Away from generalized gradient approximation: orbital-dependent exchange-correlation functionals

The local-density approximation of density functional theory (DFT) is remarkably accurate, for instance, for geometries and frequencies, and the generalized gradient approximations have also made bond energies quite reliable. Sometimes, however, one meets with failure in individual cases. One of the possible routes towards better functionals would be the incorporation of orbital dependence (which is an implicit density dependency) in the functionals. We discuss this approach both for energies and for response properties. One possibility is the use of the Hartree-Fock-type exchange energy expression as orbital-dependent functional. We will argue that in spite of the increasing popularity of this approach, it does not offer any advantage over Hartree-Fock for energies. We will advocate not to apply the separation of exchange and correlation, which is so ingrained in quantum chemistry, but to model both simultaneously. For response properties the energies and shapes of the virtual orbitals are crucial. We will discuss the benefits that Kohn-Sham potentials can offer which are derived from either an orbital-dependent energy functional, including the exact-exchange functional, or which can be obtained directly as orbital-dependent functional. We highlight the similarity of the Hartree-Fock and Kohn-Sham occupied orbitals and orbital energies, and the essentially different meanings the virtual orbitals and orbital energies have in these two models. We will show that these differences are beneficial for DFT in the case of localized excitations (in a small molecule or in a fragment), but are detrimental for charge-transfer excitations. Again, orbital dependency, in this case in the exchange-correlation kernel, offers a solution.     

密度泛函理论研究镥二聚体低电子能态的相对稳定性、结构以及成键性质

用密度泛函理论方法研究了镥二聚体（Lu2）低能量电子态的性质,计算了电子态相对能量、平衡键长、振动频率以及基态解离能,考察了密度泛函性质、相对论有效势种类以及Hartree—Fock交换作用大小对计算结果的影响．结果表明,无论采用何种密度泛函和相对论有效势,体系的基态都为三重态,与其他一些基于分子轨道理论的从头计算方法得到的结论是一致的．另外,与分子轨道从头计算结果以及实验结果比较发现,采用杂化密度泛函理论和Stuttgart小核有效势计算得到的结果总体吻合最好．最后,特别分析研究了B3LYP计算中Hartree—Fock交换作用大小对基态键长和基态解离能的影响,发现随着交换作用的增大,键长增长,解离能减小,这是由于5d轨道杂化导致的共价成键作用减弱造成的．     

Energetics of the manganese oxide cluster cations Mn(N)O+ (N = 2-5): role of oxygen in the binding of manganese atoms

The photodissociation of manganese oxide cluster cations Mn(N)O+ (N = 2-5), into Mn(N-1)O+ (one-atom loss) and Mn(N-2)O+ (two-atom), was investigated in the photon-energy range of 1.08-2.76 eV. The bond-dissociation energies D0(Mn(N-1)O+...Mn) for N = 3, 4, and 5 were determined to be 1.84+/-0.03, 0.99+/-0.05, and 1.25+/-0.14 eV, respectively, from the threshold energies for the one- and two-atom losses. As Mn2O+ did not dissociate even at the highest photon energy used, the bond dissociation energy of Mn2O+, D0(Mn+...MnO), was obtained from a density-functional-theory calculation to be 3.04 eV. The present findings imply that the core ion Mn2O+ is bound weakly with the rest of the manganese atoms in Mn(N)O+.     

Si-O bonded interactions in silicate crystals and molecules: a comparison

Bond critical point, local kinetic energy density, G(rc), and local potential energy density, V(rc), properties of the electron density distributions, rho(r), calculated for silicates such as quartz and gas-phase molecules such as disiloxane are similar, indicating that the forces that govern the Si-O bonded interactions in silica are short-ranged and molecular-like. Using the G(rc)/rho(rc) ratio as a measure of bond character, the ratio increases as the Si-O bond length, the local electronic energy density, H(rc)= G(rc) + V(rc), and the coordination number of the Si atom decrease and as the accumulation of the electron density at the bond critical point, rho(rc), and the Laplacian, inverted Delta2 rho(rc), increase. The G(rc)/rho(rc) and H(rc)/rho(rc) ratios categorize the bonded interaction as observed for other second row atom M-O bonds into discrete categories with the covalent character of each of the M-O bonds increasing with the H(rc)/rho(rc) ratio. The character of the bond is examined in terms of the large net atomic charges conferred on the Si atoms comprising disiloxane, stishovite, quartz, and forsterite and the domains of localized electron density along the Si-O bond vectors and on the reflex side of the Si-O-Si angle together with the close similarity of the Si-O bonded interactions observed for a variety of hydroxyacid silicate molecules and a large number of silicate crystals. The bond critical point and local energy density properties of the electron density distribution indicate that the bond is an intermediate interaction between Al-O and P-O bonded interactions rather than being a closed-shell or a shared interaction.     

