Article pubs.acs.org/JPCA
Cite This: J. Phys. Chem. A XXXX, XXX, XXX-XXX
Porphinogen Formation from the Co-Oligomerization of Formaldehyde and Pyrrole: Free Energy Pathways Jeremy Kua* and Helen Loli Department of Chemistry and Biochemistry, University of San Diego, 5998 Alcala Park, San Diego, California 92110, United States S Supporting Information *
ABSTRACT: We have investigated the nonoxidative stepwise co-oligomerization of formaldehyde and pyrrole to form porphinogen using density functional theory calculations that include free energy corrections. While the addition of formaldehyde to the pyrrole nitrogen is kinetically favored, thermodynamics suggest that this reaction is reversible in aqueous solution. The more thermodynamically favorable addition of formaldehyde to the ortho-carbon of pyrrole begins a stepwise process, forming dipyrromethane via an azafulvene intermediate. Subsequent additions of formaldehyde and pyrrole lead to bilanes (linear tetrapyrroles), which favorably cyclize to form porphinogen. Porphinogen is a precursor to porphin, the simplest unsubstituted porphyrin that could have played a role in primitive metabolism at the origin of life.
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INTRODUCTION Porphyrins are key molecules in extant life, primarily found as a constituent of metalloproteins. Hemoglobin and myoglobin are perhaps the two most familiar examples because of their role in oxygen transport in our bodies. Porphyrins are also key constituents in chlorophyll (for energy capture in photosynthesis) and a variety of cytochromes involved in electron transfer reactions. The biosynthesis of porphyrins in extant life proceeds through a reaction cascade involving a series of enzymes. However, we are interested in studying the potential prebiotic formation of simple porphyrins at the origin of life because they may have constituted a primitive energy transduction system by harnessing light and driving the evolution of early metabolism.1 An early synthesis of porphyrin under “simulated geochemical conditions” starting from paraformaldehyde and distilled pyrrole was reported by Hodgson and Baker.2 The reactants along with metal salts were added to evacuated sealed tubes and heated to 84 °C, although it is unlikely that neat solutions of the reactants are plausible under prebiotic conditions. More recently, Fox and Stradeit speculated that prebiotic synthesis of porphyrins could occur on volcanic islands.3 Starting with amino acids prepared in sea salt crusts, they heated samples to 350 °C under a slow stream of nitrogen gas and formed mixtures of pyrroles. Subsequent addition of mM concentrations of formaldehyde and nitrite/nitrate oxidants to pyrroles in acidic solution (pH 2) led to a complex mixture containing both linear and cyclic oligopyrroles identified by mass spectrometry. To simulate milder conditions (neutral pH) and plausibly lower concentrations (μM) of reactants, Lindsey and co-workers added micelles/vesicles to neutral solutions of formaldehyde and an alkylpyrrole, thereby synthesizing porphyrins in up to 40% yield.4 The simplest porphyrin that can be formed from the cooligomerization of formaldehyde and unsubstituted pyrrole is porphin, C20H14N4 (Figure 1, left). The first synthesis of © XXXX American Chemical Society
Figure 1. Porphin and porphinogen.
porphin from these starting materials was reported by Rothemund in 1935.5 A year later, several different starting aldehydes were used to form substituted porphins.6 Methanol was used as the solvent, and the reactions were carried out anaerobically in sealed tubes heated in a water bath at 90−95 °C for 30 hours. The porphin yield was approximately 0.02%. Yields were subsequently increased, up to 40%, with the addition of various acids, oxidizing agents, Grignard reagents, and varying the reaction conditions; a more comprehensive history over the next 40 years can be found in The Porphyrins.7 Badger et al. postulated that porphinogen, C20H20N4 (Figure 1, right) was an intermediate in the Rothemund reaction.8 A detailed study of the reaction of 3,4-dimethylpyrrole and benzaldehyde to form the corresponding porphyrin (Figure 2) was carried out by Dolphin,9 who was able to identify and isolate the porphyrinogen intermediate under mild reaction conditions (50 °C). Subsequent oxidation with six equivalents of iodine quantitatively converted the porphyrinogen into the porphyrin. Similar results were obtained with the unsubstituted pyrrole under refluxing conditions. It was proposed8 that the first steps of the co-oligomerization reaction were (a) nucleophilic addition of the pyrrole and benzaldehyde to form a carbinol, (b) dehydration to a fulvene, (c) oxidation to a Received: August 31, 2017 Revised: September 29, 2017 Published: September 29, 2017 A
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
Figure 2. Synthesis of a substituted porphyrin via its porphyrinogen
Figure 3. Coupling of benzaldehyde and two pyrroles to form a dipyrrylmethane.
