Experimental and theoretical studies on the absorption spectra of n-dodecane in the IR and VUV regions

Journal of Quantitative Spectroscopy & Radiative Transfer 236 (2019) 106582

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Experimental and theoretical studies on the absorption spectra of n-dodecane in the IR and VUV regions Kiran Kumar Gorai a, Aparna Shastri a,b,∗, Param Jeet Singh a, S.N. Jha a,b a b

Atomic and Molecular Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India

a r t i c l e

i n f o

Article history: Received 20 May 2019 Revised 23 July 2019 Accepted 23 July 2019 Available online 24 July 2019 Keywords: n-Dodecane Synchrotron radiation Infrared Vacuum ultraviolet TDDFT

a b s t r a c t We report here a comprehensive spectroscopic study of the absorption spectrum of the n-dodecane molecule using synchrotron radiation based photoabsorption and FTIR spectroscopy. Quantum chemical calculations using the DFT and TDDFT methodologies are used to predict relevant ground and excited state properties and correlate them with the experimental results. In the IR spectrum, assignment of the prominent CH stretching bands in the 280 0–30 0 0 cm−1 region are consolidated while a few new vibrational assignments are made in the 70 0–150 0 cm−1 region. The electronic absorption spectrum of n-dodecane lies entirely in the vacuum ultraviolet (VUV) region and consists of a broad continuous absorption band starting from ∼7.5 eV, with no discernible structure. TDDFT calculations of vertical excited states predict that most of the excited states are Rydberg in nature. Potential energy curves of the first few excited states with respect to various bond lengths and bond angles are studied in order to gain additional insights into the nature of the excited states. The broad nature of the absorption is attributed partly to the effect of several conformers as well as hot bands from low frequency modes in the ground state and partly due to overlap of several Rydberg series converging to the first few ionization potentials (IPs). Energy separation between the first and second IP is theoretically predicted to be ∼0.65 eV, while successive separation between the second, third, fourth and fifth IPs is ∼0.03 eV. To the best of our knowledge this is the first report of the VUV absorption spectrum of n-dodecane in the region from 6 to 10 eV, as also the first report of theoretical calculations of its electronically excited states. © 2019 Published by Elsevier Ltd.

1. Introduction The physical and chemical properties of liquid alkanes make them suitable for variety of technologically important applications. For example, they are ideal candidates for immersion lithography due to their high refractive index and near transparency in the 193 nm region [1]. The wide use of alkanes as fuels has also spurred investigations into the mechanisms of combustion and pyrolysis processes involving them [2]. n-Dodecane (C12 H26 ), an acyclic alkane, is a colourless liquid of the paraffin family and is widely used as a diluent for tributyl phosphate in nuclear waste reprocessing [3,4]. In recent years it has elicited considerable attention as a possible surrogate for kerosene-based fuels such as Jet-A, S-8 etc. [5]. Lately, vacuum ultraviolet (VUV) gas chromatography combined with time of flight mass spectrometry has been used for chemical characterization of crude oils containing a mixture of n-

∗ Corresponding author at: A&MPD, Modular Labs, Bhabha Atomic Research Centre, Trombay, Mumbai, Maharashtra 40 0 088, India. E-mail address: [email protected] (A. Shastri).

https://doi.org/10.1016/j.jqsrt.2019.106582 0022-4073/© 2019 Published by Elsevier Ltd.

alkanes, including n-dodecane [6]. The n-dodecane molecule has also been studied as a model system for analysis of Raman spectra of lipid molecules due to its relatively simple structure containing only CH2 and CH3 groups [7]. In order to understand the chemical reactions involving a particular molecule at a microscopic level, it is essential to have detailed information about the ground and excited state structure of the molecule. For instance, in use of alkanes as fuels, the understanding of how their dissociation dynamics proceeds, the role played by excited electronic states, vibrational excitations in ground and excited states, nature of potential energy curves and interactions amongst excited states are important issues. Despite the need for accurate spectroscopic data, so far there have been very few reports in literature regarding the vibrational spectroscopy of the n-dodecane molecule in the ground electronic state [7,8], and practically no reports on its electronically excited states. A detailed understanding of the ground and excited state electronic structure which in turn would be useful in probing the role of electronic and vibrational excitations in chemical reactions involving n-dodecane is essential. Towards this end, we have undertaken a combined experimental and theoretical study of the vibrational and electronic absorption spectrum of n-dodecane.

