Parr Pople Research Articles

Low-lying two-photon excitations in poly( p-phenylene vinylene) and its derivatives

We study the low-lying two-photon excited states in nonlinear optical processes in poly( p-phenylene vinylene) (PPV) and its derivatives. We find that, within the Pariser–Parr–Pople (PPP) model, the mA g state in (unsubstituted) PPV is exactly the lowest two-photon excited state (i.e., the 2 1 A g + state). Due to the breaking of charge-conjugation symmetry, the 2A g in substituted PPVs, originating from the 1 1 A g − , is weakly two-photon allowed, while the mA g has its origin from the 2 1 A g + , hence giving a strong peak in the two-photon absorption spectra.

Multiple solutions of coupled-cluster equations for PPP model of [10]annulene

Multiple (real) solutions of the coupled-cluster (CC) equations (corresponding to the CCD, ACP and ACPQ methods) are studied for the Pariser–Parr–Pople (PPP) model of [10]annulene, C 10H 10. The long-range electrostatic interactions are represented either by the Mataga–Nishimoto potential, or Pople’s R −1 potential. The multiple solutions are obtained in a quasi-random manner, by generating a pool of starting amplitudes and applying a standard CC iterative procedure combined with Pulay’s DIIS method. Several unexpected features of these solutions are uncovered, including the switching between two CCD solutions when moving between the weakly and strongly correlated regime of the PPP model with Pople’s potential.

Electronic correlation in cyclic polyenes. Behavior of approximate coupled-pair theories for large rings

We investigate the cyclic polyenes (annulenes) C M H M , described by the Pariser–Parr–Pople (PPP) model, by means of the approximate coupled-pair theories (ACP, ACPQ). For the systems with the spectroscopic value of the PPP resonance integral β=2.5 eV , the ACP method breaks down for M⩾446 and the ACPQ method—for M⩾198. In the ACPQ method, for M⩾174, two close lying solutions have been observed that become quasi-degenerate for M⩾198. The results indicate that the ACP and ACPQ methods cannot be applied to the one-dimensional metallic case.

Theoretical Studies Concerning the Optimization of Conjugated Molecules for Third-Order Nonlinear Optics

Within Hückel theory, the nonresonant third-order nonlinear optical susceptibility of a conjugated polymer is directly proportional to the bandwidth raised to the third power, and inversely proportional to the optical gap raised to the sixth power. This functional dependence, if correct, implies that polyacetylene is already an optimal organic material with regards to the magnitude of the nonresonant hyperpolarizability. Therefore, any improvements in the figure-of-merit for optical switching applications will come at the expense of the magnitude of the hyperpolarizability. Here, singles configuration-interaction (S-CI) theory is used to solve the Pariser−Parr−Pople (PPP) Hamiltonian of polyacetylene, treating both the strength of electron−electron interactions and the degree of bond alternation as model parameters. The results show that the hyperpolarizability is independent of the strength of electron−electron interactions and thus the degree of electron−hole correlation, and instead depends almost exclusively on the optical gap and the bandwidth. Furthermore, the functional dependence on the optical gap and bandwidth is nearly identical to that obtained from Hückel theory, giving strong support to the Hückel description of long chains, and its implications for materials optimization. In addition, the inverse-sixth power dependence of the hyperpolarizability is shown to imply a strong dependence of the transition moments on the optical gap. Finally, the resonant hyperpolarizability associated with two-photon absorption is found to tend toward an inverse-sixth power dependence on optical gap, although deviations from this dependence are considerably larger than for the resonant response.

