Spin Dynamics. Basics of Nuclear Magnetic Resonance.


Updated 20 March 2009.
Substantial errors are indicated by bold type.

There are some differences between the print runs. Some of the later printings introduced new errors, while correcting others. So far I know about major errors on page 533 and 566 which only occur in 2002 printings (see below). Please inform me if you detect other discrepancies.

Plate 1. The person should be thought of as lying on his/her back, feet towards the reader.

Page 9: It is not strictly true that "no large objects have angular momentum `by themselves`, without rotating". See supplementary notes.

Page 21: The last line of note 5 should read "in Figure 15.23" (Corrected in the 2002 reprint).

Page 21: In further reading, the book by Sakurai is called "Modern Quantum Mechanics."

Page 24: In Eq.2.1, should be in bold type.

Page 25: The magnetic susceptibility of pure water is The figure in my book was taken from Atkins, "Physical Chemistry", 7th edition, which is also in error.

Page 26: In Figure 2.3, the magnetic field lines circulate in the wrong direction.

Page 34: The numerical value of the nuclear susceptibility of water at 300 K should be . The sentence below should read "This is about three orders of magnitude smaller..." (see the correction to page 25). See also supplementary notes.

Page 37: Line before Eq.2.7, "timet" should be "time t".

Page 47: Insert "one" before 13C on line 7.

Page 47: The spin-0 isotope 30Si is present in 3.1% natural abundance, in addition to the spin-0 isotope 28Si, which has a natural abundance of 92.2%.

Page 49, line 1: 28Si should be replaced by 29Si.

Page 49: In the first sentence of the last paragraph, replace "larger" by "smaller".

Page 60: The second equals sign should be replaced by "approximately equal to".

Page 61: The first equation should read "=", not ""

Page 71: Seven lines from bottom, replace "many cubic centimetres" by "around a cubic centimetre".

Page 99: In Figure 5.13, the units of should be s-1, not s.

Pages 102-105 (Equation 5.10 and following): There is an unneccessary shift in notation from to .

Page 103. The absorption Lorentzian (Eq.5.11) has an integral of , not 1.

Page 104: In Figure 5.19, the units of should be s-1, not s.

Page 105: The left-hand side of the first equation should be .

Page 105: The curve in Figure 5.22 should oscillate around zero (the x-axis).

Page 111: Insert "an" before "imaginary" at the end of the first paragraph.

Page 114: 5th line, "wierd" should be spelt "weird".

Page 115: The left-hand side of the first equation should be s(t1,t2).

Page 120: The reference to Figure 5.6 should be to Figure 5.43.

Page 121, note 6. The States and TPPI methods are not fully equivalent. See supplementary notes.

Page 130, 2nd line. Replace "The expansion coefficients may be evaluated" by "The expansion coefficients in terms of the basis functions in Eq.6.1 may be evaluated".

Page 133: 2nd line of Eq.6.12: third item should be (Corrected in the 2002 reprint).

Page 143: Line after Eq.6.33 should read "see Section 6.4.4" (Corrected in the 2002 reprint).

Page 154: The annotation in Fig.6.11 should be b, not q.

Page 157: See note concerning the orbital pictures in Fig.6.16.

Page 164: In the third matrix of Eq.6.74, the lower right element should be -1.

Page 171-174: It is not strictly true that nuclei with spin=1/2 have no electric quadrupolar moment. See supplementary notes.

Page 172: The zero-order term is missing in the equation before Equation 7.4.

Page 172 and following: The description of how the spherical charge moments interact with the electric field components is loose. A revised discussion will be available shortly at this site.

Page 177: Replace the term "non-bold" by "lightface".

Page 187: Replace "cubic volume" by "spherical volume".

Page 196: Line after Figure 7.39, replace "secular induced fields" by "secular components of the induced fields".

Page 198: See note concerning the isotope shift.

Page 201-202. There are several errors concerning the definitions of the quadrupolar interaction.

In Eq.7.30, the right-hand side should be divided by 3.

In Eq.7.32, the right-hand side should be divided by hbar.

In Eq.7.33, the right-hand side should be divided by hbar.

See also page 577-578.

Page 204: In the line after Eq.7.35, " and " should be " and ".

Page 205: The heading of section 7.9.1 should read "secular dipole-dipole coupling".

Page 212: In the second row of the J matrix, Jjkzz should be Jjkyz.

Page 213, 7 lines from end, replace "around 7 Hz" by "around 7 Hz when averaged over all rotamers".

Page 214: In the caption to Figure 7.60, replace "NH protons" by "HN protons", and replace "C protons" by "H protons".

