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Coupling Constants (J)

1. 1. H. H. Coupling Constants (J). Coupling constants are a very important and useful feature of an NMR spectrum Importantly, coupling constants identifies pairs of nuclei that are chemically bonded to each other

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Coupling Constants (J)

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  1. 1 1 H H Coupling Constants (J) • Coupling constants are a very important and useful feature of an NMR spectrum • Importantly, coupling constants identifies pairs of nuclei that are chemically bonded to each other • Multiplicity identifies the number of protons (or other nuclei) that are chemical bonded to the other nuclei • The magnitude of the coupling constants identifies the coupling partner, and provides information on dihedral angles, hydrogen bonds, the number of intervening bonds, and the type of coupled nuclei (1H, 13C, 15N, 19F, etc.)

  2. 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 b b ab2 ab1 Bo a a random tumbling leads to no interaction between the spin-states despite the small magnetic fields

  3. Coupling Constants (J) -spin-spin coupling, scalar coupling or J-coupling Instead, 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 Spin state is “sensed” through bonds resulting in higher or lower energy - aligned or anti-aligned with magnetic field

  4. Coupling Constants Energy level of a nuclei are affected by covalently-bonded neighbors spin-states Mixing of Spin Systems One and Two bb b b ab ab ab ba a a aa Spin System Two Spin System One

  5. Coupling Constants Mixing of energy levels results in additional transitions – peaks are split +J/4 J (Hz) 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

  6. 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 • 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

  7. 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

  8. 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) • Negative coupling  reverse relative energy levels 3 3 3 attached nuclei Relative Intensity 1 1 J J J Quartet Pascal’s triangle

  9. 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.

  10. Coupling Constants Common NMR Splitting Patterns

  11. Coupling Constants • Coupling only occurs between non-equivalent nuclei • Chemical shift equivalence • Magnetic equivalence • For no coupling to occur, nuclei has to be BOTH chemical shift and magnetic equivalent The CH3 protons (H1, H2, H3) are in identical environments, are equivalent, and are not coupled to one another The Ha and Hb protons are in different environments (proximity to Cl), are not equivalent, and are coupled

  12. 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 Examples of Chemical Shift Equivalent Nuclei 180o Symmetry planes

  13. Coupling Constants Rules for Chemical Shift Equivalence: • Nuclei are interchangeable by a rapid process • > once in about 10-3 seconds • Rotation about a bond, interconversion of ring pucker, etc. Examples of Chemical Shift Equivalent Nuclei Rapid exchange Rapid exchange

  14. Coupling Constants Magnetic Equivalence: • Nuclei must first be chemical shift equivalent • Must couple equally to each nucleus in 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 Examples of Non-magnetically equivalent nuclei Chemical shift equivalent, but not magnetic equivalent 3JHaHc ≠ 3JHaHc’ 3JHbHc ≠ 3JHbHc’ 3JHaHc ≠ 3JHbHc 3JHaHc’ ≠ 3JHbHc’ 3Jab ≠ 3Ja’b 3Jab’ ≠ 3Ja’b’ 3JHaFa ≠ 3JHa’Fa 3JHaFa’ ≠ 3JHa’Fa’

  15. Coupling Constants Magnetic Equivalence: • Non-magnetically equivalent nuclei may lead to second order effects and very complex splitting patterns • Second order effects will be discussed later • Due to small chemical shift differences between coupled nuclei (Dn ~ J) http://www.chem.wisc.edu/areas/reich/chem605/index.htm

  16. 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

  17. 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

  18. 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

  19. 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 repeatedly matching the 1st splitting pattern • Smallest coupling constant has been assigned

  20. 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

  21. Coupling Constants Demo ACD C+H NMR Viewer software • first order coupling constants

  22. CH2ClCHCl2 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 (nAX >> JAX) • Small chemical shift differences are represented by AB (nAB < 5JAB) • Can also have mixed systems: ABX • magnetically in-equivalent nuclei are differentiated by a single quote: AA’XX’ or brackets [AX]2 CH3CH2R CH3CH2F A2X system A3X2 system A2M2X system [AX]2 or AA’XX’ system AB system

  23. A M X A M X TMS A M X J(MX) J(MX) J(AM) J(AM) = 4 Hz J(AX) J(AX) = 2.5 Hz J(AX) J(AX) J(AM) J(AM) J(AX) J(MX) = 6 Hz

  24. Coupling Constants (J) Observed splitting is a result of this electron-nucleus hyperfine interaction • Coupling is measured in hertz (Hz) • Range from 0.05 Hz to thousands of Hz • Can be positive or negative • 1JC-H and many other one-bond coupling are positive • 1JA-X is negative if g are opposite sign • 2JH-H in sp3 CH2 groups are commonly negative • 3JH-H is always positive reversed For an AX system, JAX is negative if the energy of the A state is lower when X has the same spin as A (aa or bb) The spin states and transitions are swapped reversed reversed

  25. Coupling Constants (J) Measure the Relative Sign of Coupling Constants • Multiple experimental approaches (different NMR pulse sequences) or simulations E. COSY – two-dimensional NMR experiment cross peaks identify which chemical shifts are coupled

  26. Coupling Constants (J) Measure the Relative Sign of Coupling Constants • The cross-peak patterns identifies the coupling constant sign and magnitude Based on the slopes of the diagonal line drawn through coupling pattern 3JAX and 3JBX have the same sign 3JAB opposite sign of 3JAX and 3JBX Yellow-highlighted regions are expanded

