Evaluating electronic structure methods for accurate calculation of ¹⁹F chemical shifts in fluorinated amino acids

Abstract

The ability of electronic structure methods (11 density functionals, HF, and MP2 calculations; two basis sets and two solvation models) to accurately calculate the ¹⁹F chemical shifts of 31 structures of fluorinated amino acids and analogues with known experimental ¹⁹F NMR spectra has been evaluated. For this task, BH and HLYP, ωB97X, and Hartree-Fock with scaling factors (provided within) are most accurate. Additionally, the accuracy of methods to calculate relative changes in fluorine shielding across 23 sets of structural variants, such as zwitterionic amino acids vs. side chains only, was also determined. This latter criterion may be a better indicator of reliable methods for the ultimate goal of assigning and interpreting chemical shifts of fluorinated amino acids in proteins. It was found that MP2 and M062X calculations most accurately assess changes in shielding among analogues. These results serve as a guide for computational developments to calculate ¹⁹F chemical shifts in biomolecular environments.

Graphical Abstract

Fluorinated amino acids are used to label proteins for studies of structure, dynamics, and function. Interpreting and assigning the chemical shifts in the resulting fluorine NMR spectra of fluoro-labeled proteins is a goal of computational chemists. This article provides key information toward this aim, by evaluating the ability of numerous electronic structure methods to calculate fluorine chemical shifts of amino acids and analogues. Methods are evaluated in terms of lowest deviation from experimental values.

INTRODUCTION

Fluorolabeling of biomolecules provides valuable information regarding protein structure-function-dynamics and ligand binding events, yet development of a robust computational protocol for reliable identification of fluorine chemical shifts is hampered by a lack of knowledge regarding the best electronic structure methods to accurately calculate fluorine shielding. The substitution of fluorine in place of hydrogen in biological molecules has little effect in changing molecular size, but it can significantly affect molecular properties such as electron distribution. In proteins, the C-F moieties may help to form strong interactions with hydrogen bond donors, leading to enhanced stability.^1,2 Fluorinated amino acids are valuable tools for understanding biological systems and their functions. Proteins containing fluorinated amino acids can be prepared biosynthetically by auxotrophs of the parent (canonical) amino acid³ or by endogenous tRNA synthetases designed by Tirrell and co-workers.⁴ For synthesis of small peptides and proteins containing fluorinated amino acids, solid phase chemical synthesis is a frequently used method.⁵ Insertion of unnatural amino and nucleic acids into biomolecules has received widespread attention due to their extensive applications for structure-dynamics studies^6–10 and pharmaceutical development.^2,11,12 The ability to predict fluorine chemical shifts in protein environments^13,14,15,16 will enhance the utility of fluorinated amino acids in biophysical studies.

¹⁹F nuclei have a natural abundance >99% and are considered sensitive probes of local environments.¹⁷ Whereas proton chemical shifts typically span a range of ~15 ppm, ¹⁹F NMR shifts in organic compounds have a range of over 400 ppm. Another advantage of ¹⁹F protein NMR is that fluorine is not natively found in unlabeled biomolecules, making ¹⁹F NMR more advantageous than ¹H, ¹³C or ¹⁵N NMR due to the lack of spectral crowding or background signal. The lone pair electrons of fluorine are considered to have an important role in influencing the ¹⁹F NMR chemical shifts.^18–19 Many factors in the local environment contribute to changes in fluorine chemical shifts, including short-range interactions, hydrogen bonding interactions, and electrostatic field effects. In biological systems, fluorine nuclei act as reporters in indicating changes in the local environment from different states of proteins, including folded vs. unfolded states, substrate and cofactor binding, and solvent exposed vs. buried residues.^{17–18 19}F NMR has proven to be an excellent analytical tool for many fluorinated ligands and proteins.

Many experiments have shown that there is a large change in chemical shifts for fluorinated residues in different environments. For example in analysis of the anticancer drug 5-fluorouracil,²⁰ intracellular Ca²⁺ levels were determined using free and metal bound 5F-BAPTA, which was reported by changes in fluorine shielding on the order of 5–6 ppm upon cation binding.²¹ Fluorinated tags, such as BTFA (3-bromo-1,1,1–trifluoroacetone) and TFET (2,2,2-trifluoroethanthiol), are widely useful in membrane and cellular proteins.^22,23 In 2-fluorohistidine labeled papD²⁴ and 6-fluorotryptophan labeled dihydrofolate reductase (DHFR)⁶, shifts of ~2–3 ppm are observed between native and denatured protein states.

Systematic studies of electronic structure methods for calculating fluorine chemical shifts are scarce. Isley et al. worked on a test set of fluorine-containing compounds before developing methodology for predicting fluorine chemical shifts in proteins, while commenting on the paucity of such studies.²⁵ Harding et al. examined methods for gas-phase fluorine chemical shifts in small molecules, focusing on high levels of theory.²⁶ The data set examined in this paper contains fluorinated amino acids and analogues for which fluorine chemical shifts have been determined experimentally. It surveys methods that are computationally tractable for these larger systems, in implicit solvent. In this work, computational methods for predicting relative fluorine chemical shifts are evaluated, studying fluorinated amino acids with known changes in fluorine shielding due to isomeric, backbone, and solvent effects that may serve as proxies for changes in protein environment. For the ultimate goal of developing a comprehensive and accurate method to predict fluorine chemical shifts in proteins, accurate determination of relative chemical shift (vs. absolute) is ostensibly the more necessary criterion. In addition, since amino acid chains represent many structures commonly seen in organic compounds, these results may serve as a guide to study fluorinated ligands and organic molecules.²

METHODS

The effects of protein environment can be propagated through the bonding framework,^27,28 or arise from differences in primary and secondary structure, different dielectric environments (interior vs. solvent-exposed), and site-specific differences in neighbors, close contacts, and hydrogen bonds. In this work, these effects are examined, respectively, by comparing “backbone effects” (changes in substituents on the amino acid side chain where C_α is bound); solvent effects; stereoisomers; and changes in protonation state. Figure 1 illustrates the systems studied within each of these categories.

Figure 1.

Fluorinated systems evaluated in this work. A) Backbone effects: fluorohistidine and analogues, p-fluorophenylalanine and analogues B) Backbone effects: fluorotryptophan and analogues. C) Isomeric effects: fluoroproline, trifluoroleucine and trifluorovaline D) Other systems studied, including protonation effects: fluorohistidine and analogues; solvent effects: fluoroindoles, p-fluorophenylalanine and analogues; systems for which only absolute chemical shifts are considered: fluorovaline and trifluoromethionine.

