Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

Abstract

An ab initio method for calculating the longitudinal linear polarizability of polymeric chains is described. This method is equivalent to an uncoupled Hartree-Fock scheme. It is applied to polyethylene and polysilane in minimal STO-3G and extended 4-31G basis sets. The study describes important techniques for solving the difficulties met in actual calculations: band reordering of the band structures, calculation of analytical derivatives of the energy bands &"&) and LCAO coefficients cW(k), and errors caused by the improper lattice sum truncations of the Hartree-Fock matrix.

Abinitioinvestigation of the electronic properties of planar and twisted polyparaphenylenes

“…The dipole transition strengths between the crystalline orbitals a (k) and r (k), ⍀ ar (k), sometimes called the oscillator strengths, are defined in recent papers, 23 together with their anti-Hermiticity property and a description of the analytical method used to compute them. 24 Despite its neglect of reorganizational effects, this uncoupled Hartree-Fock method is adequate to obtain correct trends of asymptotic longitudinal polarizabilities per unit cell and qualitative agreement with experimental data. [25][26][27] Equation ͑4͒ explicitly shows that it is possible to decompose the total polarizability per unit cell into the contributions of each occupied band.…”

“…This uncoupled Hartree-Fock method has recently been generalized to infinite periodic systems. 23,24 In this procedure, the frequency-independent longitudinal polarizability per unit cell of infinite periodic systems is given by…”

Ab initio determination of polarizabilities per subunit in polymeric systems using the polarization propagator: Application to model hydrogen chains

“…Barbier et al [16] provided an analytical expression of Q&) and, more recently, we published a better numerical form [12] for computation. By using the transformation of the dipole integrals into the dipole transition strengths (15) and the anti-Hermitian character of these latter integrals [16], the frequencyindependent polarization propagator for closed-shell infinite periodic systems may be written where the chemist's or Mulliken notation is used to define the two-electron integrals:…”

“…As in the case of the sos method [12], the RPA expression of the longitudinal polarizability per unit cell can also be partitioned into the contributions of each single-particle state and of each occupied band:…”

“…They are either coupled or uncoupled Hartree-Fock procedures depending upon the inclusion or not of the field-induced electron reorganizational effects. The oldest method is the uncoupled Genkin-Mednis [ll] procedure that corresponds to a sum-over-states [12] (sos) evaluation of the polarizabilities. It was first used by Cojan et ] and showed good agreement of the extrapolated oligomer results with the infinite polymer results as well as the necessity to use such a method for the most interesting systems.…”