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Cite This: J. Phys. Chem. A 2018, 122, 2542−2549

Quantum Chemical Calculations of Monomer−Dimer Equilibria of Aromatic C‑Nitroso Compounds Katarina Varga, Ivana Biljan, Vladislav Tomišić, Zlatko Mihalić,* and Hrvoj Vančik* Department of Chemistry, Faculty of Science, University of Zagreb, Horvatovac 102A, 10000 Zagreb, Croatia S Supporting Information *

ABSTRACT: Monomer−dimer equilibria of nitrosobenzene and 2nitrosopyridine in gas phase and solution were studied by range of quantum chemical methods in an attempt to find the level of theory suitable for modeling dimerization reactions of aromatic C-nitroso compounds in general. The best agreement with the experimental standard reaction Gibbs energies was obtained with a combination of double-hybrid density functionals B2PLYP-D3, PBE0DH, and DSDPBEB86, and basis sets of triple-ζ quality. Of all other tested functionals, global hybrid PBE0 behaved equally well, and proved to be more than adequate for at least preliminary work. Other tested methods either produced inferior results (MP2, MP4(SDQ), CCSD, G4(MP2), CBS-QBS, CBS-APNO), or were too demanding for practical use (CCSD(T)). Analysis of computationally obtained thermodynamic data reveal intricate details of these reactions. Both E- and Z-dimers have several different conformers, which all have different solvation energies. While in the gas phase the nitrosobenzene E-dimer is more stable that its Z-form, in chloroform, the Z-form is more stable. Gas-phase dimerization entropies are large and negative, so these reactions are strongly temperature dependent. In some cases, like with 2nitrosopyridines, entropy and enthalpy terms essentially cancel each other out, allowing structural and media effects to significantly influence dimerization equilibria.

1. INTRODUCTION Aromatic C-nitroso compounds have been investigated for more than century, and their behavior is still not fully understood.1,2 Many of them dimerize, resulting in formation of relatively weak (cca. 120 kJ/mol) azodioxide bond between two nitrogen atoms. As monomer−dimer equilibrium can be significantly influenced by structural and environmental factors, we look at these reactions as a convenient model for studying mechanisms of organic solid-state reactions in general.1 In solid state, C-nitroso compounds are usually present as dimers, and in the solution there is an equilibrium between monomers and dimers.1−13 In aromatic C-nitroso compounds at room temperature the equilibrium is usually shifted toward monomers, and Z- or E-dimers can be observed only at low temperatures.14−17 Different behavior has been observed for 2nitrosopyridines,18 where dimers can coexist with monomers even at room temperature. The principal goal of this paper is to determine which quantum mechanical level of theory is suitable for reliable modeling of gas- and solution-phase thermodynamics of dimerization reactions of 2-nitrosopyridine and nitrosobenzene, and thus presumably of aromatic C-nitroso compounds in general. Only a few papers dealing with thermodynamics of these reactions, either from experimental or computational point of view have been published so far.1,2 Orrell investigated dimerizations of nitrosobenzene3,10,11 and 2-nitrosopyridine18 derivatives in solution using NMR techniques, and Novak19 used compound G4(MP2) method to investigate computational gas-phase thermochemistry of number of C-nitroso © 2018 American Chemical Society

compounds. Our computational approach utilized in this paper is different. As a way to decide upon the optimal level of theory, we compared solution equilibrium dimerization constants computed at levels of theory ranging from DFT to composite quantum mechanical methods and coupled clusters, with the corresponding experimental data. The model compounds employed were nitrosobenzene and three 2-nitrosopyridines (1−3) (Scheme 1). Scheme 1. Monomer−Dimer Equilibrium of 2Nitrosopyridines

Although the equilibrium constants for 2-nitrosopyridine derivatives dimerizations in (CDCl2)2 have been previously determined18 we reevaluated them in more computationally friendly 1,2-dichloroethane, using UV−vis spectroscopy. Received: December 11, 2017 Revised: January 30, 2018 Published: January 30, 2018 2542

