Optimal parametrisation of the Pariser–Parr–Pople Model for benzene and biphenyl

Bursill, Robert J.; Castleton, Christopher; Barford, William

doi:10.1016/s0009-2614(98)00903-8

Cited by 49 publications

(75 citation statements)

References 19 publications

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“…The extrapolated estimate of the optimal parameters, t = 2.6 eV agrees with the value of t = 2.54 eV reported by Bursill et al 58 . The extrapolated value of U * /t ≈ 1.0 is also broadly consistent with a recently reported estimate 59 to within 10-20%.…”

Section: Hubbard U * /T From the N-aidmd Methodssupporting

confidence: 90%

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Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

Changlani

Zheng

Wagner

2015

The Journal of Chemical Physics

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We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo (QMC) calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding (AIDMD). For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U * /t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

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Section: Hubbard U * /T From the N-aidmd Methodssupporting

confidence: 90%

“…We compare our results with Bursill et al 58 , who considered only a nearest neighbor hopping and took V ij to be of the Ohno form 60…”

Section: B Extended Hubbard Modelmentioning

confidence: 84%

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

Changlani

Zheng

Wagner

2015

The Journal of Chemical Physics

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“…In the present work values for these parameters have been taken from the literature. [34][35][36][37][38] Since existing parameters have been optimized to optical excitation spectra, an exact agreement with experimental values for the molecular gaps is not to be expected.…”

Section: Pariser-parr-pople Hamiltonianmentioning

confidence: 99%

Benchmarking GW against exact diagonalization for semiempirical models

Kaasbjerg

Thygesen

2010

Phys. Rev. B

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We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW captures around 65% of the ground-state correlation energy. The lowest lying excitations are overscreened by GW leading to an underestimation of electron affinities and ionization potentials by 0.15 eV on average corresponding to ϳ3%. One-shot G 0 W 0 calculations starting from Hartree-Fock reduce the screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final-state relaxations in Hartree-Fock theory. We discuss the breakdown of the GW approximation in systems with short-range interactions ͑Hubbard models͒ where correlation effects dominate over screening/ relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchangecorrelation functional by computing the exact Kohn-Sham levels of benzene.

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“…In the following we consider oligophenyls of N repeat units (phenyl rings), as depicted in Fig. 3.When solved accurately, the P-P-P theory has proved remarkably accurate in describing many of the low-lying excitations in a wide range of conjugated molecules [8,9]. Given such debates as to the nature of exciton binding in PPV and the related issues of interpreting various spectral features [2][3][4][5][6], it is intriguing as to what the P-P-P theory predicts for large phenyl systems.…”

mentioning

confidence: 99%

“…In thin films they lie at 5.2-5.3 eV [19,20] and 5.7-6.0 eV [19,20] respectively. The 1 B − 1u state is a localised intra-phenyl (Frenkel) excitation which lies at 6.16 eV in biphenyl [8]. To track the position of this state as a function of N , we perform calculations targeting a number of 1 B − 1u states together with the ground state 1 1 A + g and calculate the dipole moments 1 1 A + g |μ|j 1 B − 1u , whereμ ≡ i x i n i (with x i the x coordinate of the ith atom) is the dipole operator along the long molecular axis.…”

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confidence: 99%

Large-scale numerical investigation of excited states in poly(para-phenylene)

Bursill

Barford²

2002

Phys. Rev. B

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A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.The phenyl-based conjugated polymers have attracted immense interest from physicists and chemists as a result of the discovery of electroluminescence in poly(phenylenevinylene) (PPV) [1]. In particular, a great deal of theoretical and experimental effort has been devoted to understanding the important neutral excitations driving nonlinear optical processes, the positions of triplet states and the nature of exciton binding and decay [2][3][4][5][6]. Correlation between π-electrons has proved to be important in obtaining an accurate description of excited states in conjugated systems. It is thus desirable to have accurate numerical solutions of correlated electron models for these systems (without recourse to uncontrolled approximation schemes such as configuration interaction approximation schemes, or perturbative schemes starting from a noninteracting molecular orbital or k-space band description). In this paper we provide, for the first time, accurate results for a realistic semi-empirical model for poly(phenylene) and its oligomers, a model system for phenyl-based conjugated polymers.As our starting point for describing poly(phenylene), we adopt the Pariser-Parr-Pople (P-P-P) model [7],where <> represents nearest neighbors, c iσ destroys a π-electron on conjugated carbon atom i, n iσ = c † iσ c iσ and n i = n i↑ + n i↓ . We use the Ohno parameterisation for the Coulomb interaction, V ij = U/ 1 + (U r ij /14.397) 2 , where r ij is the inter-atomic distance inÅ and U = 10.06 eV [8]. The transfer integrals (t ij ) and bond lengths are 2.539 eV and 1.4Å respectively for phenyl bonds, and 2.22 eV and 1.51Å respectively for single bonds [8]. In the following we consider oligophenyls of N repeat units (phenyl rings), as depicted in Fig. 3.When solved accurately, the P-P-P theory has proved remarkably accurate in describing many of the low-lying excitations in a wide range of conjugated molecules [8,9]. Given such debates as to the nature of exciton binding in PPV and the related issues of interpreting various spectral features [2][3][4][5][6], it is intriguing as to what the P-P-P theory predicts for large phenyl systems. Exact diagonalisation is currently restricted to systems with two phenyl rings. The advent of the density matrix renormalisation group (DMRG) method [10] has been fortuitous in that it has the potential to provide effectively exact numerical solutions of the P-P-P theory for systems with hundreds of conjugated carbon atoms. The DMRG has obstensively been restricted to systems with...

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Optimal parametrisation of the Pariser–Parr–Pople Model for benzene and biphenyl

Cited by 49 publications

References 19 publications

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

Benchmarking GW against exact diagonalization for semiempirical models

Large-scale numerical investigation of excited states in poly(para-phenylene)

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