Experiment and theory at the convergence limit: accurate equilibrium structure of picolinic acid by gas-phase electron diffraction and coupled-cluster computations

Natalja Vogt *ab, Ilya I. Marochkin ab and Anatolii N. Rykov b
aSection of Chemical Information Systems, University of Ulm, 89069 Ulm, Germany. E-mail: natalja.vogt@uni-ulm.de
bDepartment of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Russia

Received 15th January 2018 , Accepted 4th March 2018

First published on 22nd March 2018


The accurate molecular structure of picolinic acid has been determined from experimental data and computed at the coupled cluster level of theory. Only one conformer with the O[double bond, length as m-dash]C–C–N and H–O–C[double bond, length as m-dash]O fragments in antiperiplanar (ap) positions, ap–ap, has been detected under conditions of the gas-phase electron diffraction (GED) experiment (Tnozzle = 375(3) K). The semiexperimental equilibrium structure, rsee, of this conformer has been derived from the GED data taking into account the anharmonic vibrational effects estimated from the ab initio force field. The equilibrium structures of the two lowest-energy conformers, ap–ap and ap–sp (with the synperiplanar H–O–C[double bond, length as m-dash]O fragment), have been fully optimized at the CCSD(T)_ae level of theory in conjunction with the triple-ζ basis set (cc-pwCVTZ). The quality of the optimized structures has been improved due to extrapolation to the quadruple-ζ basis set. The high accuracy of both GED determination and CCSD(T) computations has been disclosed by a correct comparison of structures having the same physical meaning. The ap–ap conformer has been found to be stabilized by the relatively strong N⋯H–O hydrogen bond of 1.973(27) Å (GED) and predicted to be lower in energy by 16 kJ mol−1 with respect to the ap–sp conformer without a hydrogen bond. The influence of this bond on the structure of picolinic acid has been analyzed within the Natural Bond Orbital model. The possibility of the decarboxylation of picolinic acid has been considered in the GED analysis, but no significant amounts of pyridine and carbon dioxide could be detected. To reveal the structural changes reflecting the mesomeric and inductive effects due to the carboxylic substituent, the accurate structure of pyridine has been also computed at the CCSD(T)_ae level with basis sets from triple- to 5-ζ quality. The comprehensive structure computations for pyridine as well as for carbon dioxide have been used to examine the convergence with respect to the basis set size.


1. Introduction

Picolinic acid (pyridine-2-carboxylic acid) is of great interest due to its physiological properties. It is known as a L-tryptophan catabolite produced under inflammatory conditions and a selective inducer of the macrophage inflammatory proteins 1α and 1β, which are responsible for the elicitation of inflammatory processes.1 Picolinic acid is widely used in chemistry and pharmaceutics, for example, as a building block for supramolecular systems, and as a metal chelating agent, for producing polymerization catalysts2 and local anesthetics (e.g. mepivacaine and bupivacaine).3

Despite the biological and chemical importance of picolinic acid, the required fundamental knowledge about its structure and conformational behavior is very rare and not complete. There is only a partial substitution structure (rs) derived from the microwave (MW) rotational spectra of several isotopic species by I. Peña et al.4 with extremely large uncertainties (up to 0.39 Å and 0.57° for the bond lengths and angles, respectively), i.e. the determined structure is less accurate than that of the low-level quantum-chemical predictions. In the crystal structure studied by the X-ray method,5 the O[double bond, length as m-dash]C–C–N and O[double bond, length as m-dash]C–O–H fragments have antiperiplanar (ap) and synperiplanar (sp) configurations, respectively. On one hand, the molecular structure in the solid state can be distorted due to intermolecular hydrogen bonding and crystal packing forces. On the other hand, indeed, the eclipsed position of the O[double bond, length as m-dash]C and O–H bonds in the carboxylic group is more stable in comparison with the ap conformation destabilized by the repulsion of the lone electron pairs of two oxygen atoms. Therefore, this group has an sp configuration in benzoic (benzenecarboxylic),6 nicotinic (pyridine-3-carboxylic)7 and isonicotinic (pyridine-4-carboxylic)4 acids in the gas phase. In contrast, the carboxylic group of the most stable conformer of picolinic acid has an ap configuration as identified by MW and infrared (IR) spectroscopy techniques in the gas phase4 and the argon matrix,8 respectively. Such a conformation of the carboxylic group can be explained by the formation of the intramolecular hydrogen bond (IMHB) O–H⋯N as predicted by the ab initio and density functional theory (DFT) computations.4,8,9 Three further conformers, denoted here as ap–sp, sp–sp and sp–ap, were estimated to be higher in energy by 12.4, 17.9 and 47.7 kJ mol−1 (B3LYP/6-31++G**) relative to the most stable conformer, ap–ap.8 The second lowest energy conformer, ap–sp, was also identified by the analysis of the MW rotational spectra,4 whereas only one conformer was detected by the study of the IR vibrational spectra in an argon matrix before UV radiation.8

