^{1,a)}, Karol Kowalski

^{2,b)}and Wibe A. deJong

^{2}

### Abstract

Coupled-cluster theory with single and double excitations is applied to the calculation of optical properties of large polyaromatic hydrocarbons. Dipole polarizabilities are reported for benzene, pyrene, and the oligoacenes sequence . Dynamic polarizabilities were calculated on polyacences as large as pentacene for a single frequency and for benzene and pyrene at many frequencies. The basis set effect was studied for benzene using a variety of basis sets in the Pople [Theor. Chim. Acta28, 213 (1973)] and Dunning [J. Chem. Phys.90, 1007 (1989)] families up to aug-cc-pVQZ and the Sadlej pVTZ basis [Collect. Czech. Chem. Commun.53, 1995 (1998)], which was used exclusively for the largest molecules. Geometries were optimized using HF, B3LYP, PBE0, and MP2 and compared to experiment to measure method dependence and the possible role of bond-length alternation. Finally, the polarizability results were compared to four common density functionals (B3LYP, BLYP, PBE0, PBE).

One of the authors (J.R.H.) is supported by the DOE-CSGF program provided under Grant No. DE-FG02-97ER25308. The authors thank Tim Carlson for invaluable technical assistance. This work has been performed using the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at the Pacific Northwest National Laboratory. The William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory is funded by the Office of Biological and Environmental Research in the U.S. Department of Energy. The Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by the Battelle Memorial Institute under Contract No. DE-AC06-76RLO-1830. Portions of this work were supported by the Laboratory Directed Research and Development Program at the Pacific Northwest National Laboratory.

I. INTRODUCTION

II. THEORY AND COMPUTATIONAL DETAILS

III. RESULTS

A. Basis set convergence

B. Importance of iterative triples

C. Geometry effects

D. Comparison of density-functional and coupled-clusterpolarizabilities for linear oligoacenes

E. Accuracy of frequency-dependent polarizabilities

IV. CONCLUSIONS

### Key Topics

- Polarizability
- 73.0
- Basis sets
- 23.0
- Density functional theory
- 23.0
- Coupled cluster
- 14.0
- Integral equations
- 7.0

## Figures

Convention for the tensor components of the polarizability. In both cases the component comes out the plane of the page.

Convention for the tensor components of the polarizability. In both cases the component comes out the plane of the page.

Numbering scheme for carbon atoms in (a) anthracene, (b) tetracene, (c) pentacene, and (d) hexacene. The presence of double bonds indicates only that all carbons are hybridized.

Numbering scheme for carbon atoms in (a) anthracene, (b) tetracene, (c) pentacene, and (d) hexacene. The presence of double bonds indicates only that all carbons are hybridized.

## Tables

Static dipole polarizabilities of benzene calculated with CCSD and a variety of basis sets. Energies and polarizabilities are given in atomic units.

Static dipole polarizabilities of benzene calculated with CCSD and a variety of basis sets. Energies and polarizabilities are given in atomic units.

Timing data for parallel CCSD-LR calculations. All calculations were performed using the Sadlej TZ basis set in symmetry. The CCSD-LR timing refers to the axis and were taken from iteration 5 for all cases. Timings are in seconds.

Timing data for parallel CCSD-LR calculations. All calculations were performed using the Sadlej TZ basis set in symmetry. The CCSD-LR timing refers to the axis and were taken from iteration 5 for all cases. Timings are in seconds.

Benzene dipole polarizabilities calculated with CCSD and CC3 and the three small basis sets basis set using ACES (Ref. 23). Energies and polarizabilities are given in atomic units.

Benzene dipole polarizabilities calculated with CCSD and CC3 and the three small basis sets basis set using ACES (Ref. 23). Energies and polarizabilities are given in atomic units.

Geometry data for anthracene, tetracene, pentacene, and hexacene. All calculations were performed using the cc-pVTZ basis set. For MP2 only, the core orbitals were frozen. Experimental geometries are from Ref. 37 for anthracene (electron diffraction) and Ref. 38 for tetracene and pentacene (x-ray crystallography). All bond lengths are given in angstroms. See Fig 2 for the numbering scheme.

Geometry data for anthracene, tetracene, pentacene, and hexacene. All calculations were performed using the cc-pVTZ basis set. For MP2 only, the core orbitals were frozen. Experimental geometries are from Ref. 37 for anthracene (electron diffraction) and Ref. 38 for tetracene and pentacene (x-ray crystallography). All bond lengths are given in angstroms. See Fig 2 for the numbering scheme.

Benzene dipole polarizabilities calculated with the aug-cc-pVTZ basis set and various methods. Polarizabilities and frequencies are given in atomic units.

Benzene dipole polarizabilities calculated with the aug-cc-pVTZ basis set and various methods. Polarizabilities and frequencies are given in atomic units.

Dipole polarizabilities of naphthalene for various levels of theory. Polarizabilities and frequencies are given in atomic units.

Dipole polarizabilities of naphthalene for various levels of theory. Polarizabilities and frequencies are given in atomic units.

Dipole polarizabilities of anthracene for various levels of theory. Polarizabilities and frequencies are given in atomic units.

Dipole polarizabilities of anthracene for various levels of theory. Polarizabilities and frequencies are given in atomic units.

Static and dynamic polarizabilities of pentacene at different levels of theory using the Sadlej TZ basis set. The component of the dynamic polarizability (in parentheses) is erroneous for the both PBE and PBE0 since the frequency is greater than the first pole of the response function in the corresponding symmetry. Polarizabilities and frequencies are given in atomic units.

Static and dynamic polarizabilities of pentacene at different levels of theory using the Sadlej TZ basis set. The component of the dynamic polarizability (in parentheses) is erroneous for the both PBE and PBE0 since the frequency is greater than the first pole of the response function in the corresponding symmetry. Polarizabilities and frequencies are given in atomic units.

Static dipole polarizabilities of linear oligoacenes for . The first set of data are the polarizability tensor components and the second are the values per ring, , indicating the level of saturation with increasing . Polarizabilities are given in atomic units.

Static dipole polarizabilities of linear oligoacenes for . The first set of data are the polarizability tensor components and the second are the values per ring, , indicating the level of saturation with increasing . Polarizabilities are given in atomic units.

Frequency-dependent dipole polarizabilities of benzene and the lowest excited state of any symmetry (denoted by ) at the respective levels of theory using the Sadlej basis set. The CCSD is the EOM-CCSD/POL1 value was taken from Ref. 48. Polarizabilities and frequencies are given in atomic units.

Frequency-dependent dipole polarizabilities of benzene and the lowest excited state of any symmetry (denoted by ) at the respective levels of theory using the Sadlej basis set. The CCSD is the EOM-CCSD/POL1 value was taken from Ref. 48. Polarizabilities and frequencies are given in atomic units.

Frequency-dependent dipole polarizabilities of pyrene and the lowest excited state of any symmetry (denoted by ) for the four DFT methods. Polarizabilities and frequencies are given in atomic units.

Frequency-dependent dipole polarizabilities of pyrene and the lowest excited state of any symmetry (denoted by ) for the four DFT methods. Polarizabilities and frequencies are given in atomic units.

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