Electronic correlation in cyclic polyenes. Performance of coupled-cluster methods with higher excitations

In this paper we consider the electrically neutral annulenes CMHM (M=6,10,14,18) and their cations CMHM4+ (M=10,14,18), having the cyclic geometry corresponding to the CM point group, and described by the electronic Hamiltonian of the Pariser–Parr–Pople (PPP) model (in which the strength of electronic correlations is controlled by the magnitude of the resonance integral β). We study the ground-state electronic-correlation effects in these systems by means of the single-reference coupled-cluster (CC) theory employing the restricted Hartree–Fock wave function as the reference. It is known that the basic CC technique—the coupled cluster singles and doubles (CCSD) method (for the annulenes equivalent to the CCD method)—breaks down in the strongly correlated regime of annulenes. In this paper we analyze the performance of the standard extensions of the CCD method, taking into account the connected triple (T) and/or quadruple (Q) excitations in the CC operator T̂: the CCDT, CCDQ, and CCDTQ methods. For comparison we use some modifications of the CCD method that emulate the coupling between the D and Q excitations: the ACP and ACPQ methods. Whenever available, the full configuration-interaction results serve as the reference. We study not only the ground-state correlation energies, but also the quality of the CC amplitudes corresponding to the double excitations, as well as the magnitude of quasidegeneracy effects. Our results provide evidence that not only the CCD, but also the CCDT, CCDQ, and CCDTQ methods break down when the correlation effects become sufficiently strong. This indicates a failure of the standard CC theory (in which the CCD method is gradually augmented by taking into account the T, Q etc. excitations) in the strongly correlated regime of the PPP annulene model.

Relations between Pariser–Parr–Pople and Heisenberg models

AbstractNecessary conditions under which the lowest‐energy states obtained as exact (full configuration interation) solutions of the Pariser–Parr–Pople (PPP) model may be interpreted in terms of the Heisenberg model are analyzed. In particular, for a set of model lattices the range of empirical parameters in which the lowest part of the PPP spectrum corresponds to the covalent states has been determined. It has been demonstrated that the energy gap between the lowest ionic and the highest covalent states of the PPP model, as a function of empirical parameters and of the geometric structure of the lattice, behaves in a specific and regular way. The results may be useful for determining limits of applicability of the Heisenberg model and for further studies aimed at a construction of an effective, Heisenberg‐type Hamiltonian that could reproduce the lowest part of the PPP spectrum. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Electronic excitation of sulfur-organic compounds - performance of time-dependent density functional theory

To define the scope and limitations of the time-dependent density functional theory (TDDFT) method, spectral absorption data of a series of about 100 neutral or charged sulfur-organic compounds with up to 24 non-hydrogen atoms and up to four sulfur atoms were calculated in the near-UV, visible and IR regions. Although the theoretical vertical transition energies correspond only approximately to experimental absorption band maxima, the mean absolute deviation was calculated to be 0.21 eV (1600 cm−1). The main absorption features of various compounds with monocoordinated or dicoordinated sulfur atoms are well reproduced. As far as possible TDDFT results were compared with those of semiempirical Zerner's intermediate neglect of differential overlap (ZINDO/S) and of Pariser–Parr–Pople (PPP) calculations. TDDFT also works well in cases where the semiempirical methods fail. Limitations of TDDFT were encountered with calculations of spectral absorptions of dye molecules. The “vinylene shift” of polymethine dyes is not reproduced by TDDFT. Whereas electronic excitation energies delocalized polar and betainic chromophores are reasonably well reproduced, excitation energies of charge-transfer-type and charge-resonance-type transitions of weakly interacting composite chromophores are significantly underestimated.

Precise PPP molecular orbital calculations of excitation energies of polycyclic aromatic hydrocarbons. Part 6. Spectrochemical atomic softness parameter†

The excitation energies of the α-, β-, and p-bands of benzo-annelated polyacenes were estimated by the Pariser–Parr–Pople (PPP) molecular orbital calculation method using a novel concept for evaluating the two-centre electron repulsion integral, new-γA, in which the spectrochemical atomic softness (SCAS) parameter krA was taken into account. The value of krA was determined using the concept of the spectroactive portion (SP) and allotted to each carbon atom. The calculated results using new-γA were excellent for the simultaneous calculations of the p-, α- and β-bands of benzo-annelated polyacenes and were better than those obtained from the conventional N·M-γ or the usual new-γ. The C–C bond lengths calculated using new-γA reproduced quantitatively the observed values.