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COMPUTATIONAL METHODS The protocol discussed below is similar to our previous work as discussed in the Introduction, and therefore much of the text in this section is reproduced from earlier work for clarity and reading ease.11−17 All calculations were carried out using Jaguar 9.518 at the B3LYP19−22 flavor of density functional theory (DFT) with a 6-311G** basis set. To maximize the probability of finding global minima, we calculated multiple conformers of each structure both with and without different internal hydrogen bond networks. For stable molecular species (with no negative eigenvalues), conformers were generated with MacroModel 11.5 using the Merck Molecular Force Field.23,24 Only structures within 5 kcal/mol of the lowest energy conformer were included in a restricted torsional sampling search. Transition states were built individually both in extended forms and more compact structures with internal hydrogen bonds. While we made good faith efforts to use a wide range of starting structures, it is possible to fail in locating the lowest energy transition state. The Poisson−Boltzmann (PB) continuum approximation25,26 was used to describe the effect of water as a solvent by applying a dielectric constant of 80.4 and a probe radius of 1.40 Å. The forces on the quantum mechanical solute atoms due to the solvent can be calculated in the presence of the solvent. However, as in previous work, the solvation energy was calculated at the optimized gas-phase geometry because in most cases there is practically no change between the gas-phase and implicit solvent-optimized geometries. The electronic energy of the optimized gas-phase structures and the solvation energy are designated Eelec and Esolv, respectively, in Table 1. (In one structure, we reverted to using the PB solver in the older Jaguar v6.0 because of a spuriously low solvation energy.) It is important to note that even though the solvation energy contribution is to some extent a free-energy correction, it certainly does not account for all of the free energy. A comparison of our chosen level of theory, basis set, and implicit solvent scheme with other methods can be found in our previous work.17
ketone, (d) coupling of the second pyrrole, and (e) dehydration and reduction to form a dipyrrylmethane. However, under oxidative conditions, it is likely that some amount of dipyrrylmethene is formed, thereby reducing the yield. These steps are illustrated in Figure 3. Lindsey and coworkers identified small amounts of dipyrrylmethene in their work by optimizing the synthesis of porphyrin;10 they found that obtaining a “high yield of porphinogen [was] contingent on minimizing oxidation until the condensing system closely approached thermodynamic equilibrium”. The goal of our present study is to construct a free energy map for the initial steps of formaldehyde and pyrrole cooligomerization to form complex mixtures of porphinogen and linear oligopyrroles. Because this first study aims to generate a baseline map, no catalysts or additives are included other than water, which also acts as the solvent. Only neutral molecular species were considered, and free energies are reported at 25 °C as baseline conditions following a standard protocol. We also chose to limit our study to nonoxidative conditions to constrain the molecular space and potential oligomerization pathways. Future work will examine redox reactions and the addition of acid (used in most experiments to synthesize porphyrins) and metal ion cofactors. Computational chemistry is ideal for studying systems that lead to complex mixtures because one can systematically tease out various contributions to the free energy in each of the myriad species. We have previously developed a relatively fast protocol to map the free energy landscapes (both thermodynamics and kinetics) for reactions involving small water-soluble aldehydes that lead to complex mixtures. Those of relevance to prebiotic chemistry include the self-oligomerization of formaldehyde11 and glycolaldehyde12 and the co-oligomerization of formaldehyde and ammonia.13 We have also recently studied the reaction of HCN and ammonia14 and the co-oligomerization of glycine and glycolic acid15 using a similar protocol. Our present study builds on this body of work by expanding the free energy map for molecules of interest in prebiotic chemistry. B
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 1. Energies of Oligomers and Intermediatesa Reference States H2O CH2O pyrrole Species in Figure 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Additional Species in CH2(OH)2 23 24 25 26 27 28 29 30 a
Eelec (a.u.)
Esolv
Hcorr
Gcorr
−0.5TScorr
G298
ΔGr
−76.44744 −114.53629 −210.22604
−8.66 −2.75 −4.36
15.75 19.01 54.70
2.30 3.44 35.05
−6.73 −7.79 −9.83
−47971.14 −71864.15 −131878.34
0.0 0.0 0.0
−324.78386 −324.78937 −324.78613 −248.30186 −439.35344 −439.35248 −362.87687 −362.86469 −439.34361 −458.58102 −573.14416 −496.65779 −496.67105 −706.93575 −821.49904 −745.01305 −745.03325 −955.29053 −1069.85854 −993.37246 −993.41890 −1203.64461 other Figures −191.00777 −573.14017 −821.49441 −687.71071 −936.06191 −553.91660 −687.70750 −936.07340 −1184.43970
−7.26 −8.24 −9.68 −4.78 −9.97 −12.54 −4.61 −10.60 −9.06 −6.71 −11.14 −9.93 −8.80 −9.54 −13.71 −12.19 −8.38 −12.24 −13.56 −9.89 −9.12 −15.10
77.00 77.15 77.12 57.72 99.75 99.55 80.52 79.25 99.49 115.48 137.89 117.75 118.48 176.20 198.64 178.52 180.83 236.37 259.50 239.81 241.77 296.48
53.11 53.33 53.11 36.69 73.32 71.48 57.72 55.10 71.83 86.85 104.61 88.86 88.92 137.81 156.08 140.76 146.50 190.92 210.31 191.30 198.65 244.12
−11.95 −11.91 −12.01 −10.52 −13.22 −14.04 −11.40 −12.08 −13.83 −14.32 −16.64 −14.45 −14.78 −19.20 −21.28 −18.88 −17.17 −22.73 −24.60 −24.26 −21.56 −26.18
−203747.20 −203751.45 −203750.98 −155769.38 −275621.94 −275624.92 −227644.21 −227644.50 −275615.73 −287669.54 −359543.35 −311564.16 −311570.95 −443461.50 −515334.88 −467355.39 −467360.23 −599252.57 −671125.16 −623145.09 −623168.81 −755043.35
−4.7 −9.0 −8.5 +2.0 −15.3 −18.3 −8.7 −9.0 −9.1 −19.8 −29.5 −21.5 −28.3 −40.5 −49.7 −41.3 −46.2 −60.2 −68.6 −59.7 −83.4 −79.6
−10.32 −10.14 −12.87 −11.70 −15.75 −14.09 −15.37 −12.36 −9.03
38.94 137.95 198.67 160.72 221.33 122.30 160.32 221.33 282.15
20.38 106.53 157.82 126.59 176.64 92.10 122.78 177.67 232.93
−9.28 −15.71 −20.43 −17.07 −22.35 −15.10 −18.77 −21.83 −24.61
−119839.87 −359538.86 −515330.25 −431413.12 −587204.60 −347494.87 −431416.88 −587207.90 −742998.77
−4.6 −25.0 −45.1 −35.1 −55.3 −24.1 −38.9 −58.6 −78.1
All energies are in kcal/mol except where indicated (Eelec is in a.u.).