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K.K. Gorai, A. Shastri and P.J. Singh et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 236 (2019) 106582

Fig. 1. Equilibrium ground state geometry of n-dodecane.

The vibrational spectrum is studied in the liquid phase using FTIR spectroscopy, while the electronic spectrum is probed using synchrotron radiation based photoabsorption spectroscopy in the gas phase. Detailed quantum chemical calculations are performed to obtain a meaningful analysis and interpretation of the observed spectra.

2. Methodology 2.1. Experimental details Photoabsorption experiments in the wavelength region 1200– 20 0 0 A˚ (∼6–10.5 eV) are carried out using the High Resolution Ultra Violet (HRVUV) beamline [9,10] at Indus-1, a 450 MeV synchrotron radiation source at the Raja Ramanna Centre for Advanced Technology, Indore, India [11]. The wavelength selection mechanism of the HRVUV beamline comprises of a 6.65 m eagle mount spectrometer with a 1200 lines/mm grating which disperses the broadband synchrotron radiation in the 120 0–320 0 A˚ region with a spectral resolution of ∼0.1 A˚ [10]. The absorption cell is a stainless steel cylindrical chamber of length 320 mm which is mounted between the beamline focusing optics and the 6.65 m spectrometer, and is mechanically isolated from the focusing optics and the spectrometer on either side of it by UHV compatible gate valves. LiF or CaF2 windows mounted in the gate valves allow transmission of the incident radiation up to the window cut-off (1050 A˚ and 1250 A˚ respectively). The cell has several ports for evacuation, pressure measurement and sample introduction via a system of Swagelok needle valves. A base pressure of ∼10−6 mbar is maintained in the cell using a turbomolecular pump and pressure is measured using a full range gauge (Pirani-cum-cold cathode). The n-dodecane sample (stated purity ≥99%; procured from M/s. Sigma Aldrich) is taken in a glass tube connected to the inlet system via a glassmetal seal and subjected to several freeze-pump-thaw cycles to eliminate volatile impurities before introducing in the absorption cell. To obtain the optimum absorption signal free from saturation and taking into account the considerable variation in absorption cross sections over the broad spectral range covered, sample pressure is varied from ∼10−4 mbar to 1 mbar. The transmitted photon intensity is measured using a solar blind photomultiplier tube (Hamamatsu make, model no. 9408B, range 110–310 nm) mounted at the exit slit of the spectrometer. The lack of sensitivity of the PMT in the wavelength region >310 nm ensures a better signal to noise ratio due to reduced detection of scattered light, and elimination of the need for a VUV to visible scintillator. Wavelength scanning is achieved by rotation of the grating about a particular central wavelength for which the dispersed beam is focussed at the exit slit. Absorption spectra are generated using the wellknown Beer-Lambert law: ln(I0 /I) = nσ (λ)L; where I0 and I are the measured transmission intensities through the evacuated cell and through the sample respectively, n is the number density of molecules interacting with the radiation, σ (λ) is the wavelength dependent absorption cross-section and L is the absorption path length. The PMT counts are normalized with respect to the synchrotron beam current which is recorded simultaneously at every step to correct for variation in the beam current.

