Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic

Article pubs.acs.org/JPCC

Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl Manuel Hochheim,† Alexander Paulheim,‡ Moritz Sokolowski,‡ and Thomas Bredow*,† †

Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstraße 4, 53115 Bonn, Germany ‡ Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstr. 12, 53115 Bonn, Germany S Supporting Information *

ABSTRACT: The vibrational fine structure of the fluorescence spectra of isolated perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecules adsorbed on (100) surfaces of sodium chloride and potassium chloride has been studied theoretically and experimentally. In order to analyze the experimentally observed differences in the vibronic spectra of PTCDA adsorbed on the two surfaces, we simulated the spectra by calculating the Franck−Condon factors. The calculated spectra are in excellent agreement with the experiment and indicate that the difference between the two surfaces is the result of a stronger distortion of the molecular geometry on NaCl.

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INTRODUCTION

Whether a vibrational state couples to an electronic transition, and thus appears as a signal in the spectrum, or not, depends on the corresponding Franck−Condon factor (FCF).18−20 This factor is the square of the overlap of the vibrational wave functions in the initial and the target electronic state, and it is proportional to the intensity of the signal appearing in the spectrum. The FCFs can be calculated analytically within the harmonic approximation, e.g., with the ezSpectrum program.21 For the computation of the FCFs it is necessary to calculate the equilibrium geometry and the normal modes of the system in both the electronic ground and the excited state. Although there are more elaborate methods to calculate excited-state properties like equation of motion coupled-cluster methods,22 quantum Monte Carlo,23 and the Green-function Bethe− Salpeter formalism,24,25 we used time-dependent density functional theory (TD-DFT).26 In contrast to the aforementioned methods, TD-DFT provides a better compromise between accuracy and computational effort; therefore, it is applicable even to systems of more than 100 heavy atoms. In this work, we report on the simulation of the vibrational fine structure in the fluorescence spectrum of PTCDA in the gas phase and of isolated PTCDA molecules on NaCl(100) and KCl(100) surfaces. Isolated PTCDA molecules are predominantly located on terraces of the (100) surfaces after deposition on a cold sample.16 In the fluorescence spectra of isolated PTCDA molecules adsorbed on NaCl(100) and KCl(100) surfaces, especially the low-frequency region below

The research on optical properties of π-conjugated organic molecules is mainly motivated by the promising perspective that they will play a key role in the emerging field of nanoelectronics.1−3 Various devices, consisting of thin layers of organic semiconductors and inorganic materials, already exist, e.g., organic photovoltaic cells,4−7 photosensors, organic lightemitting diodes,8−10 and transistors.11−13 In such devices the interface between the organic and inorganic part is of major importance for the functionality. Since the interaction between the molecules and the substrates may affect the electronic properties, the study of these effects is in the focus of experimental studies. Müller et al. investigated the molecule− surface interaction by measuring the optical properties of the archetypal organic semiconductor perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) adsorbed on sodium chloride NaCl(100) and potassium chloride KCl(100) surfaces via fluorescence spectroscopy at low temperatures.14−17 Fluorescence spectroscopy is a powerful tool to investigate the electronic structure of molecular systems. Additionally, a wealth of information about the ground-state vibrational structure of the investigated molecule can be gained. Certain vibrational states in the electronic ground state couple to the electronic transition which results in a vibrational fine structure of the electronic signal. This vibrational structure is characteristic for each molecule. Adsorption on surfaces affects this structure due to changes in the potential and the geometry. However, it is not trivial to interpret the vibrational fine structure from recorded experimental spectra. In such cases theoretical calculations of the vibrational spectra can be essential for an improved understanding. © 2016 American Chemical Society

Received: August 24, 2016 Revised: September 25, 2016 Published: October 3, 2016 24240

DOI: 10.1021/acs.jpcc.6b08540 J. Phys. Chem. C 2016, 120, 24240−24249

Article

The Journal of Physical Chemistry C 250 cm−1 is of particular interest. In this region two additional signals appear in the spectra of isolated PTCDA molecules adsorbed on both surfaces which is simply explainable by the symmetry reduction of the molecule from D2h to C2v.16 The signals in the region above 250 cm−1 only differ slightly from the signals of PTCDA in the gas phase. The ground state vibrations of PTCDA in the gas phase have been investigated theoretically in previous studies by Scholz et al.27,28 Heating or irradiation of the sample with intense laser light induces diffusion of PTCDA molecules to step edges which result from growth defects of the surface.17 The adsorption at step edges is thermodynamically more favored, and the process is irreversible.29 Recent STM data and DFT calculations have shown that the step edge sites are so-called vacancy sites. At these sites the PTCDA molecule is partially embedded into the step edge.29,30 The diffusion of PTCDA to step edge sites induces again additional signals in the experimental spectra of PTCDA on both surfaces. Remarkable is the fact that in this case more signals appear in the spectrum of PTCDA molecules at NaCl step edges compared to the spectrum of PTCDA molecules located at step edges of the KCl surface. The aim of this work is to reveal the reasons for the differences in the spectra of PTCDA adsorbed at NaCl and KCl step edges with theoretical methods. Before doing so we validate our approach by comparing our simulated spectra to well-known systems like PTCDA in the gas phase and adsorbed at terrace sites. In the next section we give a detailed overview on the computational details followed by an explicit description of the utilized model systems. Afterward a comparison between the surfaces and between adsorbed and gas-phase molecules will be made. Finally, conclusions are drawn.

