RRKM Branching Ratios of the

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Relationships between DFT/RRKM Branching Ratios of the Complementary Fragment Ions [CHO] and [M – CHO] and Relative Abundances in the EI Mass Spectrum of N-(2-furylmethyl)Aniline 5

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Wilmer Esteban Vallejo Narváez, Paula Victoria Bacca Villota, and Eduardo Alfonso Solano Espinoza J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp306643r • Publication Date (Web): 10 Nov 2012 Downloaded from http://pubs.acs.org on November 25, 2012

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The Journal of Physical Chemistry

Relationships between DFT/RRKM branching ratios of the complementary fragment ions [C5H5O]+ and [M – C5H5O]+ and relative abundances in the EI mass spectrum of N-(2-furylmethyl)aniline AUTHOR NAMES. Wilmer E. Vallejo Narváez, Paula V. Bacca Villota, Eduardo A. Solano Espinoza*. AUTHOR ADDRESS. Laboratorio de Química Teórica (LQT), Departamento de Química, Universidad de Nariño, Sede Torobajo, Calle 18 Carrera 50, Pasto, Colombia. TELEPHONE NUMBER: +57-2-7313062 FAX NUMBER: +57-2-7313106. E-MAIL ADDRESS: [email protected]. KEYWORDS. N-(2-furylmethyl)aniline; EI mass spectrometry; [C5H5O]+; [M – C5H5O]+; UB3LYP/6-311G+(3df,2p)//UB3LYP/6-31G(d), RRKM, kinetics. RUNNING TITLE: Theoretical calculations on the EI mass spectra of N-(2-furylmethyl)anilines ABSTRACT. The energy-dependent branching ratios of the complementary fragment ions [C5H5O]+ and [HC6H4NH]+ ([M – C5H5O]+) originated from the N-(2-furylmethyl)aniline molecular ion, [HC6H4NH–C5H5O]+•, were obtained from Rice-Ramsperger-Kassel-Marcus

ACS Paragon Plus Environment

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(RRKM)

rate

calculations

based

on

DFT

energy

profiles.

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The

UB3LYP/6-

311G+(3df,2p)//UB3LYP/6-31G(d) level of theory was used to model the competitive reaction mechanisms by which the molecular ion can be fragmented. Initially, eight pairs of products were taken into account, corresponding to the combination of two isomeric structures for each fragment ion and the concomitant radicals, which can be formed by direct dissociations or through some isomerization-fragmentation pathways. A great deal of the obtained pathways was discarded by looking over the kinetic barrier heights and the individual RRKM rate coefficients calculated for all the steps. This way, the potential energy profiles were simplified to only three reaction channels, two pathways to [C5H5O]+ and one to [M – C5H5O]+. The pre-equilibrium and steady-state approximations were then applied to different regions of the remaining potential energy profiles, allowing the branching ratios of the complementary fragment ions to be easily calculated and discriminated among the three rival processes. According to these results, the major fragment ion in the ion source is [C5H5O]+ which is produced as a mixture of two structures, the furfuryl and pyrylium cations, one formed by a direct C–N bond cleavage and the other through an isomerization-fragmentation channel. In turn, the direct fragmentation is the only mechanism to produce [M – C5H5O]+.

To confront these results with the available

experimental information, the model was broadened out to the 4-substituted analogs [4-R– C6H4NH–C5H5O]+• in which R = F, Br, Cl, CH3, and OCH3, finding excellent correlations of the calculated branching ratios and the relative abundances in the EI mass spectra.


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TEXT. A. INTRODUCTION The N-(2-furylmethyl)anilines I – VI (Fig. 1) have shown very good antifungal activities and low toxicities, and can be used as precursors in the synthesis of more complex bioactive molecules1,2,3. The compounds I and II are especially promissory for the future development of non-toxic new antimycotic agents3. Knowledge of the chemistry of these systems, including information about their detection and characterization, is useful to accelerate that development. In particular, the subject of this paper is the behavior of the ions of I – VI in a mass spectrometer. The electron ionization (EI) mass spectra of these compounds (4-RC6H4NH–C5H5O, R = F, Br, Cl, H, CH3, and OCH3) at several nominal electron energies are already known4,5. A common structural characteristic is evidenced by the presence of the complementary fragment ions [C5H5O]+ (m/z = 81) and [RC6H4NH]+ ([M – C5H5O]+), whose abundances reflect the competition between the 2-methyfuran (–C5H5O) and the aniline (4-RC6H4NH–) moieties for the charge (Table 1). [C5H5O]+ is the main fragmentation product in all the spectra (with the exception of R = OCH3), even when they are acquired using low ionizing electron energies (8 eV). In turn, [M – C5H5O]+ appears in all the spectra acquired at high energies (70 and 40 eV), in most cases with much less abundance. The tendency for the charge to stay on the methylfuran moiety after the fragmentation is weakened by the electron-donor substituents, with the methoxy group having the most important effect thereby showing both fragment ions with similar abundances.[4] The ions [C5H5O]+ and [M – C5H5O]+ had been supposed to be formed by direct C–N bond dissociations of the molecular ions of N-(2-furylmethyl)aniline4,5.


