Chirality And Nuclear Magnetic Shielding

Chirality and the nuclearmagnetic shielding tensorwithDevin N. SearsCynthia J. JamesonRobert A. Harris1

A series of studies of thenuclear magnetic shieldingtensor in chiral anddiastereomeric systems: The shielding tensor of Xeinteracting with Ne helices The shielding tensor of anaked spin in Ne helices The single electron on a helixmodel The odd and even character ofthe shielding response to achiral 15)rXe@(Ne8)R(q15)l2

Questions: How do the shielding tensors of mirror imagemolecules differ? What are the measures of induced chirality ofa Xe atom in a chiral environment and also inthe chiral field of other asymmetric groups? Is the chiral potential provided by a pointcharge helix sufficient to provide a chiralshift for Xe atom of the right order ofmagnitude to be observable in the 129Xe NMRspectrum?3

I. The shielding tensor of Xeinteracting with Ne helices4

GOAL: to study the full nuclear shielding tensorof the Xe atom in a chiral environment andalso in the chiral field of other asymmetricgroups.MODEL of chiral environmenthelix 8 (or 7 or 15) Ne atoms, L or Rradius 3.260 Åpitch 3.5 ÅMODEL of second chiral fieldhelix 15 point charges ( 0.06e), l or rradius 6.3706 Åco-axial with Ne8 helix5

BASIS SET for Xe240 basis functions(uncontracted 29s 21p 17d 9f ).The core (25s 18p 13d) was takenfrom Partridge and Faegri;this was augmented by3s 2p 4d and 9f orbitalswith exponents taken from D. Bishop.Large enough so that the counterpoisecorrection to the 129Xe shieldingfunction is negligible in every case, 0.03 ppm where theintermolecular shielding is -63.35ppm (0.05%)and less ( 0.01%) at longer distances.6

The SHIELDING TENSORNorman F. Ramsey 1950sσ σ(1)diamagnetic σ(2)paramagneticσ(1)diamagnetic, xx (e2/2mc2) 〈Ψ0 i(yNi2 zNi2)/rNi3 Ψ0〉σ(2)paramagnetic, xx - (e2/2m2c2) q(Eq-E0)-1 〈Ψ0 iLxNi Ψq〉 〈Ψq i (LxNi /rNi3) Ψ0〉7

6.3706 Å3.260 ÅPitch 2π(0.557042)b 0.5570428

Model System Xe@Ne8( q)15(Ll)3.34 Å3.49 Å3.70 Å3.27 Å3.27 Å3.34 Å3.70 Å3.49 Å9

Model System Xe@Ne8Xe in a left handed helix (L)Xe in a right handed helix (R)10

Model Systems Xe@Ne8( q)15(Ll)(Rr)(Lr)(Rl)Ll and Rr are mirror imagesLr and Rl are mirror imagesLl and Lr are diastereomers11

SYMMETRYand the shielding tensorHow many different non-zero components?depends on the nuclear site symmetry(which could be lower than thesymmetry of the molecule as a whole).σ(2)paramagnetic, xx - (e2/2m2c2) q(Eq-E0)-1 〈Ψ0 iLxNi Ψq〉 〈Ψq i (LxNi /rNi3) Ψ0〉12

NUCLEAR SITE SYMMETRYand the number of non-vanishing σ tensor componentsnuclear sitesymmetryLzC3vOhA2LxLyE15Nin NH359Co in CoL6T1gTdT113CD2hB1gB3gB2gC2vCsC4vD hC vA2A′A2 g B2A′′B1A′′Eπgπin CF4in H2C O15N in NOCl55Mn in Mn(CO)519F in F21H or 19F in HF(z is the highest symmetry axis)17O13

How do the shielding tensors ofmirror image molecules differ?14

Compare shielding σ tensorfor Xe in a left-handed Ne8 helixvs. Xe in a right-handed Ne8 helixXe@Ne8Xe in a left handed helix (L)Xe in a right handed helix (R)15

Xe shielding tensor, nuclear site symmetry is C2Xe@Ne8(R)andXe@Ne8(L)full c etric tensor00000000 0.029400-0.02940-0.029400 0.0294016

How do the shielding tensors ofmirror image molecules differ?All elements are IDENTICAL,EXCEPT that correspondingoff-diagonal elementshave opposite signsin the full tensor,in the symmetric part of the tensor,and in the antisymmetric part of the tensor17

Model Systems Xe@Ne8( q)15(Ll)(Rr)(Lr)(Rl)Ll and Rr are mirror imagesLr and Rl are mirror imagesLl and Lr are diastereomers18

σ[Xe@Ne8( q)15]Rr LlRl 60-17.3762 4.53460-3.7095-29.71620 0-16.92364.19140-3.8906-28.38610 3.8906-28.3861Tensors of Rr and Ll are experimentally indistinguishable sinceonly the signs of off-diagonal tensor components are different;19ditto for Rl and Lr.