2.2. Computational methods All quantum chemical calculations reported here are carried out using the GAMESS (USA) computational chemistry code [12], implemented on a linux based cluster employing parallel mode of execution when required. Initially, the optimized equilibrium ground state geometry and vibrational frequencies of n-dodecane are calculated using density functional theory (DFT). The molecular geometry is assumed to have Cs symmetry following the report by Sebek et al. [7], wherein a conformational analysis established that of the many conformers of n-dodecane, the global minimum is of Cs geometry. The molecular geometry in the calculations is such that all the twelve carbon atoms and two out of twenty-six hydrogen atoms lie in one plane (XZ plane) and the rest of the twenty four hydrogen atoms are located symmetrically above and below this plane (in the YZ plane). Fig. 1 shows a drawing of the molecule with the numbering of atoms followed in the rest of the text. DFT calculations are performed using hybrid correlation functionals like B3LYP [13,14] along with different basis sets like the Gaussian basis sets 6-31G(2d,2p)+ and correlation consistent basis sets cc-pVDZ [15,16]. Time dependent DFT (TDDFT) calculations are performed at the optimized ground state geometry to calculate the energies of vertically excited (singlet and triplet) states. Visualization of the geometrical structures, molecular orbital contour plots and vibrational modes are facilitated by the software MacMolPlt [17]. 3. Results and discussion 3.1. Molecular orbitals The ground state electronic configuration of n-dodecane under Cs symmetry is given by: [core](30a )2 (31a )2 (7a )2 (32a )2 (8a )2 (33a )2 (34a )2 (9a )2 (35a )2 (36a )2 (10a )2 (11a )2 (12a )2 (37a )2 (38a )0 (39a )0 (40a )0 (41a )0 …, where the superscripts ‘2’ and ‘0’ denote occupied and unoccupied molecular orbitals (MOs) respectively. The contour plots of a few highest occupied and lowest unoccupied MOs at the B3LYP/6-311(2d,2p)+ level of theory are depicted in Table 1 along with their binding energies and descriptions. The highest occupied MO (HOMO) is observed to be of σ type while the HOMO-1, HOMO-2 and HOMO-3 are all of π type. The lowest unoccupied MO (LUMO) is of Rydberg type (diffuse) and can be identified with a 3 s Rydberg state. In fact, it is observed that in the case of n-dodecane, the first few unoccupied MOs all have a diffuse or Rydberg-like character. In correlating the various LUMOs with corresponding Rydberg orbitals, we use the group theoretical transformations of the atomic orbitals for guidance. For example, ns, npx and npy orbitals transform as Aʹ under Cs point group, while npz orbitals transform as Aʺ. In this manner, the next two unoccupied MOs, LUMO+1 and LUMO+2 can be assigned to 3px /3py Rydberg orbitals and the LUMO+4 orbital of aʺ symmetry correlates with 3pz . Similarly, LUMO+3, LUMO+5 and LUMO+6 are identified with the 3dz2 /3dx2-y2 /3dxy Rydberg orbitals and so on. 3.2. Ground state geometry, vibrational frequencies and IR spectrum Bond lengths and bond angles of the optimized equilibrium geometry of n-dodecane in its (neutral) ground state at the B3LYP/6-

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Table 1 Molecular orbital contour plots at the B3LYP/6-311(2d,2p)+ level of theory.

Table 2 Ground state optimized equilibrium parameters of n-dodecane at the B3LYP/6311(2d,2p)+ level of theory.

˚ Bond lengths (A)

Bond Angles (°)

C6-C7 C6-H24 C1-H13 C6-C7-C8 H27-C7-H26 H13-C1-C2

Neutral ground state

Ionic ground state

1.531 1.095 1.091 113.68 106.03 111.46

1.557 1.088 1.094 106.48 108.54 108.56

311(2d,2p)+ level of theory are listed in Table 2. The cationic vibrational frequencies are often useful in assignment of observed vibronic features accompanying Rydberg transitions in the photoabsorption spectra [18,19]. With this motivation, geometry opti-

mization and vibrational frequencies of the ground cationic state of n-dodecane are also calculated. Resultant equilibrium geometrical parameters for the cation are given in Table 2, while the calculated vibrational frequencies are listed in the supplementary data. The major change in the molecular geometry in going from the neutral to the ionic state appears to be in the C6-C7-C8 bond angles, while there is relatively little change in the bond lengths and other bond angles. The computed vertical and adiabatic ionization energies at the B3LYP/6-311(2d,2p)+ level are 9.42 eV and 8.97 eV respectively which are in reasonably good agreement with the earlier reported experimental and theoretical ionization energies of n-dodecane (9.75 eV and 9.48 eV respectively) [20], thus validating the appropriateness of the method and basis set used for the calculation. The corresponding Mulliken and Lowdin population analysis (cf. Supplementary data) shows that there is a tendency for

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Fig. 2. The IR spectrum of n-dodecane in liquid phase at 1 cm−1 resolution.

