Improved embedded molecular cluster model

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one-electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Self-consistent embedding theory for locally correlated configuration interaction wave functions in condensed matter

We present new developments on a density-based embedding strategy for the electronic structure of localized feature in periodic, metallic systems [see T. Kluner et al., J. Chem. Phys. 116, 42 (2002), and references therein]. The total system is decomposed into an embedded cluster and a background, where the background density is regarded as fixed. Its effect on the embedded cluster is modeled as a one-electron potential derived from density functional theory. We first discuss details on the evaluation of the various contributions to the embedding potential and provide a strategy to incorporate the use of ultrasoft pseudopotentials in a consistent fashion. The embedding potential is obtained self-consistently with respect to both the total and embedded cluster densities in the embedding region, within the framework of a frozen background density. A strategy for accomplishing this self-consistency in a numerically stable manner is presented. Finally, we demonstrate how dynamical correlation effects can be treated within this embedding framework via the multireference singles and doubles configuration interaction method. Two applications of the embedding theory are presented. The first example considers a Cu dimer embedded in the (111) surface of Cu, where we explore the effects of different models for the kinetic energy potential. We find that the embedded Cu density is reasonably well-described using simple models for the kinetic energy. The second, more challenging example involves the adsorption of Co on the (111) surface of Cu, which has been probed experimentally with scanning tunneling microscopy [H. C. Manoharan et al., Nature (London) 403, 512 (2000)]. In contrast to Kohn-Sham density functional theory, our embedding approach predicts the correct spin-compensated ground state.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

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Coupled‐cluster frozen‐density embedding using resolution of the identity methods

Frozen‐density embedding (FDE) is combined with resolution of the identity (RI) Hartree–Fock and a RI‐variant of a second‐order approximate coupled‐cluster singles and doubles (RI‐CC2) to determine solvatochromic shifts for the lowest excitation energy of acetone and pyridazine, respectively, each solvated in different environments with total system sizes of about 2.5 nm diameter. The combination of FDE and RI‐CC2 increases efficiency and enables the calculation of numerous snapshots with 100 to 300 molecules, also allowing for larger basis sets as well as diffuse functions needed for an accurate treatment of properties. The maximum errors in the solvatochromic shifts amount up to 0.2 eV, which are similar to other approximated studies in the literature. © 2014 Wiley Periodicals, Inc.     

Solids modeled by ab initio crystal field methods, part 22: the Fock matrix transformed supermolecule model and the structure determination of D-erythronic acid-3,4-carbonate

To eliminate the cutoff effects in the supermolecule model (SM), the Fock matrix transformed supermolecule model (FTSM) is developed. In this model a cyclization of the cluster is performed by means of transformations of elements of the Fock matrix, thereby restoring the translational symmetry. Besides this fundamental enhancement, significant CPU time savings are realized because, in this new procedure, not all Fock matrix elements need to be calculated. The method is applied in a study of the structure of D-erythronic acid-3,4-carbonate in the crystal phase, where the new model is compared to the supermolecule model as well as the XRD experiment. The results are found to be in good agreement with experimental data.     

Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory

We present a simple and efficient embedding scheme for the wave-function based calculation of the energies of local excitations in large systems. By introducing an embedding potential obtained from density-functional theory (DFT) it is possible to describe the effect of an environment on local excitations of an embedded system in wave-function theory (WFT) calculations of the excitation energies. We outline the implementation of such a WFT-in-DFT embedding procedure employing the ADF, Dalton and DIRAC codes, where the embedded subsystem is treated with coupled cluster methods. We then evaluate this procedure in the calculation of the solvatochromic shift of acetone in water and of the f-f spectrum of NpO(2)(2+) embedded in a Cs(2)UO(2)Cl(4) crystal and find that our scheme does effectively incorporate the environment effect in both cases. A particularly interesting finding is that with our embedding scheme we can model the equatorial Cl(-) ligands in NpO(2)Cl(4)(2-) quite accurately, compared to a fully wavefunction-based calculation, and this opens up the possibility of modeling the interaction of different ligands to actinyl species with relatively high accuracy but at a much reduced computational cost.     

A new boundary treatment: HF surface potential model applied to solid-state cluster calculations

A new boundary treatment, a Hartree–Fock (HF ) surface potential model, is proposed to deal with the surface effect in the solid-state cluster calculations using the LCAO –MO –SCF ab initio method. The surface potential arises from one or more atoms, which have no basis function and are added to the calculated cluster system. These atoms are placed in such sites so that the HF potential field of the calculated system should possess a point-group symmetry. The surface potential could be found by the corresponding HF potential using a symmetry operator. The fact that a rather symmetric electronic structure of the asymmetric cluster YBa₂CuZn₂O₇ is obtained using the HF surface potential shows that the surface effect in the cluster calculations could be neutralized to a great extent. © 1995 John Wiley & Sons, Inc.     

Fock space multireference coupled cluster calculations based on an underlying bivariational self-consistent field on Auger and shape resonances

The Fock space multireference coupled cluster based on an underlying bivariational self-consistent field is applied to the problem of computing complex energy associated with Auger and shape resonances in e-atom scattering. It is concluded that the Fock space multireference coupled cluster based on a bivariational self-consistent field provides a useful and practical approach to calculation of resonance parameters. Numerical results are presented for the 2P shape resonance of Mg and Auger 1 s(-1) hole of Be.     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Cluster models of ionic crystals: Band gaps

We performed electronic ab initio calculations of ion clusters simulating a piece of ionic crystal. Our main interest here is to estimate the (direct) energy band gap from the cluster energy levels. The model consists of a central cation surrounded by four shells of ions, with additional point charges embedding the cluster. We present results for the series of alkali halides with rock-salt structure. © 1996 John Wiley & Sons, Inc.     

