The splitting of atomic orbitals with a common principal quantum number revisited: np vs. ns

Atomic orbitals with a common principal quantum number are degenerate, as in the hydrogen atom, in the absence of interelectronic repulsion. Due to the virial theorem, electrons in such orbitals experience equal nuclear attractions. Comparing states of several-electron atoms that differ by the occupation of orbitals with a common principal quantum number, such as 1s(2) 2s vs. 1s(2) 2p, we find that although the difference in energies, ΔE, is due to the interelectronic repulsion term in the Hamiltonian, the difference between the interelectronic repulsions, ΔC, makes a smaller contribution to ΔE than the corresponding difference between the nuclear attractions, ΔL. Analysis of spectroscopic data for atomic isoelectronic sequences allows an extensive investigation of these issues. In the low nuclear charge range of pertinent isoelectronic sequences, i.e., for neutral atoms and mildly positively charged ions, it is found that ΔC actually reverses its sign. About 96% of the nuclear attraction difference between the 6p (2)P and the 6s (2)S states of the Cs atom is cancelled by the corresponding interelectronic repulsion difference. From the monotonic increase of ΔE with Z it follows (via the Hellmann-Feynman theorem) that ΔL > 0. Upon increasing the nuclear charge along an atomic isoelectronic sequence with a single electron outside a closed shell from Z(c), the critical charge below which the outmost electron is not bound, to infinity, the ratio ΔC/ΔL increases monotonically from lim(Z→Z(c)(+))ΔC/ΔL=-1 to lim(Z→∞)ΔC/ΔL=1. These results should allow for a more nuanced discussion than is usually encountered of the crude electronic structure of many-electron atoms and the structure of the periodic table.     

Calculation of photoelectron spectra of molybdenum and tungsten complexes using Green's functions methods

Green's functions calculations are presented for several complexes of molybdenum and tungsten, two metals that are similar structurally but display subtle, but significant, differences in electronic structure. Outer valence Green's functions IPs for M(CO)6, M(Me)6, MH6, [MCl4O](-), and [MO4](-) (M = Mo, W) are generally within +/-0.2 eV of available experimental photoelectron spectra. The calculations show that electrons in M-L bonding orbitals are ejected at lower energies for Mo while the detachment energy for electrons in d orbitals varies with metal and complex. For the metal carbonyls, the quasiparticle picture assumed in OVGF breaks down for the inner valence pi CO molecular orbitals due to the coupling of two-hole-one-particle charge transfer states to the one-hole states. Incorporation of the 2h1p states through a Tamm-Dancoff approximation calculation accurately represents the band due to detachment from these molecular orbitals. Though the ordering of IPs for Green's functions methods and DFT Koopmans' theorem IPs is similar for the highest IPs for most compounds considered, the breakdown of the quasiparticle picture for the metal carbonyls suggests that scaling of the latter values may result in a fortuitous or incorrect assignment of experimental VDEs.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

Orientation of pentacene molecules on SiO2: from a monolayer to the bulk

Near edge x-ray absorption fine structure (NEXAFS) spectroscopy is used to study the orientation of pentacene molecules within thin films on SiO2 for thicknesses ranging from monolayers to the bulk (150 nm). The spectra exhibit a strong polarization dependence of the pi* orbitals for all films, which indicates that the pentacene molecules are highly oriented. At all film thicknesses the orientation varies with the rate at which pentacene molecules are deposited, with faster rates favoring a thin film phase with different tilt angles and slower rates leading to a more bulklike orientation. Our NEXAFS results extend previous structural observations to the monolayer regime and to lower deposition rates. The NEXAFS results match crystallographic data if a finite distribution of the molecular orientations is included. Damage to the molecules by hot electrons from soft x-ray irradiation eliminates the splitting between nonequivalent pi* orbitals, indicating a breakup of the pentacene molecule.     

Very-low-lying electronic states result from n --> pi excitations in open-shell annulenes, annelated with alpha-dicarbonyl groups

UB3LYP/6-31G* calculations find that alpha-dicarbonyl-annelated cyclopentadienyl radical 1 has a sigma ground state, which is formed by excitation of an electron from the in-phase combination of carbonyl lone-pair orbitals into the singly occupied pi orbital. Similarly, tetrakis-annelated cyclooctatetraene 3 is calculated to have very-low-lying singlet and triplet excited states, which result from excitations of electrons from the b1g combination of lone pair orbitals into the empty pi nonbonding MO of the COT ring.     

