Abstract

Protonation sites in methyl nitrate (1) were evaluated computationally at the Gaussian 2(MP2) level of ab initio theory. The methoxy oxygen was the most basic site that had a calculated proton affinity of PA = 728–738 kJ mol⁻¹ depending on the optimization method used to calculate the equilibrium geometry of the CH₃O(H)–NO₂⁺ ion (2⁺). Protonation at the terminal oxygen atoms in methyl nitrate was less exothermic; the calculated proton affinities were 725, 722, and 712 kJ mol⁻¹ for the formation of the syn–syn, anti–syn, and syn–anti ion rotamers 3a⁺, 3b⁺, and 3c⁺, respectively. Ion 2⁺ was prepared by an ion–molecule reaction of NO₂⁺ with methanol and used to generate the transient CH₃O(H)–NO₂^· radical (2) by femtosecond collisional electron transfer. Exothermic protonation of 1 produced a mixture of 3a⁺–3c⁺ with 2⁺ that was used to generate transient radicals 3a–3c. Radical 2 was found to be unbound and dissociated without barrier to methanol and NO₂. Radicals 3a–3c were calculated to be weakly bound. When formed by vertical neutralization, 3a–3c dissociated completely on the 4.2 μs time scale of the experiment. The main dissociations of 3a–3c were formations of CH₃O^· + HONO and CH₃ONO + OH^·. The gas-phase chemistry of radicals 3a–3c and their dissociation products, as studied by neutralization–reionization mass spectrometry, was dominated by Franck–Condon effects on collisional neutralization and reionization. The adiabatic ionization energies of 3a–3c were calculated as 7.54, 7.57, and 7.66 eV, respectively.

Article Outline

• Experimental

• Methods

• Materials

• Calculations

• Results and discussion

• Protonation sites in methyl nitrate

• Radicals 2 and 3a–3c

• Radical energetics

• Dissociation and addition kinetics

• Conclusions

• Acknowledgements

• References

Reactions of small radicals (H, halogen, OH, alkyl, etc.) with nitrogen oxides, nitro compounds, and nitrates have been of interest because of their relevance to tropospheric photochemistry [1 and 2], combustion [3], and chemistry of energetic materials [4]. The kinetics of numerous radical reactions have been studied by photolytic methods that employed optical spectroscopy or mass spectrometry [5] as detection methods [6]. Although photolytic methods provide quantitative data on the bimolecular reactivity of simple radicals, they rarely provide information about the nature and properties of reactive intermediates of radical reactions. The knowledge of reactive intermediates is mandatory for deducing reaction mechanisms of radical reactions and determining or even predicting branching ratios in complex reaction schemes.

Neutralization–reionization mass spectrometry (NRMS) [7] provides a powerful tool for both the formation and analysis of transient intermediates [8]. In NRMS, a stable precursor ion is prepared by the methods of gas-phase ion chemistry that has the structure, i.e., bond connectivity, of the neutral intermediate of interest. The ion is accelerated to a high velocity (>100,000 m s⁻¹) corresponding to 5–10 keV kinetic energy and discharged by a glancing collision with a polarizable electron donor. Because the electron transfer event lasts only a few femtoseconds, vibrational relaxation cannot occur during the collision, and the neutral species is formed with the structure and geometry of the precursor ion. NRMS thus allows one to prepare transient neutral species in a “nonchemical” manner, meaning that the time scale for the formation of the neutral intermediate (10⁻¹⁵ s) is much shorter than that for the fastest chemical reactions (10⁻¹³ s).

The NRMS approach has been used by us and others to generate several transient molecules and radicals [8]. In addition to preparing transient intermediates, NRMS has also been used for elucidating their unimolecular dissociations. To this end, the method of variable-time NRMS has been introduced [9] to provide rate parameters for competitive dissociations of both neutral intermediates and cations formed by neutral reionization [10]. In addition, long-lived electronic states of neutral intermediates produced by femtosecond collisional electron transfer can be probed by laser photoexcitation [11]. This provided access to photochemically dark excited states of short-lived neutral intermediates that could not be populated by single photon absorption [12].