The purpose of this work is a reliable and accurate determination of the structure and conformational properties of picolinic acid by gas electron diffraction (GED) and high-level coupled-cluster computations. The high accuracy will be exploited for the observation of the fine structural effects due to the influence of the carboxylic substituent and the hydrogen bond. In order to disclose the real accuracy of the computed and experimental structures by comparison, they must have the same physical meaning. For the determination of the equilibrium structure from the GED data, the anharmonic vibrational effects have to be taken into account because their magnitudes are expected to be noticeably larger than those of the experimental uncertainties.10,11 Vibrational corrections will be estimated from the ab initio force field and a so-called semiexperimental equilibrium structure, rsee, will be determined.

The experimental studies of biomolecules in the gas phase fail very often due to their decomposition at evaporation. Because the decarboxylation of picolinic acid was observed over 433 K,12 the lower temperature would have been preferable for the GED experiment. Moreover, the presence of decomposition products (pyridine and carbon dioxide) under experimental conditions will be considered in the structural analysis.

2. GED experiment

The electron diffraction patterns were obtained on the EG-100M equipment with a vacuum in the diffraction camera of 3 × 10−5 and 2 × 10−5 mmHg at the electron beam current of 2.4 and 2.0 μA for the short (SD = 193.94 mm) and long (LD = 362.28 mm) nozzle-to-film distances, respectively. A commercial sample from Sigma-Aldrich with a purity of ≥99% was used without further purification. To avoid decarboxylation of picolinic acid, we tried to keep the experimental temperature as low as possible. Diffraction patterns of a good quality were obtained at 375(3) K, i.e. 35 and 58 degrees lower than the melting point2 and the decarboxylation temperature,12 respectively. The wavelength of the electrons λ (at the accelerated voltage of ca. 60 keV) was calibrated by means of the CCl4 standard with well-known structural parameters.13,14 In each of the two experiments, the fluctuation of λ was measured to be less than 0.04%. The diffraction patterns were scanned on a calibrated commercial scanner (EPSON PERFECTION 4870 PHOTO). The obtained data were transformed into intensity curves I(s) using the UNEX program.15 The background was approximated by cubic splines. The experimental intensities I(s) were obtained in the ranges of s = 3.6–17.8 Å−1 (LD) and s = 8.0–32.4 Å−1 (SD) in steps of 0.2 Å−1 (see Table S1 and Fig. S1 of ESI). The fitting of the theoretical molecular intensities sM(s) to the experimental counterparts was carried out by means of the same program package.15

3. Computational details

The structure calculations were performed at the level of the second-order Møller–Plesset perturbation theory (MP2)16 with the correlation-consistent polarized valence triple-ζ (cc-pVTZ)17 and weighted core–valence n-tuple-ζ (cc-pwCVnZ (n = T, Q))18 basis sets taking into account the correlation of all electrons (denoted as ae) or in the frozen core (fc) approximation (in the following, “fc” is by default). The structure optimization was also carried out at the level of the Kohn–Sham density functional theory (DFT) with the Becke's three-parameter hybrid exchange functional19 and the Lee–Yang–Parr correlation functional20 (together denoted as B3LYP) with the cc-pVTZ basis set.

The barriers to the internal rotations, harmonic and anharmonic (cubic) force constants and harmonic vibrational frequencies were calculated at the B3LYP/cc-pVTZ or MP2/cc-pVTZ level.

For the lowest-energy conformers, the structure optimizations were carried out also by the very-time consuming coupled-cluster method with single and double excitation21 and a perturbative treatment of connected triples, CCSD(T)_ae22 in conjunction with the cc-pwCVTZ basis set.

The CCSD(T)_ae structure computations for the possible decomposition products of picolinic acid (pyridine and carbon dioxide) were performed with n-tuple-ζ core–valence basis sets (n = T, Q, 5).18 Diffuse functions23 were also included in some computations.

All CCSD(T) and B3LYP calculations were performed with the MOLPRO24,25 and GAUSSIAN0926 program packages, respectively. Both programs were applied for the MP2 calculations.

