Describing polymer polarizability with localized orbital scaling correction in density functional theory

Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.

Excited-State Charge Transfer Coupling from Quasiparticle Energy Density Functional Theory

The recently developed Quasiparticle Energy (QE) scheme, based on a DFT calculation with one more (or less) electron, offers a good description of excitation energies, even with charge transfer characters. In this work, QE is further extended to calculate electron transfer (ET) couplings involving two excited states. We tested it with a donor-acceptor complex, consisting of a furan and a 1,1-dicyanoethylene (DCNE), in which two low lying charge transfer and local excitation states are involved. With generalized Mülliken-Hush and fragment charge-difference schemes, couplings from the QE approach generally agree well with those obtained from TDDFT, except that QE couplings exhibit better exponential distance dependence. Couplings from half-energy gaps with an external field are also calculated and reported. Our results show that the QE scheme is robust in calculating ET couplings with greatly reduced computational time.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

The complex permittivity of PEDOT:PSS

High permittivity materials are required for efficient organic photovoltaic devices, and the addition of the conjugated polymer composite poly(3,4-ethylenedioxythiophen) polystyrene sulfonate (PEDOT:PSS) to dielectric polymers has been shown to significantly heighten their permittivity. The permittivity of PEDOT:PSS at the optical and microwave frequencies has been investigated, but PEDOT:PSS layers are mainly used for low-frequency device applications, where accurate dielectric property measurements are hindered by their high electrical conductivity and the problems arising from the metal-polymer interfaces. Here, we determine the complex relative permittivity (εr*=εr'-jεr″) of PEDOT:PSS layers perpendicular to the layer plane in the 10-2-106 Hz range by combining data from the reactive energy estimations and electrochemical impedance spectroscopy, and discover that: εr' at <1 Hz is ultra-high (∼106) decreasing with frequency to ∼5 at 106 Hz; the experimental data fit the Cole-Cole dielectric relaxation model by considering multiple relaxation mechanisms; PEDOT:PSS polarizes nonlinearly and εr' increases with the intensity of the applied external field; low frequency εr' increases with both thickness and temperature of the layer, opposite trend of temperature-dependence prevails at >103 Hz; the dielectric properties of PEDOT:PSS are highly anisotropic and the in-plane εr' at 1.0 kHz is three orders of magnitude higher than the vertical εr'; and that the εr'' decreases proportional to the reciprocal of frequency (1/f). The latter finding provides an explanation for the ubiquitous pink noise accompanying signals transmitted through organic conductor links. The described methodology can be adopted for investigations on other conjugated polymers.

Localized orbital scaling correction for periodic systems

Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band gaps of finite and bulk systems, energy level alignments, and electron distributions at interfaces. The localized orbital scaling correction (LOSC) was developed to correct delocalization error by using orbitals localized in space and energy. These localized orbitals span both the occupied and unoccupied spaces and can have fractional occupations in order to correct both the total energy and the one-electron energy eigenvalues. We extend the LOSC method to periodic systems, in which the localized orbitals employed are dually localized Wannier functions. In light of the effect of the bulk environment on the electrostatic interaction between localized orbitals, we modify the LOSC energy correction to include a screened Coulomb kernel. For a test set of semiconductors and large-gap insulators, we show that the screened LOSC method consistently improves the band gap compared to the parent density functional approximation.

Exact Analytical Form of Diatomic Molecular Orbitals

We provide the exact analytical form of diatomic molecular orbitals, as given by the solutions of a single-electron diatomic molecule with arbitrary nuclear charges, using our recently developed method for solving Schrödinger equations. We claim that the best representation of the wave function is a factorized form including a power prefactor, an exponentially decaying term, a modulator function on the exponential, and additional factors accounting for nodal surfaces and the magnetic quantum number. Applying our method, we have identified unexpected extreme points along the potential energy curves, hence revealing the limitations of the well-known concepts of bonding and antibonding.

Exact Second-Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory

We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.