2D ADEQUATE (Adequate DoublE QUAntum Transfer Experiment) is useful for determining which signals arise from coupled carbon pairs using proton detection. It is insensitive as only 0.01% of the carbons are excited at natural abundance but the proton detection makes it much more sensitive than 2D INADEQUATE. As a result, good sensitivity is achieved with 0.2 molar samples instead of the 2 molar samples required for 2D INADEQUATE. If you can enrich the sample to about 10% ¹³C then the ADEQUATE experiment can be run with low sample concentrations. A 2D ADEQUATE spectrum yields correlations via spin-spin coupling from pairs of coupled ¹³C's to protons. The spectrum correlates the proton frequency on the f₂ axis with the double-quantum carbon frequency (i.e. the sum of the two correlating carbon frequencies) on the f₁ axis, making the spectrum somewhat complicated to interpret. There are no diagonal signals. Signals that correlate with carbons similar chemical shifts loose sensitivity due to second order coupling.

There are four common types of ADEQUATE experiments depending on the number of bonds that the correlations take place over: 1,1 one-bond proton to one-bond carbon; 1,n one-bond proton to multi-bond carbon; n,1 multi-bond proton to one-bond carbon and n,n multi-bond proton to multi-bond carbon. Fig.1 shows the pulse sequence for 1,1- and 1,n-ADEQUATE and fig. 2 shows the pulse sequence for n,1- and n,n-ADEQUATE. 1,1- and 1,n-ADEQUATE spectra are fully phase sensitive while n,1- and n,n-ADEQUATE spectra can only be phased in f₁ as with long-range heteronuclear correlation and for the same reason.

Fig. 1. Pulse sequence for 1,1- and 1,n-ADEQUATE

Δ₁ = 1/4(¹J_CH), Δ₂ = 1/4(J_CC), Δ₃ = 1/4(¹J_CH) for CH only and 1/6(¹J_CH) for all multiplicities

Fig. 2. Pulse sequence for n,1- and n,n-ADEQUATE

Δ₁ = 1/4(¹J_CH), Δ₂ = 1/4(ⁿJ_CH), Δ₃ = 1/4(J_CC)

For the purposes of the ADEQUATE pulse sequences: the one-bond carbon-carbon coupling constant (¹J_CC) is usually 35 to 45 for a single bond and about 65 Hz for a double bond and are increased by electronegative substituents. Long-range (two or three-bond) carbon-carbon coupling constants (ⁿJ_CH) are of the order of 11 Hz.

The 1,1-ADEQUATE spectrum of phenanthrene (fig. 3) is shown in fig. 4. The double-quantum correlations appear at δ_A+δ_B-δ_o where A and B are the coupled carbons and δ_o is the carbon observation chemical shift (at the center of the spectrum). In practice this formula is only accurate to about 0.05 ppm for one-bond and 0.02 for multiple bond due to ^13/12C isotope shifts. For example (fig. 4, table 1), H1 at 8.83 ppm correlates with C1-C8b (122.91 and 130.58 ppm). The center of the ¹³C spectrum was set to 127.63 ppm so the correlation would be expected at 125.86 ppm but is observed at 125.81 ppm due to the isotope shift. The same analysis is applied to the 1,n-ADEQUATE - (fig. 5), n,1-ADEQUATE (fig. 6) and n,n-ADEQUATE (fig. 7) spectra. Table 1 lists the calculated (calcd. DQ shift) and measured (meas. DQ shift) double quantum chemical shifts for each pair of carbons and lists the types of (1,1-; 1,n-; n,1- and/or n,n-)ADEQUATE spectrum for which each correlation appears. The ADEQUATE spectrum is complicated by the symmetry of the molecule and that C2 and C3 chemical shifts are too close to separate

Fig. 3. Structure of phenanthrene

Fig. 4. 1,1-ADEQUATE spectrum of phenanthrene

Fig. 5. 1,n-ADEQUATE spectrum of phenanthrene

Fig. 6. n,1-ADEQUATE spectrum of phenanthrene

Fig. 7. n,n-ADEQUATE spectrum of phenanthrene

Table 1. Correlations for the ADEQUATE of phenanthrene with a ¹³C observation shift at 127.63 ppm

C/H	13C shifts	calcd. DQ shift	meas. DQ shift	H1 8.83 ppm	H2 7.77 ppm	H3 7.81 ppm	H4 8.06 ppm	H9 7.90 ppm
C1-C2	122.91, 126.77	122.05	121.97	1,1; 1,n	1,1; 1,n
C1-C4	122.91, 128.80	124.08	124.08	1,n				1,n
C1-C4a	122.91, 132.32	127.60	125.82	1,1; 1,n; n,1				n,1
C1-C9	122.91, 127.15	122.43	122.41	1,n				1,n
C3-C4	126.77, 128.80	127.94	127.88			1,1; 1,n	1,1; 1,n
C2-C4a	126.77, 132.32	131.46	131.47	n,n	1,n		n,n
C2,3-C8a	126.77, 130.58	129.72	129.72	n,n	1,n	1,n
C3-C9	126.77, 127.15	126.29	126.27			1,n		1,n
C4-C4a	128.80, 132.32	133.49	133.44		n,1		1,1; 1,n	n,1
C4-C8a	128.80, 130.58	131.75	131.79	n,n				1,n
C4-C9	128.80, 127.15	128.32	128.31				1,n	1,n; n,n
C4a-C8a	132.32, 130.58	135.27	135.21	n,1; n,n	n,1			n,1; n,n
C4a-C9	132.32, 127.15	131.84	131.82					1,1; 1,n; n,1
C8a-C9	130.58, 127.15	130.11	130.09					1,n

The ADEQUATE experiment can be carried out for more complicated examples such as cholesteryl acetate (fig. 8). In principle, the (1,1 - fig. 9; 1,n - fig. 10; n,1 - fig.11 and n,n - fig.12) ADEQUATE spectra can be used to confirm the assignment of cholesteryl acetate. You are welcome to try.

Fig. 8. Structure of cholesteryl acetate

Fig. 9. 1,1-ADEQUATE spectrum of cholesteryl acetate

Fig. 10. 1,n-ADEQUATE spectrum of cholesteryl acetate

Fig. 11. n,1-ADEQUATE spectrum of cholesteryl acetate

Fig. 12. n,n-ADEQUATE spectrum of cholesteryl acetate