Embedded density functional approach for calculations of adsorption on ionic crystals

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Employing Pseudopotentials to Tackle Excited-State Electron Spill-Out in Frozen Density Embedding Calculations

In frozen density embedding (FDE), the properties of a target molecule are computed in the presence of an effective embedding potential, which accounts for the attractive and repulsive contributions of the environment. The formally exact embedding potential, however, is in practice calculated using explicit kinetic-energy functionals for which the resulting potentials are in many cases not repulsive enough to account fully for Pauli repulsion by the electrons of the environment and to compensate thereby the strong electron-nuclear attraction. For the excited states on the target molecule, this leads to charge spill-out when diffuse basis functions are included, which allow that valence electrons are excited to those regions of the environment where the strong nuclear attraction is not sufficiently compensated by repulsive contributions. To reduce this insufficiency, we propose in the present work the inclusion of atomic all-electron pseudopotentials for all environment atoms on top of the conventional embedding potential. In the current work, the pseudopotentials are applied for computing vertical excitation energies of local excited states in complex systems employing the second-order algebraic diagrammatic construction (ADC(2)) scheme. The proposed approach leads to significantly reduced charge spill-out and an improved agreement of FDE and supermolecular calculations in the frozen solvent approximation. In particular, when diffuse functions are employed, the mean absolute deviation (MAD) is reduced from 0.27 to 0.05 eV for the investigated cases.

Adsorption and dehydration of ethanol on isomorphously B, Al, and Ga substituted H-ZSM-5 zeolite: an embedded ONIOM study

Dehydration reactions are important in the petroleum and petrochemical industries, especially for the feedstock production. In this work, the catalytic activity of zeolites with different acidities for the dehydration of ethanol to ethylene and diethylether is investigated by density functional calculations on cluster models of three isomorphous B, Al, and Ga substituted H-ZSM-5 zeolites. Both unimolecular and bimolecular mechanisms are investigated. Detailed reaction profiles for the dehydration reaction, assuming either a stepwise or a concerted mechanism, were calculated by using the ONIOM(MP2:M06-2X) + SCREEP method. The adsorption energies of ethanol are -21.6, -28.1, and -27.7 kcal mol^-1 on H-[B]-ZSM-5, H-[Al]-ZSM-5, and H-[Ga]-ZSM-5 zeolites, respectively. The activation energies for the rate-determining step of the unimolecular concerted mechanism for the ethylene formation are 48.5, 42.6, and 43.6 kcal mol^-1 on H-[B]-ZSM-5, H-[Al]-ZSM-5, and H-[Ga]-ZSM-5 zeolites, respectively. The activation energies for the ethoxy formation as the rate-determining step for the bimolecular formation of diethylether are 42.3, 40.0, and 41.1 kcal mol^-1 on H-[B]-ZSM-5, H-[Al]-ZSM-5, and H-[Ga]-ZSM-5 zeolites, respectively. The results indicate that the catalytic activities for the dehydration of ethanol decrease in the order H-[Al]-ZSM-5 ~ H-[Ga]-ZSM-5 > H-[B]-ZSM-5. Besides the acid strength, the zeolite framework affects the reaction by stabilizing the reaction intermediates, leading to more stable adsorption complexes and lower activation barriers.

Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory

A comparison of strategies to account for environment polarisation in Frozen Density Embedding Theory (FDET).

Accurate basis set truncation for wavefunction embedding

Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)] to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.

Perspectives for hybrid ab initio/molecular mechanical simulations of solutions: from complex chemistry to proton-transfer reactions and interfaces

As a consequence of the ongoing development of enhanced computational resources, theoretical chemistry has become an increasingly valuable field for the investigation of a variety of chemical systems. Simulations employing a hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) technique have been shown to be a particularly promising approach, whenever ultrafast (i.e., picosecond) dynamical properties are to be studied, which are in many cases difficult to access via experimental techniques. Details of the quantum mechanical charge field (QMCF) ansatz, an advanced QM/MM protocol, are discussed and simulation results for various systems ranging from simple ionic hydrates to solvated organic molecules and coordination complexes in solution are presented. A particularly challenging application is the description of proton-transfer reactions in chemical simulations, which is a prerequisite to study acidified and basic systems. The methodical requirements for a combination of the QMCF methodology with a dissociative potential model for the description of the solvent are discussed. Furthermore, the possible extension of QM/MM approaches to solid/liquid interfaces is outlined.

