Many-body Green’s-function calculations on the electronic excited states of extended systems

The distinguishable cluster approach from a screened Coulomb formalism

The distinguishable cluster doubles equations have been derived starting from an effective screened Coulomb formalism and a particle-hole symmetric formulation of the Fock matrix. A perturbative triples correction to the distinguishable cluster with singles and doubles (DCSD) has been introduced employing the screened integrals. It is shown that the resulting DCSD(T) method is more accurate than DCSD for reaction energies and is less sensitive to the static correlation than coupled cluster with singles and doubles with a perturbative triples correction.

Quasiparticle band structure of infinite hydrogen fluoride and hydrogen chloride chains

We study the quasiparticle band structure of isolated, infinite (HF)(infinity) and (HCl)(infinity) bent (zigzag) chains and examine the effect of the crystal field on the energy levels of the constituent monomers. The chains are one of the simplest but realistic models of the corresponding three-dimensional crystalline solids. To describe the isolated monomers and the chains, we set out from the Hartree-Fock approximation, harnessing the advanced Green's function methods local molecular orbital algebraic diagrammatic construction (ADC) scheme and local crystal orbital ADC (CO-ADC) in a strict second order approximation, ADC(2,2) and CO-ADC(2,2), respectively, to account for electron correlations. The configuration space of the periodic correlation calculations is found to converge rapidly only requiring nearest-neighbor contributions to be regarded. Although electron correlations cause a pronounced shift of the quasiparticle band structure of the chains with respect to the Hartree-Fock result, the bandwidth essentially remains unaltered in contrast to, e.g., covalently bound compounds.

Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition

Equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) method has been applied to exciton states of polyethylene using ab initio crystal Hartree-Fock method with one-dimensional periodic boundary condition. Full transformation of two-electron integrals from atomic-orbital basis to crystal-orbital basis has been performed for EOM-CCSD calculations. In order to make transformed integrals to have correct properties of translational symmetry, a lattice summation scheme has been proposed. The EOM-CCSD excitation energies have been obtained for the lowest singlet and triplet exciton states of polyethylene. The excitation energies converge with system size much faster than oligomer calculations using n-alkanes. Quasiparticle energy-level calculations by second-order many-body perturbation theory and by solving the inverse Dyson equation have also been performed to obtain exciton binding energies. Basis set dependencies on excitation energy, quasiparticle band gap, and exciton binding energy have been investigated. At the 6-31+G level, the excitation energy of the lowest singlet-exciton state and its binding energy are calculated to be 8.1 and 3.2 eV, respectively. The calculated excitation energy is well comparable with the corresponding experimental value, 7.6 eV.

Coupled-cluster singles and doubles for extended systems

Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.

Importance of chain–chain interactions on the band gap of trans-polyacetylene as predicted by second-order perturbation theory

We employ the Laplace-transformed second-order Moller-Plesset perturbation theory for periodic systems in its atomic orbital basis formulation to determine the geometric structure and band gap of interacting polyacetylene chains. We have studied single, double, and triple chains, and also two-dimensional crystals. We estimate from first principles the equilibrium interchain distance and setting angle, along with binding energy between trans-polyacetylene chains due to dispersion interactions. The dependence of the correlation corrected quasiparticle band gap on the intrachain and interchain geometric parameters is studied, obtaining that the gap of the compound structures is substantially reduced with respect to the single chain polymer.

Laplace-transformed diagonal Dyson correction to quasiparticle energies in periodic systems

We present a method to self-consistently evaluate quasiparticle energies of periodic systems within the diagonal approximation for solving Dyson's equation. Our method is based on the Laplace transform of the second-order Møller-Plesset perturbation (MP2) theory kernel in the atomic basis formulation. The overhead computational cost of evaluating the fully self-consistent diagonal correction over the MP2 band energy calculation is negligible. We present numerical benchmark results for the band structure of trans-polyacetylene and compare it with MP2 and other approaches.

Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems

A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10(-13) a.u. on each individual density matrix element for all cell indices with only 48 k-points.