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Density functional theory is the workhorse of materials simulations. Unfortunately, the quality of results often varies depending on the specific choice of the exchange-correlation functional, and this significantly limits the predictive power of this approach. Coupled cluster theory, including single, double and perturbative triple particle-hole excitation operators, is widely considered as the `gold standard` of quantum chemistry as it can achieve chemical accuracy for non-strongly correlated applications. Because of the high computational cost, the application of coupled cluster theory in materials simulations is rare, and this is particularly true if finite-temperature properties are of interest for which molecular dynamics simulations have to be performed. By combining recent progress in machine learning models with low data requirements for energy surfaces and in the implementation of coupled cluster theory for periodic materials, we show that chemically accurate simulations of materials are practical and could soon become significantly widespread. As an example of this numerical approach, we consider the calculation of the enthalpy of adsorption of CO2 in a porous material.

Identifying the atomic structure and properties of solid hydrogen under high pressures is a long-standing problem of high-pressure physics with far-reaching significance in planetary and materials science. Determining the pressure-temperature phase diagram of hydrogen is challenging for experiment and theory due to the extreme conditions and the required accuracy in the quantum mechanical treatment of the constituent electrons and nuclei, respectively. Here, we demonstrate explicitly that coupled cluster theory can serve as a computationally efficient theoretical tool to predict solid hydrogen phases with high accuracy. We present a first principles study of solid hydrogen phases at pressures ranging from 100 to 450 GPa. The computed static lattice enthalpies are compared to state-of-the-art diffusion Monte Carlo results and density functional theory calculations. Our coupled cluster theory results for the most stable phases including C2/c-24 and P21/c-24 are in good agreement with those obtained using diffusion Monte Carlo, with the exception of Cmca-4, which is predicted to be significantly less stable. We discuss the scope of the employed methods and how they can contribute as efficient and complementary theoretical tools to solve the long-standing puzzle of understanding solid hydrogen phases at high pressures., Comment: 6 pages, 3 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, 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 Moller–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.

The electronic defect states resulting from doping $^{229}\mathrm{Th}$ in ${\mathrm{CaF}}_{2}$ offer a unique opportunity to excite the nuclear isomeric state $^{229\mathrm{m}}\mathrm{Th}$ at approximately 8 eV via electronic bridge mechanisms. We consider bridge schemes involving stimulated emission and absorption using an optical laser. The role of different multipole contributions, both for the emitted or absorbed photon and nuclear transition, to the total bridge rates are investigated theoretically. We show that the electric dipole component is dominant for the electronic bridge photon. In contradistinction, the electric quadrupole channel of the $^{229}\mathrm{Th}$ isomeric transition plays the dominant role for the bridge processes presented. The driven bridge rates are discussed in the context of background signals in the crystal environment and of implementation methods. We show that inverse electronic bridge processes quenching the isomeric state population can improve the performance of a solid-state nuclear clock based on $^{229\mathrm{m}}\mathrm{Th}$.

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., 12 pages, 7 figures

The authors show the shortcomings of density functional theory to produce a coherent description of theground state properties of ZrO${}_{2}$ polymorphs and show an alternative scheme using high-level many-electron methods.

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms that would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions, while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of second-order screened exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as [Formula: see text] or [Formula: see text] in orbital space or real space, respectively. Its memory requirement scales as [Formula: see text].

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.

We present an embedding approach to treat local electron correlation effects in periodic environments. In a single, consistent framework, our plane-wave based scheme embeds a local high-level correlation calculation (here Coupled Cluster Theory, CC), employing localized orbitals, into a low-level correlation calculation (here the direct Random Phase Approximation, RPA). This choice allows for an accurate and effcient treatment of long-range dispersion effects. Accelerated convergence with respect to the local fragment size can be observed if the low-level and high-level long-range dispersion are quantitatively similar, as is the case for CC in RPA. To demonstrate the capabilities of the introduced embedding approach, we calculate adsorption energies of molecules on a surface and in a chabazite crystal cage, as well as the formation energy of a lattice impurity in a solid at the level of highly accurate many-electron perturbation theories. The absorption energy of a methane molecule in a zeolite chabazite, for instance, is converged with an error well below 20 meV at the CC level. As our largest periodic benchmark system, we apply our scheme to the adsorption of a water molecule on titania in a supercell containing more than 1000 electrons., 6 pages, 2 figures

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 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., Comment: 9 pages, 3 figures, 6 tables

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 two orders of magnitude without compromising accuracy., 6 pages, 2 figures, 1 table