On the accuracy of frozen density embedding calculations with hybrid and orbital-dependent functionals for non-bonded interaction energies

We analyze the accuracy of the frozen density embedding (FDE) method, with hybrid and orbital-dependent exchange-correlation functionals, for the calculation of the total interaction energies of weakly interacting systems. Our investigation is motivated by the fact that these approaches require, in addition to the non-additive kinetic energy approximation, also approximate non-additive exact-exchange energies. Despite this further approximation, we find that the hybrid/orbital-dependent FDE approaches can reproduce the total energies with the same accuracy (about 1 mHa) as the one of conventional semi-local functionals. In many cases, thanks to error cancellation effects, hybrid/orbital-dependent approaches yield even the smallest error. A detailed energy-decomposition investigation is presented. Finally, the Becke-exchange functional is found to reproduce accurately the non-additive exact-exchange energies also for non-equilibrium geometries. These performances are rationalized in terms of a reduced-gradient decomposition of the non-additive exchange energy.

SLIDE AND ROLLING MECHANISMS OF Pt CLUSTERS OUT OF OXYGEN VACANCY REGION ON MgO(100) SURFACE

We present the theoretical DFT/B3LYP investigations on the cluster nucleation process and moving mechanism for the Pt n (n = 1, 2, 3, 4, 8, and 12) clusters deposited on MgO surface with an embedded cluster model. The structures and energies of the Pt n clusters adsorbed on the perfect and oxygen vacancy MgO surfaces have been calculated. Based on the nucleation of the Pt n clusters on the oxygen vacancy sites of MgO surfaces, the two moving mechanisms of slide and rolling out of the vacancy region have been energetically investigated. The results show that the needed energies per atom moving out of the vacancy region decrease as the cluster sizes increase. Consequently, the big clusters move likely out of the vacancy sites by either slide or rolling model under a certain temperature condition.

A critical assessment of theoretical methods for finding reaction pathways and transition states of surface processes

The performance of a variety of techniques for locating transition states on potential energy surfaces is evaluated within the density functional theory framework. Diffusion of a water molecule across NaCl(001) and HCl bond breaking on the same surface are treated as general test cases; the former is an example of a low barrier diffusion process and the latter an example of a relatively high barrier covalent bond rupture event. The methods considered include the nudged elastic band (NEB), Dewar, Healy and Stewart (DHS), dimer, constrained optimization (CO), activation-relaxation technique (ART) and one-side growing string (OGS) as well as novel combinations of the DHS with growing string (DHS + GS) and DHS plus climbing image (CI-DHS). A key conclusion to come from this study is that the NEB method is relatively fast, especially when just a single (climbing) image is used. Indeed, using more images represents an unnecessary computational burden for our set of processes. The dimer method exhibits variable performance; being poor for the water diffusion processes, which have small activation energies, but much more efficient for the HCl bond breaking process which has a higher barrier. When only a poor initial guess of the transition state geometry is available, the CI-DHS scheme is one of the most efficient techniques considered. And as a means to quickly establish an approximate minimum energy pathway the DHS + GS scheme offers some potential.