The topological analysis of the electronic density was performed with the AIM2000 code.27,28

4. Quantum-chemical predictions of structure and conformational behavior

The structure optimizations at the MP2 and B3LYP levels were carried out for four possible conformers of picolinic acid with the O[double bond, length as m-dash]C–C–N and O[double bond, length as m-dash]C–C–H fragments in ap or sp positions, denoted as ap–ap, ap–sp, sp–sp and sp–ap, respectively (see Fig. 1). The results are presented in Tables S2 and S3 (ESI). All conformers possess Cs point-group symmetry, except for the sp–ap conformer without symmetry (C1 point group). The calculations of the vibrational frequencies (MP2/cc-pVTZ) verified that the stationary points represent the true minima. The calculated harmonic vibrational frequencies are listed in Table S4 (ESI) in comparison with the experimental wavenumbers from the literature. The energy differences calculated at the different levels of theory are given in Table 1. As can be seen, the ap–ap conformer corresponds to the global minimum of the potential energy surface. The second low-energy conformer, ap–sp, is higher in energy by 15.7 kJ mol−1 as estimated at the CCSD(T)_ae/cc-pwCVTZ level. The energy differences of 16.4 and 15.1 kJ mol−1 from the MP2 and B3LYP calculations, respectively, being close to the CCSD(T) value seem to be also reliable. The sp–sp and sp–ap conformers are higher in energy relative to the main conformer by more than 20 and ca. 50 kJ mol−1, respectively.
image file: c8cp00310f-f1.tif
Fig. 1 Possible conformers of picolinic acid.
Table 1 Relative energies of the conformers of picolinic acid (in kJ mol−1)
Conformer B3LYP/cc-pVTZ B3LYP/6-31++G(d,p)a MP2/cc-pVTZb MP2/6-311G++(d,p)c CCSD(T)_ae/cc-pwCVTZ
a Ref. 8. b The values after slash include the zero-point energy (ZPE) corrections. c Ref. 4.
ap–ap 0.0 0.0 0.0/0.0 0.0 0.0
ap–sp 15.1 12.4 16.4/15.1 14.1 15.7
sp–sp 21.3 17.9 22.2/20.4 17.8
sp–ap 49.1 47.7 49.8/47.4


The barriers to internal rotations of the hydroxyl group around the C–O bond and the carboxylic groups around the C–C bond were estimated as the energies of the corresponding transition states, TSap–ap→ap–sp and TSap–sp→sp–sp, relative to the energies of the conformers ap–ap and ap–sp, respectively. These barriers were estimated to be 62.8 and 21.4 kJ mol−1 (B3LYP/cc-pVTZ) at the torsional coordinates τ(H–C–C[double bond, length as m-dash]O) and τ(O[double bond, length as m-dash]C–C–N) of −95° and −85°, respectively. The population ratio of the conformers at 375 K was estimated to be ap–ap[thin space (1/6-em)]:[thin space (1/6-em)]ap–sp[thin space (1/6-em)]:[thin space (1/6-em)]sp–sp[thin space (1/6-em)]:[thin space (1/6-em)]sp–ap ≈ 97.6[thin space (1/6-em)]:[thin space (1/6-em)]1.9[thin space (1/6-em)]:[thin space (1/6-em)]0.5[thin space (1/6-em)]:[thin space (1/6-em)]0.0 (in %) according to the Boltzmann distribution law with the MP2/cc-pVTZ energies. Thus, the lowest-energy conformer is predicted to be dominant under the experimental conditions, whereas the amount of the sp–sp conformer is negligibly small, and the sp–sp and sp–ap conformers are practically absent.

Finally, the structures of the two lowest-energy conformers ap–ap and ap–sp with Cs total symmetry were optimized at the CCSD(T)_ae level in conjunction with the cc-pwCVTZ basis set. Structural changes due to basis set enlargement (from triple- to quadruple-ζ quality), ΔrT→Q, were estimated at the MP2 level. Thus, the final structure was estimated as:

 
re(CCSD(T)_ae/cc-pwCVnZ(n = T→Q)) = re(CCSD(T)_ae/cc-pwCVTZ) + ΔrMP2/T→Q(1)

The results are given in Table 2.

