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This project will apply quantitative electronic structure methods to petroleum-derived hydrocarbon polymers with disorders, in particular, localized excitations in conjugated conducting polymers that play critical roles in the function and performance of organic photovoltaics and other related optoelectronic devices such as flexible light emitting diodes (LEDs). We will employ Gaussian-basis-set ab initio crystalline orbital theory to calculate correlated energy bands and band gaps of conjugated polymers with predictive accuracy at a simplified second-order Møller–Plesset perturbation level. We will also combine coherent methodologies for finite and infinite systems to treat localized excitations and other lattice defects. We will quantitatively (with the methods that go beyond usual density-functional methods) evaluate the key parameters of organic polymer-based photovoltaics, i.e., ionization potentials, electron affinities, and exciton binding energies and the impact of geometrical relaxation on them.

In the 2008–09 funding period, we have made a significant progress. Ten (10) peer-reviewed articles have been published or accepted for publication. The PI has been invited to contribute three (3) book chapters that have also been partially supported by this grant. Two of the peer-reviewed articles are invited perspectives (Chem. Phys. Lett. and Phys. Chem. Chem. Phys.) and their graphics are used in the front and inside covers. The PI received the Camille Dreyfus Teacher–Scholar Award and National Science Foundation's CAREER Award. The following are some of the highlights:

(1) Fast electron-correlation methods for molecular crystals with an application to solid formic acid. A method for routine first-principles determination of energies, structures, and phonons of molecular crystals by high-accuracy electron-correlation theories has been proposed. It approximates the energy per unit cell of a crystal by a sum of monomer and dimer energies in an embedding field of self-consistent (and, therefore, polarizable) atomic charges and dipole moments. First and second energy derivatives with respect to atom positions and lattice constants (useful for characterizing structures and phonons) have also been computed efficiently with a long-range electrostatic correction. The method has been applied to solid formic acid, which is of significant contemporary interest in relation to the structure of hydrogen-bonded solid, liquid, and aerosols, phase transitions, polymorphism, concerted proton transfer, etc. Accurate energies (with corrections for basis-set superposition errors), structural parameters, and frequencies and reliable assignments of infrared, Raman, and inelastic neutron scattering spectral bands have been obtained for three polymorphic structures (b₁, b₂, and a) with second-order Møller-Plesset perturbation (MP2) theory or higher. They have suggested that observed diffraction and spectroscopic data are consistent with the pristine b₁ form and the hitherto-inexplicable infrared band splitting can be assigned to the in-phase and out-of-phase vibrations of adjacent hydrogen-bonded molecules rather than speculated polymorphism. Spectral features expected from the b₂ and a forms have also been predicted and are shown to be incompatible with the observed Raman and inelastic neutron scattering spectra in the low-frequency region.

(2) Coupled-cluster (CC) and MP2 study of energies, structures, and phonons of solid hydrogen fluoride. With the method described in (1), we have determined the equilibrium geometry and phonon dispersion curves of solid hydrogen fluoride at the CCSD/aug-cc-pVDZ and BSSE-corrected MP2/aug-cc-pVTZ levels. The predicted geometries have been in quantitative agreement with the diffraction data. The calculated frequencies of the infrared- and/or Raman-active phonons do not agree with the observed, with the largest errors exceeding a few hundred cm^–1. The errors are not due to the electronic structure treatment, but are caused by strong anharmonicity in the potential energy surfaces of this hydrogen-bonded solid. When we perform a vibrational MP2 calculation in the Gamma approximation using the potential energy surface, vastly improved agreement is achieved between the first-principles theory and experiments. The bands in the observed inelastic neutron scattering from solid hydrogen fluoride have also been straightforwardly assignable to the peaks in the hydrogen-amplitude-weighted phonon density of states (harmonic).

(3) Efficient Brillouin-zone integrations in MP2 for extended systems of one-dimensional periodicity. The validity and accuracy of various ways of drastically reducing the number of k-points in the Brillouin zone integrations occurring in MP2 calculations of one-dimensional solids has been investigated. The most promising approximation can recover correlation energies of polyethylene and polyacetylene within 1% of converged values at less than a tenth of usual computational cost. The quasi-particle energy bands have also been reproduced quantitatively with the same approximation. In the most drastic approximation, in which only one zone-center k-point (Gamma point) in the BZ is sampled (the Gamma approximation), the correlation energies are recovered within 10% of the converged values with a speedup by a factor of 80–100. The (angle-resolved) photoelectron spectra of trans- and cis-polyacetylenes, polyethylene, and polydiacetylene have been reproduced accurately or predicted by MP2 with this scheme.

(4) Higher-order explicitly correlated CC methods and combined CC and MP methods. Efficient computer codes for the explicitly correlated CC (R12- or F12-CC) methods with up to quadruple excitations and explicitly correlated combined CC and MP methods, which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra. They form a hierarchy of systematic approximations [F12-CCSD, F12-CCSD(T), F12-CCSD(2)_T, F12-CCSD(3)_T, F12-CCSDT, F12-CCSD(2)_TQ, F12-CCSDT(2)_Q, F12-CCSDTQ] that converge most rapidly toward the exact solutions of the polyatomic Schrödinger equations with respect to both the highest excitation rank and basis-set size. Using the Slater-type function 1 – exp(–ar₁₂) as a correlation function, a F12-CC method can provide the aug-cc-pV5Z-quality results of the conventional CC method of the same excitation rank using only the aug-cc-pVTZ basis set. Combining these F12-CC methods with the grid-based, numerical Hartree–Fock equation solver, the exact solutions (eigenvalues) of the Schrödinger equations of neon, boron hydride, hydrogen fluoride, and water at their equilibrium geometries have been obtained as -128.9377 ± 0.0004, -25.2892 ± 0.0002, -100.459 ± 0.001, and -76.437 ± 0.003 E_h, respectively, without resorting to complete-basis-set extrapolations. These absolute total energies or the corresponding correlation energies agree within the quoted uncertainty with the accurate, nonrelativistic, Born–Oppenheimer values derived experimentally and/or computationally.