especially range-separated hybrid functionals yield a good description of the electronic excited state.41 Therefore, we used the CAM-B3LYP functional for our calculations.42,43 Furthermore, our previous studies showed that CAM-B3LYP provides a good description of the S1 state energy of the PTCDA molecule.44 Before we calculated the vibrational frequencies of the ground and the excited state we reoptimized the geometry of PTCDA in the S0 and the S1 state and allowed free relaxation of the molecule, while the surface atoms were kept fixed. We used the standard Gaussian geometry convergence thresholds. VeryTight thresholds did not lead to changes in the resulting vibrational energies. Subsequently, we calculated the vibrations of the molecule, while the surface atoms were again kept fixed. Finally, we used the obtained geometries, vibrational frequencies, and normal modes to calculate the Franck− Condon factors with the program ezSpectrum21 applying the parallel approximation with previous normal mode reordering. An intensity threshold of 10−3 was applied. Experimental Details. PTCDA molecules were sublimed onto thin NaCl(100) and KCl(100) layers deposited on Ag(100) at coverages between 0.02% and 1.00% of a monolayer from a Knudsen cell under ultrahigh vacuum. Both insulator layers were typically about 10 atomic layers thick and grown as in previous experiments.45,46 The sample was cooled to a range between 6 and 20 K by liquid helium. At these low temperatures the PTCDA molecules are immobile on the surface. After deposition the molecules are statistically distributed on the surface. To induce a transition of the molecule to surface step sites the sample was heated to 100− 150 K for 10 min. The migration to the step sites was previously proven by STM measurements.29 The molecule at the step site provides a much higher resolution of the vibrations in the spectrum than the terrace site spectra recorded in previous studies. The fluorescence spectra of PTCDA adsorbed on NaCl and KCl were measured in a temperature range between 6 and 20 K. The resulting spectra are averaged spectra obtained from sets of spectra measured for different sample preparations. All further experimental details can be found in “Surface Induced Vibrational Modes in the Fluorescence Spectra of PTCDA on the KCl and NaCl(100) Surfaces” by Paulheim et al.17

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METHODS Computational Details. Ground-state structural properties of the adsorbate system were calculated at the DFT-GGA-level of theory within the crystalline-orbital program CRYSTAL14.31 For this purpose the Perdew−Burke−Ernzerhof functional (PBE),32,33 which is known for providing reliable ground-state structures, has been utilized. London-type dispersion forces which play a crucial role in adsorption processes were taken into account by the DFT-D3 scheme with Becke−Johnson damping and a cutoff radius of 95 Bohr.34,35 An extra fine integration grid (XXLGRID) and tight tolerances for twoelectron integrals have been used. Considering the fact that the electronic excitation takes place in the molecule and the coupling vibrations are primarily molecular vibrations we decided to use relatively small basis sets for the surface atoms sodium,36,37 potassium,36,37 and chlorine38 in order to save computertime. For the atoms of the PTCDA molecule, on the other hand, the larger 6-311G** Pople-type basis of triple-ζquality was used.39 For the purpose of excited state and frequency calculations we switched to the molecular quantum chemical program package Gaussian0940 since electronic excited state calculations cannot be performed within the CRYSTAL14 program package. The excited-state properties were calculated on the TD-DFT level of theory with an embedded cluster approach. The surface atom positions of the adsorbate−cluster system were taken from our periodic calculations. The same basis sets were used for the surface as with CRYSTAL14, but we truncated the molecular basis set to 6-311G* to reduce computational cost. From benchmark studies it is known that

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RESULTS AND DISCUSSION Structural Properties and Modeling. We modeled the (100) surfaces as a three-layer 4 × 4 supercell slab containing 96 atoms plus the molecule adsorbed from one side. From experiments and previous theoretical studies it is known that the molecule adsorbs with its long axis parallel to the [110] or [1¯10] direction of the surface with the carbonyl oxygen atoms facing surface cations and the center of the molecule located above a surface anion.14,16,47 Hence, this orientation was used as a starting point for our optimizations with CRYSTAL14. Due to attractive electrostatic forces between the surface cations and the carbonyl oxygen atoms and repulsive forces occurring between the surface and the π-system, the molecule adopts a bent conformation on the surface. Furthermore, we calculated the ground-state vibrations of PTCDA and the surface to estimate the influence of surface atom vibrations. For the computation of the FCFs we needed the vibrational frequencies of both the S1 state and the S0 state. These were calculated with Gaussian09. The clusters employed as surface models were constructed by taking the atom positions of the supercell obtained from the periodic calculation. The cluster 24241


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The Journal of Physical Chemistry C