In this work we report on the generation and dissociations of radicals 2 and 3 derived from methyl nitrate (1). Radical 2 can be viewed as a transient product of association of methanol with nitrogen dioxide (Scheme 1). The isomeric radicals 3a–3c can be viewed as convergent intermediates of hydroxyl radical addition to methyl nitrite, hydrogen atom addition to methyl nitrate, methoxyl radical addition to nitrous acid, or methyl radical addition to nitric acid (Scheme 2). Because NRMS does not provide direct information about the energetics of transient intermediates, we also report Gaussian 2(MP2)-level ab initio and density functional theory calculations to estimate radical and ion relative and dissociation energies, and activation barriers. The latter are used for RRKM calculations of rate constants for unimolecular dissociations and transition-state theory rate constants for radical additions at the high-pressure limit.

Experimental

Methods

Neutralization–reionization mass spectra were measured on a tandem acceleration–deceleration mass spectrometer as described previously [13]. Samples were introduced into the ion source from a glass liquid inlet maintained at or below room temperature. Cation radicals were produced by electron ionization (EI) at 70 eV and 200 °C. Gas-phase ion–molecule reactions were performed in a tight chemical ionization source at 0.2–0.4 Torr of reagent gas and 250–300 °C. Precursor ions were extracted from the ion source, focused by a radio frequency (rf)-only quadrupole analyzer, and accelerated to 8250 eV kinetic energy. Collisional neutralization of fast ions was performed with dimethyldisulfide that was admitted to the first collision cell at a pressure to achieve 70% transmittance of the precursor ion beam. The cation radical of nitric acid was neutralized by collisions with xenon at 70% transmittance of the precursor ion beam. Xenon was used in order to avoid overlap of the very weak peak of HNO₃^+· at m/z 63 with peaks from residual dimethyl disulfide at adjacent m/z values. Neutral intermediates were reionized after 4.2 μs by collisions with oxygen at pressures that achieved 70% transmittance of the precursor ion beam. The ions were decelerated to 80 eV kinetic energy, energy-filtered, and mass analyzed by a second quadrupole analyzer operated at unit mass resolution. 30–130 scans were typically accumulated and averaged to give a NR mass spectrum and the measurements were reproduced over a period of several weeks. Accurate ion masses, metastable-ion, and collisionally activated dissociation (CAD) spectra were measured on a JEOL HX-110 double-focusing mass spectrometer operated at 10 kV. For accurate mass measurements the mass resolution was >10,000 (10% valley definition). CAD spectra were obtained with air as collision gas at 70 and 50% transmittance of the precursor ion beam. The mass resolution was >500 and the products were detected by a linked B/E scan.

Materials

Methyl nitrate was prepared by esterification of nitric acid with methanol in the presence of sulfuric acid [14]. Anhydrous nitric acid was obtained by treating commercial 70% azeotrope (Fisher) with phosphorus pentoxide followed by vacuum distillation.

Calculations

Standard ab initio calculations were performed by using the Gaussian 98 suite of programs [15]. Geometries were optimized with density functional theory calculations using Becke’s hybrid B3LYP functional [16] and the 6-31+G(d,p) basis set. For selected species, geometries were also optimized with B3LYP/6-311+G(2df,p) and with Møller–Plesset theory calculations [17] truncated at second order, MP2(FULL)/6-31+G(d,p) or MP2(frozen core)/6-311+G(2df,p), as discussed below. Spin unrestricted calculations (UB3LYP and UMP2) were performed for open-shell species. Spin contamination in UB3LYP calculations was small, as judged from the S² expectation values that ranged between 0.75 and 0.77. Spin contamination in UMP2 calculations was low to moderate for most species, S² = 0.76–0.78 for local minima and 0.97–0.99 for dissociation transition states. This was partially corrected by Schlegel’s annihilation procedure [18] that decreased the total energies by 2–5 mhartree (4 mhartree rmsd) for local minima and 16 mhartree for transition states. The optimized structures were characterized by harmonic frequency analysis as local minima (all frequencies real) and first-order saddle points (single imaginary frequency). The harmonic frequencies are available from the correspondence author upon request. The B3LYP frequencies were corrected by 0.963 [19], the MP2(FULL) frequencies were corrected by 0.931 and used to calculate zero-point vibrational corrections and 298 K enthalpies. For enthalpy calculations we used the rigid rotor-harmonic oscillator (RRHO) approximation. Alternatively, low-frequency vibrations, e.g., the methoxy torsion (139 cm⁻¹) and methyl torsion (202 cm⁻¹) in methyl nitrate, and the methyl torsion (68 cm⁻¹), methoxy torsion (123 cm⁻¹) and C–O–N bend (169 cm⁻¹) in ion 2⁺, were treated as free rotors. This treatment resulted in 298 K enthalpies that differed from those from RRHO calculations by 1–2 kJ mol⁻¹. Such small differences were deemed insignificant at the present level of theory, and therefore the data discussed in text refer to enthalpies that were based on the RRHO approximation.

