DFT Calculations of ¹H NMR Chemical Shifts of Geometric Isomers of Conjugated Linolenic Acids, Hexadecatrienyl Pheromones, and Model Triene-Containing Compounds: Structures in Solution and Revision of NMR Assignments

Abstract

A DFT study of the ¹H NMR chemical shifts, δ(¹H), of geometric isomers of 18:3 conjugated linolenic acids (CLnAs), hexadecatrienyl pheromones, and model triene-containing compounds is presented, using standard functionals (B3LYP and PBE0) as well as corrections for dispersion interactions (B3LYP-D3, APFD, M06–2X and ωB97XD). The results are compared with literature experimental δ(¹H) data in solution. The closely spaced “inside” olefinic protons are significantly more deshielded due to short-range through-space H^…H steric interactions and appear close to or even beyond δ-values of aromatic systems. Several regularities of the computational δ(¹H) of the olefinic protons of the conjugated double bonds are reproduced very accurately for the lowest-energy DFT-optimized single conformer for all functionals used and are in very good agreement with experimental δ(¹H) in solution. Examples are provided of literature studies in which experimental resonance assignments deviate significantly from DFT predictions and, thus, should be revised. We conclude that DFT calculations of ¹H chemical shifts of trienyl compounds are powerful tools (i) for the accurate prediction of δ(¹H) even with less demanding functionals and basis sets; (ii) for the unequivocal identification of geometric isomerism of conjugated trienyl systems that occur in nature; (iii) for tackling complex problems of experimental resonance assignments due to extensive signal overlap; and (iv) for structure elucidation in solution.

1. Introduction

Conjugated linolenic acids (CLnAs) are a group of positional and geometric isomers of octadecatrienoic acids (C18:3) that contain three conjugated double bonds primarily in positions Δ9,11,13 and Δ8,10,12 [1,2]. α-Eleostearic acid (α-ESA) has three conjugated double bonds (C18:3Δ9 cis, 11 trans, 13 trans) (Figure 1) and it is produced and stored in the seed oil of plants such as A. fordii, M. charantia, Parinarium spp., and P. mahaleb. α-ESA was reported to have anticancer properties on several tumor cell lines, such as A549 (lung), MCF-7 (breast), DLD1 (colorectal), MKN-7 (stomach), and HepG2 (hepatoma). Lipid peroxidation has been suggested as the underlying mechanism [3]. β-Eleostearic acid (β-ESA) (C18:3Δ9 trans, 11 trans, 13 trans) (Figure 1) is present in pomegranate, bitter gourd, and catalpa [4]. β-ESA was reported to have a stronger antiproliferative effect than the geometric isomer α-ESA. A decrease in Bcl-2 and an increase in Bax mRNA expression along with DNA fragmentation were observed, which indicates different signaling pathways than their cis isomers [5]. Punicic acid (PA) (C18:3Δ9 cis, 11 trans, 13 cis; Figure 1) is a fatty acid derived from the fruit of P. granatum (aspomegranate) and from T. kirilowii. PA has been reported to have several health benefits such as anticancer activity and the prevention of obesity and insulin resistance in mice [6,7,8]. The cytotoxic properties on human monocytic leukemia cells have been attributed to lipid peroxidation [9].

Molecules with three conjugated double bonds have also been identified in hexadecatrienyl systems (Figure 1) from several lepidopterous species [10]. These sex hormones from females attract male moths and, thus, have significant roles in forest ecology, human health, and communication biology [11]. Pheromone-baited traps, therefore, have been widely used for the detection, population monitoring, and control of pest species and for assessing the efficacy of eradication efforts [12]. Isolation and identification of sex pheromones, however, is a difficult task due to the very small amount of pheromone produced by the insects and the small number of individuals available for the analysis of the pheromone gland content [12]. Initially, the isomeric configuration of the natural trienals was unknown and their identity was investigated by synthesis and the use of NMR spectroscopy [13,14,15]. Several geometric isomers, however, are not amenable to complete resonance assignment due to extensive signal overlap.

Hexadecatrienyl pheromones and their synthetic analogues [11,13,14,15], conjugated linolenic acids (CLnAs) [16,17,18,19,20], and model triene-containing compounds [21,22,23,24] have been extensively investigated using ¹H and ¹³C NMR. 2D-NOESY experiments, ¹³C–¹H COSY correlations, and analysis of spin–spin coupling constants with the use of homonuclear decoupling techniques were used to identify the geometric configurations of the trienyl conjugated double bonds. However, in several cases, severe overlap in the NMR spectra leads to equivocal signal assignments even when using 2D spectra and, consequently, to ambiguities in the spectral interpretations.