DOI: 10.1021/acs.jpca.7b12179 J. Phys. Chem. A 2018, 122, 2542−2549

Article

The Journal of Physical Chemistry A

2. EXPERIMENTAL AND THEORETICAL METHODS 2.1. Preparation of Compounds. 2.1.1. 2-Nitrosopyridines (1−3). 2-Nitrosopyridine (1) and 4-methyl-2-nitrosopyridine (2) were prepared by reactions of corresponding 2aminopyridines with dimethyl sulfide and N-chlorosuccinimide, followed by deprotonation of resulting sulfonium salts with sodium methoxide to the S,S-dimethylsulfilimines and finally by oxidation with m-chloroperbenzioc acid. This route was previously reported by Taylor et al.20 4-Chloro-2-nitrosopyridine (3) was prepared analogously to the method previously described.20 To a solution of 1.20 g (9.3 mmol) of 2-amino-4-chloropyridine and 577 mg (675 μL, 9.3 mmol) of dimethyl sulfide in 21 mL of methylene chloride (DCM), 1.29 g (9.3 mmol) of N-chlorosuccinimide in 25 mL of DCM was added dropwise over a period of 1 h while the temperature was maintained at −20 °C. The reaction mixture was stirred at −20 °C for 1 h and for an additional hour at room temperature. After that, a solution of sodium methoxide (234 mg, 10 mmol) in methanol (7.5 mL) was added, the mixture was stirred for 10 min, 20 mL of water was added and stirring continued for 4 h. The organic layer was separated, and the aqueous layer was extracted with two portions of DCM (10 mL). The combined organic extracts were washed with 15 mL of water, dried and evaporated to give a brown thick gum of S,S-dimethyl-N-(4-chloro-2-pyridyl)sulfilimine which solidified upon being chilled. To a solution of 2.68 g (9.4 mmol, < 77%) of m-chloroperbenzoic acid in 90 mL of dry DCM, cooled to 0 °C, a solution of 1.77 g (9.4 mmol) of unpurified S,S-dimethylN-(4-chloro-2-pyridyl)sulfilimine in 16 mL of DCM was added all at once. The mixture was stirred at 0−5 °C for 90 min. After that, 610 μL of dimethyl sulfide was added and stirring continued for an additional 30 min. 90 mL of a saturated aqueous solution of sodium carbonate was then added to the reaction mixture, the layers were separated, the green organic layer was washed with water and dried over Na2SO4. After evaporation of solvent, a light tan solid was obtained which was recrystallized from ethanol to yield 348 mg (26%) of 4-chloro2-nitrosopyridine (3) as a light yellow solid (mp 137−139 °C). δH (600 MHz; CDCl3; TMS): 8.79 (d, 1H, J = 5.1 Hz, monomer), 7.70 (d, 1H, J = 5.1 Hz, monomer), 7.19 (s, 1H, monomer), 7.98 (d, 2H, J = 4.9 Hz, dimer), 7.92 (s, 2H, dimer), 7.36 (d, 2H, J = 4.9 Hz, dimer). δC (150.90 MHz; CDCl3; TMS): 150.3, 147.5, 129.1, 126.2, 119.1, 110.1. HRMS (MALDI−TOF) m/z: [M + H]+ calcd for C5H4ClN2O, 143.0012; found, 143.0005. 2.2. Spectroscopic Methods. 2.2.1. UV−Vis Spectroscopy. UV−vis spectra of compounds 1, 2, and 3 at the temperature range 283−343 K were recorded by a Varian Cary 5 double-beam UV−vis-NIR spectrophotometer, equipped with a Varian Cary Temperature Controller water circulator, cell with a thermistor immersed in the water and connected to a multimeter McVoice M-82Pro in the wavelength range 200−800 nm. A matched pair of quartz cells of 1 cm optical path length was used for the measurements. The thermodynamic parameters K°, ΔrH°, ΔrS°, and ΔrG° for the monomer−dimer equilibrium of compounds 1, 2, and 3 in 1,2dichloroethane (DCE) solution were determined using visible spectrophotometric data with solvent correction. Both dimers and monomers of all three studied compounds absorb in the UV region, whereas only monomers absorb in the visible region near 780 nm. Therefore, the absorbance at 780 nm was used for determination of equilibrium concentrations of monomers in

the 283−343 K temperature range. The initial concentrations of the compounds 1, 2, and 3 were 1.00 × 10−2 mol dm−3. A plot of ln K° versus 1/T produced a good linear fit from which values of ΔrH°, ΔrS°, and ΔrG° (at 298.15 K) were calculated (Table 1). Table 1. Dimerization Equilibrium Constants (K°) for Compounds 1, 2, and 3 in DCE T/K

1 (R = H)

2 (R = CH3)

3 (R = Cl)

283 293 303 313 323 333 343

170. 66.7 27.7 12.2 5.65 2.74 1.39

211. 77.5 30.7 12.8 5.65 2.62 1.27

75.2 30.4 13.1 5.92 2.82 1.40 0.730

2.2.2. NMR Spectroscopy. The liquid-state one-dimensional H and 13C NMR spectra (600.13 MHz for 1H, 150.90 MHz for 13C) were measured in CDCl3 on a Bruker AV600 spectrometer at room temperature. Chemical shifts, in ppm, were referred to tetramethylsilane (TMS) as the internal standard. 2.3. Calculation Methods. Most of the calculations were performed with Gaussian 09, rev. D.01,21 and those with APFD, DSD-PBEP86, MN15, LC-ωPBEH, and PBE0DH functionals with Gaussian 16, rev. A.03.22 Geometries of all involved species were fully optimized, mostly using tight keyword, and confirmed as minima by absence of imaginary frequencies. DFT calculations were performed using ultrafine integration grid. Solvent effects were modeled by SMD continuum solvation method23 as implemented in Gaussian. Standard solvation Gibbs energies were calculated as potential energy differences between gas-phase and solution-phase optimized structures. Standard solution-phase reaction Gibbs energies in solvent S, ΔrG*(S), were calculated from standard gas-phase Gibbs reaction energies, ΔrG°(g), and differences between standard solvation Gibbs energies of dimer (D) and monomer(s) (M): 1

