NEXAFS Spectra Study

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry 40

Identification of Four C Isomers by Means of a Theoretical XPS/NEXAFS Spectra Study Yong Ma, Sheng-Yu Wang, Jing Hu, Jun-Rong Zhang, Juan Lin, Shu-Qiong Yang, and Xiuneng Song J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03079 • Publication Date (Web): 07 May 2018 Downloaded from http://pubs.acs.org on May 8, 2018

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The Journal of Physical Chemistry

Identification of Four C40 Isomers by means of a Theoretical XPS/NEXAFS Spectra Study Yong Ma,†,‡,¶ Sheng-Yu Wang,†,¶ Jing Hu,† Jun-Rong Zhang,† Juan Lin,† Shu-Qiong Yang,† and Xiu-Neng Song∗,† †Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, School of Physics and Electronics, Shandong Normal University, 250014 Jinan, P. R. China ‡Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden ¶These two authors contributed equally to this work. E-mail: [email protected] Phone: +86 13953138878. Fax: +86 (0)531 89611170

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Abstract XPS and NEXAFS spectra of four stable C40 isomers[29(C2 ), 31(Cs ), 38(D2 ) and 39(D5d )] have been investigated theoretically. We combined the density functional theory and full core hole potential method to simulate C 1s XPS and NEXAFS spectra for nonequivalent carbon atoms of four stable C40 fullerene isomers. The NEXAFS showed obvious dependence on the four C40 isomers and XPS spectra are distinct for all four isomers, which can be employed to identify the four stable structures of C40 . Furthermore, the individual component of spectra according to different categories have been investigated and the relationship between the spectra and the local structures of C atoms was also explored.

Introduction After the discovery of C60 , 1 fullerene family has been widely studied in the past few years. They have been generally manufactured to useful industrial materials, undoubtedly promoting the development of materials science and other scientific fields resulting from their peculiar physical and chemical properties. 2–4 Obstacles to research on these important applications of fullerenes come mainly from the fact that most fullerenes have a large number of unidentified isomers. Thus, the identification of the fullerene isomers is indispensable. Up to now, useful spectroscopy techniques including X-ray,

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C NMR, Raman, infrared and

electronic spectroscopies have been employed to characterize the multitudinous isomers of fullerenes. 5–7 Compared to other spectra, soft X-ray spectroscopies are generally seen as an effective tool to explore the chemical composition for kinds of materials. 8,9 In particular, the near edge X-ray absorption fine structure (NEXAFS) and the X-ray photoelectron spectroscopy (XPS) have been mightily investigated for the identification of fullerene isomers. NEXAFS spectroscopy primarily depicts the characteristics of the unoccupied orbital, since it’s generated from the electronic excitation from the core orbit to the virtual orbital. While XPS was in concert with the ionization procedure of core electron, it mainly presented the 2


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information of the core orbital. As yet, previous researches have demonstrated that NEXAFS and XPS spectra can be efficiently applied for the identification of fullerene isomers. 10,11 In recent years, the fullerenes with less carbon atoms than C60 have attracted much attention of researchers due to the individual chemical qualities caused by small cages with the higher curvatures. The violation of the isolated pentagon rule (IPR) 12 is attributed to inevitable adjacent pentagons, which lead to the small fullerenes are magical and elusive. As a special small fullerene, the pure C40 fullerenes have not been separated, because all of the C40 isomers exist adjacent pentagons which lead to contravention of the IPR. However, this problem has had a turnaround since Fowler et al. found that the Stone-Wales re-arrangement provides an effective way to reduce the strain from adjacent pentagons for C40 . 13 Subsequently, the geometric, electronic and vibrational properties of C40 and its derivatives have been reported theoretically. 14–16 In addition, a large number of researchers have done a great deal of research on its stability in the hope of removing obstacles for the experimental separation of C40 . 17–20 For instance, Albertazzi et al. calculated 40 isomers of C40 with numerous theoretical methods to find the stable structure. 18 Their studies summarized four energetically stable configurations 29(C2 ),31(Cs ),38(D2 ) and 39(D5d ) of C40 isomers(the numbers (29, 31, 38, 39) in the isomer names for fullerene C40 are numbered in the numbering system of Fowler-Manolopoulos, which according to the spiral algorithm. 12 ), shown in Figure 1a. This result is consistent with the findings of Małolepsza et al., 16 Sun et al. 19 and Kerim et al.. 20 It is noteworthy that so far, previous studies of C40 about stability are based on thermodynamic stability. Recently, Fedorov et al. found that there are a clear correlation between the abundance and the kinetic stability of carbon nanostructures. 21 Of course, research based on thermodynamic stability had great reference value and was also widely recognized. In terms of thermodynamic stability, the above four configurations are the most likely to be separated at the earliest. Herein, in order to study deeply and promote the separation experimentally, as well as advance its application in various fields, we present a theoretical identification for the above-mentioned four stable isomers of fullerene C40 by soft X-ray spectroscopies.

