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We investigate the convergence of quasi-particle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasi-particle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-Polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations., Comment: 16 pages, 9 figures

Quantum mechanical many-electron calculations can predict properties of atoms, molecules and even complex materials. The employed computational methods play a quintessential role in many scientifically and technologically relevant research fields. However, a question of paramount importance is whether approximations aimed at reducing the computational complexity for solving the many-electron Schr\"odinger equation, are accurate enough. Here, we investigate recently reported discrepancies of noncovalent interaction energies for large molecules predicted by two of the most widely-trusted many-electron theories: diffusion quantum Monte Carlo and coupled-cluster theory. We are able to unequivocally pin down the source of the puzzling discrepancies and present modifications to widely-used coupled-cluster methods needed for more accurate noncovalent interaction energies of large molecules on the hundred-atom scale. This enhances the reliability of predictions from quantum mechanical many-electron theories across a wide range of critical applications, including drug design, catalysis, and the innovation of new functional materials, such as those for renewable energy technologies., Comment: 14 pages, 3 figures, 2 tables

We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost. The main advantage of this algorithm is that it allows for the calculation to be stopped at any time, providing an unbiased estimate, with a statistical error that goes to zero as the exact calculation is approached. We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods. Specifically, we demonstrate that a precision of 0.5 millihartree can be attained with only 10\% of the computational effort required by the full calculation. This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive.

We present a study of the self-interstitial point defect formation energies in silicon using a range of quantum chemical theories including the coupled cluster (CC) method within a periodic supercell approach. We study the formation energies of the X, T, H and C3V self-interstitials and the vacancy V. Our results are compared to findings obtained using different ab initio methods published in the literature and partly to experimental data. In order to achieve computational results that are converged with respect to system size and basis set, we employ the recently proposed finite size error corrections and basis set incompleteness error corrections. Our CCSD(T) calculations yield an order of stability of the X, H and T self-interstitials, which agrees both with quantum Monte Carlo results and with predictions obtained using the random-phase approximation as well as using screened hybrid functionals. Compared to quantum Monte Carlo results with backflow corrections, the CCSD(T) formation energies of X and H are only slightly larger by about 100 meV. However, in the case of the T self-interstitial, we find significant disagreement with all other theoretical predictions. Compared to quantum Monte Carlo calculations, CCSD(T) overestimates the formation energy of the T self-interstitial by 1.2 eV. Although this can partly be attributed to strong correlation effects, more accurate electronic structure theories are needed to understand these findings.

We present a study of the two dimensional circular quantum dot model Hamiltonian using a range of quantum chemical ab initio methods. Ground and excited state energies are computed on different levels of perturbation theories including the coupled cluster method. We outline a scheme to compute the required Coulomb integrals in real space and utilize a semi-analytic solution to the integral over the Coulomb kernel in the vicinity of the singularity. Furthermore, we show that the remaining basis set incompleteness error for two dimensional quantum dots scales with the inverse number of virtual orbitals, allowing us to extrapolate to the complete basis set limit energy. By varying the harmonic potential parameter we tune the correlation strength and investigate the predicted ground and excited state energies.

A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride employing an embedding approach is presented. The embedding approach involves an algorithm to obtain localized Wannier orbitals of various types expanded in a plane-wave basis and intrinsic atomic orbital projectors. The localized occupied orbitals are employed in combination with unoccupied natural orbitals to perform many-electron perturbation theory calculations of local fragments. The fragments are comprised of a set of localized orbitals close to the adsorbed water molecule. Although the surface model contains more than 100 atoms in the simulation cell, the employed fragments are small enough to allow for calculations using high-level theories up to the coupled cluster ansatz with single, double and perturbative triple particle-hole excitation operators (CCSD(T)). To correct for the missing long-range correlation energy contributions to the adsorption energy, we embed CCSD(T) theory into the direct random phase approximation, yielding rapidly convergent adsorption energies with respect to the fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations., Comment: 12 pages, 7 figures

We present a basis set correction scheme for the coupled-cluster singles and doubles (CCSD) method. The scheme is based on employing frozen natural orbitals (FNOs) and diagrammatically decomposed contributions to the electronic correlation energy that dominate the basis set incompleteness error (BSIE). As recently discussed in [https://doi.org/10.1103/PhysRevLett.123.156401], the BSIE of the CCSD correlation energy is dominated by the second-order M{\o}ller-Plesset (MP2) perturbation energy and the particle-particle ladder term. Here, we derive a simple approximation to the BSIE of the particle-particle ladder term that effectively corresponds to a rescaled pair-specific MP2 BSIE, where the scaling factor depends on the spatially averaged correlation hole depth of the coupled-cluster and first-order pair wavefunctions. The evaluation of the derived expressions is simple to implement in any existing code. We demonstrate the effectiveness of the method for the uniform electron gas. Furthermore, we apply the method to coupled-cluster theory calculations of atoms and molecules using FNOs. Employing the proposed correction and an increasing number of FNOs per occupied orbital, we demonstrate for a test set that rapidly convergent closed and open-shell reaction energies, atomization energies, electron affinities, and ionization potentials can be obtained. Moreover, we show that a similarly excellent trade-off between required virtual orbital basis set size and remaining BSIEs can be achieved for the perturbative triples contribution to the CCSD(T) energy employing FNOs and the (T*) approximation.

We present an implementation of equation of motion coupled-cluster singles and doubles (EOM-CCSD) theory using periodic boundary conditions and a plane wave basis set. Our implementation of EOM-CCSD theory is applied to study $F$-centers in alkaline earth oxides employing a periodic supercell approach. The convergence of calculated electronic excitation energies for neutral color centers in MgO, CaO and SrO crystals with respect to orbital basis set and system size is explored. We discuss extrapolation techniques that approximate excitation energies in the complete basis set limit and reduce finite size errors. Our findings demonstrate that EOM-CCSD theory can predict optical absorption energies of $F$-centers in good agreement with experiment. Furthermore, we discuss calculated emission energies corresponding to the decay from triplet to singlet states, responsible for the photoluminescence properties. Our findings are compared to experimental and theoretical results available in literature.

In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing (QIP). Prominent examples are the Nitrogen-Vacancy (NV) center in diamond, phosphorous dopants in silicon (Si:P), rare-earth ions in solids and V$_{\text{Si}}$-centers in Silicon-carbide (SiC). The Si:P system has demonstrated, that by eliminating the electron spin of the dopant, its nuclear spins can yield exceedingly long spin coherence times. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electron-spin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 20. Surprisingly, the new charge state allows switching the optical response of single nodes facilitating full individual addressability., Comment: 8 pages, 4 figures, 1 table