Ab initio calculations for absorption and emission energies of alkali halide crystals doped with thallium

We calculate transition energies associated with optical properties of thallium doping in alkali halide crystals via an atomic cluster of minimal size where an sp‐valence‐shell impurity enters as a substitutional defect in the model crystal. Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI) [CIS (CI with single excitation) and QCISD (single plus double and quadruple excitation)] calculations are performed to theoretically obtain the absorption and emission energies as vertical transitions evaluated at the ground and first excited‐state optimized geometries, respectively, where the optimization is carried out separately with the HF and DFT methods. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 785–790, 2000     

Quantum mechanical embedding theory based on a unique embedding potential

We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4σ and 5σ orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.     

Applications of the group-function theory to the field of materials science

The group-function theory, as proposed by McWeeny for the study of weak intermolecular interactions and developed by Huzinaga in the context of valence-electron methods, is shown to be applicable to the ab initio study of tunable solid-state laser materials made of defective ionic crystals. The applicability of the theory relies on the existence of local electronic states (to which the demonstrated/potential laser activity is ascribed), which are essentially localized in a small cluster of atoms including the defect and whose electron correlation interactions with the surrounding crystal components are negligible. According to the group-function formalism, it is possible (a) to neglect electron correlation effects beyond the defect cluster and (b) to define a quantum mechanical embedding potential which embodies the rest of the so-called host effects. Computationally, the theory becomes applicable as the embedding potential is approximated through ab initio model potentials (AIMP). The results of AIMP embedded-cluster calculations demonstrate that it is possible to calculate the local structure and spectroscopy of the active defect at an ab initio level, the attainable accuracy being comparable to the usual one in molecular ab initio studies in the gas phase. Also, in this article, we present a systematic study of the local distortions produced upon doping divalent first-series transition-metal ions in rock-salt oxides, MO:Me²⁺ (M=Mg, Ca, Sr; Me=Sc-Zn) and Tl⁺ in KMgF₃ and KF hosts. This study leads to the calculation of the local structures of the defects in these materials, which have not been measured. The results suggest that the use of the mismatch of the empirical ionic radii of the impurity and the substituted ion in order to predict local distortions in doped ionic crystals is not significant when it is smaller than 0.1 Å, and when it is larger, it should be weighted by a reduction factor depending on the host. For the first-series divalent transition-metal ion impurities, this factor is shown to be 0.15 for SrO, 0.25 for CaO, and around 0.50 for MgO. © 1996 John Wiley & Sons, Inc.     

Embedded,graph-theoretically defined many-body approximations for wavefunction-in-DFT and DFT-in-DFT: Applications to gas- and condensed-phase ab initio molecular dynamics,and potential surfaces for quantum nuclear effects

We present a graph-theoretic approach to adaptively compute many-body approximations in an efficient manner to perform (a) accurate post-Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium- to large-sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed-phase simulations at the cost of pure density functionals, (c) reduced-cost on-the-fly basis extrapolation for gas-phase AIMD and condensed phase studies, and (d) accurate post-HF-level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM-like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many-body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph-theoretic methods. Specifically, a region of chemical interest is coarse-grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many-body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one-dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two-dimensional periodic boundary conditions.     

Hartree–Fock instabilities and electronic properties

Hartree–Fock instabilities are investigated for about 80 compounds, from acetylene to mivazerol (27 atoms) and a cluster of 18 water molecules, within a double ζ basis set. For most conjugated systems, the restricted Hartree–Fock wave function of the singlet fundamental state presents an external or so‐called triplet instability. This behavior is studied in relation with the electronic correlation, the vicinity of the triplet and singlet excited states, the electronic delocalization linked with resonance, the nature of eventual heteroatoms, and the size of the systems. The case of antiaromatic systems is different, because they may present a very large internal Hartree–Fock instability. Furthermore, the violation of Hund's rule, observed for these compounds, is put in relation with the fact that the high symmetry structure in its singlet state has no feature of a diradical‐like species. It appears that the triplet Hartree–Fock instability is directly related with the spin properties of nonnull orbital angular momentum electronic systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 483–504, 2000     

EHF theory of chemical reactions V. Nature of manganese–oxygen bonds by hybrid density functional theory (DFT) and coupled‐cluster (CC) methods

Hybrid density functional theory (DFT) and post‐Hartree–Fock methods are compared by depicting potential energy curves of the O–O dissociation of hydroperoxide and the M–O dissociation of transition‐metal oxides. The former approach includes BLYP, B2LYP, B3LYP, and more general hybrid DFT methods, while the unrestricted Hartree–Fock (UHF) coulpled‐cluster (UCC) SD(T) method is considered as the latter approach. The hybrid DFT methods can reproduce the potential curve of the O–O dissociation process and the dissociation energy of HOOH by UCCSD(T). The methods are also useful for depicting potential curves of copper oxide (CuO) and manganese oxide (MnO), and reproduce the experimental M–O binding energies. The nature of Mn–O bonds in the naked Mn–O, Mn–O porphyrine system and model complexes, XH₃Mn(IV)O₂Mn(IV)H₃Y (X,Y=O,H), are examined in relation to the possible mechanisms of oxygenation reactions. It is found that the radical character of Mn–O bonds increases with the increase of the oxidation number of the Mn ion in these systems. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001