Table 2 Structural parameters of the two lowest-energy conformers (ap–ap and ap–sp) of picolinic acid (bond lengths in Å, bond angles in degrees)
r see[thin space (1/6-em)]a,b GED r a GED r e CCSD(T)_aec r s MW r e CCSD(T)_aec
a Uncertainties of the last digits given in parentheses are estimated as 3σLS. b Parameters with equal superscripts were refined in one group; differences between parameters in each group were assumed at the values from CCSD(T)_ae computations. c Extrapolated to the cc-pwCVQZ basis set (see eqn (1)). d Ref. 4. e Assumed at the value from CCSD(T)_ae computations. f Dependent parameter. g Disagreement factor image file: c8cp00310f-t1.tif, where wi is a weight of the point i.
Parameters ap–ap ap–sp
C2–C3 1.391(3)1 1.398(3) 1.3895 1.3933
C3–C4 1.389(3)1 1.396(3) 1.3876 1.40(29) 1.3873
C4–C5 1.389(3)1 1.396(3) 1.3881 1.37(17) 1.3864
C5–C6 1.391(3)1 1.398(3) 1.3900 1.41(16) 1.3917
N1–C6 1.338(4)2 1.344(4) 1.3352 1.35(39) 1.3341
N1–C2 1.340(4)2 1.346(4) 1.3376 1.3364
C1–C2 1.504(4)3 1.513(4) 1.5047 1.4968
C1[double bond, length as m-dash]O2 1.204(3)4 1.208(3) 1.2010 1.23(14) 1.2068
C1–O1 1.337(4)2 1.345(4) 1.3344 1.3380
C3–H3 1.079e 1.0790 1.0788
C4–H4 1.081e 1.0806 1.0806
C5–H5 1.080e 1.0799 1.0803
C6–H6 1.081e 1.0812 1.0819
O1–H1 0.975(21)9 0.990(21) 0.9734 0.9655
N⋯H1 1.973(27)f 2.011(27) 1.973
C2C3C4 117.6(1)5 117.5 117.8
C3C4C5 119.2(1)5 119.1 119.32(47) 118.8
C4C5C6 119.2(1)5 119.1 118.88(22) 118.8
C1C2C3 120.8(5)6 120.3 117.7
C2C1[double bond, length as m-dash]O2 122.4(6)7 123.0 123.1
C2C1O1 113.6(6)8 113.7 113.6
C1O1H1 105.9e 105.9 105.4
C2C3H3 119.4e 119.4 119.5
C3C4H4 120.5e 120.5 120.5
C4C5H5 121.1e 121.1 121.1
C5C6H6 121.1e 121.1 120.7
O1H1⋯N 121.7(6)f 121.6
C3C2N1 123.6(6)f 124.1 124.2
C5C6N1 122.0(6)f 122.5 122.15(57) 123.3
C6N1C2 118.4(12)f 117.8 117.1
N1C2C1 115.7(9)f 115.6 118.2
O2[double bond, length as m-dash]C1O1 124.0(6)f 123.4 123.3
C4C3H3 123.0(1)f 123.1 122.7
C5C4H4 120.3(1)f 120.4 120.7
C6C5H5 119.8(1)f 119.9 120.0
N1C6H6 116.9(6)f 116.4 116.0
R f (%) 3.3


5. GED structural analysis

According to theoretical predictions, the two lowest-energy conformers can exist at the experimental temperature (see section above). Although the amount of the second conformer, ap–sp, was predicted to be very small (≈2%), both conformers were considered in the analysis of the GED data. The molecular model of each conformer with Cs point-group symmetry was described by a set of 25 geometrical parameters, including 14 equilibrium bond lengths (re) and 11 equilibrium bond angles (∠e) listed in Table 2.

Because the differences between all C–C bond lengths of the pyridine ring and between the C–O and C–N bond lengths are smaller than the experimental uncertainties, these bond lengths could not be determined separately. Therefore, the small differences between them were assumed at the ab initio values as shown in Table 2. Due to the weak electron scattering by light atoms the relative positions of the hydrogen atoms could not be determined accurately. Therefore, the bond lengths and the bond angles involving these atoms were fixed at the theoretical values. Differences between the corresponding parameters of the conformers were also constrained to the ab initio values. The quality of the fit was significantly improved due to assumptions at the CCSD(T) values instead of the MP2/cc-pVTZ restraints with decreasing the disagreement factor, Rf, by 0.5% (from 3.8 to 3.3%).

The total corrections to the experimental internuclear distances ra, Δr = (rare), were calculated at the level of the first-order perturbation theory taking into account nonlinear kinematic effects32,33 by means of the SHRINK program.32,34 The harmonic and anharmonic vibrational contributions were computed from the MP2/cc-pVTZ quadratic and cubic force constants, respectively. The centrifugal distortion effect due to the overall rotation35 and rotational–vibrational interaction36 were also taken into account. The Δr corrections to the bond lengths of the main conformer are presented in Table 4 together with root-mean-square (rms) vibrational amplitudes, uh1, calculated from quadratic force constants at the same level of theory, whereas the complete sets of corrections and amplitudes for both conformers are listed in Tables S5 and S6 (ESI), respectively.

