Molecular orbital models of benzene, biphenyl and the oligophenylenes

Bursill, Robert J.; Barford, William; Daly, Helen

doi:10.1016/s0301-0104(99)00017-8

Cited by 10 publications

(8 citation statements)

References 34 publications

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“…In principle, the many body correlations between the MOs can be determined from the underlying P-P-P model. When this was done for PPP, however, it was found that there is a poor agreement with experiment [12]. This is a result of the neglect of the many body correlations involving the neglected orbitals.…”

Section: The Two State Modelmentioning

confidence: 93%

Theoretical investigation of the low-lying electronic structure of poly(p-phenylene vinylene)

et al. 1999

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The two-state molecular orbital model of the one-dimensional phenyl-based semiconductors is applied to poly͑para-phenylene vinylene͒. The energies of the low-lying excited states are calculated using the density matrix renormalization group method. Calculations of both the exciton size and the charge gap show that there are both 1 B u Ϫ and 1 A g ϩ excitonic levels below the band threshold. The energy of the 1 1 B u Ϫ exciton extrapolates to 2.60 eV in the limit of infinite polymers, while the energy of the 2 1 A g ϩ exciton extrapolates to 2.94 eV. The calculated binding energy of the 1 1 B u Ϫ exciton is 0.9 eV for a 13 phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to decrease due to solvation effects. The lowest triplet state is calculated to be at around 1.6 eV, with the triplet-triplet gap being around 1.6 eV. A comparison between theory and two-photon absorption and electroabsorption is made, leading to a consistent picture of the essential states responsible for most of the third-order nonlinear optical properties. An interpretation of the experimental nonlinear optical spectroscopies suggests an energy difference of around 0.4 eV between the vertical energy and around 0.8 eV between the relaxed energy of the 1 1 B u Ϫ exciton and the band gap, respectively.

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Section: The Two State Modelmentioning

confidence: 93%

Theoretical investigation of the low-lying electronic structure of poly(p-phenylene vinylene)

et al. 1999

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“…The other HOMO and LUMO states are non-bonding, because the wave function amplitude on the bridging carbon atoms is zero. Transitions between these states lead to high lying localised B 1u excitations, while transitions which mix the bonding and non-bonding orbitals lead to excitations with B 2u and B 3g symmetry [21]. We will not be concerned with these latter states in this paper.…”

Section: The Modelmentioning

confidence: 99%

“…A straightforward derivation of the new Hamiltonian parameters from the atomic Hamiltonian (1) gives results for the excitation energies which deviate from exact Pariser-Parr-Pople model calculations of benzene and biphenyl, as well as to over-estimating the optical gap by approximately 1 eV in long oligophenylenes [21]. We therefore take the view that eqn.…”

Section: The Modelmentioning

confidence: 99%

Density matrix renormalization group calculations of the low-lying excitations and non-linear optical properties of poly(para-phenylene)

Barford

Bursill

Lavrentiev

1998

J. Phys.: Condens. Matter

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The two state molecular orbital (2-MO) model of the phenyl based semiconductors is used to calculate the low-lying spectra of the A + g and B − 1u states of poly(para-phenylene) (PPP). The model parameters are determined by fitting its predictions to exact Pariser-Parr-Pople model calculations of benzene and biphenyl, and it is solved using the density matrix renormalisation group method. It is shown that there exists a band of 1 B − 1u ('s'-wave) excitons below the band states. In the long chain limit the lowest exciton is situated 3.3 eV above the ground state, consistent with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band PACS numbers: 42.70Jk, 71.20Rv, 78.66Qn, 71.35Cc Since the first light-emitting device based on poly(para-phenylenevinylene) (PPV) was reported [1], the non-linear optical (NLO) properties of conjugated polymers have been extensively investigated. Amongst the numerous systems studied, poly(para-phenylene) (PPP), being a linear chain of phenyl rings, possesses one of the simplest structures. However, its electronic structure and the nature of the blue light emission [2] are still controversial. First-principles local-density approximation studies by Ambrosch-Draxl et al. [3] suggest that the optical properties of PPP can be explained by a purely band picture, with intragap non-linear excitations suppressed by three-dimensional effects. However, recent experimental results on the electroabsorption (EA) and photoinduced absorption (PA) in substituted PPP by Lane et al. [4] are explained by the presence of non-linear excitations, such as singlet and triplet excitons, and charged polarons.The aim of this paper is to clarify the rôle and importance of the low-lying non-linear excitations in PPP by calculating its electronic structure and NLO properties in a realistic Hamiltonian. The EA spectrum compares favourably with recent experiments. We identify the key states which participate in the NLO processes. Moreover, by calculating the particle-hole separation of these states, we identify the band gap as the threshold state whose particle-hole separation increases linearly with oligomer size. This enables a rigorous determination of the band gap to be made.Recently, a two state molecular orbital model was introduced [5] to describe the B 1u and A g states of the phenyl based semiconductors. In the current paper we introduce a more thorough parameterisation of this model by fitting to improved exact Pariser-Parr-Pople model calculations of the molecular building blocks (i.e. benzene and biphenyl) [7]. This model is then solved for oligomers of arbitrary length without further parameterisation. As well as our earlier work, which was the first to use the DMRG method for the phenyl based semiconductors [5, 6], there have been a number of other theoretical calculations on PPP. Brédas has used the VEH pseudopotential technique [8], Champagne et al. have performed Hartree-Fock calcula...

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“…This “exponential disaster” makes the method inaccessible to most systems of chemical interests. − Some efforts have been devoted to solve this problem. Use of the frontier molecular orbitals instead of all atomic orbitals in each block space is a good scheme to implement the DMRG calculation for the quasi-one-dimensional and two-dimensional systems. , But the numerical precision of this technique is unsatisfactory in most cases. To get more precise results, another way has been suggested to deal with the two-dimensional system by choosing the blocks carefully. , The “careful choosing” including the selection of the starting blocks and the blocks added thereafter plays the important role in implementing DMRG calculations.…”

Section: Introductionmentioning

confidence: 99%

The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes

2002

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The ground-state energies of polyacenes and polyphenanthrenes are obtained with the density-matrix renormalization group method from finite up to infinite lengths under the classical valence bond theory. In comparison with the exact valence bond results, numerical errors of retaining various numbers of states are all less than 10 -5 J. Meanwhile, the linear equations in terms of the chain length are deduced for the groundstate energies of these two homologous series. And the energy gaps between the lowest singlet and triplet states (S-T gap) are also evaluated. On the other hand, the relative local hexagon energy converges as the chain length increases, and leading to an effective conjugated length of n ) 12 for polyacene and polyphenanthrene.

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Molecular orbital models of benzene, biphenyl and the oligophenylenes

Cited by 10 publications

References 34 publications

Theoretical investigation of the low-lying electronic structure of poly(p-phenylene vinylene)

Theoretical investigation of the low-lying electronic structure of poly(p-phenylene vinylene)

Density matrix renormalization group calculations of the low-lying excitations and non-linear optical properties of poly(para-phenylene)

The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes

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