Coupled Electron Pair Approximation Research Articles

From complete to selected model spaces in determinant-based multi-reference second-order perturbation treatments.

The present paper reformulates and improves a previously proposed determinant-based second-order multi-reference perturbative formalism. Through a rather simple modification of the energy denominators, this formalism takes into account the interactions between the model space determinants, which are repeated in outer space. The method has been shown to be size-consistent when the model space is a complete active space, which is a severe limit. It is shown here that the completeness of the model space is not necessary to keep this property, provided that the zero-order function satisfies some conditions. For instance, size consistency may be obtained from truncated complete active spaces. It may even be satisfied from Singles and Doubles Configuration Interactions, provided that a coupled electron pair approximation is used in the definition of the model space wave function. The physical content of the method is illustrated by a series of model problems, showing its robustness. A major benefit of the fact that the perturbers are single determinants is the possibility to revise with full flexibility the model-space component of the wave function, i.e., to treat the feedback effect of the dynamic correlation on the valence component of the wave function.

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions.

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

Wavefunction-based quantum-chemical ab initio calculations for core electron binding energies of small open shell molecules

Core electron binding energies (CEBEs), i.e. ionization energies of 1s core orbitals, are calculated by means of wavefunction-based quantum-chemical ab initio methods for a series of small open-shell molecules containing first-row atoms. The calculations are performed in three steps: (a) Koopmans’ theorem, where the orbitals of the electronic ground state are used unchanged also for the ions, (b) Hartree–Fock or self consistent field (SCF) approximation in which the orbitals are allowed to relax after 1s ionization (ΔSCF), (c) dynamic correlation effects on top of SCF. For open-shell molecules 1s ionization leads to ions in several spin states, mostly to a pair of a triplet and a singlet state. In several cases one or both of these ionic states are only poorly described by a single-reference SCF wavefunction, therefore a multi-reference complete active space self consistent field (CAS-SCF) wavefunction is used instead. The correlation effects are evaluated by means of our multi-reference coupled electron pair approximation program. The accuracy of the calculated CEBEs is in the order of 0.1–0.4 eV. This is in agreement with experimental results for NO and O2. But there exist only very few gas phase data for CEBEs of open-shell molecules.

Size-extensive seniority-zero energy functionals derived from configuration interaction with double excitations.

The doubly occupied configuration interaction (DOCI) approach can provide an accurate black-box description of nondynamic electron correlation at a computational cost that increases combinatorially with the system size. Remarkably, a pair coupled-cluster doubles (pCCD) approach (also known as the antisymmetrized product of one-reference orbital geminals) can reproduce DOCI energies with only a quadratic number of wave function parameters, and, when neglecting the cost associated with any two-electron integral transformations, these parameters can be determined at a cubic computational cost. Other simpler seniority-zero approaches derived from size-extensive modified configuration interaction doubles functionals can also provide approximations to DOCI energies at similar computational costs. We develop seniority-zero formulations of the coupled-electron pair approximation, the averaged coupled-pair functional, averaged quadratic coupled-cluster, and the parametric two-electron reduced density matrix (p2RDM) approach. These methods are Hermitian and thus offer several potential advantages over pCCD theory, including a reduction in the number of variable parameters and simplified definitions of reduced density matrices. Of the methods investigated, only the pair p2RDM (pp2RDM) approach yields energies that are comparable in quality to pCCD and DOCI. For the molecular systems investigated, pp2RDM-derived RDMs are found to be better approximations to DOCI ones than those obtained from pCCD.

Time-dependent optimized coupled-cluster method for multielectron dynamics. II. A coupled electron-pair approximation.