Abstraction of iodine from aromatic iodides by alkyl radicals: steric and electronic effects

Abstraction of the iodine atom from aryl iodides by alkyl radicals takes place in some cases very efficiently despite the unfavorable difference in bond dissociation energies of C-I bonds in alkyl and aryl iodides. The abstraction is most efficient in iodobenzenes, ortho-substituted with bulky groups. The ease of abstraction can be explained by the release of steric strain during the elimination of the iodine atom. The rate of abstraction correlates fairly well with the strain energy, calculated by density functional theory (DFT) and Hartree-Fock (HF) methods as a difference in the total energy of ortho and para isomers. However, besides the steric bulk, the presence of some other functional groups in an ortho substituent also influences the rate. The stabilization of the transition state, resembling a 9-I-2 iodanyl radical, by electron-withdrawing groups seems to explain a positive sign of the Hammett rho value in the radical abstraction of halogen atoms.     

The chemical Hamiltonian approach in density functional theory

The chemical Hamiltonian approach (CHA) for handling the basis set superposition error problem in intermolecular interactions has been implemented within density functional theory (DFT) using Gaussian atomic basis sets. As test examples, the potential curves of the water dimer were calculated using the Vosko-Wilk-Nusair, Becke-Perdew and Perdew exchange-correlation functionals. Comparisons with the counterpoise correction method show that CHA within DFT performs as well as previously for Hartree-Fock.     

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional ApproximationsSCI北大核心CSCD

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.     

The importance of electronic exchange-correlation in non-self-consistent frozen density approximation

The effects of different treatments for the exchange-correlation energy on the accuracy of non-self-consistent frozen density approximation (FDA) are discussed. Local spin density approximation (LSDA) and non-local spin density approximation (NLSDA) are employed, respectively. Corresponding results obtained by using full-self-consistent density functional theory (DFT) are also given for the purpose of comparison. Explicit calculations for hydrogen bonds, covalent bonds and ionic bonds indicate that, comparing with LSDA, NLSDA can improve the accuracy of FDA as well as that of DFT. This improvement attributed to the refinements in the treatment for the electronic exchange-correlation energy may help to extend the application of FDA.     

Separation of sigma and pi energies

This work presents an all-electron density functional theory implementation of the separation of sigma and pi energies. On the basis of the separation of the electronic density, rho, into sigma and pi parts, an ansatz for the separation of the exchange-correlation energy is proposed. The behavior of the sigma and pi energy parts in benzene is investigated under different distortions. The effect of local and nonlocal functionals on the separation of the exchange-correlation energy is studied, too.     

Experimental electron density analysis of Mn2(CO)10: metal-metal and metal-ligand bond characterization

The experimental electron density rho(r) of Mn2(CO)10 was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules (QTAM) was applied to rho(r) and its Laplacian [symbol: see text] 2 rho(r). The QTAM analysis of rho(r) showed the presence of a bond critical point (rc); its associated bond path connects the two Mn atoms, but no cross interaction line was found between one manganese and the equatorial carbonyls of the other. The distribution of [symbol: see text] 2 rho(r) indicated "closed-shell" interactions for the metallic Mn-Mn bond and the dative Mn-CO bonds. The values of the topological parameters of the density at rc, rho(rc), [symbol: see text] 2 rho(rc), G(rc) (kinetic energy density), and V(rc) (potential energy density), characterize the bonds and are intermediate to those corresponding to typical ionic and covalent bonds.     

Experimental and theoretical charge density distribution of the colossal magnetoresistive transition metal sulfide FeCr2S4

The total charge density distribution rho(r) of the colossal magnetoresistive transition metal sulfide FeCr(2)S(4) was evaluated through a multipole formalism from a set of structure factors obtained both experimentally, by means of single crystal high-quality x-ray diffraction data collected at T=23 K, and theoretically, with an extended-basis unrestricted Hartree-Fock periodic calculation on the experimental geometry. A full topological analysis, followed by the calculation of local energy density values and net atomic charges, was performed using the quantum theory of atoms in molecules. The experimental and theoretical results were compared. Good agreement was found for the topological properties of the system, as well as for the atomic net charges and the nature of the chemical bonds. An analysis of the electron density rho(r), its Laplacian nabla(2)[rho(r)], and the total energy density H(r) at the bond critical points was employed to classify all the interactions that resulted as predominantly closed shell (ionic) in nature. The topological indicators of the bonded interactions for Fe are distinct from those for Cr. The Fe-S bond distances were found to be 0.145 A shorter than the ideal values computed on the basis of Shannon's crystal radii, much shorter than the Cr-S distances with respect to their ideal Shannon lengths. Concomitantly, rho(r) and |H(r)| at the bond critical points are greater for Fe-S interactions, indicating that the local concentration of charge density in the internuclear region is larger for the tetrahedrally coordinated iron than for the octahedrally coordinated chromium. The isosurface in the real space for nabla(2)[rho(r)]=0 was plotted for both iron and chromium, pointing out the local zones of valence shell charge concentration and relating them to the partial d-orbital occupancy of the two transition metal atoms.     

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).     