Induced currents and electron counting in aromatic boron wheels: B8(2-) and B9-)

The newly discovered atom-centered polygonal wheels B8(2-) and B9- are predicted to show ring currents characteristic of aromatic systems. Ipsocentric mapping of induced current density for both molecules attributes a pi diatropic current to the four electrons of the doubly degenerate pi HOMO and a sigma diatropic current to the four electrons of the doubly degenerate sigma HOMO, each orbital pair having an available transition to corresponding LUMO orbitals in which the angular node count increases by one. Thus, on the magnetic criterion, B8(2-) and B9- are each both pi- and sigma-aromatic as a consequence of the nodal properties of the frontier orbitals of the pi- and sigma-stacks.     

原子簇与有关分子的结构规则(Ⅰ)-(nxcπ)格式

包括原子簇在内的无机和有机分子可认为由若干分子片所组成,它们的结构类型可由四个数(nxcπ)来规定。文中提出七条结构规则来阐明原子簇及有关分子的结构和成键能力,并举例说明这些结构规则和(nxcπ)格式的应用,如由分子式估算结构类型,预测新的原子簇化合物及其可能的合成途径等。     

Ab initio CI calculations on free-base porphin

Ab initio configuration interaction (CI ) calculations were carried out on low-lying singlet and triplet π–π* states and ionized states of free-base porphin. We take into account single and double excitations from σ and π electrons in the CI calculations. The composite natural orbitals were employed in order to reduce the size of orbital set to be used in the CI . The calculated excitation energies were in good agreement with experimental values. The use of split-valence-type basis and the inclusion of correlation effects of σ electrons were proved to be important to describe the low-lying π–π* states, especially the Soret band.     

Ring currents in tangentially p-p bonded sigma-aromatic systems

We report a theoretical study of ring systems that delocalize electrons in a cyclic array of p orbitals arranged tangentially in sigma-bonding fashion. Sigma-bonded arrays are compared to conventional pi-bonded analogues with respect to orbital symmetry and aromatic/antiaromatic behavior. In a one-to-one correspondence between pi and tangential molecular orbitals of a cycle, local rotation turns each pi to a tangential basis function, changing bonding interactions to antibonding and inverting the order of filling of molecular orbitals. The ipsocentric ring-current mapping approach is used to evaluate aromaticity on the magnetic criterion. As for conventional pi-ring currents, the sigma-ring current in tangential p-p bonded systems is dominated by the HOMO-LUMO transition, corresponding to circulation of four electrons in diatropic (4n + 2)-electron cycles but two in paratropic (4n)-electron cycles. The systems examined here utilize either C 2p or Si 3p orbitals for delocalization. Although interchangeable with C with respect to the fundamental orbital symmetry and ring-current rules, Si bonds at greater internuclear distances, a feature that allows easier design of potentially stable sigma-aromatic structures. Calculations show the wheel-like Si10C50H70 structure 6 as a stable, neutral aromatic molecule with a diatropic ring current following the sigma-bond path formed by Si 3p orbitals.     

电场对Ni3（dpa）4Cl2金属串配合物结构影响的理论研究

应用密度泛函UBP86方法对具有分子导线潜在应用性的金属串配合物Ni3(dpa)4Cl2进行研究,分析了外电场对配合物的几何构型和电子结构的影响.结果表明,零电场条件下存在沿着Ni63+轴及轴向配体Cl的Ni—Ni及Ni—Cl离域作用.沿金属轴Cl4→Cl5方向施加外电场,可使高电势端的Ni2—Cl4键长增大而Ni1—Ni2键长减小,低电势端的Ni3—Cl5键长减小而Ni1—Ni3键长增大;分子能量降低,偶极矩线性增大;HOMO与LUMO能隙减小,前线占据轨道分布向低电势方向移动且轨道能升高,空轨道分布则向高电势方向移动且轨道能降低,其中沿着金属轴方向离域的前线轨道分布及其轨道能随电场的变化尤为显著.在电场作用下,电荷分布发生改变,低电势端Cl5的负电荷向高电势端Cl4转移,但金属和桥联配体的电荷变化很小;同样,在电场作用下,配合物存在明显的结构变化和电子转移现象,呈现出类似导电过程中电子定向转移的变化规律.     

