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New questions about Tautomerism in Cytosine Quantum chemical and matrix isolation spectroscopic studies Géza Fogarasi Research Laboratory of Theoretical Chemistry, Eötvös L. University, H-1518, Pf. 32, Budapest/Hungary.

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2 Nucleic acid bases are the most conspicuous examples of tautomerism. 1. Background and motivation The double helix of DNA is fixed by H-bonds, based on specific tautomeric forms of the bases

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3 Example: the H-bonds between cytosine and guanine

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4 Watson and Crick, Nature …………………………… The significance of tautomerism was recognized from the beginnings:

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6 Tautomers - unlike conformers – have completely different electronic structures. At the same time, the energy differences may be as low as for conformers, just a few kcal/mol. Then: can we calculate (relative) energies for different electronic systems with an accuracy of ~ 0.5 kcal/mol?! (This is realistic for conformers, but quite questionable for tautomers.) However, the basic challenge for theory should be realized at the beginning: For the structural chemist, very first question: energy differences

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7 2. Test calculations, relative energies Formamide Formamidic acid Acetaldimine Vinylamine

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8 Methods: Electronic theory: RHF, B3LYP, MP2, CCSD(T) Basis sets: from 6-31G(d,p) to G(3df, 3pd) and cc-PVTZ to aug-cc-PV5Z

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9 Table 1. Computed energies for tautomer pairs (energies, E in a.u.= J, differences, E in kcal = kJ). Method a Form- amide E+168 Formami- dic acid E+168 E kcal/ mol Acet- aldimine E+132 Vinyl- amine E+132 E kcal/ mol RHF /6-31G(d,p)//~ /6-311G(d,p)//~ / G(2d,2p)//~ / G(3df,3pd)//~ B3LYP /6-31G(d,p)//~ /6-311G(d,p)//~ / G(2d,2p)//~ / G(3df,3pd)//~ MP2 /6-31G(d,p)//~ /6-311G(d,p)//~ / G(2d,2p)//~ / G(3df,3pd)//~

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10 / G(3df,3pd)//~ MP2 /PVTZ//~ /aug-PVTZ//~ /PVQZ//aug-PVTZ /aug-PVQZ//aug-PVTZ /PV5Z//aug-PVTZ /aug-PV5Z//aug-PVTZ Table 1. contd1. Method a Form- amide E+168 Formami- dic acid E+168 E kcal/ mol Acet- aldimine E+132 Vinyl- amine E+132 E kcal/ mol

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11 Table 1. contd2. CCSD//MP2 /PVTZ /aug-PVTZ /PVQZ /aug-PVQZ /pV5Z /aug-pV5Z CCSD(T)//MP2 /PVTZ /aug-PVTZ /PVQZ /aug-PVQZ /pV5Z /aug-pV5Z CCSDT//MP2 b /PVTZ Method a Form- amide E+168 Formami- dic acid E+168 E kcal/ mol Acet- aldimine E+132 Vinyl- amine E+132 E kcal/ mol a Notations follow standard convention except that in the correlation consistent basis sets “cc” is tacitly assumed, thus omitted for brevity. After the double slash ‘//’ the level of geometry optimization is indicated; ’~’ means optimization at the same level as the energy calculation. b All coupled cluster calculations were done at the MP2/aug-pVTZ geometry.

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12 Tautomer energy differences with the largest basis sets from above, kcal/mol RHFDFTMP2CCSDCCSD(T) Famid-Facid Acimin-Vinam Bad news: a) the two systems behave differently!! b) CC (coupled cluster) level is needed Good news: SD and SD(T) essentially the same Conclusion of highest level test calculations

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13 3. CYTOSINE tautomers The most prominent example of a “multiform” molecule: Five low-energy isomers (three tautomers plus two rotamers) N 3 2 N NH 2 H O N 3 2 N NH 2 OO H N 3 2 N NH 2 H N 3 2 N H O N H N 3 2 N H O N H 1 2a 2b 3a 3b H H

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14 Theoretical results, e.g.: CCSD(T)[f.c.]/cc-pVTZ// rfg 12b3a Watch out, black-box users!: DFT gives a qualitatively different picture! B3LYP/ G(2d,2p): B3PW91/ G(2d,2p): Summary of extensive calculations Relative energies 1: the “canonical” oxo form; 2b: enol; 3a: imino

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15 Theoretical results CCSD(T)[f.c.]/cc-pVTZ// rfg 12b3a Conclusion: the three low-energy tautomers of cytosine are within a range of ~ 2 kcal/mol And, rotamers: 2a 0.8 kcal/mol above 2b, 3b 2 kcal/mol above 3a

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16 The effect of entropy: differences between tautomers made even smaller (T = 298 K, kcal/mol) ________________________________________________________________________________________________________________________________________________________________ a Geometries (moments of inertia) from CCSD/TZP, vibrational frequencies from MP2/TZP, electronic energies CCSD(T)/cc-pVTZ. b B3LYP/ G(2d,2p). c Total Gibbs free energy from nuclear motions, including the constant contributions from translation and H rot. d Relative to tautomer 2b. e After adding the electronic energies, from Tables 3 and 5, respectively, including the corrections for non-planarity from Table 4, see also text. Note again the failure of DFT!