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We used the density functional theory(DFT) and full core-hole (FCH) 22 potentials methods to generate C K-shell (1s) NEXAFS/XPS spectra of C40 isomers 29(C2 ),31(Cs ),38(D2 ) and 39(D5d ). Subsequently, we discussed the relationship between the XPS/NEXAFS spectra and the different isomers of C40 . In addition, the sensitivity of spectra on local environment have been investigated. No doubt, our report should be essentially significative and active for the experimental research and can greatly facilitate the application of C40 in aspects of functional materials.

Computational Details We obtained the structures of the four C40 isomers with fully optimized geometries. The optimizations were performed with the Gaussian09 package. 23 After optimizing configurations, we calculated their C 1s XPS and NEXAFS by the StoBe program. 24 The BE88 25 exchange and PD86 26 correlation functional were used for the procedure of calculations. The IGLOIII 27 basis set was used for core excited carbon atoms. While for the remaining non-excited atoms, the TZVP 28 basis set was applied. Additionally, we used the FCH method combined with a double and an augmented emanative (19s, 19p, 19d) 29 basis set in excited carbon atom. The value of C 1s ionization potential(IP) was obtained by the following equation with the ∆Kohn-Sham (∆KS) scheme. 30 IP = N −1 EFCH − N EGS .

Here

N −1

(1)

EFCH denoted the FCH state which represented the core-ionized state, while N EGS

represented the ground-state (GS) energy. As stated from the final state rule, 31 the precise spectra of a limited systems could be obtained only by core-exited state(final state). Furthermore, since the transition process was more abrupt than other passive electrons in the relaxation times, the problem could be solved by a approximate method of single electron 4


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picture used two final-state molecular orbitals(MOs). The distributions of molecular are random orientations in space.

ff i =

2mεf i 2 2 2 2 (|⟨ψf |x|ψi ⟩| + |⟨ψf |y|ψi ⟩| + |⟨ψf |z|ψi ⟩| ), 3¯ h

(2)

where ψi,f represents MOs of initial and final state, and εf i represents the transition energies which were the energy difference of these two MOs. For the purpose of gaining absolute energy locations of resonances, the transition energy from GS to the first core-excited state (1s→LUMO) were calculated by ∆KS to calibrate the absorption spectra.

N N ε∆KS 1s→LUMO = E1s→LUMO − EGS ,

(3)

In consideration of the relativistic effect, we add a shift of 0.2 eV to all spectra according to previous studies. 30 The XPS spectra were produced by the calculated IP’s of all nonequivalent carbon atoms. The range of below ionizing energy in the NEXAFS spectral line was convoluted the discrete strengths by Gaussian function with the full width at half maximum(FWHM) of 0.3 eV, while for the above region, a Stieltjes imaging approach 32 was used. In previous studies, such broadening was verified to be dependable and precise. 33–35 The XPS and NEXAFS spectra of C40 molecules are not available in experiments at present. So we can’t make a comparison between the theoretical calculation and experimental result directly. Here, we taken the theoretical study 22 and the corresponding experimental results 36 of fullerene C60 as a reference, and the theoretical results are in good agreement with the experimental results. The computational method we adopted for the spectral calculation of C40 was also identical with that implemented for C60 , so our calculations should be trusty and accurate.