Δr G*(S) = [G°(D,g) − 2G°(M,g)] + [Δsolv G°(D,S) − 2Δsolv G°(M,S)] − ΔG°→*

The last term is the correction for the standard concentration change between the gas phase (1 atm) and the solution (1 mol/ L), which at 298.15 K equals to 7.926 kJ/mol. QTAIM analysis was performed by the AIMAll program.24 Dimerization energies were calculated at various DFT and post-HF levels of theory, including combinations of density functionals of diverse types (hybrid, double-hybrid, including empirical dispersion corrections, etc.), and post-HF methods (MP2, MP4, CCSD and CCSD(T)), with several Pople and Dunning basis sets of increasing complexity. Functionals tested were as follows: APFD, B2PLYP, B2PLYPD, B2PLYP-D3, B3LYP, B3LYP-D3, B97D, B97-D3, DSD-PBEP86, LCωHPBE, LC-ωPBE, LC-ωPBE-D3, M06-2X, M11, MN15, MPW2PLYP, MPW2PLYP-D3, PBE0, PBE0-D3, PB0DH, TPSSh, TPSSh-D3, and ωB97X-D. Three quantum-mechanical composite methods for calculations of thermodynamic quantities were used as well: G4(MP2), CBS-QB3, and CBSAPNO. The preliminary calculations have shown that for meaningful results basis set has to be at least of triple-ζ quality and include 2543


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The Journal of Physical Chemistry A Table 2. Thermodynamic Data (in kJ/mol and J/Kmol) for the Dimerization of Compounds 1, 2, and 3 in DCE

a

compound

ΔrH°

ΔrS°

−TΔrS°a

ΔrG°a

1 (R = H) 2 (R = CH3) 3 (R = Cl)

−57.1 ± 0.1 −58.5 ± 0.3 −58.3 ± 0.3

−158.8 ± 0.1 −162.5 ± 0.8 −170.1 ± 0.3

47.4 ± 0.0 48.5 ± 0.2 50.7 ± 0.1

−9.7 ± 0.1 −10.1 ± 0.4 −7.6 ± 0.3

At 298.15 K.

Figure 1. Conformers of 2-nitrosopyridine dimers.

−59 kJ/mol indicate that the formation of dimers is an exothermic process. As one would expect for the dimerization process, ΔrS° values are high and negative, falling in the range of −160 to −170 J/Kmol. Finally, ΔrG° values at 298.15 K are negative and in the range −8 to −10 kJ/mol, suggesting that at room temperature dimerization of all three dimers in DCE is thermodynamically favorable. From the data shown in Table 2, it is obvious that standard reaction Gibbs energies for these equilibria are the result of delicate balance between two larger values of opposite signs, enthalpy (ΔrH°) and entropy (−TΔrS°) component. The log K° values calculated from ΔrG° at 298 K correlate well (R2 = 0.9994) with the corresponding Hammett σm values (substituents in 2 and 3 are meta relative to nitroso group). A negative value of the Hammett ρ constant (−1.06 ± 0.02) indicates that electrondonating substituents enhance the dimerization. Comparison of the values of thermodynamic parameters determined earlier18 with the values obtained in the present work reveals small differences, the most significant one being about 5 kJ/mol more negative standard reaction Gibbs energies. They can probably be attributed to solvation effects, in accord with the previous observation that the extent of dissociation of 2-nitrosopyridine dimers is solvent dependent.18 3.2. Computational Studies of Dimerization Equilibria in the Solution. There are several issues that make computational studies of these equilibria not so straightforward. The question of optimal level of theory can be resolved by the comparison of calculated and experimental thermodynamic data. As all of the existing experimental equilibrium constants

both diffuse and extra polarization functions. Two basis set strategies were found to yield very similar gas-phase DFT energies. In the first, geometry optimization using 6-311+G(2df,2p) basis set is followed by the counterpoise energy correction, while in the second, geometry is optimized with may-cc-pVnZ (n = D and T) basis sets, followed by QZ singlepoint energy calculation at TZ geometry, and three-point CBS extrapolation of obtained energies. For the production calculations we adopted the first, simpler and faster, approach.

