Electronic and Vibrational Properties of ... - ACS Publications

Nov 7, 2017 - Pobedy 37, 03056 Kiev, Ukraine. •S Supporting Information. ABSTRACT: We analyzed the vibrational and electronic properties of diamondo...
1 downloads 0 Views 8MB Size
Subscriber access provided by READING UNIV

Article

Electronic and Vibrational Properties of Diamondoid Oligomers Christoph Tyborski, Roland Gillen, Andrey A Fokin, Tetyana V. Koso, Natalie A. Fokina, Heike Hausmann, Vladimir N Rodionov, Peter R. Schreiner, Christian Thomsen, and Janina Maultsch J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07666 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 10, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 27

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

The Journal of Physical Chemistry

The analyzed structures of a) [4.4](1,3)adamantanophan-trans,trans-1,8-diene, b) 3,10-bis-(2adamantylidene)diamantane, c) 3-(2-adamantylidene)diamantane, and d) 1,3-(bis-4-diamantyl)prop-1-ene are plotted. 730x428mm (96 x 96 DPI)

ACS Paragon Plus Environment

∗4

DIA a) The Journal of Physical Chemistry 5

2



∗3

2

∗1 ∗

∗5

∗3 BLM

BLM ADA+DIA c)

∗4

ADA+DIA d)

∗4 ∗

∗2

∗3

3

∗5

∗5

BLM 500

BLM 1000

1500

2000

BLM

257 nm 532 nm

2500 3000 500 Raman shift cm−1 e)

1000

1500

2000

×0.15 ∗4

∗3

2500

f) 2 ∗1 ∗

3000

×0.33

BLM ∗4

Intensity (arb. units)

Intensity (arb.units)

1 ∗ 2 3 4 5 6 7 8 9 ∗2 10 11 12 13 14 15 16 17 18 19 2 20 ∗ 21 22 23 24 ∗1 25 26 27 28 2 ∗ 29 30 31 32 33 34 200 35 36

ADA 2b) Page of 27

∗4

∗3

g)

×0.2

BLM

∗2

h) BLM

∗4

∗3

∗3

×0.15 ∗4

ACS Paragon Plus Environment 400

600

800

1000

1200

1400

1600

200

Raman shift cm−1

400 

600

800

1000

1200

1400

1600

H

R

∗3

C rnal of=C Physical 3H of 27 Ch RPage B2g





H R C=C R1 H B3u −→ H2 R C=C R3 H ←− B3g 4 ←− H5 R ∗4 C=C R6 −→ H Ag H7 R ∗1 C=C R8 H rot. 9 aragon Plus Enviro −→ ←− H10 R ∗2 C=C 11 R H DBM ←



The Journal of Physical Chemistry

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

Isosurfaces of the pi (top) and pi* (bottom) orbitals of [4.4](1,3)adamantanophan-trans,trans-1,8-diene (left) and 1,3-(bis-4-diamantyl)prop-1-ene (right) are plotted. We used a GGA approach with the PBE functional and a plain-wave basis set with pseudopotentials for the computations. Isosurfaces of the HOMO and HOMO-1 of the other oligomers can be found in Ref.14 1263x758mm (96 x 96 DPI)

ACS Paragon Plus Environment

Page 4 of 27

5.46 eV

Intensity (arb. units)

5.42 eV Page 5 ofThe 27 Journal of Physical Chemistry 5.08 eV 5.25 eV 5.21 eV 5.32 eV 5.00 eV

Intensity (arb. units)

1 2 3 4.82 eV 4 4.7 eV 5 2.33 eV 6 1.49 eV 7 8 Raman shift (arb. units) 9 10 11 12 13 14 15 16 17 18 19 20 ACS Paragon Plus Environment 21 4.5 5 5.5 1.5 2 4.5 2 221.5 Excitation energy (eV) 23

5

5.5

The Journal of Physical Chemistry

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

Page 6 of 27

Electronic and Vibrational Properties of Diamondoid Oligomers Christoph Tyborski,

∗, †

Natalie A. Fokina,

Schreiner,





Roland Gillen,

†, ‡

Andrey A. Fokin,

Heike Hausmann,



Christian Thomsen,

¶,§

Tetyana V. Koso,

Vladimir N. Rodionov,



and Janina Maultzsch





Peter R.

†, ‡

†Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraÿe 36, 10623

Berlin, Germany ‡Department für Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraÿe

7, 91058 Erlangen, Germany ¶Institute of Organic Chemistry, Justus-Liebig University, Heinrich-Bu-Ring 17, 35392

Gieÿen, Germany §Department of Organic Chemistry, Kiev Polytechnic Institute, pr. Pobedy 37, 03056 Kiev,

Ukraine E-mail: [email protected]

1

ACS Paragon Plus Environment

Page 7 of 27

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

The Journal of Physical Chemistry

November 2, 2017

Abstract We analyzed the vibrational and electronic properties of diamondoid oligomers via resonance Raman spectroscopy. The compounds consist of lower diamondoids such as adamantane or diamantane that are interconnected with double bonds. Therefore, all oligomers have ethylene-like centers strongly inuencing the character of the optical transitions. The double bond localizes the HOMO (highest occupied moluecular orbital) in between the diamondoids accompanied by a signicant decrease of optical transition energies. Comparing Raman spectra of the compounds to pristine diamondoids, we nd several characteristic modes originating from the ethylene moieties. Supported by DFT (density functional theory) computations, we attribute these modes to highly localized vibrations that can partially be derived from the vibrational modes of parent ethylene. We further observe two new Raman modes in the compounds: a dimer breathing mode and a rotational mode of the entire ethylene moieties.