Molecular adsorption on surfaces plays a central role in catalysis, corrosion, desalination, and many other processes of relevance to industry and the natural world. Few adsorption systems are more ubiquitous or of more widespread importance than those involving water and carbon, and for a molecular level understanding of such interfaces water monomer adsorption on graphene is a fundamental and representative system. This system is particularly interesting as it calls for an accurate treatment of electron correlation effects, as well as posing a practical challenge to experiments. Here, we employ many-body electronic structure methodologies that can be rigorously converged and thus provide faithful references for the molecule-surface interaction. In particular, we use diffusion Monte-Carlo (DMC), coupled cluster (CCSD(T)), as well as the random phase approximation (RPA) to calculate the strength of the interaction between water and an extended graphene surface. We establish excellent, sub-chemical, agreement between the complementary high-level methodologies, and an adsorption energy estimate in the most stable configuration of approximately -100\,meV is obtained. We also find that the adsorption energy is rather insensitive to the orientation of the water molecule on the surface, despite different binding motifs involving qualitatively different interfacial charge reorganisation. In producing the first demonstrably accurate adsorption energies for water on graphene this work also resolves discrepancies amongst previously reported values for this widely studied system. It also paves the way for more accurate and reliable studies of liquid water at carbon interfaces with cheaper computational methods, such as density functional theory and classical potentials.

We report on a many-electron wavefunction theory study for the reaction energetics of hydrogen dissociation on the Si(100) surface. We demonstrate that quantum chemical wavefunction based methods using periodic boundary conditions can predict chemically accurate results for the activation barrier and the chemisorption energy in agreement with experimental findings. These highly accurate results for the reaction energetics enable a deeper understanding of the underlying physical mechanism and make it possible to benchmark widely used density functional theory methods.

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 many-electron 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., 4 figures

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.

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 (RPA), and second order M{\o}ller-Plesset (MP2) theory. These explicitly correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is $-107\pm7$ 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.

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., 8 pages, 4 figures, 1 table

In this work, we present a model of the surface states of nonsymmorphic semimetals. These are derived from surface mass terms that lift the high degeneracy imposed in the band structure by the nonsymmorphic bulk symmetries. Reflecting the reduced symmetry at the surface, the bulk bands are strongly modified. This leads to the creation of two-dimensional floating bands, which are distinct from Shockley states, quantum well states or topologically protected surface states. We focus on the layered semimetal ZrSiS to clarify the origin of its surface states. We demonstrate an excellent agreement between DFT calculations and ARPES measurements and present an effective four-band model in which similar surface bands appear. Finally, we emphasize the role of the surface chemical potential by comparing the surface density of states in samples with and without potassium coating. Our findings can be extended to related compounds and generalized to other crystals with nonsymmorphic symmetries., Comment: 8 pages, 5 figures

We study the decomposition of the Coulomb integrals of periodic systems into a tensor 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^4) 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 present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Moller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cut-off radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artefacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid and water adsorption on a LiH surface, at the level of second-order M\{o}ller--Plesset perturbation theory.

The properties of all materials arise largely from the quantum mechanics of their constituent electrons under the influence of the electric field of the nuclei. The solution of the underlying many-electron Schrodinger equation is a ‘non-polynomial hard’ problem, owing to the complex interplay of kinetic energy, electron–electron repulsion and the Pauli exclusion principle. The dominant computational method for describing such systems has been density functional theory. Quantum-chemical methods—based on an explicit ansatz for the many-electron wavefunctions and, hence, potentially more accurate—have not been fully explored in the solid state owing to their computational complexity, which ranges from strongly exponential to high-order polynomial in system size. Here we report the application of an exact technique, full configuration interaction quantum Monte Carlo to a variety of real solids, providing reference many-electron energies that are used to rigorously benchmark the standard hierarchy of quantum-chemical techniques, up to the ‘gold standard’ coupled-cluster ansatz, including single, double and perturbative triple particle–hole excitation operators. We show the errors in cohesive energies predicted by this method to be small, indicating the potential of this computationally polynomial scaling technique to tackle current solid-state problems. Recent developments that reduce the computational cost and scaling of wavefunction-based quantum-chemical techniques open the way to the successful application of such techniques to a variety of real-world solids. Computational descriptions of solid-state materials are currently dominated by methods based on density functional theory. An attractive and potentially more accurate approach would be to adopt the wavefunction-based methods of quantum chemistry, although these have not received as much attention because of the computational complexities involved. Now George Booth and colleagues show how recent developments that serve to reduce the computational cost and scaling of such quantum-chemical techniques open the way to their successful application to a variety of real-world solids.