Effects of the zeolite framework on the adsorptions and hydrogen-exchange reactions of unsaturated aliphatic, aromatic, and heterocyclic compounds in ZSM-5 zeolite: a combination of perturbation theory (MP2) and a newly developed density functional theory (M06-2X) in ONIOM scheme

The confinement effect on the adsorption and reaction mechanism of unsaturated aliphatic, aromatic and heterocyclic compounds on H-ZSM-5 zeolite has been investigated by the four ONIOM methods (MP2:M06-2X), (MP2:B3LYP), (MP2:HF), and (MP2:UFF). The H-ZSM-5 'nanoreactor' porous intersection, where chemical reactions take place, is represented by a quantum cluster of 34 tetrahedral units. Ethene, benzene, ethylbenzene, and pyridine are chosen to represent reactions of various adsorbates of aliphatic, aromatic and heterocyclic compounds. Among the four combined methods, (MP2:M06-2X) outperforms the others. The results confirm that the method that takes weak interactions, especially the van der Waals interaction, into account is essential for describing the confinement effect from the zeolite framework. The effects of the infinite zeolitic framework on the cluster model are also included by a set of point charges generated by the embedded ONIOM model. The energies for the adsorption of ethene, benzene, ethylbenzene, and pyridine on H-ZSM-5 from an embedded ONIOM(MP2:M06-2X) calculation are predicted to be -14.0, -19.8, -24.7, and -48.4 kcal/mol, respectively, which are very close to available experimental observations. The adsorption energy of pyridine agrees well with the experiment data of -47.6 kcal/mol. We also applied the same computational methodology on the systematic investigation of the H/H exchange reaction of benzene and ethylbenzene with the acidic H-ZSM-5 zeolite. The H/H exchange reaction was found to take place in a single concerted step. The calculated apparent activation energies for benzene and ethylbenzene are 12.6 and 4.9 kcal/mol, which can be compared to the experimental estimates of 11.0 and 6.9 kcal/mol, respectively. The confinement effect of the extended zeolite framework has been clearly demonstrated not only to stabilize the adsorption complexes but also to improve their corresponding activation energies to approach the experimental benchmark.

Advances in correlated electronic structure methods for solids, surfaces, and nanostructures

Calculations of the electronic structure of solids began decades ago, but only recently have solid-state quantum techniques become sufficiently reliable that their application is nearly as routine as quantum chemistry is for molecules. We aim to introduce chemists to the pros and cons of first-principles methods that can provide atomic-scale insight into the properties and chemistry of bulk materials, interfaces, and nanostructures. The techniques we review include the ubiquitous density functional theory (DFT), which is often sufficient, especially for metals; extensions such as DFT + U and hybrid DFT, which incorporate exact exchange to rid DFT of its spurious self-interactions (critical for some semiconductors and strongly correlated materials); many-body Green's function (GW and Bethe-Salpeter) methods for excited states; quantum Monte Carlo, in principle an exact theory but for which forces (hence structure optimization and dynamics) are problematic; and embedding theories that locally refine the quantum treatment to improve accuracy.

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.

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

We have investigated the functional derivative of the nonadditive kinetic-energy bifunctional, which appears in the embedding potential that is used in the frozen-density embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kinetic-energy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a H2O...Li+ complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too low-lying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.

Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.

Mechanisms of and Effect of Coadsorption on Water Dissociation on an Oxygen Vacancy of the MgO(100) Surface

The dissociation mechanism of a water molecule at an oxygen vacancy on the MgO(100) surface was studied by using the embedded cluster method at the DFT/B3 LYP level, while the energetic information was refined by using the IMOMO method at the CCSD level. We found that a water molecule initially adsorbs on one of the magnesium ions surrounding the vacancy site with a binding energy of 15.98 kcal mol(-1). It then can dissociate on the MgO(100) surface along two possible dissociation pathways. One pathway produces a hydroxyl group bonded to the original magnesium with a proton filling the vacancy via a transition state with a barrier of 4.67 kcal mol(-1) relative to the adsorbed water configuration. The other pathway yields two hydroxy groups; the hydroxy group originally belonging to the water molecule fills the vacancy, while the hydrogen atom binds with the surface oxygen to form the other hydroxy group. Hydrogen atoms of these hydroxy groups can recombine to form a hydrogen molecule and the surface is healed. Although the barrier (14.09 kcal mol(-1)) of the rate-controlling step of the latter pathway is higher than that of the former one, the energies of all of its stationary points are lower than that of the separated reactants (H(2)O+cluster). The effects of water coadsorption are modeled by placing an additional water molecule near the active center, which suggests that the more coadsorbed water molecules further stabilize the hydroxy species and prevent the hydrogen molecule formation through the latter pathway. The results support the photoemission spectral evidence of water dissociation on the defective MgO(100) surface at low water coverage.