2

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Introduction Diamondoids have been investigated widely since the discovery of adamantane in 1933. 1 They form a homologous series of well-dened, saturated hydrocarbons and are the smallest possible units of diamond. 2 Many of their properties, such as the chemical inertness, mechanical hardness, or optical transparency are comparable to those of diamond. 25 Besides choosing diamondoids with respect to their structures and sizes, 610 covalent functionalization tailors desired properties of diamondoids for various applications. 1117 For instance, it was shown that the optical gap can be signicantly tuned by covalent functionalization. 1820 The inclusion of C=C double bonds is another route to tune the electronic properties of diamondoids. 2123 sp2 − sp3 Diamondoid oligomers have been synthesized recently. 24 They exhibit an unsaturated bridge between diamondoids, with highly localized π and π ∗ orbitals leading to a signicant decrease of optical transition energies. 2123 In the solid phase the diamondoid dimers form van-der-Waals crystals further lowering optical transition energies due to van-der-Waals interactions of adjacent molecules in the periodic lattice. 25,26 Tailoring the optical properties of diamondoids crystallites by the chemical functionalization of their constituents is therefore a possible path for new wide-gap semiconductors. In this article we analyze the vibrational and electronic properties of four diamondoid oligomers. In particular, we focus on the inuence of the C = C double bond on the vibrational properties. The C = C double bond causes new modes in the Raman spectrum whose intensities are partly sensitive to the excitation energy. Further, by resonance Raman spectroscopy, we derive the π → π ∗ optical transition energies. We support the experimental ndings by DFT computations.

Experimental and Theoretical Methods The samples were analyzed in the solid state,

i.e., as small crystallites on a Si /SiO2 sub-

strate. We performed resonance Raman spectroscopy using a HORIBA T64000 spectrometer 3

ACS Paragon Plus Environment

Page 8 of 27

Page 9 of 27

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

The Journal of Physical Chemistry

(equipped with a Symphony cryogenic back-illuminated UV CCD) for excitation energies in the UV (ultra violet) range and a LabRAM HR800 (euqipped with a Horiba Jobin YvonDU420A-OE-323 CCD) for excitation energies in the visible range. For the UV excitation energies, an Ar-ion laser was used providing second harmonic generation (SHG), as well as a HeNe and a frequency doubled Nd: YAG laser for excitation energies in the visible. All measurements were performed in backscattering geometry. Due to the fast sample degeneration in the presence of UV light, Raman spectra were taken from dierent crystallites and from dierent positions on the crystallites. The individual Raman spectra were then summed up to a nal spectrum. We observed a bright luminescence from most of the crystallites both in the UV and in the visible range. Therefore, we had to carefully choose crystallites that did not luminesce in order to obtain a Raman signal under excitation in the UV range. Quantum mechanical computations of adamantane, diamantane, and the more complex diamondoid systems were performed with the QUANTUM Espresso package. 27 We used standard norm-conserving pseudopotentials for C and H with a cuto energy of 80 Ry, the Perdew-Burke-Ernzerhof 28 exchange-correlation functional and a discrete 2 × 2 × 2 k -point sampling for which the total energies of the structures were converged below a threshold of 0.001 eV. Based on the geometries from Ref., 29 we optimized the cell parameters and atomic positions of all systems until cell stress and interatomic forces were below 0.01 GPa and 0.01 eV/Å respectively. Comparable to Ref., 25,29 we assumed that the measured diamondoid compounds form van-der-Waals crystals. Non-covalent interactions were included through adaptive dispersion corrections from the D3(BJ) method. 30 Following geometry optimization, the phonon modes at the Γ point were computed through density functional perturbation theory. The analyzed materials are four diamondoid oligomers. They are connected through C = C double bonds between the diamondoids (adamantane and/or diamantane). In two of them, the double bonds are directly attached to the carbon cages:

4

(i) 3,10-bis-(2-adamantylidene)diamantane

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 10 of 27

Figure 1: The analyzed structures of a) [4.4](1,3)adamantanophan- trans,trans -1,8-diene, b) 3,10-bis-(2-adamantylidene)diamantane, c) 3-(2-adamantylidene)diamantane, and d) 1,3(bis-4-diamantyl)prop-1-ene are plotted. and

(ii) 3-(2-adamantylidene)diamantane [Fig. 1 b),c)]. In the other two dimers, the double

bonds are between carbon atoms that do not belong to a diamondoid cage:

(iii) 1,3-(bis-4-

diamantyl)prop-1-ene and (iv) [4.4](1,3)adamantanophan- trans,trans -1,8-diene [Fig. 1 d),a)]. In the latter compound the adamantane molecules are connected by double bonds on either side of the adamantane core structure. Chemical structures are depicted in Fig. 1. Details on the chemical synthesis of compounds a) and d) can be found in the Supplemental Material; further details on the chemical synthesis of other diamondoid oligomers can be found in Ref. 24