Only amino acids and analogues with known, experimental ¹⁹F NMR chemical shifts were considered. Experimental ¹⁹F NMR chemical shifts were obtained from the literature for aqueous 2- and 4-fluorohistidine, 2- and 4-fluoro-(5-methyl)-imidazole, and 2- and 4-fluoroimidazole;²⁹ 3S- and 3R-fluoroproline;³⁰ (2S, 3R)- and (2S, 3S)-4,4,4-trifluorovaline;³¹ (2S, 4R)- and (2S, 4S)-5,5,5-trifluoroleucine;³¹ trifluoromethionine;³² 3-fluorovaline.³³ Experimental NMR spectra were acquired for 4-, 5-, 6-fluorotryptophan (aqueous only); 4-, 5-, and 6-fluoroindole (in ethanol, pyridine or N,N-dimethylformamide (DMF), water, dimethylsulfoxide (DMSO) solvents); p-fluorophenylalanine, p-fluorotoluene, and fluorobenzene (in ethanol, pyridine or DMF, water, DMSO solvents). Spectra were acquired on a 400 MHz Varian NMR spectrometer equipped with a 400 ID Triax probe, and were internally –referenced to −76.55 ppm using a co-axial insert containing 0.01% TFA in D₂O.

The goal of this work is to identify efficient and accurate electronic structure calculations that can be carried out by typical computational resources. For that reason, Hartree-Fock, DFT, and MP2 methods (without computationally-expensive augmented correlation consistent basis sets) were considered. All the calculations were performed with the Gaussian 09 package³⁴ with Hartree-Fock (HF), MP2, and the density functional methods: BLYP, B3LYP,^35,36 BH and HLYP, M06, M06L, M062X,³⁷ PW91PW91,³⁸ PBE0,³⁹ PBEPBE,³⁸ ωB97X,⁴⁰ and ωB97XD.⁴¹ While this set is not exhaustive, it does contain both GGA, hybrid, and local functionals, commonly used methods, and those shown in other literature reports to provide reliable NMR chemical shifts. For instance, PBE1PBE (a.k.a. PBE0) has been shown to provide reliable values of ¹H, ¹³C and ¹⁹F chemical shifts in large and small organic compounds.^42,25 Yu et al. showed BH and HLYP to provide reliable data for amino acids,⁴³ and our previous work indicated that BH and HLYP provided good prediction of ¹⁹F chemical shifts in fluorohistidine isomers (much better than B3LYP).¹⁹ This latter result hinted that a higher amount of Hartree-Fock exact exchange may improve accuracy for ¹⁹F chemical shifts. Therefore, ωB97X, which has 100% long range Hartree-Fock exchange, was added to the set of methods, while ωB97XD allows for investigation of the extent to which dispersion affects calculated chemical shifts. When nuclear shielding is calculated with MP2 methods, values are provided for both the MP2 and SCF shielding. Both of these are considered in this work, indicated by “MP2” or “SCF” in tables and charts.

Two sizes of basis set were examined for each method, each containing both diffuse and polarization functions: 6–31+G* and 6–311++G(3df,2p). Solvation via the self consistent reaction field (SCRF) method with Conductor Polarized Continuum Model (CPCM)⁴⁴ and universal solvent model SMD⁴⁵ were used to perform the calculations, in order to see whether choice of implicit solvent model makes a difference in accuracy. The molecular structures were optimized with each level of method, and frequency calculations resulting in all positive frequencies indicated that the structures are at energy minima. NMR shielding tensors were calculated on optimized geometries, using the GIAO (Gauge Independent Atomic Orbital) method.^46,47 For the chemical shift reference, CFCl₃ was used, and chemical shifts of the amino acids, δ_{amino acid}, are provided as

$${\delta }_{\mathit{\text{amino acid}}}={\sigma }_{\text{CFCl}3}-{\sigma }_{\mathit{\text{amino acid}}}+{\delta }_{\mathit{\text{ref}}}.$$ (1)

The absolute chemical shielding of CFCl₃ (σ_CFCl3) was calculated with each method (using optimized geometry at the same method), and the absolute chemical shielding of the amino acid, σ_{amino acid},, is provided in the GIAO calculations (at the same level of theory as the reference compound). In order to compare calculated values to experimental data, many of which were acquired with reference to different compounds, including trifluoroacetic acid (TFA) and hexafluorobenzene (C₆F₆), chemical shielding values were adjusted with δ_ref, which is the experimental difference between CFCl₃ and other reference compounds.⁴⁸ Error is evaluated throughout by taking the absolute value of the deviation of the calculated value from the experimental chemical shift, so that cancellation of positive and negative deviations from experimental values does not give rise to misleading conclusions regarding mean error. In the case of “relative” chemical shifts, in which changes in shielding of structural analogues or isomers with respect to a similar reference structure are evaluated, the absolute deviation of the difference in chemical shifts (Δppm) is reported (see Relative ¹⁹F Chemical Shifts in Results below).

Unless otherwise stated, geometries were prepared in GaussView 5,⁴⁹ using amino acid templates, modified by substitution of fluorine for hydrogen, and adjusted for specified stereochemistry. For histidine, the different tautomeric states (τ and π) of 2-fluoro and 4-fluoro histidines and analogues were considered.^19,50,51 The fluorine chemical shift of the lowest energy tautomer is reported. In the two amino acids studied with trifluoromethyl groups, the fluorine chemical shifts are reported as the average of the three fluorine chemical shifts.

One of the other fluorinated amino acid used for this study is 3-fluoroproline. Proline is an amino acid with two unique properties, having a saturated pyrrolidine ring and being a secondary amine.⁵² These two unique properties give rise to another uniqueness of proline, having two equilibria.⁵³ A first equilibrium due to pyrrolidine ring puckering gives rise to the endo and exo conformers, and the second equilibrium is due to rotation about the prolyl peptide bond that gives rise to trans (Z) and cis (E) isomers.⁵³ Fluorination of the proline creates another equilibrium in addition to these two previously mentioned isomers. Depending on the position of the fluorine atom with respect to the plane of the pyrrolidine ring, the stereoisomers 3S- and 3R-fluoroproline arise.

Input files for all the variants of 3F-proline were carefully prepared using GaussView 5, using as a template the coordinates provided by Raines and co-workers for endo and exo conformations of 4-thiaproline.⁵³ Free energy differences between endo and exo isomers were calculated, and Boltzmann-averaged chemical shifts at 308 K³⁰ are reported here for both stereoisomers of cis and trans 3-fluoroproline.

RESULTS

The accuracy of computational methods in calculating the ¹⁹F chemical shifts of different fluorinated amino acids and analogues, as shown in Figure 1, have been examined. In the present work, these are referred to as the absolute chemical shifts, in contrast to the relative chemical shifts (differences in shielding) among structurally similar molecules (see Figure 1), which are considered in the next section. The values evaluated here are the chemical shifts with respect to a reference compound such as CFCl₃, as given by Eq. 1.