corrections to the free energy for concentration differentials among species (to obtain the chemical potential) can be significant, especially if the solubility varies among the different species in solution. Furthermore, because the reactions being studied are in solution, the free energy being accounted for comes from two different sources: thermal corrections and implicit solvent. Neither of these parameters is easily separable, nor do they constitute all the required parts of the free energy under our approximations of the system. To estimate the free energy, we followed the approach of Lau and Deubel,30 who assigned the solvation entropy of each species as half of its gas-phase entropy. Wertz31 and Abraham32 had previously proposed that upon dissolving in water, molecules lose a constant fraction (∼0.5) of their entropy. In Table 1, this is designated −0.5TScorr and is calculated by 0.5(Gcorr − Hcorr). Recent computational studies in other unrelated systems have come to the same conclusion.33−35 The free energy of each species, designated G298 in Table 1, is the sum of Eelec, Esolv, Hcorr, and −0.5TS. Although we calculated multiple conformers, only the most stable conformer (both stable minima and transition states) for each unique molecular
The analytical Hessian was calculated for each optimized structure, and the gas-phase energy corrected for zero-point vibrations. Negative eigenvalues in transition-state calculations were not included in the zero-point energy (ZPE). The temperature-dependent enthalpy correction term is straightforward to calculate from statistical mechanics, where we assume that translational and rotational corrections are a constant times kT, that low frequency vibrational modes will generally cancel out when calculating enthalpy differences, and that the vibrational frequencies do not change appreciably in solution. The vibrational scaling factor of 0.967 for B3LYP//6-311G** was not applied because when relative energies are calculated, the difference to the enthalpy correction becomes negligible within the computational error. The combined ZPE and enthalpy corrections to 298 K are designated Hcorr, and the corresponding gas-phase free energy correction to 298 K is designated Gcorr in Table 1. The corresponding free-energy corrections in solution are much less reliable.27−29 Changes in free energy terms for translation and rotation are poorly defined in solution, particularly as the size of the molecule increases. Additional C
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 2. Transition State Energiesa Eelec (a.u.) Reactions in Figure 4 rcts → 1 −477.65744 rcts → 2 −477.64683 rcts → 3 −477.63138 1→5 −592.21981 1→9 −592.23324 2→4 −477.67523 2→5 −592.22825 2→6 −592.21155 2 → 10 −649.53744 2 → 11 −725.99092 4 → 10 −611.42531 5→7 −668.67799 6→8 −592.24104 10 → 11 −726.00320 10 → 14 −859.78418 11 → 12 −726.03135 11 → 14 −897.89347 11 → 15 −974.34082 12 → 13 −649.54095 12 → 14 −859.77654 14 → 15 −974.35659 14 → 18 −1088.93760 15 → 16 −974.39466 15 → 18 −1146.24911 15 → 19 −1222.70049 16 → 17 −897.91110 16 → 18 −1108.12861 18 → 19 −1222.71187 19 → 20 −1222.74377 19 → 21 −1299.18727 20 → 21 −1146.27261 20 → 22 −1356.48350 Additional Reactions in Other Figures 10 → 23 −726.02325 14 → 24 −974.37793 11 → 25 −840.58367 15 → 26 −1088.93760 19 → 22 −1394.60085 a
Esolv
Hcorr
Gcorr
−0.5TScorr
G298
ΔGr
−23.71 −25.10 −29.40 −22.65 −18.17 −26.69 −28.17 −30.35 −23.36 −33.60 −27.91 −42.12 −28.41 −30.24 −31.92 −19.25 −30.14 −37.72 −24.50 −33.09 −32.98 −26.42 −18.52 −32.09 −37.72 −21.30 −36.44 −34.83 −21.77 −31.21 −22.53 −38.68
104.89 105.62 105.46 128.02 127.60 107.17 128.19 128.34 149.83 167.64 145.27 148.72 129.99 166.71 204.43 167.09 210.04 226.07 147.45 204.94 226.82 249.98 229.53 270.78 286.95 213.58 265.00 287.58 288.90 307.89 269.91 325.08
75.68 76.65 76.15 96.07 93.19 77.79 96.55 95.33 116.64 128.77 110.47 111.08 97.06 127.93 161.92 130.61 169.43 180.52 112.42 160.88 181.37 202.76 185.01 221.14 233.34 172.30 214.27 232.79 235.50 249.02 221.25 267.07
−14.61 −14.49 −14.66 −15.98 −17.21 −14.69 −15.82 −16.51 −16.60 −19.44 −17.40 −18.82 −16.47 −19.39 −21.26 −18.24 −20.31 −22.78 −17.52 −22.03 −22.73 −23.61 −22.26 −24.82 −26.81 −20.64 −25.37 −27.40 −26.70 −29.44 −24.33 −29.01
−299668.05 −299661.94 −299656.87 −371534.22 −371539.82 −299680.00 −371544.71 −371536.95 −407481.10 −455451.67 −383575.29 −419514.08 −371551.82 −455456.90 −539371.57 −455462.04 −563277.18 −611242.64 −407487.75 −539368.21 −611247.00 −683118.85 −611253.25 −719068.45 −767033.87 −563276.20 −695158.15 −767038.08 −767043.02 −815005.24 −719074.02 −850949.02
+16.7 +22.8 +27.9 +14.7 +9.1 +4.8 +4.2 +12.0 +3.9 +4.5 +16.7 +6.0 −2.9 −0.8 −8.3 −5.9 −20.9 −15.2 −2.8 −4.9 −19.5 −27.3 −25.8 −40.8 −35.1 −19.9 −23.5 −39.3 −44.2 −35.3 −46.3 −43.0
−29.57 −32.20 −23.48 −26.42 −34.85
167.73 228.25 190.04 249.98 330.17
131.71 183.25 150.79 202.76 275.96
−18.01 −22.50 −19.63 −23.61 −27.11
−455466.41 −611257.96 −527327.39 −683118.85 −874857.21
−10.3 −30.5 −7.1 −27.2 −58.2
All energies are in kcal/mol except where indicated (Eelec is in a.u.).