Results and Discussion The article is organized in two sections: First, we analyze the vibronic properties of the measured systems and compare the results to unfunctionalized adamantane (ADA) and diamantane (DIA), supported by (DFT) computations. Then we discuss their electronic structure based on resonance Raman scattering. Adamantane and diamantane are highly symmetric hydrocarbons exhibiting Td and D3d symmetry, respectively. As a consequence, 22 and 27 vibrational modes are Raman active in ADA and DIA. 7 The diamondoid oligomers exhibit a lower symmetry down to the C1 5

ACS Paragon Plus Environment

Page 11 of 27

DIA a)

∗4 2

Intensity (arb.units)



5

b)



∗3

2

∗1 ∗

BLM

∗5

∗3

ADA+DIA c)

∗4



∗2

∗3

2

ADA

∗4

BLM



ADA+DIA d)

∗4

3

∗5

∗5

BLM 500

BLM 1000

1500

2000

BLM

4.82 eV 2.33 eV

2500 3000 500 Raman shift cm−1 e)

1000

1500

2000

×0.15 ∗

∗3

∗2 Intensity (arb. units)

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

The Journal of Physical Chemistry

4

2500

f)

2 ∗1 ∗

3000

×0.33

BLM ∗4 ∗3

∗1 g)

BLM



∗3

∗2

200

×0.2

400

600

800

1000

1200

1400

∗2

h) BLM

4

1600

200

Raman shift cm−1

400 

600

3



800

1000

1200

1400

×0.15 ∗4

1600

Figure 2: Upper part: Raman spectra of the diamondoid oligomers (blue spectra) vs. Raman spectra of equivalent, unfunctionalized diamondoids (black curves). The excitation energy is 5.08 eV. Simplied structures of the oligomers are given next to the spectra and are the same for the spectra in the lower part of the Figure. Lower part: Raman spectra of the measured samples for an excitation energy in the UV (blue) and in the visible (black). Asterisks depict Raman modes that are exclusively observed in the diamondoids compounds. BLM stands for breathing-like mode. Corresponding frequencies are summarized in Table 1.

6

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

point group for 1,3-(bis-4-diamantyl)prop-1-ene [compound d)]. [4.4](1,3)Adamantanophan-

trans,trans -1,8-diene [a)] exhibits the C2 , 3,10-bis-(2-adamantylidene)diamantane [b)] the C2h , and 3-(2-adamantylidene)diamantane [c)] exhibits the CS point group. Thus we generally expect more complex Raman spectra in terms of the amount of Raman active vibrations. In Figure 2 (upper part) we compare measured Raman spectra of the analyzed samples (blue) to unfunctionalized adamantane and/or diamantane (black) for a likewise laser excitation energy of 5.08 eV. The molecular structures of the diamondoid oligomers are given as insets. By comparison to DFT computations, we separated the measured Raman modes of the diamondoid compounds into three classications: monomers,

(i) Raman modes from the unfunctionalized

(ii) Raman modes from the ethylene centers, and (iii) Raman modes from the

relative movement of entire monomers within the compounds. We further separated vibrational modes that have a "direct" double bond from those where the double bond is not attached to a carbon atom belonging to a diamondoid cage. The extra carbon atoms enlarge the vibrational degree of freedom of the ethylene centers. This leads to highly localized Raman active vibrations that are equivalent to those of pristine ethylene (compare Fig. 3). In the compounds we nd six types of diamondoids motions that are also known in their unfunctionalized counterparts. 7 They are C - C - C bend and C - C - C wag modes (≈ 150 −

600 cm−1 ), C - C stretch (600 − 900 cm−1 ) and C - H stretch modes (≥ 2900 cm−1 ), C - H and CH2 wag (≈ 1350 cm−1 ) modes, CH2 twist modes (1100 − 1200 cm−1 ), CH2 rock modes (1100 cm−1 ), and CH2 scissors modes (1450 cm−1 ). 31 The frequencies of Raman active C - C stretch modes in the functionalized oligomers reach from ≈ 300 − 900 cm−1 and are due to larger inertia of the oligomers lower compared to the pristine constituents. This also counts for the C - C - C bend and wag modes and explains the variety of new Raman modes below the breathing-like mode (BLM) in the spectra (compare Fig. 2 upper panel). CH2 scissors modes are not aected by the functionalization and are thus found around

1438 cm−1 ; they are the same for all samples, including unfunctionalized adamantane and diamantane. Frequencies of the C - H stretch modes do not dier substantially comparing the

7

ACS Paragon Plus Environment

Page 12 of 27

Page 13 of 27

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

The Journal of Physical Chemistry

oligomers to adamantane/diamantane. We observe two strong peaks around 2850 cm−1 and

2915 cm−1 that are attributed to symmetric and antisymmetric stretch vibrations, both for the oligomers and ADA/DIA. However, all compounds exhibit an additional mode around 5