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Results and Discussion Structures The aforementioned four energetically stable isomers of C40 fullerene have been optimized and their molecular geometries are shown in Figure1a. The relative energies and HOMO-LUMO gaps of the aforementioned four configurations are shown in Table 1. The result marked that the energy of 39(D5d ) is 10.77 kcal/mol higher than 38(D2 ) isomer, which is the most stable isomer besides 38(D2 ) isomer. According to our result of the calculation, the order of the four C40 isomers from high to low is 38(D2 ), 39(D5d ), 31(Cs ), 29(C2 ) according to stability. The current results are consistent with the previous studies. 16,19,20 The highest energy isomers 29(C2 ) has the smallest HOMO-LUMO gap, while relative stable isomers 38(D2 ) and 39(D5d ) have big HOMO-LUMO gap. In comparison, the isomers 38(D2) and 39(D5d) have a higher chemical stability, which corresponds to their larger HOMO-LUMO gaps. So, the isomers 38(D2 ) and 39(D5d ) are the most likely to be separated in future experiments. For the further discussion for the spectra of different isomers, we currently classify carbon atoms in the fullerene C40 according to local structures, shown in Figure1b: (1)the carbon atom is shared by three pentagons, namely 3pen, (2)the carbon atom is surrounded by one hexagon and two pentagons, namely 1hex2pen, (3)the carbon atom is embraced by two hexagons and one pentagon, namely 2hex1pen. Two relatively stable configurations 38(D2 ) and 39(D5d ) do not contain carbon atoms at 3pen site, which might be caused that adjacent pentagons will lead to the high strain and reduced stability of fullerenes. Table 1: Number of Carbon Atoms of Non-equivalence(Cnon ), Relative Energies(kcal/mol) and HOMO-LUMO Gaps(eV) of C40 are Calculated C40 isomers Cnon 29(C2 ) 20 31(Cs ) 23 38(D2 ) 10 39(D5d ) 3

relative energy HOMO-LUMO gap 21.61 1.20 16.08 1.65 0 2.00 10.77 2.14

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Figure 1: (a)Four optimized geometries for C40 fullerene isomers. (b)Schematic diagram of carbon atoms in different chemical environments, the excited carbon atoms are shown in green, blue and red.

XPS Spectra Figure 2 presents the simulated C 1s XPS spectra of four C40 isomers. At first glance, the XPS spectra of 31(Cs ) and 38(D2 ) have similar profile. Both of them show two distinct features, the weak peaks b are at around 289.95 eV and the strong peaks c are at about 290.31 eV. In fact, there is a greatly inconspicuous peaks a at 289.65 eV in spectral of isomer 31(Cs ) through careful observation. The energy position of feature a for configuration 29(C2 ) is lower than the 31(Cs ). Besides, there are three peaks with the same intensity in the isomer 29(C2 ), namely b, c and c’ respectively. In addition to the existence of a strong peak b at 289.93eV, the configuration of 39(D5d ) also has two peaks, c and c’, where the energy position is slightly higher. Obviously, the configurations 31(Cs ) and 38(D2 ) can be separated by the fingerprint a, and the XPS of the remaining configurations have very different contours. Therefore, we can use XPS to distinguish the above four configurations easily. The current results agree with previous research 37 which point out that the fullerene isomers with different symmetry cloud be identified by XPS. In order to observe if the actual number of carbon atoms in the fullerene cage may have some impact on the results, we calculated the XPS spectrum of the most stable fullerene C38 isomers(17(C2 )-C38 ) mentioned in previous studies, 38 as shown 7