Band deconvolution analysis of the absorption and magnetic circular dichroism spectral data of a planar phthalocyanine dimer.

The electronic absorption and magnetic circular dichroism spectral data of a phthalocyanine dicopper complex that is deduced to be very planar and to share a common benzene ring have been studied by band deconvolution analysis. The results were compared with those of the molecular orbital (MO) calculations within the framework of the Pariser-Parr-Pople (PPP) approximation. The results of the band deconvolution analysis are in good agreement with those of the PPP calculations, allowing many bands to be reasonably assigned on the basis of the MO calculations. The validity of the PPP method for the MO calculation of large molecules is also emphasized.

Ring currents and charge stiffness in molecular and extended models of interacting fermions

The diamagnetic susceptibility χ of half-filled fermion models with N=4n+2 sites is related to chemical shifts in molecules and charge stiffness in extended systems. The slow evolution of χ(N) with N in Hubbard models or spinless fermions indicates a small energy gap, as known from exact solutions of regular chains. A gap due to alternating transfer integrals (1±δ) suppresses χ for Nδ>1, but is a small correction for Nδ<1. Exact ring currents Nχ of Pariser–Parr–Pople (PPP) and Hubbard models are extended to N=18 in D18h symmetry. Hydrocarbon PPP parameters account for the anisotropy of proton shifts in 14 and 18 annulenes, for smaller shifts at larger N, and for larger shifts of anions with 4n+2 π-electrons. Fermion models with arbitrary spin-independent interactions are shown to have vanishing χ for open boundary conditions (chains) at half filling or finite N. Diamagnetic currents in molecules require rings but are not sensitive to small bond-length variations, while an energy gap rather than topology enters in the charge stiffness of extended systems. Although formally identical, χ has different applications in finite and extended systems and its convergence with N can be rapid or very slow. Spin–charge separation reflects correlations rather than topology in half-filled Hubbard, PPP, and spinless fermion models; 4n and 4n+2 rings with oppositely signed χ show similar spin–charge separation with increasing correlations.

IPM approach to Hubbard model. Applications and limitations of restricted CI calculations to ground states of some ? networks containing fused 5- and 6-membered rings

The validity of the independent particle model (IPM) approach in treating the Hubbard model with uniform hopping parameter t and uniform on-site repulsion term U is investigated for several |U/t| ratios on the ground states of some π networks containing fused 5- and 6-membered rings with up to N=32 π electrons. It is shown that single and double excitation configuration interaction (SD-CI) based on a closed-shell Hückel-type reference determinant plus a correction added for the size consistency error using appropriate known correction terms leads to sensible estimates of the ground-state energy for up to |U/t|≤4. The IPM approach is hence well suited for treating the chemically relevant region of |U/t|≈1.5−2 for π systems. The systems studied in this work involve several fullerene-type fragments with up to N=16, for which a full configuration interaction (FCI) calculation is possible, and three larger systems, namely Corannulene (N=20), the C26 fullerene (N=26) and the C fullerene anion of Td symmetry (N=32), for which only a limited CI involving single, double, triple, and quadruple excitations (SDTQ-CI) could be performed as a guide. SD-CI calculations on these latter systems further reproduced qualitatively correct charge densities and nearest-neighbor bond orders. Wherever possible, the obtained results were compared with those obtained by different methods present in the literature, based on Monte Carlo approaches. Further we indicated a strategy as to how to perform optimum FCI Hubbard/Pariser–Parr–Pople (PPP) calculations as far as computation time is concerned. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 83–98, 2000

Molecular orbital models of benzene, biphenyl and the oligophenylenes

A two-state (2-MO) model for the low-lying long axis-polarised excitations of poly( p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser–Parr–Pople (P-P-P) model of π-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four-state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest-lying dipole-allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many-body processes of the electronic system.