negative charge to be concentrated on the C atoms and relatively greater electronic charge accumulated on the end C atoms as compared to the inside ones. The infrared spectrum of n-dodecane in the liquid phase is shown in Fig. 2. n-Dodecane has 108 vibrational modes spanning the irreducible representations 61A + 47A under the Cs point group. A complete list of the theoretically predicted vibrational frequencies in the electronic ground state at the B3LYP/6-311(2d,2p)+ level of theory is given in the Supplementary data, while the major experimentally observed IR peaks with their assignments and theoretically predicted values are listed in Table 3. The most intense features in the infrared spectrum of ndodecane occur in the wavenumber region ∼280 0–310 0 cm−1 and are attributed to various CH stretching type of vibrations. The observed spectrum in this region agrees well with an earlier work by Klingbeil et al. [8], in which integrated intensity measurements were reported, but vibrational assignments were not discussed. By comparing both the predicted peak positions and IR intensities with the experimentally observed ones, the four major bands observed at 2854 cm−1 , 2873 cm−1 , 2924 cm−1 and 2960 cm−1 may be attributed to CH2 symmetric stretches, CH3 symmetric stretches, CH2 asymmetric stretches and CH3 asymmetric stretches respectively. The agreement between the theoretically predicted frequencies and experimentally observed peaks is reasonable within the limits of the harmonic oscillator approximation. In the work by Sebek et al. [7], the Raman spectra of ndodecane in the region of the CH stretching modes of n-dodecane have been assigned based on anharmonic calculations of the vibrational frequencies, listed in Table 3 for comparison. The anharmonic calculations predict the CH2 symmetric stretches, CH3 symmetric stretches, CH2 asymmetric stretches and CH3 asymmetric stretches at ∼2870, 2856, 2960 and 2923 cm−1 respectively (taking average values of several peaks for each type of vibration). While these values are in better agreement with the experimentally observed peak positions, it is interesting to note that inclusion of anharmonicity in the calculation has reversed the relative energy ordering of CH2 and CH3 stretches. Therefore, going by the anharmonic values [7], the observed peaks at 2854 and 2873 cm−1 should be assigned to CH3 and CH2 symmetric stretches respectively; while the peaks at 2924 and 2960 cm−1 should be assigned to CH3 and CH2 asymmetric stretches respectively. However, such an assignment is not consistent with the observed and calculated relative intensities in the present study, hence we retain the as-

Fig. 3. The experimental absorption spectrum of n-dodecane. (The stick spectrum is the theoretically simulated spectrum; the arrows mark the expected positions of Rydberg series converging to the first IP).

signments predicted by the harmonic calculations. For the lower frequency modes (70 0–150 0 cm−1 ), attributed essentially to angular deformations, the agreement between the current theoretical calculations and experimental values is much better, which could be due to the fact that the anharmonic corrections are not very important for these vibrations. Apart from the effects of anharmonicity, one cannot rule out contributions to line shifts and broadening due to the presence of a large number of conformers [7]. 3.3. VUV photoabsorption spectrum, correlation with theoretical results and spectral analysis The photoabsorption spectrum of n-dodecane recorded using synchrotron radiation in the region ∼6–10 eV is shown in Fig. 3. As the VUV absorption spectrum of n-dodecane has not been reported so far, we find it convenient to discuss the present results in relation with the known spectra of n-alkanes (n up to 10). It is observed that there is practically no absorption up to about 7.5 eV, after which there is a rise in intensity in the region 7.5–8.0 eV, followed by a continuous broad absorption up to the CaF2 window transmission cut-off at about 10.5 eV. Such an onset of the electronic transitions at high energies is a characteristic feature of molecules with σ bonds and indeed all the n-alkanes studied so far [1,19,21]. We may also mention here that its transparency in the 193 nm region makes n-dodecane an ideal candidate for immersion lithography [1]. It has been discussed in the context of linear nalkanes that the LUMO is Rydberg in nature and that the ionization potential as well as the position of the first Rydberg transition progressively shifts to lower energies as one adds more Carbon atoms [1]. This has been explained in terms of the diffuse Rydberg-like LUMO being more or less constant in energy, while the HOMO gets more and more destabilized as one adds more carbon atoms. As an aid to the assignment and interpretation of observed spectral features, vertical excited state energies have been computed and listed in Table 4 along with their symmetries, initial and final MOs involved in the transition, transition amplitudes, oscillator strengths (f) and lambda diagnostic values (). The  value which lies between 0 and 1 is a measure of the overlap between the ground and excited state wavefunctions [22]; and provides an insight into the nature of the transition. As a general guideline, relatively higher values of  (> 0.5) indicate valence nature, lower values of  (<0.3) indicate Rydberg nature and intermediate val-

