On the electronic structure of methyl butyrate and methyl valerate

. We present novel results of the analysis of the electronic structure of two aliphatic esters: methyl butyrate and methyl valerate. High-resolution photoabsorption spectra were collected and analyzed over the energy range 4.0–10.8 eV and showed for both the molecules not only a clear band of the HOMO to LUMO transition, but also vibronic structure associated with the ﬁrst Rydberg-valence transition. Photoelectron spectra recorded from 9 to over 28 eV revealed many ionization states with the ﬁrst adiabatic ionization energies found to be 9.977 eV and 9.959 eV for methyl butyrate and methyl valerate, respectively. Ab initio calculations have been performed in order to help assign the photoabsorption and photoelectron features. Photolysis life times in the atmosphere were calculated revealing that photolysis is not competitive over hydroxyl radical scavenging in the process of removal of these esters from the atmosphere.


Introduction
The knowledge of the electronic structure and properties of esters is of common interest in many disparate areas and therefore has been studied over many decades, however the data still needs to be updated either because they are outdated, were recorded with poor resolution, or are simply absent. Esters occur both naturally, being secreted from plants, and as a by-product of industrial processes. These compounds are widely used in the food and flavoring industry due to their distinct aroma [1,2], but they also are of potential interest to astrochemists, who find the smallest members of this group in the interstellar medium, which is of interest for their possible role in the origins of life [3]. Both molecules of interest can serve as insecticides [4]. Methyl valerate in its pure form is used as plasticizer [5] and shows potential for use in the production of biofuels [6]. Due to their low vapour pressure that makes them easy to handle, both esters are produced on a massive scale and thus are likely to be released into Contribution to the Topical Issue "Atomic Cluster Collisions (2019)", edited by Alexey Verkhovtsev, Pablo de Vera, Nigel J. Mason, Andrey V. Solov'yov.
Supplementary material in the form of one pdf file available from the Journal web page at https://doi.org/10.1140/epjd/e2020-10125-5 a e-mail: smialek@pg.edu.pl the atmosphere. Since it was shown that the main products of photolysis of such esters are carbon monoxide and dioxide, it is crucial to gain an insight into their structure, properties and photoabsorption cross sections [7]. Previously we have reported our findings on methyl formate [8], ethyl formate [9], isobutyl formate [10], ethyl acetate [11], isobutyl acetate [12] and some acetates and propionates [13]. Here we present our findings on a further two methyl esters: butyrate and valerate. The high-resolution VUV photoabsorption and photoelectron spectra presented here were measured for the first time for these compounds. The measured photoabsorption cross-sections have been used to calculate the photolysis lifetimes of these compounds in the upper atmosphere (20-50 km) of the Earth. The experimental findings are supported by theoretical calculations that allowed the determination of the ionization energies in the photoelectron spectra of both compounds and revealed predominantly mixed valence-Rydberg character of the transitions resolved in the photoabsorption spectra.
(PES) experiments were purchased from Sigma-Aldrich with a stated purity of 99%. The samples were degassed by repeated freeze-pump-thaw cycles with no further purification.

Photoelectron measurements
The photoelectron spectra of methyl butyrate, Figure 1, and methyl valerate, Figure 2, were measured at the VLS-PGM beamline [14] at the Canadian Light Source facility in Saskatoon, Canada, using a Double Toroidal Coincidence Spectrometer, that was designed and used for analysis of noble gases and small, diatomic molecules [15], but it has recently been demonstrated that it may also be used for measurements of more complex systems [16]. In our experiments we have used the data collected by the 180 • toroidal detector, set at a pass energy of 4 eV. The measured resolution from the nitrogen calibration spectra was 60 meV. The photoexcitation energy of the photoelectron spectrum presented here was 80 eV, recorded with the entrance and exit slits of the VLS-PGM beamline set at 50 µm. Spectra presented here were calibrated against the X 2 Σ + g , ν = 0 and A 2 Π u , ν = 0 peaks of N + 2 , rounded to three decimal places [17,18].
The stars marked on the spectra in the figures denote the 2 B 1 ionic state from some water contamination could also be used to check the accuracy of the calibration of the energy scale.