3. RESULTS AND DISCUSSION 3.1. Experimental Studies of Dimerization Equilibria. Dimerization equilibria of compounds 1, 2, and 3 in 1,2dichloroethane (DCE) were investigated by following the changes in the 780 nm region of the UV/vis spectra, assigned to the n ← π* transition in monomers. Absorption spectra of all three studied compounds show that the absorption peak near 780 nm grows as temperature increases from 283 to 343 K. Obtained standard dimerization equilibrium constants K° for compounds 1, 2, and 3 at different temperatures are listed in Table 1. Values of K° for all three compounds follow similar trend, decreasing with temperature. While compounds 1 and 2 have similar constants, values for 3 are somewhat lower, suggesting more pronounced dissociation to monomers. Thermodynamic parameters ΔrH°, ΔrS°, and ΔrG° for the dimerization of compounds 1, 2, and 3 calculated from the temperature dependence of the equilibrium constants K° are shown in Table 2. Negative ΔrH° values in the range −57 to 2544


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(ρBCP = 0.014) and its Laplacian (∇2ρBCP = 0.055) in bond critical point(s) (BCP) calculated at ωB97X-D/6-311+G(d,p) level of theory suggest closed-shell bonding interaction of the order of magnitude of weak hydrogen bond. Conversely, in nitrosobenzene dimer (Figure 2a), similar interactions stabilize E-conformer (ρBCP = 0.018, ∇2ρBCP = 0.072). It is interesting to note that 2-nitrosopyridine dimer ring substitution (in compounds 2 and 3) does not influence the transannular bonding interactions, i.e. corresponding ρBCP and ∇2ρBCP values are almost the same in all three compounds. However, the substitution noticeably changes the topological parameters of C−N, N−O, and NN bonds of azodioxide bridge, qualitatively in accord with the observed ρσm Hammett correlation (vide supra). In an attempt to find the level of theory adequate for the analysis of dimerization reactions of aromatic C-nitroso compounds, corresponding gas- and solution-phase standard reaction Gibbs energies were calculated using various levels of theory, and compared with the existing experimental data (Tables 4 and 5). (The corresponding absolute values are given in the Supporting Information, Tables S1−S4.) Among DFT results, only functionals that gave Gibbs energies with mean absolute deviation (MAD) within cca. 12 kJ/mol from three experimental values are shown here. Among all tested methods, the best agreement with the experimental data was obtained with DFT approach in combination with Pople’s 6-311+G(2df,2p) basis set. More than 20 functionals were tested (Supporting Information, Table S5), and the best results were obtained with hybrid functional PBE025 and three double-hybrid functionals B2PLYP-D3,26 PBE0DH, 27 and DSD-PBEB86. 28 Their mean absolute deviations (MAD) from the experimental standard reaction Gibbs energies were 1.9, 2.0, 1.9, and 3.8 kJ/mol, and maximum absolute deviations 4.0, 4.8, 3.2, and 6.8 kJ/mol, respectively. Small deviation from experimental values (MAD 3.4) was also obtained with B97D, but analysis of intermediate results demonstrated that the agreement was coincidental, i.e. result of error cancellations. Among other tested functionals, even for qualitative agreement with the experimental data, it was mandatory that they include some kind of dispersion correction. In some cases, inclusion of D3 correction29 (B3LYP-D3, TPSSh-D3) improved the reaction energy for as much as 30 kJ/mol. Even double-hybrid B2PLYP without D3 correction has MAD 16 kJ/mol, too high to be included in Tables 4 and 5. The exception to this rule is PBE0, which produces better results than both of its dispersion-corrected forms. Performance of PBE0, likely candidate for the most economical functional, was further tested on larger set of 15 dimerization Gibbs energies. Along with three values from Tables 4 and 5, the set also contained two values for 2nitrosopyridine derivatives in DCE (2 and 3, Table 1), and 10 additional values for the substituted nitrosobenzenes in chloroform from ref 3. The MAD value for the differences between calculated and experimental standard reaction Gibbs energies remained low (1.8 kJ/mol), and average deviation was −1.2 ± 2.2 kJ/mol. In view of performance of double-hybrid functionals, the catastrophic results of MP2 method come as a surprise. Although inclusion of third and fourth order corrections improves things, CBS extrapolated MP4(SDQ)/may-cc-pVnZ (n = 2−4) energies are still 30−40 kJ/mol higher than the experimental values. CCSD results are equally bad, and only the