Table 1 presents the average absolute deviation of fluorine chemical shifts (with respect to experimental values), determined for multiple methods (DFT, HF, MP2), with two basis sets (6–31+G* and 6–311++(3df,2p)) and two solvation models (SMD and CPCM). Also presented in Table 1 is the percentage of systems in which the method calculates the chemical shift within 1 ppm of the experimental value. It can be seen in Table 1 that the top 11 methods are all combinations of basis sets and solvent models with three functionals: ωB97X, BH and HLYP, and ωB97XD, which are the only methods to have average absolute errors of less than 5 ppm. With the functionals ωB97X and BH and HLYP, error values were less than 1.0 ppm for ~30% of the systems studied (with judicious choice of solvent model and basis set, according to Table 1); it is notable that M06L with a larger basis and SMD solvation also performed precisely, giving <1.00 ppm error for 26% of the systems.

Table 1.

Evaluation of electronic structure methods to predict chemical shifts (¹⁹F) of fluorinated amino acids in water: mean absolute error and percentage of molecules for which calculated ¹⁹F chemical shift is < 1.0 ppm.

Method ranked from lowest to highest error	Mean absolute error (ppm)	Percent systems error < 1.00 ppm
ωB97X/ 6–31+G* SMD, water	2.68	29.03
BH and HLYP/ 6–311++G(3df,2p) SMD, water	3.01	35.48
BH and HLYP/ 6–31+G* SMD, water	3.09	16.13
ωB97XD/ 6–31+G* CPCM, water	3.18	12.90
BH and HLYP/ 6–31+G* CPCM, water	3.59	29.03
ωB97X/ 6–311++G(3df,2p) CPCM, water	3.85	19.35
ωB97X/ 6–31+G* CPCM, water	3.89	22.58
BH and HLYP/ 6–311++G(3df,2p) CPCM, water	3.92	16.13
ωB97XD/ 6–31+G* SMD, water	4.21	6.45
ωB97X/ 6–311++G(3df,2p) SMD, water	4.48	9.68
ωB97XD/ 6–311++G(3df,2p) CPCM, water	4.81	9.68
M06/ 6–31+G* SMD, water	5.47	9.68
MP2/ 6–31+G* CPCM, water - MP2	5.93	12.90
M062X/ 6–31+G* CPCM, water	6.19	3.23
M06/ 6–31+G* CPCM, water	6.23	3.23
M06L/ 6–311++G(3df,2p) SMD, water	6.46	25.81
M06L/ 6–311++G(3df,2p) CPCM, water	6.71	6.45
ωB97XD/ 6–311++G(3df,2p) SMD, water	7.11	0.00
MP2/ 6–31+G* SMD, water - MP2	7.39	12.90
M062X/ 6–311++G(3df,2p) CPCM, water	8.15	9.68
M062X/ 6–31+G* SMD, water	8.15	0.00
M06/ 6–311++G(3df,2p) CPCM, water	8.49	3.23
M06L/ 6–31+G* SMD, water	8.62	6.45
M06L/ 6–31+G* CPCM, water	8.95	0.00
PBE0/ 6–311++G(3df,2p) CPCM, water	10.39	3.23
M062X/ 6–311++G(3df,2p) SMD, water	10.48	0.00
M06/ 6–311++G(3df,2p) SMD, water	10.94	0.00
PBE0/ 6–31+G* CPCM, water	11.14	0.00
MP2/ 6–31+G* SMD, water- SCF	12.48	0.00
MP2/ 6–31+G* CPCM, water - SCF	14.06	0.00
B3LYP/ 6–31+G* CPCM, water	16.03	0.00
B3LYP/ 6–311++G(3df,2p) CPCM, water	18.25	0.00
B3LYP/ 6–31+G* SMD, water	18.29	0.00
HF/ 6–311++G(3df,2p) SMD, water	18.48	0.00
B3LYP/ 6–311++G(3df,2p) SMD, water	19.37	0.00
HF/ 6–311++G(3df,2p) CPCM, water	20.00	0.00
HF/ 6–31+G* SMD, water	20.22	0.00
HF/ 6–31+G* CPCM, water	21.64	0.00
PBEPBE/ 6–31+G* SMD, water	22.37	0.00
PBEPBE/ 6–311++G(3df,2p) SMD, water	22.54	0.00
PBE0/ 6–311++G(3df,2p) SMD, water	28.00	0.00
PBE0/ 6–31+G* SMD, water	28.51	0.00
PBEPBE/ 6–311++G(3df,2p) CPCM, water	28.87	0.00
PBEPBE/ 6–31+G* CPCM, water	29.99	0.00
BLYP/ 6–311++G(3df,2p) CPCM, water	31.72	3.23
PW91PW91/ 6–31+G* SMD, water	32.85	0.00
BLYP/ 6–31+G* CPCM, water	32.94	0.00
PW91PW91/ 6–311++G(3df,2p) SMD, water	33.11	0.00
PW91PW91/ 6–311++G(3df,2p) CPCM, water	35.50	0.00
PW91PW91/ 6–31+G* CPCM, water	36.70	0.00
BLYP/ 6–311++G(3df,2p) SMD, water	38.63	0.00
BLYP/ 6–31+G* SMD, water	39.03	0.00

In Figure 2, a pie graph indicates how many times each method provides the lowest error (in a set of 31 molecules). It can be see that BH and HLYP/6–31+G* method using CPCM solvent model and ωB97X/6–31+G* with SMD solvent model are nominally the best methods in predicting absolute ¹⁹F NMR shift values, with each having the lowest error in 4 of the 31 systems studied. When considering only computational method and disregarding the specifics of basis set and solvation model, BH and HLYP, M06L, ωB97XD, and ωB97X functionals perform well for calculations of ¹⁹F NMR chemical spectra. Figure 3 indicates how many times each method is within the top 3 methods for calculating absolute chemical shift calculation, based on the least absolute deviation. It also confirms that BH and HLYP and ωB97X methods are the most outstanding methods for absolute chemical shifts of fluorinated amino acids in water. In addition to DFT methods, the MP2 method, which is a wave function theory (WFT) approach, performs well only in non-aromatic fluorinated systems in water, namely 3-fluoroproline, (2S, 3R)- and (2S, 3S)-4,4,4-trifluorovaline; (2S, 4R)- and (2S, 4S)-5,5,5-trifluoroleucine.

Figure 2.

Number of molecules (out of 31) for which a method provides the least absolute error value in chemical shift calculations.

Figure 3.

Number of fluorinated amino acids/analogues for which a method is ranked in the top 3 most accurate ¹⁹F chemical shifts.

