A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Abstract

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C 2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the 1 1 B u exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.

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Low-Lying Excited States in Thiophene-Based Cyclic Molecule Suitable for Optoelectronics: A Density Matrix Renormalization Group Study

“…49 The transfer integrals t ij of the thiophene unit have been taken from the earlier calculation on low-lying excitations in the polythiophene system with t C–S = 3.0 eV, U S = 5 eV, and ϵ S = −7.8 eV. 50,51 The rest of the transfer integrals of two adjacent carbon atoms are taken to be 2.4 eV, and onsite Hubbard repulsion is U C = 11.26 eV for carbon. The PPP Hamiltonian-based DMRG technique has been successfully and accurately adopted in earlier correlated electronic structure calculations in conjugated polyenes, zigzag, armchair polyacences, and porphyrins.…”

“…The model Hamiltonian also includes onsite electron–electron repulsion U i and long-range intersite Coulomb interaction potential V ij parametrized in the Ohno interpolation scheme The transfer integrals t ij of the thiophene unit have been taken from the earlier calculation on low-lying excitations in the polythiophene system with t C–S = 3.0 eV, U S = 5 eV, and ϵ S = −7.8 eV. , The rest of the transfer integrals of two adjacent carbon atoms are taken to be 2.4 eV, and onsite Hubbard repulsion is U C = 11.26 eV for carbon. The PPP Hamiltonian-based DMRG technique has been successfully and accurately adopted in earlier correlated electronic structure calculations in conjugated polyenes, zigzag, armchair polyacences, and porphyrins. − In the beginning, DMRG calculation starts with a small system of four carbon atoms that can be fully diagonalizable followed by augmenting the system size up to the desired structure of TTA.…”