We demonstrate that natural orbitals allow for reducing the computational cost of wave function based correlated calculations, especially for atoms and molecules in a large box, when a plane wave basis set under periodic boundary conditions is used. The employed natural orbitals are evaluated on the level of second-order Moller-Plesset perturbation theory (MP2), which requires a computational effort that scales as [Formula: see text](N(5)), where N is a measure of the system size. Moreover, we find that a simple approximation reducing the scaling to [Formula: see text](N(4)) yields orbitals that allow for a similar reduction of the number of virtual orbitals. The MP2 natural orbitals are applied to coupled-cluster singles and doubles (CCSD) as well as full configuration interaction Quantum Monte Carlo calculations of the H2 molecule to test our implementation. Finally, the atomization energies of the LiH molecule and solid are calculated on the level of MP2 and CCSD.

We employ Hartree–Fock, second-order Moller-Plesset perturbation, coupled cluster singles and doubles (CCSD) as well as CCSD plus perturbative triples (CCSD(T)) theory to study the pressure induced transition from the rocksalt to the cesium chloride crystal structure in LiH. We show that the calculated transition pressure converges rapidly in this series of increasingly accurate many-electron wave function based theories. Using CCSD(T) theory, we predict a transition pressure for the structural phase transition in the LiH crystal of 340 GPa. Furthermore, we investigate the potential energy surface for this transition in the parameter space of the Buerger path.

We introduce a novel and efficient explicitly correlated implementation of second-order perturbation theory for solids. The required three-electron integrals are computed directly using a plane wave basis set. We parametrize the employed correlation factors using results previously obtained for a finite uniform electron gas simulation cell. We demonstrate for a range of solids that basis set converged correlation energies, equilibrium volumes, and bulk moduli can be obtained efficiently in this theory using a few ten orbitals per atom. To stretch the capabilities of this novel method we compute the Schottky defect formation energy in MgO, studying systems with 54 atoms in the supercell. We verify the accuracy of the calculated formation energies using the more accurate coupled cluster singles and doubles theory. Furthermore, we discuss other potential applications for the derived and implemented expressions such as an occupied orbital only correlation energy functional.

The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansatze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. This perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids.

The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the $GW$ approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the $GW{\ensuremath{\Gamma}}^{1}$ approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by $GW{\ensuremath{\Gamma}}^{1}$ for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the $GW$ approximation is almost on par with $GW{\ensuremath{\Gamma}}^{1}$ as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both $\ensuremath{\sim}0.1\text{eV}$, indicating a good overall transitivity of the band offsets. The alignment based on IPs from selected nonpolar surfaces performs comparably well in the prediction of band offsets at most of the considered interfaces. The maximum errors are, however, as large as 0.3, 0.4, and 0.7 eV for the alignments based on the average band offsets, branch point energies, and IPs, respectively. This margin of error should be taken into account when performing materials screening using these alignments.

The ionization potential is a fundamental key quantity with great relevance to diverse material properties. We find that state of the art methods based on density functional theory and simple diagrammatic approaches as commonly taken in the GW approximation predict the ionization potentials of semiconductors and insulators unsatisfactorily. Good agreement between theory and experiment is obtained only when diagrams resulting from the antisymmetry of the many-electron wave function are taken into account via vertex corrections in the self-energy. The present approach describes both localized and delocalized states accurately, making it ideally suited for a wide class of materials and processes.

We investigate the accuracy of a number of wavefunction based methods at the heart of quantum chemistry for metallic systems. Using Hartree-Fock as a reference, perturbative (M{\o}ller-Plesset, MP) and coupled cluster (CC) theories are used to study the uniform electron gas model. Our findings suggest that non-perturbative coupled cluster theories are acceptable for modelling electronic interactions in metals whilst perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely-used coupled-cluster singles and doubles plus perturbative triples method (CCSD(T)) that lifts the divergent behaviour and is shown to give very accurate correlation energies for the homogeneous electron gas., Comment: Comments welcome. arXiv admin note: text overlap with arXiv:1208.6103

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Moller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at $r_s$ = 0.5 a.u., in a Hilbert space of $10^{108}$ Slater determinants. At this value of $r_s$, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems., 4-page letter

Results for the lattice constants, atomization energies, and band gaps of typical semiconductors and insulators are presented for Hartree-Fock and second-order Moller-Plesset perturbation theory (MP2). We find that MP2 tends to undercorrelate weakly polarizable systems and overcorrelates strongly polarizable systems. As a result, lattice constants are overestimated for large gap systems and underestimated for small gap systems. The volume dependence of the MP2 correlation energy and the dependence of the MP2 band gaps on the static dielectric screening properties are discussed in detail. Moreover, the relationship between MP2 and the G(0)W(0) quasiparticle energies is elucidated and discussed. Finally, we demonstrate explicitly that the correlation energy diverges with decreasing k-point spacing for metals.