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Nevertheless, isomerizations can be more important than direct dissociations for the structural units that compose N-(2-furylmethyl)aniline –aniline and 2-methylfuran–, when considered separately. The fragment ion [C5H5O]+ is also produced from the 2-methylfuran molecular ions ([VII]+••), being the base peak in the 70-eV mass spectrum and the main product formed by metastable decomposition.6 According to previous DFT/RRKM theoretical calculations, the metastable ion [VII]+•• undergoes a multi-step ring-expansion before dissociation (Scheme 1) that ends in the pyrylium ion (C) as the structure of [C5H5O]+, in a process initiated by a 1,2hydrogen migration from the methyl group7,8 (ring expansions of furan-like systems had even been reported in other gas-phase ionic reactions, such as the rearrangements of protonated alkylfurans9,10). In turn, the aniline molecular ion can also experience extensive rearrangement before fragmentation. Some of these processes lead to [M – HNC]+• (m/z 66) as both one of the more abundant fragment ions in the EI mass spectrum[11] and the main metastable fragmentation product12,13,14. In a simplified way (Scheme 2), the aniline ring must be contracted to a fivemembered ring which leads to the cyclopentadiene fragment ion13 (the reactions highlighted by the box in Scheme 2 represent the minimum energy reaction pathway (MERP) to [M – HNC]+•). An RRKM/DFT kinetic model based on this mechanism13 has managed to successfully reproduce the photoelectron-photoion coincidence (PEPICO) decomposition rate15 of the aniline molecular ion. The process can be initiated by a 1,3-hydrogen migration from the amino group (another possibility reported is the 1,2-hydrogen shift). The ring-expansion to produce [M – H]+ ions is also possible, but fragmentations by this reaction channel result energetically more demanding13.


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In the present work, density functional theory is employed to generate the potential energy profiles for multiple parallel and consecutive processes by which the molecular ions of I – VI might be fragmented to [C5H5O]+ (m/z = 81) and [M – C5H5O]+, with each fragment ion (and the corresponding neutral) having two possible structures, depending on whether the dissociation process takes place on the original molecular ion or on some isomer.

The isomerization

mechanisms checked here are based on the previous results for the aniline13 and 2-methylfuran7,8 ions. The calculations are carried out at the UB3LYP/6-311G+(3df,2p)//UB3LYP/6-31G(d) level of theory, which is the same level as used by Choe to study the competitive losses of HNC and H• from the aniline molecular ion13 and isomerizations of chlorotoluene molecular ions16. (Among fourteen DFT functionals, the best ones to accurately calculate homolytic C–N bond dissociation energies for three different types of molecules are BB1K, MPWB1K and M06, however B3LYP becomes the best choice for amines such as methylamine with a deviation of 1 kJ / mol17). Molecular parameters and energies obtained by DFT calculations are then employed in RRKM calculations of individual rate coefficients for a large number of reaction steps. (The vibrational frequencies and potential energy distribution for the amino group in adenine obtained from the B3LYP calculations are more reliable than those obtained at the MP2 level18). Some steps are discarded by analyzing their rate coefficients, the energy barrier heights or both. To simplify the kinetic equations, some approximations are applied to the main isomeric ions, allowing the relative overall decomposition rate coefficients to be calculated.


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B. COMPUTATIONAL METHODS All density functional theory calculations were carried out by the Gaussian 03 package19. The geometric parameters for all ions and transition states were completely optimized at the UB3LYP/6-31G(d) level. Each stationary structure was characterized as a minimum or a saddle point of first order by frequency calculations, which were also used to obtain the zero-point vibrational energies (ZPVE) and the vibrational modes.

Intrinsic reaction coordinate

calculations20 were carried out in all cases to verify that the localized transition state structures connect with the corresponding minimum stationary points associated with reactants and products. To obtain more reliable energy results, single-point calculations were performed at the UB3LYP/6-311G+(3df,2p) level using the UB3LYP/6-31G(d) equilibrium geometries. The UB3LYP/6-31G(d) harmonic frequencies were scaled down by 0.980621 to calculate the zero-point vibrational energies (ZPVE), and by 0.961421 to be used in the RRKM calculations. RRKM microcanonical rate coefficients, k(E), for a great deal of reaction steps were calculated from Eqn (1) 22, using the vibrational frequencies, and critical energies (barrier heights) from the DFT calculations as input data. ‡ 1 In Eqn (1), σ is the reaction degeneracy23, N‡(E – E0) is the transition state sum of states from 0 to E – E0, h is Planck’s constant, and ρ(E) is the parent ion density of states at energy E. The low frequency internal torsional modes were treated as vibrations in the RRKM calculations. All RRKM calculations were performed by the MassKinetics program24 (which uses the Beyer– Swinehart algorithm to calculate the density and sum of states by a direct count).