Measures of induced chirality of Xe: non-zero antisymmetric tensor elements,0.4126 and 0.1504 ppm for (Rr) and (Rl)respectively; non-vanishing butdifficult to measure experimentally isotropic chemical shift betweendiastereomers-0.9342 ppm for (Rr) – (Rl)appears as a splitting20

isotropic 129Xe shielding, ppmModelXe@Ne7( q)13 Xe@Ne8( q)15 Xe@Ne15L, R-64.7656-68.9434Rr, Ll-26.4683-20.9015Lr, Rl-25.5027-19.9673diastereomeric shift-0.9656-0.9342(Ll - Lr)or (Rr - Rl)-75.81721

129XeNMR spectrum of Xe in Ne helicesdiastereomeric ppmfree Xe atomD.N. Sears, C. J. Jameson, R. A. Harris, J. Chem. Phys. 119, 2685 (2003)22

CONCLUSIONS I: Chiral potential provided by point chargehelix is sufficient to provide a chiral shift for Xeatom of the right order of magnitude to beobservable in the 129Xe NMR spectrum. Therefore, can calculate Xe shielding atcenter of the chiral cryptophane cageattached to chiral tethers by using pointcharges to represent the atoms of the tether.23

II. Shielding tensor of a naked spinin Ne8 helicesZZYY24

II. Shielding tensor of a naked spin in Ne8 helicesExamine the molecular shielding of the chiral systemitself. This is the shielding that can be mapped byplacing a magnetic moment anywhere around (or in)the molecule.GOALS: To find out To what extent does the molecular shielding tensorreflect its chiral character? Is the sign of the chiral shift betweendiastereomers related to the same or oppositehandedness of the two chiral systems that25make the diastereomeric pair?

Isotropic shielding of a naked spin in chiral systemsσiso, ppmSystemMirror image systemn@Ne8 (L)n@Ne8 (R)-0.0016[n@Ne8 ( q)15] (Ll)[n@Ne8 ( q)15] (Rr) 0.9218[n@Ne8 ( q)15] (Rl)[n@Ne8 ( q)15] (Lr) 0.9409[n@Ne8 (-q)15] (Ll)[n@Ne8 (-q)15] (Rr)-0.9277[n@Ne8 (-q)15] (Rl)[n@Ne8 (-q)15] (Lr)-0.9535Chiral shifts:[n@Ne8 ( q)15]Ll - Lr-0.0191[n@Ne8 (-q)15]Ll - Lr 0.025826

NMR spectrum of a naked spin in Ne rRl 0.922n@Ne8 0.941 ppmn@Ne8( q)1527

CONCLUSIONS II The molecular shielding of the system of Ne8 and pointcharge helices is sampled by the naked spin at the center,revealing the diastereomerism in the scalar property,the diastereomeric shift. Replacing Xe by a naked spin gives a clear indication ofthe induced diastereomerism of the Xe electrons:the diastereomeric shift is 0.9342 ppm for Xecompared to 0.0191 ppm for the naked spin. When the sign of the chiral potential is changed, both thesign and the magnitude of the diastereomeric shift changed.Thus, the sign of the shift between diastereomersis not uniquely related to the handedness of thediastereomeric pairs. In other words, it is not possible to a prioriassign the individual peaks which would be observed in anNMR spectrum unequivocally: which is (Ll, Rr) which (Lr, Rl)?28

antisymmetric componentsSystemppmσanti(Xe@Ne8Ll )σanti(Xe@Ne8Lr )σanti(n@Ne8Ll )σanti(n@Ne8Lr 3920.214229

diastereomeric shiftsSystemppmσ(Xe@Ne8Ll )- σ(Xe@Ne8Lr )σ(n@Ne8Ll )- σ(n@Ne8Lr )σ(n@Ne8Ll-)- σ(n@Ne8Lr-)σ(n@e-Ll)- σ(n@e-Lr)-0.9342-0.0191 0.0258 0.0360530

GRAND CONCLUSIONS from I and II:Manifestation of chirality in a scalar measurement(nuclear shielding tensor):Chirality appears explicitly if and only if the givenchiral system is coupled to another chiral system(diastereomerism).I.We looked at induced chirality and induceddiastereomerism.Replacing tethers with chiral potentials appearsan adequate method of simulating diastereomerism31

II. We replaced the Xe by a naked spin to examineexplicitly how the Xe electrons are affected by theirinteraction with diastereomers: The effects of the chiral environments are alsoobserved in the shielding tensor for the naked spin. Antisymmetric tensor element splitting is an order ofmagnitude larger in Xe than in the naked spin.This is a new manifestation of diastereomerism.Interaction of Xe electrons with the chiral environmentamplifies the effects.32

The odd and even character of theshielding response to a chiralpotential.Questions: What determines the sign of thediastereomeric splitting? For a given configuration, does thesign of the splitting depend on thesign ( q or –q) of the electrostatic potential? Does the geometry affect the signof the diastereomeric splitting? Is a unique assignment of the peaks(which is Rl, which Rr) possible?33