Linear-scaling computation of ground state with time-domain localized-density-matrix method

Recently developed time-domain localized-density-matrix (LDM) method for calculating the electronic excited-state properties has been applied to calculate the electronic ground state. The computational time remains to scale linearly with the system size. To test the method, we use it to determine the ground states of polyacetylene oligomers containing up to 20000 carbon atoms. The Pariser–Parr–Pople (PPP) Hamiltonian is employed for the π electrons of the systems. Comparison to the conventional diagonalization shows the high efficiency as well as accuracy of the time-domain LDM method.

Calculation of Electronic Spectra ofTrans-Polyacetylene

We present in this work theoretically calculated electronic spectraof charged trans-polyacetylene chains containing solitons. Thesecalculations are based on the random phase and rotating waveapproximation. Further we use correlation corrected energy levelscomputed in the framework of the Pariser–Parr–Pople (PPP)Hamiltonian. The geometries of the chains as functions of time havebeen taken from simulations within theSu–Schrieffer–Heeger (SSH) model. The spectra obtained formany time steps within a simulation are subsequently superimposed andaveraged. The Su–Schrieffer–Heeger model was chosen forthe simulation because it is often stated, that this one-particlemodel is based on renormalized parameters which essentially containalready the effects of electron–electron interactions. Furtherat least for charged solitons the theory gives quite correct solitonwidths as compared to Pariser–Parr–Pople calculations.Thus the present study is also aimed as a first step to investigatewhether the SSH model is really able to yield reliable geometries intime simulations. We found that our spectra reproduce theexperimentally known peaks of the solitons and band to bandexcitations quite well within an uncertainty of 0.3–0.5eV.Further, the ratio of intensities of the two peaks as obtained in ourcalculation agrees quite well with the corresponding experimentalones. The remaining small error in intensities should be due to ouruse of transition dipole moments calculated from HF orbitals. Chainlength might play a role in the appearance of several minima andmaxima of the absorption which are not present in the experimentalspectra. These different effects are currently under furtherstudy.

Correlated π-electronic states: Pyrene, 16-site polyene, and D2h symmetry adaptation

Diagrammatic valence bond (DVB) theory is a general approach to electron correlations in quantum cell models that conserve total spin. VB diagrams are a convenient many-electron basis for combining spin, point-group, and other symmetries in oligomers with a large but finite basis. Half-filled Hubbard or Pariser–Parr–Pople (PPP) models with 16 sites have ∼34.7×106 singlet diagrams. Improved DVB methods yield exact low-lying states of the 16-site polyene in C2h symmetry and of pyrene in D2h symmetry. Several generalizations of symmetry adaptation are necessary for large bases, including new rules for linearly independent basis vectors and an iterative method for Hamiltonian matrix elements that avoids overlap and inversion. The number and dimensions of the disjoint invariant subspaces Sm encountered in symmetry adaptation depend on the connectivity. D2h symmetry adaptation is much simpler for acenes than for pyrene, linear stilbene, or polyphenyls. Standard PPP parameters account well for the 11 pyrene states identified in linear and two-photon spectra. Polyenes to N=16 show systematic deviations, with the 2 1Ag threshold decreasing less rapidly with N than experiment. We discuss perturbations that break electron-hole, parity, or point-group symmetry on the low-energy states, test the second π-electron approximation for pyrene, and comment on the feasibility of DVB for N=18 or 20 sites.