3010 cm−1 (∗ ). By comparison to DFT computations, we assigned these bands to highly localized C - H stretch vibrations of carbon and hydrogen atoms neighboring double bonds in the oligomers. The double bonds cause a local stiening, slightly increasing the frequency of the C - H stretching modes. We observe breathing-like modes (BLM) for all diamondoid oligomers (named BLM in Fig. 2, upper panel). They are referred to C - C stretch vibrations of the diamondoid cages. Their frequencies downshift for larger molecules and generally depend on functionalization. 7,15,32 For adamantane and diamantane, the reported frequencies are 758 cm−1 and 709 cm−1 , in good agreement with our measurements. We nd two dierent BLM in case there are two dierent diamondoids in the compounds, both in the measurements and computations (compare Table. 1, Fig. 2). Except for 1,3-(bis-4diamantyl)prop-1-ene [Fig. 2 a)], the BLM frequencies are slightly downshifted compared to the diamondoids due to larger inertiae. However, a top (4-position) functionalization [as in the case of 1,3-(bis-4-diamantyl)prop-1-ene] only marginally aects the BLM frequencies. 15 The 4-position carbon atoms in diamantane are not deected during a BLM oscillation and thus inductive eects of the attached molecules lead to a slight upshift of the BLM rather than a downshift due to the additional mass attached. 15 In the computations the BLMs are further split into in-phase and out-of-phase vibrations separated by a few cm −1 (compare Table 1). We nd three types of vibrations that originate from the ethylene centers. One mode that all compounds have in common is a C = C stretching mode at 1660 cm−1 in good agreement with previous measurements on similar diamondoid and trishomocubane dimers. 21 It corresponds to the Ag mode in ethylene (D2h point group) and is marked with

∗4

in Fig. 2. In the

computations, we nd several vibrational patterns for the C = C stretching mode in which the vibrations are localized in varying molecules within the unit cell of the van-der-Waals

8

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 14 of 27

Table 1: Overview of experimental and computed frequencies of characteristic Raman peaks from the diamondoid oligomers. In the upper part we show Raman modes that all diamondoid compounds have in common and compare them to the corresponding vibrational modes of ethylene. 33 In the lower part we compare Raman modes of dimers in which the double bond is not directly attached to the diamondoid cage to the characteristic vibrational modes of ethylene. Modes marked with asterisks can be found in the Raman spectra in Fig. 2. We used a GGA approach with the PBE functional and a plain-wave basis set with pseudopotentials for the computations. Intermolecular, long-range interactions are accounted for through the DFT+D3(BJ) method. All frequencies are given in cm−1 . The replacement marker ∼ stands for {CH2 -CH=CH-CH2 }.

Sample ADA-2 × {∼} -ADA

Mode type DBM ∗2

exp. calc. Mode type 285/- 281/138 BLM

exp. 712

DIA-CH=CH-CH2 -DIA DBM ∗2 ADA=DIA DBM ∗2 ADA=DIA=ADA DBM ∗2

177 168 200 191 171 162

715 705 / 711 698 / 779 689 / 772 683 / 785 731 / 772

Ethylene ADA-2 × {∼}-ADA DIA-CH=CH-CH2 -DIA ADA=DIA ADA=DIA=ADA

B2g C=C bend ∗3 C=C bend ∗3 C=C bend ∗3 C=C bend ∗3

944 803 773 731 743

Ethylene B3u ADA-2 × {∼} -ADA DIA-CH=CH-CH2 -DIA ADA-2 × {∼} -ADA ethylene rotation ∗1 DIA-CH=CH-CH2 -DIA ethylene rotation ∗1

952

BLM BLM BLM

Ag 811 C =C 812 C =C 725 C =C 725 /694 C=C

B3g

967 968 189 194 231 236

9

ACS Paragon Plus Environment

stretch stretch stretch stretch

4

∗ ∗4 ∗4 ∗4

1621 1666 1667 1661 1660 1234

calc. 689 / 705

1663 1664 1653 1639

1303 1261

Page 15 of 27

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

The Journal of Physical Chemistry

crystal, respectively. The dimer in which adamantane is connected by two carbon chains, the double bond vibrations are also split into an in-phase and an out-of-phase vibration resulting in even more dierent C = C stretching modes. However, they are separated only by

≈ 1.5 cm−1 for all diamondoid oligomers and are thus not resolvable in the measurements. A second type of motion is observed around 190 cm−1 and only appears for the dimers where the C=C double bond is not directly attached to the diamondoid carbon cage ( ∗ in Fig. 2). 1

It corresponds to a hindered rotation of the ethylene moities. Since the vibrational pattern is similar to a pure rotation of ethylene, there is no Raman active equivalent in the unfunctionalized material. The third type of motion can be attributed to a localized bending mode as reported in Ref. 21 (∗ in Fig. 2). It is a torsional oscillation in which the double-bond carbon 3

atoms pyramidalize in opposite directions. We nd Raman frequencies around 750 cm−1 in both the experiments and computations for all diamondoid compounds. In ethylene ( D2h point group) the equivalent vibration has the irreducible representation B2g and is found at 954 cm−1 (compare Fig. 3). It is thus ≈ 200 cm−1 higher compared to the diamondoid oligomers. For the dimers where the C =C double bond is not directly attached to the diamodoid cage, we nd two more localized vibrations that have a direct equivalent in ethylene. They correspond to an asymmetrical stretching and a wagging vibration having the irreducible representations B3g and B3u in ethylene. The vibrational patterns are summarized in Fig. 3 and computed frequencies are given in Table 1. However, we can not provide the experimental Raman frequencies since we can not separate these two specic Raman modes from others convincingly. The broad shoulder on the low-energy side of the C = C peak (Fig. 2

≈ 1650 cm−1 ) is attributed to amorphous carbon due to sample degeneration under UV excitation. 34 All diamondoid oligomers show a second breathing-like mode in which the containing dia2

mondoids oscillate towards each other ( ∗ in Fig. 2). We will refer to it as dimer breathing mode (DBM). Since the vibration includes a collective displacement of whole diamondoids,

