Conjugated polymers offer potential for many diverse applications but we still lack a fundamental microscopic understanding of their electronic structure. Elementary photoexcitations - excitons - span only a few nanometres of a molecule, which itself can extend over microns, and how their behaviour is affected by molecular dimensions is not fully understood. For example, where is the exciton formed within a conjugated segment, is it always situated on the same repeat units? Here, we introduce structurally-rigid molecular spoked wheels, 6 nanometres in diameter, as a model of extended pi-conjugation. Single-molecule fluorescence reveals random exciton localisation, leading to temporally-varying emission polarisation. Initially, this random localisation arises after every photon absorption event because of temperature independent spontaneous symmetry breaking. These fast fluctuations are slowed to millisecond timescales following prolonged illumination. Intramolecular heterogeneity is revealed in cryogenic spectroscopy by jumps in transition energy, however, emission polarisation can also switch without a spectral jump occurring, implying long-range homogeneity in local dielectric environment.
Inter- or intramolecular coupling processes between chromophores such as excimer formation or H- and J-aggregation are crucial to describing the photophysics of closely packed films of conjugated polymers. Such coupling is highly distance dependent, and should be sensitive to both fluctuations in the spacing between chromophores as well as the actual position on the chromophore where the exciton localizes. Single-molecule spectroscopy reveals these intrinsic fluctuations in well-defined bi-chromophoric model systems of cofacial oligomers. Signatures of interchromophoric interactions in the excited state - spectral red-shifting and broadening, and a slowing of photoluminescence decay - correlate with each other but scatter strongly between single molecules, implying an extraordinary distribution in coupling strengths. Furthermore, these excimer-like spectral fingerprints vary with time, revealing intrinsic dynamics in the coupling strength within one single dimer molecule, which constitutes the starting point for describing a molecular solid. Such spectral sensitivity to sub-Angstrom molecular dynamics could prove complementary to conventional FRET-based molecular rulers.
The spectral breadth of conjugated polymers gives these materials a clear advantage over other molecular compounds for organic photovoltaic applications and is a key factor in recent efficiencies topping 10%. But why do excitonic transitions, which are inherently narrow, lead to absorption over such a broad range of wavelengths in the first place? Using single-molecule spectroscopy, we address this fundamental question in a model material, poly(3-hexylthiophene). Narrow zero-phonon lines from single chromophores are found to scatter over 200nm, an unprecedented inhomogeneous broadening which maps the ensemble. The giant red-shift between solution and bulk films arises from energy transfer to the lowest-energy chromophores in collapsed polymer chains which adopt a highly-ordered morphology. We propose that the extreme energetic disorder of chromophores is structural in origin. This structural disorder on the single-chromophore level may actually enable the high degree of polymer chain ordering found in bulk films: both structural order and disorder are crucial to materials physics in devices.
Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large spheres surface element. Using it, the density distribution of the small spheres around the large sphere can be obtained experimentally. In a similar manner, in this letter, we propose a transform theory for surface force apparatus, which transforms the force acting on the cylinder into the density distribution of the small spheres on the cylindrical surface. The transform theory we derived is briefly explained in this letter.
The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field variant ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that MLtype DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values.
We develop numerical methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta generalized gradient approximation (meta-GGA) proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt a predictor-corrector step for stable time-evolution. Since energy functional is not known for the TB-mBJ potential, we propose a method to evaluate electronic excitation energy without referring to the energy functional. Calculations using the HSE hybrid functional is computationally expensive due to the nonlocal Fock-like term. We develop a computational method for the operation of the Fock-like term in Fourier space, for which we employ massively parallel computers equipped with graphic processing units. To demonstrate significances of utilizing potentials providing correct band gap energies, we compare electronic excitations induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: results using TB-mBJ and HSE are close to each other, while the excitation of the LDA calculation is more intensive than the others. At high laser intensities close to a damage threshold, we have found that electronic excitation energies are similar among the three cases.
It is well known from the quantum theory of strongly correlated systems that poles (or more subtle singularities) of dynamic correlation functions in complex plane usually correspond to the collective or localized modes. Here we address singularities of velocity autocorrelation function $Z$ in complex $omega$-plain for the one-component particle system with isotropic pair potential. We have found that naive few poles picture fails to describe analytical structure of $Z(omega)$ of Lennard-Jones particle system in complex plain. Instead of few isolated poles we see the singularity manifold of $Z(omega)$ forming branch cuts that suggests Lennard-Jones velocity autocorrelation function is a multiple-valued function of complex frequency. The brunch cuts are separated from the real axis by the well-defined gap. The gap edges extend approximately parallel to the real frequency axis. The singularity structure is very stable under increase of the temperature; we have found its trace at temperatures even several orders of magnitude higher than the melting point. Our working hypothesis that the branch cut origin is related to the interference in $Z$ of one-particle kinetics and collective hydrodynamic motion.
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfests theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the `Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated to another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models previously appeared in the chemical physics literature.
This review article discusses advances in the use of time-resolved photoelectron spectroscopy for the study of non-adiabatic processes in molecules. A theoretical treatment of the experiments is presented together with a number of experimental examples.
