Coupled cluster

About: Coupled cluster is a research topic. Over the lifetime, 6280 publications have been published within this topic receiving 301055 citations.

Coupled-cluster theory for atoms and molecules in strong magnetic fields.

Abstract: An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles–doubles–perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field.

Coupled cluster theory in materials science

Abstract: The workhorse method of computational materials science is undeniably density functional theory in the Kohn-Sham framework of approximate exchange and correlation energy functionals. However, the need for highly accurate predictions of ground and excited state properties in materials science motivates the further development and exploration of alternative as well as complementary techniques. Among these alternative approaches, quantum chemical wavefunction based theories and in particular coupled cluster theory hold the promise to fill a gap in the toolbox of computational materials scientists. Coupled cluster (CC) theory provides a compelling framework of approximate infinite-order perturbation theory in the form of an exponential of cluster operators describing the true quantum many-body effects of the electronic wave function at a computational cost that, despite being significantly more expensive than DFT, scales polynomially with system size. The hierarchy of size-extensive approximate methods established in the framework of CC theory achieves systematic improvability for many materials properties. This is in contrast to currently available density functionals that often suffer from uncontrolled approximations that limit the accuracy in the prediction of materials properties. In this tutorial-style review we will introduce basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the connection between coupled cluster theory and the random-phase approximation to bridge the gap between traditional quantum chemistry and many-body Green’s function theories that are widely-used in the field of solid state physics. We will discuss various approaches to improve the computational performance without compromising accuracy. These approaches include large-scale parallel design as well as techniques that reduce the prefactor of the computational complexity. A central part of this article discusses the convergence of calculated properties to the thermodynamic limit which is of significant importance for reliable predictions of materials properties and constitutes an additional challenge compared to calculations of large molecules. Furthermore we mention technical aspects of computer code implementations of periodic coupled cluster theories in different numerical frameworks of the one-electron orbital basis; the projector-augmented-wave formalism using a plane wave basis set and the numeric atom-centered-orbital with resolution-of-identity.

Addition by subtraction in coupled-cluster theory: A reconsideration of the CC and CI interface and the nCC hierarchy

Abstract: The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.

The potential energy curve and dipole polarizability tensor of mercury dimer

Abstract: Scalar relativistic coupled cluster calculations for the potential energy curve and the distance dependence of the static dipole polarizability tensor of Hg2 are presented and compared with current experimental work. The role of the basis set superposition error for the potential energy curve and the dipole polarizability is discussed in detail. Our recently optimized correlation consistent valence basis sets together with energy adjusted pseudopotentials are well suited to accurately describe the van der Waals system Hg2. The vibrational–rotational analysis of the best spin–orbit corrected potential energy curve yields re=3.74 A, D0=328 cm−1, ωe=18.4 cm−1, and ωexe=0.28 cm−1 in reasonable agreement with experimental data (re=3.69±0.01 A, De=380±25 cm−1, ωe=19.6±0.3 cm−1 and ωexe=0.25±0.05 cm−1). We finally present a scaled potential energy curve of the form ∑ja2jr−2j which fits the experimental fundamental vibrational transition of 19.1 cm−1 and the form of our calculated potential energy curve best (re=3.69 A, D0=365 cm−1, ωe=19.7 cm−1, and ωexe=0.29 cm−1). We recommend these accurate two-body potentials as the starting point for the construction of many-body potentials in dynamic simulations of mercury clusters.