come from the solution-phase experiments, the calculations must include the solvation effects. As used solvents are not very polar, discrete solvation effects are probably not very important, and continuum solvation approach should be adequate. Another possible complication is that aromatic C-nitroso dimers have several conformational degrees of freedom, and therefore can exist in more than just one Z- and one E-form, making the dimerization equilibria studies potentially complex. Potential energy surfaces of parent nitrosobenzene and 2nitrosopyridine dimers in vacuum and in chloroform were systematically searched for minima at DFT level of theory using combinations of different functionals and basis sets of triple-ζ quality. It was found that while nitrosobenzene dimer has one Z- and two E-conformers, 2-nitrosopyridine dimer, depending on the media and used density functional, can end with up to three conformers of both Z- and E-forms (Figure 1). In vacuum, two nitrosobenzene E-dimer conformers (of Ci and C2 symmetry, similar to anti-E-I and anti-E-II in Figure 1), with similar standard Gibbs energies, are cca. 10 kJ/mol more stable than Z-dimer of C2 symmetry. In chloroform, however, due to 15 kJ/mol more favorable standard solvation Gibbs energy, Z-form is 2−5 kJ/mol more stable than the closer (C2) E-conformer. At some DFT levels of theory, Ci structure is actually a transition structure separating two C2 E-conformers. The most stable form of 2-nitrosopyridine dimer, both in gas phase and in chloroform, is anti-Z-I (C2) conformer (Table 3). Table 3. Relative Potential and Standard Gibbs Energies at 298 K (in kJ/mol) and Dipole Moments (in D) of 2Nitrosopyridine Dimer Conformers at the PBE0/6311+G(2df,2p) Level of Theory in Gas Phase and Chloroform (S) conformation

Erel(g)

G°rel(g)

Erel(S)

G°rel(S)

μ(g)

μ(S)

anti-Z-I (C2) anti-Z-II (C2) syn-Z anti-E-I (Ci) anti-E-II syn-E (C2)

0.0 a 16.7 18.9b 18.1 19.2

0.0 a 13.2 15.3b 10.3 14.8

0.0 13.8 10.7 18.2b 17.1 18.5

0.0 9.8 8.7 16.2b 9.1 12.3

7.6 a 8.7

10.1 12.5 11.8

1.4 1.9

2.0 3.0

a

Not a stationary point on this PES. bTransition structure (NImag = 1) on this PES.

In the gas phase at the B2PLYP-D3/6-311+G(2df,2p) level of theory, its pyridine nitrogens are separated by 2.96 Å, exactly like in the crystal structure.18 All other dimer forms are at least 9 kJ/mol less stable. Some functionals predict anti-Z-II (C2) to be a minimum on potential energy surface, others do not. Of Econformers, the most stable is anti-E-II (C1), in which the angle between pyridine rings is 40−50°. Although some functionals predict anti-E-I (Ci) to be minimum on PES, for most it is transition structure between two mirror-image anti-E-II conformers. Corresponding barriers (Δ≠G°) are 5 kJ/mol in vacuum and 7 kJ/mol in chloroform. Finally, if one wants to study Z−E equilibrium of 2-nitrosopyridines, it is sufficient to consider only anti-Z-I and anti-E-II conformers. For the monomer−dimer equilibrium study, anti-Z-I is sufficient. The origins of different conformational preferences of nitrosobenzene and 2-nitrosopyridine dimers can be analyzed by the QTAIM approach. The Z-form of 2-nitrosopyridine dimer is stabilized relative to its E-form by two transannular bonding interactions between pyridine nitrogen and the closest carbon of the other ring (Figure 2b). Values of electron density 2545


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Figure 2. Transannular interactions in Z- and E-forms of (a) nitrosobenzene and (b) 2-nitrosopyridine dimers revealed by QTAIM analysis of ωB97X-D/6-311+G(2df,2p) electron densities.

Table 4. Nitrosobenzene Dimerization Energies (in kJ/mol) Calculated at Various Levels of Theory in Gas Phase (g) and Chloroform (S) at 298.15 Ka Z-

E

level of theory

ΔE(g)

ΔrH°(g)

ΔrG°(g)

ΔrG*(S)

ΔE(g)

ΔrH°(g)

ΔrG°(g)

ΔrG*(S)

B2PLYP-D3/6-311+G(2df,2p) B3LYP-D3/6-311+G(2df,2p) B97D/6-311+G(2df,2p) DSD-PBEP86/6-311+G(2df,2p) LC-ωPBE-D3/6-311+G(2df,2p) M11/6-311+G(2df,2p) PBE0/6-311+G(2df,2p) PBE0DH/6-311+G(2df,2p) TPSSh-D3/6-311+G(2df,2p) ωB97X-D/6-311+G(2df,2p) MP2/6-311+G(2df,2p) MP4(SDQ)/may-cc-pVnZb CCSD/6-311+G(2df,2p)c CCSD(T)/6-311+G(2df,2p)c G4(MP2) CBS-QB3 CBS-APNO experiment (in CHCl33)

−38.1 −27.2 −45.2 −41.8 −41.3 −21.0 −38.3 −37.8 −47.5 −32.6 −103.1 −2.3 5.2 −30.0 −31.8 −44.0 −51.0 −37.2g