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To compare the various rate coefficients obtained from the same potential energy surface, and perform mathematical operations on them, all these k(E) curves were displaced to coincide with the same zero-point energy: the ground-state energy of the corresponding molecular ion. Magnitudes of the k(E)’s at the same energy were used as the criterion to accept or reject steps in a reaction mechanism, and to decide whether a step was or not reversible. Differential rate equations were set up on the basis of the simplified profiles. Then their complexity were reduced by using either the pre-equilibrium approximation or the steady-state approximation25. Mathematica package26, version 8.0, was used to solve the resulting simultaneous algebraic equations and find expressions for the concentrations. The expressions obtained for the overall rate coefficients of the two fragmentations from the N-(2-furylmethyl)aniline molecular ion turn out to be too much complicated to be broadened out to the other ions, however the calculations were enormously simplified by taking the product branching ratios as the quotients of each fragmentation over the total rate coefficients. Once the branching ratios were obtained for the six molecular ions, a new zero-point energy was chosen to compare the substituted ions with one another. Since most of the excess energy of molecules is deposited by electrons in the ion source, the ground-state energy of all the molecules was considered as the zero point. With this aim, the ionization potentials of the molecules were calculated as the energy differences between the ground states of the molecular ion and the corresponding molecule.

C. RESULTS AND DISCUSSION Fig. 2 shows the potential energy profiles for the several pathways by which the molecular ion of the unsubstituted N-(2-furylmethyl)aniline can be decomposed until the complementary fragment ions [C5H5O]+ and [M – C5H5O]+. The corresponding reaction mechanisms are represented in


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Scheme 3. The molecular models obtained for some selected ions are provided in Supporting Information. Simplifying the energy profiles The structures tested for the fragmentation products are highlighted by a double-line box in Scheme 3. For products [C5H5O]+ + [HC6H4NH]•, these structures are (i) A (furfuryl cation) and B• (anilenium radical), (ii) A and D• (azatropylium radical), (iii) C (pyrylium cation) and B•, and (iv) C and D•. The complementary products [C5H5O]• + [4-HC6H4NH]+ have the analogous structures: (i) A• (furfuryl radical) and B (anilenium cation), (ii) A• and D (azatropylium cation), (iii) C• (pyrylium radical) and B, and (iv) C• and D. Energetics of these and other species can be seen in Fig. 2. Which of these products can be formed depends on whether or not the molecular ion undergoes isomerization processes before the C–N bond dissociation, and on what kind of isomerization occurs. Rearrangement reactions might come about on the aniline ring (to yield products (ii)), the methyl furan moiety (products (iii)), or both (products (iv)). On the other hand, direct dissociations yield products (i). However, according to Fig. 2 most of the steps that exclusively take place on the methylfuran moiety seem to be much more probable than others because of their smaller energetic requirements. These steps are highlighted by wider lines in the profiles. At first, because of the internal rotor that contains the H–CH–N–H dihedral angle, the molecular ion can exist as two conformers (models 1 and 1a in Supporting Information) having a relatively small energy barrier between them (Fig. 2). Further reactions might be initiated at the CH–H, C–N or N–H bonds of the CH2–NH group in these conformers. The C–H bond can commence 1,2-hydrogen shifts to the furan ring, 1 2 and 1a 2a; the C–N bond can be broken by either heterolytic cleavages


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that lead to [C5H5O]+ (1 A + B• and 1a A + B•) or homolytic ruptures that give rise to [HC6H4NH]+ (1 A• + B, 1a A• + B); and the hydrogen atom of the N–H might be transferred to the aniline ring, 1 3 and 1a 4. The last steps would lead to intermediates analogous to those obtained from the aniline molecular ion (Scheme 2), nevertheless in this case aniline-ring rearrangements have the highest barriers in Fig. 2, which is true not only for the first steps but also in posterior reactions of isomeric species, such as 2 7, 2 8 and 11 28. Steps like these will be suppressed to simplify a subsequent approximate kinetic treatment. Other reactions that will be discarded because of their higher energetic requirements are the dissociation step of the isomeric ion 12, 12 C• + B, and the two-step ring expansion pathway from 2, 2 5 18. In turn, as suggested in Scheme 4(a), the remaining steps from the molecular ions (1 A + B•, 1 2, 1 A• + B, 1a A + B•, 1a A• + B and 1a 2a) will be considered as irreversible for the following two reasons. First, the barrier heights for reverse rearrangement reactions (e.g. 2 1 or 2a 1a) are greater than those corresponding to the successive steps through the isomerization pathways (e.g. 2 10 or 2a 9), and second, under low-pressure mass-spectrometric conditions, once an ion is dissociated the products will not be recombined back. The microcanonical rate coefficients for the individual reaction steps from the initial conformers are represented in Fig. 3. (It should be noted that the transition states for the dissociation reactions marked out by dashed lines in Fig.2 could not be found. In these cases, the RRKM rate coefficients were estimated by taking the set of vibrations of the dissociating ions minus one, which was believed to correspond to the reaction coordinate, as the frequencies required in the transition state sum of states in Eqn (1). In turn, the reaction energies at 0 K were used as an estimation of the kinetic barriers E0).

