Analysis of the viscoelastic coefficients in the Vignale-Kohn functional: The cases of one- and three-dimensional polyacetylene

In this work we employ the Vignale-Kohn (VK) current functional in the calculation of the linear response properties of polyacetylene for both the one-dimensional infinite chain and the infinite three-dimensional crystal. We test the two existing parametrizations of the longitudinal and transverse exchange-correlation kernels of the homogeneous electron gas that enter the VK functional and show that they lead to very different results. We argue that this is mainly caused by the different values of these kernels in the zero-frequency limit in the two parametrizations. In this limit knowledge of the exchange correlation part of the shear modulus of the homogeneous electron gas becomes very important. It is exactly this quantity that is not known accurately. Furthermore, we show that our results are in good qualitative agreement with results obtained earlier using the Vignale-Kohn functional for polyacetylene oligomers.