Asymptotic behavior of the RHF energy of the PPP model of alternant cyclic polyenes

The large N expansion of the restricted Hartree–Fock (RHF) exchange energy per atom E(N) of the Pariser–Parr–Pople (PPP) model of cyclic polyenes (annulenes) CNHN is derived in detail. We explicitly derive the coefficients E0 and E1 of the asymptotic expansion: E(N)=E0+E1 ln N/N2+O(N−2), N→∞, in the very simple case of half-filling and no bond alternation. The exchange energy per atom in the infinite chain can be written as Eex=(2/π2)∑∞j=1{[γ∞(2j−1)]/[(2j−1)2]}, where γ∞ is the two-electron repulsion integral in the infinite chain. On the other hand, the second coefficient E1 giving a finite-size correction is found to be 1/2b, where b is the bond length. This value of E1 differs slightly from that of a linear chain with periodic boundary conditions because the distance between sites depends upon the radius of the ring, i.e., upon N. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 397–407, 1998

New aspects in the theory of ? electron systems on the basis of quantum statistical considerations

The electronic properties of π systems are studied under special consideration of the quantum statistical constraints experienced by a fermionic ensemble. In a many-electron basis of atomic occupation numbers these constraints decompose into a formal on-site constraint and a formal intersite constraint. The on-site constraint can be equated with the Pauli exclusion principle (PEP) while the intersite constraint can be equated with the Pauli antisymmetry principle (PAP). Under special molecular topologies the intersite constraints of fermion ensembles are suppressed. In this case the conventional fermionic statistics coincides with a mixed quantum statistics with fermionic on-site and bosonic intersite properties. Such a mixed statistics is realized in the π subspace of polyenes, (4n+2) Hückel annulenes (n=0, 1, 2,…) and the odd spin space of (2n+1) annulenes (n=1, 2, 3,…) if the π electron hoppings are restricted to nearest-neighbor centers. We discuss the topological conditions to conserve this statistical peculiarity at least approximately in two-dimensional (2D) π topologies. The quantities “aromaticity” and “antiaromaticity,” widely used in the chemical literature, are traced back to quantum statistical, topological, and molecular size considerations. The competition between the quantum constraints PEP and PAP, on the one hand, and the strength of the two-electron interaction in a given π Hamiltonian, on the other, is analyzed on the basis of Pariser–Parr–Pople (PPP), Hubbard (Hu), and simple Hückel molecular orbital (HMO) calculations. The influence of the PAP is reduced with increasing correlation strength while the influence of the PEP does not depend on this coupling parameter. The numerical results have been derived by Green's function quantum Monte Carlo (GF QMC) simulations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 727–752, 1998

Convergence behaviour of Green's function quantum Monte Carlo simulations of pi electron systems

Green's function quantum Monte Carlo (GF QMC) simulations of fermionic ensembles require the definition of a so-called spectral parameter W to yield trustworthy estimates of the fully correlated ground state energy E. In the present work we discuss the influence of the shift parameter, W, on the convergence behaviour of GF QMC simulations. As model systems we have considered some π molecules which are studied in the framework of the Pariser–Parr–Pople (PPP) Hamiltonian. The influence of the W parameter on the convergence of the GF QMC simulations in many-electron systems with an odd number of electronic permutations within one spin direction exceeds the influence observed in systems without such odd permutations. They do not occur in polyenes and Huckel annulenes with an electron count of (4n + 2) (n = 0, 1, 2…). The GF QMC technique adopted as a computational tool has been developed to study π molecules with fermionic sign problems owing to odd electronic interchanges within one spin direction.

BaxC60 fullerides: ? Electronic peculiarities of the C60 molecule and their consequences for the solid state