Several studies have been published that combine experimental NMR chemical shifts with computations for tackling the complex problems of resonance assignment, resonance reassignment, and structural revision [25,26,27,28,29,30,31,32,33,34,35,36,37] and for investigating high-resolution structures in solution [38,39,40,41,42,43,44,45,46,47]. DFT calculations of NMR chemical shifts in conjugated systems, however, are limited to ¹H and ¹³C NMR chemical shifts of retinal isomers [48], and geometric isomers of diene-containing compounds [47]. Since no X-ray structures of conjugated linolenic acids (CLnAs) and hexadecatrienyl pheromones have so far been published, it would be of interest to use quantum chemical calculations of δ(¹Η) for structure elucidation in solution. In this paper, we discuss (i) the effect of various functionals and basis sets on the accuracy of the DFT calculation of ¹H NMR chemical shifts using the GIAO [49] technique on several geometric conjugated linolenic acids, hexadecatrienyl pheromones, and model triene-containing compounds (Figure 1); (ii) the use of δ(¹H) for the unequivocal assignment of geometric isomerism and revision of literature experimental assignments; and (iii) the use of δ(¹H) as a tool for structure elucidation in solution.

2. Results and Discussion

2.1. DFT-Calculated vs. Experimental ¹H NMR Chemical Shifts of Model Compounds in Solution: Effects of Various Functionals and Basis Sets

The experimental ¹H NMR chemical shifts of the trienyl model compounds (Z)-1,3,5-hexatriene, (E)-1,3,5-hexatriene, (E,Z,E)-2,4,6-octatriene and (E,E,E)-2,4,6-octatriene (Figure 1 and

Table 1. Literature experimental ¹H NMR chemical shifts, δ_exp, and the sample and spectral specifications of the compounds of Figure 1.

A		B	C	D	E		F	G		H	I	J	K		L	M
Group	δexp (ppm)	δexp (ppm)	δexp (ppm)	δexp (ppm)	Group	δexp (ppm)	δexp (ppm)	Group	δexp (ppm)	δexp (ppm)	δexp (ppm)	δexp (ppm)	Group	δexp (ppm)	δexp (ppm)	δexp (ppm)
H1a	5.15	5.1	5.09	5.05	H1	1.8	1.84	H9	2.09	2.12	2.18	2.17	H11	6.10	6.19	6.48
H1b	5.24	5.23	5.17	5.18	H2	5.7	5.69	H10	5.70	5.74	5.48	5.40	H12	6.10	6.40	6.48
H2	6.8	6.36	6.74	6.3	H3	5.83	6.12	H11	6.10	6.50	6.43	5.98	H10	6.04	6.01	6.08
H3	6.0	6.22	5.93	6.16	H4	6.5	6.10	H12	6.18	5.98	6.13	6.37	H13	6.04	6.12	6.08
H4	6.0	6.22	5.93	6.16	H5	6.5	6.10	H13	6.41	6.16	5.96	6.16	H9	5.66	5.4	5.46
H5	6.8	6.36	6.74	6.3	H6	5.83	6.12	H14	6.02	6.46	6.52	6.07	H14	5.66	5.74	5.46
H6a	5.15	5.1	5.09	5.05	H7	5.7	5.69	H15	5.47	5.56	5.75	5.70	H2	2.37	2.40	2.37
H6b	5.24	5.23	5.17	5.18	H8	1.8	1.84	H16	1.76	1.77	1.80	1.77	H8	2.10	2.20	2.22
													H15	2.10	2.20	2.22
													H3	1.65	1.64	1.65
													H4	1.39	1.41	1.39
													H5	1.39	1.41	1.39
													H6	1.39	1.41	1.39
													H7	1.39	1.41	1.39
													H16	1.33	1.33	1.32
													H17	1.33	1.33	1.32
													H18	0.91	0.97	0.94

