Coupling Constants (J)

1. Bo Coupling Constants (J) -spin-spin coupling, scalar coupling or J-coupling Random tumbling of molecules averages through-space effect of nuclear magnets to zero Nuclear spin state is communicated through bonding electrons Energy of electron spin states are degenerate in absence of nuclear spin With a nuclear spin, the electron spin opposite to nuclear spin is lower energy Number of possible energy states of nuclear-electron spin pairs increases with the number of nuclear spins

2. Coupling Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states +J/4 J (Hz) bb I S ab ba -J/4 S I I S aa +J/4 Spin-States of covalently-bonded nuclei want to be aligned The magnitude of the separation is called coupling constant (J) and has units of Hz

3. 1 H 1 3 C 1 1 1 1 1 H H H H H Coupling Constants • through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities • The spacing in hertz (hz) between the peaks is a constant • Independent of magnetic field strength • Multiple coupling interactions may exist • Increase complexity of splitting pattern • Coupling can range from one-bond to five-bond • One, two and three bond coupling are most common • Longer range coupling usually occur through aromatic systems • Coupling can be between heteronuclear and homonuclear spin pairs • Both nuclei need to be NMR active i.e. 12C does not cause splitting three-bond four-bond one-bond five-bond

4. Coupling Constants • Splitting pattern depends on the number of equivalent atoms bonded to the nuclei • Determines the number of possible spin-pair combinations and energy levels • Each peak intensity in the splitting pattern is determined by the number of spin pairs of equivalent energy • Peak separation determined by coupling constant (J) • Negative coupling  reverse relative energy levels

5. 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1 Coupling Constants • Splitting pattern follows Pascal’s triangle • Number of peaks and relative peak intensity determined by the number of attached nuclei • Peak separation determined by coupling constant (J) 3 3 4 attached nuclei Relative Intensity 1 1 J J J Quartet Pascal’s triangle

6. Coupling Constants singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1 Common NMR Splitting Patterns • Coupling Rules: • equivalent nuclei do not interact • coupling constants decreases with separation ( typically #3 bonds) • multiplicity given by number of attached equivalent protons (n+1) • multiple spin systems  multiplicity  (na+1)(nb+1) • Relative peak heights/area follows Pascal’s triangle • Coupling constant are independent of applied field strength • Coupling constants can be negative IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.

7. Coupling Constants Common NMR Splitting Patterns

8. Coupling Constants • Rules for Chemical Shift Equivalence: • Nuclei are interchangeable by symmetry operation • Rotation about symmetric axis (Cn) • Inversion at a center of symmetry (i) • reflection at a plane of symmetry (s) • Higher orders of rotation about an axis followed by reflection in a plane normal to this axis (Sn) • Symmetry element (axis, center or plane) must be symmetry element for entire molecule • Nuclei are interchangeable by a rapid process • > once in about 10-3 seconds 180o Rapid exchange

9. Coupling Constants • Magnetic Equivalence: • Nuclei must first be chemical shift equivalent • Must couple equally to each nucleus to every other set of chemically equivalent nuclei • need to examine geometrical relationships • the bond distance and angles from each nucleus to another chemical set must be identical • Nuclei can be interchanged through a reflection plane passing through the nuclei from the other chemical set and a perpendicular to a line joining the chemical shift equivalent nuclei • Complex (second-order) splitting pattern Examples of Non-magnetically equivalent nuclei Chemical shift equivalent, but not magnetic equivalent 3JHaFa ≠ 3JHa’Fa 3JHaFa’ ≠ 3JHa’Fa’ 3Jab ≠ 3Ja’b 3Jab’ ≠ 3Ja’b’

10. 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1 Coupling Constants Multiple Spin Systems multiplicity  (na+1)(nb+1) 3JHb = 6 Hz What is the splitting pattern for CH2? 3JHa = 7 Hz 3JHb = 6 Hz Coupling to Hb splits the CH2 resonance into a doublet separated by 6 Hz Down-field resonance split into quartet up-field resonance split into quartet Coupling to Ha splits each doublet into a quartet separated by 7 Hz

11. Coupling Constants What Happens to Splitting Pattern if J changes? 3JHb = 7 Hz Looks like a pentet! 3JHa = 7 Hz Intensities don’t follow Pascal’s triangle (1 4 6 4 1) 3JHb = 6 Hz 3JHa = 3 Hz Looks like a sextet! Intensities don’t follow Pascal’s triangle (1 5 10 10 5 1) Occurs because of overlap of peaks within the splitting pattern

12. Coupling Constants • Coupling Constants Provide Connectivity Information • chemical shifts identify what functional groups are present NMR Peaks for coupled nuclei share the same coupling constants CH3 CH CH2 7 Hz 7 Hz 6 Hz 6 Hz 6 Hz 6 Hz 7 Hz 7 Hz Integral: 1 2 3

