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.     

Electronic states and nature of the chemical bond in the molecule CrC by all-electron ab initio calculations

All-electron ab initio Hartree–Fock (HF ), valence configuration interaction (CI ), and multiconfiguration self-consistent-field (CASSCF ) calculations have been applied to investigate the electronic states of the CrC molecule. The molecule is predicted as having four low-lying electronic states, ³∑^?, ⁵∑^?, ⁷∑^?, and ⁹∑^?, separated by an energy gap of 0.55 eV from the next higher-lying state, ¹∑^?, which is followed by the states ⁵Π and ⁷Π. The four lowest-lying electronic states are due to the coupling of the angular momenta of the ⁶S_g Cr⁺ ion with those of the ⁴S_u C^? anion. The chemical bond in the ³∑^? ground state can be viewed as a quadruple bond composed of two σ and two π bonds. One σ bond is due to the formation of a molecular orbital that is doubly occupied. The remaining bonds, i.e., one σ and two π bonds, arise from valence-bond couplings. The π bonds originate from the valence-bond couplings of the electrons in the C 2pπ orbitals with those in the Cr 3dπ orbitals. The σ bond originates from the valence-bond coupling of the C 2pσ electron with an electron in the Cr 4s, 4p hybrid that is polarized away from the C atom.     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.     

A “double-zeta” type wavefunction for an organometallic: Bis-(π-allyl)nickel

A wavefunction which is of double-zeta quality at the level of the valence orbitals [based on a (11, 7, 5/8, 4/4) gaussian basis set contracted to (4, 3, 2/3, 2/2)] is reported for thebis-(π-allyl)nickel molecule. Independant SCF calculations for two ionized states substantiate the conclusion reached previously for a number of organometallics with a minimal basis set that Koopmans' theorem is not valid for these molecules, namely that the highest occupied orbital from the ground state calculation for the neutral molecule is mostly a ligand π orbital whereas the lowest ionization potential corresponds to the removal of an electron from a molecular orbital which is mostly a metal 3d orbital. The nature of the bonding inbis-(π-allyl)nickel is discussed on the basis of the possible interactions between the metal orbitals and the π orbitals of the allyl group. The interaction between the filled nonbonding π orbital of the allyl group and the empty 3d _xz orbital of the Ni atom appears responsible for most of the bonding, together with some backbonding through an interaction between the 3d x ²?y ²and 3d xyorbitals and the σ and π orbitals of the ligands. The computed value for the rotation barrier about the C-C allyl bond, 90 kcal/mole, rules out this rotation as one of the possible mechanisms which account for the equivalence of the terminal hydrogens in the proton magnetic resonance spectra of π-allyl complexes.     

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the system. The remaining spectral bands are due to Rydberg transitions of higher energy. The two lowest singlet-triplet transitions involve the same valence states. The results are in agreement with available experimental data and provide a number of new assignments of the experimental spectra.     

Electronic structure of clusters modeling silica

Self-consistent-field-Xα-scattered wave calculations on clusters Si₂O₇^6? and H₆Si₂O₇ modeling silica have been performed. Incorporation of Si 3d orbitals produces significant changes in the overall valence structure. In addition to σ Si — O bonds, there exists a bonding π character due to the participation of O 2p and Si 3d. Hydrogen terminators do not seem to correct edge effects for these π states.     

第一过渡系金属硅烯配合物的理论研究

以HF/6-311+G^*基组研究了硅烯SiH₂同第一过渡系金属的配合物MSiH₂的分子轨道特征及键解离能.MSiH₂为共平面构型.其中基态的3TiSiH₂和4CoSiH₂带有明显的双键特征.M-Si键具有共价性质.M-Si的键解离能,从Sc到Cu呈现周期性变化,这种变化趋势同M的金属离子激发能之间存在近似的线性关系.     

Etude structurale de composes organosilicies par diffusion rayleigh depolarisee: VI. Effets electroniques dans les systemes Cz.dbnd;CSi,PhSi,SiCC, SiNSi Et Si3N