^A (Z)-1,3,5-hexatriene (CDCl₃), ¹H and 2D ¹H–¹H COSY NMR (270 MHz) [15]; ^B (E)-1,3,5-hexatriene (CDCl₃), ¹H and 2D ¹H–¹H COSY NMR (270 MHz) [15]; ^C (Z)-1,3,5-hexatriene (CCl₄), ¹H NMR (100 MHz) [21,22]; ^D (E)-1,3,5-hexatriene (CCl₄), ¹H NMR (100 MHz) [21,22]; ^E (E,Z,E)-2,4,6-octatriene (CDCl₃), ¹H NMR (300 MHz) [23]; ^F (E,E,E)-2,4,6-octatriene (CCl₄), ¹H NMR (100 MHz) [21]; ^G 10E,12E,14Z-hexadecatrienyl acetate (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (270 MHz) [13]; ^H 10E,12Z,14Z-hexadecatrienyl acetate (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (270 MHz) [13]; ^I 10Z,12Z,14E-hexadecatrienyl acetate (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (270 MHz) [13]; ^J 10Z,12E,14E-hexadecatrienyl acetate (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (270 MHz) [13]; ^K β-eleostearic acid (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (400 MHz) [18]; ^L α-eleostearic acid (CDCl₃), ¹H, ¹³C, and 2D ¹H-¹H COSY NMR (400 MHz) [18]; ^M punicic acid (CDCl₃), ¹H, ¹³C, and 2D ¹H–¹H COSY NMR (400 MHz) [18].

) exhibit resonances of the olefinic protons of the conjugated double bonds in the range of 5.0 to 6.8 ppm. The =CH₂ protons are shielded with respect to the rest of the olefinic protons and appear in a narrow range of 5.05 to 5.23 ppm. Alkyl substitution of the H_1a proton, as in the case of (E,Z,E)-2,4,6-octatriene, results in a deshielding of ~0.5 ppm, which is in excellent agreement with ¹H additive contribution to ethylene of Δδ_gem = 0.45 ppm [50]. Interestingly, the closely spaced “inside” olefinic 2,5 protons of (Z)-1,3,5-hexatriene and 3,6 protons of (E,Z,E)-2,4,6-octatriene (Figure 1) are the most deshielded and appear close to or even beyond δ-values of aromatic systems. This deshielding effect can be attributed to rigid geometries and significant H^…H van der Waals repulsive effects of specific protons [22]. It has been demonstrated that hydrogen atoms, which are subject to significant steric compression, exhibit a deshielding that is dependent on the geometrical relationship between the H–C bond and the interacting proximate hydrogen [51]. This occurs because the symmetry of the electron cloud about the proton is disturbed, thus resulting in reduced electronic charge and diamagnetic shielding [52,53]. Trienyl model compounds, therefore, are ideally suited for the study of steric effects on δ(¹H) using various functionals and basis sets. Energy minimization of the structures was performed with standard functionals (B3LYP and PBE0) as well as with corrections for dispersion interactions (B3LYP-D3, APFD, M06–2X, and ωB97XD). Inclusion of nonlocal van der Waals density functionals has been shown to improve the accuracy of standard DFT functionals [54,55]. The 6–31+G(d) and 6–311++G(d,p) basis sets were used to compare the results of a low computational cost basis set with a medium-size one. Computations of δ_calc(¹H) were performed (a) using a single methodology at the GIAO/B3LYP/6–311+G(2d, p)/CPCM level (Figure S1 and Figure S2 and Table S1), as recommended in [28], and (b) using the same level of theory as geometry optimization (Figure 2, Figure S3, and Table S2).

For all the functionals and basis sets used, the literature experimental chemical shifts of the closely spaced “inside” olefinic protons with δ(H (3,6)) = 5.83 ppm and δ(H (4,5)) = 6.50 ppm of (E,Z,E)-2,4,6-octatriene [23] strongly deviate from linearity (Figure S2A and Figure S3A). Revision of the literature experimental chemical shift data so that the inner H(3,6) protons to be deshielded to a larger degree than H(4,5) (Figure S2B and Figure S3B) results in very significant improvements of the regression coefficients and standard deviations for all the functionals and basis sets used (Table S3 and Table S4). The use of several DFT functionals with distinct contributions (long-range corrections or dispersion interactions) would provide distinct results for the geometry. The use, however, of a single methodology at the GIAO/B3LYP/6–311+G(2d,p) level for chemical shift computations results in identical correlations coefficients and mean square errors for all the functionals and basis sets used (Table S3). The use of the same level of theory in δ_calc (¹H) as geometry optimization results in similar but not identical statistical data (Table S4). The quality of the linear regression procedure is a criterion whether the computational method is able to reproduce the experimental chemical shifts free from random error [28]. Furthermore, the extent to which the slope of the correlation line deviates from unity and the intercept from zero is a measure of the overall systematic error. Among the functionals with corrections for dispersion interactions, the ωB97XD with the 6–31+G(d) basis set performs better (intercept: 0.003, slope: 1.046; Table S4). The M06–2X functional is less suitable for shielding calculations of the selected molecules in agreement with literature data on several small molecules [56].