The odd and even character ofthe shielding response. Models:in a chiralmolecule(modeledby a Ne8 helix)whensubjectedto a chiralpotential(modeledby a helixof pointcharges).34

V( q,r) a potential at point r due to an outerhelix of partial charges of value q:V( q, r) q V(r)From a right-handed helix of partial charges,[V(r)] right Veven(r) Vodd(r)From a left-handed helix of partial charges,[V(r)] left Veven(r) – Vodd(r)35

For Xe in a right-handed Ne8 helix Rthere are four unique nuclear magneticshieldings due to right or left-handed helixof charges q or -q:σRr ( q), σRr (-q), σRl( q),andσRl(-q)36

σRr ( q) q(σe σo) (q2/2!)( σee σoo 2σeo) (q3/3!)( σeee σooo 3σeoo 3σeeo) σRl ( q) q(σe - σo) (q2/2!)( σee σoo - 2σeo) (q3/3!)( σeee - σooo 3σeoo- 3σeeo) The derivatives of the shieldingwith respect to Veven and Voddare denoted by subscripts e and o37

{σRr( q) - σRl( q) - σRr(-q) σRl(-q)}/4qprovides values of thederivatives:q2 and q3 terms give:(a) The intercept is σo,and the slope is[σooo 3σeeo]/3!.(b) The intercept is σe,and the slope is[σeee 0080.0120.0160.0200.0120.0160.020q2{σRr( q) σRl( q) - σRr(-q) - σRl(-q)}/4qThe chargedependence ofthe Xe 000.0040.008q238

In the limit q 0,the values are(a) σeoand(b) {σee σoo }{σRr( q) - σRl( q) σRr(-q) - σRl(-q)}/4q2provides values of 0.100.120.140.100.120.14 q {σRr( q) σRl( q) σRr(-q) σRl(-q)}/2q2The chargedependence ofthe Xe shielding0200(b)1501005000.000.020.040.060.08 q 39

The diastereomeric splittings areδ( q) ( 2q)σo (q2/2!)( 4σeo) (q3/3!)2(σooo 3σeeo) Thus,the diastereomeric splittings are ameasure of odd powers of Vodd.40

0.050.00-0.05-0.10-0.15-0.15σRr - σRl is the samefor q or –q charges-0.10-0.050.000.050.100.15q4(b)XeXe2(σRr - σRl), ppm(b) for Xe, the sign ofnaked spin0.10(a) for the naked spin, thesign of σRr - σRl dependson the sign of the charges(a)Naked Spin(σRr - σRl), ppmThe dependenceof thediastereomericsplitting on 41

CONCLUSION: For Xe, although the magnitude of the splittingdepends on the magnitudes of the electrostaticpotential, for a given configuration of diastereomers,the chirality of the potential alone determines thesign of the diastereomeric splitting. In otherwords, unique assignment of the peaks to Rl or Rr ispossible. Geometry affects the sign of the diastereomericsplitting. For a second configuration ofdiastereomers, the sign of the splitting can bedifferent, but as above, does not change with q or -q42

ZYACKNOWLEDGMENTS:The National Science FoundationThe Miller Research InstituteE. Janette Ruiz and Megan Spence for inspirationAlex Pines and his Pinenuts for their hospitality 43

Epilogue44

Xe signal is splitWith D3d symmetry,the cryptophane-Acage is chiral.When a further chiralfunctional group issubstituted onto thecryptophane-A cage,the 129Xe NMRsignal from thexenon sequesteredwithin the cage is splitinto two or more peaks.Arg Lys Arg Lys1 ppmM. M. Spence, E. J. Ruiz, S. M. Rubin,T. J. Lowery,N. Winssinger, P. G. Schultz, D. E. Wemmer, A. Pines,J. Am. Chem. Soc. 126, 15287 (2004)45

To understand diastereomericshifts of Xe we studied model systems:Xe in helicalarrangementsof atoms andpartial chargesat coaxial orperpendicularconfigurations,to establishthat the chiralnature of realtethers can bemodeled bydifferentlyorientedpartial charges46

The MoMo(-) enantiomerof the cryptophane-A cage.The L label used for thiscage is consistent withthe L label for theleft-handed helix.47

Diastereomerism of functionalized cageschiralcomponentsdiastereomerssame σcageaminoacidsconfigurationRlRlLrLlLlRr Nuclearshieldings are related by symmetryσ(Rr ) σ(Ll ) andσ(Rl ) σ(Lr )48

Quantum mechanical Xe shieldings for twospatial configurations of the amino acid tetherwith respect to the cryptophane-A cage(L)-cryptophane-A-(l)-tether0.3453LlLlLl LrLr64.5 63.5 62.562.5 61.5 60.560.5 59.5 58.558.5 57.5 56.556.564.5σiso(Xe@cryptophane-A-rkrk) – σ(free Xe atom)Lr(L)-cryptophane-A-(r)-tether49