Single-point energies were calculated with the composite G2(MP2) procedure [20] using the B3LYP and MP2(FULL) optimized geometries and ZPV energies. The G2(MP2) energies were much less sensitive to spin contamination because of cancellation of errors in the MP2 energies. The UMP2 and PMP2 based G2(MP2) energies were within 0.4 mhartree (1 kJ mol⁻¹) for local minima and within 0.7 mhartree (1.8 kJ mol⁻¹) for transition states. Franck–Condon energies (E_FC) were calculated as differences in the single-point energies of radicals formed by adding an electron to the optimized cation structures and fully optimized radical structures. No ZPVE corrections were made in the E_FC estimates. RRKM calculations were performed with direct count of quantum states using Hase’s program [21] as reported previously [22].

Results and discussion

Protonation sites in methyl nitrate

Formation of transient neutral intermediates relies upon unambiguous preparation of stable precursor ions. For hydrogen atom adducts, gas-phase protonation provides a general methodology for the preparation of precursor cations [23]. Hence, protonation sites in multifunctional molecules become of interest and importance [24]. Protonation of 1 has been reported to yield two isomers, 2⁺ and CH₃O–NO₂H⁺, 3⁺, depending on the gas-phase acid used [25 and 26]. Ions 2⁺ and 3⁺ were distinguished by ion–molecule reactions, and also through metastable-ion and CAD spectra [26]. Previous high-level ab initio calculations of Lee and Rice [27] and Glaser and Choy [28] identified a single conformer of 2⁺ to be a complex of methanol and NO₂⁺ (Figure 1). Isomer 3⁺ belongs to a group of three stable rotamers 3a⁺–3c⁺ (Figure 2). Lee and Rice reported the topical proton affinity at the methoxyl oxygen atom in 1 as PA(0 K) = 740 kJ mol⁻¹, whereas the terminal oxygen atom in 1 had PA(0 K) = 720 kJ mol⁻¹.

Because the PA values and isomer relative stabilities of Lee and Rice differed from those of Glaser and Choy [28] and also from the earlier, lower-level, calculations of Bernardi et al. [29], we performed new calculations at the G2(MP2) level using equilibrium structures that were optimized with B3LYP and MP2(FULL) and two different basis sets (Figure 1 and Figure 2). The G2(MP2) calculations use a similar level of theory [QCISD(T)] to treat the correlation energy as did the CCSD(T) calculations of Lee and Rice. However, the G2(MP2) single-point energies are extrapolated to the 6-311+G(3df,2p) basis sets, which is substantially larger than the DZP basis set used by Lee and Rice [27]. The G2(MP2) calculated ion relative energies, dissociation energies, and proton affinities are summarized in Table 1. Our data confirm the conclusions of Lee and Rice in that 2⁺ is more stable than the most stable rotamer 3a⁺. The G2(MP2) topical proton affinity in 1 to form 2⁺ depended on the basis set and, in particular, on the method used to optimize the ion structure. B3LYP optimizations consistently yielded shorter CH₃O(H)–NO₂ bonds than did MP2 optimizations (Figure 1). In contrast, very similar structures were obtained for 1 using B3LYP and MP2(FULL) (Figure 1). The MP2 optimized structures of 2⁺ agreed reasonably well with those reported by Lee and Rice at their highest levels of theory [27]. The topical proton affinity of 1 to form 2⁺ was calculated as 727–745 kJ mol⁻¹ (Table 1); the closest agreement with the experimental value (733.6 kJ mol⁻¹ [30]) was obtained by G2(MP2) calculations that were based on B3LYP/6-311+G(2df,p) optimized geometries, ΔPA = PA_calc − PA_exp = 4.2 kJ mol⁻¹) and MP2(FULL)/6-31+G(d,p) optimized geometries (ΔPA = −4.7 kJ mol⁻¹) (Table 1). Table 1 also shows the 0 K values which are in a reasonable agreement with the previous values reported by Lee and Rice [27]. The lowest dissociation energy of 2⁺ to form CH₃OH and NO₂⁺ at 298 K was calculated with G2(MP2) as ΔH_r,298 = 71 and 89 kJ mol⁻¹ when based on the B3LYP and MP2(FULL) optimized geometries, respectively. This bracketed the estimate based on experimental heats of formation, ΔH_r,298 = 82 kJ mol⁻¹. Thus, ion 2⁺ is relatively weakly bound against dissociation.

