UMR CNRS 8182, Université Paris-Sud / Université Paris-Saclay, Bât. 410, F-91405 Orsay cedex, France.

___________________________________________________________ Abstract: Despite its low natural abundance, deuterium NMR in weakly oriented (chiral) solvents gives easy access to deuterium residual quadrupolar couplings (2H-RQCs). These are formally equivalent to one-bond 1DCH (13C-1H)-RDCs for calculation of the Saupe tensor, and furnish similar information for the study of molecular structure and orientational behavior. Since the, quadrupolar interaction is one order of magnitude larger than the dipolar one, 2H-RQC analysis is a much more sensitive tool for the detection of subtle structural differences as well as tiny differences in molecular alignment such as those observed for different enantiomers in chiral aligning media. In order to promote the analytical advantages of anisotropic, natural abundance deuterium NMR (NAD NMR) in the organic chemistry community, we describe a 2 H-RQC/DFT-based integrated computational protocol for the evaluation of the order parameters of aligned solutes via singular value decomposition. Several examples of 2H-RQCassisted analysis of chiral and prochiral molecules dissolved in various polypeptide lyotropic chiral liquid crystals are reported. The role of molecular shape in the ordering mechanism through the determination of inter-tensor angles between alignment tensors and inertia tensors using the proposed protocol.

[a] Dr. Armando Navarro-Vázquez Departamento de Química Fundamental, Universidade Federal de Pernambuco Cidade Universitária, CEP: 50.740-540 Recife, PE, Brazil.

[b] Dr. Philippe Berdagué, Dr. Philippe Lesot (DR CNRS) RMN en Milieu Orienté, ICMMO, UMR CNRS 8182, Université Paris-Sud / Université Paris-Saclay Bât. 410, F-91405 Orsay cedex, France. E-mail: [email protected]

Supporting information for this article is available on the WWW under :

Keywords: NMR, deuterium quadrupolar splitting, natural abundance, hyphenated software, small molecules.

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Graphical abstract: When 2H-RQCs replace (13C-1H)-RDCs. An integrated computational protocol based on deuterium residual quadrupolar couplings is proposed as a new and efficient analytical tool for studying the structure and alignment properties of small molecules in oriented media.

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Introduction Multidimensional (nD) NMR spectroscopy in weakly aligning anisotropic media such as lyotropic liquid crystals or mechanically strained gels has become an useful tool in structural elucidation of small organic molecules.[1-6] Applications of aligning media NMR are rooted in the fact that anisotropic NMR parameters such as residual dipolar couplings (RDCs, D) or residual chemical shift anisotropies (RCSAs, ).[7,8] are univocally correlated with molecular

⌢

geometry, through the Saupe or order tensor S .[9] This second-rank tensor (3 x 3 matrix) encodes the orientational distribution of the molecule respect to the external magnetic field direction. In combination with acceptable approximations and adequate theoretical model,[10-15] aligning media NMR can also be used to investigate the conformation behavior of flexible small molecules.[16,17] The “re-discovery” of analytical potential of this tool has been nicely illustrated in a series of recent key papers, investigating the relative configuration[18-23] and orientational/conformational behavior of various organic molecules, including chiral drugs. [24-30] Although one-bond proton-carbon RDCs (1DCH) are by far the most used ones, all combinations of I = ½ magnetically active nuclei (1H,

13C, 15N, 19F,

…) can provide useful

homo- and heteronuclear RDCs.[31,32] Among other nuclei intrinsically present in all organic molecules, the deuterium nucleus, at natural abundance level (NA), has a peculiar position in terms of structural analysis for three main reasons. First, although the natural abundance of deuterium is very low (1.55  10-2 % compared to 1H), isotropic and anisotropic 2H spectra still can be experimentally detected with routine NMR spectrometers (> 9.4 T) and pioneering NAD experiments were recorded using 2H non-cryogenic probes.[33-37] Of course, the use of dedicated 2H cryogenic probes can dramatically increase the observed S/N ratio.[38] Second, spectra can be recorded under 1H-decoupling, as it is the case in this work, yielding a “pure-shift” spectrum formed only by 2H singlet lines.[39,40] Third, deuterium nuclei possess a small quadrupolar moment (QD = 2.86  10-31 e/m2)[41-43] which makes quadrupolar relaxation in 2H much less efficient as compared to other quadrupolar nuclei.[44] Consequently decoupled NAD-{1H} NMR spectra present generally narrow spectral lines allowing for straightforward measurements of 2H quadrupolar splittings. Hence, 2H has become a very useful isotope for diverse analytical investigations such as natural isotopic fractionation (D/H) process,[45-47] the evaluation of enantiopurity in mixtures,

[33,34]

the

determination of relative or absolute configuration,[35,36,48,49] conformational analysis[48,50] as well as investigation on the properties of chiral liquid crystal (CLC) phases.[51-53] From the point of view of Saupe order parameters, 2H residual quadrupolar couplings (2H-RQCs noted also Q) measured on anisotropic natural abundance deuterium (NAD)

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are formally equivalent to one-bond

1D CH

RDCs for a given hydrogen site. Since the 2H-

RQCs are larger than the corresponding 1DCH RDCs by a 5 to 6 factor[54] they are much more sensitive to small differences of molecular ordering. Hence, while spectral enantioresolution in chiral liquid crystals (CLCs) is easily attainable from

2H-RQC

measurement this is not generally the case when RDCs are measured since the difference in 1DCH couplings for pairs of enantiomers or enantiotopic elements is usually smaller than the observed linewidths. Therefore, while it is possible to extract separated sets of

2H-

RQCs for each enantiomers in a scalemic or racemic mixtures in the same chiral liquidcrystalline sample,[49] two samples of pure enantiomer (R or S) are generally required when using

1D CH

RDCs,[53,55] clearly introducing uncertainties in terms of composition,

temperature, or physical homogeneity of the alignment medium. Despite the above mentioned advantages of 2H-RQCs vs. one-bond 1DCH RDCs, only a few studies concerning the investigation of orientational behavior or structural determination based on the extraction of 2H-RQCs have been reported.[36,52] So far, most applications on NMR in anisotropic media in structural studies of small molecules mostly prefer the extraction of 1DCH RDCs using different types of F1 or F2 coupled HSQC experiments,[56-58] sometimes supplemented with long-range (13C-1H)-RDCs.[59,60] Two main reasons explain this situation: i) the idea that anisotropic NAD 1D/2D NMR spectroscopy is not sensitive enough to record exploitable spectra; it is the case however that they can be conveniently obtained with current routine NMR instruments even equipped with non-cryogenic probes;[33,61] ii) the absence of a “plug and play” integrated computational protocol similar to those available for analysis of RDCs[62-64] through which the Saupe order matrix elements and derived parameters can be easily obtained from modeled 3D structures. To this day, calculations of Saupe order matrix from RQCs and initial 3D structures resorted to manual procedures as the use of spreadsheets.[52] One important point needs to be mentioned though. In contrast to RDCs, which just needs the molecular coordinates, the treatment of order parameters from RQC measurements needs also the knowledge of deuteron quadrupolar coupling constant CQD that in principle can differ from one 2H site to another depending on the hybridization state of carbon bonded to the 2H and electronic mesomeric and inductive effects.[65-68] Electronic effects however are generally small, with variations in the order of 5 kHz, and Saupe matrix calculations can be performed using generic values of CQD (sp3) and CQD (sp2) of 170 kHz and 185 kHz, respectively[69,70] It is also assumed that the EFG tensor has axial symmetry (zero-rhombicity) and its principal z-axis is collinear with the C-D bond. Additionally, one can safely assume that mirror-related deuterium sites between enantiomeric pairs, or enantiotopic sites in prochiral molecules, experience identical This article is protected by copyright. All rights reserved.

