Quantum chemical ab initio calculations of correlation effects in complex polymers: Poly(para-phenylene)

Abstract

Different quantum chemical approaches to the ground state correlation energy per unit cell of infinite poly(para-phenylene) (PPP) chains are presented. PPP is an organic polymer with interesting optical properties, due to its conjugated, aromatic pi system. The inclusion of correlation effects is crucial for a sound quantum chemical description of such a system. The correlation calculations were performed on the coupled cluster with single and double excitations (CCSD) level of theory using Dunning's spd correlation consistent polarized valence double-zeta basis sets. The correlation energy per unit cell is determined by means of the incremental method, which comprises series of CCSD calculations with partial excitation spaces. The resulting correlation energy per unit cell of PPP is -21.797 eV and compares well with that obtained by a simple but much more demanding cluster convergence approach (-21.775 eV). In addition, the accuracy and performance of the incremental scheme is discussed with respect to full CCSD benchmark calculations on PPP oligomers. Two variants are considered, the conventional one based on bond-type local units, and an extended one based on natural chemical subunits. Whereas it is difficult to reach "chemical" accuracy with the first variant, the second variant allows an accurate and efficient treatment with only a few individual CCSD calculations for a polymer with an aromatic pi system such as PPP.

A Simplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

“…The same calculations are used to generate embedding potentials which describe the influence of the infinite bulk surroundings on finite cluster models 26 . Results for the band structure of diamond 34 and hydrogen fluoride chains 35 with this approach are under preparation in our laboratory.…”

“…3) The data of steps 1 and 2 were transferred via our CRYSTAL-MOLPRO interface 27 to the molecular program MOLPRO 31,40 and are used as input for generating embedded C 8(18) and Si 8(18) clusters 34 . Here, the central C-C or Si-Si bond and its six nearest-neighbor bonds inside the C 8 (Si 8 ) kernel are treated as active, while the basis functions from the surrounding shell of 18 C (Si) atoms are only added to assist in the representation of the localized occupied and virtual orbitals of the kernel.…”

The method of increments—a wavefunction-based ab initio correlation method for solids

“…In this work not enough far-away terms may have been included. The applications to graphite and the fullerene as well as to the -bound polymers polyacetylene [49,50,223] and poly-paraphenylene [54] show, that the incremental expansion is useful also for more delocalised electronic systems. The price to be paid is the inclusion of more far-away pairs of bonds or a tiny loss of accuracy of about 2% of the correlation energy.…”

“…But of course a combination of the method of increments with the local correlation method of Pulay is possible to reduce the computational effort even further [31,32]. The focus of this review lies on the method of increments and its application to ground-state properties of various material classes: From insulators [33][34][35][36][37] over semiconductors [20,21,[38][39][40][41][42] to metals [22,43,44], from strongly bound ionic or covalent systems to weakly bound van der Waals solids [45][46][47], from large molecules [31,48] over polymers [49][50][51][52][53][54][55][56] to three-dimensional solids, from weakly correlated systems to strongly correlated ones such as transition-metal oxides [57,58] and rare-earth nitrides and oxides [59][60][61]. The generalisation to metals is discussed for the example of solid mercury [44,62] and the inclusion of multi-reference treatments for strongly correlated systems is presented for a one-dimensional lithium chain [43].…”

A general-order local coupled-cluster method based on the cluster-in-molecule approach

“…This general strategy is followed in the old papers of Förner and co-workers, 7,8 in the incremental method proposed by Stoll and studied by many others, [30][31][32][33][34][35] in the CC method based on the fragment molecular-orbital method, 36 in particular, in the divide-andconquer methods such as the one published by Li and Li,37 and more recently by Ziółkowski et al 38 In other local correlation methods, the correlation energy is expressed as a simple sum of the local contributions without the need for the explicit treatment of interactions of the fragments. The divide-and-conquer CC method recently published by Kobayashi and Nakai 39 applies a buffer region for each fragment to incorporate the effect of the fragmentfragment interactions at the calculation of fragment energies.…”