^{1,a)}

### Abstract

The gas-to-crystal-shift denotes the shift of electronic excitation energies, i.e., the difference between ground and excited state energies, for a molecule transferred from the gas to the bulk phase. The contributions to the gas-to-crystal-shift comprise electrostatic as well as inductive polarization and dispersive energy shifts of the molecular excitation energies due to interaction with environmental molecules. For the example of 3,4,9,10-perylene-tetracarboxylic-diimide (PTCDI) bulk, the contributions to the gas-to-crystal shift are investigated. In the present work, electrostatic interaction is calculated via Coulomb interaction of partial charges while inductive and dispersive interactions are obtained using respective sum over states expressions. The coupling of higher transition densities for the first 4500 excited states of PTCDI was computed using transition partial charges based on an atomistic model of PTCDI bulk obtained from molecular dynamics simulations. As a result it is concluded that for the investigated model system of a PTCDI crystal, the gas to crystal shift is dominated by dispersive interaction.

Financial support by the Deutsche Forschungsgemeinschaft through Project No. ME 4215/2-1 is gratefully acknowledged. The author is indebted to Tillmann Klamroth (University of Potsdam) for fruitful discussions.

I. INTRODUCTION II. INTERMOLECULAR INTERACTION A. Electrostaticinteraction B. Inductive polarization C. London dispersion III. COMPUTATION OF LONDON DISPERSION IN MOLECULAR AGGREGATES A. Obtaining the

*Q*-factor IV. COMPUTATION OF INDUCTIVE POLARIZATION AND DISPERSION VIA A DIRECT COMPUTATION OF THE SUM OVER STATES EXPRESSIONS A. Calculating inductive polarization and dispersion for the example of

**PTCDI**bulk V. RESULTS VI. CONCLUSIONS

### Key Topics

- Excitation energies
- 32.0
- Polarization
- 29.0
- Electrostatics
- 23.0
- Electric dipole moments
- 19.0
- Intermolecular forces
- 16.0

_{4}in solution: MD simulations based studies of exciton states,” Chem. Phys. Lett. 444(1-3), 118–124 (2007).

_{y}states of the photosynthetic reaction center in purple bacteria,” J. Phys. Chem. B 116(3), 1164–1171 (2012).

_{4}in solution,” Chem. Phys. 351(1-3), 117–128 (2008).

^{15}) due to retardation effects does not scale with r

^{−6}as suggested by London

^{50}but with r

^{−7}(see also Ref. 51 for an up to date description of retardation effects). It, however, was found in Ref. 12 that the dispersive interaction for intermolecular distances smaller than 5 nm was neglectable for the investigated molecular crystal. This result can be assumed to hold for molecular assemblies with similar Q-factors (see, e.g., Refs. 4 and 22).

^{32}

^{*}excited singlet states of linear polyenes: Time-dependent density-functional theory versus multiconfigurational methods,” Phys. Rev. A 77, 012510 (2008).

^{17}was utilized. The interaction energy was calculated using the formula ΔE

^{(int)}= E

^{(dim)}− 2E

^{(mono)}. The other components of the interaction energy (the orbital overlap and Pauli repulsion cf. Ref. 53) can be neglected for the non-bonded PTCDI dimer (orbital overlap is neglectable). One can thus rewrite ΔE

^{(int)}= ΔE

^{(el,ind,disp)}. Here, ΔE

^{(el,ind,disp)}is the overall interaction energy of the molecules due to electrostatics, inductive polarization, and dispersion.

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### Abstract

The gas-to-crystal-shift denotes the shift of electronic excitation energies, i.e., the difference between ground and excited state energies, for a molecule transferred from the gas to the bulk phase. The contributions to the gas-to-crystal-shift comprise electrostatic as well as inductive polarization and dispersive energy shifts of the molecular excitation energies due to interaction with environmental molecules. For the example of 3,4,9,10-perylene-tetracarboxylic-diimide (PTCDI) bulk, the contributions to the gas-to-crystal shift are investigated. In the present work, electrostatic interaction is calculated via Coulomb interaction of partial charges while inductive and dispersive interactions are obtained using respective sum over states expressions. The coupling of higher transition densities for the first 4500 excited states of PTCDI was computed using transition partial charges based on an atomistic model of PTCDI bulk obtained from molecular dynamics simulations. As a result it is concluded that for the investigated model system of a PTCDI crystal, the gas to crystal shift is dominated by dispersive interaction.

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