Averting the Infrared Catastrophe in the Gold Standard of Quantum Chemistry.

Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely used coupled cluster singles and doubles plus perturbative triples [CCSD(T)] method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism denoted as (cT) that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three-dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.

Focal-point approach with pair-specific cusp correction for coupled-cluster theory.

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, which dominate the basis set incompleteness error (BSIE). As recently discussed in the work of Irmler et al. [Phys. Rev. Lett. 123, 156401 (2019)], the BSIE of the CCSD correlation energy is dominated by the second-order Møller-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.

A periodic equation-of-motion coupled-cluster implementation applied to F-centers in alkaline earth oxides.

We present an implementation of the 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 the calculated electronic excitation energies for neutral color centers in MgO, CaO, and SrO crystals with respect to the 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 the literature.

Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: The case of water on graphitic carbon nitride.

A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride is reported employing an embedding approach for many-electron correlation methods. To this end, a plane-wave based implementation to obtain intrinsic atomic orbitals and Wannier functions for arbitrary localization potentials is presented. In our embedding scheme, the localized occupied orbitals allow for a separate treatment of short-range and long-range correlation contributions to the adsorption energy by a fragmentation of the simulation cell. In combination with unoccupied natural orbitals, the coupled cluster ansatz with single, double, and perturbative triple particle-hole excitation operators is used to capture the correlation in local fragments centered around the adsorption process. For the long-range correlation, a seamless embedding into the random phase approximation yields rapidly convergent adsorption energies with respect to the local 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.

Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories.

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by 2 orders of magnitude without compromising accuracy.

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory.

We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed coupled cluster singles and doubles (CCSD) correlation energy. Only the second-order energy and the particle-particle ladder term are corrected for their basis-set incompleteness error. We present absolute correlation energies and results for a large benchmark set. Our findings indicate that basis set reductions by two cardinal numbers are possible for atomization energies, ionization potentials, and electron affinities without compromising accuracy when compared to conventional CCSD calculations. In the case of reaction energies, we find that reductions by one cardinal number are possible compared to conventional CCSD calculations. The employed technique can readily be applied to other many-electron theories without the need for three- or four-electron integrals.

Multipole-based distance-dependent screening of Coulomb integrals.

We derive a new estimate for two-electron repulsion integrals (ERIs), when evaluated within a local atomic basis set. It is based on the multipole expansion and provides a rigorous upper bound of an ERI for well-separated charge distributions. The scheme is generally applicable in any formalism that uses ERIs. We employ it here to screen for potentially negligible contributions in the calculation of the Fock exchange matrix. Using Gaussian basis functions, we show that the estimate allows us to accelerate the construction of the exchange matrix by up to a factor of two without introducing further approximations.

Redox-Active Tetraruthenium Macrocycles Built from 1,4-Divinylphenylene-Bridged Diruthenium Complexes.

Metallamacrocylic tetraruthenium complexes were generated by treatment of 1,4-divinylphenylene-bridged diruthenium complexes with functionalized 1,3-benzene dicarboxylic acids and characterized by HR ESI-MS and multinuclear NMR spectroscopy. Every divinylphenylene diruthenium subunit is oxidized in two consecutive one-electron steps with half-wave potential splittings in the range of 250 to 330 mV. Additional, smaller redox-splittings between the +/2+ and 0/+ and the 3+/4+ and 2+/3+ redox processes, corresponding to the first and the second oxidations of every divinylphenylene diruthenium entity, are due to electrostatic effects. The lack of electronic coupling through bond or through space is explained by the nodal properties of the relevant molecular orbitals and the lateral side-by-side arrangement of the divinylphenylene linkers. The polyelectrochromic behavior of the divinylphenylene diruthenium precursors is retained and even amplified in these metallamacrocyclic structures. EPR studies down to T=4 K indicate that the dications 1-H(2+) and 1-OBu(2+) are paramagnetic. The dications and the tetracation of macrocycle 3-H display intense (dications) or weak (3-H(4+) ) EPR signals. Quantum chemical calculations indicate that the four most stable conformers of the macrocycles are largely devoid of strain. Bond parameters, energies as well as charge and spin density distributions of model macrocycle 5-H(Me) were calculated for the different charge and spin states.

Highly Ordered Surface Self-Assembly of Fe4 Single Molecule Magnets.

Single molecule magnets (SMMs) have attracted considerable attention due to low-temperature magnetic hysteresis and fascinating quantum effects. The investigation of these properties requires the possibility to deposit well-defined monolayers or spatially isolated molecules within a well-controlled adsorption geometry. Here we present a successful fabrication of self-organized arrays of Fe4 SMMs on hexagonal boron nitride (h-BN) on Rh(111) as template. Using a rational design of the ligand shell optimized for surface assembly and electrospray as a gentle deposition method, we demonstrate how to obtain ordered arrays of molecules forming perfect hexagonal superlattices of tunable size, from small islands to an almost perfect monolayer. High-resolution low temperature scanning tunneling microscopy (STM) reveals that the Fe4 molecule adsorbs on the substrate in a flat geometry, meaning that its magnetic easy axis is perpendicular to the surface. By scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations, we infer that the majority- and minority-spin components of the spin-split lowest unoccupied molecular orbital (LUMO) can be addressed separately on a submolecular level.

Robust Periodic Fock Exchange with Atom-Centered Gaussian Basis Sets.

In this work, we present a robust implementation of the periodic Fock exchange for atom-centered Gaussian-type orbitals (GTOs). We discuss the divergence, appearing in the formulation of the periodic Fock exchange in the case of a finite number of k-points, and compare two schemes that remove it. These are the minimum image convention (MIC) and the truncated Coulomb interaction (TCI) that we use here in combination with k-meshes. We observe artifacts in four-center integrals of GTOs, when evaluated in the TCI scheme. They carry over to the exchange and density matrices of Hartree-Fock calculations for TCI but are absent in MIC. At semiconducting and insulating systems, we show that both MIC and TCI yield the same energies for a sufficiently large supercell or k-mesh, but the self-consistent field algorithm is more stable for MIC. We therefore conclude that the MIC is superior to TCI and validate our implementation by comparing not only to other GTO-based calculations but also by demonstrating excellent agreement with results of plane-wave codes for sufficiently large Gaussian basis sets.

Electric transport properties of surface-anchored metal-organic frameworks and the effect of ferrocene loading.

Understanding of the electric transport through surface-anchored metal-organic frameworks (SURMOFs) is important both from a fundamental perspective as well as with regards to possible future applications in electronic devices. To address this mostly unexplored subject, we integrated a series of representative SURMOF thin films, formed by copper nodes and trimesic acid and known as HKUST-1, in a mercury-drop-based tunneling junction. Although the transport properties of these SURMOFs are analogous to those of hybrid metal-organic molecular wires, manifested by a very low value of the tunneling decay constant (ß ≈ 0.006 Å(-1)), they are at the same time found to be consistent with a linear increase of resistance with film thickness. Upon loading of SURMOF pores with ferrocene (Fc), a noticeable increase in transport current was observed. A transport model and ab initio electronic structure calculations were used to reveal a hopping transport mechanism and to relate the changes upon Fc loading to those of the electronic and vibrational structures of the SURMOF films.