the vibrational wave functions related to the electronic states; and μ̂e is the electronic dipole moment operator which has three components that transform as x, y, and z. The first factor, describing the pure electronic transition, is nonzero if the triple direct product Γ(Ψi) × Γ(μ̂ e) × Γ(Ψi) encloses the totally symmetric representation. Accordingly, a vibronic transition is only allowed if the second factor, the integral over the vibronic wave functions, is nonzero, too. Most transitions take place from the totally symmetric vibrational ground state of Ψi to the first excited vibrational state of Ψj. In this case only normal modes corresponding to the totally symmetric irreducible representation of the point group should couple to the electronic transition, e.g., the Ag symmetric normal modes of the D2h symmetric PTCDA molecule. All vibrations of other symmetries remain dark. The first Ag symmetric vibration is the intense breathing mode at 229 cm−1 in the experimental spectrum. Besides the experimental work by Stienkemeier et al. there are previous theoretical works on the ground state vibrations of PTCDA in the gas phase to explain the Raman and IR spectra.27,28 However, to our knowledge, there has not been a previous simulation of the full vibronic fluorescence spectrum of PTCDA in the gas phase. In Table 1 our calculated vibronic signals are compared to the experimental data. The positions of the experimental signals and their relative intensities have been evaluated by the authors from the corresponding experimental data set.48 Graphical representations of all corresponding normal modes can be found in the SI. We were able to identify an equivalent for each experimental peak in our simulated spectrum. In addition our calculated vibrational energies of the ground state are in good agreement with previous calculations by Scholz et al.28 Our used scaling factor makes the comparison difficult. Therefore, in the following we will give the scaled ω̃ corr and the unscaled vibrational energies ω̃ and compare them to the vibrational energies calculated by Scholz ω̃ Scholz for all fundamental vibrations marked in Figure 1 (ω̃ corr/ω̃ /ω̃ Scholz). The calculated breathing mode along the long axis of the molecule at 225/234/234 cm−1 (A) in Figure 1 is clearly dominating the spectrum. It not only is the most intense signal but also appears in several combination bands and in form of two overtones at 451 cm−1 (A′) and 676 cm−1 (A″). Furthermore, intense and characteristic modes appear at 530/ 552/542 cm−1 (B), 612/637/630 cm−1 (C), 1298/1352/1361 cm−1 (D), 1372/1429/1381 cm−1 (E), and 1590/1656/1623 cm−1 (F). (B) corresponds to the breathing along the short axis of the molecule, and (C) corresponds to a skeletal vibration in combination with an anhydride deformation vibration. While the previous signals were primarily caused by skeletal vibrations, (D), (E), and (F) are the result of bending vibrations of the hydrogen atoms. Our calculations indicate that the broad band at 1594 cm−1 in the experimental spectrum consists of (F), a combination band of (A) and (E), and another fundamental vibration at 1609/1676/1641 cm−1 (G), based on hydrogen vibrations. The deviation from the calculated vibrational energies by Scholz increases with the vibrational energy of the vibrations. This is a result of the different potentials caused by the different functional and basis set pairs, but for vibrations with lower vibrational energies than 1000 cm−1 the deviation is usually less than 10 cm−1. Vibrational Spectra on NaCl(100) and KCl(100) Terrace Sites. The adsorption of PTCDA on the NaCl(100) and KCl(100) surfaces leads to significant changes in the fluorescence spectra. Besides the fact that the electronic

was embedded in a point charge array generated by translating the Na/K and Cl surface atoms in the xy-plane along the surface lattice vectors. These translated image atoms were thereupon replaced by point charges of ±1.0 e. All structural properties and the calculated optical excitation energies are in good agreement with the experiment. Our detailed evaluation of these properties, the associated convergence tests, and further information have already been published.44 Gas-Phase Spectrum. The next step is the investigation of the distinct vibrational fine structure of the electronic transition. As a starting and reference point we calculated the vibrations and the resulting FCFs of the D2h-symmetric PTCDA molecule in the gas phase. Experimental reference data are available from a previous study by Stienkemeier et al., who measured the fluorescence spectrum of PTCDA in ultracold He nanodroplets (400 mK)48 which leads to a very good resolution of the vibrational fine structure. Almost exclusively the vibrational ground state of the S1 state is populated which leads to a simplification of the vibronic spectrum because the number of hot bands is very low. Furthermore, the weak interaction with the helium leads to a very small perturbation and is the reason for the observed narrow spectral lines.48,49 The comparison of the experimental and the calculated vibronic spectrum shows a quantitative agreement, but it also reveals a systematic error. The calculated vibrational energies are systematically overestimating the experimental vibrational energies. The overestimation increases with increasing vibrational energy. This is a well-known problem which results from the difference between the real and the DFT potential. It is common to introduce a scaling factor for each functional/basis set pair.50 A scaling factor for the combination of CAM-B3LYP and the 6-311G* basis set could not be found in the literature. Therefore, we evaluated a scaling factor by assigning the vibrations of the experimental spectrum matching those in the simulated spectrum and minimizing the square error. Details can be found in the SI. Figure 1 shows the corrected simulated

Figure 1. Comparison of the experimental (upper part)48 and corrected calculated (lower part) vibrational fine structure in the fluorescence spectrum of PTCDA in the gas phase. The calculated line spectrum is convoluted into Lorentzian profiles. The intensities of the simulated spectrum is scaled to the experimental breathing mode signal at 229 cm−1. The energies in cm−1 are given relative to the S0−0 transition energy.

gas-phase spectrum compared to the experimental spectrum. The root-mean-square deviation of the simulated vibrational energies is reduced from 48 to 8 cm−1 with a scaling factor of 0.96. The simulated line spectrum is convoluted in Lorentzian profiles to simulate experimental line broadening. A transition is permitted if the product of ⟨Ψi|μ̂ e|Ψj⟩ and ⟨χiν|χjν′⟩ is nonzero. Ψ are the electronic wave functions; χ are 24242


