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This project seeks to establish quantitative electronic and vibrational many-body methods for polymers and solids. With their predictive accuracy, these methods can be used to compute various key parameters of conjugated conducting polymers that are the base materials for organic photovoltaics and other related optoelectronic devices. In this way, laborious, expensive, sometimes even dangerous synthetic work can be avoided for all but the most promising polymers identified by quantitative computational modeling. Cheap, durable, and efficient organic photovoltaics and light emitting diodes are perhaps one of the most forward-looking ways of utilizing increasingly valuable petroleum resources.

We developed Gaussian-basis-set ab initio crystalline orbital theory to calculate correlated energy bands and band gaps of conjugated polymers with predictive accuracy at the second- and third-order Møller–Plesset perturbation (MP2 and MP3) levels as well as at the coupled-cluster singles and doubles (CCSD) level. The key parameters of organic photovoltaics are the ionization potentials, electron affinities, and exciton binding energies, which can be extracted from the computed energy bands. These ab initio methods are distinguished from the more widely used methods based on density-functional theory (DFT), which is known to perform poorly for band gaps and all of the aforementioned key quantities. The ab initio methods are not only generally more accurate for these properties but also they allow the accuracy of the results to be systematically increased. We furthermore extended these mathematical techniques to anharmonic lattice vibrations in polymers and solids. The highlights of our results are as follows:

For electrons, we use both delocalized and localized orbital approaches. In the delocalized orbital framework, we explore several new approximations that involve the dimension unique to periodic extended systems: the reciprocal (k) space. We introduce the mod-n and log-n MP2 as well as mod-n MP3 and CCSD methods, in which uniform or progressive downsampling of wave vectors in the Brillouin zone integrations is invoked to dramatically accelerate the electron-correlation calculations for solids. The mod-n scheme has enabled a correlation and correlated energy band calculation of an infinitely extended hydrocarbon polymer to be completed within a few hours on a single CPU. This capability is immediately useful for characterizing polymers for applications in optoelectronics. The mod-n scheme achieved an incredible 1,300-fold speedup in MP3 and CCSD calculations and the first anharmonic frequency calculations of infinite polymer chains at these levels (see below).

Our localized orbital approach enables a facile implementation of electron-correlation methods for molecular crystals. This scheme allowed us to apply MP2/aug-cc-pVTZ to solid hydrogen fluoride with a basis-set superposition error correction and to resolve a long-standing debate about its precise three-dimensional structure (parallel, antiparallel, or disordered). We also made a preliminary application of this scheme at the MP2 level to proton-ordered form of ice. Our quantitative results of phonon density of states did not support the controversial claim that there were two types of hydrogen bonds in ice that differed in strength by as much as a factor of two. 

For vibrations, systematic many-body methods such as vibrational self-consistent-field (VSCF), vibrational configuration-interaction (VCI), vibrational perturbation (VMP), and vibrational coupled-cluster (VCC) methods are established presently only for molecules. These methods allow anharmonicity in potential energy surfaces and resulting mode-mode coupling to be accounted for in vibrational spectra and vibrationally averaged properties. However, these methods have not thus far been applied to anharmonic lattice vibrations in solids; nor have their formalisms been shown rigorously to have the correct size dependence. We present strictly size-extensive generalization of VSCF, VMP, and VCC. An effective one-mode potential of size-extensive VSCF is harmonic with the quadratic force constant renormalized with contributions from quartic and higher even-order force constants of a certain type. VMP and VCC can account for anharmonicity due to all odd- and even-order force constants. We reported anharmonic frequencies of the infrared- and Raman-active vibrations of polyacetylene and polyethylene with potential energy surfaces calculated at the MP2, MP3, or CCSD level.

In 2009–10, 16 papers and 4 book chapters have been published from our group acknowledging the support of this ACS PRF grant. One of them is an invited perspective article on "quantum chemistry of macromolecules and solids," which summarizes the PI's as well as others' work on the electronic structure methods for hydrocarbon polymers as well as other solids. Another is J. Chem. Phys. Editor's Choice. During the period, the PI received National Science Foundation CAREER Award, Camille Dreyfus Teacher-Scholar Award, and Alumni Research Scholar Award (University of Illinois). The PI was an invited speaker at 8 university seminars and 12 conferences. The PI also served as a Guest Editor of Special Issues in Int. J. Quantum Chem. and Theor. Chem. Acc. The PI was invited to join the advisory editorial boards of Phys. Chem. Chem. Phys. and Theor. Chem. Acc.

One of our student members (Toru Shiozaki) graduated with a Ph.D. degree (University of Tokyo), who also received numerous awards including ACS Graduate Student Award in Computational Chemistry. Murat Keçeli won the Best Poster Award from the 18^th Conference on Current Trend in Computational Chemistry. Olaseni Sode won the Best Poster Award from the 2009 Sanibel Symposium. Our undergraduate member, Michael Durante, was selected to become a University Scholar.