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electron-field-gradient (EFG) values, even when embedded in a chiral medium leading to equivalent CQD . To the best of our knowledge, no experimental evidence of differences between ( CQD )R/pro-R and ( CQD )S/pro-S has been reported. Although the use of the above assumptions can suffice for the resolution of simpler structural problems using 2H-RQCs from C-D bonds,

[33,36]

the ab-initio prediction of EFG

tensors from the optimized 3D structure would undoubtfully broaden the applicability of the technique[65-68] allowing inclusion of uncommon structural motifs and quadrupolar coupling constants from other I > ½ nuclei as 7Li, for instance.[71] Note that, for the purpose of the resolution of structural problems, computations need only to be accurate in the prediction of the relative values between different sites since any global discrepancy between theory and experiment would be absorbed in the computation of the Saupe matrix. In brief, to take advantage of the analytical wealth of 2H-RQC’s extracted from NAD NMR in aligning media, an integrated computational protocol for the determination of Saupe matrix elements from computed geometries, ab-initio computed 2H EFG tensors, and experimental RQC data was developed. Note that this procedure can be extended to any other quadrupolar nuclei (I >1/2). The main purpose and aim of this development is to facilitate and therefore promote towards the widest community of organic chemists the use of the technique for the resolution of structural problems in small molecules, in similar way to current RDC-based approaches. Rooted in the already described MSpin-RDC program[63] we propose and describe here a computational protocol for small-molecule-oriented RQC analysis. Analytical potentialities of this novel hyphenated approach to understand the subtle differences in orientational behavior of chiral and prochiral molecules dissolved in polypeptide-based lyotropic chiral liquid crystals are herein reported. Basic and analytical interests of NAD NMR in CLC For high-field experiments the quadrupolar contribution from deuterium is much smaller than the Zeeman term and the corresponding truncated 2H quadrupolar Hamiltonian, HQ, can be written, when expressed in Hz, as: [69,72]

HQ =

1 e2QD qizz å 4 éë 3I 2zi - I i2 ùû h i

(Eq. 1)

where eQD is the nuclear electric quadrupole moment of deuterium, and eqizz

is the

principal component of the EFG tensor, Vizz along the Bo (z-axis) at deuterium site i. The quadrupolar interaction splits the 2H signal into a symmetric quadrupolar doublet (QD) centered at the 2H anisotropic chemical shift position. The separation between the two lines of the doublet corresponds to the quadrupolar splitting, Qi or 2H-RQC). Hence, NAD-

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NMR spectra in aligned solvents consist of independent (not coupled) QDs; each of them being associated to a particular deuterium site.[73] If the EFG tensor is axially symmetric (EFG

Vxx - Vyy) / Vzz = 0), the quadrupolar

splitting, Qi, in units of Hz, associated with the i-th C-D bond is simply written as:

3 Dn Qi = QCCiD ´ SC-Di 2

(Eq. 2)

with:

SC-Di =

1 B0 3cos2 qC-D -1 i 2

(Eq.

3)

where QCCiD is the 2H quadrupolar coupling constant, SC-Di is the local order parameter of B0 the C-Di bond, and q C-D is the angle between the C-Di and the magnetic field B0 axis. i

In weakly oriented solvents such as polypeptide lyotropic CLCs, the quadrupolar splittings tipically varies from zero (“magic angle”) to a maximum of ca. one KHz in absolute value.[70,72] For liquid crystals with good homogeneity,[74] linewidths of QD components rarely exceed 7-8 Hz and even values as low as 2-3 Hz can be reached in highly homogeneous polypeptide samples.[33,72,73] The more complex and larger distribution of QDs (compared to the range of 2H chemical shift) and the doubling of lines (compared to isotropic spectra) on the spectral window can lead to numerous peak overlapping and/or interweaving, turning rather complex the analysis of NAD 1D-NMR spectra. This problem can be efficiently addressed by recording 2H homo- or heteronuclear 2D-NMR experiments.

[37,75-77]

They turned out to be

unavoidable for the determination/identification of QDs in CLCs where the number of QDs generally doubles respect to an achiral environment Dn QiR ¹ Dn QSi .[33,49,72,73]. It is worth noting that doubling of QDs is also observed for enantiotopic elements in prochiral molecules . In NAD NMR, this doubling of signals corresponds to detection of a pair of Dn Qipro-R ¹ Dn Qpro-S i enantio-isotopomers (R-C*(DH)-R’).[35,36,78-80] In a similar way to RDCs, the observed quadrupolar splittings provide only the absolute value but not the sign of the 2H-RQCs. To access this sign, the Q.E COSY 2D-NMR experiment for spin systems consisting of one I = 1 spin coupled to one I = 1/2 nucleus has been recently proposed.[81] Due to the stringer requirements of this approach, we have simply determined here the sign of the quadrupolar splitting by taking into account that it must be opposite to that of the corresponding 1DCH RDC.[38,82] Description of RQC-based integrated computational protocol In short, the 2H-RQC-based protocol proposed here can be divided into five key steps:

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i)

optimization of molecular structure by DFT calculation;

ii)

determination at DFT level of the EFG tensors for the 2H sites;

iii)

calculation of the Saupe order parameters from DFT geometry and EFG tensors using the singular value decomposition procedure;

iv)

back-prediction of 2H-RQC values from using the calculated Saupe Tensor and prediction of quality factors;

v)

calculation, through diagonalization, of Saupe tensor eigenvectors and eigenvalues and related properties such as Euler angles and asymmetry parameters [83]

Steps ii to v were accomplished by modifying the MSpin-RDC program, initially designed for the analysis of RDCs in small organic molecules,[63] addressing the specificities associated to 2H-RQC data. Following the spirit of the MSpin-RDC module, the input to the new software, called here MSpin-RQC, has been kept as simple as possible, making it user-friendly for nonspectroscopists, while still retaining the necessary flexibility and richness of features. The NMR experimental data are input as a plain text file, containing list of atom indexes with the corresponding experimental DQ values. Examples and description of the input files are provided with the SI. Noteworthy, the EFG tensors are directly read from the Gaussian09 output files without the need for manual extraction. The details of the computation can be controlled via the graphical user interface of MSpin-RDC, or in command line through specific keywords. The graphical interface provides also useful graphical analysis tools such as representation in three-dimensional space of the principal axes system for Saupe, inertia or gyration tensors as well as a valued-surface representation of the Saupe tensor. The analysis of 2H-RQCs benefits from tools already available in MSpin-RDC such as the possibility of bootstrapping analysis, or the possibility of performing conformational analysis and fitting to populations.[24] Molecular modeling and determination of alignment tensors. Since sufficiently accurate geometries are normally obtained at moderate levels of theory, cheap DFT procedures, such as for instance standard B3LYP[84] calculations, can be employed for determination of molecular geometries Bailey, recommended the use of the B3LYP functional along with the relatively large 631G(df,3p) basis set for accurate computation of the EFG tensors.[67] We want to note that, if the RQC data are not to be mixed with other anisotropic data, the tensors can be computed also at lower levels of theory since only Euler angles respect to molecular frame and the relative CQD magnitude between different 2H sites are relevant to the SVD fitting and