species is reported in our free energy map. ΔG values are calculated from the difference in G298 between the reactants and products and therefore include the zero-point energy, enthalpic, and entropic corrections to 298 K for a reaction in aqueous solution. In Table 1, the rightmost column (ΔGr) is the relative free energy of each species with respect to formaldehyde, pyrrole, and water as the reference states. Using this choice of reference states, formaldehyde and pyrrole are assigned ΔGr = 0.0 and water molecules are added where necessary to ensure the reactions are stoichiometrically balanced. This allows us to quickly and easily visualize a map of the energy landscape for the myriad reactions that can take place. Although water is a reactant in hydration reactions, concentration corrections are not included in this landscape, the advantages and disadvantages of which are discussed in our previous work.12 One drawback to this approach is that in aqueous solution, formaldehyde primarily exists as its hydrate, methanediol, CH2(OH)2. However, using formaldehyde is more facile for
transition state calculations. We will discuss why and present a potential postcorrection to our baseline numbers in the Results and Discussion section. To optimize transition states, additional water molecules were explicitly added to the system to find the lowest energy barrier for proton transfers. We tried different numbers of water molecules and report the free energies of the optimal structures with the lowest barriers, as discussed explicitly in previous work.11,12 All calculated transition states have one large negative eigenvalue corresponding to the reaction coordinate involving bond breaking/forming and accompanying proton transfer. The corresponding energy components of the transition states are listed in Table 2. One weakness in our protocol: SN2-like transition states required a chain of water molecules to connect the incoming nucleophile with the leaving group, leading to higher calculated barriers. It was significantly more facile to calculate a two-step reaction with dehydration as a first step where possible. Thus, formaldehyde was used instead of CH2(OH)2 in transition state calculations, although D
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
Figure 4. Free energy landscape for oligomerization of CH2O and pyrrole
dehydration, (3) pyrrole addition to a fulvene, (4) addition of 1-azafulvene, (5) addition of 1-azafulvene accompanied by loss of CH2O, and (6) isomerizations or ring closures that do not involve additions or eliminations. Relative free energies are calculated in the following way. For example, for the addition of CH2O to the ortho-position of pyrrole to form 2, the reaction free energy change (referring to Table 1 values) is G298(2) − [G298(CH2O) + G298(pyrrole)] = −9.0 kcal/mol. Because CH2O and pyrrole are reference states, ΔGr(2) = −9.0 kcal/mol. Two additional water molecules are involved in the optimal transition state, hence the reaction barrier is G298(rcts → 2) − [G298(CH2O) + G298(pyrrole) + 2 G298(H2O)] = +22.8 kcal/mol, and thus ΔGr(rcts → 2) = +22.8 kcal/mol. As a second example, consider the addition of a second formaldehyde, thereby converting 2 to 5. The change in free energy is G298(5) − [G298(2) + G298(CH2O)] = −6.3 kcal/mol; but relative to the reference states, ΔGr(5) = −15.3 kcal/mol as shown in Figure 4. The −6.3 kcal/mol could also have been calculated as the difference between ΔGr(2) and ΔGr(5). The optimal transition state also involves two additional water molecules. The calculated barrier for this reaction, G298(2 → 5) − [G298(2) + G298(CH2O) + 2G298(H2O)] = +13.2 kcal/mol, but relative to the reference states ΔGr(2 → 5) = +4.2 kcal/ mol. The barrier can also be calculated from ΔGr(2 → 5) − [ΔGr(2) + 2ΔGr(H2O)] = +4.2 − [−9.0 + 2(0.0)] = +13.2 kcal/mol. We will use “calculated barrier” when referring to the reaction barrier of a single step, i.e., +13.2 kcal/mol in this example. However, when referring to the relative free energy of a transition state (+4.2 kcal/mol in this example), we will explicitly use “ΔGr” in the text. Care should be taken when using Figure 4 to elucidate the reaction free energy and calculated barrier for single steps involving 1-azafulvene (4) addition because ΔGr(4) = +2.0 kcal/mol, i.e., it is not zero. For the reaction 2 + 4 → 11 (yellow arrow with +4.5 kcal/mol in Figure 4), the free energy change is ΔGr(11) − [ΔGr(2) + ΔGr(4)] = −29.5 − [−9.0 + 2.0] = −22.5 kcal/mol and the calculated barrier is ΔGr(2 →