卟吩复合体的电子结构

本文用EHMO法对卟吩及其复合体的电子结构进行了计算。由卟吩复合体的差示电荷分布的分析表明, 在卟吩复合体中卟吩分子属于两性电子施受体, 分子中有固定的施体中心和受体中心部位。体系在相对取向角φ为45°时能量最小。两个分子相对旋转一周要克服四重势垒, 势垒高度为～0.09 eV。本文把简并态微扰理论推广运用于两个分子组成的复合物体系, 并由此定量地解释了卟吩与其复合体之间存在的能级对应现象。     

A study of porphin analogues—II: Reactivity indices and spin distribution in some conjugated polyaza macrocycles and their radical ions

Some of the calculated ground state properties of the π-electron system of seven conjugated polyaza macrocyclic ligands are reported, and contrasted with the analogous calculated properties of porphin, tetra-aza porphin and their closed shell dianions.The calculated spin and charge distributions in the anion and cation radicals of the eleven molecules referred to above are also reported in order to assess the perturbation of predicted reactivities by coordination to a central paramagnetic metal ion. The similarity between the Elvidge macrocycle (2) and tetra-aza porphin is particularly noteworthy.     

Geometry of simple molecules: nonbonded interactions, not bonding orbitals, and primarily determine observed geometries.

The forces responsible for the observed geometries of the YX(3) (Y = N or P; X = H, F, or Cl) molecules were studied through ab initio computations at the HF-SCF/6-31G level. The calculated molecular orbitals were grouped as contributing primarily to (a) the covalent bonds, (b) the terminal atom nonbonding electrons (for X = F or Cl), and (c) the central atom nonbonding electrons. This grouping was accomplished through 3-D plotting and an atomic population analysis of the molecular orbitals. The molecules were then moved through a X-Y-X angular range from 90 degrees to 119 degrees, in four or five degree increments. Single-point calculations were done at each increment, so as to quantify the energy changes in the molecular orbital groups as a function of geometry. These calculations show that the nonbonding electrons are much more sensitive to geometry change than are the bonding orbitals, particularly in the trihalide compounds. The molecular orbitals representing the nonbonding electrons on the terminal atoms (both valence and core electrons) contribute to the spreading forces, as they favor a wider X-Y-X angle. The contracting forces, which favor a smaller X-Y-X angle, consist of the orbitals comprising the nonbonding electrons on the central atom (again, both valence and core electrons). The observed geometry is seen as the balance point between these two sets of forces. A simple interaction-distance model of spreading and contracting forces supports this hypothesis. Highly linear trends are obtained for both the nitrogen trihalides (R(2) = 0.981) and phosphorus trihalides (R(2) = 0.992) when the opposing forces are plotted against each other. These results suggest that a revision of the popular conceptual models (hybridization and VSEPR) of molecular geometry might be appropriate.     

All-Metallic Zn=Zn Double-π Bonded Octahedral Zn2M4 (M=Li,Na) Clusters with Negative Oxidation State of Zinc

Zn=Zn double bonded-especially double-π bonded-systems are scarce due to strong Coulomb repulsion caused by the Zn atom's internally crowded d electrons and very high energy of the virtual π orbitals in Zn₂ fragments. It is also rare for Zn atoms to exhibit negative oxidation states within reported Zn−Zn bonded complexes. Herein, we report Zn=Zn double-π bonded octahedral clusters Zn₂M₄ (M=Li, Na) bridged by four alkali metal ligands, in which the central Zn atom is in a negative oxidation state. Especially in D_4h−Zn₂Na₄, the natural population analysis shows that the charge of the Zn atom reaches up to −0.89 |e| (−1.11 |e| for AIM charge). Although this cooperation inevitably increases the repulsion between two Zn atoms, the introduction of the s¹-type ligands results in occupation of degenerated π orbitals and the electrons being delocalized over the whole octahedral framework as well, in turn stabilizing the octahedral molecular structure. This study demonstrates that maintaining the degeneracy of the π orbitals and introducing electrons from equatorial plane are effective means to construct double-π bonds between transitional metals.     

The leap-frog effect of ring currents in benzene

Symmetry arguments show that the ring-current model proposed by Pauling, Lonsdale, and London to explain the enhanced diamagnetism of benzene is flawed by an intrinsic drawback. The minimal basis set of six atomic 2p orbitals taken into account to develop such a model is inherently insufficient to predict a paramagnetic contribution to the perpendicular component of magnetic susceptibility in planar ring systems such as benzene. Analogous considerations can be made for the hypothetical H(6) cyclic molecule. A model allowing for extended basis sets is necessary to rationalize the magnetism of aromatics. According to high-quality coupled Hartree-Fock calculations, the trajectories of the current density vector field induced by a magnetic field perpendicular to the skeletal plane of benzene in the pi electrons are noticeably different from those typical of a Larmor diamagnetic circulation, in that (i) significant deformation of the orbits from circular to hexagonal symmetry occurs, which is responsible for a paramagnetic contribution of pi electrons to the out-of-plane component of susceptibility, and (ii) a sizable component of the pi current density vector parallel to the inducing field is predicted. This causes a waving motion of pi electrons; streamlines are characterized by a "leap-frog effect".     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.     