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any general deviation from the absolute values will be absorbed in the degree of order of the Saupe tensor. Although here the computations were performed inside the commercially available Gaussian09 package,[85] virtually any other QM package can provide the necessary EFG tensors. Once geometries and EFG tensors are computed, they are parsed directly from the Gaussian09 output files by the herein modified MSpin-RDC program.[63] The molecular Saupe tensor can be calculated from a combination of RCSAs, RDCs, or RQCs experimentally determined. For simplicity we will cast here the necessary

2 ˆ [86] equations in terms of the alignment tensor Aˆ = S . 3 In its general tensorial form, the RCSA value for the ith nucleus is defined as:[7]

ˆ dˆ i = Dd i = A⊙

å

a ,b =x,y,z

i Aabd ab

(Eq. 4)

where dˆ i is the chemical shift tensor for the ith nucleus. Similarly, the RDC value for the jth coupled pair I, S is given by Eq. 5:[86]

(Eq. 5)

where m0 is the permittivity constant in vacuo, R is the vibrationally averaged internuclear distance, and

is an unit vector pointing from nucleus I to S. Under this form, the spin-spin

total coupling, Ti (TIS) measured on spectra is conventionally defined as Jij + Dij, which

ˆ , rather than Hˆ = 2DIˆ Sˆ (for corresponds to a dipolar coupling Hamiltonian, Hˆ D = DIˆZ S Z D Z Z which Tij = Jij + 2Di).[54] Finally, the 2H-RQC values used in this work are calculated, in an arbitrary molecular frame as

Dn Qk =

3eQk ˆ Vˆ = bk A⊙ ˆ Vˆ å A V A⊙ Q ab ab 2hI k ( 2I k -1) ab =x,y,z

(Eq. 6)

Here, Qk is the electric quadrupolar moment of the nucleus and Ik its spin principal quantum number. For 2H these values and Qk = 2.86 x 10-31 e/m2 and Ik = 1 respectively.[87] Note that the electric field gradient components in the Gaussian computations are expressed in atomic units of hartrees/e*a02. To convert these atomic units to SI units of V/m2 a factor of 9.717362356 x 1021 has to be applied. A natural manner to mix the different anisotropic observables in the determination of the alignment tensor is to weight each particular datum with its determined or expected accuracy . In this way the SVD equations[88] can be expressed as

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(Eq. 7)

æ ... ç i 2 ç Dd / s i ç ... ç j 2 ç D /s j ç ... ç k 2 ç Dn Q / s k ç ... è

ö ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ø

æ ... ç i d xx - d zzi ç ç s i2 ç ... ç 2 j 2 ç r - ( rzj ) j ( x ) ç = bD s 2j ç ç ... ç ç Vk - Vk bQk xx 2 zz ç sk ç ç ... è

... d + d yxi i xy

s

2 i

...

d +d s i2 i xz

... j D

b

2rxj ryj

s 2j

... 2V k bQk 2xy

sk

... d + d zyi

... d - d zzi

s i2

s i2

...

...

i yz

i zx

... j D

b

bQk

...

2rxj rzj

j D

2ryj rzj

s 2j

b

...

... 2V k bQk 2yz

k xz 2 k

2V

s

s 2j

j D

b

(r ) - (r ) j y

2

j 2 z

s 2j ... V k - Vzzk k yy

bQ

sk

...

ö ÷ ÷ ÷æ ÷ ÷ç ÷ç ÷ç ÷ç ÷ç ÷ç ÷ çè ÷ ÷ ÷ ø

i yy

...

s k2 ...

Axx ö ÷ Axy ÷ Axz ÷÷ Ayz ÷ ÷ Ayy ÷ø

The system is then resolved using a least-squares singular value decomposition (SVD) procedure using the DGELSS routine in LAPACK.[89] The quality of the solution, corresponding to the set of smallest differences between experimental and computed (backcalculated) anisotropic observables (Q or D or ), is given by a error weighted Cornilescu’s quality factor, Q, (Eq. 8). It can be expressed in the more general form as:[83] 2

æ D j ,Exptl - D j ,Comp ö æ Dn Qk,Exptl - Dn Qk,Comp ö æ Dd i ,Exptl - Dd i ,Comp ö + + å çè å å ç ÷ ÷ø çè ÷ø si sj sk è ø 2

Q=

æ Dd

å çè

i ,Exptl

si

æD ö ÷ø + å ç s è j 2

j ,Exptl

2

ö æ Dn ÷ + åç s è ø k

k,Exptl Q

ö ÷ø

2

(Eq. 8)

2

Dd Q values from free rotors such as methyl or phenyl groups is implemented following a described procedure.[24] Further details are available in the SI.

After SVD determination of the alignment tensor components principal values and eigenvectors were determined by diagonalization. Once the alignment tensor is computed, 2H-RQCs

are back calculated and can be shown in a table (see Figure 1). The eigenvalues

and eigenvectors of the Saupe matrix, as well as additional properties, useful for analyzing the orientational behavior, such as general degree of order (GDO,[90] rhombicity,[91] or Euler angles[92,93] are computed.

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Figure 1. Screenshot displaying different graphical components of the MSpin-RDC program for a typical 2HRQC computation. Middle: OpenGL molecular visor with experimental vs. calculated 2H-RQCs 3D labels. Right top: widget with the different computation and display options; Left; text summary of the output of the computation with Saupe matrix components are displayed in both user-choice initial frame and also principal frame along with properties of the Saupe tensor; Right bottom, table with experimental vs. computed 2H-RQCs and computation summary. All information shown in the graphical interface is available in a text output file. An example of input and text output file of the program is provided with the SI.