As expected, the interconversion between the two


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conformers (1 ⇔ 1a) is by far the most probable step over the full range of energies, which allows these structures to be considered as being practically at equilibrium in an approximate kinetic treatment. On the other extreme, the rearrangements initiated at nitrogen, 1 3 and 1a 4 are less likely reactions, thereby strengthening their rejection from the mechanism. Up to this point, the 1,2-hydrogen migrations initiated at the CH2 group (1 2, 1a 2a) seem to be more important than direct dissociations such as 1 A + B• or 1a A + B•, but it is necessary to wait for the rate coefficients for successive steps along these isomerization pathways and their corresponding kinetic handling. Kinetic treatment of the N-(2-furylmethyl)aniline molecular ion decomposition mechanism In Fig. 3, the forward and reverse rate coefficients of the conformational change step 1 ⇔ 1a are much larger than all the others, hence it should be reasonable to apply the pre-equilibrium approximation to these species. According to this approximation, the slowness of the other steps gives 1 and 1a enough time to essentially reach an equilibrium state25, that is, [1] = [1]eq and [1a] = [1a]eq. This way, the ratio [1a]/[1] can be considered as a microcanonical equilibrium constant over the energy range in which the pre-equilibrium is maintained. The equilibrium constant can be calculated either from the density of states of the ions 1 and 1a27 or from the mass action law as the ratio of the forward rate coefficient to the reverse one, K3 = k3/k-3 (Eqn (2)). In turn, the ions 1 and 1a can be grouped together and called M1, then the total concentration of the conformers [M1] is that given in Eqn (3). Eqns (4) and (5) define the concentrations of the conformers in terms of M1.

≡

2, ≡ 3


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1 4, 5 1 1

The decay rate of the initially formed N-(2-furylmethyl)aniline molecular ions is obtained by adding d[1]/dt and d[1a]/dt, which under the equilibrium condition (Eqn (2)) yields Eqn (6), with the k’s being defined as in Scheme 4(a). This rate is made up of the following three competitive channels, namely: two direct dissociations –one leading to the fragment ion A (1 A + B•, 1a A + B•) and the other to the complementary ion B (1 A• + B, 1a A• + B) –, and the 1,2hydrogen migrations to the furan ring (1 2 and 1a 2a). The reaction rate for each channel can be extracted from Eqn (6) and rewritten in terms of the total concentration of the molecular ion conformers [M1] by using Eqns (4) and (5), which is set up in Eqns (7) – (9). This way, the rate coefficients for the three channels turn into kd1, kd2 and krH = krH1 + krH2, thereby simplifying Scheme 3 to 4(b). ! " # $ % 6

# '( , where '(

# 7 for → 1 2• 1

! $ '3 , where '3

! $ 8 for → 1• 2 1

" % 56 , where 56 56( 563 , and 56(

" % , 563 9 for ;, ;< 1 1

The three decomposition modes of the conformers M1 are plotted against energy in Fig. 4. At low energies, the most important process is the isomerization krH, but the dissociation kd1 has a slightly more pronounced slope and overcomes krH at high enough energies. Following the


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isomerization channel, the rearranged furan-like ring of the ions 2 and 2a can easily be opened to give rise to a mixture of 9, 10, 11, 14, 15 and 16. The magnitudes of the corresponding RRKM rate coefficients (Supporting information) suggest that these ring-opened intermediates form a loop (Scheme 4(b)). The most important node in the loop is located at 11 because it corresponds to the isomeric species that undergoes a ring closure to the six-membered ring ion 12, which, in turn, initiates the dissociation that lead to the pyrylium ion C via the non-covalent complex 13 (it should be noted that, our analysis according to the NBO methodology28, 13 has most of its positive charge on the pyran ring, consequently it has to give rise to C rather than C•). The ten intermediates of Scheme 4(b), including 12 and 13, bring about ten differential rate equations which can be simplified by applying the steady-state approximation as a hypothesis to attain ten simultaneous algebraic linear equations. The solution of this system yields the steady-state concentrations of all the intermediates as functions of [M1] (these expressions are too complicated to be written here). =>?@AB@C=

RRKM Branching Ratios of the

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