Table 3 Structural parameters of pyridine and carbon dioxide computed at the CCSD(T)_ae level in comparison with experimental data (bond lengths in Å, bond angles in degrees)
Pyridine
Basis seta wCVT CVQ wCVQ aCVQ wCV5
Experiment MWb MWc MWc
Parameter r e r e r e r e r e r see r s r 0
a The basis sets cc-pwCVTZ, cc-pCVQZ, cc-pwCVQZ, aug-cc-pCVQZ and cc-pwCV5Z are denoted as wCVT, CVQ, wCVQ, aCVQ and wCV5, respectively. b Ref. 29. c Ref. 30. d High-resolution infrared spectroscopy, ref. 31.
N–C2 1.3382 1.3360 1.3358 1.3365 1.3353 1.3362(5) 1.340(2) 1.340(5)
C2–C3 1.3926 1.3911 1.3909 1.3915 1.3904 1.3902(4) 1.390(3) 1.397(6)
C3–C4 1.3905 1.3889 1.3886 1.3893 1.3882 1.3890(4) 1.394(2) 1.394(6)
C2–H 1.0832 1.0826 1.0826 1.0829 1.0824 1.0816(4)
C3–H 1.0809 1.0803 1.0802 1.0806 1.0800 1.0795(4)
C4–H 1.0816 1.0810 1.0810 1.0814 1.0808 1.0803(4)
CNC 116.71 116.94 116.94 117.00 117.0 116.90(4) 116.8(2) 117.1(5)
NC2C3 123.94 123.80 123.79 123.75 123.75 123.80(4) 123.8(3) 123.7(5)
C2C3C4 118.46 118.47 118.47 118.48 118.48 118.54(4) 118.6(3) 118.5(6)
C3C4C5 118.50 118.52 118.53 118.54 118.54 118.42(4) 118.3(2) 118.5(6)
NC2H 115.89 115.94 115.95 115.95 115.96 115.90(5)
C2C3H 120.18 120.19 120.19 120.18 120.18 120.11(6)
C3C4H 120.75 120.74 120.74 120.73 120.73 120.71(2)
C4C3H 121.35 121.34 121.34 121.34 121.34 121.34(5)

Carbon dioxide
Basisa CVQ aCVQ CV5 aCV5
Experiment IRd
Parameter r e r e r e r e r e
C[double bond, length as m-dash]O 1.1604 1.1609 1.1598 1.1600 1.1599792(22)


Table 4 Total corrections Δr = (rare) to the experimental bond lengths, ra, and calculated, uh1, and experimental, uexp, rms vibrational amplitudes (in Å) for the ap–ap conformer of picolinic acid
Term r a r area u h1 u exp
a Calculated with the MP2/cc-pVTZ cubic force constants. b Calculated from the MP2/cc-pVTZ quadratic force constants. c Assumed at the calculated value. d Amplitudes with this superscript were refined in one group. Differences between amplitudes in the group were fixed at the calculated values.
O1–H1 0.990 0.0145 0.071 0.071c
C3–H3 1.094 0.0152 0.075 0.075c
C5–H5 1.095 0.0152 0.075 0.075c
C4–H4 1.096 0.0153 0.075 0.075c
C6–H6 1.097 0.0156 0.075 0.075c
C1[double bond, length as m-dash]O2 1.208 0.0039 0.036 0.036c
C6–N1 1.344 0.0064 0.044 0.042(4)d
C1–O1 1.345 0.0085 0.045 0.043(4)d
C2–N1 1.346 0.0062 0.045 0.043(4)d
C3–C4 1.396 0.0069 0.045 0.043(4)d
C4–C5 1.396 0.0069 0.045 0.043(4)d
C2–C3 1.398 0.0073 0.045 0.043(4)d
C5–C6 1.398 0.0071 0.045 0.044(4)d
C1–C2 1.513 0.0090 0.050 0.048(4)d


Three different theoretical models, namely, two models of the single conformers ap–ap and ap–sp and the model of their mixture, were considered. The fit by the model of the single ap–ap conformer was essentially better (Rf = 3.3%) than that of the single ap–sp conformer (Rf = 6.6%). The model of the conformational mixture with an increased number of refined parameters did not improve the quality of the fit in comparison to the model of the single ap–ap conformer; the Rf factor considerably increased to 3.8%, i.e. by 0.5%, on account of only 5 mol% of the ap–sp conformer. Thus, under conditions of the GED experiment, picolinic acid exists as a single ap–ap conformer. The refined structures, re and ra, are given in Table 2.