We report the implementation of a cost-effective approximation method within the framework of the time-dependent optimized coupled-cluster (TD-OCC) method [T. Sato et al., J. Chem. Phys. 148, 051101 (2018)] for real-time simulations of intense laser-driven multielectron dynamics. The method, designated as TD-OCEPA0, is a time-dependent extension of the simplest version of the coupled-electron pair approximation with optimized orbitals [U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 139, 054104 (2013)]. It is size extensive, gauge invariant, and computationally much more efficient than the TD-OCC method with double excitations. We employed this method to simulate the electron dynamics in Ne and Ar atoms exposed to intense near infrared laser pulses with various intensities. The computed results, including high-harmonic generation spectra and ionization yields, are compared with those of various other methods ranging from uncorrelated time-dependent Hartree-Fock to fully correlated (within the active orbital space) time-dependent complete-active-space self-consistent field (TD-CASSCF). The TD-OCEPA0 results show good agreement with TD-CASSCF ones for moderate laser intensities. For higher intensities, however, TD-OCEPA0 tends to overestimate the correlation effect, as occasionally observed for CEPA0 in the ground-state correlation energy calculations.

A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework.

The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.

Calculation of the inner-shell contribution to the correlation energy through DLPNO-CEPA/1 and scaled same-spin second-order Møller-Plesset perturbation theory.

The use of two low-cost methods for the prediction of the inner-shells contribution to the correlation energy is analyzed. The Spin-Component-Scaled second-order Møller-Plesset perturbation theory (SCS-MP2) was reparameterized for the prediction of such contributions. The best results are found when only the same spin term is considered (SSS-MP2). The Coupled Electron Pair Approximation (CEPA) using the Domain-based Local Pair Natural Orbital approximation (DLPNO) was also studied for the same purpose. The methods were tested for atomization energies on the W4-11 test set using basis sets up to quadruple zeta quality. The SSS-MP2 proved to be a marked improvement upon MP2 decreasing the root-mean-square-error (RMSE) from 0.443 to 0.302 kcal mol-1 . The RMSE of DLPNO-CEPA/1 in the test set is only 0.147 kcal mol-1 and its computational cost is very low considering the intended applications. Furthermore, a linear combination of both methods decreased the RMSE to 0.118 kcal mol-1 .

Linear and quadratic internally contracted multireference coupled-cluster approximations.

Linear and quadratic approximations to the internally contracted multireference coupled-cluster (icMRCC) method are implemented and analyzed by using the linked and unlinked coupled-cluster formalisms. This includes methods based on perturbation theory as well as the coupled-electron pair approximation, CEPA(0). The similarities and differences between all the approximations serve to highlight and provoke discussion about methodological peculiarities of the icMRCC ansatz. When calculating potential energy curves (PECs), discontinuities are observed for the linear icMRCC energies. Using a diagrammatic representation, the terms that cause but also reduce these discontinuities are identified. For benchmarking test cases such as calculating PECs, singlet-triplet splittings, and barrier heights, the multireference CEPA(0) approximation performs well; however, it suffers from a lack of size consistency and so cannot represent a step forward to the goal of developing a computationally cheap and accurate icMRCC method.

Hybrid Correlation Energy (HyCE): An Approach Based on Separate Evaluations of Internal and External Components.

A novel hybrid correlation energy (HyCE) approach is proposed that determines the total correlation energy via distinct computation of its internal and external components. This approach evolved from two related studies. First, rigorous assessment of the accuracies and size extensivities of a number of electron correlation methods, that include perturbation theory (PT2), coupled-cluster (CC), configuration interaction (CI), and coupled electron pair approximation (CEPA), shows that the CEPA(0) variant of the latter and triples-corrected CC methods consistently perform very similarly. These findings were obtained by comparison to near full CI results for four small molecules and by charting recovered correlation energies for six steadily growing chain systems. Second, by generating valence virtual orbitals (VVOs) and utilizing the CEPA(0) method, we were able to partition total correlation energies into internal (or nondynamic) and external (or dynamic) parts for the aforementioned six chain systems and a benchmark test bed of 36 molecules. When using triple-ζ basis sets it was found that per orbital internal correlation energies were appreciably larger than per orbital external energies and that the former showed far more chemical variation than the latter. Additionally, accumulations of external correlation energies were seen to proceed smoothly, and somewhat linearly, as the virtual space is gradually increased. Combination of these two studies led to development of the HyCE approach, whereby the internal and external correlation energies are determined separately by CEPA(0)/VVO and PT2/external calculations, respectively. When applied to the six chain systems and the 36-molecule benchmark test set it was found that HyCE energies followed closely those of triples-corrected CC and CEPA(0) while easily outperforming MP2 and CCSD. The success of the HyCE approach is more notable when considering that its cost is only slightly more than MP2 and significantly cheaper than the CC approaches.

Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions

Model space quantum Monte Carlo (MSQMC) is an extension of full configuration interaction QMC that allows us to calculate quasi-degenerate and excited electronic states by sampling the effective Hamiltonian in the model space. We introduce a novel algorithm based on the state-selective partitioning for the effective Hamiltonian using left eigenvectors to calculate several electronic states simultaneously at much less computational cost than the original MSQMC with the energy-dependent partitioning. The sampling of walkers in MSQMC is analyzed in the single reference limit using a stochastic algorithm for higher-order perturbation energies by the analogy of the deterministic case utilizing a full configuration interaction program. We further develop size-consistency corrections of the initiator adaptation (i-MSQMC) in three different ways, i.e., the coupled electron pair approximation, a posteriori, and second-order perturbative corrections. It is clearly demonstrated that most of the initiator error is originating from the deficiency of proper scaling of correlation energy due to its truncated CI nature of the initiator approximation and that the greater part of the error can be recovered by the size-consistency corrections developed in this work.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation.

We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-reference and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is nonorthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

Isomerization and fragmentation pathways of 1,2-azaborine.

The generation of 1,2-azaborine (4), the BN-analogue of ortho-benzyne, was recently achieved by elimination of tert-butyldimethylchlorosilane under the conditions of flash vacuum pyrolysis. The present investigation identifies by computational means pathways for the thermal isomerization and fragmentation of 1,2-azaborine. The computations were performed using single reference (hybrid/density functional, second order Møller-Plesset perturbation, and coupled cluster theories) as well as multiconfiguration methods (complete active space SCF based second order perturbation theory, multireference configuration interaction, and multiconfiguration coupled electron pair approximation) with basis sets up to polarized triple-ζ quality. The 1,2-azaborine is, despite the distortion of its molecular structure, the most stable C4H4BN isomer investigated. The formation of BN-endiyne isomers is highly unfavorable as the identified pathways involve barriers close to 80 kcal mol(-1). The concerted fragmentation to ethyne and 2-aza-3-bora-butadiyne even has a barrier close to 120 kcal mol(-1). The fragmentation of BN-enediynes has energetic requirements similar to enediynes.

Accurate, precise, and efficient theoretical methods to calculate anion-π interaction energies in model structures.

A correct description of the anion-π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion-π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π-anion-π' sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion-π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion-π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6-17 times faster) for the binary complexes studied in this paper. For 30 ternary π-anion-π' sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95-D3(BJ) and B2PLYP-D3(BJ) functionals perform better than the GGA and meta-GGA functionals for the present test set.

Absolute configuration of 1,5-diazepin-2-ones: A critical test case for density functional theory

The absolute configuration of a series of 4(R)-methyl-1,3,4,5-tetrahydro-2H-1,5-benzodiazepin-2-ones is assigned by comparison of experimental and calculated CD spectra using time-dependent density functional theory (TDDFT) in combination with four different functionals (B3PW91, CAM-B3LYP, M06-2X, BMK). Closest agreement with experiment is obtained with B3PW91. All compounds except those bearing an acyl group at N5 exist in two nearly isoenergetic conformations of the seven-membered ring (G⩽0.5kcalmol−1 with the local pair natural orbital coupled-electron pair approximation LPNO-CEPA/1/def2-TZVPP//B3LYP/6-311G(d,p)). Agreement between simulated and experimental CD spectra was found to critically depend on a proper description of conformer population as well as the position of the calculated longest-wavelength transitions of the individual conformers.

Effect of molecular-orbital rotations on ground-state energies in the parametric two-electron reduced density matrix method

Different sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric two-electron reduced density matrix (2-RDM) methods [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the ground-state energies from the parametric 2-RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical Hartree-Fock calculations.

Understanding the Nature of the CH···HC Interactions in Alkanes.

