Correction: New insights into the 1D carbon chain through the RPA.

Correction for 'New insights into the 1D carbon chain through the RPA' by Benjamin Ramberger et al., Phys. Chem. Chem. Phys., 2021, 23, 5254-5260, https://doi.org/10.1039/D0CP06607A.

New insights into the 1D carbon chain through the RPA.

We investigated the electronic and structural properties of the infinite linear carbon chain (carbyne) using density functional theory (DFT) and the random phase approximation (RPA) to the correlation energy. The studies are performed in vacuo and for carbyne inside a carbon nano tube (CNT). In the vacuum, semi-local DFT and RPA predict bond length alternations of about 0.04 Å and 0.13 Å, respectively. The frequency of the highest optical mode at the Γ point is 1219 cm-1 and about 2000 cm-1 for DFT and the RPA. Agreement of the RPA to previous high level quantum chemistry and diffusion Monte-Carlo results is excellent. For the RPA we calculate the phonon-dispersion in the full Brillouine zone and find marked quantitative differences to DFT calculations not only at the Γ point but also throughout the entire Brillouine zone. To model carbyne inside a carbon nanotube, we considered a (10,0) CNT. Here the DFT calculations are even qualitatively sensitive to the k-points sampling. At the limes of a very dense k-points sampling, semi-local DFT predicts no bond length alternation (BLA), whereas in the RPA a sizeable BLA of 0.09 Å prevails. The reduced BLA leads to a significant red shift of the vibrational frequencies of about 350 cm-1, so that they are in good agreement with experimental estimates. Overall, the good agreement between the RPA and previously reported results from correlated wavefunction methods and experimental Raman data suggests that the RPA provides reliable results at moderate computational costs. It hence presents a useful addition to the repertoire of correlated wavefunction methods and its accuracy clearly prevails for low dimensional systems, where semi-local density functionals struggle to yield even qualitatively correct results.

RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods.

We present a method to approximate post-Hartree-Fock correlation energies by using approximate natural orbitals obtained by the random phase approximation (RPA). We demonstrate the method by applying it to the helium atom, the hydrogen and fluorine molecule, and to diamond as an example of a periodic system. For these benchmark systems, we show that RPA natural orbitals converge the MP2 correlation energy rapidly. Additionally, we calculated full configuration interaction energies for He and H2, which are in excellent agreement with the literature and experimental values. We conclude that the proposed method may serve as a compromise to reach good approximations to correlation energies at moderate computational cost, and we expect the method to be especially useful for theoretical studies on surface chemistry by providing an efficient basis to correlated wave function based methods.

Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling.

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

Analytic Interatomic Forces in the Random Phase Approximation.

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the GW approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites.

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)-an accurate many body theory-is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI_{3}, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI_{3}, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis.

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N4), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy.

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation, and second order Møller-Plesset theory. These wavefunction based correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is -107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions, but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

Physisorption of Water on Graphene: Subchemical Accuracy from Many-Body Electronic Structure Methods.

Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world's largest supercomputers. From this effort a consensus on the water-graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.