Experimental section Liquid-crystalline samples. Chiral and achiral lyotropic LCs were prepared by dissolving neat PBLG or a 50% w/w mixture of PBLG and PBDG polypeptides (PBG) as described previously.[72,94] The degree of polymerization (DP) evaluated by viscosity measurement of polymers (PBLG and PBDG from Sigma) varies between 512 and 914, namely from 120,000 to 200,000 g/mol, respectively). For fenchone (FCH), the samples were composed of 100 mg of analyte (ee(S) of 30%), 90 mg of polymer (DPPBLG = 743; DPPBG= 743/914), and 500 mg of dry CHCl3. For norbornene (NBN) in PBLG/DMF, the composition was 100 mg of analyte, 130 mg of polymer (DPPBLG = 743) and 350 of freshly distillated DMF. For NBN in PBLG/CHCl3, the composition was 100 mg of analyte, 100 mg of polymer (DP PBLG = 562; DPPBG = 562/854) and 350 mg of dry CHCl3. 5-mm o.d. NMR tubes of oriented samples were fire-sealed to avoid evaporation of the organic co-solvent. Experimental NMR measurements. Unless specified otherwise, NAD 2D-NMR spectra (QCOSY Fz experiments) in the PBLG/PBG phases were recorded at 14.1 T (92.1 MHz) on a Bruker Advance II spectrometer equipped with a 5-mm 2H selective cryogenically cooled probe,[95] whilst 2D maps were recorded using 1750(t2)  700(t1) data points with 96 scans per t1 increments and then zero-filled to 4096(t2)  4096(t1) to achieve a digital resolution at

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0.45 Hz/points (SW = 20 ppm). Decreasing exponential filtering (LB = 1.0 Hz) was applied in both spectral dimensions.

13C

and

13C-{1H}

(100.3 MHz) 1D/2D NMR measurements in

isotropic solvents and CLCs were carried out on a 9.4 T spectrometer equipped with a 5mm QXO probe. All anisotropic NAD and

13C

spectra were recorded at 300/305 K with

proton decoupling using the WALTZ-16 CPD sequence. To reach a good thermal equilibrium and ensure an uniform solute orientation of all mesophases, each sample was spun at a frequency of 7 Hz for 1-2 hours inside the magnet before recording NAD 2D-NMR spectra. 1DC-H values listed in Tables SI-1 and SI-4 were determined as the difference 1DCH = 1TCH -1JCH. 1TCH and 1JCH values were extracted from the anisotropic and isotropic protoncoupled 13C NMR spectra, respectively. Molecular modeling. Geometries of solutes were optimized in vacuo at the B3LYP[84]/631G* level. 2H-EFG tensors were computed at the same level of theory. [67] All computations were performed inside the Gaussian09 package.[85]

Results and discussions To illustrate the usefulness of the here proposed 2H-RQC-based integrated computational protocol, we chose fenchone (FCH) and norbornene (NBN) as examples of chiral and prochiral compounds respectively. Both molecules were oriented in polypeptide chiral and achiral liquid crystals (see Figure 2). Fenchone : analysis of a chiral molecule. Fenchone, a typical chiral, bicyclic rigid molecule, has ten non-equivalent 2H spin sites. Hence in the presence of a CLC, up to twenty QDs (associated to ten distinct enantio-isotopomers) are expected to be observed for racemic/scalemic mixtures.[33] As discussed above, in order to evaluate the subtle differences in ordering of the two enantiomers in the presence of a CLC, we prepared a single sample containing a scalemic mixture of the chiral analyte (here, ee = 30% with (2S,5R)-(+)-FCH as major enantiomer). Thereafter this mixture will be noted in short as (ee)-(S)-FCH.[93,96] The difference of intensity between the (R)- and (S)-NAD signals allows the easy assignment of each QD to a particular enantio-isotopomer (see Table 1). Since even for a small molecule as fenchone, the anisotropic NAD-{1H} 1D spectrum of (S)-FCH recorded in PBLG/CHCl3 shows a large degree of interweaving of QDs and overlapping of DQ components (see Figure SI-1 in SI), the splitting of each QD was measured using the QUOSY 2D experiment (see above). Figure 3a shows the NAD-{1H} QCOSY Fz 2D spectrum of FCH where both components of each QD can be easily identified

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Figure 2. Structure, atomic numbering, and stereodescriptors for (a) (2S,5,R)-(+)-fenchone ((S)-FCH) and (b) norbornene (NBN). Note that in NBN, the heteronuclear bond pairs denoted (1-10/4-13), (2-11/3-12), (5-14/616) and (5-15/6-17) are enantiotopic directions. Each of them is associated to a monodeuterated enantioisotopomer.

and assigned, to a particular enantio-isotopomer (series of NAD-{1H} 1D sub-spectra is presented in Figure SI-2). NAD-{1H} 2D-NMR spectra of FCH (and NBN) were also recorded in the PBG achiral liquid crystal (ALC), using the same sample composition and experimental temperature in order to resolve possible ambiguities in the assignment of DQs (see Figure 3b). Interestingly, in this compensated achiral environment made by a racemic mixture of PBLG and its enantiomer PBDG, the effect of enantiodiscrimination mechanisms disappears on the average, at the NMR time scale, and a single QD is observed for each enantioisotopomeric pair.[52,94] The comparison of the quadrupolar splitting values in both LCs allows also to determine the relative sign of 2H-RQCs for a given monodeuterated enantioisotopomer pair,[94] their absolute signs being determined from the

13C-1H

RDC data

analysis as explained above. A detailed table of all experimental data is given in SI (see Table SI-1). In practice, the recording of NAD spectra in ACL is not needed if the assignment and/or the sign of the QDs in the chiral phase are not ambiguous. However, the extraction of anisotropic data and their comparison with those obtained in the CLCs can provide information about the mechanisms involved in chiral discrimination phenomenon in the CLCs (see below).[97] As seen in Tables 1 and SI-1, a total of 19 distinct 2H-RQCs (over 20) can been extracted from the 2D analysis of NAD 2D-NMR spectra of a scalemic mixture of FCH in PBLG, thus providing a sufficient number of independent anisotropic data to determine the Saupe tensor for each isomer. The experimentally determined 2H-RQCs for both enantiomers were tabulated as an input for the MSpin-RQC program (see example at the SI) along with the Gaussian09 file containing the optimized geometry and computed EFG tensors at nuclear positions. Saupe tensor parameters and quality factors were computed for both enantiomers of fenchone

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Figure 3. NAD-{1H} 2D spectra at 92 MHz extracted from the tilted Q-COSY Fz 2D spectrum of FCH dissolved in (a) PBLG/CHCl3 and (b) PBG/CHCl3 both recorded at 295 K and about 15 h. The assignment of 2H QDs is based on the assignment made from isotropic 2H chemical shifts assuming (2H)aniso ≈ (2H)iso (no inversion of the relative position of QDs).

by performing SVD analysis as described before. Excellent agreement was obtained between experimental and back-calculated data with quality factors Q of 0.007 and 0.013 for (S)-FCH and (R)-FCH in PBLG, respectively;

and 0.008 in PBG. For a better

comparison between achiral (PBG) and chiral (PBLG) oriented phases, the experimental 2H-RQC

values in PBG listed in Table 1 (see also Table SI-1) were corrected by the ratio

[Q(chloroform) in PBLG / Q(chloroform) in PBG] in order to take into account small experimental variations, (composition of sample, homogeneity of the phase, …) that could cause small differences in the degree of alignment.[36] To assess the robustness of calculation, final computed (back-calculated) 2H-RQC and experimental values can be compared to experimental ones using gravimetric plots (see Figure 4a and 4b).