To understand the dispersion stabilization of hydrocarbons in solids and of encumbered molecules, wherein CH···HC interactions act as sticky fingers, we developed here a valence bond (VB) model and applied it to analyze the H···H interactions in dimers of H2 and alkanes. The VB analysis revealed two distinct mechanisms of "dispersion." In the dimers of small molecules like H-H···H-H and H3CH···HCH3, the stabilization arises primarily due to the increased importance of the VB structures which possess charge alternation, e.g., C(+)H(-)···H(+)C(-) and C(-)H(+)···H(-)C(+), and hence bring about electrostatic stabilization that holds the dimer. This is consistent with the classical mechanism of oscillating dipoles as the source of dispersion interactions. However, in larger alkanes, this mechanism is insufficient to glue the two molecules together. Here, the "dispersion" interaction comes about through perturbational mixing of VB structures, which reorganize the bonding electrons of the two interacting CH bonds via recoupling of these electrons to H···H, C···C, and C···H "bonds." Finally, an attempt is made to create a bridge from VB to molecular orbital (MO) and local pair natural-orbital coupled electron pair approximation (LPNO-CEPA/1) analyses of the interactions, which bring about CH···HC binding.

Connection of an elementary class of parametric two-electron reduced-density-matrix methods to the coupled electron-pair approximations

Parametric two-electron reduced-density-matrix (p-2RDM) methods have recently been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) at a lower computational cost. In this paper we derive an elementary class of parametric 2-RDM methods with connections to the coupled electron pair approximations (CEPA). Three parametric 2-RDM methods p-2RDM/n are presented that correspond to the CEPA/n family where n = 1, 2, 3. We isolate the function distinguishing the stationary condition of the parametric 2-RDM methods from the nonlinear equations of CEPA. Calculations of energies, geometries, and harmonic frequencies show that p-2RDM/n and CEPA/n are very similar for a variety of closed-shell systems. Finally, each of the p-2RDM/n methods is extended to satisfy particle–hole symmetry by the removal of exclusion principle violating terms in the virtual space. These extensions denoted p-2RDM′/n are shown to be essential for the proper dissociation of CH radical. Both p-2RDM/n and p-2RDM′/n form an elementary class of parametric 2-RDM methods with accuracy like CCSD; more general parametric 2-RDM methods [D.A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] have an accuracy approaching CCSD with full triple excitations.

Some non-relativistic many electron theories: single reference case

Abstract There has been substantial progress in the development of electron correlation methods with some benefits and drawbacks. In this paper, we give a review of electron correlation effects on many body particles system. We focus more on atoms and molecules rather than solid state and take into account single reference case only. We mainly discuss perturbation theory, coupled electron many electron theory and a few versions of coupled electron pair approximations with comparison configuration interaction and some coupled cluster methods in which coupled cluster method is crucially important for the crystalline solids, the electron gas and the heat of the reaction. We also show some results, reported by several authors, to fairly compare and judge the methods’ feasibility mentioned above.

Ab initio calculation of correlation effects for the O 1s core electron binding energy in MgO

Wavefunction based ab initio embedded cluster calculations are employed to calculate the O 1s core electron binding energies (CEBEs) of bulk MgO and the MgO(001) surface. A quantum cluster consisting of 61 atoms in five layers and embedded in a large point charge field is used for bulk MgO, the cluster for the MgO(001) surface is chosen accordingly. The O 1s CEBEs are calculated at the Koopmans’ theorem (KT) and ΔSCF levels and with inclusion of correlation effects by means of the MC-CEPA method (multi-configuration coupled electron pair approximation), which is an approximate multi-reference coupled cluster approach. The correlation contributions to the O 1s CEBE of the central O atom due to the Mg atoms in the first and the O atoms in the second coordination shell turned out to be additive to a large extent. Therefore, they could be evaluated in an incremental fashion by a series of smaller calculations, where only a few atoms are included in the correlation treatment rather than all atoms of the first coordination shells or of the full quantum cluster. This makes the calculations feasible, even if large basis sets are used. The final results for the O 1s CEBEs are 533.47 and 533.50 eV for bulk MgO and the MgO(001) surface, to which electron correlation contributes 0.77 and 0.70 eV, respectively.