10

ACS Paragon Plus Environment

The Journal of Physical Chemistry

H R C=C R H

∗3

B2g





H R C=C R H B3u −→ H R C=C R H ←− B3g H ←− R ∗4 C=C R −→ H Ag H R ∗1 C=C R H rot. −→ ←− H R ∗2 C=C R H DBM ←



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

Figure 3: Localized vibrational patterns of ethylene centers in two diamondoid dimers. R stands for diamantane [1,4-(bis-4-diamantyl)but-2-ene] or a carbon atom with an attached adamantane ([4.4](1,3)adamantanophan- trans,trans -1,8-diene). The irreducible representations of the equivalent vibrations in ethylene are given next to the simplied chemical structures. Corresponding frequencies of both ethylene and the diamondoid oligomers are summarized in Table 1. "rot." and "DBM" stand for (hindered) rotations of the entire ethylene centers and dimer breathing mode, respectively. Asteriks correspond to the modes in the Raman spectra of Fig. 2. The vibrational patterns are given in the Supplemental Material.

11

ACS Paragon Plus Environment

Page 16 of 27

Page 17 of 27

the frequency is generally lower than 200 cm−1 both in the computations and measurements. The sample with two carbon chains connecting the adamantane molecules resembles a ring-like structure and thus, the oscillation patterns are slightly dierent. We nd two breathing-like modes with frequencies around 138 cm−1 and 285 cm−1 in the computations of which only the latter was experimentally accessible. Displacement vectors of the DBM and other characteristic modes of the oligomers are illustrated in the Supplemental Material.

Intensity (arb. units)

5.46 eV 5.42 eV 5.08 eV 5.25 eV 5.21 eV 5.32 eV 5.00 eV 4.82 eV 4.7 eV 2.33 eV 1.49 eV Raman shift (arb. units)

Intensity (arb. units)

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

The Journal of Physical Chemistry

1.5

2

4.5

5 5.5 1.5 2 Excitation energy (eV)

4.5

5

5.5

Figure 4: Normalized Raman intensities of the C = C stretch vibration ( ∗ in Fig. 2) are plotted. Simplied structures of the measured diamondoid oligomers are given in the gures. 4

Besides the inuence on the vibrational characteristics, the C = C double bond has a determining impact on the electronic structure. 14,2123 In contrast to unfunctionalized diamondoids, the HOMO (highest occupied molecular orbital) is highly localized at the C =C double bond. 14,2123 It is furthermore undisturbed by surrounding carbon atoms because of screening eects. 14 In contrast, the LUMO was found to be more delocalized towards neighboring carbon atoms. 15,22,23 This fact is accompanied by a geometry change between 12

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

the ground states S0 and the rst excited states S 1 for the electronically blended diamondoids. 22,23 However the optical absorption is dominated by higher excited states and always has a π → π ∗ character in the chemically blended diamondoids. 22,23 Resonance Raman spectroscopy can provide information about the geometrical structure of electronic states in molecules. If an optical transition is accompanied by an elongation of a bond length, a vibrational mode in which the atoms are distorted correspondingly is resonantly enhanced. 35,36 As a consequence, the intensity of the C = C stretch vibration is indicative for the dominant π → π ∗ absorption where the bond length in the excited state is signicantly increased. 22,25 We measured π → π ∗ transitions of the diamondoid oligomers with resonance Raman spectroscopy and show the results in Fig. 4. The upper part shows normalized Raman spectra of the C = C stretch vibration ( ∗ in Fig. 2) for dierent excitation energies and one chosen 4

diamondoid dimer. Frequencies are oset by 30 cm−1 for reasons of clarity. In the lower part we plot Raman peak intensities of the C = C stretch vibration for all measured diamondoid oligomers and excitation energies. Raman spectra are normalized to the most intense breating-like modes that are not selectively, resonantly enhanced. We observe a resonant enhancement of the C = C stretch vibration starting from ≈ 4.7 eV for all diamondoid compounds. This value is in good agreement to Refs. 22,23,25 where resonance Raman spectra for various diamondoid dimers and trimers are computed and experimentally determined. Higher excitations correspond to optical transition in higher vibrational states of the π ∗ orbital. In our experiments, the optical transition energies are widely independent from the structure of the compounds or the diamondoid constituents. In fact, they are close to the π → π ∗ transition of ethylene ( 4.4 eV). 37,38 Moreover, the measured transition energies are close to the energy of the M -point exciton in other sp2 materials such as graphene or graphite 3942 emphasizing the dominant character of the double bond in the chemically blended hydrocarbons. With these results, we show that ( i ) the HOMOs in diamondoid oligomers are highly 13