From the above, it can be concluded that the accuracy of the DFT calculations can provide a practical guide for future experimental assignments and help in the reassignment of literature experimental ¹H NMR chemical shifts of triene-containing compounds based on a typical workflow that includes the following steps:

(i)

the ¹H NMR spectra are recorded in, e.g., a CDCl₃ solution at 298 K, and a preliminary assignment is performed using a variety of 1D and 2D NMR experiments;

(ii)

the ¹H NMR chemical shifts are computed with the CPCM model at the same level of theory as geometry optimization or at the GIAO/B3LYP/6–311+G(2d,p) level, even with less demanding functionals and basis sets;

(iii)

a very good linear correlation between experimental NMR chemical shifts, δ_exp, and calculated shifts, δ_calc, provides a strong indication that the assignment procedure is correct.

2.2. Out-of-Plane Deformation of the Trienyl System and Steric Effects in Model Compounds

Variation of the torsion angle φ(C₁,C₂,C₃,C₄) of the trienyl system of (Z)-1,3,5-hexatriene, in steps of 10° in the range of 180° to 0°, with energy minimization at the B3LYP/6–31+G(d) level, results in significant changes in the electronic energy (ΔE) (Figure 3A). A second minimum at φ = 40° was observed with ΔG = 2.37 kcal·mol⁻¹ higher than that of the φ = 180° conformer. The significant ΔG energy difference of the two low-energy conformers with φ = 40° and φ = 180.0° shows that the δ_calc(¹H) data (at the GIAO/B3LYP/6–311+G(2d,p) level), weighted by the respective Boltzmann factor, are nearly identical with those of the φ = 180.0° conformer. The effect of the population of the φ = 40° conformer can, thus, be neglected. The effect of variation of the torsion angle φ on ¹H NMR chemical shifts is shown in Figure 3B and Table S5. The δ_calc(¹H) data indicate similar behavior of the “inside” H2 and H5 protons with a pronounced shielding at 100° < φ < 180° (Figure 3B). In the range of torsion angles 0°< φ < 100°, the H5 proton shows a strong deshielding with a maximum value of δ = 7.32 ppm at φ = 0°. This clearly demonstrates that the strong, through-space, steric interaction with the H_1b is the primary factor that results in δ values in the range of aromatic protons. The effect of variation of the torsion angle φ of (Z)-1,3,5-hexatriene on calculated olefinic ¹H NMR chemical shifts using the same level of theory as geometry optimization (APFD/6–311++G(d,p)) is shown in Figure S4 and Table S6. The results are very similar to those of Figure 3 and Table S5; however, the ΔΕ and ΔG values are slightly smaller and the deshielding effect is slightly more pronounced due to the dispersion interaction of the APFD functional.

The electronic energy ΔΕ (kcal/mol) and shielding changes due to the variation in the torsion angle φ₁ (C₂C₃C₄C₅) of the (E,Z,E)-2,4,6-octatriene (Figure 4, Table S7) are very similar to those due to the variation in the torsion angle φ of (Z)-1,3,5-hexatriene. Thus, the δ_calc(¹H) data of the low-energy conformers, weighted by the respective Boltzmann factor, are identical with those of the φ₁ = 180° conformer. Again, the effect of variation of the φ₁ torsion angle on δ_calc(¹H), using the same level of theory as geometry optimization (APFD/6–311++G(d,p)), is to decrease slightly the ΔΕ and ΔG values and increase the deshielding effect (Figure S5 and Table S8).

The effect of the variation in the torsion angle φ₂(C₁C₂C₃C₄) of (E)-1,3,5-hexatriene, with energy minimization at the B3LYP/6–31+G(d) level, on the electronic energy ΔΕ(kcal·mol⁻¹), and δ_calc(¹H), at the GIAO/B3LYP/6–311+G(2d,p) level, are shown in Figure 5. A second broad minimum in the range of φ₂ = 30° to 0° was observed with ΔE=3.66 kcal·mol⁻¹ (ΔG = 3.28 kcal·mol⁻¹) higher than that of the φ₂ = 180.0° conformer. The δ_calc (¹Η) values of the low-energy conformers with φ₂ = 30° to 0° and φ₂ = 180.0° (Table S9), weighted by the respective Boltzmann factors, are essentially the same as those of the φ₂ = 180.0° conformer. This is due to the negligible population of the higher minimum conformers. Of particular interest is the parallel behavior of the H₄ and H_1b protons as a function of the torsion angle φ₂, with strong deshielding in the range of 0° < φ₂ < 90°. Again, the effect of the variation in the φ₂ torsion angle on δ_calc(¹H), using the same level of theory as geometry optimization (APFD/6–311++G(d,p)), is to decrease slightly the ΔΕ and ΔG values and increase the deshielding effect (Figure S6 and Table S10).