Photoabsorption measurements
The high-resolution VUV photoabsorption spectra of methyl butyrate, Figure 3, and methyl valerate, Figure 4, were measured at the UV1 beam line of the ASTRID synchrotron light source at Aarhus University, Denmark. The  experimental apparatus has been described in detail previously [19]. The sample pressure is measured using a capacitance manometer (Baratron). To ensure that the data were free of any saturation effects [20,21], the cross sections were measured over the pressure range 0.07-1.27 mbar with typical attenuations below 50%. A background scan is recorded with the cell evacuated. Absolute photoabsorption cross sections are then obtained using the Beer-Lambert attenuation law where I t is the radiation intensity transmitted through the gas sample, I 0 is that through the evacuated cell, n is the molecular number density of the sample gas, σ is the absolute photoabsorption cross section, and x is the absorption path length (15.5 cm) [22]. A small amount of water contamination (<15%) was observed in the spectra recorded for these samples. The water contribution was subtracted in the present spectra. Due to this, the accuracy of the cross-section is estimated to be around ±15%.

Computational methods
All the calculations have been performed using the Gaussian 16 rev B.01 code [23]. The geometry of the conformers was optimised at the MP2 level, as well as with density functional theory (DFT), using the ultrafine grid size. As discussed in detail in the Supplementary Information (SI), several methods were tested on the relative energies of the conformers and compared with previous works [24,25]. The M06-2X [26] was thus employed. The optimized geometry of the conformers was obtained using the tight criteria and unscaled zeropoint vibrational energies were calculated within the   harmonic approximation. The basis set used for these calculations is Dunning's aug-cc-pVTZ [27,28]. For the calculation of higher Rydberg states, this basis set was supplemented with a set of (8s8p3d) diffuse functions taken from Kaufmann et al. [22,29] centred on the carbon atom close to the middle of the molecule. The oscillator strengths were evaluated with the length gauge. The assignment of the transitions was performed by visual inspection of the Natural Transition Orbitals (NTO's) [30] using the Chemcraft software [31]. Finally, the ionization energies were obtained at the OVGF, P3 and renormalized P3+ levels (see [32,33] for recent reviews). Detailed information on computational methods and structure on both molecules can be found in the SI.

Structure of methyl butyrate and methyl valerate
According to previous results, there are eight possible conformers for methyl valerate [24] and four for methyl butyrate [25]. Nonetheless, the analysis of the rovibrational spectroscopic data shows that for both of these esters, only the (a, a), with C S symmetry, and (g±, a), with no symmetry, conformers are present in almost the same quantities. Therefore, only these two conformers were investigated. In Figures 5 and 6 the structures together with the highest occupied molecular orbital, HOMO, HOMO-1, HOMO-2 localization on both the conformers and LUMO for the (a, a) one, are shown for methyl butyrate and methyl valerate. The bond lengths can be found in the SI. The orbitals in square brackets denote the core ones, the remaining are valence orbitals. For the (a, a) conformer of methyl butyrate the electron configuration is [ Similarly, for methyl valerate the configuration of the (a, a) conformer is [1a 2 2a 2 3a 2 4a 2 5a 2 6a 2 7a 2 ] 8a 2 9a 2 10a 2 11a 2 12a 2 13a 2 14a 2 15a 2 16a 2 17a 2 1a 2 18a 2 2a 2 19a 2 3a 2 20a 2 21a 2 4a 2 22a 2 23a 2 5a 2 24a 2 6a 2 7a" 25a 2 and for the (g±, a) one: In all cases the HOMO, as in previously analyzed ester molecules, in the neutral ground state is localized predominantly on the terminal oxygen in-plane lone pair. In the case of methyl butyrate the HOMO is (22a ) 2 for the (a, a) conformer and (28a) 2 for the (g±, a) one, whereas for methyl valerate the HOMO is (25a ) 2 for the (a, a) conformer and (30a) 2 for (g±, a).
Since the distinct presence of both conformers contribute equally to the spectra, in this work we will refer to the states as the HOMO, HOMO-1, etc., meaning e.g. for HOMO of methyl butyrate both (22a ) 2 for (a, a) conformer and (28a) 2 for the (g±, a) one.