13. Coupling Constants • Deconvoluting a spin system • determining the J-values • determining the multiplicities present • J coupling analysis: • Is the pattern symmetric about the center? • Assign integral intensity to each line, outer lines assigned to 1 • Are the intensities symmetric about the center? • Add up the assigned intensities • Sum must be 2n, n = number of nuclei • Ex: sum = 16, n = 4 • Separation of outer most lines is a coupling constant • Relative intensity determines the number of coupled nuclei • Ex: intensity ratio: 1:2, 2 coupled nuclei • 1st splitting pattern is a triplet (1:2:1) • Draw the first coupling pattern • Account for all the peaks in the spin pattern by repeatidly matching the 1st splitting pattern • Smallest coupling constant has been assigned

14. Coupling Constants • Deconvoluting a spin system • determining the J-values • determining the multiplicities present • J coupling analysis: • ix. Coupling pattern is reduced to the center lines of the 1st splitting pattern. • x. Repeat process • Ex: sum = 8, n = 3 • Ex: intensity ratio: 1:1, 1 coupled nuclei • 2nd splitting pattern is a doublet (1:1) xi. Repeat until singlet is generated

15. Coupling Constants • Demo ACD HNMR Viewer software • first order coupling constants

16. CH2ClCHCl2 A2X system Coupling Constants • Description of Spin System • each unique set of spins is assigned a letter from the alphabet • the total number of nuclei in the set are indicated as a subscript • the relative chemical shift difference is represented by separation in the alphabet sequence • Large chemical shift differences are represented by AX or AMX • Small chemical shift differences are represented by AB • Can also have mixed systems: ABX • magnetically inequivalent nuclei are differentiated by a single quote: AA’XX’ or brackets [AX]2 CH3CH2R CH3CH2F A3X2 system A2M2X system [AX]2 system

18. Coupling Constants (J) • Observed splitting is a result of this electron-nucleus hyperfine interaction • Magnitude of the splitting is dependant on: • Number of bonds • Bond order (single, double triple) • Angles between bonds • Proportional to gagb • s character of bonding orbital • Increases periodically with atomic number (see chemical shift range) • Attenuated as the number of bonds increase • not usually seen over more than 5 to 6 bonds • Coupling is measured in hertz (Hz) • Range from 0.05 Hz to thousands of Hz • Can be negative sign

19. Coupling Constants (J) • Magnitude of the splitting is dependant on: • Geminal protons (H-C-H) usually larges coupling (Jgem ~ -12 Hz) • J falls rapidly as number of intervening bonds increase • 7 to 8 Hz for vicinal protons (H-C-C-H) • ~ 0 Hz for four or more bonds • Coupling enhanced by unsaturated bonds • 9J(H-H) = 0.4 Hz • Coupling enhanced by planar zig-zag configuration • Coupling over 4 to 5 bonds • Depends on the dihedral angle • Fixed or average conformation • Nature of other substituents • Electronegativity • Orientation • Carbon hybridization • Bond angles • Bond length

20. Coupling Constants (J)

21. Coupling Constants (J)

22. Coupling Constants (J)

23. Coupling Constants (J) • Second-Order Effects • occurs when chemical shift differences is similar in magnitude to coupling constants • chemical shifts and coupling constants have similar energy and intermingle • perturbs peak intensity and position • as chemical shift differences decrease, intensity of outer lines become weaker • Depends on J/nod • nod – chemical shift difference in Hz between the nucleim, • results from mixing of the equivalent ab and ba spin states • none of the transitions are purely one nuclei • Described by quantum mechanical wave functions AB spin system

24. AB spin system Coupling Constants (J) • Second-Order Effects • as the chemical shifts coalesce • intensity of outer lines decrease • inner peaks eventually collapse to singlet • nuclei become chemically and magnetically equivalent Weaker outer lines may be overlooked and interpreted as a doubley May be misinterpreted as a quartet

25. Coupling Constants (J) • Second-Order Effects (AB) • analysis of second-order splitting patterns • remember: resonance positions are also perturbed • separation between outer lines and inner lines (a-b, c-d) yields coupling constant (JAB) • true chemical shift is not the doublet centers • nod = √ (a – d) (b – c) Generally use computer programs to interpret second-order splitting patterns by simulating the spectra

26. Coupling Constants (J) Second-Order Effects (AB2)

27. AB X Coupling Constants (J) • Second-Order Effects (ABX) • spin state of X nuclei may be also perturbed • if X and AB chemical shift difference is large relative to J(AX) and J(BX) X is not perturbed • can treat AB part of spectra as composed of two AB sub-spectra • two AB sub-spectra are centro-symmetric with same J(AB) • nod = √ (g – m) (h – k) Two possible solutions for J(AX) and J(BX), use simulations to resolve Two AB sub-spectra are boxed in different colors

28. Coupling Constants (J) Second-Order Effects ([AX]2)

29. Coupling Constants (J) • Demo ACD HNMR Viewer software • second order coupling constants