Merging two traditional methods: the Hartree–Fock and the Heitler–London and adding density functional correlation corrections

The variational combination of the Hartree– Fock (HF) with the Heitler–London (HL) methods, yielding the Hartree–Fock–Heitler–London (HF–HL) method is analyzed for diatomic hydrides and homonuclear molecules of the first and second row atoms. This recent quantum chemistry development is considered in the light of the continuous evolution of hypotheses and corresponding verifications occurring in quantum chemistry. The correlation energy correction needed in HF and HL computations is reduced in the HF–HL method to its dynamic component, since the non-dynamical correlation is accounted by explicitly considering near degeneracy and state crossing. The dynamical correlation is computed either (1) via expansion with multi-configuration of HF and HL functions or (2) including ionic HL structures, yielding a large fraction of the molecular extra correlation energy or (3) using the Coulomb hole density functional. With the latter the computed total and binding energies for all internuclear separations are in excellent agreement with laboratory data. Contribution to the Serafin Fraga Memorial Issue.     

Pairwise additivity of energy components in protein-ligand binding: the HIV II protease-Indinavir case

An energy expansion (binding energy decomposition into n-body interaction terms for n ≥ 2) to express the receptor-ligand binding energy for the fragmented HIV II protease-Indinavir system is described to address the role of cooperativity in ligand binding. The outcome of this energy expansion is compared to the total receptor-ligand binding energy at the Hartree-Fock, density functional theory, and semiempirical levels of theory. We find that the sum of the pairwise interaction energies approximates the total binding energy to ～82% for HF and to >95% for both the M06-L density functional and PM6-DH2 semiempirical method. The contribution of the three-body interactions amounts to 18.7%, 3.8%, and 1.4% for HF, M06-L, and PM6-DH2, respectively. We find that the expansion can be safely truncated after n=3. That is, the contribution of the interactions involving more than three parties to the total binding energy of Indinavir to the HIV II protease receptor is negligible. Overall, we find that the two-body terms represent a good approximation to the total binding energy of the system, which points to pairwise additivity in the present case. This basic principle of pairwise additivity is utilized in fragment-based drug design approaches and our results support its continued use. The present results can also aid in the validation of non-bonded terms contained within common force fields and in the correction of systematic errors in physics-based score functions.     

环己烯分子2b和3a轨道的电子动量谱学研究

The electron momentum profile for inner valence orbitals 2b and 3a of cyclohexene (C6H10) was firstly studied by the binary (e,2e) electron momentum spectroscopy (EMS), at the impact energy of 1200 eV plus binding energy using symmetric non-coplanar kinematics. The complete valence shell binding energy spectrum of C6H10 was also obtained. The experimental momentum profile of the summed orbitals was compared with Hartree Fock (HF) and density functional theory (DFT) methods with various basis sets. The experimental measurement was well described by the HF and DFT calculations except for the low-p region (p<0.25 a.u.). Experimental small “turn-up” effects of momentum profile in the low-p region could be due to the distorted wave effects.     

O2 dissociative adsorption on the Cu‐, Ag‐, and W‐doped Al(111) surfaces from DFT computation

The O₂ adsorption and dissociation on M‐doped (M = Cu, Ag, W) Al(111) surface were studied by density functional theory. The adsorption energy of adsorbate, the average binding energy and surface energy of Al surface, and the doping energy of doping atom were calculated. All the doped atoms can be stably combined with Al atoms, while being slightly embedded in the surface to a certain depth. The TOP‐type surfaces are the most stable doped surfaces for O₂ adsorption, which is related to the orbital hybridization between the adsorbate and the surface atoms, the electronegativity, and the orbital energy level of the doping atoms. Moreover, the O atoms and doping atoms contribute significantly to the density of states (DOS), especially the O‐p orbital electrons and the d orbital electrons of doping atoms. The degree of O₂ dissociation is related to the doping atoms on Al surfaces, and the doping atoms actually resist the dissociation of O₂. W atoms have the best resistance effect on the O₂ dissociation as compared with Cu and Ag atoms, especially W‐1NN surface, which has both large barrier energy and reaction energy.     

Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-12. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.     

Hydrogen fluoride adsorption and reaction on the α-Al2O3(0001) surface: a density functional theory study

The adsorption and reaction behaviors of HF on the α-Al(2)O(3)(0001) surface are systematically investigated using density functional theory method. By increasing the number of HF molecules in a p(2 × 1) α-Al(2)O(3)(0001) slab, we find that HF is chemically dissociated at low coverage; while both physical and dissociative adsorption occurs at a 3/2 monolayer (ML) coverage. At the same coverage (1.0 ML), diverse configurations of the dissociated HF are obtained in the p(2 × 1) model; while only one is observed in the p(1 × 1) slab due to its smaller surface area compared with the former one. Preliminary fluorination reaction study suggests that the total energy of two dissociated HF in the p(2 × 1) slab increases by 1.00 and 0.72 eV for the formation and desorption of water intermediate, respectively. The coadsorption behaviors of HF and H(2)O indicate that the pre-adsorbed water is unfavorable for the fluorination of Al(2)O(3), which is well consistent with the experimental results. The calculated density of states show that the peak of σ(H-F) disappears, while the peaks of σ(H-O) and σ(Al-F) are observed at -8.4 and -5 to -3 eV for the dissociated HF. Charge density difference analysis indicates that the dissociated F atom attracts electrons, while no obvious changes on electrons are observed for the surface Al atoms.     