−26.8 −15.9 −34.2 −30.0 −29.0 −9.3 −26.5 −25.9 −36.2 −20.6

30.3 41.6 23.0 25.6 29.8 50.0 31.4 32.3 19.6 37.3

9.1 20.5 7.2 3.0 1.5 22.5 9.7 8.7 0.8 11.6

−31.7 −26.2 −34.0 −33.1 −35.3 −24.2 −40.3 −38.9 −43.1 −24.7

25.0 31.5 23.3 24.0 23.6 35.0 17.5 19.2 13.8 32.8

17.4 24.7 17.7 14.3 9.9 24.4 11.0 11.3 9.4 21.4

−18.5d −21.5 −34.0 −41.3 −25.7g

39.5e 35.8 23.4 17.8 32.2g

17.1f 13.4f 1.0f −4.7f 9.8

−43.0 −37.4 −45.1 −44.9 −47.3 −36.1 −52.1 −50.9 −54.4 −36.5 −94.3 −11.1 −6.4 −37.8 −36.6 −52.7 −55.2 −48.8g

−26.7d −25.6 −42.4 −45.6 −37.3g

31.8e 32.2 14.9 13.5 20.8g

23.6f 24.1f 6.8f 5.4f 12.6

a

All DFT energies are CP-corrected. Bold values are within 5−6 kJ/mol from the experiment. bThree-point CBS extrapolation (n = 2−4) of sp energies calculated at MP4(SDQ)/6-311+G(d,p) geometries. cSingle-point energy at B2PLYP/6-311+G(d,p) geometry. dCalculated from ΔE(g) and DFT/G4(MP2)/CBS-X average ΔrH°(g) − ΔE(g) value (11.5 ± 0.6 kJ/mol). eCalculated from ΔE(g) and DFT/G4(MP2)/CBS-X average ΔrG°(g) − ΔE(g) value (69.5 ± 1.2 kJ/mol). fCalculated from ΔrG°(g) and average ΔΔsolvG*(S) values (Z, −22.4 ± 3.4 kJ/mol; E, −8.2 ± 2.6 kJ/ mol). gCalculated from the experimental ΔrG*(S) values.

compounds dimerizations.19 However, as can be seen from Tables 4 and 5, neither in gas phase nor in the solution, none of these methods actually produce consistent and satisfactory results. Their MADs are 7.1, 6.4, and 9.6 kJ/mol. This can be, at least partly, attributed to the unfortunate circumstance that all three of them include calculations based on methods that behave particularly badly with aromatic C-nitroso compounds: MP2 in G4(MP2) and CBS-APNO, and B3LYP in G4(MP2) and CBS-QB3. As a reminder, B3LYP/6-311+G(2df,2p) results were not good enough to be included in Tables 4 and 5, and MP2 and MP4(SDQ) results were included just for the illustration of their awful performance. It seems that DFT calculations based on (dispersion-corrected) double-hybrid

inclusion of perturbative triple substitutions move coupled cluster energies closer to the experimental values (Tables 4 and 5). Although of all tested post-HF methods, CCSD(T) results are closest to the experimental values, method’s slow convergence toward CBS limit prohibits its practical use in studying these reactions. Different approach altogether is to use quantum-mechanical composite methods, which are designed for computation of high-quality thermodynamic values. We tested economical variant of G4 method, G4(MP2),30 and two CBS methods, faster CBS-QB331 and more demanding CBS-APNO.32 G4(MP2) was recently selected as optimal method for the computational thermochemistry study of gas-phase C-nitroso 2546


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Table 5. 2-Nitrosopyridine Z-Dimerization Energies (in kJ/mol) Calculated at Various Levels of Theory in the Gas Phase (g) and DCE (S) at 298.15 Ka level of theory

ΔE(g)

ΔrH°(g)

ΔrG°(g)

ΔrG*(S)

B2PLYP-D3/6-311+G(2df,2p) B3LYP-D3/6-311+G(2df,2p) B97D/6-311+G(2df,2p) DSD-PBEP86/6-311+G(2df,2p) LC-ωPBE-D3/6-311+G(2df,2p) M11/6-311+G(2df,2p) PBE0/6-311+G(2df,2p) PBE0DH/6-311+G(2df,2p) TPSSh-D3/6-311+G(2df,2p) ωB97X-D/6-311+G(2df,2p) MP2/6-311+G(2df,2p) MP4(SDQ)/may-cc-pVnZb CCSD/6-311+G(2df,2p)c CCSD(T)/6-311+G(2df,2p)c G4(MP2) CBS-QB3 CBS-APNO experiment (in DCE, this work)

−75.8 −66.0 −83.0 −77.2 −72.8 −56.0 −79.0 −76.5 −86.5 −66.3 −135.3 −36.9 −25.0 −61.6 −63.7 −75.2 −80.5 −73.8g