the barrier for CH2(OH)2 dehydration back to formaldehyde is relatively low (∼13 kcal/mol) and readily occurs at room temperature.36 Our protocol was put to the test with a detailed comparison of our computational results with NMR measurements for the self-oligomerization of a 1 M solution of glycolaldehyde.12 Our calculated equilibrium concentrations of the dominant species in solution (monomers and dimers) agreed very well with experiment. In addition, our calculations allowed us to successfully predict the concentrations of trimers in solution, 2 orders of magnitude lower than the monomers. Our protocol performs well in calculating the relative free energies of stable species, typically within 0.5 kcal/mol of experimental results, or an uncertainty of within a factor of 2.3 in terms of equilibrium constant ratios.11,12 The activation barriers compared to experiment are reasonable, but the agreement is not as close, and our protocol typically overestimates the barrier by 2−3 kcal/mol. The barriers were calculated in reference to the separated reactants rather than a preassociated complex because in previous cases we found differences of 0−2 kcal/mol between the two methods, and we were willing to tolerate this error in favor of a streamlined protocol.13 Potential issues stemming from the approximations and assumptions made in our protocol are discussed more extensively in our previous study.12
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RESULTS AND DISCUSSION Overall Scheme and Reference States. The main free energy map summarizing our results is shown in Figure 4. The reference state molecules are H2O, CH2O, and pyrrole. These three molecules are assigned a relative free energy of zero. Labels for the molecular species 1−22 are shown in each structure, and their relative free energies with respect to the reference molecules are shown in black font underneath each structure. Transition state relative free energies with respect to the reference molecules are shown in blue font next to the arrow between two species. There are six main reaction types in Figure 4, with the arrows color-coded in the figure key. They are (1) CH2O addition, (2) E
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A 11) − [ΔGr(2) + ΔGr(4) + 2ΔGr(H2O)] = +4.5 − [−9.0 + 2.0 + 2(0.0)] = +11.5 kcal/mol. Addition of CH2O to Pyrrole. There are three possible positions where the first CH2O may add to pyrrole: nitrogen, ortho-carbon, and meta-carbon. All three reactions are exergonic, with reaction free energies of −4.7, −9.0, and −8.5 kcal/mol to form the hydroxymethylpyrroles 1, 2, and 3, respectively. Although formation of the C−N bond is the least exergonic, it has the lowest calculated barrier (+16.7 kcal/mol). Forming a C−C bond in the ortho-position has a calculated barrier of +22.8 kcal/mol, while the meta-position is disfavored kinetically with a calculated barrier of +27.9 kcal/mol. Transition-state structures of rcts → 1 and rcts → 2 are shown in Figure 5. Both optimal structures contain two
significantly easier for the transition state to converge if formaldehyde is used rather than its hydrate, CH2(OH)2, even though the latter is thermodynamically favored. If CH2(OH)2 is used, additional water molecules need to be included in the calculation, and we find that the transition states converge on CH2(OH)2 dehydration. The calculated barriers are also higher and less likely to correspond to experimental values because of the additional entropic cost as found in our earlier work on CH2O oligomerization.11 For the rest of this article, we do not consider meta- species in our main scheme because of the higher barriers, lower thermodynamic favorability compared to the ortho-species, and also because they do not lead to porphinogen. We expect metaspecies to be formed at higher temperatures, and this partially explains why many of the porphyrin synthesis experiments described in the Introduction make use of 3,4-dialkylpyrroles in starting material. The alkyl groups also serve to activate the ring to electrophilic substitution. The thermodynamic and kinetic trends for these reactions hold in the larger oligomers. A selection is shown in Figure 6. Additional examples less relevant to the main pathway in Figure 4 may be found in the Supporting Information. In the top panel of Figure 6, addition of CH2O to the pyrrole nitrogen for the dimer and trimer are −5.2 and −4.6 kcal/mol, respectively, similar to −4.7 kcal/mol for the monomer. The barriers are however significantly lower (+9.6 and +10.0 kcal/mol, respectively) because the N−H of the neighboring pyrrole unit forms a stabilizing hydrogen bond in the transition state (see Figure 7, left; H-bond marked with black dashed line). In the middle panel of Figure 6, addition of CH2O to the pyrrole ortho-carbon for the dimer and trimer are −9.7 and −9.2 kcal/mol, respectively, similar to −9.0 kcal/mol for the monomer. The barriers (+19.1 and +20.9 kcal/mol, respectively) are marginally lower than for the monomer (+22.8 kcal/ mol). In the bottom panel of Figure 6, we see that the presence of a neighboring N-CH2OH moiety can reduce the calculated
Figure 5. Transition-state structures for first CH2O addition.