Figure 6 shows the effect of variation in the torsion angle φ₃(C₂C₃C₄C₅) of the (E,E,E)-2,4,6-octatriene, with energy minimization at the B3LYP/6–31+G(d) level, on the electronic energy ΔΕ, and the computational olefinic ¹H NMR chemical shifts (at the GIAO/B3LYP/6–311+G(2d,p) level with CPCM in CHCl₃). As in the case of (E)-1,3,5-hexatriene, a second broad minimum in the range of φ₃ = 30° to 0° was observed with ΔE = 3.68 kcal·mol⁻¹ (ΔG = 3.42 kcal·mol⁻¹). The δ_exp(¹H) data of the olefinic protons (Table S1) are in excellent agreement with the δ_calc(¹H) values of the minimum energy conformer with φ₃ = 180.0^o. The δ_calc(¹H) values of the low-energy conformers (Table S11), weighted by the respective Boltzmann factor, are essentially the same as those of the φ₃ = 180.0° conformer. This demonstrates that the weights of the higher minimum conformers are of minor importance. As in the previous cases, the effect of variation in the φ₃ torsion angle on δ_calc(¹H) of the olefinic protons, using the same level of theory as geometry optimization (APFD/6–311++G(d,p)), is to decrease slightly the ΔΕ and ΔG values and increase the deshielding effect (Figure S7 and Table S12).

It can, therefore, be concluded that δ_exp(¹H) are reproduced very accurately for the lowest-energy DFT-optimized single conformer. The other low-energy conformers have negligible effects on the δ_calc(¹H) data of the conjugated olefinic protons. Furthermore, the minor functional dependence can result in the levels of accuracy that are necessary for structure elucidation in solution (see below).

Abraham et al. [50] showed that there is a deshielding effect above the C=C bond at short distances, due to the van der Waals term, and a deshielding effect in the plane of the C=C bond [57]. Figure S8 illustrates a plot of NBO bond order of the olefinic C-H bonds vs. δ_calc(¹H). The resulting very poor correlation (R² = 0.554) shows that the NBO bond order is not a significant factor that determines δ_calc(¹H). Furthermore, no functional relationship was found for NBO charge densities of the olefinic C-H protons vs. δ_calc(¹H). Α detailed experimental and computational (with the CHARGE 7 model) study by Abraham et al. [50,57] showed a steric deshielding effect on both alkene and aromatic ring protons, contrary to a shielding effect of H^…H steric interactions in alkanes. All these steric interactions were described by a simple r⁻⁶ dependence,

δ_steric = a_s/r⁶

where a_s is a constant of the given hybridization of the atom. Figure S9 and Figure S10 show that, in most cases, an r^-n dependence is observed, which for H^…H distances shorter than those of the van der Waals radius of the hydrogen atom (~1.2 Å), becomes approximately a linear correlation. According to the semi empirical model of Cheney [51], a much better agreement with the experimental deshielding effect was obtained by correlation with f(r_i, θ_i) than with the exponential exp(−ar_i) term, where r_i is the distance between the interacting pair of hydrogens and θ_i is the angle between H^…H internuclear line and the H–C bond of interest. The above results clearly demonstrate that the deshielding effect due to non-bonded H^…H repulsive interaction is a primary factor affecting δ(¹H) in the trienyl systems reported therein, as in the case of simple alkenes, conjugated dienyl, and aromatic systems [47,50,51,57].

2.3. DFT-Calculated vs. Experimental ¹H NMR Chemical Shifts: Structure Elucidation in Solution of Geometric Isomers of 18:3 Conjugated Linolenic Acids and Hexadecatrienyl Pheromones

Table 2. Conformational properties, ΔG values (kcal·mol⁻¹), and % populations of various low-energy conformers of the 9,11,13-conjugated fatty acid and 10,12,14-conjugated hexadecatrienyl acetate geometric isomers with geometry optimization at the B3LYP/6–31+G(d) and APFD/6–31+G(d) levels.