The presence of decarboxylation products during the experiment was also investigated. The thermal-average structures of pyridine and carbon dioxide were estimated from the equilibrium structures optimized at the CCSD(T)_ae level with the cc-pCVQZ and aug-cc-pCV5Z basis sets (see Table 3) taking into account the anharmonic vibrational corrections calculated with the MP2/cc-pVTZ cubic force constants. It was found that the experimental intensities are very sensitive to the presence of carbon dioxide and less sensitive to pyridine: only 1 mol% of CO2 leads to a rigorous increase of the Rf factor (by 0.5%), whereas up to 5 mol% of pyridine enlarge it insignificantly (by only 0.1%). An increase of the Rf factors with an enlargement of the numbers of geometrical parameters in the models points unambiguously to the absence of both carbon dioxide and pyridine in the vapor at least outside the given uncertainties.

The experimental molecular intensity curves sM(s) and their theoretical counterparts for the final molecular model of the single ap–ap conformer as well as the difference curves ΔsM(s) (experiment – theory) are shown in Fig. 2, whereas the corresponding radial distribution curves f(r) and their difference Δf(r) are shown in Fig. 3.


image file: c8cp00310f-f2.tif
Fig. 2 Experimental (open circles) and theoretical (solid line) molecular intensity curves sM(s) of picolinic acid for the long (above) and short (below) nozzle-to-film distances and difference curves ΔsM(s) = sM(s)expsM(s)theor.

image file: c8cp00310f-f3.tif
Fig. 3 Experimental (open circles) with damping factor of exp(−0.002s2) and theoretical (solid line) radial distribution curves f(r) for picolinic acid with vertical bars of the terms. Difference curve Δf(r) = f(r)expf(r)theor.

6. Results and discussion

6.1. Accuracy of the experimental and computed structures of picolinic acid, pyridine and carbon dioxide

To estimate the accuracy of the structure computations at the CCSD(T)_ae level, the structures of the simpler molecules, i.e. pyridine and carbon dioxide, were optimized with several basis sets up to 5-ζ quality taking into account the core–valence correlation and diffuse function effects (see Table 3). As can be seen, the C[double bond, length as m-dash]O bond length in CO2 computed at the CCSD(T)_ae/aug-cc-pCV5Z level is in remarkable agreement with the experimental value determined by high-resolution infrared (IR) spectroscopy.31 Unfortunately, the computations at such a level are too expensive for middle-size molecules, for instance, for picolinic acid. However, such a high accuracy can be also achieved using a smaller basis set. For pyridine, the convergence of structural parameters with respect to basis set size is practically reached at the basis set of quadruple-ζ quality. Moreover, a small shortening of the bond lengths due to enlargement of the basis set from Q- to 5-ζ quality (ΔrQ→5 ≤ 0.0005 Å) and the elongation of the bonds on account of the diffuse functions (Δraug = r(aug-cc-pCVQZ) − r(cc-pCVQZ) ≤ 0.0005 Å) compensate each other. The cc-pwCVQZ basis set does not decrease the accuracy of computations in comparison with the cc-pCVQZ one but saves a lot of computing time. Therefore, its use is expedient for the study of large molecules. The excellent agreement between the structures of pyridine computed at the CCSD(T)_ae/cc-pwCVQZ level and derived from the MW rotational constants, rsee, in ref. 29 (see Table 3) confirms the high quality of this computation.

The structure of picolinic acid can be optimized at the CCSD(T)_ae/cc-pwCVTZ level at moderate cost. Structural changes due to the enlargement of the basis set ΔrT→Q were estimated at the MP2 level (see eqn (1)). The high accuracy of such an extrapolation was confirmed previously (see for instance ref. 37). For organic molecules, the accuracy of the CCSD(T)_ae/cc-pwCVQZ structure was estimated to be a few thousandths of Å units for the bond lengths and a few tenths of degree for the bond angles.11,37,38 The small error in the CCSD(T) structure is a result of the compensation of errors occurring due to approximate treatment of connected triples and the neglect of higher-order connected excitations.39–41Table 2 and Fig. 4 demonstrate the excellent agreement between the equilibrium structures computed at the CCSD(T)_ae level and determined from the GED data. This points to the high accuracy of both the computed and experimental equilibrium structures of picolinic acid. The thermal-average bond lengths ra deviate very much from the equilibrium re values (see Fig. 4) mainly due to vibrational effects including anharmonicity. Very large discrepancies between the re structure and the structure derived on account of only harmonic vibrational effects, rh1, indicate (see Fig. 4) that the anharmonicity effects are very large and cannot be ignored even if the Rf factor is non-sensitive to them (for both fits Rf = 3.3%).


image file: c8cp00310f-f4.tif
Fig. 4 Histogram of deviations of different structures relative to re(GED) for the ap–ap conformer of picolinic acid (in Å). The cc-pVTZ and cc-pwCVnZ basis sets are denoted as VTZ and wCVnZ, respectively.