additional water molecules to mediate proton transfer. The 8center transition states have typical bond breaking/forming distances, with two small exceptions in rcts → 2, where the forming C−C bond at 1.60 Å is shorter and the newly forming O−H bond from C−H abstraction is longer at 1.53 Å. As mentioned in the Computational Methods section, it is
Figure 6. Selection of reaction free energies and calculated barriers for CH2O addition. F
DOI: 10.1021/acs.jpca.7b08685 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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the dehydration endergonicity. These reactions remain kinetically favorable but are no longer favored thermodynamically. In contrast, adding CH2O to the ortho-carbon of pyrrole is exergonic ∼9 kcal/mol, and therefore even with CH2(OH)2 as the dominant reactant species in aqueous solution, addition is still overall favored by 4−5 kcal/mol thermodynamically. The higher barrier to C−C bond formation also means that once formed, the reaction is unlikely to be reversible. Over time, equilibrium shifts to the formation of the more stable species, in this case 6. Figure 8 illustrates what is likely taking place. (Double arrows indicate equilibrium reactions, and dashed lines show kinetically less favorable reactions.) Adding the first CH2O to form 1 assists by adding the second CH2O to form 5. The labile CH2O may pop off the nitrogen to form 2 (in equilibrium). Adding a third CH2O to 5 is also facilitated to form 27, and as more CH2O is depleted in solution, the amount of 6 will increase. We will consider a postcorrection to the relative free energies accounting for CH2(OH)2 in a later section of this article. Two adjacent CH2OH moieties can potentially form a ring via dehydration as illustrated by 5 to 7 in Figure 4. This reaction however is endergonic 6.6 kcal/mol with a calculated barrier of 21.3 kcal/mol, so we think species such as 7 are unlikely to remain stable in solution, and no mention of them is made in the NMR study.37 Dehydration to Fulvenes and Subsequent Addition of Pyrroles. While the addition of CH2O to pyrrole is straightforward, adding subsequent pyrroles is more difficult. Our initial attempts to directly react 2 with pyrrole to form the dipyrrlmethane 10 met with failure because the H on the pyrrole nitrogen would disrupt transition states leading to 10. Replacing H with a capping CH3 group allowed us to find converged transition states with calculated barriers of ∼30 kcal/ mol. We then attempted to react 1 and 5 to form a dipyrrylmethane with two N−CH2OH moieties, but the calculated barrier was ∼40 kcal/mol and the forming C−C and breaking C−O bonds were long (2.69 and 2.36 Å, respectively); see Supporting Information for transition state structures. This however gave us a clue because the transition states contained fulvene-like structures. Therefore, we decided to split the reaction into two steps: (1) Start with a dehydration step that forms a fulvene, and (2) add the fulvene to a pyrrole. This mirrors our strategy for using CH2O rather than CH2(OH)2 as the adding reactant and we recognize this limitation in our calculations, i.e., we have to split up reactions into multiple steps, otherwise the addition of more water molecules required to move hydrogens leads to entropy and solvation energy penalties that raise the calculated barriers. Dehydration of 2 to 1-azafulvene (4) is endergonic by 11 kcal/mol, and the calculated barrier is only slightly higher at 13.8 kcal/mol. Thus, while 4 is kinetically accessible, it is likely only to be formed transiently because it will quickly hydrate back to 2 in aqueous solution. If, however, a pyrrole molecule is close by, there is the opportunity for an addition reaction to form species containing two pyrrole rings. For example, the addition of 1 and 4 to produce 10 is highly exergonic. The reaction is downhill 21.8 kcal/mol, and the calculated barrier is 14.7 kcal/mol. Similarly, the addition of 2 and 4 to produce 11 (discussed in detail in the earlier subsection Overall Scheme and Reference States) is downhill 22.5 kcal/mol, with a calculated barrier of 11.5 kcal/mol. Analogous reactions (diagonal golden arrows in Figure 4) for the larger oligomers are shown in Figure 9 (top panel) with similar results, i.e.,
Figure 7. Transition state structures for CH2O addition with stabilizing H-bond.
barrier. A stabilizing hydrogen bond can be formed as shown in Figure 7 (on the right). The magnitude of stabilization is typically in the range of 1−3 kcal/mol, i.e., barriers are typically in the 17−20 kcal/mol range instead of the 19−22 kcal/mol. On the other hand, a CH2OH moiety on the opposite orthocarbon is too far to provide a stabilizing hydrogen bond, e.g., the calculated barrier for 2 → 6 is 21.0 kcal/mol. Instead of forming a new bond to the pyrrole ring, it is possible that the second CH2O is added to a CH2OH moiety to form a hemiformal, as illustrated by the formation of 9 from 1. The reaction is exergonic by 4.4 kcal/mol and the calculated barrier is 13.8 kcal/mol, similar to values we find for the formation of linear (OCH2)n oligomers found in our study of formaldehyde oligomerization.11 Because adding the first CH2O to form 1 is significantly favored kinetically over forming 2, and adding the second CH2O to 1 to form 9 is significantly favored kinetically over forming 5, should we not just see hemiformal formation where dangling −(OCH2)n-OH groups are found attached to the pyrrole nitrogen at lower temperatures? In fact, yes! Katritzky and Law conducted a low-temperature 13C NMR study for the reaction of pyrrole with formaldehyde and found that 1 is indeed the first species formed.37 Small amounts of 9 are observed after 10 days. Starting material, formaldehyde, and pyrrole are also present. After one month, 2, 5, 6, and the tris(hydroxymethyl)pyrrole 27 (see Figure 8) are formed along
Figure 8. Formation and equilibria of hydroxylmethylpyrroles
with their respective hemiformals. The hemiformal peaks disappear with the addition of aqueous ammonia. When the reaction is sped up by raising the temperature, the eventual major product is 6, i.e., the CH2OH moiety is labile when attached to the pyrrole nitrogen. This makes sense because in aqueous solution CH2(OH)2 is more stable than CH2O by 4.6 kcal/mol. Addition of CH2O to either the pyrrole nitrogen or a dangling CH2OH moiety is exergonic in the 4−5 kcal/mol range; hence, if CH2(OH)2 is the reactant (or product from hydrolysis), the exergonicity is approximately canceled out by G
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Figure 9. Selection of reaction free energies and calculated barriers for pyrrole and fulvene addition.