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17 4. The mechanism of intramolecular proton transfer Transition states B3LYP /6-31G(d,p) / G(2d,2p) / G(3df,3pd) MP2 /6-31G(d,p) / G(2d,2p) / G(3df,3pd) /PVTZ//~ Imag. frequency (1894 cm-1) (1925 cm-1) /aug-PVTZ//~ /PVQZ//aug-PVTZ /aug-PVQZ//aug-PVTZ /PV5Z//aug-PVTZ aug-PV5Z//aug-PVTZ Tautomer pairs formamide- formamidic acid and formamidine - formamidine FMD-FAC FIM-FIM E TS +167 TS E TS +149 TS Vibrational frequencies have been calculated at the MP2/PVTZ level. Each system has one single imaginary frequency, indicating that the TS is indeed a first order saddle point.

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18 /aug-PVTZ /PVQZ /aug-PVQZ /PV5Z /aug-PV5Z CCSD//MP2 aug-PVTZ /PVQZ /aug-PVQZ /PV5Z /aug-PV5Z CCSD(T)//MP2 E TS +167 TS E TS +149 TS Tautomer pairs formamide- formamidic acid and formamidine – formamidine contnd. FMD-FAC FIM-FIM Conclusion: all barriers are far too high for proton transfer to occur. TS in cytosine (amine – imine) : ~ 40 kcal/mol

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19 5. The effect of water a) Affects the relative energies b) Affects the TS barrier Model: supermolecule water molecule(s) added explicitly

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20 a) Relative energies of cytosine-monohydrates Questions: 1) favorite binding positions? 2) binding energy difference between tautomers?

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21 The favorite binding place is the same in all three tautomers. Optimized structures:

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22 Dissociation energies of cytosine-monohydrates (stabilization by water), kcal/mol. One single water molecule makes already the keto form 1 more stable energetically than the hydroxy form 2b. The keto form binds water significantly stronger

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23 Test: Formamide plus water, water may mediate proton transfer b) The TS barrier: Water as a catalyst

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24 Formamide ↔ Formamidic acid Monohydrate For comparison, remember: w/o water it was E ~10.5, E TS ~ 45 kcal _______________________________________________________________________________________________________

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25 Quantum Chemical Transition State Barrier for Cytosine.H 2 O and Cytosine.2H 2 O MethodBasis setCyt.H 2 OCyt.2H 2 O DFT (b3lyp)6-31G(d,p)15.8 a G(d,p) cc-pVTZ MP26-31G(d,p) G(d,p) cc-pVTZ CCSD(T)//MP2/pVTZaug-pVDZ cc-pVTZ a Imaginary frequency: 1577 cm-1 Cytosine 1 ↔ 3a TS with water TS reduces by more than a factor of 2; second H 2 O indifferent

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26 6. The elusive question of cytosine tautomers Solid state and aqueous solution: general agreement that only the “canonical” keto form is present In the gas phase, however: hydroxy form dominates (experimental and theoretical information)

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27 Experimental data (spectroscopy) (temperature poorly defined, o C) Estimated ratios for amino-hydroxy : amino-oxo : imino-oxo (2 : 1 : 3a) Matrix isolation IR Radchenko,.. Blagoi, 1984 Nowak, Lapinski, Fulara 1989 Szczesniak,.. Person, 1988 Theor., from G above Molecular beam MW Brown et al., (b rotam. only) : 1.0 : (b+a rotam) : 0.5 : : 0.4 : 0.4 Discrepancy about the “rare” imino form

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28 Experimental details Cytosine sample from Sigma-Aldrich (solid sample, 99% purity), evaporation at 155 oC, matrix: Argon ( %) and Krypton (99.998%). UV Spectrometer: Varian Cary 3E UV-VIS (1 nm resolution), IR spectrometer: Bruker FTS 55 (1 cm-1 resolution). Own experiments 1.: matrix isolation IR spectrum C1(keto): 1730 (C=O) 1660 (C=C) C3a(imino): 1680 (C=N)