ACS Paragon Plus Environment

Page 18 of 27

Page 19 of 27

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

The Journal of Physical Chemistry

Figure 5: Isosurfaces of the π (top) and π ∗ (bottom) orbitals of [4.4](1,3)adamantanophantrans,trans -1,8-diene (left) and 1,3-(bis-4-diamantyl)prop-1-ene (right) are plotted. We used a GGA approach with the PBE functional and a plain-wave basis set with pseudopotentials for the computations. Isosurfaces of the HOMO and HOMO-1 of the other oligomers can be found in Ref. 14 localized at the C = C double bond and ( ii ) the inuence of the surrounding constituents on the π → π ∗ transition is only marginal due to screening eects, as already proposed in Ref. 14 Isosurfaces of the π and π ∗ orbitals are plotted for two diamondoid oligomers in Fig. 5 showing their localization at the C =C double bond, widely independent from the structure of the dimers. Isosurfaces of HOMO and HOMO-1 from other sp2 − sp3 diamondoid oligomers can be seen in Ref. 14 The optical transitions are signicantly lowered in the diamondoid oligomers. They exhibit around 6.5 eV for the smallest diamondoids adamantane and diamantane but decrease with increasing size due to quantum connement. 3,6,9,10,14,22 Using resonance Raman measurements we show that the dominant π → π ∗ optical transition energies in sp2 /sp3 diamondoid oligomers decrease by at least ≈ 1.5 eV down to below

≈ 5 eV. 14,2123 The luminescence even for excitation energies in the visible cannot be explained by the inherent electronic structures of the diamondoid oligomers. The exposure to air might cause nitrogen or oxygen impurities changing their electronic structure. However its origin is still unclear. Comparing the Raman spectra e)-h) in Fig. 2, we observe other modes that are resonantly 14

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

enhanced under UV excitation. A clear enhancement in intensity is observed for the C = C 2

3

bend/twist modes ( ∗ ) and the dimer breathing modes ( ∗ ). In both cases the vibrational patterns are accompanied by an elongation of the C = C double bond and are thus resonantly enhanced. However, the enhancement factor is lower compared to the pure C = C stretch vibration since the eigenvectors only have a projection in the direction of the C = C bond. Further, we observe a relative enhancement of CH 2 twist and wag modes ( ≈ 1100 − 1350 cm−1 ) for UV excitation energies. In the computations, we nd CH 2 twist and wag vibrations that are localized on carbon atoms directly attached to the double bond. These vibrations cause a displacement of the double bonded carbon atoms along the direction of their bond and thus they are also resonantly enhanced under UV excitation. In case of the dimers in which the double bond is not directly attached to the diamondoid cage, the localization of the vibrations is slightly stronger and we generally observe a stronger enhancement of Raman intensities.

Conclusions In summary, we performed Raman measurements of diamondoid compounds interconnected by ethylene bridges. We nd several analogies to ethylene: In all compounds, we observe highly localized vibrations that are equivalent to the Ag and B2g modes in ethylene, but they are downshifted in frequency. The ethylene moities in the dimers where the C =C double bond is not directly attached to the diamondoid cage have a larger vibrational degree of freedom. This leads to additional, localized vibrations comparable to the B3u and B3g modes in ethylene. Further, we nd a hindered rotation of the ethylene moities between the diamondoids that does not have an Raman-active equivalent in ethylene. Due to the structure of the compounds, a new dimer breathing mode was identied that can not be found in unfunctionalized diamondoids. Typical positions of this mode are around 200 cm−1 . Utilizing resonance Raman scattering we determine the π → π ∗ transition at ≈ 4.7 eV in all

15

ACS Paragon Plus Environment

Page 20 of 27

Page 21 of 27

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

The Journal of Physical Chemistry

analyzed diamondoid oligomers . Furthermore, we show that π and π ∗ orbitals are highly localized at the double bond. The π → π ∗ transition is thus laregely independent of the structure or individual constituents of the diamondoid compounds.

Supporting Information The supporting information contains coordinates of the relaxed structures from all computed diamondoid oligomers and illustrated eigenvectors of characteristic vibrational modes. The chemical synthesis of [4.4](1,3)Adamantanophan- trans,trans -1,8-diene, 4-Allyldiamantane, and 1,3(Bis-4-diamantyl)prop-1-ene with corresponding NMR (nuclear magnetic resonance) spectra are given.

Acknowledgments The authors acknowledge nancial support from the DFG under grant number MA 4079/6-2 and SCHR 597/24-1 within the Forschergruppe 1282 and the European Research Council (ERC) Grant No. 259286. The authors also gratefully acknowledge the North-German Supercomputing Alliance (HLRN) for providing the computational resources used for the simulations in this work.

References (1) Landa, S.; Machá£ek, V. Sur l'adamantane, nouvel hydrocarbure extrait du naphte.

Collect. Czech. Commun.

1933, 5, 15

(2) Dahl, J. E.; Liu, S. G.; Carlson, R. M. K. Isolation and Structure of Higher Diamondoids, Nanometer-Sized Diamond Molecules.

Science

2003,

299, 9699

(3) Drummond, N. D.; Williamson, A. J.; Needs, R. J.; Galli, G. Electron Emission from 16

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 22 of 27

Diamondoids: A Diusion Quantum Monte Carlo Study.

Phys. Rev. Lett.

2005,

95,

096801 (4) Yang, W. L.; Fabbri, J. D.; Willey, T. M.; Lee, J. R. I.; Dahl, J. E.; Carlson, R. M. K.; Schreiner, P. R.; Fokin, A. A.; Tkachenko, B. A.; Fokina, N. A. et al. Monochromatic Electron Photoemission from Diamondoid Monolayers.

Science

2007,

316, 14601462

(5) Roth, S.; Leuenberger, D.; Osterwalder, J.; Dahl, J.; Carlson, R.; Tkachenko, B.; Fokin, A.; Schreiner, P.; Hengsberger, M. Negative-electron-anity diamondoid monolayers as high-brilliance source for ultrashort electron pulses.