Intra-cluster proton transfer in anilide-(HF)n (n = 1-4): Can the size of HF cluster influence the N?H-F → N-H?F switching

The impact of the HF cluster size on the proton-transfer switch between N⁻?H-F and N-H?F⁻ in the anilide-(HF)_n = 1-4 complexes was investigated by means of the quantum chemical methods. The change in the H-bond strength due to variation of the HF cluster size was well monitored by change in the binding energy (BE), structural parameter, electron density topology, natural charge and charge transfer. For n = 1, our results at the MP2/6-311++G(2d,2p) level show that the minimum-energy structure corresponds to the H-bonded complex PhNH⁻?HF with excess negative charge localized on the N atom of the anilide anion. For n > 1, minimum energy structures correspond to PhNH₂?F⁻(HF)_1-3 ones, namely a solvated F⁻ ion. This is a case in which the relative change in the acidity of the HF is observed in the ground state as the size of cluster increases. The nature of the weak interactions in the complexes was characterized by means of atoms in molecules (AIM) and the natural bond orbital (NBO) analyses.     

Total energies of molecules with the local density functional approximation and gaussian basis sets

Total energies of small molecules were calculated with a local density functional (LDF) approximation within the LCAO MO SCF scheme. The local spin density functional (LSD) of Gunnarsson and Lundqvist was used. The basis sets used are of contracted gaussian type which allow comparison of LSD with Hartree-Fock (HF) results. The program for calculation of the LSD term was incorporated into the standard ab initio package. The LSD binding energies were in better agreement with experiment than those from HF.     

Semiclassical description of large multipole-deformed metal clusters

We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.     

Single d-metal atoms on F(s) and F(s+) defects of MgO(001): a theoretical study across the periodic table

Single d-metal atoms on oxygen defects F(s) and F(s+) of the MgO(001) surface were studied theoretically. We employed an accurate density functional method combined with cluster models, embedded in an elastic polarizable environment, and we applied two gradient-corrected exchange-correlation functionals. In this way, we quantified how 17 metal atoms from groups 6-11 of the periodic table (Cu, Ag, Au; Ni, Pd, Pt; Co, Rh, Ir; Fe, Ru, Os; Mn, Re; and Cr, Mo, W) interact with terrace sites of MgO. We found bonding with F(s) and F(s+) defects to be in general stronger than that with O2- sites, except for Mn-, Re-, and Fe/F(s) complexes. In M/F(s) systems, electron density is accumulated on the metal center in a notable fashion. The binding energy on both kinds of O defects increases from 3d- to 4d- to 5d-atoms of a given group, at variance with the binding energy trend established earlier for the M/O2- complexes, 4d < 3d < 5d. Regarding the evolution of the binding energy along a period, group 7 atoms are slightly destabilized compared to their group 6 congeners in both the F(s) and F(s+) complexes; for later transition elements, the binding energy increases gradually up to group 10 and finally decreases again in group 11, most strongly on the F(s) site. This trend is governed by the negative charge on the adsorbed atoms. We discuss implications for an experimental detection of metal atoms on oxide supports based on computed core-level energies.     

钙元素对焦炭表面NO吸附行为的影响:密度泛函理论研究

采用密度泛函理论研究了Ca元素对焦炭表面NO吸附行为的影响。使用周期性石墨烯模型近似模拟实际焦炭表面的石墨化结构,并在石墨烯表面装饰Ca原子(按质量计Ca原子覆盖率为13.3%),考察了Ca元素对焦炭表面NO吸附的催化作用。计算结果表明,NO分子在纯净石墨烯表面的吸附属于物理吸附,结合能仅为-19.34 kJ/mol;石墨烯表面掺入Ca原子后,由于Ca原子4s轨道和3d轨道的电子转移到NO分子,结合能显著提高至-206.02 kJ/mol。     

What makes an N12 cage stable?

Much recent attention has been given to molecules containing only nitrogen atoms. Such molecules N(x) can undergo the reaction N(x) --> (x/2)N(2), which is very exothermic. These molecules are potential candidates for high energy density materials (HEDM). However, many all-nitrogen molecules dissociate too easily to be stable, practical energy sources. It is important to know which nitrogen molecules will be stable and which will not. In the current study, a variety of N(12) cages with all single bonds are examined by theoretical calculations to determine which ones are the most thermodynamically stable. Calculations are carried out using Hartree-Fock (HF) theory, gradient-corrected density functional theory (DFT), and Moller-Plesset perturbation theory (MP2 and MP4). Relative energies among the various isomers are calculated and trends are examined in order to determine which structural features lead to the most energetically favorable molecules.     

