Quasispin symmetry for the derivation of coupled cluster equations for the Hubbard model of benzene

The concept of quasispin is applied to a special case of the Pariser–Parr–Pople (PPP ) model of the benzene molecule, namely, the Hubbard Hamiltonian. Added to the spin, space, and alternancy symmetries already taken into account in the PPP Hamiltonian, this new symmetry, called quasispin symmetry, has the effect of reducing the size of the CI matrix. Coupled cluster (CC ) equations are then obtained after applying the CC approach with doubles as well as its extension that accounts for triexcited clusters (CCSDT -1). The derivation of these equations following the use of quasispin to the Hubbard model of benzene constitutes the most simple nontrivial example of CC results. In addition, the CC equations can be written in explicit algebraic form using the symbolic computation language MAPLE.     

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, C₁₀H₁₀. 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.     

Molecular weight dependent structure and charge transport in MAPLE‐deposited poly(3‐hexylthiophene) thin films

In this work, poly(3‐hexylthiophene) (P3HT) films prepared using the matrix‐assisted pulsed laser evaporation (MAPLE) technique are shown to possess morphological structures that are dependent on molecular weight (MW). Specifically, the structures of low MW samples of MAPLE‐deposited film are composed of crystallites/aggregates embedded within highly disordered environments, whereas those of high MW samples are composed of aggregated domains connected by long polymer chains. Additionally, the crystallite size along the side‐chain (100) direction decreases, whereas the conjugation length increases with increasing molecular weight. This is qualitatively similar to the structure of spin‐cast films, though the MAPLE‐deposited films are more disordered. In‐plane carrier mobilities in the MAPLE‐deposited samples increase with MW, consistent with the notion that longer chains bridge adjacent aggregated domains thereby facilitating more effective charge transport. The carrier mobilities in the MAPLE‐deposited simples are consistently lower than those in the solvent‐cast samples for all molecular weights, consistent with the shorter conjugation length in samples prepared by this deposition technique. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 652–662     

Molecular organization in MAPLE‐deposited conjugated polymer thin films and the implications for carrier transport characteristics

The morphological structure of poly(3‐hexylthiophene) (P3HT) thin films deposited by both Matrix Assisted Pulsed Laser Evaporation (MAPLE) and solution spin‐casting methods are investigated. The MAPLE samples possessed a higher degree of disorder, with random orientations of polymer crystallites along the side‐chain stacking, π–π stacking, and conjugated backbone directions. Moreover, the average molecular orientations and relative degrees of crystallinity of MAPLE‐deposited polymer films are insensitive to the chemistries of the substrates onto which they were deposited; this is in stark contrast to the films prepared by the conventional spin‐casting technique. Despite the seemingly unfavorable molecular orientations and the highly disordered morphologies, the in‐plane charge carrier transport characteristics of the MAPLE samples are comparable to those of spin‐cast samples, exhibiting similar transport activation energies (56 vs. 54 meV) to those reported in the literature for high mobility polymers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 39–48     

Coupled cluster calculation of the n --> pi* electronic transition of acetone in aqueous solution

The combined linear response coupled cluster/molecular mechanics (CC/MM) scheme including mutual polarization effects in the coupling Hamiltonian is applied together with supermolecular CC methods to the study of the gas-to-aqueous solution blue shift of the n --> pi* excitation energy in acetone. The aug-cc-pVDZ basis set is found to be adequate for the calculation of this excitation energy. In the condensed phase, the shift in the excitation energy is obtained by statistical averaging over 800 solute-solvent configurations extracted from a molecular dynamics simulation. We find the shift to be around 1100-1200 cm(-1) depending on the specific model used to describe solvent polarization. The importance of including explicit polarization in both the molecular dynamics simulation as well as the CC/MM calculations is emphasized. Furthermore, the significant dependence of the excitation energy on the CO bond length of acetone is discussed.     

Excitation energy calculation of conjugated hydrocarbons: a new Pariser-Parr-Pople model parameterization approaching CASPT2 accuracy

A new parameterization for the Pariser-Parr-Pople (PPP) model for conjugated hydrocarbons is proposed in this work. The distance-dependence of PPP parameters are obtained from CASPT2 ground state and low-lying excited state energies of ethylene and its cation at various C-C single bond lengths and are fitted to a set of carefully chosen mathematical functions. Our new PPP model is applied to the calculation of vertical singlet-triplet energy gaps and the excitation energies for low-lying π→π(*) valence excitations in various π-conjugated molecules. Results with the new PPP model are consistently better than the standard PPP model in use. It often surpasses density functional theory and single-reference excited state methods such as configuration interaction singles or time-dependent density functional theory in terms of its accuracy and agrees reasonably well with high-level theories or experiments.     