Page 215: Fig.7.61 and the accompanying discussion are confused. Since the electrons have negative gyromagnetic ratio, their magnetic moments are in the opposite direction to their spin angular momentum. Neighbouring nuclei and electrons with the same sense of angular momentum therefore have decreased energy, compared to a situation of opposite nuclear and electronic spin angular momentum.

A corrected version of Fig.7.61 is here. The figure caption should read: "(b) When one nuclear spin is present, the two electron states are no longer exactly degenerate. Due to the electron-nucleus hyperfine interaction, and the negative value of the electron gyromagnetic ratio, the state with the electron spin parallel to the nuclear spin is slightly lower in energy. (c) When two nuclear spins are present, the state with antiparallel nuclear spins is slightly lower in energy than the state with parallel nuclear spins, since in the former case the electrons may also be aligned so as to minimize their interaction energy with both nuclear spins. "

The paragraph below the figure should read "The introduction of a nuclear spin on one side change matters, because the nuclear spin has a magnetic hyperfine interaction with the electron. The energy of the state shown in the left-hand side of Figure 7.61(b), in which the electron spin close to the nucleus has the same direction as the nuclear spin polarisation, is slightly reduced. The electron spin distribution is therefore slightly shifted by the presence of the nuclear spin: There is a slight tendency for electrons near the nucleus to be polarized in the same sense as the nucleus, while electrons distant from the nucleus are polarized in the opposite sense. When a second nucleus is introduced, the energy of the system now depends on whether the two nuclei have the same or opposite polarizations: The state in which the two nuclei have opposite polarizations is relatively low in energy, because in this state both nuclei couple to electrons with favourable spin orientations, while keeping the electron spin polarizations opposite: The state where the two nuclei have the same polarization is relatively high in energy, because it is not possible to achieve consistently favourable spin orientations (Figure 7.61(c)). This mechanism therefore predicts a positive value of the J-coupling, as found experimentally for one-bond couplings between spins with the same sign of .

Page 217: The reference to Figure 7.3 should be to Figure 7.63.

Page 220: "momentum" is misspelt in line 8.

Page 229: In figure 8.12, one hydrogen should be going into the plane.

Page 234: Remove one of the "+" signs in Eq.8.11.

Page 246: Replace "This is state is an eigenvalue" by "This is an eigenstate" halfway down the page.

Page 281: In figure 10.7, left hand side, the phase should be marked as the angle between the Re axis and the arrow.

Page 307: In summary step (6) - the reference to Equation 10.50 should read Equation 10.48.

Page 313: In exercise 10.2(iii), the pulse durations should be 2.5 s, 5.0 s, 2.5 s.

Page 320: In figure 11.8, the on the time axis should be (Corrected in the 2002 reprint).

Page 326: "protons" is misspelt in the last line.

Page 327: In Figure 11.24, the magnetic field lines circulate in the wrong direction.

Page 330: In Figure 11.31, the magnetic field lines circulate in the wrong direction.

Page 331: In Figure 11.33, the magnetic field lines circulate in the wrong direction.

Page 340-341: It should be clearer that Eq.12.1 assumes the validity of the weak-coupling approximation (Eq.12.2). See section 8.6.

Page 350: The reference to Equation 12.19 should be to Equation 12.9(Corrected in the 2002 reprint).

Page 350: The terms ab and ba should be exchanged in the last equation on the page (Corrected in the 2002 reprint).

Page 353: The reference to Equation 12.2 should be to Equation 12.12.

Page 354-360: There are several mistakes in figures 12.13, 12.14, 12.15, 12.19 and 12.20. Corrected figures are available here.

Page 363: second paragraph from bottom, 1st sentence, replace 2 by -2.

Page 366: Insert "be" before "used".

Page 370: Replace 1/(2i) in second-last equality before Fig.12.30 by 1/2.

Page 380: At the end of the page, J12 should be replaced by 20 four times.

Page 393: In strongly-coupled systems, the signal induced by a coherence transfer pathway incurs an additional factor representing the coupling strength of the coherence to the receiver coil. See supplementary notes and pages 590-591.

Page 401: In Figure 13.18, the isotopomer labels (in the caption and the graphics) should be II and III.

Page 402: In Figure 13.19, the isotopomer label (in the caption and the graphics) should be IV.

Page 417: The word "magnetogyric" is misspelt(Corrected in the 2002 reprint).

Page 417: The formula relating the signal-to-noise ratio to and B0 is very rough and assumes comparable linewidths and probe performance.