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Table 3 Observed IR peaks of n-dodecane (in cm−1 ) and their assignments. Present work

Earlier work [7]

Observed peak

Theoreticala

Assignment

Description

722 889(w) 1382 1457(sh) 1464 2854

728 (0.172) 892 (0.068) 1390 (0.041) 1508 (0.283) 1524 (0.419) 3014 (6.925)

ν 73 ν 11 ν 30 ν 95 ν 47 ν 57

CH2 rock C-C-C ang. def CH2 wag CH3 sym def CH2 sym def CH2 sym str

2873

3024 (2.215) 3024 (0.112)

ν 58 (Aʹ) ν 59 (Aʹ)

CH3 sym str CH3 sym str

3077 3077

2924

3043 (<0.001) 3055 (5.830) 3080(0.160) 3080(3.112)

ν 104 ν 106 ν 107 ν 108

CH2 CH2 CH2 CH2

str str str str

3094 3095 3097 3102 3107 3115 3122 3127 3132 3135

2960

3082 (2.096) 3082 (0.025)

ν 60 (Aʹ) ν 61 (Aʹ)

CH3 asym str CH3 asym str

3175 3175

(Aʺ) (Aʹ) (Aʺ) (Aʺ) (Aʹ) (Aʹ)

(Aʺ) (Aʺ) (Aʺ) (Aʺ)

asym asym asym asym

Harmonic

Anharmonic

3053 3053 3054 3054 3056 3057 3061 3071 3071

2864 2867 2866 2862 2886 2866 2874 2878 2867 2870(avg) 2850 2861 2856(avg) 2941 2940 2942 2949 2958 2961 2970 2973 2977 2984 2960(avg) 2935 2941 2923(avg)

a DFT/B3LYP/G-311(2d,2p)+; w:weak; sh: shoulder; values in parenthesis are theoretically predicted IR intensities.

ues indicate mixed nature of the transitions. The predicted Rydberg transitions are further assigned to ns, np, nd type based on energy ordering and symmetry of the final molecular orbital involved, i.e. the Rydberg orbitals of ns, npx , npy , dx2-y2 , dz2 , dxy type belong to the totally symmetric irreducible representation A , and orbitals of pz , dyz and dxz belong to the irreducible representation A under the Cs point group. It can be seen from Table 5 that most of the excited states of n-dodecane are of Rydberg type, with a few transitions exhibiting mixed nature, but there are no pure valence transitions. This appears to be a feature peculiar to linear alkanes and we note that the present theoretical studies are in agreement with earlier works on the electronic structure of the lower n-alkanes [23] which have reported that the first few excited states are all Rydberg in nature. The low oscillator strengths predicted for the first few transitions is consistent with the flat appearance of the spectrum in the region up to ∼7.8 eV. The first ionization potential (IP) of n-dodecane has been reported to be at 9.75 eV by Zhao et al. [20]. Using the standard Rydberg formula En = IP − R/(n − δ l )2 , where En is the energy of the transition, IP is the ionization potential, R is the Rydberg constant, n is the principal quantum number and δ l is the orbital angular momentum dependent quantum defect (QD), Rydberg series of ndodecane converging to the first IP can be predicted. Table 5 lists the first few Rydberg series converging to the first IP, assuming QDs of ∼1, 0.5 and 0.1 for ns, np and nd series respectively, a reasonable assumption as the HOMO from which the transitions occur is localized on C atoms. As no sharp transitions are discernible in the experimental spectrum, we compare the theoretically predicted Rydberg transitions from the HOMO with the expected positions of the Rydberg series from the Rydberg formula (cf. Table 5).