Low-valent cobalt complexes with three different pi acceptor ligands: experimental and DFT studies of the reduced and the low-lying excited states of (R-DAB)Co(NO)(CO), R-DAB = substituted 1,4-diaza-1,4-butadiene

The complexes (RN=CH-CH=NR)Co(NO)(CO) with R = isopropyl, 2,6-diisopropylphenyl, or p-tolyl are chemically and electrochemically reducible to radical anions at potentials which strongly depend on R. The DFT calculated structure for the neutral compound with R = iPr agrees with the experiment, and the computed structure of the anion radical reveals changes according to a reduction of the R-DAB ligand. EPR results confirm an (R-DAB)-based singly occupied molecular orbital in [(RNCHCHNR)Co(NO)(CO)](.-), with minor but detectable contributions from NO as supported by IR spectroelectrochemistry and as quantified by DFT spin density calculations. The calculations indicate increasingly stabilized CO, NO, and RNCHCHNR pi* acceptor orbitals, in that order. On the basis of TD-DFT (time-dependent density functional theory) calculations, the lowest-lying excited states are assigned to metal-to-(R-DAB) charge transfer transitions while bands due to the metal-to-nitrosyl charge transfer occur at higher energies but still in the visible region. Resonance Raman studies were used to probe these assignments.     

DFT studies on the magnetic exchange across the cyanide bridge

Exchange coupling across the cyanide bridge in a series of novel cyanometalate complexes with CuII-NC-MIII (M = Cr and low-spin Mn, Fe) fragments has been studied using the broken-symmetry DFT approach and an empirical model, which allows us to relate the exchange coupling constant with sigma-, pi-, and pi*-type spin densities of the CN- bridging ligand. Ferromagnetic exchange is found to be dominated by pi-delocalization via the CN- pi pathway, whereas spin polarization with participation of sigma orbitals (in examples, where the dz2 orbital of MIII is empty) and pi* orbitals of CN- yields negative spin occupations in these orbitals, and reduces the CuII-MIII exchange coupling constant. When the dz2 orbital of MIII is singly occupied, an additional positive spin density appears in the sigma(CN) orbital and leads to an increase of the ferromagnetic Cu-NC-M exchange constant. For low-spin [MIII(CN)6]3- complexes, the dz2 orbital occupancy results in high-spin metastable excited states, and this offers interesting aspects for applications in the area of molecular photomagnetism. The DFT values of the exchange coupling parameters resulting from different occupations of the t2g orbitals of low-spin (t2g5) FeIII are used to discuss the effect of spin-orbit coupling on the isotropic and anisotropic exchange coupling in linear Cu-NC-Fe pairs.     

The bonding in the ozone molecule: From a different perspective

A new qualitative treatment of the bonding in ozone is presented. It is based upon a combination of several simple concepts: the nonparticipation of the pairs of electrons tightly held in the atomic 2s orbitals; simple overlap of the 2p orbitals to form sigma bonds; interaction of three 2p orbitals to yield bonding and nonbonding pi molecular orbitals that are populated by electron pairs; and van der Waals repulsion between the two terminal oxygen atoms forcing these atoms apart to yield the bond angle of 117° as a compromise. Both the assumptions and the resulting bonding picture are in accord with the photoelectron spectroscopic data, the results from sophisticated molecular orbital calculations, and the common physical properties of ozone.     

Modulating Electronic Coupling Using O- and S-donor Linkers

Structures of compounds having two dimolybdenum units Mo2(DAniF)3+ (DAniF = N,N'-di-p-anisylformamidinate) connected by unsubstituted oxamidate (1) and dithiooxamidate (2) linkers are isomorphous, and the cores of the molecules are planar because of two intramolecular hydrogen bonds within the linkers. Molecular mechanics calculations show a barrier of rotation along the C-C bond of approximately 10 kcal x mol(-1), which suggests that planar conformations are also expected in solution. Changing the two oxygen atoms in the linker of 1 to sulfur atoms results in a significant enhancement of the electronic coupling between the dimetal units (Delta(E1/2) = 204 mV for 1 and 407 mV for 2). The electronic spectrum of 2 shows an intense low energy (600 nm) metal-to-ligand charge transfer (MLCT) band, whereas that for 1 shows only a weak absorption band at 460 nm. DFT calculations on models 1' and 2', in which the anisyl groups were replaced by hydrogen atoms, show that the energy of the pi* orbital of the linker is much lower for 2'. This allows dpi-ddelta interactions from the electrons in the delta orbitals of the Mo2 unit to the sulfur atom that in turn facilitates an electron hopping pathway.