Quantum chemistry of many-electron systems: high-priority aspects

The review generalizes the studies devoted to the development of a new quantum chemistry method representing an alternative to the Hartree–Fock approximation. Based on the hypothesis of prohibition of equipotential surfaces, which clarifies the physical sense of the Pauli exclusion principle, and taking account of the condition for antisymmetrical wave function of the triplet state (3S) of He atom, the Hartree–Fock approximation is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWFs) for the test systems traditionally used in quantum chemistry, namely, excited triplet state of H₂ molecule and the ground electronic states of Li atom and LiH molecule. The nodal surfaces of the wave functions corresponding to the minimum basis set of Slater orbitals in the Hartree–Fock approximation are constructed and analyzed. An alternative to the Hartree–Fock approximation is provided by the MWF quantum chemical method being developed by the authors. In the MWF method, the nodal surfaces for H₂(³Σ _u ^v ) and Li(²S) are specified a priori. Some aspects of geometric interpretation of the Pauli exclusion principle are discussed. Unlike the MWF method, the Hartree–Fock approximation is unsuitable for taking account of the dependence of the MWF nodal surfaces on the nuclear charges and on correlation effects related to the motion of electrons with antiparallel spins because such nodal surfaces are predefined by the mathematical properties of Slater determinants rather than by physically clear and more practically valuable algebraic products of electrostatic potential differences.     

Nodal surfaces of the wave functions of the hydrogen molecule in the triplet state 3Σu +

For molecular hydrogen in the triplet state ³Σ_u ⁺, the nodal surfaces of the wave function corresponding to the minimum basis set of Slater orbitals in the Hartree—Fock approximation and those of the wave function used in calculations by the diffusion quantum Monte Carlo method were plotted and analyzed. Taking account of the condition for antisymmetrical wave function of the triplet state ³ S of He atom, the Hartree-Fock approximation in the minimum basis set of one-electron orbitals is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWF). An MWF quantum chemical method developed by the authors is outlined. The alternative nodal surfaces for H₂ (³Σ_u ⁺) a priori specified in this method are presented.     

Orbital topology. III. Orbital mapping of unsymmetrical molecules. A survey of the thermal ring opening of isoelectronically substituted cyclobutenes and benzocyclobutenes

Orbital mapping analysis based on CNDO /2 molecular orbitals has been used to survey the thermal ring-opening isomerizations of cyclobutenes and benzocyclobutenes. Isoelectronic substitutions within the molecular framework of cyclobutene (e.g., CH₂ replaced by CH^?, OH⁺, NH, NH₂⁺) result in ground-state orbital correlations via both conrotatory and disrotatory pathways in several cases, in contrast to the parent hydrocarbon conrotatory stereochemistry. The results substantiate the heteroatom effects previously revealed by orbital mapping for the disrotatory thermal isomerizations of isoelectronic Dewar benzenes. Qualitative patterns, such as nodal shifts in the butadiene π orbital, are discussed in relation to the mapping correlations. The isoelectronic benzocyclobutenes give ground-state orbital correlations via conrotatory pathways only, which suggests that delocalization may reduce the heteroatom perturbation.     

The nodal structure of the momentum distributions of molecules

The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H₂⁺ momentum distribution, it is shown that an infinite sequence of nodes does exist along the p_z axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the p_z axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the p_z axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J( q ) are discussed.     

A priori estimation of the nodal surfaces of trial wave functions of lithium atom

Some aspects of geometric interpretation of the Pauli exclusion principle in the Hartree—Fock approximation and in the framework of the many-electron wave function (MWF) method developed by the authors are discussed taking the Li (²S) ground electronic state as an example. Arguments are brought forward that indicate insufficient adequacy of the Hartree—Fock approximation for a priori estimation of the MWF nodal surfaces. It was pointed that, unlike the MWF method, the Hartree—Fock approximation can not describe the dependence of the shape of the MWF nodal surfaces on the nuclear charge of Li atom and on electron-electron correlation effects.     

Computational study of osmabenzyne: The solvent effects on the structure and spectroscopic properties (IR,NMR)

In this article, the structural, electronic, and spectroscopic properties of osmabenzyne Os{≡CC(SiH₃)=C(CH₃)C(SiH₃)=CH}Cl₂(PH₃)₂ are explored in the gas phase and five solvents. The effects of solvents on the structural parameters, frontier orbital energies, and spectroscopic parameters of the complex are elucidated using the polarizable continuum model. The wavenumbers of selected IR-active vibrations in different solvents are obtained and correlated with the Kirkwood–Bauer–Magat equation. In addition, thermodynamic parameters of solvation are calculated for the complex. ¹H and ¹³C NMR chemical shifts are estimated using the gauge-invariant atomic orbital method.     