As for pyridine (see Table 3), the substitution structure should be relatively close to the equilibrium one. Very large discrepancies between the re and rs structures of picolinic acid demonstrate again that the Kraitchman's method fails.41,42

6.2. Intramolecular hydrogen bond

There are several ways to confirm the existence of the hydrogen bond. According to the definitions by Jeffrey43 and Steiner,44 the hydrogen bond X–H⋯Y is possible if r(Y⋯H) < 3.0 Å and ∠(Y⋯H–X) is larger than 90°. This bond is classified as intermediate if 1.5 Å < r(Y⋯H) < 2.2 Å and 130°< ∠(Y⋯H–X) < 170°. For picolinic acid, the experimental values of re(N⋯H1) and ∠e(N⋯H–O) are found to be 1.973(27) Å and 121.7(6)°, respectively. Therefore, the hydrogen bond in this molecule can be defined as rather intermediate than weak.

The Bader's theory “Atoms in Molecules” (AIM) also predicts the occurrence of the N⋯H1 bond in the main conformer of picolinic acid. The bond path between the hydrogen and nitrogen atoms contains the (3,−1) bond critical point (BCP), as well as the ring critical point (RCP) existing in the five-member ring (see Fig. 5). Thus, the necessary criteria for the existence of the hydrogen bond45–47 are found to be satisfied. The parameters of BCP, namely, the electron density ρ(r) of 0.029 and 0.032 Å and the Laplacian of electron density ∇2ρ(r) of 0.104 and 0.109 (in a.u.) calculated from the B3LYP/cc-pVTZ and MP2/cc-pVTZ wave functions, respectively, are of the same order of magnitude as for well-defined hydrogen bonds.48


image file: c8cp00310f-f5.tif
Fig. 5 Molecular graph showing the path and BCP for the N⋯H bond as well as the RCPs of the rings in the ap–ap conformer of picolinic acid.

6.3. Inductive and mesomeric effects in picolinic acid by natural bond orbital (NBO) analysis

The high accuracy of the structure computations at the CCSD(T) level allows the observation of fine structural effects. The inductive effect due to the carboxylic substituent can be revealed by comparison of the structural parameters of pyridine and the ap–sp conformer of picolinic acid (see Tables 2 and 3 and Fig. 6), whereas the structural changes occurring due to the formation of a hydrogen bond can be seen by comparison of the two lowest-energy conformers of picolinic acid (see Table 2 and Fig. 6).
image file: c8cp00310f-f6.tif
Fig. 6 The CCSD(T)_ae structures of the lowest energy conformers (ap–ap and ap–sp) of picolinic acid and pyridine in comparison (see also Tables 2 and 3).

In the NBO model, the strength of the interaction of electron donor and electron acceptor NBOs is defined by the stabilization energy E(2). In the ap–sp conformer of picolinic acid, the sum of the energies of interactions between the donor NBOs of the pyridine fragment with non-bonding orbitals of the carboxylic group, Σ1E(2), exceeds that of the reverse processes, Σ2E(2), by 60.2 kJ mol−1 (B3LYP/cc-pVTZ, see Table S7, ESI). Thus, the carboxylic group possesses an electron withdrawing ability relative to the pyridine fragment. The NCipsoC3 angle in the ap–sp conformer of picolinic acid is larger than that in pyridine by 0.4°, i.e. the carboxylic group pushes the Cipso atom to the center of the ring. A similar structural effect was observed for other compounds with acceptor substituents, see for instance ref. 49.

The hydrogen bond in the ap–ap conformer of picolinic acid, defined by the interaction between the lone pair (LP) on the nitrogen atom and the nonbonding orbital σ* of the O1–H1 bond, LP(N) → σ*(O–H), leads to a relatively large lowering in energy by 22.6 kJ mol−1. A small additional increase of the electron density on the σ*(O–H) orbital and corresponding elongation of the O–H bond occurs due to the interaction π(C[double bond, length as m-dash]O) → σ*(O–H) (E(2) = 3.6 kJ mol−1). In total, the O–H bond length in the ap–ap conformer is larger than that in the ap–sp conformer by 0.007 Å. The delocalization of electron density from the bonding π(Cipso–C3) NBO to the non-bonding π*(C[double bond, length as m-dash]O) orbital is more favorable in energy in the ap–sp conformer (E(2) = 74.0 kJ mol−1) than in the ap–ap one (E(2) = 63.1 kJ mol−1). Therefore, the corresponding increase of the C[double bond, length as m-dash]O bond in the ap–sp conformer is larger than that in the main conformer. Thus, the C[double bond, length as m-dash]O bond in the ap–ap conformer is shorter than that in the ap–sp one by 0.006 Å.