From weak interactions to covalent bonds: a continuum in the complexes of 1,8-bis(dimethylamino)naphthalene

Experimental charge density distributions in a series of ionic complexes of 1,8-bis(dimethylamino)naphthalene (DMAN) with four different acids: 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid), 4,5-dichlorophthalic acid, dicyanoimidazole, and o-benzoic sulfimide dihydrate (saccharin) have been analyzed. Variation of charge density properties and derived local energy densities are investigated, over all inter- and intramolecular interactions present in altogether five complexes of DMAN. All the interactions studied [[O...H...O](-), C[bond]H...O, [N[bond]H...N](+), O[bond]H...O, C[bond]H...N, C pi...N pi, C pi...C pi, C[bond]H...Cl, N[bond]H(+)] follow exponential dependences of the electron density, local kinetic and potential energies at the bond critical points on the length of the interaction line. The local potential energy density at the bond critical points has a near-linear relationship to the electron density. There is also a Morse-like dependence of the laplacian of rho on the length of interaction line, which allows a differentiation of ionic and covalent bond characters. The strength of the interactions studied varies systematically with the relative penetration of the critical points into the van der Waals spheres of the donor and acceptor atoms, as well as on the interpenetration of the van der Waals spheres themselves. The strong, charge supported hydrogen bond in the DMANH(+) cation in each complex has a multicenter character involving a [[Me(2)N[bond]H....NMe(2)](+)....X(delta-)] assembly, where X is the nearest electronegative atom in the crystal lattice.     

How short can the H...H intermolecular contact be? New findings that reveal the covalent nature of extremely strong interactions

Ab initio calculations at the MP2/6-311++G(d,p) and MP2/aug-cc-pVDZ//MP2/aug-cc-pVTZ levels have been performed for the following complexes: H2OH+...HBeH, H2OH+...HBeBeH, H2OH+...HBeF, HClOH+...HBeH, Cl2OH+...HBeH, and Cl2OH+...HBeF. For all dimers considered, extremely short H...H intermolecular contacts (1.0-1.3 A) were obtained. These are the shortest intermolecular distances which have ever been reported, with binding energies within the range of 13.7-24.3 kcal/mol (MP2/aug-cc-pVDZ//MP2/aug-cc-pVTZ level). The interaction energies of the complexes analyzed were also extrapolated to the complete basis set (CBS) limit. To explain the nature of such strong interactions, the Bader theory was applied, and the characteristics of the bond critical points (BCPs) were analyzed. It was pointed out that for the major part of the H...H contacts considered here the Laplacian of the electron density at H...H BCP is negative indicating the partly covalent nature of such a connection. The term "covalent character of the hydrogen bond" used sometimes in recent studies is discussed. An analysis of the interaction energy components for dihydrogen bonded systems considered indicates that in contrast to conventional hydrogen bonded systems the attractive electrostatic term is outweighed by the repulsive exchange energy term and that the higher order delocalization energy term is the most important attractive term.     

Weak metal-metal bonding in small manganese cluster ions, Mn(N)+ (N < or = 7)

The binding energies of manganese cluster ions Mn(N)+ (N = 5-7) were determined by the photodissociation experiments in the near-infrared and visible-photon-energy ranges. The bond dissociation energies of Mn(N)+, D0(Mn(N-1)+...Mn), were obtained to be 1.70+/-0.08, 1.04+/-0.10, and 1.46+/-0.11 eV, respectively, for N = 5, 6, and 7 from the threshold energies for the two-atom loss processes and the bond dissociation energies of Mn3(+) and Mn4(+) reported previously [A. Terasaki et al., J. Chem. Phys. 117, 7520 (2002)]. Correspondingly, binding energies per atom are obtained to be 0.99+/-0.03, 1.00+/-0.03, and 1.06+/-0.03 eV/at. for N = 5, 6, and 7, respectively. A gradual increase in the binding energy from N = 2 to N = 7 shows an increasing contribution of nonbonding 3d orbitals to the bonding via weak hybridization with valence 4s orbitals as the cluster size increases. These binding energies per atom are still much smaller than the bulk cohesive energy of manganese (2.92 eV/at.), and this finding indicates exceptionally weak metal-metal bonds in this size range.     

Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).     

Bond paths as privileged exchange channels

Evidence that the bond paths of the quantum theory of atoms-in-molecules (QTAIM) signal preferred quantum-mechanical exchange channels is presented. We show how bond paths between an atom A and the atoms B in its environment appear to be determined by competition among the A-B exchange-correlation energies that always contribute to stabilize the A-B interactions. These pairwise additive stabilizations depend neither on the attractive or repulsive nature of the classical electrostatic interaction between the atoms' charge densities, nor on the change in the self energies of the atoms involved. These other terms may well cause an overall molecular-energy increase in spite of a possibly large A-B exchange-correlation stabilization. After our proposal, bond paths, both at and out of equilibrium geometries, are endowed with a specific energetic meaning that should contribute to reconcile the orthodox QTAIM interpretation with other widely accepted views, and to settle recent controversies questioning the meaning of hydrogen-hydrogen bonding and the nature of the so-called "steric interactions", the role of bond paths in endohedral complexes, and the generality of the results provided by the QTAIM. Implications for the nature of more general closed-shell interactions are also briefly discussed.