It may be mentioned here that Wu et al., in their comparative study on n-alkanes [21], reported that the first absorption shoulder at around 1600 A˚ in lower alkanes does not have a clear consensus on assignment. While Raymonda and Simpson [24] attributed it to intra-molecular charge transfer excitation between adjacent C-C bonds, Robin [19] assigned to a 3s Rydberg and Lombos et al. [25] suggested that the excitation is localized in one ethyl group. The present calculations clearly predict the first excited state to be Rydberg, as is borne out both by the low  value for the transition (cf. Table 4) as well as the diffuse nature of the upper state MO (cf. Table 1). However, the calculated oscillator strength is zero, and the difference between its expected position according to the QD analysis and the TDDFT prediction is unusually high (−1.1 eV). As TDDFT calculations of excited states are generally known to be in good agreement with experimental values up to │HOMO│+1 eV [26], this is somewhat surprising and warrants further investigation. For the 3p, 3d, 4s and 4p Rydberg series converging to the first IP, the agreement between the QD analysis and TDDFT predictions is quite good (cf. Table 5). We also note that except for the 3s Rydberg state, at the expected positions of other Rydberg series, there is some intensity of absorption observed experimentally, even though there is no spectrally resolved peak (cf. Fig. 3). Another unique feature observed in the electronic excitations of n-dodecane is that practically no pure valence transitions are predicted, most of the predicted transitions are predominantly Rydberg, while a few have mixed character. It is observed that after the first few Rydberg states belonging to the first IP, several 3s states arising from inner orbitals are predicted to lie lower in energy than the higher members Rydberg series of the first IP. This suggests that the next few higher IPs are somewhat close in energy to the first IP. Although there is no experimental report on

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K.K. Gorai, A. Shastri and P.J. Singh et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 236 (2019) 106582 Table 4 Vertical excited state (singlet) energies of n-dodecane at the B3LYP/6-311(2d,2p)+ level of theory. Sym

Energy(eV)

f



Type

Assignment

Transition

Amplitude

2A 3A 4A 5A 1A 2A 3A 4A 6A 7A 5A 6A 8A 9A 7A 8A 9A 10A 10A 11A 11A 12A 12A 13A 14A 15A 16A 17A 13A 14A 18A 19A 15A 20A 21A 16A 17A 18A 22A 19A 20A 23A 21A 24A 25A 26A 27A 28A 29A 22A

7.483 7.677 7.770 7.872 7.905 8.055 8.068 8.088 8.093 8.145 8.197 8.254 8.264 8.297 8.374 8.377 8.386 8.391 8.452 8.459 8.480 8.508 8.508 8.510 8.524 8.527 8.554 8.577 8.583 8.591 8.611 8.627 8.628 8.632 8.635 8.641 8.669 8.706 8.714 8.719 8.727 8.752 8.758 8.772 8.777 8.787 8.796 8.813 8.817 8.842

0.000 0.012 0.011 <0.001 <0.001 <0.001 0.000 0.000 <0.001 0.034 <0.001 0.000 0.000 0.012 0.051 <0.001 <0.001 0.000 0.061 0.064 <0.001 0.003 0.000 <0.001 0.002 0.016 0.055 0.155 0.001 0.000 <0.001 0.031 <0.001 0.174 <0.001 0.182 <0.001 <0.000 <0.000 <0.000 0.000 0.149 <0.001 0.000 <0.000 <0.000 <0.000 <0.000 0.007 0.012

0.255 0.236 0.214 0.262 0.247 0.379 0.340 0.344 0.200 0.275 0.340 0.223 0.415 0.356 0.324 0.338 0.342 0.386 0.309 0.408 0.221 0.344 0.326 0.315 0.344 0.243 0.332 0.391 0.336 0.299 0.358 0.331 0.321 0.371 0.338 0.383 0.335 0.361 0.387 0.221 0.302 0.353 0.340 0.346 0.290 0.232 0.358 0.383 0.315 0.302

R R R R R R/V R/V R/V R R R/V R V/R R/V R/V R/V R/V R/V R/V R/V R R/V R/V R/V R/V R R/V R/V R/V R R/V R/V R/V R/V R/V R/V R/V R/V R/V R R/V R/V R/V R/V R R R/V R/V R/V R/V