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surface more vibrations are visible than in the gas phase. The first clearly visible signal in the experimental gas phase spectrum is the breathing mode at 229 cm−1, but on the surface additional signals of lower frequencies appear. This is the result of the lowering of the molecular symmetry by adsorption. The adsorption of the D2h symmetric PTCDA molecule on a perfect NaCl(100) or KCl(100) surface results in a C2v symmetry of the adsorbate−substrate system. Vibrations belonging to the A1 representation of the C2v point group are symmetry allowed to couple to the electronic transition. In addition to D 2h −A 1g also the D 2h −B 1u representation correlates to the C2v−A1 representation and becomes potentially visible. Our simulated spectra are again in good agreement with the experiment (Figure 2a and Figure 2b). They reproduce the experimental spectra quantitatively and we are again able to identify an equivalent for each experimental peak in our simulated spectra. The same scaling factor was applied as for the gas-phase spectrum. To achieve an electroneutral and perfectly C2v symmetric adsorbate−substrate system we had to set up our system in a different manner than described above. We could not use the three-layered 4 × 4 supercell obtained from our periodic calculation without modifications because formerly translational equivalent atoms on the border of the supercell are only located on one side of the resulting cluster which would lead to a symmetry lowering from C2v to C1. To create a C2v symmetric model we duplicated border atoms and translated them along the surface lattice vector. We further had to modify the number of atomic layers. To achieve an electroneutral C2v symmetric surface cluster an even number of atomic layers is necessary. Therefore, we have chosen a reduced model with two atomic layers already in the CRYSTAL calculation. The asymmetric unit cell of the 4 × 4model and the C2v symmetric model can be seen in Figure 3. As expected from group theory, only A1 symmetric vibrations are allowed to couple to the electronic transition in C2v symmetry. A characteristic representative of those A1 symmetric vibrations that correspond to B1u modes in the gas-phase molecule are the signals at 91 cm−1 on NaCl and 84 cm−1 on KCl denoted as L1 which represent bending modes of the anhydride groups of PTCDA toward the surface. The calculated vibrational energies underestimate the experimental energies of 104 cm−1 on NaCl and 94 cm−1 on KCl by roughtly 10 cm−1. Furthermore, a new signal in the simulated spectra appears at 191 cm−1 on NaCl and at 189 cm−1 on KCl denoted as L2 which corresponds to a vibration of the hydrogen atoms toward the surface. In this case only the simulated vibrational energy on NaCl underestimates the experimental vibrational energy of 206 cm−1. On KCl the experimental value of 184 cm−1 is

Table 1. Assignment of Calculated Spectral Lines of PTCDA in the Gas Phase to Signals in the Experimental Spectrum of PTCDA in Helium Nanondropletsa simulation

experiment48

no.

ω̃ corr

rel. int.

ω̃ exp.

rel. int.

characterization

1

225

1.000

229

1.000

2

451

0.228

454

0.293

3

530

0.123

537

0.171

4

612

0.143

620

0.159

5

676

0.031

680

0.068

6

714

0.031

725

0.033

7

756

0.054

764

0.080

8

837

0.063

851

0.067

9 10 11 12 13 14

1042 1298 1334 1372 1445 1523

0.063 0.633 0.229 0.637 0.115 0.277

1054 1303 1337 1387 1443 1529

0.064 0.352 0.083 0.257 0.194 0.133

15 16

1590 1597

0.387 0.279

1584 1603

0.198 0.176

17 18

1609 1670

0.237 0.051

1614 1676

0.147 0.013

19

1748

0.060

1752

0.014

20

1815

0.169

1834

0.084

21

1909

0.040

1914

0.027

breathing along the long axis first overtone of no. 1 breathing along the short axis δC−O−C, δC−C, δC−H, νC−C second overtone of no. 1 δC−O−C, δC−C, δC−H, νC−C, νC=O combination band (no. 1 + no. 3) combination band (no. 1 + no. 4) δC−H, νC−C δC−H δC−H, δC−C, νC−C δC−H, νC−C δC−H, νC−C combination band (no. 1 + no. 10) δC−H, δC−C, νC−C combination band (no. 1 + no. 12) δC−H, νC−C combination band (no. 1 + no. 13) combination band (no. 2 + no. 10) combination band (no. 1 + no. 15) combination band (no. 4 + no. 10)

Figure 1 (A) (A′) (B) (C) (A″)

(A+B) (A+C)

(D) (E) (A+D) (F) (A+E) (G)

(A+F)

a

The positions of the experimental signals and their relative intensities have been evaluated by the authors from the corresponding experimental data set. A characterization of the corresponding vibrations is given referring to Figure 1. The characterization refers to the corrected simulated vibrational energies ω̃ corr. All energies are given in cm−1. The given intensities of the stick spectrum are relative to the breathing mode along the long molecular axis.

transition is influenced by the adsorption process,14,16,44 the vibrational fine structure changes as well, especially in the region below 250 cm−1. First, one has to note that on the

Figure 2. Comparison of the experimental14,16 and corrected (see text) simulated vibrational fine structure in the fluorescence spectrum of PTCDA adsorbed on NaCl (a) and KCl (b) terrace sites. The energies in cm−1 are given relative to the S0−0 transition energy. 24243


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Figure 3. Top view on NaCl(100) adsorbate−surface-cluster used for Gaussian calculation. C2v symmetric cluster achieved from periodic CRYSTAL calculation and subsequent duplication and translation of border atoms along the surface lattice vector (left). C1 symmetric cluster achieved from periodic CRYSTAL calculation without subsequent duplication and translation of border atoms of the unit cell (right). Sodium atoms are light blue; chlorine atoms are yellow; carbon is gray; hydrogen is white; and oxygen is red.