Formations from 1 of the less stable isomers 3a⁺, 3b⁺, and 3c⁺ were accompanied with −ΔH_r,298 = PA = 725, 722, and 712 kJ mol⁻¹, respectively (Table 1). Note that for 3a⁺–3c⁺ the G2(MP2) proton affinities that were based on B3LYP and MP2(FULL) geometries agreed within 1 kJ mol⁻¹.

In addition to isomers 2⁺ and 3a⁺–3c⁺ we also sought a proton-bound complex, CH₃O H⁺ ONO (4⁺), following a suggestion by a referee. However, attempts at geometry optimization with B3LYP and MP2(FULL)/6-31+G(d,p) resulted in dissociation of the CH₃OH–ONO bond. This result is not that unusual, given the fact that the oxygen atoms in NO₂⁺ carry a positive charge [+0.22 each from Mulliken populations with the 6-311+G(2df,p) basis set], and so they are not suitable for hydrogen bonding. The calculations indicated the existence of an ion–dipole complex between NO₂⁺ and CH₃OH, which was less stable than 2⁺ and was not studied in further detail.

The topical proton affinities in 1 were too close to allow for selective protonation of either oxygen atom. However, isomer 2⁺ can be prepared selectively by an ion–molecule reaction of NO₂⁺ with methanol (eq 1) [25]. In this work, NO₂⁺ was generated by dissociative ionization of 1 and allowed to react with an excess of methanol in a CI ion source:

Note that 1 does not provide a stable molecular ion that could contaminate 2⁺ by its ¹³C satellite. Note also that 1 cannot be protonated by methanol CI, because the proton affinity of methanol (754 kJ mol⁻¹) makes the proton transfer from CH₃OH₂⁺ to 1 endothermic by 20 kJ mol⁻¹. Ion 2⁺ was characterized by accurate mass measurements (measured 78.0191, CH₄NO₃ requires 78.0191) and by metastable-ion and CAD spectra (Table 2).

The less stable isomers 3a⁺–3c⁺ were generated by exothermic protonation of 1 with CH₅⁺ in methane CI (PA(CH₄) = 543.5 kJ mol⁻¹) [30]. According to the calculated topical PA values (Table 1) protonation at the terminal oxygen atoms was 168–182 kJ mol⁻¹ exothermic, whereas protonation at the methoxyl oxygen was 190 kJ mol⁻¹ exothermic. The latter energy exceeded the dissociation energy of the CH₃O(H)–NO₂⁺ bond in 2⁺ (82.5 kJ mol⁻¹) and indicated that a fraction of 2⁺ formed by methane CI should dissociate rapidly. The fraction of remaining 2⁺ that would contaminate isomers 3a⁺–3c⁺ should depend on (1) the initial internal energy of 2⁺ that determines the rate constant for unimolecular dissociation, (2) the collision frequency that determines the rate of collisional cooling, and (3) the energy transferred to the methane bath gas in a collision (ΔE).