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29 X-H stretching range C2b(enol) 3620 (O-H) C3a(imino): 3490 (N1-H) 3440 (N3-H)

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30 Disturbing results in the literature …. 1.Previous UV spectra restricted to solid state or solution All interpretations based on the keto form. 2. Sophisticated, elegant new, multiphoton experiments in the gas phase (molecular beams) yield contradictory results. UV and ionization spectra

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31 Method Electronic excited states: Equation of Motion Coupled Cluster (EOM-CC) Vibrational structure: Linear Vibronic Coupling (LVC) Theoretical calculation of the UV spectrum While previous computations were restricted to vertical excitations, we have performed the first simulation of the complete spectrum of cytosine, using the Linear Vibronic Coupling (LVC) method.[12] In this method the full (electronic and nuclear) wave function is evaluated as a coordinate-dependent combination of the excited electronic wave functions at a reference geometry, normally the ground state equilibrium. The calculations require the derivatives of the excited state energy with respect to the ground state normal coordinates. The nuclear wave functions are expanded in the harmonic oscillator basis of the ground state. We used in the LVC model the four lowest excited electronic states (Table 1) and fourteen vibrational modes with several quanta on each of them. We have carried out extensive calculations on all three tautomers

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32 Own experiments 2.: matrix isolation UV spectrum intensity energy (eV) Theory: keto form only

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33 Theory: Mixture of 3 tautomers energy (eV) intensity

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34 Theory: keto onlyTheory: mixture

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35 Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half [7]. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers [8,9]. We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a [5]. Each tautomerization has its own transition state barrier as indicated under the picture. Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half [7]. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers [8,9]. We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a [5]. Each tautomerization has its own transition state barrier as indicated under the picture. Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half [7]. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers [8,9]. We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a [5]. Each tautomerization has its own transition state barrier as indicated under the picture. Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half [7]. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers [8,9]. We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a [5]. Each tautomerization has its own transition state barrier as indicated under the picture. Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers. We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a. Each tautomerization has its own transition state barrier as indicated under the picture. How may tautomers form during experiments?

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36 : E(TS) = 6.3 kcal/mol : E(TS) = 4.90 kcal/mol : E(TS) = 7.7 kcal/mol : 6.3, : 4.9, : 7.7 Three H-bonded dimers derived from 1. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a. The lowest TS leads to the hydroxy form 2b. The transition states which lead, partly or fully, to the imino form 3a lie significantly higher. Thus, this model may explain why the imino form appears in the gas state with much smaller abundance than expected.

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37 7. The mechanism of proton transfer Ab initio simulation of dynamics The notion of reaction mechanisms is based on the Born- Oppenheimer (B-O) approximation: atoms move on a potential energy surface (PES) defined by the electronic energy as a function of nuclear positions. In the simplest models reactions follow the minimum energy pathway (MEP), going through a transition state (TS). The MEP expressed in mass-weighted Cartesians is referred to as the internal reaction coordinate, IRC. Recent computations have shown that reactions may follow a route totally different from the IRC. (W.L. Hase, Science 2002; M. Dupuis, Science 2003).

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38 True dynamics calculations require knowledge of the complete PES, and recent methods generate it "on the fly". The well-known Car-Parrinello method is most efficient computationally because the electronic wave function is "propagated", and not optimized, at the trajectory points. As a consequence, the system is moving close to, but not exactly on the B-O surface. In B-O dynamics, the wave function of a QC method is fully optimized in each step along the trajectory. Energy and first derivatives are determined from ab initio wf, with the atomic movements calculated from them classically. This is the approach adopted here. using Verlet's algorithm. The QC method was DFT(B3LYP)/3-21G.

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39 Ab initio simulation of cytosine tautomerization Note the synchronous change of the relevant N – H bonds

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41 Movies …

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42 The End Acknowledgement. Financial support has been provided by Hungarian science grants NKTH-OTKA-A07, no. K and OTKA K72423.