Figure 10. Transition-state structures for formation of structure 14 via addition.
significantly higher barriers (23.6, 23.9, and 24.4 kcal/mol, respectively) compared to the dehydration of monomeric pyrrole to 1-azafulvene (13.8 kcal/mol). It is unclear why this difference is so large. We have tried many transition-state conformations, some extended structures, some having a number of internal hydrogen bonds, and the results are very similar in all cases. Decomposition of the energetic contributions suggest that solvation energy significantly stabilizes the monomer dehydration transition state compared to reactants much more than the larger oligomers. It is possible that there is an artifact in our calculated solvation energies, but because we were unable to determine the cause, we let the results stand as calculated. While the calculated barriers for the addition of 1-azafulvene with pyrroles to form successively longer oligopyrroles are
reactions are exergonic by 21−23 kcal/mol and calculated barriers are 10−13 kcal/mol. An alternative way to form 14 and 18 is the addition of pyrrole to the fulvenes 12 and 16, respectively (red zigzag arrows in Figure 4). These reactions, shown in the middle panel of Figure 9, are exergonic by ∼19 kcal/mol with calculated barriers of 17−18 kcal/mol. Examples of transition state structures for 10 → 14 and 12 → 14 are shown in Figure 10. Two additional water molecules are present to form the optimal 9-center transition states. Because this route has higher barriers, we expect that the formation of oligopyrroles to more likely proceed via the addition of 1-azafulvene to (oligo)pyrrole rather than the addition of pyrrole to a larger fulvene. A second reason larger fulvenes are disfavored is that the dehydration reactions 11 → 12, 15 → 16, and 19 → 20 have H
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The Journal of Physical Chemistry A relatively low, in the 10−13 kcal/mol range, we find that the calculated barriers are lower if the addition reaction is accompanied by elimination of CH2O. This is perhaps not surprising because it is likely easier to break a C−C instead of a C−H bond. The reaction of 2 and 4 to form 10 (with loss of CH2O) is exergonic 12.8 kcal/mol, with a calculated barrier of 10.9 kcal/mol. In comparison, the reaction of 2 and 4 to form 11 (with no loss of CH2O) is more exergonic (by 22.5 kcal/ mol), with a slightly higher barrier of 11.5 kcal/mol. When larger (hydroxymethyl)oligopyrroles are reactants, the barrier range is now 7−11 kcal/mol and the reaction exergonicities are similar. Two examples are shown in the bottom panel of Figure 9, and the transition state for 11 → 14 is shown in Figure 10. The newly forming C−C bond and the breaking C−C bond with CH2O elimination are equidistant at ∼1.6 Å. We have opted to restrict our discussion of addition reactions to species that do not possess N−CH2OH moieties. This is because addition and removal of CH2O at pyrrole nitrogens is labile as discussed in the previous section. One can imagine analogous sets of reactions involving structures 10−12, 14−16, and 18−20 with varying numbers of hydroxymethyl groups attached to pyrrole nitrogens although we expect the thermodynamics and kinetics to look similar. Note however that the N−CH2OH moiety prevents a pyrrole ring from becoming a fulvene and therefore could hinder subsequent addition reactions. For example, there is no easy route for 5 to form a neutral fulvene. On the other hand, 6 could form a hydroxymethyl-1-azafulvene (8). This fulvene can participate in an analogous set of reactions that may involve oligopyrroles (as reactants or products) with ortho-CH2OH moieties on both ends of the molecule as shown in Figure 11. We have included the ΔGr values for these three molecules (28, 29, 30) so we can quickly see their relative energies with respect to the species shown in Figure 4.
Once the trimeric oligopyrrole is formed, there is the potential for cyclization. Because the cyclization reaction is simply an intramolecular addition of a pyrrole to a fulvene, dehydration of 15 to 16 may be followed by cyclization to 17. The cyclization step of 16 to 17 is slightly exergonic (by 4.9 kcal/mol) and the calculated barrier is 21.4 kcal/mol. However, 16 is a transient species (at best) as discussed in the previous section and is likely to rehydrate back to 15, which would be more favorable both thermodynamically and kinetically. Addition of pyrrole to form 18 is also thermodynamically and kinetically more favorable than cyclization. We therefore expect very little of 17 to be formed (if any), and in aqueous solution hydration is likely to open the ring to reform 15. On the other hand, the tetramer ring (porphinogen, 21) is very stable thermodynamically. The ring closure from 20 to 21 is exergonic 23.7 kcal/mol, with a low calculated barrier of 13.4 kcal/mol. The transition state for this reaction is shown in Figure 12. If a small amount of transient 20 is formed, the
Figure 12. Transition state of ring closure to porphinogen
cyclization reaction is thermodynamically and kinetically more favorable than rehydration to 19 or addition to form the pentapyrrole 22. We explored the possibility of direct cyclization of 19 to 21, but the transition states suffer from the same limitation mentioned earlier: a longer chain of water molecules is required to transfer the hydrogens, and the calculated barrier is higher (in this case 33.3 kcal/mol) due to entropic contributions and solvation energies. (The transition state is shown in Supporting Information.) From the previous section, we would instead expect the most favorable reaction of 19 to be addition of 4 (if transiently present) to form 22 while eliminating CH2O. This reaction is exergonic 13.0 kcal/mol, with a calculated barrier of 10.4 kcal/mol, and is entry 19 → 22 in Table 2. Overall Free Energy Landscapes and Route to Porphinogen. Returning to our overall free energy map in Figure 4, how do we get from monomeric pyrrole and CH2O to porphinogen? We expect formaldehyde to first add to the pyrrole nitrogen (forming 1). The N−CH2OH moiety lowers the barrier for addition of CH2O to the ortho-carbon (forming 5). Because CH2O addition to the pyrrole nitrogen is labile, it can leave (forming 2), providing the opportunity to form transient amounts of 4. If a neighboring 2 is present when 4 is formed, addition of the two leads to 10 (with elimination of CH2O). 10 could add to 4 to form 14, or first add CH2O to form 11 before reacting with 4 to form 14 (with elimination of CH2O). The steps from the oligopyrrole trimers to the tetramers are similar.