For predicting NMR spectra, it is common to use a scaling factor for values calculated with electronic structure methods.^54,55 The top methods in Table 1 indicate calculations for which the scaling factor is close to 1. We considered the possibility that some of the poorly performing methods could accurately predict experimental chemical shifts if a scaling factor were used. The calculated chemical shielding σ was plotted versus experimental chemical shift δ (referenced to CFCl₃) for all of the compounds in Figure 1. This was done for each method, and methods having a value of R² ≥ 0.995 are presented in Table 2, which gives the adjusted average error and values for linear scaling factors for CFCl₃ referenced chemical shifts. The performance criterion of R² ≥ 0.995 was used previously by Pierence et al. in fitting ¹H and ¹³C DFT data.⁴² A salient result from the linear regression analysis is that Hartree-Fock methods with a small basis set perform extremely well, becoming the top two methods with lowest average error: 2.26 and 2.32 ppm for CPCM and SMD solvation, respectively. This is a dramatic change from the mean absolute error values of 20.22 ppm (SMD) and 21.64 ppm (CPCM) for the unadjusted chemical shifts. The functionals BH and HLYP, ωB97X, and ωB97XD continue to perform well, and B3LYP with a larger basis set also makes an appearance in the top 12 lowest error methods after linear scaling is applied.

Table 2.

Linear scaling values and adjusted mean absolute error for electronic structure methods having values of R² ≥ 0.995 in linear regression analysis of calculated chemical shielding versus experimental chemical shift (relative to CFCl₃).

Methods ranked according to adjusted mean absolute error	Adjusted mean absolute error (ppm)	Linear scaling factors for CFCl3 referenced chemical shifts
		Slope	Intercept
HF/ 6–31+G* CPCM, water	2.26	0.934	−23.415
HF/ 6–31+G* SMD, water	2.32	0.940	−21.937
BH and HLYP/ 6–31+G* SMD, water	2.46	0.977	−1.831
BH and HLYP/ 6–31+G* CPCM, water	2.49	0.969	−3.936
ωB97X/ 6–31+G* SMD, water	2.64	0.999	0.035
HF/ 6–311++G(3df,2p) SMD, water	2.75	0.935	−20.440
BH and HLYP/ 6–311++G(3df,2p) SMD, water	2.86	0.971	−0.566
ωB97XD/ 6–31+G* CPCM, water	2.87	0.995	1.533
HF/ 6–311++G(3df,2p) CPCM, water	3.04	0.929	−22.025
ωB97X/ 6–311++G(3df,2p) SMD, water	3.21	0.987	3.078
B3LYP/ 6–311++G(3df,2p) SMD, water	3.26	1.001	19.440
BH and HLYP/ 6–311++G(3df,2p) CPCM, water	3.37	0.965	−2.823
M06/ 6–311++G(3df,2p) SMD, water	3.38	0.969	9.070
MP2/ 6–31+G* CPCM, water - SCF	3.44	0.906	−17.124
ωB97X/ 6–31+G* CPCM, water	3.60	0.994	−2.844
ωB97XD/ 6–311++G(3df,2p) SMD, water	3.61	0.984	6.212
M06/ 6–31+G* SMD, water	3.72	0.968	1.699
ωB97XD/ 6–31+G* SMD, water	3.72	1.002	3.989
MP2/ 6–31+G* SMD, water- SCF	3.77	0.912	−15.374
ωB97XD/ 6–311++G(3df,2p) CPCM, water	3.78	0.979	3.334
ωB97X/ 6–311++G(3df,2p) CPCM, water	3.92	0.983	0.059
M062X/ 6–31+G* SMD, water	4.12	0.992	7.707
M06/ 6–311++G(3df,2p) CPCM, water	4.15	0.958	5.920
M06/ 6–31+G* CPCM, water	4.18	0.998	4.912
M062X/ 6–31+G* CPCM, water	4.54	0.982	5.184
PBEPBE/ 6–31+G* CPCM, water	4.63	1.024	31.864
BLYP/ 6–31+G* SMD, water	6.00	1.024	41.104

As recently pointed out in a study by Medvedev et al. some DFT methods accurately calculate energies but have not shown increased accuracy in calculating electron density, which may affect structural parameters, such as bond length.⁵⁶ A more holistic way to evaluate the validity of electronic structure methods is to consider how well other structural properties are reproduced. To do so, the C_α chemical shifts were also evaluated for all of the compounds having reported experimental values; these were 4-fluorohistidine, 2-fluorohistidine, 4-, 5-, and 6-fluorotryptophan, 4-fluorophenylalanine, and trifluoromethionine. Experimental ¹³C NMR data for 2-fluorohistidine and 4-fluorohistidine was obtained using Varian 400 MHz NMR and for other molecules: 4-fluorophenylalanine,⁵⁷ 4- 5- 6-fluorotryptophan^58,57,59and trifluoromethionine³² the ¹³C shifts were acquired from literature. In order to evaluate a somewhat reduced data set, the top 12 performing methods in Table 1, plus Hartree-Fock methods (which perform very well with linear scaling), were considered. The average of the absolute error in ¹⁹F and ¹³C_α chemical shifts for the 7 fluorinated amino acids is presented in Table 3. Individual ¹³C_α chemical shifts and absolute errors for the specific fluorinated amino acids studied here are provided in Supporting Information (Tables S3 and S4). In Table 3, it can be seen that HF methods are very accurate for ¹³C chemical shifts, and with linear scaling factors, they are also very accurate for ¹⁹F chemical shifts. Overall, Hartree-Fock methods, namely, HF/6–31+G* with either SMD or CPCM solvation, offer high accuracy and low computational cost. This finding should be advantageous for NMR chemical shifts prediction in large biomolecular systems.

Table 3.

The average of the absolute error in ¹⁹F and ¹³C_α chemical shifts averaged over 7 fluorinated amino acids for which experimental ¹³C_α values were available.

Methods ranked according to average of the absolute error in 19F and 13Cα chemical shifts	Mean absolute error in 19F and 13Cα chemical shifts (ppm)
BH and HLYP/ 6–31+G* CPCM, water	1.47
ωB97X/ 6–31+G* CPCM, water	1.87
BH and HLYP/ 6–31+G* SMD, water	2.45
ωB97X/ 6–31+G* SMD, water	2.65
ωB97X/ 6–311++G(3df,2p) CPCM, water	3.15
BH and HLYP/ 6–311++G(3df,2p) CPCM, water	3.27
ωB97XD/ 6–31+G* CPCM, water	3.35
BH and HLYP/ 6–311++G(3df,2p) SMD, water	3.92
ωB97XD/ 6–311++G(3df,2p) CPCM, water	4.06
ωB97X/ 6–311++G(3df,2p) SMD, water	4.22
ωB97XD/ 6–31+G* SMD, water	4.52
M06/ 6–31+G* SMD, water	5.99
HF/ 6–31+G* SMD, water	9.61
HF/ 6–31+G* CPCM, water	12.11

Relative ¹⁹F Chemical Shifts

In addition to determining the capability of computational methods to accurately calculate absolute values of ¹⁹F chemical shifts in water, the ability to predict correct relative changes in fluorine shielding as a result of isomer effects, backbone effects, and protonation effects was examined. The sets of comparative systems are illustrated in Figure 1. The relative chemical shift is defined as Δppm = δ_{amino acid} − δ_analogue. Here, the chemical shift of the reference amino acid structure is given by δ_{amino acid}, while δ_analogue represents the chemical shift of the modified structure (i.e. protonation in case of fluorohistidine; side chain vs. zwitterionic amino acid in cases of fluorotryptophans, 4-fluorophenylalanine). Experimental values of Δppm are taken from published data, and evaluated error (absolute deviation) in calculated Δppm comes from reference to these experimental values.