  27. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Number of bonds • Bond order (single, double triple) • Angles between bonds 3JAB 9.4 Hz 4JAC 1.1 Hz 5JAB 0.9 Hz 3JHH 8 Hz 3JHH 9.1 Hz 3JHH 11.6 & 19.1 Hz trans3JHH ~ 17 Hz cis3JHH ~10 Hz geminal2JHH ~2.5 Hz

  28. Coupling Constants (J) • Magnitude of the splitting is dependent on: • dihedral angle • Fixed or average conformation

  29. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Cyclohexanes dihedral angles • Fixed or average conformation 3Jaa 9-12 Hz 3Jee or 3Jea 3-4 Hz 3Jaa >>3Jee,3Jea Dual Karplus curves for the axial and equatorial protons

  30. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Cyclohexanes dihedral angles • examples

  31. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Cyclopentanes dihedral angles • Fixed or average conformation

  32. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Comparison between Cyclohexanes and Cyclopentanes • Because of range of cyclopentane conformations, vicinal couplings are variable: Jcis > Jtrans and Jcis > Jtrans • Only in rigid cyclopentanes can a stereochemistry be defined: Jcis > Jtrans In chair cyclohexane, only one vicinal coupling can be large (>7 Hz) In cyclopentane, two or three vicinal coupling can be large (>7 Hz)

  33. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Cyclobutanes are flatter than cyclopentanes, so: Jcis > Jtrans • unless structure features induce strong puckering of the ring or electronegative substituents are present • Cyclopropanes are rigidly fixed, so Jcis > Jtrans is always true

  34. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Orientation • unless structure features induce strong puckering of the ring or electronegative substituents are present • Internal hydrogen bonds may lead to constrained conformations and distinct different coupling constants Since methyl groups can freely rotate, the observed coupling is the average of the three individual coupling constants

  35. Coupling Constants (J) Magnitude of the splitting is dependent on: • Electronegativity of Substituents 3JH-H coupling constant decreases as electronegativity increases 3JH-H decreases even more with two electronegative substituents

  36. Coupling Constants (J) Magnitude of the splitting is dependent on: • Electronegativity of Substituents 3JH-H coupling constant decreases as electronegativity of substituents increases for cycloalkenes 3JH-H coupling constant decreases as electronegativity of substituents increases for alkenes

  37. Coupling Constants (J) Magnitude of the splitting is dependent on: • Ring Size • Coupling constants decrease as ring size gets smaller • Coupling constants also decrease as ring is formed and gets smaller

  38. Coupling Constants (J) Magnitude of the splitting is dependent on: • Bond order • Coupling constant decreases as bond order decreases • Heterocycles • Heterocycles have smaller coupling constants compared to hydrocarbons systems 3JH-H = 8.65 x (n bond order) + 1.66

  39. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Proportional to gagb • s character of bonding orbital • Increases with increasing s-character in C-H bond 1JC-H 125 Hz 2JF-H 48.2 Hz 1JN-H 95 Hz

  40. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Attenuated as the number of bonds increase • Usually requires conjugated systems (aromatic, allylic, propargylic, allenic) or favorable geometric alignment (W-coupling) • Not usually seen over more than 4 to 5 bonds (acetylenes and allenes)

  41. Coupling Constants (J) • Magnitude of the splitting is dependent on: • Geminal protons (H-C-H) fall into two major groups • Unstrained sp3 CH2 protons: 2JH-H -12 Hz • Vinyl sp2 CH protons: 2JH-H 2 Hz

  42. Coupling Constants (J) Magnitude of the splitting is dependent on: • Geminal protons coupling constants are effected by the electronic effects of substituents • Based on the interaction between the filled and empty orbitals of the CH2 fragment Note: opposite trend

  43. Coupling Constants (J) Magnitude of the splitting is dependent on electronic effects: • In acyclic and unstrained ring systems: 2JH-H ~ -10 to -13 Hz • When CH2 is substituted with a p-acceptor, like carbonyl or cyano coupling becomes more negative: 2JH-H ~ -16 to -25 Hz • Reliable and can help with structure assignments • Conjugated aryl, alkene and alkyne substituents also makes coupling becomes more negative

  44. Coupling Constants (J) • Magnitude of the splitting is dependent on electronic effects: • In unsaturated carbons: 2JH-H ~ 2.5 Hz • Electronegative substituents (F,O) behave as p-acceptors with a negative effect with 2JH-H close to zero • Electropositive substituents (Si, Li) behave as p-donors with a negative effect with 2JH-H • Oxygen substituents can behave as a strong s-acceptor and strong p-donor (lone pair), both positive effects leading to a large 2JH-H or as a strong p-acceptor leading to large negative coupling

  45. Coupling Constants (J) Magnitude of the splitting is dependent on electronic effects: • Summary of effects, s and p acceptors have opposite effects on coupling, as do s and p donors

  46. Coupling Constants (J)

  47. Coupling Constants (J)

  48. Coupling Constants (J)

  49. Coupling Constants • Weak coupling or first-order approximation • Up to now, we have assumed the frequency difference (chemical shift) between the coupled nuclei is large • Dn >> J • Second order effects come into play when this assumption is no longer valid • Dn < 5J • Second order effects lead to very complex splitting patterns that are difficult, if not impossible to interpret manually and leads to incorrect chemical shifts and coupling constants • Interpreting NMR spectra with second-order effects usually requires software

  50. Coupling Constants (J) Second-Order Effects (Strong Coupling) • occurs when chemical shift differences is similar in magnitude to coupling constants (Dn/J < 5) • chemical shifts and coupling constants have similar energy and intermingle • 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

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