The

excellent fit between back-calculated and experimental data indicates the correct assignment of QDs for both R- and S-isomers. Figure SI-1 shows the assignment of 2H lines in the isotopic NAD 1D-NMR spectra of FCH dissolved in neat chloroform, assuming that no swapping of closest resonances occurs compared to the PBLG/CHCl 3 system. In terms of 2H (1H) chemical shifts, the assignment of peaks in Figure SI-1 agrees with spectral interpretation of FCH performed by Kolehmainen et al in 1990,[98] and Nowakowski et al in 2014,[99] but diverges for positions 15 and 16 (relative inverted position) with the earlier analysis made by Abraham et al in 1999,[100] and in fact swapping the QD values of the two sites in our assignment resulted in a high quality factor of 0.4.

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Table 1 . Experimental and computed 2H-RQC dataset (Hz) of FCH in PBLG/CHCl3 and PBG/CHCl3 phases

PBLG CLC (S)-FCH

Set Group

2H-Sites

CHD

PBG ALC FCH[a]

(R)-FCH Diff.[b]

Diff [b]

Diff.[b]

Exptl [c]

Comp.[d]

+0.22

-191.3

-191.7

+0.21

+112.1

-2.59

+122.0

+120.2

-1.49

+120

+121.2

+0.99

+122.0

+122.7

+0.57

-0.16

-151

-150.7

-0.20

-137.6

-137.4

-0.15

+134.3

+0.22

+120

+121.5

+1.23

+126.9

+127.9

+0.78

-83

-83.6

+0.71

-111

-111.3

+0.27

-96.6

-96.8

+0.21

17

+59

+58.1

-1.55

+65

+64.2

-1.25

+61.5

+61.0

-0.81

CDH2

18-20

-39

-38.0

-2.63

-39

-37.1

-5.12

-38.1

-37.4

+1.87

CDH2

21-23

+45

+44.7

-0.67

+33

+33.8

+2.37

+40.1

+39.3

-1.78

CDH2

24-26

+23

+21.6

-6.48

+33

+31.4

-5.10

+27.3

+26.3

-3.80

Exptl

Comp.

Exptl

Comp.

11

-205

-205.6

+0.29

-177

-177.4

CDH

12

+129

+127.8

-0.93

+115

CHD

13

+124

+124.1

+0.08

CDH

14

-127

-126.8

CHD

15

+134

CDH

16

CD

Q value

0.007

0.013

0.008

[a] The geometry of (R)-structure of FCH has been used for calculation (identical back-calculated 2H-RQC values are obtained using the geometry (S)-FCH). [b] Relative difference (%) between experimental and computed back-calculated RQC’s calculated as 100[QComp. - QExptl]/QComp.. [c] Corrected experimental 2H-RQC values (see Table SI-1). [d] Computed 2H-RQCs from corrected experimental 2H-RQC values.

Figure 4. Gravimetric plots of back-calculated versus experimental dataset (2H-RQCComp. vs. 2H-RQCExptl) for (a) (S)-(+)-FCH and (b) (R)-(-)-FCH in the PBLG/CHCl3 chiral system.

Finally, a quick comparison of Saupe matrix elements obtained from the RDC data measured in the PBG/CHCl3 with those obtained from quadrupolar couplings in the same medium showed the consistency of the two set of data (Table 3). Compared to the step-by-step calculation approaches applied so far for investigating the alignment properties when RQC’s is used as source of anisotropic information, the hyphenated protocol here proposed presents three major achievements in the analysis of results. First of all, the 2H-QCCi value for each deuterium site (related to C-

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Table 2. Ab-initio computed Vzz, QCCi and RQCi values for each 2H site of FCH Group

2

H site

Vzz[a]

(Vxx - Vyy)/2[b]

C-D[c]

/ a.u.

/ a.u.

/ deg

QCCi[d] / kHz

RQCi[e] / Hz

CHD

11

0.286

0.004

0.3

192.4

-205.6 / -177.4

CDH

12

0.284

0.004

0.2

190.7

+127.8 / +112.1

CHD

13

0.284

0.001

0.3

190.6

+124.1 / +121.2

CDH

14

0.283

0.001

0.2

190.5

-126.8 / -150.7

CHD

15

0.284

0.001

0.2

191.1

+134.3 / +121.5

CDH

16

0.289

0.001

0.3

194.1

-83.6 / -111.3

CD

17

0.286

0.002

0.0

192.1

+58.1 / +64.2

CDH2

18-20

0.287-0.288

~ 0.002-0.004

0.2-0.5

193.0-193.3

-38.0 / -37.1

CDH2

21-23

0.286-0.290

~ 0.002-0.004

0.3-0.4

192.4-194.6

+44.7 / +33.8

CDH2

24-26

0.286-0.289

~ 0.002-0.004

0.2-0.4

192.0-194.2

+21.6 / +31.4

[a] Axial component of Vzz. [b] Rombic component of Vzz. [c] C-D: Polar Euler angle between the z axis of the principal axis system of EFG tensor and a local frame for which the z axis is aligned with the C-D vector. [d] QCCi computed values when SC-D = 1. [e] Computed 2H-RQCi values for S and R enantiomers in the PBLG/CHCl3 (300 K) chiral system, respectively.

D internuclear direction) can be simply tabulated and expressed in Hz. For FCH, the QCC data obtained are shown in Table 2. This computational option allows to comparing the QCC values for the different deuteron sites of a molecule under investigation or between analogous series of analytes. In the case of fenchone, we can see that the relative variation in the QCC values does not exceed 2% for deuterons bonded to sp 3 hybridized carbon atoms. Collecting such data for various molecules and correlating them to the strength of experimental enantiodiscrimination could provide new insights for a better prediction of sites susceptible of exhibiting large chiral discrimination magnitude. Second, the output data of calculation provides directly all pertinent data relative to the alignment properties of solute, such as the Saupe matrix elements, principal axis system (PAS), Euler angles between molecular and PAS axis systems, axial and rhombic components, and general degree of order (GDO).

[86,90]

Table 3 lists all ordering-related parameters obtained from the

experimental 2H-RQC’s of FCH, along with the SVD condition and the quality factor. Third, the graphical interface of the program shows the optimized molecular structure as well as the principal axis system and/or inertia tensor principal axis. Even more, the Saupe tensor can be represented as a valued 3D surface.[101] All these graphical utilities are of great help to visualize and simply compare the alignment properties reduced to simple vectors or surfaces, in particular in the case of two enantiomers. To illustrate this last point but not least, Figure 5 shows an example of graphical screen in the case of enantiomers of

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Table 3. Order-based molecular data for FCH in the PBLG/CHCl3 and PBG/CHCl3 phases Parameters

PBLG phase (CLC) (S)-(+)-FCH

(R)-(-)-FCH

FCH[a]

0.007

0.013

0.008

0.010

Sx’ = +4.353 Sy’ = +4.901 Sz’ = -9.254

Sx’ = +3.817 Sy’ = +5.547 Sz’ = -9.364

Q factor Saupe matrix Eigenvalues (10-4) Saupe matrix eigenvectors[c]

PBG phase (ALC)

Sx’ = +4.516 Sy’ = +4.890 Sz’ = -9.407 e[x’] = ( 0.966,-0.201,-0.163) e[y’] = ( 0.240, 0.932, 0.273) e[z’] = ( 0.097,-0.302, 0.948)

