Modern electronic structure theories can predict and simulate a wealth of phenomena in surface science and solid-state physics. In order to allow for a direct comparison with experiment, such ab initio predictions have to be made in the thermodynamic limit, substantially increasing the computational cost of manyelectron wave-function theories. Here, we present a method that achieves thermodynamic limit results for solids and surfaces using the "gold standard" coupled cluster ansatz of quantum chemistry with unprecedented efficiency. We study the energy difference between carbon diamond and graphite crystals, adsorption energies of water on h-BN, as well as the cohesive energy of the Ne solid, demonstrating the increased efficiency and accuracy of coupled cluster theory for solids and surfaces.

We study a tensor hypercontraction decomposition of the Coulomb integrals of periodic systems where the integrals are factorized into a contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.

We propose an approach for computing the Gibbs free energy difference between phases of a material. The method is based on the determination of the average force acting on interfaces that separate the two phases of interest. This force, which depends on the Gibbs free energy difference between the phases, is computed by applying an external harmonic field that couples to a parameter which specifies the two phases. Validated first for the Lennard-Jones model, we demonstrate the flexibility, efficiency and practical applicability of this approach by computing the melting temperatures of sodium, magnesium, aluminum and silicon at ambient pressure using density functional theory. Excellent agreement with experiment is found for all four elements, except for silicon, for which the melting temperature is, in agreement with previous simulations, seriously underestimated

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between thermal fluctuations between virial and potential-energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the dense part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Gr{\"u}neisen parameter, are in good agreement with experimental values for 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W and Hg), most post-transition metals (Ga, In, Sn, and Tl) and the metalloids Si and Ge cannot be explained by the IPL assumption. Thus, hidden scale invariance can be present even when the IPL-approximation is inadequate. The virial-energy correlation coefficient of iron and phosphorous is shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Gr{\"u}neisen equation of state and a number of well-known empirical melting and freezing rules.Comment: 12 pages, 11 figure

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.