The nature of transition-metal-oxide surfaces

The surfaces of the 3d-transition-metal oxides form a rich and important system in which to study the effects of atomic geometry, ligand coordination and d-orbital population on surface electronic structure and chemisorption. This article considers the properties of those surfaces in terms of the types of surface structures that can exist, including steps and point defects, and their relation to the experimental data that is available for well characterized, single-crystal surfaces. The electronic structure of nearly perfect surfaces is very similar to that of the bulk for many of the oxides that have been studied; atoms at step sites also appear to have properties similar to those of atoms on terraces. Point defects are often associated with surfaces 0 vacancies and attendant transfer of electrons to adjacent metal cations. Those cations are poorly screened from each other, and the excess charge is presumably shared between two or more cations having reduced ligand coordination. Point defects are generally more active for chemisorption than are perfect surfaces, however for Ti₂O₃ and V₂O₃, whose cations have 3d¹ and 3d² electronic configurations respectively, the cleaved (047) surface is more active than are surfaces having a high density of defects. The chemisorption behavior of both nearly perfect and defect surfaces of 3d-transition-metal oxides varies widely from one material to another, and it is suggestive to correlate this with cation d-orbital population. However, too few oxides have yet been studied to draw any firm conclusions. Additional theoretical work on perfect surfaces, defects and chemisorption is also necessary in order to gain a more complete understanding of transition-metal-oxide surfaces.     

A High Pressure Study on NH4Pb2Br5 Type Compounds Part II: Electronic Structure and Changes under High Pressure

In this work, we present a theoretical study (based on DFT‐calculations) of the electronic properties of compounds crystallising in a NH₄Pb₂Br₅ type structure in a wide pressure range. The main focus of this study is to elucidate the nature of bonding of the ns²‐cations at ambient and elevated pressure. For a better understanding of the structure and bonding, the DOS of these compounds are evaluated and discussed on the basis of a simple model assuming mainly ionic interactions. The calculations are complemented by an orbital analysis using the crystal orbital Hamilton population (COHP) and an analysis of the electronic density topology with the electron localisation function (ELF). Structural and theoretical investigations give results that are in excellent agreement: The DFT‐calculations confirm the existence of bonding interactions between the ns²‐cations at elevated pressure. Our study indicates that the “character” of the additional electron pair changes with increasing pressure from nonbonding to bonding in agreement with a simple model system of two interacting ns²‐cations.     

A momentum-space view of the chemical bond. I. The first-row Homonuclear diatomics

The electronic probability distribution in momentum space or electron momentum density (EMD) is studied in detail for the first-row homonuclear diatomics. The total density difference (molecule minus constituting atoms)is analyzed in terms of the separate orbital contributions. The nodal structure shown by the orbital EMD is characteristic for the various types of orbital (σ,σ*,=,=*), and is affected, by the amount of s-p hybridization. Directional and isotropic Compton profiles are used to study the bond-oscillation and bond-directional principles. The bond- directional principle does not hold for pe bonding. Spherically averaged EMD differences (SA Δ EMDs) are related to the changes in kinetic energy (ΔT) upon bond formation. The SA ΔEMDs and ΔT are rationalized by considering the different ranges of internuclear distance that are optimal for 2s-2s, 2p_o-2p_o and 2p_o-2p_o interaction. This leads to a reassessment of the role of the various orbitals in bonding complementing the picture based on orbital Hellmann- Feynman forces.     

The Use of Bridging Ligand Substituents to Bias the Population of Localized and Delocalized Mixed-Valence Conformers in Solution

The electronic structure and associated spectroscopic properties of ligand-bridged, bimetallic ‘mixed-valence’ complexes of the general form {M}(μ-B){M⁺} are dictated by the electronic couplings, and hence orbital overlaps, between the metal centers mediated by the bridge. In the case of complexes such as [{Cp*(dppe)Ru}(μ-C≡CC₆H₄C≡C){Ru(dppe)Cp*}]⁺, the low barrier to rotation of the half-sandwich metal fragments and the arylene bridge around the acetylene moieties results in population of many energy minima across the conformational energy landscape. Since orbital overlap is also sensitive to the particular mutual orientations of the metal fragment(s) and arylene bridge through a Karplus-like relationship, the different members of the population range exemplify electronic structures ranging from strongly localized (weakly coupled Robin-Day Class II) to completely delocalized (Robin-Day Class III). Here, we use electronic structure calculations with the hybrid density functional BLYP35-D3 and a continuum solvent model in combination with UV-vis-NIR and IR spectroelectrochemical studies to show that the conformational population in complexes [{Cp*(dppe)Ru}(μ-C≡CArC≡C){Ru(dppe)Cp*]⁺, and hence the dominant electronic structure, can be biased through the steric and electronic properties of the diethynylarylene (Ar) moiety (Ar=1,4-C₆H₄, 1,4-C₆F₄, 1,4-C₆H₂-2,5-Me₂, 1,4-C₆H₂-2,5-(CF₃)₂, 1,4-C₆H₂-2,5-ⁱPr₂).     