the black line in Figure 2. The XPS spectral profiles of the 17(C2 )-C38 isomer and 31(Cs ), 38(D2 ) isomers of C40 have great similarities, but still differ somewhat in energy position. For example, the peak c of the 17(C2 )-C38 isomer obviously moves toward the high energy position. To further observe the characteristics of these spectral profiles, the portion of the total XPS of every C40 isomer based on the above classification were shown in Figure 3. The numbers of carbon atoms of each type are listed in parentheses after the spectra of each type of carbon atoms. The numbers of carbon atoms at the same site could influence the relative strength of the spectra produced by carbon atoms at this site. The feature a at the lowest location of energy in the 29(C2 ) and 31(Cs ) isomers is very weak and it’s arisen from the 3pen site which contains only two carbon atoms. The feature b of above mentioned four configurations originate from the 1hex2pen site and the feature c(c’) derived from the 2hex1pen site. Above display, the carbon atoms with different types produce diverse spectral peak. The increase in the number of pentagons around the carbon atoms may cause the position of peak to move toward lower energy region. Contrarily, the position of peak to move toward the higher energy region. Further more, the carbons with the same types engender similar spectral characteristic in different molecules. For instance, the 1hex2pen carbon in these four isomers all produce a similar intensity peak b at about 289.95 eV.

NEXAFS Spectra Here, we have calculated NEXAFS spectra of 29(C2 ), 31(Cs ), 38(D2 ) and 39(D5d ) isomers, the results are shown in Figure 4. Besides, the positions of peak between 282 and 286 eV in the spectra are marked and shown in the Table 2. We labelling the main peaks according to the source of these peaks in most cases, but not absolutely. NEXAFS spectra of the 29(C2 ) and 31(Cs ) isomers show the feature a at the 282.6 eV and 282.9 eV respectively, while the other isomers don’t exist this peak, which readily distinguish 29(C2 ) and 31(Cs ) from the other two isomers. Moreover, the intensities of features a, b, c, d, e increases by degrees in the 29(C2 ) isomer. In addition, the intensity of peak e of 38(D2 ) is stronger than the other 8


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b 29(C2)

c

XPS

c'

a c b

Intensity(arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31(Cs)

a c b

38(D2)

b c

c'

39(D5d) b

c

17(C2)-C38 289

290

291

Energy(eV)

Figure 2: The calculated XPS of a C38 and four C40 isomers, the the main features between 282 and 286 eV are labeled.

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29(C ) 2 b


total

3pen(2)

c

c'

c

31(C ) s

b

a

total

a

3pen(2)

a

a

b

b 1hex2pen(16)

1hex2pen(16)

c c'

c 2hex1pen(22)

2hex1pen(22)

Energy(eV)

c

Energy(eV) b

38(D ) 2

total

39(D ) 5d

b


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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c

c'

c

c'

total

b b 1hex2pen(20)

1hex2pen(20)

c

2hex1pen(20)

289

2hex1pen(20)

290

291 289

Energy(eV)

290

291

Energy(eV)

Figure 3: The calculated total XPS (the main features are labeled) and the individual components of XPS according to above categories. The number of each typological carbon atoms are listed in parentheses.