3s 3px/y 3px/y 3dz2/xy/x2-y2 3pz 3s(H-1) 3s(H-2) 3s(H-3) 3dz2/xz/x2-y2 3dz2/xz/x2-y2 3s(H-6) 3dxz/yz 3s(H-4) 3s(H-5) 3px/y (H-2) 3px/y (H-6) 3px/y (H-1) 3px/y (H-5) 3px/y (H-3) 3px/y (H-4) 3px/y (H-2) 3s(H-7) 3px/y (H-1) 4s 3pz (H-1) 4px/y 3dz2/xy/x2-y2 (H-5) 3pz (H-2) 3dz2/xy/x2-y2 (H-6) 3px/y (H-6) 3px/y (H-5) 3px/y (H-4) 3dz2/xy/x2-y2 (H-1) 3pz (H-3) 3px/y (H-7) 3pz (H-4) 3dz2/xy/x2-y2 (H-2) 3px/y (H-3) 3dz2/xy/x2-y2 (H-4) 3dxz/yz 3pz (H-5) 3px/y (H-8) 3dz2/xy/x2-y2 (H-3) 3pz (H-6) 3px/y (34aʹ) 4px/y 3dz2/xy/x2-y2 (H-8) 3px/y (H-5) 3dz2/xy/x2-y2 (H-7) 3px/y (H-9)

37a –38a 37a –39a 37a –40a 37a –41a 37a –13a 12a –38a 11a –38a 10a –38a 37a –42a 37a –43a 9a –38a 37a –14a 36a –38a 35a –38a 11a –40a 9a –39a 12a –40a 35a –39a 10a –40a 36a –40a 11a –39a 34a –38a 12a –39a 37a –45a 12a –13a 37a –44a 35a –41a 11a –13a 9a –41a 9a –40a 35a –40a 36a –39a 12a –41a 10a –13a 34a –39a 36a –13a 11a –41a 10a –39a 36a –41a 37a –15a 35a –13a 33a –40a 10a –41a 9a –13a 34a –40a 37a –46a 33a –41a 35a –39a 34a –41a 8a –40a

−0.93 −0.93 0.98 0.91 −0.98 −0.79 0.62 −0.56 −0.96 −0.91 −0.66 −0.95 0.87 0.71 0.96 −0.56 −0.90 0.59 −0.84 0.75 0.77 0.73 −0.64 −0.73 −0.58 0.81 0.59 −0.78 0.61 −0.78 −0.65 −0.66 0.45 −0.74 0.73 0.94 0.71 0.60 0.60 0.91 −0.77 −0.75 −0.50 0.74 −0.77 0.83 0.58 −0.50 0.75 0.55

f: Oscillator strength; : lambda diagnostic value; R: Pure Rydberg R/V: Rydberg with some valence character; H:HOMO.

Table 5 Comparison of the Rydberg series positions (in eV) predicted by the Rydberg formula with the corresponding theoretically computed transitions. Rydberg series

Expecteda

Predictedb

Difference

3s 3p

6.350 7.573

3d

8.132

4s 4p

8.238 8.639

7.483 7.677 7.770 7.905 7.872 8.093 8.145 8.254 8.719 8.509 8.527 8.787

−1.134 −0.104 −0.197 −0.332 0.260 0.039 −0.013 −0.122 −0.587 −0.271 0.112 −0.148

a b

By QD analysis. TDDFT/B3LYP/6-311(2d,2p)+.

higher IPs of n-dodecane, one may logically make some inferences from the theoretically calculated binding energies of the MOs (cf. Table 1). It is observed that the difference in binding energies between the HOMO and HOMO-1 is about 0.65 eV and the separations between the next three inner MOs are ∼0.027 eV each. From this we can roughly estimate that the 2nd , 3rd , 4th and 5th IPs would occur at ∼10.4, 10.61, 10.63, 10.66 eV respectively. Rydberg series converging to each of these close-lying IPs would then show considerable overlap, leading to a quasi-continuum absorption as observed. The role of conformers in explaining the broad absorption feature also may be substantial as discussed in the nest section. 3.4. Potential energy curves (PECs) of excited states There is, in general, a correlation between the nature of the spectral absorption features observed and the excited state potential energy curves (PECs). In the case of n-dodecane, the character-

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lated binding energies of the few MOs below the HOMO, the second and next few higher IPs are very closely spaced. Due to this, in the 8–9 eV region, there is an onset of Rydberg series converging to several higher IPs (excitation from inner orbitals) which lie in the same energy region as higher members of the Rydberg series converging to the first IP (cf. Table 4). Hence, Rydberg series converging to the first few IPS show considerable overlap. The third important factor is the contribution of hot bands to the room temperature absorption spectrum, an effect which would be quite pronounced in a molecule such as n-dodecane, having several low frequency vibrational modes which would be appreciably populated at room temperature. A more conclusive analysis would require experiments with higher resolution on jet cooled beams. 4. Conclusions Fig. 4. Potential energy curves with respect to change C6-C7 bond length for the ground and first six excited states of n-dodecane (cf. Fig. 1 for atom numbering).