Compound	Conformer	B3LYP/6–31+G(d)			APFD/6–31+G(d)
		φc7c8c9c10 (°)	φc13c14c15c16 (°)	ΔG (kcal/mol) (% Population)	φc7c8c9c10 (°)	φc13c14c15c16 (°)	ΔG (kcal/mol) (% Population)
9E,11E,13E Isomer (β-Eleostearic acid)	A	120.26 (S)	118.59 (S)	+0.36 (33.41)	119.21 (S)	117.99 (S)	+0.16 (38.68)
	B	120.11 (S)	−119.97 (S’)	0.00 (61.35)	118.73 (S)	−118.59 (S’)	0.00 (50.67)
	C	−0.78 (Syn)	−0.03 (Syn)	+3.00 (0.39)	−0.59 (Syn)	−0.11 (Syn)	+2.13 (1.39)
	D	−117.53 (S’)	−0.83 (Syn)	+1.89 (2.53)	−116.94 (S’)	−0.62 (Syn)	+1.38 (4.94)
	E	−0.75 (Syn)	−118.55 (S’)	+1.94 (2.32)	−0.58 (Syn)	−117.27 (S’)	+1.46 (4.31)
9Z,11E,13E Isomer (β-Eleostearic acid)	A	116.67 (S)	119.18 (S)	+0.03 (25.07)	111.25 (S)	117.87 (S)	0.00 (36.53)
	B	−118.92 (S’)	−119.37 (S’)	+0.15 (20.48)	−114.31 (S’)	−117.53 (S’)	+0.48 (16.25)
	C	116.88 (S)	−119.16 (S’)	+0.02 (25.50)	112.96 (S)	−117.54 (S’)	+0.18 (26.96)
	D	−118.88 (S’)	119.28 (S)	0.00 (26.38)	−113.83 (S’)	118.32 (S)	+0.47 (16.52)
	E	−119.43 (S’)	−0.76 (Syn)	+1.38 (2.57)	−113.80 (S’)	−0.22 (Syn)	+1.35 (3.74)
9Z,11E,13Z Isomer (Punicic acid)	A	117.46 (S)	119.33 (S)	0.00 (38.54)	113.45 (S)	114.70 (S)	0.00 (44.84)
	B	117.76 (S)	−118.63 (S’)	+0.08 (33.67)	112.18 (S)	−112.33 (S’)	+0.31 (26.57)
	C	−119.22 (S’)	119.55 (S)	+0.27 (24.43)	−113.43 (S’)	113.54 (S)	+0.27 (28.43)
	D	1.52	−121.09 (S’)	+3.83 (1.51)	5.34	−110.17 (S’)	+3.77 (0.08)
	E	117.81 (S)	2.02 (Syn)	+3.63 (1.85)	111.01 (S)	4.55 (Syn)	+3.78 (0.08)
10E,12E,14Z-Hexadecatrienyl acetate	A	120.04 (S)		+0.28 (25.59)	118.73 (S)		+0.08 (28.88)
	B	−119.39 (S’)		0.00 (41.05)	−118.73 (S’)		+0.03 (31.42)
	C	120.03 (S)		+0.20 (29.29)	118.73 (S)		0.00 (33.05)
	D	1.56 (Syn)		+1.37 (4.07)	1.16 (Syn)		+0.95 (6.65)
10E,12Z,14Z-Hexadecatrienyl acetate	A	119.67 (S)		+0.44 (22.44)	118.45 (S)		+0.20 (26.06)
	B	−119.64 (S’)		0.00 (47.15)	−118.86 (S’)		0.00 (36.52)
	C	119.56 (S)		+0.35 (26.12)	118.28 (S)		+0.12 (29.82)
	D	1.22 (Syn)		+1.42 (4.29)	0.87 (Syn)		+0.93 (7.60)
10Z,12Z,14E-Hexadecatrienyl acetate	A	119.01 (S)		0.00 (30.52)	112.30 (S)		+0.04 (20.48)
	B	−119.51 (S’)		+0.51 (12.91)	−113.47 (S’)		+0.10 (18.51)
	C	118.80 (S)		0.00 (30.52)	112.24 (S)		0.00 (21.92)
	D	−119.50 (S’)		+0.48 (13.57)	−113.16 (S’)		+0.02 (21.19)
10Z,12E,14E-Hexadecatrienyl acetate	A	119.05 (S)		0.00 (31.98)	113.03 (S)		0.00 (33.79)
	B	−121.15 (S’)		+0.54 (12.85)	−116.62 (S’)		+0.63 (11.67)
	C	118.73 (S)		+0.04 (29.89)	113.00 (S)		+0.04 (31.59)
	D	−121.06 (S’)		+0.56 (12.43)	−116.57 (S’)		+0.65 (11.28)

