A study of excited states in trans‐polyacetylene in the Hartree–Fock, Tamm–Dancoff, and random‐phase approximation

Abstract

We report calculations of the excitonic spectra for trans-polyacetylene obtained in the Hartree-Fock, Tamm-Dancoff, and random-phase approximations. In the first case, in terms of two-particle propagator theory, the interaction between the excited electron and the hole is neglected. In the latter two cases, this interaction is considered in the first order. In this framework, the interaction between excitations of different bands and k-vectors has been included. We discuss the bandwidths and density of states for

Derivative Couplings between Time-Dependent Density Functional Theory Excited States in the Random-Phase Approximation Based on Pseudo-Wavefunctions: Behavior around Conical Intersections

“…The random-phase approximation (RPA) has been an extremely useful tool for calculating excited state properties and the oscillator strength of atoms and molecules since the 1960s. − More recently, the application of RPA in time-dependent density functional theory (TD-DFT/RPA) has played an increasingly important role in the field of theoretical chemistry for several reasons: (i) As a single-reference ab initio method, TD-DFT/RPA is computationally affordable and sometimes retains relatively high accuracy. , (ii) TD-DFT/RPA is a size-consistent method which is able to give pure singlet and triplet states for closed-shell molecules . (iii) In contrast to TD-DFT within the Tamm–Dancoff approximation (TDA), TD-DFT/RPA maintains the Thomas–Reiche–Kuhn sum rule of the oscillator strengths by taking into account the B matrix in the TD-DFT working equation; as such, TD-DFT/RPA gives improved results for transition moment calculations. , For these reasons, despite its well-known triplet instability, , TD-DFT/RPA is one of the most widely used approaches for modeling excited-state electronic structure. − …”

Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers

“…7,[21][22][23][24] Periodic CIS and time dependent HF (TD-HF) methods and their DFT counterparts (TDA, TD-DFT) have been formulated 25 and implemented for 1D periodic systems. 21,[25][26][27][28][29] The periodic CIS treatment has been complemented with schemes, allowing for a low level inclusion of correlation effects. 21,22 The most elaborate scheme within the theoretical description of excited states in periodic systems presently is EOM-CC theory with periodic boundary conditions, which was applied to polyethylene.…”

Electronic Structure-Factor, Density Matrices, and Electron Energy Loss Spectroscopy of Conjugated Oligomers

“…We will rely on the INDO (intermediate neglect of differential overlap) approximation, without alluding to a specific Hamiltonian parametrization. For better numerical precision, one might want to use a higher-level approach, such as ab initio calculations described in refs −32. Various approaches that were successfully used for calculating polymer response were extensively analyzed and compared in ref , which included discussion of TDDFT computations in polymers and numerical convergence issues for different algorithms.…”