Table 4 ranks the methods from lowest to highest average relative error, averaged over all the comparative fluorinated systems used. It also includes the percent time that the relative error is equal to or less than 0.5 ppm. The values of error in Δppm range from 0.02 ppm for 5-fluorotryptophan vs 5-fluoroindole (PBE0/6–31+G*/SMD water) to 40.4 ppm for 4-fluorohistidine vs. 4-fluoroimidazole (BLYP/6–31+G*/CPCM water). The error in Δppm averaged across the 23 systems studied and all methods is 3.4 ppm. As a point of reference, the mean absolute experimental value of Δppm for this data set is 3.15 ppm; the maximum is 8.243 ppm (6-fluorotryptophan vs. 6-fluoroindole) and the minimum is 0.22 (2S, 4R- vs. 2S, 4S-trifluoroleucine). Taken altogether, this indicates a rather stringent requirement for accuracy and precision in computational methods that can reliably predict changes in shielding due to structural or environmental effects. Table 4 indicates that MP2/6–31+G* with CPCM solvent model has the lowest error in calculating relative ¹⁹F chemical shifts, predicting the relative error within 0.5 ppm for 22% of the systems (SMD model also has a low average error, but lower accuracy as well, predicting a Δppm within 0.5 ppm for only 9% of the systems).

Table 4.

Mean absolute error in calculations of relative changes in ¹⁹F chemical shifts (Δppm values) among sets of amino acids and analogues having structural changes (protonation, C_α substitution, isomers).

Methods ranked according to the lowest error in relative chemical shift values (Δppm)	Mean relative error (ppm)	Percent systems with error < 0.5 ppm
MP2/ 6–31+G* CPCM, water - MP2	1.84	21.74
MP2/ 6–31+G* SMD, water - MP2	1.88	8.70
M062X/ 6–31+G* SMD, water	2.13	13.04
ωB97X/ 6–31+G* SMD, water	2.19	8.70
ωB97X/ 6–311++G(3df,2p) SMD, water	2.30	13.04
M062X/ 6–311++G(3df,2p) SMD, water	2.31	21.74
BH and HLYP/ 6–31+G* SMD, water	2.32	4.35
ωB97XD/ 6–31+G* SMD, water	2.33	13.04
HF/ 6–31+G* SMD, water	2.33	17.39
ωB97XD/ 6–311++G(3df,2p) SMD, water	2.36	8.70
HF/ 6–311++G(3df,2p) SMD, water	2.39	4.35
M06/ 6–311++G(3df,2p) SMD, water	2.41	13.04
B3LYP/ 6–31+G* SMD, water	2.60	0.00
PBE0/ 6–31+G* SMD, water	2.62	8.70
PBE0/ 6–311++G(3df,2p) SMD, water	2.64	0.00
MP2/ 6–31+G* SMD, water- SCF	2.66	8.70
PBEPBE/ 6–311++G(3df,2p) SMD, water	2.67	8.70
BH and HLYP/ 6–311++G(3df,2p) SMD, water	2.69	8.70
ωB97X/ 6–31+G* CPCM, water	2.70	13.04
B3LYP/ 6–311++G(3df,2p) SMD, water	2.71	4.35
HF/ 6–31+G* CPCM, water	2.72	17.39
M062X/ 6–31+G* CPCM, water	2.75	17.39
BH and HLYP/ 6–31+G* CPCM, water	2.77	13.04
HF/ 6–311++G(3df,2p) CPCM, water	2.78	13.04
ωB97X/ 6–311++G(3df,2p) CPCM, water	2.78	4.35
PBE0/ 6–311++G(3df,2p) CPCM, water	2.83	8.70
MP2/ 6–31+G* CPCM, water - SCF	2.92	8.70
PBEPBE/ 6–31+G* SMD, water	2.92	4.35
M06L/ 6–311++G(3df,2p) SMD, water	2.94	13.04
M062X/ 6–311++G(3df,2p) CPCM, water	2.95	8.70
BLYP/ 6–311++G(3df,2p) SMD, water	2.96	0.00
PW91PW91/ 6–31+G* SMD, water	3.00	4.35
BH and HLYP/ 6–311++G(3df,2p) CPCM, water	3.05	8.70
BLYP/ 6–31+G* SMD, water	3.08	0.00
PBEPBE/ 6–31+G* CPCM, water	3.08	4.35
PBE0/ 6–31+G* CPCM, water	3.09	0.00
PBEPBE/ 6–311++G(3df,2p) CPCM, water	3.12	13.04
M06/ 6–311++G(3df,2p) CPCM, water	3.16	0.00
PW91PW91/ 6–31+G* CPCM, water	3.24	4.35
PW91PW91/ 6–311++G(3df,2p) CPCM, water	3.26	8.70
ωB97XD/ 6–31+G* CPCM, water	3.33	17.39
ωB97XD/ 6–311++G(3df,2p) CPCM, water	3.52	0.00
M06/ 6–31+G* SMD, water	3.55	0.00
M06/ 6–31+G* CPCM, water	3.57	8.70
M06L/ 6–311++G(3df,2p) CPCM, water	3.79	13.04
M06L/ 6–31+G* SMD, water	4.24	4.35
PW91PW91/ 6–311++G(3df,2p) SMD, water	4.71	0.00
M06L/ 6–31+G* CPCM, water	4.98	4.35
B3LYP/ 6–31+G* CPCM, water	5.69	8.70
B3LYP/ 6–311++G(3df,2p) CPCM, water	6.08	4.35
BLYP/ 6–311++G(3df,2p) CPCM, water	10.50	8.70
BLYP/ 6–31+G* CPCM, water	13.73	0.00

A key criterion in identifying reliable methods is the ability to accurately predict shielding and deshielding due to environmental or structural changes. Table 5 presents the percentage of systems in which each method calculated the correct sign of Δppm (positive or negative, indicating shielding or deshielding of an analogue with respect to its reference structure, respectively). M062X/6–31+G* method with SMD solvent model performs best according to this criterion, correctly predicting relative shielding/deshielding for 91% of the systems studied. Other top performers, at 87%, are MP2 calculations and DFT methods with M06 and ωB97X functionals.

Table 5.

Methods ranked according to percentage of systems for which methods get correct "order" (relative shielding/deshielding) of ¹⁹F chemical shifts in amino acids and analogues with structural changes (protonation, backbone differences, isomers).