Chem. Phys. Let.

2010,

495, 102  108 (6) Landt, L.; Klünder, K.; Dahl, J. E.; Carlson, R. M. K.; Möller, T.; Bostedt, C. Optical Response of Diamond Nanocrystals as a Function of Particle Size, Shape, and Symmetry.

Phys. Rev. Lett. 2009, 103, 047402

(7) Filik, J.; Harvey, J. N.; Allan, N. L.; May, P. W.; Dahl, J. E.; Liu, S.; Carlson, R. M. Raman spectroscopy of diamondoids.

Spectrochim. Acta A Mol. Biomol. Spectrosc.

2006,

64, 681692 (8) Willey, T. M.; Bostedt, C.; van Buuren, T.; Dahl, J. E.; Liu, S. G.; Carlson, R. M. K.; Meulenberg, R. W.; Nelson, E. J.; Terminello, L. J. Observation of quantum connement in the occupied states of diamond clusters.

Phys. Rev. B

2006,

74, 205432

(9) Richter, R.; Rohr, M. I. S.; Zimmermann, T.; Petersen, J.; Heidrich, C.; Rahner, R.; Möller, T.; Dahl, J. E.; Carlson, R. M. K.; Mitri¢, R. et al. Laser-induced uorescence of free diamondoid molecules.

Phys. Chem. Chem. Phys.

2015,

17, 47394749

(10) Richter, R.; Wolter, D.; Zimmermann, T.; Landt, L.; Knecht, A.; Heidrich, C.; Merli, A.; Dopfer, O.; Reiÿ, P.; Ehresmann, A. et al. Size and shape dependent photoluminescence and excited state decay rates of diamondoids.

Phys. Chem. Chem. Phys.

30703076 17

ACS Paragon Plus Environment

2014,

16,

Page 23 of 27

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

The Journal of Physical Chemistry

(11) Schwertfeger, H.; Fokin, A.; Schreiner, P. Diamonds are a Chemist's Best Friend: Diamondoid Chemistry Beyond Adamantane.

Angew. Chem. Int. Ed. 2008, 47, 10221036

(12) Gunawan, M. A.; Poinsot, D.; Domenichini, B.; Dirand, C.; Chevalier, S.; Fokin, A. A.; Schreiner, P. R.; Hierso, J.-C. The functionalization of nanodiamonds (diamondoids) as a key parameter of their easily controlled self-assembly in micro- and nanocrystals from the vapor phase.

Nanoscale

2015, 7, 19561962

(13) Rander, T.; Staiger, M.; Richter, R.; Zimmermann, T.; Landt, L.; Wolter, D.; Dahl, J. E.; Carlson, R. M. K.; Tkachenko, B. A.; Fokina, N. A. et al. Electronic structure tuning of diamondoids through functionalization.

J. Chem. Phys. 2013, 138

(14) Zimmermann, T.; Richter, R.; Knecht, A.; Fokin, A. A.; Koso, T. V.; Chernish, L. V.; Gunchenko, P. A.; Schreiner, P. R.; Möller, T.; Rander, T. Exploring covalently bonded diamondoid particles with valence photoelectron spectroscopy.

J. Chem. Phys.

2013,

139 (15) Meinke, R.; Richter, R.; Möller, T.; Tkachenko, B. A.; Schreiner, P. R.; Thomsen, C.; Maultzsch, J. Experimental and theoretical Raman analysis of functionalized diamantane.

J. Phys. B At. Mol. Opt. Phys.

2013,

46, 025101

(16) Kahl, P.; Wagner, J. P.; Balestrieri, C.; Becker, J.; Hausmann, H.; Bodwell, G. J.; Schreiner, P. R. [2](1,3)Adamantano[2](2,7)pyrenophane: A Hydrocarbon with a Large Dipole Moment.

Angew. Chem. Int. Ed.

2016,

55, 92779281

(17) Fokin, A. A.; Gunchenko, P. A.; Novikovsky, A. A.; Shubina, T. E.; Chernyaev, B. V.; Dahl, J. E. P.; Carlson, R. M. K.; Yurchenko, A. G.; Schreiner, P. R. Photoacetylation of Diamondoids: Selectivities and Mechanism.

European J. Org. Chem.

2009,

2009,

51535161 (18) Vörös, M.; Demjén, T.; Szilvási, T.; Gali, A. Tuning the Optical Gap of Nanometer-Size

18

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 24 of 27

Diamond Cages by Sulfurization: A Time-Dependent Density Functional Study.

Phys.

Rev. Lett. 2012, 108, 267401 (19) Landt, L.; Bostedt, C.; Wolter, D.; Möller, T.; Dahl, J. E. P.; Carlson, R. M. K.; Tkachenko, B. A.; Fokin, A. A.; Schreiner, P. R.; Kulesza, A. et al. Experimental and theoretical study of the absorption properties of thiolated diamondoids. 2010,

J. Chem. Phys.

132, 144305

(20) Landt, L.; Staiger, M.; Wolter, D.; Klünder, K.; Zimmermann, P.; Willey, T. M.; van Buuren, T.; Brehmer, D.; Schreiner, P. R.; Tkachenko, B. A. et al. The inuence of a single thiol group on the electronic and optical properties of the smallest diamondoid adamantane.