Table 2. Assignment of Calculated Spectral Lines to Signals in the Experimental Spectrum of PTCDA Adsorbed on the NaCl(100) Terracea experiment14

simulation no.

ω̃ corr

rel. int.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

91 191 237 474 538 616 711 776 854 1050 1302 1342 1370 1444 1588 1606 1606 1681 1778 1824 1919

0.035 0.276 1.000 0.167 0.121 0.207 0.018 0.041 0.070 0.108 0.965 0.171 0.703 0.123 0.477 0.237 0.373 0.042 0.045 0.161 0.067

ω̃ exp. 104 206 230 454 530 613 688 762 836 1039 1281 1302 1357 1461 1550 1570 1617 1671 1758 1785 1870

rel. int. (νB) (νE) (ν1) (2 × ν1) (ν3) (ν4) (2 × ν1) (ν1 + ν3) (ν1 + ν4) (ν6) (ν10) (ν11) (ν13) (ν14) (ν15) (ν1 + ν13) (ν16)    

0.929 0.829 1.000 0.251 0.259 0.220 0.131 0.120 0.099 0.100 0.528 0.482 0.538 0.302 0.495 0.481 0.300 0.228 0.186 0.200 0.125

characterization oop oop oop δC−O−C , δoop CO, δC−H, δC−C oop oop δC−H, δC−C breathing along the long axis first overtone of no. 3 breathing along the short axis δC−O−C, δC−C, δC−H, νC−C second overtone of no. 3 combination band (no. 3 + no. combination band (no. 3 + no. δC−H, νC−C δC−H δC−H, δC−C, νC−C δC−H, νC−C δC−H, νC−C δC−H, δC−C, νC−C combination band (no. 3 + no. δC−H, νC−C combination band (no. 3 + no. combination band (no. 2 + no. combination band (no. 3 + no. combination band (no. 6 + no.

Figure 2a

4) 5)

(L1) (L2) (A) (A′) (B) (C) (A″) (A+B) (A+C) (D) (E)

12) 14) 15) 15) 11)

(F) (A+E) (G) (L2+F) (A+F) (C+D)

a

The positions of the experimental signals and their relative intensities have been evaluated by the authors from the corresponding experimental data set. A characterization of the corresponding vibrations is given referring to Figure 2a. The characterization refers to the corrected simulated vibrational energies ω̃ corr. All energies are given in cm−1. The given intensities are relative to the breathing mode along the long molecular axis.

adsorbed at step edges. The effect is more pronounced on NaCl than on KCl. The adsorption of the molecule at step edges further reduces the symmetry of the system from the pointgroup C2v to C1. As already mentioned the symmetry of the adsorbate−cluster system is reduced to C1 as well when it is constructed by taking the atom positions of the three-layered 4 × 4 supercell obtained from our periodic calculation. A picture of this adsorbate− surface cluster can be found in Figure 3. Even though the chemical environment differs significantly from the chemical environment at step edge sites we used this C1 symmetric model as a zero-order approximation of the molecule adsorbed

slightly overestimated by the calculated vibrational energy. An assignment of the calculated signals for PTCDA adsorbed on terrace sites can be found in Tables 2 (NaCl) and 3 (KCl). The positions of the experimental signals and their relative intensities have been evaluated by the authors from the corresponding experimental data sets.14,16 Symmetry Reduction. The adsorption at step edge positions has a notable effect on the measured fluorescence spectrum. Especially in the region below 250 cm−1 the step edge spectra differ significantly from both the gas phase and terrace site spectra. On both surfaces in this region more signals are visible in the experimental spectra when the molecule is 24244


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Table 3. Assignment of Calculated Spectral Lines to Signals in the Experimental Spectrum of PTCDA Adsorbed on the KCl(100) Terracea experiment16

simulation no.

ω̃ corr

rel. int.

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

84 189 232 316 391 465 536 615 697 768 848 1049 1301 1339 1366 1443 1534 1586 1598 1604 1675 1766 1776 1818 1836

0.055 0.102 1.000 0.019 0.022 0.173 0.140 0.145 0.020 0.049 0.050 0.087 0.954 0.176 0.688 0.139 0.331 0.499 0.239 0.262 0.048 0.057 0.018 0.173 0.091

ω̃ exp. 94 184 227 318 388 457 531 611 687 760 843 1038 1286 1336 1367 1443 1523 1565 1576 1603 1670 1758 1772 1802 1820

rel. int. (νB) (νE) (ν1) (νB + ν1) (ν2) (2 × ν1) (ν3) (ν4) (3 × ν1) (ν1 + ν3) (ν1 + ν4) (ν6) (ν10) (ν11) (ν13) (ν14) (ν1 + ν10) (ν15) (ν1 + ν13) (ν16)     

0.550 0.293 1.000 0.240 0.163 0.204 0.213 0.167 0.072 0.083 0.062 0.071 0.509 0.199 0.412 0.183 0.245 0.329 0.288 0.200 0.135 0.102 0.102 0.126 0.113

characterization

Figure 2b

oop oop oop δC−O−C , δoop CO, δC−H, δC−C oop oop δC−H, δC−C breathing along the long axis combination band (no. 1 + no. δC−O−C, δC=O, δC−H first overtone of no. 3 breathing along the short axis δC−O−C, δC−C, δC−H, νC−C second overtone of no. 3 combination band (no. 3 + no. combination band (no. 3 + no. δC−H, νC−C δC−H δC−H, δC−C, νC−C δC−H, νC−C δC−H, νC−C combination band (no. 3 + no. δC−H, δC−C, νC−C combination band (no. 3 + no. δC−H, νC−C combination band (no. 3 + no. combination band (no. 6 + no. combination band (no. 2 + no. combination band (no. 3 + no. combination band (no. 3 + no.