We used RRKM calculations to estimate the unimolecular rate constants for the lowest-energy dissociation of 2⁺ to CH₃OH and NO₂⁺, k(E), and compared them with the frequency for cooling collisions of 2⁺ with methane (k_coll) at typical ion source conditions (0.4 Torr and 523 K) that was estimated from the Langevin formula as k_coll = 7.7 × 10⁶ s⁻¹ [31]. The internal energy in 2⁺ formed by exothermic protonation with CH₅⁺ was estimated by partitioning the reaction exothermicity between the reaction products (2⁺ and methane) according to their 523 K heat capacities. Partitioning among vibrational degrees of freedom apportioned 177 kJ mol⁻¹ to 2⁺, partitioning among vibrational and rotational degrees of freedom predicted that 2⁺ received 151 kJ mol⁻¹. These estimates were not too different from those based on the dynamics calculations of Uggerud that predicted 80%–85% of protonation exothermicity to be deposited in the ion [32]. The RRKM rate constants for the dissociation to CH₃OH and NO₂⁺ of 2⁺ possessing 151 and 177 kJ mol⁻¹ internal energy were 4.6 × 10⁹ and 1.4 × 10¹⁰ s⁻¹, respectively. Thus, even if allowance is made for the neglect of anharmonicity effects that could make the RRKM rate constants too high [33], energetic ions 2⁺ from protonation with CH₅⁺ should dissociate before undergoing the first cooling collision.

Can stable 2⁺ be formed by methane CI? Methane plasma contains significant fractions of C₂H₅⁺ and C₃H₅⁺ ions [31]. From the proton affinity of C₂H₄ (PA = 680 kJ mol⁻¹) [30] it follows that protonation of 2 with C₂H₅⁺ was 53 kJ mol⁻¹ exothermic, so that a fraction of 2⁺ thus formed should be formed with internal energies below the lowest dissociation threshold.

Unimolecular isomerization of 3a⁺ to 2⁺ was studied previously by Glaser and Choy who obtained a 238 kJ mol⁻¹ barrier in the transition state [28]. This barrier appears too high to allow a fraction of energetic 3a⁺–3c⁺ formed by exothermic protonation with CH₅⁺ isomerize to the more stable 2⁺. However, even if the barrier was lower and isomerization occurred, ion 2⁺ would be formed with a large excess of energy and it should dissociate rapidly to CH₃OH and NO₂⁺ (vide supra). Hence in the absence of cooling collisions, unimolecular isomerization of 3a⁺–3c⁺ cannot produce stable 2⁺.

The predictions based on the ion dissociation energetics and RRKM calculations were compatible with experiment. Isomer 2⁺, prepared according to eq 1, and 3a⁺–3c⁺ prepared by methane CI protonation of 1 gave distinct CAD spectra (Table 2). The major differences were in the relative intensities of NO⁺ which was produced more abundantly from 3a⁺–3c⁺, and CH₃OH^+·/CH₂OH⁺ which were produced more abundantly from 2⁺ [26]. However, the CAD spectrum of 3a⁺–3c⁺ did not contain unique fragment ions for either precursor structure, and could correspond to a mixture of 2⁺ and 3a⁺–3c⁺.

Radicals 2 and 3a–3c

Collisional neutralization of 2⁺ and the mixture of 2⁺ with 3a⁺–3c⁺ followed by reionization provided distinct NRMS spectra (Figure 3). A common feature of the NRMS spectra was the absence of survivor ions corresponding to reionization of intermediate radicals 2 and 3a–3c. However, the NRMS spectra differed in the relative intensities of NO₂⁺, NO⁺, methanol ions CH₃OH^+· and CH₂OH⁺, and CHO⁺, OH⁺, and O^+·. The formation of methanol ions from 2⁺ may in part be due to reionization of neutral methanol molecules produced by collateral CAD of 2⁺. Presuming exclusive formation of neutral CH₃OH and NO₂ from dissociation of 2, the ion currents pertinent to those products should be given by the pertinent cross sections for collision ionization. Although the latter are unknown for collisional ionization of molecules of kiloelectron volt kinetic energies, they can be approximated by the cross sections for electron ionization which indicate σ(CH₃OH)/σ(NO₂) = 4.25/3.69 = 1.15 [34 and 35]. In contrast, the ion currents in the NR mass spectrum of 2⁺ due to CH₃OH and NO₂, as determined from the sums of pertinent ion intensities, were in a 4.95/1 ratio, which indicated that 77% of the CH₃OH that appeared in the NR mass spectrum was formed by CAD of 2⁺. In contrast, the low relative intensity of methanol ions in the NRMS spectrum of 3a⁺–3c⁺ indicated that collateral CAD of 3a⁺–3c⁺ was not efficient to compete with collisional neutralization. Note that loss of neutral CH₃OH was the most abundant dissociation upon CAD of 3a⁺–3c⁺ (Table 2).