The nickel-group IV molecules NiC,NiSi, and NiGe

All electron ab initio calculations have been applied to elucidate the electronic states and the nature of the chemical bonds in the molecules NiC, NiSi, and NiGe. The calculations have revealed that the ground states of all three molecules are¹Σ⁺, but due to the open 3d shell of the Ni atom the molecules have many low-lying electronic states. The NiC molecule is strongly polar, and the low-lying electronic states have been identified as those arising when the angular momenta of the³F_g Ni⁺ ion are coupled to the angular momenta of the⁴S_uC^? anion. The chemical bond in the NiC molecule has triple bond character due to the valence bond couplings between the Ni 4s and 3dπ electrons and theC 2p electrons. The chemical bonds in the molecules NiSi and NiGe are very much alike; they are double bonds composed of oneσ and oneπ bond. Theσ bond is due to the doubly occupied delocalized molecular orbital composed of the Ni 4s orbital and the Si 3pσ or the Ge 4pσ orbital. Theπ bond originates from the valence bond coupling between the localized hole in the Ni 3dπ orbital and the valencepπ electron of Si or Ge.     

The electronic structure of Cu(ethanediimine)+2

Extended-Hückel and multiple-scattering Xα molecular orbital calculations are reported for the Cu(ethanediimine)⁺₂ complex. The results obtained are in agreement. From the calculated electronic transition energies, it is inferred that the lowest excited state is a B₂ state of metal-to-ligand charge-transfer type, confirming resonance Raman results.     

The Importance of Ligand-Induced Backdonation in the Stabilization of Square Planar d10 Nickel π-Complexes

The electronic nature of Ni π-complexes is underexplored even though these complexes have been widely postulated as intermediates in organometallic chemistry. Herein, the geometric and electronic structure of a series of nickel π-complexes, Ni(dtbpe)(X) (dtbpe=1,2-bis(di-tert-butyl)phosphinoethane; X=alkene or carbonyl containing π-ligands), is probed using a combination of ³¹P NMR, Ni K-edge XAS, Ni K_β XES, and DFT calculations. These complexes are best described as square planar d¹⁰ complexes with π-backbonding acting as the dominant contributor to M−L bonding to the π-ligand. The degree of backbonding correlates with ²J_PP from NMR and the energy of the Ni 1s→4p_z pre-edge in the Ni K-edge XAS data, and is determined by the energy of the π*_ip ligand acceptor orbital. Thus, unactivated olefinic ligands tend to be poor π-acids whereas ketones, aldehydes, and esters allow for greater backbonding. However, backbonding is still significant even in cases in which metal contributions are minor. In such cases, backbonding is dominated by charge donation from the diphosphine, which allows for strong backdonation, although the metal centre retains a formal d¹⁰ electronic configuration. This ligand-induced backbonding can be formally described as a 3-centre-4-electron (3c-4e) interaction, in which the nickel centre mediates charge transfer from the phosphine σ-donors to the π*_ip ligand acceptor orbital. The implications of this bonding motif are described with respect to both structure and reactivity.     

Photoelectron spectrum and ground state electronic structure of chromyl chloride vapor

The electronic structure of chromyl chloride CrO₂Cl₂ has been investigated by ultraviolet (HeI) photoelectron spectroscopy. Mulliken-Wolfsberg-Helmholtz molecular orbital calculations have been performed in order to provide a model for interpretation of the photoelectron spectra and to assist in assigning the low-energy optical absorption and emission transitions. The first ionization potential of CrO₂Cl₂ at 11.8 eV is due to ionization of the near-degenerate oxygen and chlorine nonbonding 2a₂, 4b₁, and 4b₂ MO's. The first unoccupied orbital is basically a chromium dπ^* orbital. The excitations (2a₂, 4b₁, 4b₂)→ 7a₁^* correlate well with the three low energy absorption transitions observed.     