On the origin of the forward peak and backward oscillations in the F + H(2)(v = 0) --> HF(v' = 2) + H reaction

We present a semiclassical complex angular momentum (CAM) analysis of the forward scattering peak which occurs at a translational collision energy around 32 meV in the quantum mechanical calculations for the F + H(2)(v = 0, j = 0) --> HF(v' = 2, j' = 0) + H reaction on the Stark-Werner potential energy surface. The semiclassical CAM theory is modified to cover the forward and backward scattering angles. The peak is shown to result from constructive/destructive interference of the two Regge states associated with two resonances, one in the transition state region and the other in the exit channel van der Waals well. In addition, we demonstrate that the oscillations in the energy dependence of the backward differential cross section are caused by the interference between the direct backward scattering and the decay of the two resonance complexes returning to the backward direction after one full rotation.     

Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.     

Binding maps for the study and prediction of bimetallic catalyst surface reactions: The case of methanol oxidation

Focusing on the competing pathways of methanol oxidation on platinum and platinum/gold bimetallic catalysts, we explore a novel density functional theory (DFT)‐based approach to the study of reactions on catalyst surfaces. Traditionally, DFT has been used to compute binding energies of products and intermediates as proxies for catalytic activity, and to compute full reaction pathways and their activation energy barriers. Merging the computational simplicity and intuitive clarity of binding energy calculations with the site sensitivity of transition state calculations, we construct maps of the binding energies of relevant atoms and molecules at all sites on a surface. We show that knowledge of the arrangement of strong and weak binding sites on a surface is powerful in rationalizing the ease with which a reaction step proceeds on a given local motif of surface atoms. We highlight the prospects and challenges of this approach toward catalyst screening and prediction.     

Structures and electronic properties of germanium-doped Ni<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters, <Emphasis Type="Italic">n</Emphasis> = 13–23

The magnetic property and electronic properties such as binding energy, charge transfer, ionization potential and electron affinity of the Ni _n–1Ge (n = 13–23) neutral and ionic clusters have been studied using the density functional theory calculations with the PBE exchange-correlation energy functional. The calculated total magnetic moments decrease with the addition of Ge atom. Both the calculated ionization potential and electron affinity exhibit an oscillating behavior as the cluster size increases.     

A theoretical study on the electronic structures of TiO2: Effect of Hartree-Fock exchange

The effects of the Fock exchange on the geometries and electronic structures of TiO2 have been investigated by introducing a portion of Hartree-Fock (HF) exchange into the traditional density functional. Our results indicate that the functional with 13% HF exchange can correctly predict the band gap and the electronic structures of rutile TiO2, and such an approach is also suitable to describe the structural and electronic properties of anatase and brookite phases. For the TiO2 (110) surfaces, although the surface relaxations are insensitive to the variation of HF exchange, there are larger effects on the positions of the occupied surface-induced states. When 13% HF exchange is employed, the predicted band gap of the perfect surface and position of defect state of the reduced surface are consistent with the experimental values. Moreover, the electronic structures of TiO2 (110) surface are carefully reexamined by using this hybrid density functional method.     

Theoretical mechanism study of UF6 hydrolysis in the gas phase

The mechanism of the gas-phase reaction UF 6 + H 2O --> UOF 4 + 2HF is explored using relativistic density functional theory calculations. Initially, H 2O coordinates with UF 6 to form a 1:1 complex UF 6.H 2O. Over an activation energy barrier of about 19 kcal/mol, H 2O transfers a H atom to a nearby ligand F, resulting in UF 5OH + HF. The eliminated HF or another H 2O molecule may form a hydrogen bond with UF 5OH. Starting from UF 5OH, the second HF elimination results in UOF 4. If UF 5OH is in the isolated form, UF 5OH --> UOF 4 + HF takes place over a barrier of 24 kcal/mol. If UF 5OH is hydrogen-bonded with H 2O or HF, the conversion barrier is less than 10 kcal/mol. Once formed, the unstable UOF 4 tends to associate with additional ligands and hydrogen-bonding donors. The calculated binding energies indicate the significance of such interactions, which may have profound impact on further HF eliminating reactions. The IR spectra features can be used to indicate the formation and interaction type of the intermediates and products.     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

Hydrogen-bonded and van der Waals complexes studied by a Gaussian density functional method. The case of (HF)2, ArHCl and Ar2HCl systems

Summary Linear combination of Gaussian-type orbitals local spin density calculations (LCGTO-LSD) have been performed to further test the applicability to the method of hydrogen-bonded and van der Waals systems. The calculated minimum energy structures and binding energies for the (HF)₂, ArHCl and Ar₂HCl complexes are presented. In addition, the harmonic vibrational frequencies are reported for (HF)₂. The results show that by using nonlocal corrections and increasing the number of radial points in the grid, the calculated parameters are close to experimental ones and provide some encouraging evidence for the reliable use of density functional theory for these complex systems.