In order to identify potential dissociation products of neutral 2 and 3a–3c, e.g., methanol, OH, NO, NO₂, HONO, HNO₃, CH₃ONO, and 1, we recorded the pertinent NR mass spectra (Figure 4). 1 does not give a stable molecular ion [36], and so the dissociations of reionized 1 were deduced from the EI mass spectrum of 1, which showed a dominant peak of NO₂⁺ (100%) and peaks of NO⁺ (31%) and CHO⁺ (25%) [36]. NR mass spectra of HONO [37] and CH₃ONO [38] gave only very weak survivor ions that were unsuitable for identifying these potential dissociation products. The NR mass spectrum of HNO₃ was also measured and showed a weak survivor ion in keeping with the EI mass spectrum [39]. The NR mass spectra further showed convergent formation of O^+· and NO⁺ from NO₂, HONO, HNO₃, and CH₃ONO. The CHO⁺ ion indicated formation from 2 or 3a–3c of neutral CH₃OH, CH₃ONO, and/or CH₃O. The NO₂⁺ ion could originate from NO₂, HNO₃, or 1, the NO⁺ ion could be formed from NO, NO₂, HONO, HNO₃, and/or CH₃ONO, and the OH⁺ peak could be formed from HONO and/or OH. In summary, the NR mass spectra of 2 and 3a–3c indicated very facile dissociations of these radicals following collisional neutralization. However, the various possible dissociations of neutral 2 and 3a–3c could not be distinguished unambiguously because of convergent NR dissociations of the potential products.

Radical energetics

Because of the difficult interpretation of the NR mass spectra we sought to gain some insight into the chemistry of 2 and 3a–3c through theoretical calculations of dissociation energetics and kinetics. The G2(MP2) relative energies at 0 K are shown in the potential energy diagram in Figure 5. The relative energies calculated at several levels of theory are summarized in Table 3. Radical 2 was found to be unbound, and upon attempted geometry optimization it dissociated exothermically to methanol and NO₂. This finding was not too surprising, because the analogous CH₃O(H)–NO radical has also been found to be unbound [37]. Furthermore, vertical neutralization of 2⁺ was accompanied by large Franck–Condon effects, such that vertically formed 2 was 152 kJ mol⁻¹ above the energy of CH₃OH and NO₂. Three stable structures were found for radicals 3a–3c (Figure 6). In contrast to ion structures 3a⁺–3c⁺ which had planar NO₃ groups (Figure 2) [27 and 28], radicals 3a–3c were all pyramidized at the nitrogen atoms (Figure 6). This resulted in smaller O–N–O bond angles in the radicals. In addition, the methyl groups and the O–H bonds which were in plane in the ions were rotated out of the O–N–O planes in the radicals. The most significant differences between the ion and radical structures were in the N–OCH₃ and N–OH bonds which were 0.1 Å longer in the radicals (Figure 6). According to Mulliken population analysis, the spin density in radicals 3a–3c was equally distributed between the nitrogen and terminal oxygen atoms. This could be viewed as the unpaired electron being delocalized in the singly occupied molecular orbital (SOMO) that was a π-type orbital with major expansion coefficients at the nitrogen and terminal oxygen atoms. The adiabatic ionization energies of 3a–3c were IE_a = 7.54, 7.57, and 7.66 eV, respectively, from G2(MP2) calculations (Table 4). Hence, collisional electron transfer from dimethyl disulfide (IE_a = 8.1 eV [40], IE_v = 8.96 eV [30]) to 3a⁺–3c⁺ was mildly endothermic, if equilibrium ion and neutral energies were concerned, but became >2 eV endothermic in femtosecond collisions that involved vertical transitions between the neutral and ion potential energy surfaces.