The electronic structure of BaxC60 fullerides was studied theoretically under special consideration of π electronic effects in the C60 molecule. Band structure data were derived by an intermediate neglect of differential overlap (INDO) crystal orbital (CO) approach. Different electronic configuration were evaluated in the Ba-doped C60 fullerides. BaxC60 solids with x=0, 3, 4, 6 are insulators. For a Ba5C60 model extrapolated from the crystal structure of Ba6C60, a finite band gap is also predicted. For a Ca5C60-like structure of Ba5C60, a quasi-degeneracy between a metallic configuration and an insulating Mott-like state was found. With an increasing Ba-to-C60 charge transfer (CT), sizable changes in the π system of C60 occur. In the neural molecule and for not too high an electron count, the π electrons form more or less electronically isolated hexagon–hexagon (6–6) “double” bonds with only minor hexagon–pentagon (6–5) “double-bond” admixtures. In the vicinity of C6012−, the 6–6 bonds have lost most of their double-bond character while it is enhanced for the 6–5 bonds. In highly charged anions, the π electron system of the soccer ball approaches a configuration with 12 decoupled 6π electron pentagons. For electron numbers between C60 and C6012−, the net π bonding is not weakened. The INDO CO results of the BaxC60 solids are supplemented by INDO MO and ab initio (3-21 G* split-valence basis) calculations of molecular C60 and some highly charged anions. Ab initio geometry optimizations show that the bond alternation of C60 with short 6–6 and long 6–5 bonds is inverted in C12−60. The high acceptor capability of C60 is explained microscopically on the basis of quantum statistical arguments. In the π electron configurations of C60 and C6012−, the influence of the Pauli antisymmetry principle (PAP) is minimized. The quantum statistics of (π) electron ensembles with a deactivated PAP is of the so-called hard-core bosonic (hcb) type. In these ensembles, the on-site interaction is fermionic while the intersite interaction is bosonic. Energetic consequences of the quantum statistical peculiarities of π systems are explained with the aid of simple model systems; we selected annulenes and polyenes. Computational tools in this step are Green's function quantum Monte Carlo (GF QMC) and full configuration interaction (CI) calculations for the π electrons of the model systems. These many-body techniques were combined with a Pariser–Parr–Pople (PPP) Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 333–373, 1997

BaxC60 fullerides: π Electronic peculiarities of the C60 molecule and their consequences for the solid state

The electronic structure of BaxC60 fullerides was studied theoretically under special consideration of π electronic effects in the C60 molecule. Band structure data were derived by an intermediate neglect of differential overlap (INDO) crystal orbital (CO) approach. Different electronic configuration were evaluated in the Ba-doped C60 fullerides. BaxC60 solids with x=0, 3, 4, 6 are insulators. For a Ba5C60 model extrapolated from the crystal structure of Ba6C60, a finite band gap is also predicted. For a Ca5C60-like structure of Ba5C60, a quasi-degeneracy between a metallic configuration and an insulating Mott-like state was found. With an increasing Ba-to-C60 charge transfer (CT), sizable changes in the π system of C60 occur. In the neural molecule and for not too high an electron count, the π electrons form more or less electronically isolated hexagon–hexagon (6–6) “double” bonds with only minor hexagon–pentagon (6–5) “double-bond” admixtures. In the vicinity of C6012−, the 6–6 bonds have lost most of their double-bond character while it is enhanced for the 6–5 bonds. In highly charged anions, the π electron system of the soccer ball approaches a configuration with 12 decoupled 6π electron pentagons. For electron numbers between C60 and C6012−, the net π bonding is not weakened. The INDO CO results of the BaxC60 solids are supplemented by INDO MO and ab initio (3-21 G* split-valence basis) calculations of molecular C60 and some highly charged anions. Ab initio geometry optimizations show that the bond alternation of C60 with short 6–6 and long 6–5 bonds is inverted in C12−60. The high acceptor capability of C60 is explained microscopically on the basis of quantum statistical arguments. In the π electron configurations of C60 and C6012−, the influence of the Pauli antisymmetry principle (PAP) is minimized. The quantum statistics of (π) electron ensembles with a deactivated PAP is of the so-called hard-core bosonic (hcb) type. In these ensembles, the on-site interaction is fermionic while the intersite interaction is bosonic. Energetic consequences of the quantum statistical peculiarities of π systems are explained with the aid of simple model systems; we selected annulenes and polyenes. Computational tools in this step are Green's function quantum Monte Carlo (GF QMC) and full configuration interaction (CI) calculations for the π electrons of the model systems. These many-body techniques were combined with a Pariser–Parr–Pople (PPP) Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 333–373, 1997