3)

(L1) (L2) (A) (A+L1)

4) 5)

(A′) (B) (C) (A″) (A+B) (A+C) (D) (E)

13) 15) 16) 13) 18) 18) 20)

(A+D) (F) (A+E) (G) (A′+D) (L2+F) (A+F) (A+G)

a

The positions of the experimental signals and their relative intensities have been evaluated by the authors from the corresponding experimental data set. A characterization of the corresponding vibrations is given referring to Figure 2b. The characterization refers to the corrected simulated vibrational energies ω̃ corr. All energies are given in cm−1. The given intensities of the stick spectrum are relative to the breathing mode along the long molecular axis.

Figure 4. Comparison of the experimental step edge spectrum and corrected simulated vibrational fine structure of a C1 symmetric model of the fluorescence spectrum of PTCDA adsorbed on NaCl (a) and KCl (b). The energies in cm−1 are given relative to the S0−0 transition energy.

at step edges. A detailed study of molecular vibrations at step edges is beyond the scope of the present work and is the subject of an ongoing project. The resulting simulated spectra in comparison to the experimental step edge spectra are shown in Figure 4a for NaCl and in Figure 4b for KCl. The simulated spectra are again corrected by the previously mentioned scaling factor. Despite the fact that we froze the motion of the surface atoms during the freuqency calculation and only allowed the atoms of the molecule to vibrate we found matching signals in the region below 250 cm−1. An assignment of the simulated low-energy signals for PTCDA can be found in Tables 6 (NaCl) and 7 (KCl).

As a result of the symmetry lowering further vibrations that do not belong to the A1 representation in a C2v symmetric model couple to the electronic transition. It is remarkable that our low-symmetry simulations reproduce the experimentally observed difference between the spectra of PTCDA adsorbed at NaCl and at KCl surface step edges in the energy range below 250 cm−1. In both theoretical and experimental spectra more vibrations are visible on NaCl than on KCl. In the region from 250 to 2000 cm−1 only minor changes appear. As observed in our previous theoretical study,44 already the ground-state structure of PTCDA is more distorted on NaCl(100) compared to KCl(100) due to the different cation−cation distances on the two surfaces. The electronic transition causes a change of the distortion. The distortion is 24245


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calculated distortion in the S0 state from ref 47 is a result of the different DFT functional, dispersion correction, and basis set. The displacement ΔQ of the target state relative to the initial state geometry along a normal mode is substantial for the visibility of the vibrational excitation since the intensity is proportial to the Huang−Rhys factor Si = (Miω̃ i/2ℏ) × ΔQ2. Mi is the reduced mass, and ω̃ i is the vibrational frequency. A comparison of the vibrations below 250 cm−1 and the displacements ΔQ along the normal coordinates of PTCDA/ NaCl(100)-C1 and PTCDA/KCl(100)-C1 can be found in Table 5. The displacements corresponding to the vibrations 1, 2, 3, and 6 are up to ten times larger on NaCl than on KCl, and these vibrations are only visible on NaCl. Vibration numbers 5, 9, 13, and 14, on the other hand, show a quite large displacement on both surfaces and are therefore visible in both cases. Certainly, as already mentioned, the DFT-potential differs from the real potential. This error is systematic for the vibrational energies and can be corrected by empirical scaling factors.50 From the comparison of calculated and experimental relative intensities shown in Tables 1, 2 and 3 it can be seen that the calculated relative intensities of the bands do not match the measured ones. The intensities are calculated with the program ezSpectrum based on the normal vectors obtained from DFT. This means that the relative intensities of fundamental and combination modes have the same sources of error which are determined by the accuracy of the DFT potential. The errors of the normal mode vectors are less systematic than those of the vibrational energies and cannot be corrected by a simple scaling factor. The fact that our simulation of purely molecular vibrations on the surface reproduces the experimental finding of an increased number of signals appearing on NaCl compared to KCl strengthens the assumption that the signals occurring below 250 cm−1 in the experimental spectra are essentially of intramolecular nature. Even though we used a completely different chemical environment our model triggers the same effects as the step edge does. This implies that the larger number of signals occurring at the NaCl step edge is a result of

given in Table 4 in terms of the geometric parameters that refer to Figure 5. This shows that, even though the total geometry Table 4. Comparison of the Calculated Geometry Parameters for Adsorbed PTCDA on the NaCl(100) and KCl(100) Surfaces in the S0 and S1 States According to Figure 5a

a

system

state

d1

d2

m1

m2

PTCDA/NaCl-C1 PTCDA/NaCl-C1 Δ PTCDA/KCl-C1 PTCDA/KCl-C1 Δ

S0 S1 S1−S0 S0 S1 S1−S0

2.51 2.51 −0.01 2.88 2.88 0.00

3.47 3.49 0.03 3.44 3.45 0.01

0.90 0.93 0.04 0.52 0.54 0.02

0.54 0.60 0.06 0.27 0.30 0.03

All values are given in Å.

