We synthesized a two-dimensional (2D) crystalline covalent organic framework (sp2c-COF) that was designed to be fully π-conjugated and constructed from all sp2 carbons by C=C condensation reactions of tetrakis(4-formylphenyl)pyrene and 1,4-phenylenediacetonitrile. The C=C linkages topologically connect pyrene knots at regular intervals into a 2D lattice with π conjugations extended along both x and y directions and develop an eclipsed layer framework rather than the more conventionally obtained disordered structures. The sp2c-COF is a semiconductor with a discrete band gap of 1.9 electron volts and can be chemically oxidized to enhance conductivity by 12 orders of magnitude. The generated radicals are confined on the pyrene knots, enabling the formation of a paramagnetic carbon structure with high spin density. The sp2 carbon framework induces ferromagnetic phase transition to develop spin-spin coherence and align spins unidirectionally across the material.

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Two-dimensional sp2 carbon–conjugated covalent organic frameworks

Predicting the electronic structure of extended organic molecules constitutes an important fundamental task of modern chemistry. Studies of electronic excitations, charge-transfer, energy-transfer, and isomerization of conjugated systems form the basis for our understanding of the photophysics and photochemistry of complex molecules1-3 as well as organic nanostructures and supramolecular assemblies.4,5 Photosynthesis and other photochemical biological processes that constitute the basis of life on Earth involve assemblies of conjugated chromophores such as porphyrins, chlorophylls, and carotenoids.6-8 Apart from the fundamental interest, these studies are also closely connected to numerous important technological applications.9 Conjugated polymers are primary candidates for new organic optical materials with large nonlinear polarizabilities.10-19 Potential applications include electroluminescence, light emitting diodes, ultrafast switches, photodetectors, biosensors, and optical limiting materials.20-27 Optical spectroscopy which allows chemists and physicists to probe the dynamics of vibrations and electronic excitations of molecules and solids is a powerful tool for the study of molecular electronic structure. The theoretical techniques used for describing spectra of isolated small molecules are usually quite different from those of molecular crystals, and many intermediate size systems, such as clusters and polymers, are not readily described by the methods developed for either of these limiting cases.28

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Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Optical spectroscopy of conjugated molecules is described by using collective electronic coordinates, which represent the joint dynamics of electron-hole pairs. The approach relates the optical signals directly to the dynamics of charges and bond orders (electronic coherences) induced by the radiation field and uses only ground-state information, thus avoiding the explicit calculation of excited molecular states. The resulting real-space picture is reminiscent of the normal-mode analysis of molecular vibrations and offers a unified framework for the treatment of other types of systems including semiconductor nanostructures and biological complexes. Spatial coherence displayed in two-dimensional plots of the five electronic normal modes that dominate the optical response of poly(p-phenylene vinylene) oligomers with up to 50 repeat units (398 carbon atoms) in the 1.5- to 8-electronvolt frequency range suggests a saturation to bulk behavior at about five repeat units.

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Electronic coherence and collective optical excitations of conjugated molecules

The metadynamics or hills method is a relatively new molecular dynamics technique aimed to enhance the sampling of separated regions in phase space and map out the underlying free energy landscape as a function of a small number of order parameters or collective variables. The high efficiency allows for the application of metadynamics in combination with first principles dynamics methods, in particular with Car−Parrinello molecular dynamics, to study processes in which changes in the electronic structure play a dominant role, such as chemical reactions. The option to choose several independent collective variables is important to tackle complex and concerted transformations that lack an obvious a priori choice for a single reaction coordinate. In this Account, we discuss the role of metadynamics in the search of transition states, local minima, reaction paths, free energy profiles, and reaction coordinates among a growing list of alternative methods.

Metadynamics as a tool for exploring free energy landscapes of chemical reactions.

This paper reports the effect of homogeneous broadening of the optical gain on lasing spectra in self-assembled ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dot lasers. We measured the current-output power characteristics and light-emission spectra for columnar-shaped self-assembled ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum-dot lasers that show lasing from the ground state. While lasing occurred with a narrow line including a few longitudinal modes at room temperature, spectra at 80 K showed broad-band lasing emission over a range of 50--60 meV. Based on a coupled set of rate equations taking into account both the size distribution of quantum dots and a series of longitudinal cavity modes, we could clearly explain the measured temperature dependence of lasing spectra in terms of homogeneous broadening of optical gain of a single quantum dot. Dots with different energies start lasing independently at 80 K due to their spatial localization as well as a \ensuremath{\delta}-function-like gain, while at room temperature the dot ensemble contributes to a narrow-line lasing collectively via the homogeneous broadening of optical gain. The magnitude of the homogeneous broadening was found to reach 16 to 19 meV at room temperature, which corresponds to the polarization dephasing of 70 to 80 fs. We present a model on the dephasing process. This paper is a demonstration of the effect of homogeneous broadening on quantum-dot laser characteristics.

Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled In x Ga 1 − x A s / G a A s quantum dot lasers

A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. $81,$ 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.

Diagrammatic quantum Monte Carlo study of the Fröhlich polaron

The resonance Raman and infrared spectra of sulfuric-acid-treated poly(p-phenylenevinylene) (PPV) have been observed and analyzed on the basis of the resonance Raman spectra of the radical-cation and dication species of the model compounds CH 3 (C 6 H 4 CH=CH) n C 6 H 4 CH 3 (PVn, n=1-3), which correspond, respectively, to positive polarons and bipolarons in PPV. Sulfuric-acid-treated PPV is considered to contain a considerable amount of positive polarons having a more or less uniform length and a relatively small amount of positive bipolarons. Of the two electronic absorption bands at 2.25 and 1.00 eV of sulfuric-acid-treated PPV, the former absorption band is due to the positive polarons, whereas the latter has overlapping components arising from the positive polarons and bipolarons

Resonance Raman and Ultraviolet to Infrared Absorption Studies of Positive Polarons and Bipolarons in Sulfuric-Acid-Treated Poly(p-phenylenevinylene)

The infrared and Raman spectra of poly(p-phenylenevinylene) (PPV) and its low molecular weight model compounds CH 3 (C 6 H 4 CH=CH) n C 6 H 4 CH 3 (n=1-3) have been studied, and the following points have been made clear.

Infrared and Raman studies of poly(p-phenylenevinylene) and its model compounds

The resonance Raman spectra of sodium-doped poly(p-phenylenevinylene) (PPV) and the radical anions and dianions of three model compounds CH 3 (C 6 H 4 CH=CH) n C 6 H 4 CH 3 (PVn, n=1-3) have been studied. The Raman spectra of sodium-doped PPV show marked changes with laser wavelengths used for Raman excitation. These spectra have been analyzed on the basis of the resonance Raman spectra of the radical anions and dianions of the model compounds, which correspond, respectively, to negative polarons and bipolarons in PPV

Akira Sakamoto

Papers

Effect of homogeneous broadening of optical gain on lasing spectra in self-assembled In x Ga 1 − x A s / G a A s quantum dot lasers

Diagrammatic quantum Monte Carlo study of the Fröhlich polaron

Resonance Raman and Ultraviolet to Infrared Absorption Studies of Positive Polarons and Bipolarons in Sulfuric-Acid-Treated Poly(p-phenylenevinylene)

Infrared and Raman studies of poly(p-phenylenevinylene) and its model compounds

Resonance Raman characterization of polarons and bipolarons in sodium-doped poly(p-phenylenevinylene)