Methods ranked from highest to lowest according to performance in predicting relative shielding/deshielding in comparative sets	Percent systems with correct order of chemical shifts
M062X/ 6–31+G* SMD, water	91.3
MP2/ 6–31+G* CPCM, water - SCF	87.0
M06/ 6–311++G(3df,2p) SMD, water	87.0
ωB97X/ 6–31+G* SMD, water	87.0
ωB97X/ 6–311++G(3df,2p) SMD, water	87.0
B3LYP/ 6–31+G* CPCM, water	82.6
B3LYP/ 6–311++G(3df,2p) CPCM, water	82.6
MP2/ 6–31+G* CPCM, water - MP2	82.6
M062X/ 6–31+G* CPCM, water	82.6
M062X/ 6–311++G(3df,2p) CPCM, water	82.6
ωB97X/ 6–31+G* CPCM, water	82.6
ωB97X/ 6–311++G(3df,2p) CPCM, water	82.6
MP2/ 6–31+G* SMD, water - MP2	82.6
M062X/ 6–311++G(3df,2p) SMD, water	82.6
ωB97XD/ 6–31+G* SMD, water	82.6
ωB97XD/ 6–311++G(3df,2p) SMD, water	82.6
BH and HLYP/ 6–31+G* CPCM, water	78.3
BLYP/ 6–31+G* CPCM, water	78.3
HF/ 6–31+G* CPCM, water	78.3
HF/ 6–311++G(3df,2p) CPCM, water	78.3
M06/ 6–31+G* CPCM, water	78.3
PBE0/ 6–31+G* CPCM, water	78.3
ωB97XD/ 6–31+G* CPCM, water	78.3
BH and HLYP/ 6–31+G* SMD, water	78.3
HF/ 6–31+G* SMD, water	78.3
PBE0/ 6–311++G(3df,2p) SMD, water	78.3
M06L/ 6–311++G(3df,2p) SMD, water	78.3
BH and HLYP/ 6–311++G(3df,2p) CPCM, water	73.9
M06/ 6–311++G(3df,2p) CPCM, water	73.9
PW91PW91/ 6–31+G* CPCM, water	73.9
PW91PW91/ 6–311++G(3df,2p) CPCM, water	73.9
B3LYP/ 6–31+G* SMD, water	73.9
MP2/ 6–31+G* SMD, water- SCF	73.9
PBE0/ 6–31+G* SMD, water	73.9
BLYP/ 6–311++G(3df,2p) CPCM, water	69.6
PBE0/ 6–311++G(3df,2p) CPCM, water	69.6
PBEPBE/ 6–31+G* CPCM, water	69.6
ωB97XD/ 6–311++G(3df,2p) CPCM, water	69.6
BH and HLYP/ 6–311++G(3df,2p) SMD, water	69.6
B3LYP/ 6–311++G(3df,2p) SMD, water	69.6
HF/ 6–311++G(3df,2p) SMD, water	69.6
PBEPBE/ 6–31+G* SMD, water	69.6
PBEPBE/ 6–311++G(3df,2p) CPCM, water	65.2
BLYP/ 6–311++G(3df,2p) SMD, water	65.2
M06/ 6–31+G* SMD, water	65.2
PBEPBE/ 6–311++G(3df,2p) SMD, water	65.2
PW91PW91/ 6–311++G(3df,2p) SMD, water	65.2
M06L/ 6–311++G(3df,2p) CPCM, water	60.9
BLYP/ 6–31+G* SMD, water	60.9
PW91PW91/ 6–31+G* SMD, water	60.9
M06L/ 6–31+G* CPCM, water	56.5
M06L/ 6–31+G* SMD, water	52.2

The number of times each method appeared as the best method (with the most accurate calculation, represented by the least relative error) is shown in Figure 4. According to Figure 4, when neglecting the details of basis set and solvation model, both MP2 and PBE0 methods have the higher number of most accurate Δppm values. Overall, MP2/6–31+G*/CPCM solvent performed best, with most accurate values calculated for 4 of the 23 comparative systems. Figure 5 indicates how many times each method is within the top 3 methods for relative chemical shift calculations (Δppm values), based on lowest relative error. Figure 5 also confirms that MP2 methods generally provide accurate relative changes in ¹⁹F chemical shifts of fluorinated systems in water. Simultaneously, M062X method also emerges many times among the best three methods. Other good performers include ωB97XD, PBE0, HF, M06, and PBEPBE.

Figure 4.

Number of comparative systems (out of 23 total) for which a method provides the lowest error value in relative chemical shift (Δppm value).

Figure 5.

Number of comparative systems (out of 23) for which a method is ranked in the top 3 most accurate relative (Δppm) ¹⁹F chemical shifts.

When examining each fluorinated system solely considering lowest relative error, MP2, PBE0, M062X, HF and M06L methods appear the most reliable in procuring correct relative ¹⁹F chemical shifts for aromatic fluorinated compounds. The non-aromatic systems have a different behavior. In fluoroproline isomers, where cis-trans isomerization effects are considered, ωB97X and BH and HLYP methods also perform well in addition to MP2, M062X and HF methods. But for the trifluorovaline systems, M062X method does not have good performance. When considering fluorinated systems independently, it is evident that SMD solvent model is better in most cases for calculating relative shifts. This is evident in data for fluorohistidine, fluoroimidazole, and fluoro-(5-methyl)-imidazole protonation effects, and fluorotryptophan vs. fluoroindole backbone effects. It is also noticeable that the 6–31+G* basis set is the best performer, since it appears to correctly calculate changes in shielding in many comparative systems.

To summarize, in a situation where the absolute ¹⁹F NMR shifts of a fluorinated system are needed, the best methods appear to be BH and HLYP and ωB97X DFT calculations and Hartree-Fock calculations with the scaling factors given in Table 2, which also accurately predicts shielding of ¹³C_α atoms. For calculating relative changes in chemical shift, MP2 or M062X calculations are the recommendations for newly-considered systems, with a smaller basis set (6–31+G*). In the case of the specific fluorinated amino acids studied here, it may be useful to examine the tables in Supporting Information, which rank the methods individually for each fluorinated amino acid or analogue (Tables S1, S2, S5, S6 and S7).

Fluorinated amino acids in organic solvents

The ability of computational methods to accurately calculate ¹⁹F chemical shifts in different solvent environments was investigated in this work, since the dielectric environment surrounding an amino acid within a protein depends on the local structure. For instance, the interior of proteins is estimated to have a dielectric of ~9, whereas surface-exposed amino acids experience a dielectric approaching that of bulk water, but still measurably lower (ε~30).⁶⁰ With that in mind, the experimental ¹⁹F chemical shifts in a variety of organic solvents were acquired for 4-, 5-, and 6-fluoroindole (tryptophan side chains) and 4-fluorophenylalanine and its analogues fluorobenzene and p-fluorotoluene. A truncated set of computational methods was tested versus this set of data. The density functionals BH and HLYP, ωB97X, M062X, M06, and PBE0 were selected because of their good performance on aqueous systems; B3LYP was included because of its ubiquity; MP2 calculations were also included for their demonstrated accuracy. As in the aqueous work on fluorinated amino acids and their analogues, two sizes of basis set (6–31+G* and 6–311++G(3df,2p)) were surveyed along with two solvation methods: SMD and CPCM.