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45 Before drawing conclusions, we have to carefully analyze the available experimental information. Among numerous studies on cytosine, the UV spectrum in trimethylphosphate solution[8], in films[9] and for single crystal and aqueous solution[10] are of special interest for the present work. All spectra show broad, envelop-type bands; thus, the major question has been one of the number of individual electronic transitions. Although the deconvolution seems rather uncertain, it is common in all studies that the UV spectrum is discussed in terms of four electronic transitions. Specifically, a classic circular dichroism (CD) study on cytosine-nucleosides from Eyring's group[11] relates the spectrum to benzene: "The results give […] conclusive evidence for four electronic transitions in the cytosine bases above 190 nm which may be related to the B2u, B1u and E1u bands of benzene." Other studies relied on semiempirical quantum chemical calculations to resolve the spectrum.[9b] A linear dichroism (LD) study on the single crystal gave better resolution of the absorption bands by making use of the variation of intensities as a function of the polarization direction.[10] Also, the polarization behavior indicates that no A'' transition gives appreciable contribution to the spectrum. This study reports also the aqueous spectrum that we have redrawn in Figure 1a. The authors quote four excitations, with = 37.5, 43.0, 45.2 and 50.0 x 103 cm-1, all of - * type. While previous computations were restricted to vertical excitations, we have performed the first simulation of the complete spectrum of cytosine, using the Linear Vibronic Coupling (LVC) method.[12] In this method the full (electronic and nuclear) wave function is evaluated as a coordinate- dependent combination of the excited electronic wave functions at a reference geometry, normally the ground state equilibrium. The calculations require the derivatives of the excited state energy with respect to the ground state normal coordinates. The nuclear wave functions are expanded in the harmonic oscillator basis of the ground state. We used in the LVC model the four lowest excited electronic states (Table 1) and fourteen vibrational modes with several quanta on each of them. In addition, applying a new development to be published separately, the effect of non- adiabatic couplings was also included. The theoretical and experimental spectra are shown in Figure 1. The resolution of the simulated spectra was deliberately made low, to conform to the experimental spectrum. For details see the Supplement

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46 There is, however, a serious discrepancy with a REMPI study of laser-desorped, jet- cooled cytosine.[14] In the limited range studied, cm-1, two vibronic regions were found and assigned to two tautomers! Region R1, cm-1, should belong to the keto form and region R2, cm-1, to the enol form. This interpretation would completely contradict our theoretical results: for the relevant transition I we have the range cm-1 and accepting R1 would mean that our calculation is off by ~ 1 eV. This seems highly improbable: for four analogous - * excitations in pyrimidine, the differences are 0.3 to 0.4 eV[15] at the CCSD level and even less if triples are considered. The REMPI study on cytosine is supported by spectral hole-burning[14b] but the vibrational structure of R1 with splittings of cm-1 is totally unexplained. It may be added that region R2, rather than R1, would be a reasonable candidate for the keto form in our results. By contrast, two other experiments support our results. First, a recent study[16] measured the resonance Raman spectra of cytosine around its 267 nm absorption (band I above). When scanning the exciting laser wavelengths from 290 nm to 244 nm, the spectra showed no change, "indicating that the Raman spectra are enhanced by a single electronic transition." At 244 nm a significant change in the excitation profile was observed, suggesting that "enhancement of the vibrations by the ~200 nm absorption band is becoming a factor". Thus, although the authors do not discuss explicitly the number of electronic transitions, their interpretation of the spectra is based on only two transitions, 267 and ~200 nm, corresponding to I and IV above. Second, transition moments, an integral part of the calculations, can be compared with linear dichroism (LD) measurements on single crystals,[10,13] as well as on polycrystalline cytosine embedded in stretched polyvinyl alcohol sheets[9,17] (Table 2). The experimental values being by nature rather uncertain, we confirm ref.[17b] as opposed to ref.[17a] on band I. For band IV, theory makes clear selection between the alternatives in ref.[10] These LD measurements also give information about the spectrum interpretation discussed above: all experiments agree that the four absorptions involve transition moments in the plane of the molecule. In the theoretical results (Table 1), two of the four excitations are type A'' involving transition moments perpendicular to the molecular plane.

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47 Table 2. Transition Moment (µ) Directions in Cytosine [a] TransitionSingle Crystal [1 3] Single Crystal [1 0] PVA Film [17 a] PVA Film [1 7b] Theo r. CCS D Theor. CC3 I14 (48) IV---86 (-27) [a] angle in degrees between µ and the N 1 -C 4 line, see Scheme 1. PVA - Polyvinylalcohol.

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51 Method: ab initio dynamics* Contrary to Car-Parrinello, the wave function is truly recalculated at each point …. * Pulay, P., Fogarasi, G.: Fock matrix dynamics, CPL 386, (2004) Section 3: Dynamics: Try to ‘see’ the process of tautomerization

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53 CONCLUSIONS ON THE TESTS: _________________________________________________________________ Even the best results are uncertain to ~ 1 kcal/mol

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56 The population of various tautomers in the gas phase is quite uncertain. There is general agreement about the dominance of the amino-hydroxy form (2), but theory also predicts a relative free energy of only G ≤ 1 kcal/mol for the amino-oxo (1) and even the imino-oxo form (3a). For both of the latter, this implies relative abundances of up to 20%. Spectroscopic studies do „see” these isomers but with smaller abundance.

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