Figure 5. Side view of a single PTCDA molecule adsorbed on a KCl(100) surface. The distance between the carbonyl oxygen atoms and the underlying surface cations (d1) and the distance between the center of the molecule and the underlying anion (d2) is highlighted. m1 and m2 are the downward movement of the carbonyl oxygen atoms and of the anhydride oxygen relative to the center of the molecule, respectively. Potassium atoms are violet; chlorine atoms are yellow; carbon is gray; hydrogen is white; and oxygen is red.

change is small, the change is roughly two times larger on NaCl than on KCl. This could be the reason for the larger amount of visible signals on NaCl than on KCl. In both cases the S1-state geometry is stronger distorted. The small deviation of our

Table 5. Comparison of the Fundamental Vibrations below 250 cm−1, Their Irreducible Representations Γ, and Displacement ΔQ of the Target State Relative to the Initial State Geometry along a Normal Mode of D2h Symmetric PTCDA in the Gas Phase and Adsorbed on C1 Symmetric NaCl(100) and KCl(100) Surfacesa PTCDA no.

ω̃ corr

PTCDA/NaCl-C1 Γ

1

21

au

2 3 4 5 6 7 8 9 10 11 12

36 60 71 88 126 127 136 171 179 207 225

b1u b3g au b2g b2g b1u b2u b2g b1u b1u ag

ΔQ

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.358

PTCDA/KCl-C1

no.

ω̃ corr

ΔQ

no.

ω̃ corr

ΔQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

71 75 82 88 94 106 115 117 146 153 162 186 197 215 237

−0.152 −0.126 −0.157 0.043 0.204 0.108 −0.023 −0.004 −0.106 0.037 0.031 −0.017 −0.105 −0.060 0.279

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

62 63 67 72 81 96 102 107 142 153 158 185 190 218 232

−0.046 −0.022 −0.013 0.014 0.120 −0.018 0.001 −0.040 0.088 0.018 −0.003 0.022 −0.109 −0.055 0.298

All vibrational energies are given in cm−1, and ΔQ is given in Å· amu . All vibrations visible in the vibronic spectra according to ezSpectrum results are underlined. The numbering indicates the order of the calculated vibrations.

a

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Table 6. Assignment of Low-Energy Signals in the Simulated to Signals in the Experimental Spectrum of PTCDA Adsorbed on NaCl-C1a simulation no.

ω̃ corr

rel. int.

1 2 3 4 5 6 7 8 9 10 11 12 13

70 75 82 94 106 146 196 215 237 307 330 343 383

0.088 0.064 0.114 0.217 0.068 0.087 0.117 0.041 1.000 0.025 0.062 0.019 0.025

experiment ω̃ exp. 63 63 63 96 131 173 186  233 297 326 366 407

(νA) (νA) (νA) (νB) (νC) (νD) (νE)  (ν1) (ν1 + (ν1 + (ν1 + (ν1 +

νA) νB) νC) νD)

rel. int.

characterization

0.358 0.358 0.358 0.227 0.443 0.297 0.315  1.000 0.242 0.201 0.240 0.189

oop oop δoop CO, δC−H, δC−C oop oop δCO, δC−H, δoop C−C oop oop δoop CO, δC−H, δC−C oop oop oop δC−O−C , δoop , CO δC−H, δC−C oop oop oop δC−O−C , δoop , δ , δ CO C−H C−C bending (ip) along the long axis oop δoop C−H, δC−C oop oop oop δC−O−C , δoop CO, δC−H, δC−C breathing along the long axis combination band (no. 1 + no. 8) combination band (no. 3 + no. 8) combination band (no. 4 + no. 8) combination band (no. 5 + no. 8)

Figure 4a

(L1)

(L2) (A)

a

A characterization of the corresponding vibrations is given referring to Figure 4a. The characterization refers to the corrected simulated vibrational energies ω̃ corr. All energies are given in cm−1. The given intensities of the stick spectrum are relative to the breathing mode along the long molecular axis.

Table 7. Assignment of Low-Energy Signals in the Simulated to Signals in the Experimental Spectrum of PTCDA Adsorbed on KCl-C1a simulation no. 1 2 3 4

ω̃ corr. 81 190 232 313

experiment ω̃ exp.

rel. int. 0.058 0.110 1.000 0.018

97 186 228 324

rel. int. (νB) (νE) (ν1) (ν1 + νB)

0.304 0.193 1.000 0.160

characterization oop δC−O−C , δoop CO, oop δoop , δ C−H C−C

oop δC−H ,

Figure 4b

δoop C−C

breathing along the long axis combination band (no. 1 + no. 3)

(L1) (L2) (A) (A+L1)

a A characterization of the corresponding vibrations is given Figure 4b. The characterization refers to the corrected simulated vibrational energies ω̃ corr. All energies are given in cm−1. The given intensities of the stick spectrum are relative to the breathing mode along the long molecular axis.

