Numerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene

Abstract

We present the formalism for the correction of the band structure for correlation effects of polymers in the framework of a localized orbital approximation, using the quasiparticle model. For this purpose we use in an ab initio framework Mo/ller–Plesset perturbation theory in second order, the coupled cluster doubles method, and its linear approximation. The formalism is applied to a water stack and two different forms of a water chain as model systems to test the reliability of the approximations involved. From our previous work we know that, e.g., in polyacetylene difficulties due to the localizability of the canonical crystal orbitals do not arise from the π or π* bands, but from bands of σ symmetry. Thus we concentrate in this work again on polyacetylene as an example of a realistic polymer. We find that the localized orbital approximation is quite useful also in the case of band structure corrections due to correlation effects. However, the coupled cluster calculations, in particular, turn out to be computationally very costly for infinite systems. But it seems to us that localized orbital approximations are at the moment the only way to make coupled cluster calculations on realistic polymers with covalent bonds between the unit cells possible at all.

Correlation-induced corrections to the band structure of boron nitride: A wave-function-based approach

“…It provides a set of canonical Bloch orbitals which are then subject to an orbital localization procedure that yields optimally localized Wannier orbitals; see, e.g.,. 7,8,42,43 Alternative approaches were introduced by Shukla et al 11,50 and Malrieu et al, 40 who carried out the ground-state HF calculation in real rather than reciprocal space and obtained directly localized orbitals.…”

“…4,5,6,7,8,9,10,11,12,13,14,15,16,17 DFT is strictly speaking a ground-state theory. Nevertheless the eigenvalues of the Kohn-Sham (KS) equations have been interpreted as the electronic energy bands.…”

“…The electron correlation problem is addressed in these schemes either by secondorder Møller-Plesset theory (MP2) 4,5,6,38,39,40 or coupledelectron-pair and coupled cluster methods. 7,8,9 By realizing that the correlation hole of an added electron or hole is a local object, use can be made of local operators. 27,28 The latter are most naturally associated with a set of real-space, localized Wannier orbitals (WO's).…”

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg2+-sensitive dye

“…͑The van der Waals interactions are not included in the total QM/MM Fock or KS matrix, but into the total energy.͒ On the other hand, we have also seen significant development based on a fully QM description for large-scale calculations. [6][7][8][9][10][11][12][13][14][15][16][17][18] One of the authors ͑W.Y.͒ has developed the linear-scaling treatment, the divide-and-conquer ͑DC͒ method. [26][27][28] In this method, the entire system is first divided into several subsystems and their electron densities are calculated separately.…”

“…In this subject, many methods have been proposed so far. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] The most well-known and commonly used approach is the quantum-mechanical/molecularmechanical ͑QM/MM͒ method. [19][20][21][22] In this method, the electronically important part is described by quantum mechanics ͑QM͒, while the rest of the system is described by molecular mechanics ͑MM͒.…”