−64.0 −54.3 −71.2 −64.9 −60.3 −43.9 −66.8 −64.2 −74.7 −53.8

−4.0 5.6 −11.4 −4.7 1.5 16.0 −6.4 −3.3 −14.8 7.1

−10.2 −0.3 −12.4 −12.7 −12.6 1.6 −13.7 −12.9 −19.3 −4.0

−50.1d −52.6 −64.0 −70.4 −62.3g

10.6e 4.6 −6.3 −8.7 −1.6g

2.5f −3.5f −14.4f −16.8f −9.7

a All DFT energies are CP corrected. Bold values are within 5-6 kJ/mol from the experiment. bThree-point CBS extrapolation (n = 2−4) of sp energies calculated at MP4(SDQ)/6-311+G(d,p) geometries. cSingle-point energy at B2PLYP/6-311+G(d,p) geometry. dCalculated from ΔE(Z,g) and DFT/G4(MP2)/CBS-X average ΔrH°(Z,g) − ΔE(Z,g) value (11.5 ± 0.6 kJ/mol). eCalculated from ΔE(Z,g) and DFT/G4(MP2)/CBS-X average ΔrG°(Z,g) − ΔE(Z,g) value (72.2 ± 1.2 kJ/mol) fCalculated from ΔrG°(Z,g) and average ΔΔsolvG*(Z,S) value (−8.1 ± 3.1 kJ/mol). g Calculated from the experimental ΔrG*(Z,DCE) value.

in DCE are practically the same, so Z-dimer is more stable both in gas phase and in DCE solution.

density functionals and moderately large basis sets are much better choice. To fully understand these reactions, it is useful to compare their gas and solution phase thermodynamics (Figure 3). The Figure 3 is based on the average computational values obtained at the levels of theory that closely reproduce the experimental data. Although both standard reaction enthalpies for gas-phase Zdimerizations of nitrosobenzene and 2-nitrosopyridine are negative, 40 kJ/mol lower 2-nitrosopyridine value indicates formation of more tightly bound dimer. It is probably the result of somewhat stronger azodioxide bond and transannular interactions depicted in Figure 2. 4-Methyl substitution slightly decreases, and 4-chloro substitution increases, standard reaction enthalpy, which is in accord with previously mentioned Hammett correlation. However, this comes with a price. Formation of tighter dimer makes the corresponding standard reaction entropy more negative, and entropy term -TΔrS°(g) for 2-nitrosopyridine Zdimerization almost cancels out the reaction enthalpy (Figure 3). While calculated gas-phase standard reaction entropies for the formation of nitrosobenzene Z- and E-dimers are identical (−194 ± 3 and −193 ± 5 J/Kmol), gas-phase entropies for 2nitrosopyridine Z- and E-dimerization are −201 ± 4 and −174 ± 4 J/Kmol, amounting to 8 kJ/mol difference between their entropy terms. Standard reaction Gibbs energy for such a dimerization is small, and very temperature dependent. Another complications are the solvation effects, which are in this paper modeled by the SMD continuum approach. Standard solvation Gibbs energies of nitrosobenzene Z- and E-dimers in chloroform differ by 14 ± 4 kJ/mol in favor of Z-dimer, which reverses their relative order on transfer from the gas phase to the solution (Figure 3). Oppositely, calculated standard solvation Gibbs energies of 2-nitrosopyridine Z- and E-dimers

4. CONCLUSIONS Results presented in this paper suggest that reliable approach toward modeling monomer−dimer equilibria of aromatic Cnitroso compounds might be a combination of double-hybrid density functional with basis sets of triple-ζ quality containing diffusion and extra polarization functions. All three doublehybrid functionals tested in this paper, B2PLYP-D3, PBE0DH, and DSD-PBEB86, produced standard reaction Gibbs energies close to the experimental values for two parent compounds. First two somewhat closer, with MAD values of 2.0 and 1.9 kJ/ mol, compared to 3.6 for DSD-PBEB86. Global hybrid PBE0 also performed well, and due to its speed relative to doublehybrid functionals, it is obvious choice for at least preliminary work. All other tested post-HF methods are either incapable of producing results close the experimental ones (MP2, MP4(SDQ), CCSD, G4(MP2), CBS-QBS, and CBS-APNO), or too demanding for practical use (CCSD(T)). It is important to note that the differences between standard reaction Gibbs energies and reaction (potential) energies for particular conformer are relatively constant, showing only limited dependence on calculation method. As the same holds for differences in standard solvation Gibbs energies, failure to reproduce experimental values, either in gas phase or in solution, is almost sole consequence of method’s incapability to produce reliable reaction potential energies. Prior to calculation of thermodynamic parameters, proper conformational analysis should be performed. As dimers contain two rotatable single bonds, both Z- and E-forms can have more than one conformer, especially in the case of heteroaromatic C-nitroso compounds. Conformational equilibrium can be complex and strongly media dependent. 2547



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AUTHOR INFORMATION

Corresponding Authors

*(Z.M.) E-mail: [email protected]. Telephone: (+) 385-14606403. Fax: (+) 385-1-4606401. *(H.V.) E-mail: [email protected]. ORCID

Ivana Biljan: 0000-0002-0650-1063 Vladislav Tomišić: 0000-0002-1191-2123 Zlatko Mihalić: 0000-0002-5313-1528 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support to this work from the Croatian Science Foundation, Grant No. 7444, Project ORGMOL.