Page 421: In Fig.13.32, the sign of the "transferred" signal is incorrect. The total signal should have an enhanced negative peak on the left, and a diminished positive peak on the right. I had overlooked the relative signs of the Boltzmann factors. Furthermore, note that experimental implementations of this pulse sequence may give different results if the signs of the phases have not been implemented correctly on the relevant spectrometer channels (see note 4 on page 87, the references cited there, and this page).

Page 421, third line up: replace 5 by 4.

Page 424: "Gramicidin" is a more common spelling than "gramicydin".

Pages 427-429: It is possible that lipids do not actually form disk-like bicelles under the conditions typically used for biochemical NMR. See supplementary notes.

Page 429: The reference to Equation 13.6 should be to Equation 13.16.

Pages 429-430: The doublet splitting is actually 2IS, not IS. The second paragraph of section 13.4.4 should begin: "The 13C spectrum therefore consists of a doublet with splitting 2IS = 2dIS+2 JIS". Similarly, Equation 13.17 should be "2IS = (1/2)bIS+2 JIS" and Equation 13.18 should be "2IS = -(1/4)bIS+2 JIS".

Page 438: "Lasso" is misspelt

Page 442: The density matrix element in position 3,8 should be "+ beta+" not "alpha beta +".

Page 484: Figure 15.9 may give the misleading impression that molecules are caused to flow by a magnetic field gradient. This was not the intention.

Page 486: The timescale for protons should be 64 s, not 32 s.

Page 469: Paragraph after equation 14.14, replace "long compared to the J-couplings" by "long compared to the inverse of the J-couplings".

Page 509: Last line. Replace T1 by T1-1.

Page 519: In equation 16.3, the term d is missing after the integral sign.

Page 532: The field symbol in Figure 16.29 is incorrect. For the correct version, see here. (Corrected in the 2002 reprint).

Page 533: The 2002 printing, but not earlier printings, has the incorrect Figure 16.30. For the correct version, see here.

Page 566: In the caption to Figure 16.69, change "is" to "in" (first printing). The 2002 printing has a mangled caption. It should read "local field generated by the proton in the | > state, when the NH vector is parallel to the external field."

Page 566: The paragraph after Figure 16.69 should read "If the 1H spin is in the | > state..". The 2002 printing has partially corrected this error, but the vertical bar has been omitted.

Page 577-578. There are several errors concerning the definitions of the quadrupolar interaction. In Eq.17.11, the right-hand side should be divided by (3*hbar). In the first equation on page 578, the right-hand side should be divided by (3*hbar). See also pages 201-202.

Page 580: Just above the last equation, the sentence should read "with non-degenerate eigenvalues (1/2)omega0.

Page 582: There are two references to Eq.17.33 which should refer to Eq.17.18.

Page 587: Remove the factors 1/2 from the second-last and third-last equations on the page.

Page 589: The factor 1/2 should be removed after "tan".

Page 623: /4 should be replaced by /2 in the two equations at the bottom of the page (two places) (Corrected in the 2002 reprint).

Page 624: /4 should be replaced by /2 in the two equations at the top of the page (four places) (Corrected in the 2002 reprint).

Page 630: The factor Omega^bar (defined in the first part of Eq.15.5) should be added to the values of both eigenvalues, defined in the last equation on the page.

Page 631: In the right-hand side of the third equation, replace 1/(2i) by 1/(4i). The factor of (1/2) arises since the initial spin order is divided between sites in the A and B states (see the first equation on page 628). The right-hand sides of the two following equations should also be divided by two. The last equation on page 631 is correct as stated.

Page 634: The bottom-right element of the matrix in Eq.17.82 should be -4W1.

Page 635: The bottom-right element of the matrix in the second equation on the page should be -4W1. This does not affect the subsequent argument since the matrix is still block-diagonal.

Page 671: "Coalescence" is misspelt. 

See also supplementary notes.


Some of these errors were detected by: P.K.Madhu, Arnold Maliniak, Tatyana Polynova, David Siminovitch, Young Lee, Alan Kenwright, Juan Alberdi, Slobodan Macura, Geoffrey Bodenhausen, Bernard Ancian, Gareth Morris, Jan Rainey, Bill Wallace, Vladimir Hnizdo, Dave Bryce, Eric Johnson, Ian Malcolm, Tanja Pietrass, Michael Roehrl, Linda Lai, Tom Bloemberg, Karel Klika, E. J. Pone, Olivier Lafon, Steven Wimperis, Emi Miyoshi, Henri Kivel, Andr Dorsch, Shidong Chu and Richard Green.

Please let me know by email if you detect any more errors.

Back to Spin Dynamics home page