The experimental results for 4-, 5-, and 6-fluoroindole are presented in Figure 6. It can be seen that the chemical shifts of fluoroindoles are not a linear function of solvent dielectric constant. However, ethanol (ε=24.8) always results in the most shielded ¹⁹F chemical shift, and dimethylsulfoxide (DMSO, ε=46.8) results in the most deshielded chemical shift for fluoroindoles. The values of water and an organic solvent, either N,N-dimethylformamide (DMF, ε=37.2) or pyridine (ε=12.9), are book-ended by DMSO and ethanol, though the order varies. The experimental data set presents a challenge for computational methods using continuum solvation models, since solvent dielectric is a primary (though not sole) parameter upon which solvent-dependent behavior in such models depends. That is to say, any specific, atomic solvent-solute interactions that may influence chemical properties are neglected.

Figure 6.

Experimental chemical shifts for (a) 4F-indole, (b) 5F-indole, and (c) 6F-indole in water (blue), DMSO (green), ethanol (orange), and pyridine (purple) or DMF (pink) solvents.

The solvent-dependent ¹⁹F chemical shifts of 4-fluorophenylalanine and its analogues, fluorobenzene and p-fluorotoluene, were acquired in water, DMSO, ethanol, and either pyridine or DMF solvents. Although some fluorophenyl compounds (such as para-fluoronitrobenzene)⁶¹ show clear trends between ¹⁹F chemical shifts and solvent dielectric, there is not a clear trend in para-fluorotoluene, fluorobenzene, or 4-fluorophenylalanine. The relative order from shielded to deshielded is the same for fluorobenzene and toluene, but not 4-fluorophenylalanine. The experimental results for 4-fluorophenylalanine and analogues are illustrated in Figure S1 in Supporting Information. There does appear to be some correlation between the solvent-dependent fluorine chemical shifts of 4-fluorophenylalanine and the solvent polarity using the parameter E_T, which is based on the solvatochromism of pyridinium N-phenolate betaine dye (Reichhardt’s dye). In 4-fluorophenylalanine, the trend indicates fluorine is more deshielded in solvents having higher values of m E_T (more polar).⁶² This relationship was shown by Giam and Lyle to hold for 2-fluoropyridine (more polar solvent giving rise to fluorine deshielding), with opposite effects in 3-fluoropyridine and 4-fluoro-2-picoline, where the reference compound for fluorine chemical shifts was fluorobenzene. Clearly, solvent effects of fluorine chemical shifts are complex, and implicit solvent models are not capable of capturing the phenomena. However, from the data presented in this work, it does appear that implicit solvent models are adequate for modeling most relative chemical shifts of fluorinated compounds in aqueous solution.⁶³

In general, the calculated fluorine chemical shifts in almost all methods trend from deshielded to shielded as solvent dielectric increases. This can be rationalized as more polar solvents stabilizing more polar electronic configurations through inductive effects of the fluorine, which result in shielding of the fluorine nucleus. We recently reported similar calculated effects for 4-fluorohistidine (increased shielding with dielectric constant), although calculated shielding of 2-fluorohistidine decreases with higher dielectric.⁵¹ The only method with notable deviations between shielding and dielectric is M062X; however, the method did not perform better at ordering the relative shielding/deshielding in the presence of different solvents. Overall, our results indicate that electronic structure calculations with implicit solvent models are not able to reliably predict solvent effects on fluorine chemical shifts. On an optimistic note, work by Prosser and co-workers showed that B3LYP/6–31G(3d,p) calculations predicted the solvent polarity dependence (using Reichhardt's E_T scale) of trifluoromethyl groups.⁶⁴

The average absolute deviations of calculated chemical shifts were calculated for the solvents studied, and they are presented in Table 6. The method with the lowest error is BH and HLYP/6–311++G(3df,2p) with CPCM model, but it can be noted that, in general, the SMD solvent model and 6–31+G* basis set performs comparatively better in capturing solvent effects on ¹⁹F NMR shifts with most methods. Since not one method was successful in reproducing experimentally-observed changes in ¹⁹F NMR shifts for even one of the 6 molecules studied, the obvious next step is to use explicit solvent (e.g. via microsolvation) to see if solvent effects can be captured when more atomic detail of the solvation shell is provided.

Table 6.

Methods ranked from lowest to highest according to their accuracy in calculating solvent dependent ¹⁹F chemical shifts.

Method ranked from lowest to highest average absolute error in solvent- dependent chemical shifts	Mean absolute error (ppm)	Standard deviation (ppm)	Minimum error (ppm)	Maximum error (ppm)
BH and HLYP/ 6–31+G* CPCM	0.89	0.72	0.14	2.86
BH and HLYP/ 6–311++G(3df,2p) SMD	0.89	0.71	0.03	2.16
ωB97X/ 6–311++G(3df,2p) CPCM	0.92	0.72	0.07	2.50
M062x/ 6–311++G(3df,2p) CPCM	1.07	0.82	0.20	3.15
ωB97X/ 6–31+G* SMD	1.20	0.90	0.04	3.44
ωB97X/ 6–31+G* CPCM	1.28	1.01	0.10	3.91
BH and HLYP/ 6–31+G* SMD	1.65	1.07	0.08	3.71
M062x/ 6–31+G* CPCM	1.75	1.06	0.01	3.65
ωB97X/ 6–311++G(3df,2p) SMD	2.18	1.15	0.16	4.38
M062x/ 6–311++G(3df,2p) SMD	2.25	1.24	0.34	4.98
M06/ 6–31+G* CPCM	2.25	1.71	0.01	5.72
BH and HLYP/ 6–311++G(3df,2p) CPCM	2.32	1.17	0.37	4.16
M06/ 6–31+G* SMD	2.77	2.01	0.23	6.03
MP2/ 6–31+G* SMD- SCF	2.82	1.67	0.14	5.93
M062x/ 6–31+G* SMD	2.82	1.36	0.20	4.97
PBE0/ 6–311++G(3df,2p) CPCM	3.21	1.26	1.01	5.52
MP2/ 6–31+G* CPCM- SCF	4.44	1.69	1.55	7.33
M06/ 6–311++G(3df,2p) CPCM	4.63	2.94	0.27	8.53
PBE0/ 6–311++G(3df,2p) SMD	5.25	1.03	3.08	6.87
MP2/ 6–31+G* CPCM - MP2	7.13	1.27	4.39	9.50
PBE0/ 6–31+G* CPCM	7.38	1.67	4.39	10.23
MP2/ 6–31+G* SMD- MP2	8.61	1.18	6.61	10.97
M06/ 6–311++G(3df,2p) SMD	9.00	1.51	6.51	11.85
PBE0/ 6–31+G* SMD	9.13	1.45	6.59	11.73
B3LYP/ 6–311++G(3df,2p) CPCM	14.53	1.23	12.19	16.60
B3LYP/ 6–311++G(3df,2p) SMD	16.94	1.22	14.78	18.98
B3LYP/ 6–31+G* CPCM	17.70	1.50	14.67	20.11
B3LYP/ 6–31+G* SMD	19.72	1.44	17.46	22.16