The C1–C2 bond length in the ap–ap conformer increases by 0.008 Å mainly due to the relatively strong interaction LP(O1) → σ*(C1–C2) with E(2) = 29.2 kJ mol−1.

Notably that the relaxation of the bond lengths due to presence of a hydrogen bond leads to a decrease of the C1C2N angle by 2.6°.

7. Conclusions

For the first time, a reliable and accurate structure of picolinic acid in the gas phase has been determined by the experimental method. Only one of four conformers, predicted by quantum-chemical computations, with the O[double bond, length as m-dash]C–C–N and H–O–C[double bond, length as m-dash]O fragments in antiperiplanar (ap) positions, ap–ap, could be detected under the conditions of the GED experiment (T = 375(3) K). The determined re(N⋯H1) distance being relatively short (1.973(27) Å) indicates the formation of a hydrogen bond in this conformer.

It has been revealed that the anharmonic vibrational corrections to the experimental bond lengths, ra, are many times larger than the uncertainties of the structure determination. Therefore, they have to be taken into account in a reliable determination of the molecular structure even if the Rf factor appears to be non-sensitive to them. Moreover, it has been confirmed that the rh1 structure, accounting for only harmonic vibrational effects, deviates very much from the equilibrium structure (see also ref. 49). Therefore, the rh1 structures determined for a lot of molecules (see Landolt–Börnstein handbooks50,51) cannot be used to verify the accuracy of quantum-chemical computations. Furthermore, it has been confirmed that the Kraitchman's method can fail in the determination of accurate structure (see also ref. 41, 42 and 52).

The comprehensive analysis of the molecular structures of pyridine and carbon dioxide computed at the CCSD(T)_ae level of theory with basis sets up to 5-ζ quality has shown that the convergence limit is practically reached at the quadruple-ζ basis set. Furthermore, it has been revealed that the core–core and core–valence electron correlation effects are relatively large, whereas the diffuse function effects are negligibly small at the limit of the basis set size. The same conclusions have been found in the studies of other molecules consisting first-row elements, see for instance BF2OH53 and uracil.37

The remarkable agreement between the equilibrium structures of the ap–ap conformer derived from the GED data and computed at the CCSD(T) level points to the high accuracy of both the experiment and computations. The high accuracy of the computations allows the observation of the structural changes reflecting the inductive and mesomeric effects due to the carboxylic group with electron withdrawing ability relative to the pyridine fragment.

The ap–sp conformer is estimated to be higher in energy by 15.7 kJ mol−1 (CCSD(T)_ae/cc-pwCVTZ) than that of the main conformer. The two further conformers of picolinic acid, sp–sp and sp–ap, are noticeably higher in energy.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This study has been supported by the Dr Barbara Mez-Starck Foundation (Germany).

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Footnote

Electronic supplementary information (ESI) available: Table S1. Experimental total intensity curves I(s) for picolinic acid and background lines B(s). Fig. S1. Experimental total intensity curves I(s) (points) for picolinic acid with background lines G(s) for the long and short nozzle-to-film distances. Table S2. Optimized geometries of the two lowest-energy conformers of picolinic acid (bond lengths in Å, bond angles in degree). Table S3. Optimized geometries of the sp–sp and sp–ap conformers of picolinic acid (bond lengths in Å, bond angles in degrees). Table S4. Experimental and calculated vibrational frequencies (cm−1). Table S5. Total corrections Δ(rij,erij,a) to internuclear distances rij,a, theoretical uij,h1 and experimental uij,exp rms vibrational amplitudes (in Å) for the ap–ap conformer of picolinic acid. Table S6. Total corrections Δ(rij,erij,a) to internuclear distances rij,a, theoretical uij,h1 and experimental uij,exp rms vibrational amplitudes (in Å) for the ap–sp conformer of picolinic acid. Table S7. Energy of NBO interactions, E(2) in kJ mol−1 and natural charges on the atoms (B3LYP/cc-pVTZ). See DOI: 10.1039/c8cp00310f

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