Linear scaling calculation of excited-state properties of polyacetylene

A new method based on the equation of motion (EOM) for the reduced single-electron-density matrix is developed to calculate the excited-state properties of very large electronic systems. When the distance between two local Orbitals is larger than a critical length, the corresponding off-diagonal density-matrix element is negligible and may be set to zero. This reduces the dimension of the EOM and the number of required matrix elements. The computational cost scales thus linearly with the system size. As an illustration, the new method is implemented to evaluate the absorption spectra of polyacetylene oligomers containing 30-500 carbon atoms. The resulting spectra agree well with those of the full calculation, and more importantly, the linear scaling of the computational time versus the size is clearly demonstrated. ©1999 The American Physical Society.published_or_final_versio

Generalized linear-scaling localized-density-matrix method

A generalized linear scaling localized-density-matrix (LDM) method is developed to adopt the nonorthonormal basis set and retain full Coulomb differential overlap integrals. To examine its validity, the method is employed to evaluate the absorption spectra of polyacetylene oligomers containing up to 500 carbon atoms. The semiempirical Hamiltonian for the π electrons includes explicitly the overlap integrals among the π orbitals, and is determined from the ab initio Hartree-Fock reduced single-electron density matrix. Implementation of the generalized LDM method at the ab initio molecular orbital calculation level is discussed. © 1999 American Institute of Physics.published_or_final_versio

Linear-scaling time-dependent density-functional theory

A linear-scaling time-dependent density-functional theory is developed to evaluate the optical response of large molecular systems. The two-electron Coulomb integrals are evaluated with the fast multipole method, and the calculation of exchange-correlation quadratures utilizes the locality of exchange-correlation functional within the adiabatic local density approximation and the integral prescreening technique. Instead of many-body wave function, the equation of motion is solved for the reduced single-electron density matrix in the time domain. Based on its "nearsightedness", the reduced density matrix cutoffs are employed to ensure that the computational time scales linearly with the system size. As an illustration, the resulting time-dependent density-functional theory is used to calculate the absorption spectra of linear alkanes, and the linear scaling of computational time versus the system size is clearly demonstrated.published_or_final_versio

Localized-density-matrix method and nonlinear optical response

The linear-scaling localized-density-matrix (LDM) method was generalized to calculate the nonlinear optical response of very large systems. The computational time was shown to scale linearly with the system size for polyacetylene oligomers containing up to 3200 carbon atoms. The second hyperpolarizabilities of polyacetylene oligomers were accurately determined. Further, the values of off-resonant polarizabilities were found depending on the optical gap and N while small variation of geometry showed minimal effect.published_or_final_versio

Localized-density-matrix implementation of time-dependent density-functional theory

The localized single-electron density matrix implementation of time-dependent density-functional theory (TDDFT) was discussed. The excited state properties of atoms and molecules were calculated using the TDDFT. In this regard, the calculations of the absorption spectra of polyacetylene oligomers and linear alkanes by using the TDDFT, were also presented.published_or_final_versio

Localized-density-matrix method and its application to nanomaterials

The localized-density-matrix (LDM) method has been developed to calculate the excited state properties of very large systems containing thousands of atoms. It is particularly suitable for simulating the dynamic electronic processes in nanoscale materials, and has been applied to poly(p-phenylenevynelene) (PPV) aggregates and carbon nanotubes. Absorption spectra of PPVs and carbon nanotubes have been calculated and compared to the experiments.published_or_final_versio

Localized-density-matrix, segment-molecular-orbitals and poly(p-phenylenevinylene) aggregates

The segment-molecular-orbital representation is developed and incorporated into the recently developed linear-scaling localized-density-matrix method. The entire system is divided into many segments, and the molecular orbitals of all segments form the basis functions of the segment-molecular-orbital representation. Introduction of different cutoff lengths for different segment-molecular-orbitals leads to a drastic reduction of the computational cost. As a result, the modified localized-density-matrix method is employed to investigate the optical responses of large Poly(p-phenylenevinylene) aggregates. In particular, the interchain excitations are studied. The complete neglect of differential overlap in spectroscopy hamiltonian is employed in the calculation. © 1999 American Institute of Physics.published_or_final_versio

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

Ultrafast Coulomb-induced dynamics of 2D magnetoexcitons

We study theoretically the ultrafast nonlinear optical response of quantum well excitons in a perpendicular magnetic field. We show that for magnetoexcitons confined to the lowest Landau levels, the third-order four-wave-mixing (FWM) polarization is dominated by the exciton-exciton interaction effects. For repulsive interactions, we identify two regimes in the time-evolution of the optical polarization characterized by exponential and {\em power law} decay of the FWM signal. We describe these regimes by deriving an analytical solution for the memory kernel of the two-exciton wave-function in strong magnetic field. For strong exciton-exciton interactions, the decay of the FWM signal is governed by an antibound resonance with an interaction-dependent decay rate. For weak interactions, the continuum of exciton-exciton scattering states leads to a long tail of the time-integrated FWM signal for negative time delays, which is described by the product of a power law and a logarithmic factor. By combining this analytic solution with numerical calculations, we study the crossover between the exponential and non-exponential regimes as a function of magnetic field. For attractive exciton-exciton interaction, we show that the time-evolution of the FWM signal is dominated by the biexcitonic effects.Comment: 41 pages with 11 fig