shows conformational properties, ΔG values (kcal·mol⁻¹) and % populations of various low-energy conformers of the 18:3 ω-5 CLA with energy minimization at the B3LYP/6–31+G(d) and APFD/6–31+G(d) levels. The structures of five low-energy conformers (A), (B), (C), (D), and (E) of β-eleostearic acid and the definition of various torsion angles are shown in Figure 7 and Figure 8, respectively. The general tendency of the torsion angles φ(C₇C₈C₉C₁₀) and φ(C₁₃C₁₄C₁₅C₁₆), which involve the allylic C(8) and C(14) carbons, respectively, is to adopt a low-energy gauche conformation, also known as skew (S = 120°) or skew′ (S′ = −120°). On the contrary, the eclipsed syn conformation (φ = 0°) results in high energy and, thus, low population (Table 2). The results are very similar for both B3LYP/6–31+G(d) and APFD/6–31+G(d) levels. An anti-zigzag conformational behavior was observed for the two polymethylene (CH₂)_n groups, which are attached to the conjugated trienyl system, for all conformers of the geometric isomers of 18:3 ω-5 CLA for both B3LYP/6–31+G(d) and APFD/6–31+G(d) levels (Table 2 and Figure S11).

Crystallographic data for cis-monounsaturated fatty acids [58,59,60] revealed that the zigzag (anti) conformation of the polymethylene chains (CH₂)_n is the most rigid and stable, whereas the gauche conformer is less stable, in agreement with our computational data. For the allylic carbons, the most stable conformations are skew (S) and skew′ (S′) in the γ-crystallization form, again in agreement with our computational data of Table 2. However, the anti-cis-anti and skew-cis-anti conformations have been observed in the α- and β-crystallization forms, respectively [58]. The formation of these high-energy conformers can be attributed to specific crystal packing interactions, which are absent in solution.

Figure S12 shows a graphical presentation of the calculated ¹H NMR chemical shifts (at the GIAO/B3LYP/6–311+G(2d,p) (CPCM, CHCl₃) level), weighted by the respective Boltzmann factors of the various conformers of Table 2 vs. experimental chemical shifts (Table 1 and Table S13) of the three geometric isomers of the 9,11,13-CLA. The experimental chemical shifts of the H11 and H12 of β-eleostearic acid [18] deviate from linearity. Revision of the literature assignment so that H12 is deshielded to a larger degree than H11 results in very good agreement with the computational data and significant improvement of the statistical data (Table S13 and Table S14). Similar results were obtained with calculations of ¹H NMR chemical shifts using the same level of theory as geometry optimization (APFD/6–31+G(d) level) (Table S14).

Table 2 shows conformational properties, ΔG values (kcal·mol⁻¹), and % populations of various low-energy conformers of the 10,12,14-conjugated hexadecatrienyl acetate geometric isomers with geometry optimization at the B3LYP/6–31+G(d) and APFD/6–31+G(d) levels. As in the case of CLnAs, the torsion angle φ(C₇C₈C₉C₁₀) adopts a low-energy skew (120°) or skew′ (120°) conformation. On the contrary, the eclipsed syn conformation with φ angles around 0^o results in high energy and, thus, low population. Figure S13 and Table S15 and Table S16 show an improvement in the correlation of δ_calc vs. δ_exp when the literature experimental chemical shifts of H13 and H15 of 9Z,11Z,13E and H13 and H14 of 9Z,11E,13E-conjugated hexadecatrienyl acetates (Table 1, [13]) have been revised (Figure S14). Similar results were obtained with the calculation of ¹H NMR chemical shifts using the same level of theory as geometry optimization (APFD/6–31+G(d) level) (Table S15 and Table S16).

Figure 9 and

Table 3. Linear regression correlation coefficient, mean square error, intercept, and slope of the calculated vs. experimental olefinic ¹H NMR chemical shifts of Figure 9.