Figure 11. Oligopyrroles with hydroxymethyl groups on both orthoends.
Ring Closure and Isomerization Reactions. In this section, we consider isomerization and ring closure reactions (green arrows in Figure 4). Oligopyrrolefulvenes have the potential to undergo a 1,3-H shift to extend its conjugated system. This is illustrated by the isomerization of 12 to form 13. The trans isomer of 13 is thermodynamically more stable than the cis isomer. The sigmatropic rearrangement of 12 to 13 is exergonic by 6.8 kcal/mol, with a calculated barrier of 18.7 kcal/mol. Because this path does not lead to the porphinogen, we do not consider its downstream reactions in the present study. (The same applies to 16 and 20, which can undergo similar rearrangements.) Note that these reactions are likely to further reduce the yield of porphinogen. I
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Figure 13. Modified free energy landscape using CH2(OH)2 reference state.
the transition-state structures make use of CH2O. For this reason, and because we use the same approach of choosing the aldehyde as the reference state in previous work, the results and discussion focus on Figure 4, the main figure in this article. Figure 13 is provided for comparison if a different reference state is used.
When the tetrapyrroles are formed, they can continue to lengthen using similar steps to form pentamers and higher oligomers, but there is also a thermodynamically very favorable channel leading to porphinogen. However, the kinetics of dehydration from 19 to 20 or the direct cyclization of 19 to 21 are limiting factors. These may be artifacts of the calculation as discussed previously, but they may also inherently be bottleneck steps to form porphinogen. To facilitate the experimental synthesis of porphyrins, acids, and metal ions are added to the mixture. Metal ions would certainly favor “curled” up structures that template the formation of ring structures. Furthermore, we have limited this study to nonoxidative conditions. The reduction of a pendant hydroxymethyl to an aldehyde would provide alternative pathways that may be favorable thermodynamically and kinetically, possibly obviating the need for fulvene intermediates. Earlier in this article, we discussed the possibility of using CH2(OH)2 as the reference species instead of CH2O because the hydrate is thermodynamically more stable. The transition states however are much easier to converge using the aldehyde (rather than the hydrate), and the barriers compare reasonably with experimental values where available for small water-soluble aldehydes, as shown in our previous work.11,12,16,17 What might the energy landscape look like if CH2(OH)2 was the reference species? A simple “correction factor” would be to add −4.6 kcal/mol for every formaldehyde in a species or transition state. Doing this to all values shown in Figure 4 leads to Figure 13. The most notable difference is that “CH2O” additions are no longer as thermodynamically favorable. For additions to pyrrole nitrogen forming an N−C bond, or to a hydroxymethyl to form a hemiformal via an O−C bond, the reaction free energies are close to zero. Additions to the pyrrole ortho-carbon are still favorable, although reactions are now exergonic by 4−5 kcal/ mol instead of ∼9 kcal/mol. Additions of 1-azafulvene (without CH2O elimination) are also less exergonic in the 16−19 kcal/ mol range rather than 20−23 kcal/mol. In terms of the kinetics, all CH2O addition barriers increase by 4.6 kcal/mol. It is unclear if this is the best way to correct the barriers given that
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CONCLUSION We have constructed a free energy map at 25 °C for the cooligomerization of CH2O and pyrrole to form porphinogen. We limited the scope of our exploration to neutral molecules, and the calculations assume water acting as a solvent via a dielectric and explicitly aiding hydrogen transfers in transition states. This study complements our previous work using the same computational protocol, thereby allowing the extension of our baseline energy maps to include ever more complex mixtures. While our present trajectory focuses on reactions relevant to prebiotic chemistry, it contributes more widely to understanding the energetic contributions to the distribution of molecules in complex oligomeric mixtures starting from a few simple monomeric compounds. Within the limitations of our study, we find that additions of CH2O to the ortho-carbon of pyrroles and subsequent reaction with the transient intermediate 1-azafulvene is an energetically feasible route to forming oligopyrroles. Once the tetrapyrrole is formed, ring closure is highly exergonic, however high calculated barriers for dehydration of the tetrameric fulvene (20) or the direct reaction of the hydroxymethylene species (19) may be a limiting factor to forming porphinogen. Current and future work includes the addition of acids and metal ions which may concomitantly modify the baseline free energy map, providing more feasible routes to porphyrins. In parallel, we are considering oxidation and reduction pathways that may avoid relying on an intermediate transient fulvene species. All this will build on the baseline free energy map presented in this article and further enrich our knowledge of how catalysts and cofactors change the distribution of species in a complex mixture as they shift the free energies of molecular species and transition states. J
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08685. Additional reaction free energies and transition state structures, and XYZ coordinates of all optimized structures (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Jeremy Kua: 0000-0002-2472-1887 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This research was supported by a Camille and Henry Dreyfus Teacher−Scholar award. Shared computing facilities were provided by the saber1 high-performance computing cluster at the University of San Diego.
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