SVD condition number Axial component (10-4) Rhombic component (10-4) GDO (10-3)

Sx’ = +4.233 Sy’ = +4.989 Sz’ = -9.222 e[x’] = ( 0.906,-0.406,-0.123) e[y’] = ( 0.423, 0.878, 0.222) e[z’] = ( 0.018,-0.253, 0.967)

e[x’] = ( 0.928,-0.337,-0.156) e[y’] = ( 0.367, 0.899, 0.241) e[z’] = ( 0.059,-0.281, 0.958)

FCH[b]

e[x’] = ( 0.991, 0.124,-0.047) e[y’] = (-0.105, 0.949, 0.296) e[z’] = ( 0.081,-0.288, 0.954)

3.26

3.26

3.26

3.26

-9.407 -0.249

-9.222 -0.504

-9.254 -0.365

-9.364 -1.153

1.087

1.067

1.069

1.090

[a] Calculation from corrected 2H-RQC dataset. See data in output file in SI. [b] Order matrix calculated from (13C-2H)-RDC dataset. [c] Coordinates expressed in the molecular frame (Gaussian standard orientation).

Figure 5. Displaying of principal axis system (Sx’, Sy’, Sz’) of diagonalised Saupe matrix, the inertia tensor axes, (Ix’, Iy’, Iz’) and the Saupe tensor surface representation (red and green surfaces indicate positive and negative 2H-RQCs, respectively) for (a) (S)-FCH and (b) (R)-FCH oriented in PBLG/CHCl3.

FCH where the principal axis systems of Saupe (Sx’, Sy’, Sz’) and inertia tensors (Ix’, Iy’, Iz’) are simultaneously displayed. From the orientational data provided as data output, we can calculate the generalized “5D” angle theta, , between any molecular alignment tensors, for instance between those for two enantiomers or between the molecular alignment and inertia tensors.[86,102] This angle between tensors, analogous to an angle between 3D vectors, is computed as:

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Sˆ R ⊙Sˆ S cosq = R S = Sˆ Sˆ

å

a ,b =x,y,z

å

a ,b =x,y,z

SaR,b SaS,b

SaR,b SaR,b

å

a ,b =x,y,z

SaS,b SaS,b

(Eq. 9)

Interestingly, this angular parameter could be used to quantity the efficiency of enantiodiscrimination mechanisms towards two enantiomers or to compare two orienting solvents (as PBLG and PBG, for instance). It provides an alternative to the Euler angles,

q, f, y , used so far to compare relative orientation of the PAS of the two enantiomers.[93,96] Table 4 reports the values obtained for various situations. Thus, an angle of 9º is obtained between the molecular tensors for each enantiomer of FCH in PBLG/CHCl3. This value could seem to be small but it is sufficient to enantioresolve 90% of deuterium sites in the NAD 2D spectrum. The magnitude of the “5D” angle can be correlated to the molecular properties of solute such as the shape anisotropy or the presence of polar groups susceptible to establish hydrogen bonds with PBLG. Formation of these bonds would increase the residence time of the solute in the closest vicinity of polypeptide helices enhancing therefore enantiodiscrimination.[52,103] In the case of FCH, the absence of polar groups and the rather spherical shape can explain the small value of observed angle. We determined also ”5D” angles between the (S)- or (R)-tensors in the PBLG chiral medium and the PBG achiral one (see Table 4). A small value of 4-5° is obtained, i.e., half the value between (S)- and (R)-tensors. This indicates that the orientation of (R/S)-PAS in PBG corresponds approximately to an intermediate situation between the (R)-PAS and the (S)-PAS in PBLG.[94,97] From graphical representation of the PAS for alignment and inertia tensor as well as their “5D” angles (ca. 30°, Table 2) we can see that they are moderately close. This indicates an important role of steric interactions (shape recognition phenomena) in the aligning process, at least in the the case of FCH (see below).[104] Analysis of the inter-tensor angles between enantiomers or between chiral and non chiral phases provide crucial information on the enantiorecognition mechanism and possibly data related to the absolute configuration of the solute. Indeed experimental data could be used to optimize parameters for molecular dynamics simulations of the alignment mechanism. As was discussed in a previous paper,[105] only comparison of experimental and theoretically obtained values, using molecular dynamics approaches for instance, would allow to assign the absolute configuration of the solute. Given the small changes between molecular alignment between enantiomers in weakly orienting chiral systems, the degree of accuracy currently obtainable in MD procedures, and the complexity of these lyotropic systems where the role of the organic co-solvent (see discussion on NBN, below) and the

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Table 4. “5D” angles (°) between the three sets of order tensors and the inertia tensor of FCH (S)-tensor (CLC)

(R)-tensor (CLC)

(R/S)-tensor (ALC)[a]

Inertia tensor

(S)-tensor (CLC)

-

9

4

31

(R)-tensor (CLC)

9

-

5º

24

(R/S)-tensor (ALC)[a]

4

5

-

28

Inertia tensor

31

24

28

-

[a] Order tensor calculated from corrected 2H-RQC dataset.

conformation of the polypeptide side-chain have to be taken into account for the prediction of absolute configuration is an extremely challenging task. Norbornene: Analysis of a prochiral molecule. To explore the possibilities of the proposed protocol for the analysis of prochiral molecules in CLCs, we have examined the case of norbornene, a rigid, prochiral compound of Cs symmetry (see Figure 1b). This is an interesting example to test for various reasons: i) it is a particular case of meso compound with two stereogenic carbons ((S)-C1 and (R)-C4), ii) five non-zero order parameters are needed to describe its orientational ordering in a CLC;[36,78] iii) similarly to enantiomers, enantiotopic elements (nuclei or group of nuclei, internuclear directions, …) in prochiral molecules are spectrally discriminable in CLCs. A doubling of 2H QDs corresponding to each pair of monodeuterated enantio-isotopomers are expected to be detected in NAD experiments in CLCs. Contrarily to a mixture of enantiomers, the spectral R/S identification of NAD signals based on the preparation of an scalemic mixture where the major isomer is known cannot be obviously applied to prochiral molecules. This drawback can be however overcome by calculating the Saupe matrix of the solute, as we will see below.[36] Additionally, in this second study, we examined also the orientational behavior of NBN using two different co-solvents for PBLG, namely chloroform and DMF. These two orienting lyotropic systems differ by the polarity of the organic co-solvent (DMF 3.86 D vs. CHCl3 =1.04 D). Such comparative investigations are important to understand the role of the bulk polarity in the alignment processes of the analyte in lyotropic liquid crystals and the associated effects on the

enantiorecognition mechanisms.[106] Actually, they are

unavoidable to propose reliable predictive, theoretical models of molecular ordering in future.[50,53,107-111]

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Figure 6. (a) 92 MHz NAD-{1H} Q-COSY Fz 2D spectrum (tilted map) of NBN in PBLG/DMF recorded at 305 K. Peaks marked by an asterisk on F2 projection are associated to residual diagonal NAD peaks of DMF. Scale of the horizontal axis F2 has no spectral meaning. NAD signals of DMF were used to calibrate the 2D spectrum. (b) Series of NAD-{1H} 1D sub-spectra associated to the four pairs of enantio-isotopomers-d1 and extracted from the tilted 2D map. Peaks marked with a star in the D10,13 sub-spectrum come from close NAD DMF doublet.