Discussion

The wave function method MP2 clearly provides accurate calculation of relative changes in fluorine nuclear shielding: MP2/6–31+G* in both SMD and CPCM implicit water had average relative error under 2 ppm, while the best 4 density functional methods and HF (rounding out the top 10 methods in Table 4) had average relative error values ranging from 2.13–2.33 ppm. Our group has recently investigated the fluorine chemical shifts of a series of substituted aryl fluoro-bicyclo-octane compounds with MP2 and BH and HLYP calculations (see Fig. S2 for structure). The bicyclo-octane compounds display a narrow range in experimental fluorine chemical shift variation of 0.97 ppm across substitutions at the para position of the phenyl ring,⁶⁵ which is lower than the average relative error found for any methods in this work. Remarkably, it was found that MP2/6–31+G*/SMD calculations had an average absolute deviation across the series of 0.05 ppm (see Table S8). Although MP2 methods are more costly than DFT, they may be most reliable when high precision is required.

A commonality in most of the best-performing functionals is that they contain a higher amount of Hartree-Fock (HF) exchange than other functionals evaluated. The best functionals for absolute fluorine chemical shifts were BH and HLYP, ωB97X, M06L, and ωB97XD. BH and HLYP has 50% HF exchange and 50% B88 GGA exchange. ωB97X and ωB97XD are range-separated hybrid functionals that split the exact exchange contribution into short-range and long-range. In ωB97X, the exchange-correlation function is composed of 16% short-ranged HF exchange, 100% long-ranged HF exchange and a value of 0.3 for ω. It should be noted that the smaller the ω value, the longer the range of the short-ranged operator will be.⁴⁰ In ωB97XD, the long-range exchange has a longer length scale (value of 0.2 for ω); however, the amount of exact exchange in the short-range component is increased to 22%. Note the comparative performance of BH and HLYP over BLYP and B3LYP. As stated before, BH and HLYP has 50% HF exchange, whereas B3LYP has only 20% HF exchange and BLYP is not a hybrid functional (no HF exchange). The comparison across the series of functionals with Becke exchange and Lee-Yang-Parr GGA correlation may indicate that accurate shielding calculations of fluorine require higher amounts of HF exchange. Note that B3LYP, as a hybrid functional contains several exchange and correlation components. While it is tempting to say that a component of HF exchange seems to increase the accuracy of DFT methods in calculating fluorine chemical shifts, the strong performance of the M06L functional prevents this from being a general statement. The M06L functional is a local functional with no component of HF exchange. The fact that DFT methods generally perform as well or better with a smaller basis set indicates that cancellation of error is taking place in the calculations (as convergence should be seen with increasing basis size), and so a number of error cancellations may be taking place in DFT calculations among different functionals, such that a single component or feature of functionals cannot be assigned to give rise to more accurately-calculated chemical shifts.

The best performing functionals for relative changes in fluorine nuclear shielding (evaluated over structural analogues and isomers) are the Minnesota functionals M062X and M06. M062X is one of the recently developed Minnesota functionals with double the amount of nonlocal exchange. It is a global hybrid meta GGA with 54% HF exchange.³⁷ The M06 functional, however, has a lower amount of HF exchange (27%). M062x performed particularly well with fluorohistidine analogues and 4F-tryptophan vs. 4F-indole, and performed poorly with trifluorovaline, whereas M06 did well calculating ¹⁹F chemical shifts of trifluorovaline. Our data set is admittedly biased toward fluorinated aromatic amino acids, which have been been commoly used in protein fluorolabeling studies. It is possible that our data set indicates that better results are obtained for fluorinated aromatic compounds when functionals with higher amounts of HF exchange are used. A summary of recommended methods to calculate absolute ¹⁹F chemical shifts for each family of fluorinated compounds is depicted in Figure 7.

Figure 7.

Flowchart showing recommended methods for different types of fluorinated families.

Basis sets

In the present study, 6–31+G* and 6–311++G(3df,2p) basis sets are used. It has been found in previous studies that having extra polarization in second row elements (3df) leads to better results in fluorine-containing systems.⁶⁶ When comparing performance between the smaller and larger basis sets, from Figures 2–5, 7 and Tables 1,4–6, it is noticeable that 6–31+G* basis set generally performs as well or better than the larger 6–311++G(3df,2p) basis set. This is in line with previous studies^67,68,69 showing better results for fluorine-containing systems when smaller basis sets, including 6–31+G*, are used. Meanwhile, a study of high-level calculations for ¹⁹F chemical shifts of (very) small molecules in the gas phase found that for relative chemical shifts, basis set enlargement does little to change mean deviations from experimental values (i.e. basis set enlargement matters for accurate calculation of absolute chemical shifts).²⁶ None of the previous work has examined aromatic systems, but this present study indicates accurate fluorine chemical shifts in both aromatic and aliphatic fluorinated compounds can be studied with a smaller basis set (that contains both diffuse and polarization functions). This is encouraging, since reliable results can be obtained with less computational effort when smaller basis sets are used. As researchers seek to calculate fluorine chemical shifts in protein environments (with many atoms), treatment with a smaller basis may be a more tractable method for routine work.

Solvent Model

Both CPCM and SMD solvent models⁷⁰ were considered in this work. The CPCM solvent model is a conductor-like polarizable continuum model parametrized on a wide variety of molecules containing C, H, N, O, and Cl.^71,72 The SMD model⁴⁵ accounts for nonelectrostatic effects such as dispersion, in addition to electrostatic treatment by a polarizable continuum model. There is no clear trend favoring SMD or CPCM solvent model for absolute ¹⁹F chemical shift calculations. However, it is clear in Table 4 that relative fluorine shielding changes in water are generally more accurate using the SMD model vs. CPCM solvation.

Conclusions

When considering future work on the fluorinated amino acids surveyed here, Figure 7 provides general recommendations, while Tables S1, S2, S5, S6 and S7 in Supporting Information may provide helpful guidance in selecting specific methods. In general, absolute chemical shifts of fluorine are most accurate using ωB97X and BH and HLYP functionals, and Hartree-Fock calculations with scaling factors (provided in Table 2). Relative chemical shifts, i.e. when examining effects of protein or structural changes on shielding, are most accurately calculated by MP2 calculations and the M062X functional. Best performance for relative changes in ¹⁹F shielding is generally obtained with a small basis set (6–31+G*) and the SMD implicit solvation model (in aqueous solutions).