molecular character. In the region below 250 cm−1 the molecular vibrations couple to the vibrations of the surface atoms and split into several normal modes. Step edge atoms should be more loosely bound, and therefore it is more likely that they influence the vibrational properties. But this alone can not explain the experimental finding of more vibrations on NaCl than on KCl. Previous studies suggest that the step edge cavities of both surfaces are similar.29,30 We have further seen from our vibrational calculations that the vibrational properties of the surface atoms of both surfaces do not differ much. From this finding we conclude that the coupling to the vibrations of the surface atoms mainly leads to a line broadening which is observed in the experimental spectrum. Nevertheless, we are able to find corresponding molecular vibrations for the experimental signals in our simulated spectra. Therefore, the applied approximations give a qualitatively correct description of the vibrational fine structure of the molecule adsorbed at surface step edges. Most importantly our model gives an explanation for the larger number of signals at the NaCl surface step edge in comparison with the KCl surface step edge. The simulated higher-energy vibrations show a good correlation with the experimental signals. We are again able to find a counterpart to every experimental signal in our simulated spectrum. This remaining part of the spectrum of PTCDA on NaCl and KCl is quite similar on both surfaces except for some combination bands including low frequency vibrations. On NaCl such bands can be found, but they are not very intense. All of the signals with high intensity show no

the stronger distortion of PTCDA caused by the electronic transition. The low-energy vibrations also have an impact on other parts of the spectrum because they emerge in combination bands. Also in the range between 250 and 350 cm−1 the experimental spectra of PTCDA adsorbed on NaCl and KCl have a different fine structure. On NaCl again more signals are visible. Our simulated spectra show the same behavior because in this region combination bands of the dominant breathing mode at 237 cm−1 on NaCl and 232 cm−1 on KCl and the low frequency vibrations appear. On KCl there is just one combination band, while on NaCl there are four of them. This behavior once again suggests that similar effects are responsible for the additional low frequency vibrations at step edges. However, due to our approximate modeling it is no surprise that these additional low energy frequency vibrations exhibit a larger deviation from the experimental spectra. As already mentioned one and probably the most important reason for this behavior is the fact that the molecule at the step edge has a different chemical environment than in our model. Nevertheless, it is likely that the additional vibrations are of intramolecular character. Only the low-frequency vibrations seem to be influenced by surface vibrations at all. To estimate the influence of the surface atom vibrations we additionally calculated the ground-state vibrations of all atoms in the periodic model and compared them to the pure molecular vibration on the surface. Our analysis shows that vibrations of the surface atoms have contributions in the region from 0 to roughly 250 cm−1. Higher energetic vibrations are of pure 24247



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significant difference between NaCl and KCl, and their positions are similar to the gas phase. In general, the vibrational energy is increased when large normal mode vector components parallel to the surface normal (z) exist. The potential well of these normal modes is affected by the Pauli repulsion of the surface, the so-called ”wall effect”.51 Vibrations in the xy-plane are considerably less affected, but all visible higher energy vibrations on NaCl and KCl are in-plane (ip) vibrations of the gas-phase molecule. Therefore, these vibrations are not significantly shifted in comparison to the gas-phase vibrations. Visible out-of-plane (oop) vibrations are only present in the low-energy region. They are usually shifted by roughly 30−40 cm−1 to higher energies in comparison to their calculated gas-phase analogons. At higher energies the surface influence decreases, and even the vibrations toward the surface are not shifted much. In this region the difference between the vibrational energies on NaCl and KCl is comparatively small, less than 10 cm−1.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b08540. Additional spectral information, figures of all normal modes, and method tests (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)228 733839. Fax: +49 (0)228 739064. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the Paderborn Center for Parallel Computing, PC2, and the Leibniz University IT Services (former Regionales Rechenzentrum fü r Niedersachsen [RRZN]) for providing computational resources. This work was supported by the DFG under the project SO407/8-1. M. H. thanks the Studienstiftung des deutschen Volkes for support. A special thanks goes to Prof. Dr. Frank Stienkemeier for providing the experimental spectrum of PTCDA in Henanodroplets.

■

CONCLUSION The vibronic spectra of PTCDA in the gas phase and adsorbed on insulator surfaces were simulated by explicit calculation of the Franck−Condon factors. The molecular geometry and vibrations in the electronic ground and excited state were calculated on DFT and TD-DFT level of theory applying periodic and nonperiodic models. We compared our results to experimental findings and previous theoretical calculations. We were able to reproduce the experimental spectra quantitatively. The deviation of our calculated signals from the experimental signals is usually within the magnitude of ±10 cm−1 for PTCDA molecules in the gas phase and adsorbed on terrace sites of the NaCl(100) and KCl(100) surfaces. This demonstrates that our approach of modeling the vibrational fine structure of PTCDA in the gas phase and adsorbed on NaCl and KCl surfaces is suitable for the investigated systems. Since we froze the surface atom vibrations during our frequency calculation we confirmed that the additional modes appearing in the spectra of PTCDA adsorbed on NaCl and KCl surface terrace sites are of intramolecular character. Ground state frequency calculations in a periodic model where we allowed vibrations of the molecule and the surface atoms have further shown that the molecular vibrations are only influenced by surface atom vibrations in the low frequency region up to 250 cm−1. Molecular vibrations of higher vibrational energies are almost unaffected by the surface. For the calculation of the vibronic spectra of PTCDA at NaCl and KCl step edge sites we used surface models that exhibit reduced symmetry as the step edges (C1). Even though these models differ significantly in their chemical environment from the real step edges we were able to find an explanation for the occurrence of more signals in the experimental spectrum of PTCDA at NaCl step edge sites than at KCl step edge sites. These models which serve as a zero-order approximation of the real step edges trigger the same effects as the real step edges do and are therefore suitable for a qualitative analysis. Our calculations imply that the PTCDA molecule on NaCl undergoes a heavier geometric distortion caused by the electronic transition than on KCl. Apparently this increased distortion leads to larger displacements along normal modes on NaCl than on KCl and hence to more visible signals in the spectrum. As a result we conclude that the larger number of visible vibrations at NaCl step edge sites is a consequence of a stronger geometric distortion of the PTCDA molecule.

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REFERENCES

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