Ab initio electronic analysis of the hydride transfer in the [CH3-H-CH3]+ system

Summary The electronic aspects of the hydride transfer process between CH₄ and CH ₃ ⁺ fragments, are studied theoretically withab initio molecular orbital methods, subject to the constraint of maintaining a fix distance between both fragments. Mulliken and Natural population analyses are performed to gain an insight into the hydride character of the atom being transferred. From these analyses, charge migrating diagrams are depicted to obtain a more visual information. Further analysis is performed from the contour maps of the electronic charge density, together with the analysis of its gradient and laplacian. Basis set and electronic correlation effects are also discussed. Finally, the effect of applying a uniform electric field is assessed.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

He++N2 Charge Transfer Reaction: An Ab initio Analysis

An ab initio analysis on the involved potential energy surfaces is presented for the investigation of the charge transfer mechanism for the He⁺+N₂ system. At high collision energy, as many as seven low-lying electronic states are observed to be involved in the charge transfer mechanism. Potential energy surfaces for these low-lying electronic states have been computed in the Jacobi scattering coordinates, applying multireference configuration interaction level of theory and aug-cc-pVQZ basis sets. Asymptotes for the ground and various excited states are assigned to mark the entrance (He⁺+N₂) and charge transfer channels (He+N₂⁺). Nonadiabatic coupling matrix elements and quasi-diabatic potential energy surfaces have been computed for all seven states to rationalize the available experimental data on the charge transfer processes and to facilitate dynamics studies.     

A re-examination of the infrared and ultraviolet spectroscopy of trifluoroacetyl fluoride and trifluoroacetyl chloride: An experimental and theoretical study

The fundamental IR vibrational modes of trifluoroacetyl fluoride CF₃C(O)F and trifluoroacetyl chloride CF₃C(O)Cl have been re-examined by ab initio molecular orbital calculations and compared with literature assignments. Several bands of the IR spectrum are reassigned. The Q-branch and integrated absorption cross-sections have been measured for ν₁, ν₃, ν₄ and ν₁₁ fundamental bands for both pressurized and unpressurized samples on each molecule. The UV absorption spectra of CF₃C(O)F and CF₃C(O)Cl show a structureless continuum with a maximum at 21Onm (σ_max=3.20±0.02 × 10⁻²⁰ cm² molecule⁻¹) and 255 nm (σ_max=7.66±0.26 × 10⁻²⁰ cm² molecule⁻¹), respectively. The nature of the electronic transition giving rise to the UV absorption spectrum for CF₃C(O)F and CF₃C(O)Cl has been examined by ab initio molecular orbital calculations. It is attributed to the A¹A″←X¹A′ electronic transition.     

Octacarbonyl Ion Complexes of Actinides [An(CO)8]+/− (An=Th,U) and the Role of f Orbitals in Metal–Ligand Bonding

The octacarbonyl cation and anion complexes of actinide metals [An(CO)₈]^+/− (An=Th, U) are prepared in the gas phase and are studied by mass-selected infrared photodissociation spectroscopy. Both the octacarbonyl cations and anions have been characterized to be saturated coordinated complexes. Quantum chemical calculations by using density functional theory show that the [Th(CO)₈]⁺ and [Th(CO)₈]⁻ complexes have a distorted octahedral (D_4h) equilibrium geometry and a doublet electronic ground state. Both the [U(CO)₈]⁺ cation and the [U(CO)₈]⁻ anion exhibit cubic structures (O_h) with a ⁶A_1g ground state for the cation and a ⁴A_1g ground state for the anion. The neutral species [Th(CO)₈] (O_h; ¹A_1g) and [U(CO)₈] (D_4h; ⁵B_1u) have also been calculated. Analysis of their electronic structures with the help on an energy decomposition method reveals that, along with the dominating 6d valence orbitals, there are significant 5f orbital participation in both the [An]←CO σ donation and [An]→CO π back donation interactions in the cations and anions, for which the electronic reference state of An has both occupied and vacant 5f AOs. The trend of the valence orbital contribution to the metal–CO bonds has the order of 6d≫5f>7s≈7p, with the 5f orbitals of uranium being more important than the 5f orbitals of thorium.     

Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc,Y, La) and the 18‐Electron Rule

We report the gas‐phase synthesis of stable 20‐electron carbonyl anion complexes of group 3 transition metals, TM(CO)₈^? (TM=Sc, Y, La), which are studied by mass‐selected infrared (IR) photodissociation spectroscopy. The experimentally observed species, which are the first octacarbonyl anionic complexes of a TM, are identified by comparison of the measured and calculated IR spectra. Quantum chemical calculations show that the molecules have a cubic (O_h) equilibrium geometry and a singlet (¹A_1g) electronic ground state. The 20‐electron systems TM(CO)₈^? are energetically stable toward loss of one CO ligand, yielding the 18‐electron complexes TM(CO)₇^? in the ¹A₁ electronic ground state; these exhibit a capped octahedral structure with C_3v symmetry. Analysis of the electronic structure of TM(CO)₈^? reveals that there is one occupied valence molecular orbital with a_2u symmetry, which is formed only by ligand orbitals without a contribution from the metal atomic orbitals. The adducts of TM(CO)₈^? fulfill the 18‐electron rule when only those valence electrons that occupy metal–ligand bonding orbitals are considered.