Figure 6 shows the NAD Q-COSY Fz 2D spectrum of NBN recorded in PBLG/DMF system at 305 K. This map can be compared to that reported in 2001 but obtained with the PBLG/CHCl3 phase (see Figure SI-6a).[36] Eight QDs are observed in the spectrum corresponding to the four enantiotopic sites (10/13, 11/12, 14/16 and 15/17) (see Figure SI6b), thus indicating that all enantiotopic directions are spectrally discriminated, with differences of 2H-splittings varying from 18 Hz (sites 11/12) to 90 Hz (sites 15/17 or 10/13). The determination of sign of 2H-RQCs in PBLG/DMF was achieved accordingly to the procedure described for FCH. As previously, Gaussian computations on the optimized molecular structure of NBN allows the calculation, inside MSpin-RQC, of QCCi values for each 2H site from the EFG values, Vzz. Associated data are reported in Table SI-2. Associating QDs associated to each enantiotopic face, is not trivial. This can be accomplished by performing a SVD determination of the Saupe matrix in MSpin-RQC for each possible permutation of the values. In the case of NBN, there are four pairs of enantiotiopic deuterium sites, and therefore eight possible assignments of the 2H-RQC values to the different sites, since only relative rather than absolute configuration can be determined.[36] Similarly to the way diastereotopic protons are assigned through RDC data,[112-115] we can also assign the relative configuration of each enantiotopic site to a particular 2H-RQC, but not determine the absolute configuration. [36] Consequently, we named the two enantiotopic faces related by the plane of symmetry as A and B (see Figure 2b). This article is protected by copyright. All rights reserved.

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Table 5. Q factor value vs. permutation of enantiotopic pairs of NBN in the PBLG/DMF and PBLG/CHCl3 phases N° perm.

1

2

3

4

5

6

7

8

Y[a] Y[b] Y[c]

NYY

NNY

YNY

YYN

NYN

YNN

NNN

Q factor (DMF)

0.019

0.041

0.076

0.111

0.213

0.225

0.227

0.390

Q factor (CHCl3)

0.017

0.030

0.056

0.087

0.174

0.184

0.185

0.181

Permutation

[a] Pair 11/12 permuted (Y) or not (N) with respect to original assignment. [b] Pair 14/16 permuted (Y) or not (N). [c] Pair 15/17 permuted (Y) or not (N).

After arbitrarily assigning the (S)-10 and (R)-13 bridgehead positions (see Figure 2b) to the more and less negative QD values, namely to -229 and -139 Hz, respectively (see Table SI3) all possible combinations of 2H-RQC data were examined. As we can see in the same table, one of the assignments furnishes a distinctly lower Q value (0.019). The second best assignment corresponds to the swapping of the 11 and 12 sites and has a higher Q factor of 0.041. As shown in Table 6 the average relative difference between experimental and backcalculated values, for the correct assignment, does not exceed 3 %, the largest discrepancies being observed for the deuteron bonded to sp 2 carbon atoms. The gravimetric plot is presented in Figure 7a. Experimental

2H-RQC

data associated to NBN dissolved in

PBLG/CHCl3 at 305 K were extracted from a previous work (see Table SI-3).[36] Similarly to the PBLG/DMF system, all enantiotopic sites are discriminated with Dn Q differences varying from 10 (sites 11/12) to 47 Hz (sites 10/13) (see Figure SI-5). However, the degree of alignment of NBN is smaller in PBLG/CHCl3 than in PBLG/DMF (GDO=0.8 x 10-3 vs. 1.3 x 103).

This can be due to the lower mass fraction of polypeptide (18 instead of 22 %w/w)

compared to PBLG/DMF sample, thus reducing the density of polymer and the packing effect as well as the higher polarity of DMF, which would increase the time of residence of the rather apolar NBN molecule in the vicinity of the PBLG helices.[103,106] For the grouping of the QD (and associated 2H-RQC) to a given face A or B to the PBLG/CHCl3 data set we applied the same protocol as for PBLG/DMF sample (see Table 6). The results are identical to those reported in 2003.[36,116] Here again the agreement between experimental and back-calculated value is excellent (see Figure 7b). Table 7 lists all ordering-related parameters obtained from the experimental 2H-RQC’s of NBN in PBLG/CHCl3 and PBLG/DMF, along with the SVD condition and the Q factor.

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Table 6. Experimental vs. computed 2H-RQC (Hz) dataset of NBN in the PBLG/DMF and PBLG/CHCl3 phases [a] PBLG/DMF

PBLG/CHCl3

13C

2H

Bridgeh.

1

10

(A)

-229

-228.5

-0.22

(A)

-146

-145.3

-0.48

Bridgeh.

4

13

(B)

-139

-137.4

-1.16

(B)

-99

-98.6

-0.41

C=C

2

11

(A)

-82

-78.5

-4.46

(A)

-50

-48.3

-3.52

C=C

3

12

(B)

-64

-60.7

-5.44

(B)

-40

-39.9

-0.25

Exo

5

14

(B)

+40

+41.4

+3.38

(B)

+28

+28.6

+2.09

Exo

6

16

(A)

+82

+83.5

+1.80

(A)

+47

+49.6

+5.24

Endo

5

15

(B)

-143

-141.4

-1.13

(B)

-74

-73.2

-1.09

Endo

6

17

(A)

-53

-52.5

-0.95

(A)

-28

-27.5

-1.81

Syn

7

8

NA

+239

+243.5

+1.85

NA

+152

+153.8

+1.17

Anti

7

9

NA

+78

+75.1

-3.86

NA

+52

+49.8

-4.44

Group

Q factor

Face

Exptl

Comp.

Diff. %[b]

Face

0.019

Exptl

Comp.

Diff. %[b]

0.017

[a] Experimental data in PBLG/CHCl3 are extracted from ref. 46. [b] Relative difference (%) between experimental and back-calculated 2HRQC’s calculated as 100[QComp. - QExptl]/QComp..

Figure 7. Gravimetric plots of back-calculated versus experimental dataset (2H-RQCComp. vs. 2H-RQCExptl) for NBN dissolved in (a) PBLG/DMF and (b) PBLG/CHCl3.