J. Chem. Phys. 2010, 132, 024710

(21) Meinke, R.; Richter, R.; Merli, A.; Fokin, A. A.; Koso, T. V.; Rodionov, V. N.; Schreiner, P. R.; Thomsen, C.; Maultzsch, J. UV resonance Raman analysis of trishomocubane and diamondoid dimers.

J. Chem. Phys. 2014, 140

(22) Banerjee, S.; Saalfrank, P. Vibrationally resolved absorption, emission and resonance Raman spectra of diamondoids: a study based on time-dependent correlation functions.

Phys. Chem. Chem. Phys.

2014,

16, 144158

(23) Banerjee, S.; Stuker, T.; Saalfrank, P. Vibrationally resolved optical spectra of modied diamondoids obtained from time-dependent correlation function methods.

Phys. Chem.

Chem. Phys. 2015, 17, 1965619669 (24) Zhuk, T. S.; Koso, T.; Pashenko, A. E.; Hoc, N. T.; Rodionov, V. N.; Seran, M.; Schreiner, P. R.; Fokin, A. A. Toward an Understanding of Diamond sp2-Defects with Unsaturated Diamondoid Oligomer Models.

J. Am. Chem. Soc. 2015, 137, 65776586

(25) Tyborski, C.; Meinke, R.; Gillen, R.; Bischo, T.; Knecht, A.; Richter, R.; Merli, A.; Fokin, A. A.; Koso, T. V.; Rodionov, V. N. et al. From isolated diamondoids to a van-

19

ACS Paragon Plus Environment

Page 25 of 27

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

The Journal of Physical Chemistry

der-Waals crystal: A theoretical and experimental analysis of a trishomocubane and a diamantane dimer in the gas and solid phase.

J. Chem. Phys. 2017, 147, 044303

(26) Sasagawa, T.; xun Shen, Z. A route to tunable direct band-gap diamond devices: Electronic structures of nanodiamond crystals.

J. Appl. Phys. 2008, 104, 073704

(27) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.

dens. Matter

2009,

J. Phys. Con-

21, 395502 (19pp)

(28) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple.

Phys. Rev. Lett. 1996, 77, 38653868

(29) Koso, T. Unsaturated Nanodiamonds:

Synthesis and Functionalization of Cou-

pled Diamondoids as a Direct Route to Nanometer-sized Building Blocks. doctoral

thesis,

Justus-Liebig

University,

Giessen,

2013;

http://geb.uni-

giessen.de/geb/volltexte/2013/9874/ (30) Grimme, S.; Ehrlich, S.; Goerigk, L. Eect of the damping function in dispersion corrected density functional theory.

J. Comput. Chem. 2011, 32, 14561465

(31) Jensen, J. O. Vibrational frequencies and structural determination of adamantane.

trochim. Acta A Mol. Biomol. Spectrosc.

2004,

Spec-

60, 18951905

(32) Filik, J.; Harvey, J. N.; Allan, N. L.; May, P. W.; Dahl, J. E. P.; Liu, S.; Carlson, R. M. K. Raman spectroscopy of nanocrystalline diamond: An ab initio approach.

Rev. B

2006,

Phys.

74, 035423

(33) Walker, I. C.; Stamatovic, A.; Wong, S. F. Vibrational excitation of ethylene by electron impact: 1-11 eV.

J. Chem. Phys. 1978, 69, 55325537

20

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 26 of 27

(34) Yoshikawa, M.; Katagiri, G.; Ishida, H.; Ishitani, A.; Akamatsu, T. Raman spectra of diamondlike amorphous carbon lms.

J. Appl. Phys. 1988, 64, 64646468

(35) Tsuboi, M.; Hirakawa, A. Y. A correlation between vibronic coupling, adiabatic potential, and Raman scattering: A theoretical background of a proposed rule.

J. Raman

Spectrosc. 1976, 5, 7586 (36) Hirakawa, A. Y.; Tsuboi, M. Molecular Geometry in an Excited Electronic State and a Preresonance Raman Eect.

Science

1975,

188, 359361

(37) Buenker, R. J.; Peyerimho, S. D. All-valence-electron conguration mixing calculations for the characterization of the 1(pi, pi ∗ ) states of ethylene.

Chem. Phys. 1975, 9, 75 

89 (38) Veen, E. V. Low-energy electron-impact spectroscopy on ethylene. 1976,

Chem. Phys. Let.

41, 540  543

(39) Painter, G. S.; Ellis, D. E. Electronic Band Structure and Optical Properties of Graphite from a Variational Approach.

Phys. Rev. B

1970, 1, 47474752

(40) Taft, E. A.; Philipp, H. R. Optical Properties of Graphite.

Phys. Rev.

1965,

138,

A197A202 (41) Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejón, P. Tight-binding description of graphene.

Phys. Rev. B

2002,

66, 035412

(42) Tyborski, C.; Herziger, F.; Gillen, R.; Maultzsch, J. Beyond double-resonant Raman scattering: Ultraviolet Raman spectroscopy on graphene, graphite, and carbon nanotubes.

Phys. Rev. B

2015,

92, 041401

21

ACS Paragon Plus Environment

Dimer-breathing modes

hePage Journal 27 of of27 Physical Chemistr

ACS 1 Paragon Plus Environment 2 Diamondoid oligomers 3