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three configurations. Thus the peak e cloud be seen as a fingerprint of the configuration 38(D2 ). Visibly, the NEXAFS spectra of four C40 isomers exhibit noticeable distinction on both outlines and energies of spectral features. So, the NEXAFS spectra can effectively identify above four C40 isomers. We also calculated the NEXAFS spectrum of the most stable fullerene C38 isomers(17(C2 )-C38 ) mentioned in XPS section, as shown the black line in Figure 4. The NEXAFS spectra of these four C40 isomers and 17(C2 )-C38 are still quite different. It can be easily identified with NEXAFS, which may indicate that the NEXAFS spectrum could be employed to identify fullerenes with carbon atoms of similar numbers. It is worth mentioning here, a recent report pointed out that giant fullerenes with similar cage curvature might have similar spectra and therefore it might not be possible to distinguish between various isomers solely on the base of a single physical property, but the differences in the properties of the small fullerene isomers are because the geometric diversity of the isomers induced by the topology of carbon connections. 39 For small fullerene C40 isomers, the diversities in spectra are also mainly due to the differences of the local structure at different isomers. In order to investigate deeply the relevancy between NEXAFS spectra and local structures of fullerenes and acquire an legible ascription of the spectral characteristics, we have given each spectral component which is derived from the sum of all carbon atoms at the same site, as shown in figure 5. It is noticed that the peaks c of the four isomers are both provided by the carbon atoms at the 2hex1pen site. Carbon atoms on the 3pen site universally display a lower excitation energy than other sites and it generates the feature a in the NEXAFS spectra of 29(C2 ) and 31(Cs ) at the lowest energy position. The difference of lowest energy positions may be due to the pentagons which directly adjacent with the carbon atom. Meanwhile, because there are fewer carbon atoms at the 3pen position, the feature a can hardly be shown in the total spectra. With the increase of the hexagons around the carbon atom, the position of absorption is also moving towards higher energy region. Furthermore, Zhao, et al. 40 pointed out that the polygonal arrangement in the second layer can also affect the NEXAFS spectrum of the atoms that are at the same site within the first

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layer. NEXAFS c a

e

29(C2)

d

b

e 31(Cs) b

e

c

a


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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b

38(D2)

c e

39(D5d)

bc d e

17(C2)-C38

bc

282

284

286

288

290

292

294

Energy(eV)

Figure 4: The calculated NEXAFS spectra of a C38 and four C40 isomers, the main features between 282 and 286 eV are labeled.

Summary Herein, we have simulated XPS and NEXAFS spectra of four C40 stable isomers[29(C2 ), 31(Cs ), 38(D2 ), and 39(D5d )]. Judging from the calculated results, the NEXAFS showed obvious dependence on the four C40 isomers and XPS spectra are distinct for all four isomers. So the XPS and NEXAFS could be employed to identify these four stable C40 isomers. Besides, we explained the source of each spectral feature by decomposing XPS and NEXAFS according to the classification of carbon atoms with different types. Meanwhile, we find the 12


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31(C )

29(C )

e

s

2

e total

total


c

b

d

b

c

a

a d a

3pen(2)

e

a

3pen(2)

e

e 1hex2pen(16)

b

1hex2pen(16)

b e e

2hex1pen(22)

c

284 38(D2 )

2hex1pen(22)

c b

286 e

288

290

292

284 e286 288 290 39(D5d ) Energy(eV)

Energy(eV)

292

total

c d b


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


total

b c

e

de b

1hex2pen(20)

b 1hex2pen(20)

e

c c

284

e

2hex1pen(20)

286

288

290

292

2hex1pen(20)

284

Energy(eV)

286

288

290

292

Energy(eV)

Figure 5: The calculated NEXAFS spectra(the main features are labeled) and individual components of NEXAFS spectra according to above categories. The number of each typological Carbon atoms are listed in parentheses.

Table 2: Positions of Major Peaks between 282 and 286 eV for the Four C40 Isomers. C40 isomers a b c d e 29(C2 ) 282.6 283.0 284.3 285.1 285.6 31(Cs ) 282.9 283.7 284.3 285.5 38(D2 ) 283.6 284.0 285.6 39(D5d ) 283.6 284.0 284.7 285.2

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number of pentagons and hexagons around a C atom have an impact on the binding energy of this C atom. In addition, spectral profiles of spectra generated by carbon atoms at the same site in different isomers have greater similarity. Furthermore, the current research shows that the tortuosity at the local site, like the diverse polygons around the carbon atom, also affect the individual spectra.

Acknowledgement This work is supported by the Taishan scholar project of Shandong Province and the National Natural Science Foundation of China (Grant NO. 11404193, 21303096, 11374195).

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