Minimization Method	Correlation Coefficient (R2)	Mean Square Error	Intercept	Slope
B3LYP/6–31+G(d) a	0.873	0.037	−0.002	1.062
APFD/6–31+G(d) a	0.868 (0.825)	0.041(0.044)	−0.102 (0.518)	1.085 (0.956)
B3LYP/6–31+G(d) b	0.984	0.005	−0.387	1.127
APFD/6–31+G(d) b	0.982 (0.942)	0.005 (0.015)	−0.506 (0.138)	1.153 (1.020)

^a Data of Figure 9A; calculation of ¹H NMR chemical shifts at the GIAO/B3LYP/6–311+G(2d,p) level and ^b data of Figure 9B; calculation of ¹H NMR chemical shifts at the GIAO/B3LYP/6–311+G(2d,p) level. The data in parenthesis were obtained at the GIAO with the same level of theory as geometry optimization.

show that a significant improvement can be achieved in the linear regression correlation coefficient and mean square error of the correlation δ_calc vs. δ_exp of the olefinic protons of all the compounds of Figure 1 when the literature experimental chemical shifts of the compounds shown in Figure S14 have been revised. This clearly demonstrates that the accuracy of the DFT ¹H NMR shift prediction can be used to resolve ambiguities in resonance assignment.

3. Computational Methods

The computational study was performed using the Gaussian 09 Rev. D.01 software [61]. The initial structures of the model triethyl compounds (Z)-1,3,5-hexatriene, (E)-1,3,5-hexatriene, (E,Z,E)-2,4,6-octatriene, and (E,E,E)-2,4,6-octatriene were drawn using the GaussView program and were energy minimized at the B3LYP/6–31+G(d), B3LYP/6–311++G(d,p), B3LYP-D3/6–31+G(d), B3LYP-D3/6–311++G(d,p) (the D3 version of Grimme dispersion with Becke–Johnson damping), APFD/6–31+G(d), APFD/6–311++G(d,p), PBE0/6–31+G(d), PBE0/6–311++G(d,p), M06–2X/6–31+G(d), M06–2X/6–311++G(d,p), ωB97XD/6–31+G(d), and ωB97XD/6–311++G(d,p) levels (gas phase). In the case of α-oleostearic acid (9Z, 11E, 13E), β-oleostearic acid (9E, 11E, 13E), punicic acid (9Z, 11E, 13Z), (10E, 12E, 14Z)-, (10E,12Z,14Z)-, (10Z, 12Z, 14E)-, and (10Z, 12E, 14E)-hexatrienyl acetates, a conformational analysis was, firstly, performed by rotation of the aliphatic carbons of the (CH₂)_n chains, which constitute with the rigid conjugated double bonds a flat system. The resulting conformers were energy minimized with DFT at the B3LYP/6–31+G(d) and APFD/6–31+G(d) levels, while the subsequent energy minimization of the selected stable structures was carried out at the same level of calculation. The optimized geometries were verified by performing frequency calculation at the same level (zero imaginary frequencies). The scanning of torsional angles was performed using the redundant coordinates in Gaussian 09 [47]. ΔG values were calculated from the thermochemistry results, either between the stable conformers or between the stable conformers and the corresponding transition states. The computed proton chemical shifts were performed using (i) a single methodology at the GIAO/B3LYP/6–311+G(2d,p) level and (ii) GIAO at the same level of theory as geometry optimization. In both cases, the conductor-like polarizable continuum model (CPCM) was used in CHCl₃ or CCl₄, for experimental values obtained in CDCl₃ and CCl₄, respectively (Table S1 and Table S2). δ_calc(¹Η) were referenced with respect to the standard TMS, which was optimized at the same level (Table S17).

4. Conclusions

From the DFT data of the trienyl conjugated compounds of Figure 1 reported therein, it can be concluded that:

(a)

Very good linear correlations can be obtained between DFT-calculated and experimental ¹H NMR chemical shifts of the olefinic protons of the lowest-energy DFT-optimized single conformer using standard functionals (B3LYP and PBE0) as well as corrections for dispersion interactions (B3LYP-D3, APFD, M06–2X and ωB97XD). The ωB97XD performs slightly better, but again the accuracy of the functionals used was rather similar.

(b)

Through-space H^…H steric interaction is the primary factor that results in strong deshielding of closely spaced trienyl olefinic protons, in excellent agreement with literature data on alkenes and aromatic systems [50,51,57].

(c)

The accuracy of computational ¹H NMR chemical shifts can facilitate (i) the unequivocal assignment of the geometric isomerism in conjugated trienyl systems of biological systems, such as CLnAs and hexadecatrienyl pheromones, and especially in the case of problematic resonance assignment due to extensive signal overlap, and (ii) structure elucidation in solution [28,36].