Photoelectron spectra
The photoelectron spectra of methyl butyrate and methyl valerate are shown in Figures 1 and 2. Based on the calculated values for both conformers, which are shown for methyl butyrate in Table 1 and methyl valerate in Table 2, it was possible to identify most of the ionization energies of both molecules. The values obtained based on the experimental spectra are also shown in the tables for comparison with the results of the calculations. The best accuracy was obtained for energies obtained from calculations using the P3+ method.
In the case of methyl butyrate it was not possible to resolve unambiguously the ionization energies of the third, fourth and fifth orbitals, since they appeared too close together. For methyl valerate it was the position of additional 2 orbitals for the (a, a) conformer and one for (g±, a) that were impossible to determine from the experimental spectrum.
The analysis of the first ionic state of both esters allowed not only the determination of the value of the first adiabatic and vertical ionization energies of the compounds, but also revealed a vibronic progression, similar to one seen for previous esters. This vibrational structure is depicted in Figure 7, top for methyl butyrate and bottom for methyl valerate. The obtained values are summarized in Table 3. With an average spacing of ν A = 0.153 eV for methyl butyrate and ν A = 0.151 eV for methyl valerate, the vibration corresponds to a combination of C-O stretch combined with C=O stretch, as found previously for other esters.

Valence states, transitions and Rydberg series in photoabsorption spectra
According to the calculations presented in Tables 4 and 5 The spectra of both molecules present distinct similarities in shape and energy position of detected transitions. Calculations reveal the highly mixed character of the transitions within the investigated range, thus there are no distinct features present, apart from the second band that was assigned to HOMO → 3s/σ* and HOMO-1 → 3s/σ* transitions, localized on the CH bond in both compounds. The mixed character of the transitions together with the complexity of the molecules and continuous overlap of the states at higher energies made it difficult to perform any unambiguous assignments. In the case of methyl butyrate, apart from a few members of some Rydberg series, a shoulder feature, marked A, was assigned to the HOMO-1 → LUMO transition for the (a, a) conformer together with a mixed transition HOMO-1 → LUMO + HOMO → 3d for the (g±, a) conformer, centered at 8.683 eV. A band labeled B at 9.124 eV was identified either as HOMO-3 → 3s/σ* for (a, a) or a mixed transition from HOMO-4 in (g±, a). The structure centered at 9.311 eV is most likely either another mixed transition from HOMO-4 orbital, but in (a, a), or a HOMO → 4p one in (g±, a).
Similarly, for methyl valerate, there are 3 bands A , B , C marked in the spectrum. The first, at 8.562 eV, was also assigned to a combination of HOMO-1 → LUMO for the (a, a) conformer together with a mixed transition HOMO-1 → LUMO + HOMO → 3d for (g±, a) conformer. The B band was tentatively assigned at 8.744 eV and corresponds to HOMO-1 → 3pπ + HOMO → 3dσ for the (a, a) conformer mixed with HOMO-1 → + HOMO-3 → 3sσ/σ* for (g±, a) one. The last band C at about 9.107 eV was assigned based on the calculations to either a mixed transition from HOMO-2 in (a, a) conformer or also a mixed one from HOMO-3 in (g±, a) conformer.
The HOMO → 3s/σ* transition in the case of both methyl butyrate and methyl valerate is associated with rather complex vibronic structure, marked for both esters in Figure 8. For both esters we identified three vibrational modes ν a , ν b , ν c (labeled with prime for methyl valerate) with an average energy spacing of 180, 68 and 48 meV,   respectively. The first mode, ν a , is present in all PA spectra of esters and corresponds to the most distinct vibration, resulting from the combination of C-O and C=O stretch. The ν b mode is most likely to be O=C-O deformation combined with a C-O stretch. A similar structure with an energy spacing of c.a. 90 meV was seen in the spectrum of ethyl formate [9]. The mode of average spacing of 48 meV, ν c , is ascribed to an OCC out-of-plane bend,   seen in the PA spectrum of isuobutyl acetate [10]. For methyl valerate we also resolved a ν d mode of 130 meV and assigned this to skeletal C-C stretching, which was also observed in methyl and ethyl formates [8,9].
In the photoabsorption spectrum of methyl valerate, a series of three peaks, evenly spaced with ν α = 144 meV appear at about 6.5 eV (Fig. 4). Such feature has not been observed previously for other ester molecules [8][9][10][11][12]. This series may be an additional vibrational mode, such as a series of C-C skeletal stretching, already seen here as ν d associated with the ν a mode.
Over the whole range of the photoabsorption spectrum investigated, only the first two members of the Rydberg series converging to the two highest ionic states were resolved, mainly due to state overlap as a result of the presence of the two conformers for each compound. The other transitions were assigned based purely on the results from the computer calculations and the value of the oscillator strength, since it was not possible to unambiguously determine the value of the ionization energy from HOMO-2, HOMO-3 and HOMO-4 for both esters. The resolved states are marked in Figure 3 for methyl butyrate and Figure 4.
The values obtained for Rydberg series converging to the first two ionization energies are summarized in Table 6 with the value of the quantum defect calculated using the well-known Rydberg formula. As for previously investigated esters, the ns series values of δ are between 0.7 and 0.9 for members of all transition families with the quantum defect values being higher for the transitions converging to HOMO-1 ionization band than those converging to the HOMO.