Fig. 5. Potential energy curves with respect to change in C5-C6-C7 bond angle for the ground and first six excited states of n-dodecane (cf. Fig. 1 for atom numbering).

istic broad absorption band observed devoid of vibronic structure may be either due to a repulsive nature of excited state potential energy curves, or overlapping of many closely spaced transitions. In order to gain additional insights into the nature of the excited states, potential energy curves (PECs) for ground state and first few excited states are generated at the B3LYP/6-311(2d,2p)+ level of theory with respect to various bond lengths and bond angles. As the PECs for different bond lengths and different bond angles show very similar trends, only one representative plot is shown for each (Figs. 4 and 5 respectively); the rest of the plots are included in the Supplementary data. In the Franck–Condon region, the PECs of the first few excited states with respect to bond lengths (cf. Fig. 4) show a very regular and non-repulsive behaviour. On the other hand, the PECs with respect to bond angles (cf. Fig. 5) exhibit very shallow minima, and may partly explain the lack of vibronic structure in the spectrum. However, this alone cannot account for the extremely broad and continuous absorption band which may be more likely due to overlapping of many closely spaced transitions. Three factors could responsible for this crowding of the spectral lines: First of all, ndodecane has a large number of conformers, with the population in the lowest energy conformer reported to be ∼15% [7], therefore, electronic transitions from different conformers with comparable intensity may overlap. Secondly, as mentioned in the previous section, the electronic absorption spectrum is predicted to be dominated by Rydberg series, and if we take a cue from the calcu-

The electronic absorption spectrum of the twelve carbon member linear alkane, n-dodecane has been investigated using synchrotron radiation based photoabsorption spectroscopy and TDDFT calculations. The ground state vibrational spectrum has also been reinvestigated in using FTIR spectroscopy and DFT calculations in order to obtain a comprehensive picture of the ground state molecular structure and vibrational modes. The IR bands in the region 70 0–30 0 0 cm−1 are assigned to various normal mode vibrations of n-dodecane based on a comparison with the theoretical calculations. Of these, the four most prominent bands observed in the 280 0–30 0 0 cm−1 region are assigned to CH stretching modes in general agreement with earlier reports. The five bands observed in the 70 0–150 0 cm−1 region are assigned for the first time. Of these, the more intense ones at 722, 1382 and 1464 cm−1 are attributed to CH2 rock, wag and symmetric deform modes respectively while the weak band at 882 cm−1 and the shoulder at 1457 cm−1 are associated with CCC angular deform and CH3 symmetric deform modes respectively. The electronic absorption spectrum lies entirely in the VUV region and comprises of a broad and continuous absorption with a considerable rise in intensity commencing at ∼7.5 eV. The theoretical calculations of vertical excited states establish that all excited states are Rydberg in nature, with a few showing slight valence-Rydberg mixing. Potential energy curves of the first few excited states with respect to bond lengths and bond angles show regular non-repulsive nature in the Franck–Condon region. The broad nature of the VUV absorption band devoid of vibronic structures may be attributed partly to the presence of several conformers and partly to crowding of several Rydberg series converging to the first few IPs, which are theoretically predicted to lie rather close together in energy. To the best of our knowledge this is the first report of the VUV absorption spectrum of ndodecane in the region from 6 to 10 eV, as also the first report of theoretical calculations of its electronically excited states. We believe that the results presented here would form valuable inputs for further studies involving photochemistry of n-dodecane, and understanding its chemical reactivity at the molecular level. Acknowledgements The authors wish to express their gratitude to Mr. Asim Das and Dr. B.N. Raja Sekhar, (A&MPD, BARC) for valuable help rendered during the experiments. We wish to thank Dr. Arup Banerjee (RRCAT) for useful discussions in quantum chemistry and Dr. Ankita Rao, (RPAD, BARC) for providing the n-dodecane sample. We would also like to acknowledge the efforts of RRCAT Computer Division staff that enabled effective utilization of centralized scientific computing resources for carrying out computations reported in this paper and INDUS control room personnel for the SR beam. We thank Dr. M.N. Deo (Head, A&MPD, BARC) for encouragement and support.

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