Hartree–Fock MO–LCAO equations with charge-dependent atomic integrals

The Hartree–Fock equations are derived in the MO -LCAO approximation for the case when the integrals (except overlap integrals) over the atomic orbitals are charge-dependent. It is shown that inclusion of the overlap matrix in the iterative procedure gives equations which are too complicated for the simple model under consideration. The approach is applied to the VESCF method in the PPP scheme.     

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. I. Single-reference-state formulation

The impact of the choice of molecular orbital sets on the results of single-reference-state coupled-cluster (CC) methods was studied for the H4 model. This model offers a straightforward way of taking into account all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its ground state can be varied over a wide range by changing its geometry. The CCD, CCSD, and CCSDT approaches are considered. Surfaces representing the dependence of the energy on the parameters defining the orbitals are obtained. It is documented that for every method there exist alternative orbital sets which allow one to obtain more accurate energies than the standard (HF, BO, and NO) ones. However, for many of the former orbital sets, one obtains relatively large one-body amplitudes or one may encounter problems with solving the CC equations by conventional methods. An interesting variety of orbitals which might be useful for studies of quasi-degenerate states by the CCD method was found. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 205–219, 1998     

Preparation of nodular carbon cryogel from simple and inexpensive polycondensation reaction of commercial modified black wattle tannin

Tannin–formaldehyde cryogels (TFC) were synthesized by sol–gel polycondensation of low molecular weight and highly reactive modified tannin with formaldehyde using HCl as a catalyst. Carbon cryogels (CC) were obtained by the TFC pyrolysis at an inert atmosphere at 800 °C. Pyrolysis caused significant changes in the physical and chemical properties of the material. The pyrolysis induced the decomposition of acid superficial groups and the development of basic ones. Pyrolysis also provoked significant change in the pore volume, forming a great amount of micropores. TFC and CC showed amorphous and turbostratic structures, respectively. Unpurified samples had inorganic impurities in their compositions.     

Valence bond corrected single reference coupled cluster approach

Summary An extension of the single reference coupled cluster method truncated to 1- and 2-body cluster components (CCSD) to quasidegenerate systems, where 3-and 4-body connected cluster components play an important role, is proposed. The basic idea is to extract the information concerning the 3- and 4-body clusters from some independent source, similarly as was implicitly done in the so-called ACPQ or ACC(S)D methods, and correct accordingly the absolute term in the CCSD equations. As a source of these approximate 3- and 4-body clusters, simple valence bond (VB) type wave functions are employed, since they are capable of describing electronic structure of various molecular systems for a wide range of nuclear conformations including their dissociation. The cluster analysis of these VB wave functions, that provides the desired information concerning the connected 3- and 4-body cluster components, is outlined and the explicit form of required correction terms to the CCSD equations is given.     

The relationship between the unrestricted and projected Hartree–Fock methods in a simple three-electron model system

Various forms of the unrestricted Hartree–Fock (UHF ) scheme are studied for a simple three-electron model system, represented by the PPP (Pariser–Parr–Pople) π-electron model of the allyl radical. Both spin and space symmetry are violated in the UHF trial wave function, either individually or simultaneously. A comparison with the projected Hartree–Fock (PHF ) schemes studied earlier is made and the effect of the order in which various symmetries are broken in both UHF and PHF schemes is studied. The effectiveness of various schemes follows from a comparison of the correlation energy and the wave function is obtained by various UHF (or projected UHF ) and PHF schemes, in the whole range of the coupling constant, with the corresponding quantities given by the exact solution of the model. Finally, the implications of the stability of the restricted HF solutions for the behavior of various single- and multiparameter UHF and PHF schemes are briefly outlined and exemplified on the studied model.     

Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique

Summary A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.Also affiliated with the Department of Chemistry, and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo Campus, University of Waterloo, Waterloo, Ontario, Canada. Killam Research Fellow 1987–89