On the electron leak problem in orbital-free embedding calculations

Computer simulation methods using orbital level of description only for a selected part of the larger systems are prone to the artificial charge leak to the parts which are described without orbitals. The absence of orbitals in one of the subsystems makes it impossible to impose explicitly the orthogonality condition. Using the subsystem formulation of density functional theory, it is shown that the absence of explicit condition of orthogonality between orbitals belonging to different subsystems, does not cause any breakdown of this type of description for the chosen intermolecular complexes (F(-)H(2)O and Li(+)H(2)O), for which a significant charge-leak problem could be a priori expected.

Size-dependent structures of NanIn−1+ cluster ions with a methanol adsorbate: A combined study by photodissociation spectroscopy and density-functional theory calculation

Methanol adsorption sites on NanI+n-1 ions were investigated. Photoexcitation to charge-transfer states of NanI+n-1 (methanol) predominantly produces two fragment ions: Nan-1I+n-2 (methanol) (neutral NaI loss) and Nan-1I+n-2(neutral NaI and methanol loss), without forming NanI+n-1 (methanol loss). The relative intensities of these fragments are correlated with the geometries and binding energies.

An environmental pseudopotential approach to molecular interactions: Implementation in MOLPRO

We present the implementation into the MOLPRO package of a model for the interaction of a central system with its surrounding environment. The properties of a target system enclosed by a noncovalently bound environment or solvent are modeled as those of a system embedded into the effective pseudopotential arising from the exact electrostatic Coulomb potential and the approximated exchange-repulsion potential. For the latter we use the charge-density overlap model, which relates the exchange-repulsion interaction energy between two species with the overlap of their ground-state electron charge densities. The solutions of the modified Hartree-Fock equations for the target system are obtained self-consistently. This way the exchange-induction effects arising from the converged electron-charge density of the embedded system are implicitly included. Inclusion of the correlation effects is provided by the use of post-Hartree-Fock and density-functional techniques available in the MOLPRO package. The computational and conceptual advantages provided by this approach are shown in the calculation of the dipole polarizabilities of halide and chalcogenide anions in different environments.

On the dissolution processes of Na2I+ and Na3I2+ with the association of water molecules: mechanistic and energetic details

The sequential association energies for one through six water molecules clustering to Na(2)I(+), as well as one and two water molecules clustering to Na(3)I(2)(+), are measured. The association energies show a pairwise behavior, indicating a symmetric association of water molecules to the linear Na(2)I(+) and Na(3)I(2)(+) ions. This pairwise behavior is well reproduced by Density Functional Theory (DFT) calculations. DFT calculations also suggest that a significant separation of charge for the Na-I ion pair occurs when four or more water molecules cluster to a single sodium center. Two different solvent-separated ion pairs have been identified with the DFT calculations. Experiments also show that the dissolution processes, loss of a neutral NaI unit, occurs when six or more water molecules have been added to Na(2)I(+) cluster. However, one or two water molecules are able to detach an NaI unit from the Na(3)I(2)(+) cluster. The difference in solubility of the Na(2)I(+) and Na(3)I(2)(+) ions is due to the difference in the energies required to lose an NaI unit from these two species. The experiment also confirms that the loss of a neutral NaI unit, instead of an Na(+) ion, occurs during the dissolution processes of Na(3)I(2)(+). The microsolvation schemes proposed to explain our experimental observations are supported by DFT and phase space theory (PST) calculations.