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Figure 8. Displaying of principal axis system of Saupe (Sx’, Sy’, Sz’) and inertia tensors (Ix’, Iy’, Iz’) as well as Saupe tensor surface (red and green surfaces indicate positive and negative 2H-RQCs, respectively). (a) NBN in PBLG/DMF (b) NBN in PBLG/CHCl3. The difference in the size of surfaces reflects the difference of magnitude of 2H-RQCs in both media, also shown by the variation of GDO parameter, from 1.3 x 10-3 to 0.80 x 10-3. Table 7. Order-based molecular data for NBN dissolved in the PBLG/DMF and PBLG/CHCl3 phases Parameters Q factor Saupe matrix eigenvalues ( 10-4)

Saupe matrix eigenvectors[b]

PBLG/DMF[a] 0.019 Sx’ = -2.922 Sy’ = -7.830 Sz’ = +10.75 e[x’] = (-0.925, -0.220, +0.311) e[y’] = (+0.257, +0.243, +0.935) e[z’] = (-0.281, +0.945, -0.169)

PBLG/CHCl3[a] 0.017 Sx’ = +1.513 Sy’ = -4.966 Sz’ = +6.509 e[x’] = (-0.946, -0.241, +0.216) e[y’] = ( 0.173, +0.189, +0.967) e[z’] = (-0.274, +0.952, -0.137)

SVD condition number

2.48

2.48

Axial component (10-4)

10.75

6.509

Rhombic component (10-4)

3.273

2.322

GDO ( 10-3)

1.305

0.804

[a] Calculation from experimental 2H-RQC dataset. [b] Coordinates expressed in the user-choice molecular frame (Gaussian standard orientation).

Solvent effect. To complete this study of NBN, we have compared the results obtained in the achiral PBG/DMF and PBG/CHCl3 phases with those recorded in the two chiral phases. Data relative to experimental and back-calculated RQC data are reported in Table 8 (see also Tables SI-3 and SI-4), whilst all ordering-related parameters are summarized in Table SI-5. Analysis of data in Tables 7 and 9 interestingly indicates that changing DMF by CHCl3 both in PBLG or PBG oriented phases does not produce dramatic variations in the rhombicity and the “5D” angles which quantify the orientation differences of the principal axes in the four orienting media, being the inter-tensor angle of only 5°. This occurrence

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Table 8. Experimental vs. computed 2H-RQC dataset (Hz) of NBN in “PBG”/DMF and PBG/CHCl3

“PBG”/DMF Group

13C

1H

Face

Exptd.[a]

PBG/CHCl3

Comp. Diff. %[b]

Face

Corr.[c]

Comp.[d]

Diff. %[d]

Bridgeh.

1/4

10/13

(A/B)

-184

-183.0

-0.55

(A/B)

-127.2

-126.6

-0.47

C=C

2/3

11/12

(A/B)

-73

-69.6

-4.89

(A/B)

-46.5

-45.2

-2.88

Exo

5/6

14/16

(A/B)

+61

+62.5

+2.24

(A/B)

+40.6

+42.0

+3.33

Endo

5/6

15/17

(A/B)

-98

-97.0

-1.03

(A/B)

-55.4

-54.7

-1.28

Syn

7

8

NA

+239

+243.5

+1.85

NA

+157.6

+159.8

+1.38

Anti

7

9

NA

+78

+75.1

-3.86

NA

+55.1

+53.0

-3.96

Q factor

0.019

0.016

[a] Expected 2H-RQC values in the PBG/DMF phase corresponding to the averaged values of 2H-RQCi measured in the PBLG/DMF phase for a given 2H-site). [b] Relative difference (%) between expected and computed back-calculated RQC’s calculated as 100[QComp. QExptd.]/QComp.. [c] Corrected experimental 2H-RQC values (see Table SI-4). [d] Computed back-calculated 2H-RQCs from corrected experimental 2H-RQC values.

indicates that the solvent, at least in this case, plays a minor role in the overall orientation, and the changes in inter-tensor angle are appreciably larger in going from the achiral to the chiral phases with “5D” angles in the order of 20º. Table 9. “5D” angle (°) between the order tensor, in several conditions, and the inertia tensor of NBN PBLG/DMF[a]

“PBG”/DMF[b]

PBLG/CHCl3[a]

PBG/CHCl3[c]

Inertia tensor

PBLG/DMF

-

20

5

21

110

PBG/DMF

20

-

17

4

112

PBLG/CHCl3

5

17

-

17

108

PBG/CHCl3

21

4

17

-

109

110

112

108

109

-

Inertia tensor

[a] Order tensor calculated from the experimental 2H-RQC dataset. [b] Order tensor calculated from the expected 2H-RQC dataset. [c] Order tensor from the corrected experimental 2H-RQC dataset. (see Table SI-4).

Correlation between inertia and alignments tensors and orientation mechanisms. For the FCH and NBN molecules (see Figures 4 and 8), the PAS of the determined Saupe tensors were in all cases close to the inertia tensor as determined by the “5D” angles between them (see Tables 4 and 9), indicating a fundamental steric alignment mechanism. Nevertheless noticeable differences between Saupe tensors for FCH enantiomers, as well as deviations of the Saupe tensor from molecular symmetry in the case of the NBN meso compound, could be efficiently quantified in terms of “5D” angles. This kind of analysis is of maximum interest for a robust mechanistic rationalization of enantiodiscrimination phenomena, maybe with the help of molecular dynamics, as this would in principle allow the determination of the absolute configuration. [105,117] This article is protected by copyright. All rights reserved.

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Conclusion and perspectives With the purpose of facilitating the use of anisotropic NAD NMR as a analytical tool, we present here the first 2H-RQC/DFT-based integrated computational protocol for simply and robustly evaluating the order parameters of aligned solutes through a SVD procedure. The potential of this approach has been illustrated by two examples of 2H-RQC-assisted analysis involving chiral and prochiral rigid molecules dissolved in polypeptide lyotropic chiral liquid. The quality of the results in terms of computed quality factors points out some important advantages of 2H quadrupolar interaction as compared to RDCs or RCSAs as its much larger magnitude, and therefore higher sensitivity to small changes in molecular ordering, and the absence of strong-coupling effects which hamper an accurate measurement of RDC data. This approach appears to be highly valuable to acutely understand the alignment process of solutes and specifically the role of parameters governing their enantiodiscrimination mechanisms in weakling orienting CLCs (molecular shape anisotropy, electronic effects, …). Next challenge of this approach will be the development and implementation of new computational approaches to simply investigate the case of flexible molecules and solve the problem of their conformational dynamics when dissolved in achiral or chiral mesophases. This exciting work is currently in progress in our laboratories. Through its associated observables (RCSA, RDC, RQC), anisotropic natural abundance NMR spectroscopy, greatly enriches traditional isotropic NMR techniques based on  values J-couplings, and nuclear Overhauser effects. So far, (13C-1H)-RDC’s and/or (1H-1H)-RDC’s data have been used intensively for determining molecular structures, assigning relative configuration or understanding the alignment properties and orientational mechanisms of solute by the mesophases. anisotropic observables such as here the 2H-RQC data

[36,48]

13C-RCSA

[18,20,53]

The advent of two other

data recently successfully exploited

[8,118]

or

as an alternative to classical RDC information and using

integrated computational tools significantly broadens the analytical interests of NMR in oriented media. All these recent achievements pave the avenue to a series of novel and fruitful prospects in the field of NMR of partially oriented small molecules. Acknowledgments P.L. and P.B. acknowledges both the CNRS and the University of Paris-Sud for their recurrent funding of fundamental research. A.N.-V. thanks KIT for a GästwissenschaftlerStipendium and UFPE for a visiting professorship as well as the HGF programme BIFTM,

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the DFG 555 (instrumentation facility Pro2NMR, LU 835/11), and FACEPE (APQ-05071.06/15) for financial support.

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