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(1) Vančik, H. Aromatic C-Nitroso Compounds; Springer Verlag: New York, 2013. (2) Beaudoin, D.; Wuest, J. D. Dimerization of Aromatic C-Nitroso Compounds. Chem. Rev. 2016, 116, 258−286. (3) Fletcher, D. A.; Gowenlock, B. G.; Orrell, K. G. Structural investigations of C-nitrosobenzenes. Part 2. NMR studies of monomer−dimer equilibria including restricted nitroso group rotation in monomer. J. Chem. Soc., Perkin Trans. 2 1998, 797−804. (4) Fletcher, D. A.; Gowenlock, B. G.; Orrell, K. G.; Šik, V. Dynamic NMR study of the factors governing nitroso group rotation in pnitrosoanilines in the solution and solid states. Magn. Reson. Chem. 1995, 33, 561−569. (5) Fletcher, D. A.; Gowenlock, B. G.; Orrell, K. G.; Šik, V.; Hibbs, D. E.; Hursthouse, M. B.; Malik, A. K. M. 4-Iodonitrosobenzene. Structural and spectroscopic studies of the monomeric solid and of previously unreported dimers. J. Chem. Soc., Perkin Trans. 2 1996, 191−197. (6) Gowenlock, B. G.; Lüttke, W. Structure and properties of Cnitroso-compounds. Q. Rev., Chem. Soc. 1958, 12, 321−340. (7) Gowenlock, B. G.; Richter-Addo, G. B. Dinitroso and polynitroso compounds. Chem. Soc. Rev. 2005, 34, 797−809. (8) Greene, F. D.; Gilbert, K. E. Cyclic azo dioxides. Preparation, properties, and consideration of azo dioxide- nitrosoalkane equilibria. J. Org. Chem. 1975, 40, 1409−1415. (9) Greer, M. L.; Sarker, H.; Mendicino, M. E.; Blackstock, S. C. Azodioxide Radical Cations. J. Am. Chem. Soc. 1995, 117, 10460− 10467. (10) Orrell, K. G.; Šik, V.; Stephenson, D. Study of the monomerdimer equilibrium of nitrosobenzene using multinuclear one- and twodimensional NMR techniques. Magn. Reson. Chem. 1987, 25, 1007− 1011. (11) Orrell, K. G.; Stephenson, D.; Rault, T. NMR study of the monomerdimer equilibria of dimethylnitrosobenzenes in solution. Identification of mixed azodioxy dimeric species. Magn. Reson. Chem. 1989, 27, 368−376. (12) Snyder, J. P.; Heyman, M. H.; Suciu, E. Cis azoxy alkanes. VI. Cis azo N,N’-dioxide synthesis and the importance of entropy in the nitrosoalkane-azo dioxide equilibrium. J. Org. Chem. 1975, 40, 1395− 1405. (13) Wajer, T. A. J.; De Boer, T. J. C-nitroso compounds. Part XXIII†: Cis/trans-isomerisation of aliphatic azodioxy compounds (dimeric nitrosoalkanes). Recueil 1972, 91, 565−577. (14) Azoulay, M.; Fischer, E. Low-temperature proton magnetic resonance and ultraviolet absorption spectra and photochemistry of the system nitrosobenzene−azodioxybenzene and its methyl derivatives. J. Chem. Soc., Perkin Trans. 2 1982, 637−642.

Figure 3. Comparison of calculated thermodynamic parameters (in kJ/mol) for dimerization of nitrosobenzene and 2-nitrosopyridine in gas phase and in solution (CHCl3 and DCE).

Analysis of computationally obtained thermodynamic data reveal intricate details of these reactions, both in gas phase and in solution. While dimerization enthalpy is negative, entropy term is large and positive, and in some cases different for the formation of Z- or E- stereoisomer. When these two terms become similar, structural and media effects, as well as temperature changes, strongly influence the equilibrium position.

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REFERENCES

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b12179. Gas-phase and chloroform energies of Z- and (C2) Enitrosobenzene dimers (Table S1) and nitrosobenzene (Table S2), gas-phase and DCE energies of Z-2nitrosopyridine dimers (Table S3) and anti-2-nitrosopyridine (Table S4), and gas-phase reaction energies calculated with various density functionals and corresponding mean absolute deviations from the experimental values (Table S5) (PDF) 2548


Article

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