We use first-principles calculations to extract two essential microscopic parameters, the charge-transfer energy and the inter-cell oxygen-oxygen hopping, which correlate with the maximum superconducting transition temperature Tc,max across the cuprates. We explore the superconducting state in the three-band model of the copper-oxygen planes using cluster Dynamical Mean-Field Theory. We find that the variation in the charge-transfer energy largely accounts for the empirical trend in Tc,max, resolving a long-standing contradiction with theoretical calculations. perconductors with the charge-transfer energy Abstract -Supplementary material providing the details of the extraction of the materials parameters and the numerical method used to solve the 3-band Hubbard model.Appendix: Table of parameters. -We summarize in Table 1 the parameters extracted via downfolding for the three-band model and discuss the details of the downfolding procedure.

The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the hybridization expansion continuous time quantum Monte Carlo (CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: a) skip lists and b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with d electrons, we find speedups of ∼ 25 up to ∼ 500 compared to the direct evaluation of the matrix product. Even larger speedups are likely with f electron systems and with clusters of correlated atoms.

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We describe a framework for designing novel materials, combining modern first-principles electronic structure tools, materials databases, and evolutionary algorithms capable of exploring large configurational spaces. Guided by the chemical principles introduced by Antipov, et. al., for the design and synthesis of the Hg-based high-temperature superconductors, we apply our framework to design a new layered copper oxysulfide, Hg(CaS)2CuO2. We evaluate the prospects of superconductivity in this oxysulfide using theories based on charge-transfer energies, orbital distillation and uniaxial strain.The superconductors with the highest known transition temperatures at ambient pressure are all layered compounds containing planes of copper and oxygen where the superconducting electrons reside, separated by "spacer layers" composed of other elements. For a given compound, varying the doping level to an optimal value near 0.15 holes per copper maximizes the superconducting transition temperature T c . Since the copper oxide planes are a common ingredient, the large variabilty in optimal T c 's between compounds must then be controlled by the spacer layers, which function to tune the chemical and structural properties of the copper oxide layer. Finding novel compositions for the spacer layers is key to discovering new superconductors with higher transition temperatures.Theoretical design of new compounds is challenging due to the vast combinatorial space of elements and the large number of constraints: preferred oxidation state, electronegativity, atomic radii, preferred local coordination environment, and overall electrical neutrality. These microscopic properties in turn determine the local structural stability, global configurational minimum, and thermodynamic stability. Finding the global low-energy structure is the computational bottleneck. If a given composition results in a stable compound, we still need to determine whether it tunes the low-energy Hamiltonian so that T c is enhanced, which imposes further screening criteria.Rather than design a compound from scratch, we adopt a more moderate approach: we take as a starting point the family of cuprates with the highest transition temperatures, the Hg-based cuprates, and modulate its spacer layers. We benefit from the vast body of chemical intuition accumulated for the cuprates, for instance, laid out especially clearly in Ref. 1, and use modern electronic structure methods [2,3], materials databases [4,5] and evolutionary algorithms [6] to efficiently screen for compositions which have the desired structure and the best prospects for stability. We use three proposed theories, based on epitaxial strain [7], the charge-transfer energy [8], and orbital distillation [9], to evaluate the resultant compound's prospects for superconducivity. In this manuscript, we describe the general framework for guided design of new materials, and demonstrate its workflow by applying the principles to design a new layered copper oxysulfide Hg(CaS) 2 CuO 2 , which we abbreviate (HC-SCO). ...

The lack of a mechanistic framework for chemical reactions forming inorganic extended solids presents a challenge to accelerated materials discovery. We demonstrate here a combined computational and experimental methodology to tackle this problem, in which in situ X-ray diffraction measurements monitor solid-state reactions and deduce reaction pathways, while theoretical computations rationalize reaction energetics. The method has been applied to the LaCuO S (0 ≤ ≤ 4) quaternary system, following an earlier prediction that enhanced superconductivity could be found in these new lanthanum copper(II) oxysulfide compounds. In situ diffraction measurements show that reactants containing Cu(II) and S(2-) ions undergo redox reactions, leaving their ions in oxidation states that are incompatible with forming the desired new compounds. Computations of the reaction energies confirm that the observed synthetic pathways are indeed favored over those that would hypothetically form the suggested compounds. The consistency between computation and experiment in the LaCuO S system suggests a role for predictive theory: to identify and to explicate new synthetic routes for forming predicted compounds.