We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method is self-correlation free for one-electron systems. From a practical point of view, the approach yields correlation energies for atoms, as well as for the jellium electron gas within a few kcal/mol of exact values, atomization energies within typically 2-3 kcal/mol of experiment, and excellent lattice constants for ionic and covalently bonded solids (0.2% error). The computational complexity is only O(N(5)), comparable to canonical second-order Møller-Plesset perturbation theory, which should allow for routine calculations on many systems.

There has been considerable recent interest in density functionals incorporating random phase approximation (RPA) ground-state correlation. By virtue of its full nonlocality, RPA correlation is compatible with exact Hartree-Fock-type exchange and describes van der Waals interactions exceptionally well [B. G. Janesko et al., J. Chem. Phys. 130, 081105 (2009); J. Chem. Phys. 131, 034110 (2009)]. One caveat is that RPA correlation contains one-electron self-interaction error, which leads to disturbingly large correlation energies in the stretched bond situation of, e.g., H(2)(+), He(2)(+), or Ne(2)(+). In the present work, we show that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation. We present a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second-order screened exchange correlation. This correction has a generally small, and sometimes undesirable, effect on RPA predictions for chemical properties, but appears to be very beneficial for the dissociation of H(2)(+), He(2)(+), and Ne(2)(+).

Kohn-Sham density functional theory is the workhorse computational method in materials and surface science. Unfortunately, most semilocal density functionals predict surfaces to be more stable than they are experimentally. Naively, we would expect that consequently adsorption energies on surfaces are too small as well, but the contrary is often found: chemisorption energies are usually overestimated. Modifying the functional improves either the adsorption energy or the surface energy but always worsens the other aspect. This suggests that semilocal density functionals possess a fundamental flaw that is difficult to cure, and alternative methods are urgently needed. Here we show that a computationally fairly efficient many-electron approach, the random phase approximation to the correlation energy, resolves this dilemma and yields at the same time excellent lattice constants, surface energies and adsorption energies for carbon monoxide and benzene on transition-metal surfaces.

We present an ab initio investigation of the band gap of the ${\text{Pb}}_{1\ensuremath{-}x}{\text{Eu}}_{x}\text{Se}$ $(0\ensuremath{\le}x\ensuremath{\le}1)$ alloy using the special quasirandom structure approach proposed by Wei et al. [Phys. Rev. B 42, 9622 (1990)]. Due to the complexity of this particular system, i.e., (i) the narrow-band gap of the parent compound PbSe, (ii) spin-orbit coupling induced by relativistic effects in the Pb atoms, and (iii) the strongly localized $f$ electrons of Eu, an accurate description of its properties represents a serious challenge to density-functional theory. We discuss results obtained from Perdew, Burke, and Ernzerhof density functional and Heyd, Scuseria, and Ernzerhof Hartree-Fock hybrid functional calculations, both with and without an additional Hubbard $U$ treatment of the Eu $f$ electrons. At low Eu concentrations $(xl0.13)$ the HSE functional gives a good description of the band gap of ${\text{Pb}}_{1\ensuremath{-}x}{\text{Eu}}_{x}\text{Se}$. At high Eu concentrations an additional Hubbard $U$ treatment of the Eu $f$ electrons is mandatory.

4 pages, 4 figures.-- Printed version published Dec 12, 2007., We study a simple highly resistive molecular circuit by detecting the transfer of individual electrons. The circuit consists of a Au nanoparticle, a carbon nanotube transistor, and a gate electrode, and the tube−particle resistance is about 1019 Ω. The high-impedance measurements are carried out by counting the electrons that are transferred onto the particle using the nanotube transistor as the charge detector. These measurements allow for the electron characterization of the circuit. In addition, single-electron detection is used to determine the separation between the electron states in the particle or to monitor the decay in time of the electron number in the particle., This research has been supported by an EURYI grant and EU-funded project CARDEQ (FP6-IST-021285-2).