Atmospheric photolysis
There is a very little information on the possible interaction of free radicals with methyl butyrate and methyl valerate. There is also no information in the literature on the photolysis rate and thus the lifetimes of these esters in the upper atmosphere. Therefore, the present absolute cross sections can be used in combination with solar actinic flux [34] measurements from the literature to estimate the photolysis rate of both methyl esters in the atmosphere from an altitude close to the ground, to the stratopause at 50 km. Details of the calculation programme were published previously [35] and the quantum yield for dissociation following absorption in that programme is assumed to be unity. The reciprocal of the photolysis rate at a given altitude corresponds to the local photolysis lifetime.
Photolysis lifetimes of less than 1 sunlit day were calculated at altitudes above 30 km for methyl butyrate, which means that the molecules can be broken up quite efficiently by VUV absorption above this altitude. Also at ground level the lifetimes are shorter than one day. UV photolysis is therefore expected to play a significant role in the tropospheric and stratospheric removal of methyl butyrate.
For both methyl butyrate and methyl valerate the stratospheric lifetime is long, about 6 days at 30 km. The lifetimes at 10 km are extremely long for these molecules, reaching thousands of years. Therefore, photolysis will not be the main sink mechanism for the removal of the molecules from the atmosphere. This is similar to previously analyzed esters, ethyl and methyl formate, for which UV photolysis was also not expected to play a significant role, but in contrast to isobutyl formate, where photolysis may be a major removal mechanism.
The only relevant investigations found for these esters presented kinetic studies of hydroxyl radical reactions [36]. The lifetimes obtained there with typical tropospheric OH concentrations of 10 6 molecules per cm 3 yielded 3.5 days for methyl butyrate and 2.4 days for methyl valerate. This would certainly suggest that the reaction with OH radical would be a prevalent sink mechanism for both methyl butyrate and methyl valerate.

Conclusions
For the first time the complete electronic spectra of methyl butyrate and methyl valerate are presented here together with absolute photoabsorption cross sections from 4.5 to 10.8 eV. The structures that can be observed in the spectrum can be assigned to both valence and Rydberg transitions, based on ab initio calculations of vertical excitation energies and oscillator strengths of these molecules. Fine structure, that was resolved both in the photoelectron and photoabsorption spectra, has been assigned to vibrational series involving, predominantly, excitations of c.a. 180 meV, attributed to C=O and C-O stretching. Other vibrations resolved in the photoabsorption spectrum of both molecules correspond to further stretches and deformations that were also seen in the previously analyzed molecules. The theoretical calculations presented here are in good agreement with experimental data. The photoabsorption cross sections were used to calculate the photolysis lifetimes of methyl butyrate and methyl valerate for the Earth's troposphere and stratosphere. From this and Publisher's Note The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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