Depolarised Rayleigh scattering is sensitive to conjugated electronic effects. The proper effect of silicon bonded to an sp² carbon atom in Me₃SiPh and Me₃SiCHCHΣ (Σ = H, Me, t-Bu, SiMe₃) has been illustrated by comparison of the systems containing a C_sp²M bond with the corresponding systems containing a C_sp³M bond for M = C, Si. To be able to make this comparison it was necessary to study the additivity of the bond and group optical anisotropies in alkenes with Me, CMe₃, SiMe₃ groups by means of a more approximate model assuming axial symmetry for the CC bond but of more convenient and more general use than a more realistic model without axial symmetry. Contrary to the NSi (from monosilylamines), SiOC and SiOSi systems, silicon adjacent to an unsaturated system, causes an exaltation of the optical anisotropy which mainly results from increase of the longitudinal optical polarisability. This exaltation is consistent with electron delocalisation in an orbital obviously longer than the basic π orbital. Such an effect seems strengthened in (Me₃Si)₂NΣ if the donating ability of Σ increases, Σ = H, Me, t-Bu. For Me₃SiCHCHSiMe₃ and if the molecules Me₃SiNHΣ¹ (Σ¹ = Me, t-Bu), (Me₃Si)₂NH and (Me₃Si)₃N are compared, a compensation is observed between the effect of the new lengthening of the π orbital and the π electronic density fall by CSi or NSi bonds.     

CASSCF study of bonding in NiCO and FeCO

A series of CASSCF calculations were performed on the ground states of NiCO and FeCO. The contributions of the σ/π interactions are checked by examining the validity of the CASSC calculation to describe the molecule with a particular choice of the active space. The calculation results substantiate that the stability of MCO is determined by a balance between π donation from the metal 3d_π to the CO 2π and repulsion between the metal σ electrons and the CO 5σ lone pair and, at the same time, emphasizes the importance of the synergistic σ/π interactions between the metal and the CO group. The relative importance of σ/π interactions depends on the nature of the metal. In the case of NiCO, it is the π donation from Ni 3d_π to CO 2π that makes the largest contribution to the formation of the Ni CO bond, while in the case of FeCO, it is the correlation of σ electrons that holds the metal and CO together. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 221–231, 1999     

Electronic states and nature of bonding of the molecule PdSi by all electron ab initio HF-CI calculations and mass spectrometric equilibrium experiments

Six low-lying electronic states of the PdSi molecule have been investigated by performing all electron ab initio Hartree-Fock (HF) and configuration interaction (CI) calculations. The molecule is predicted to have a³∏ ground state and two low-lying excited states,³Σ^? and¹Σ⁺. The electronic structure of the PdSi molecule has been rationalized in a simple molecular orbital diagram. As part of the PdSi molecule the Pd atom essentially retains its (4d)¹⁰ ground term configuration. The chemical bond in the PdSi molecule has been interpreted in terms of donation and back-donation of charge. The bond is polar with charge transfer from the Pd to the Si atom. The dissociation energy of the PdSi molecule has been determined from the mass spectrometric equilibrium data in combination with the theoretical results asD ₀ ^o =257±12 kJ mol^?1.     

Electronic structure and bonding in clusters: Theoretical studies

The electronic structures of small Al _n ,n=5, 9, 13, clusters with bulk geometry are studied using the ab initio Hartree-Fock-LCAO method. The cluster ground states have always multiplicity higher than the lowest possible value. However, the energy difference between ground and lowest low spin state decreases with increasing cluster size. The energy range of the Al _n cluster valence levels is comparable with the width of the occupied part of the 3sp band in bulk Al. The different binding mechanisms that arise when a CO molecule interacts with Al _n clusters in different coordination sites are analyzed in detail with the constrained space orbital variation (CSOV) method. Electrostatic and polarization contributions to the interaction are found to be important. Among charge transfer (donation) contributions π electron transfer from Al _n to CO corresponding to π backbonding is energetically more important than σ electron transfer from CO to Al _n characterizing the σ bond.     

Orbital mechanism of upright CO activation on Fe(100)

The knowledge of bond activation forms a cornerstone for modern chemistry, wherein symmetry rules of electronic activation lie in the heart of bond activation. However, the question as to how a chemical bond is activated remains elusive. By taking CO activated on Fe(100), herein, we have resolved the long-standing fundamental question; we have found that excitations in the adsorbate feature the bond activation. We essentially have discovered contrasting electronic processes in respective σ and π electron systems of the adsorbed CO molecule. The σ electron system is involved in reversible hidden excitations/deexcitations between two occupied σ orbitals, whereas the π electron system is subject to irreversible π to π* excitations dispersed along the d-band region, which is coupled to the rotational 2π electron couplings depending on the strength of molecule-metal interactions. The σ excitations pertain to the Pauli repulsion mediated quantum nature with energy and entropy marked by the two energy levels, whereas the π to π* excitations fall into a new category of electronic excitations contributing to energy and entropy exchanges in a wide and continuous d-band region. The findings that the internal states of the adsorbate are excited and that fundamental connections between the frontier orbitals and low-lying orbitals are established as the molecule comes to the surface may open up new channels to realize more efficient bond activation and renew our thinking on probing the quantum mechanical nature of bond activation at surfaces with further possible impact on manipulation of orbital activation in femtochemistry and attochemistry.     

σ−π Contributions in metal-co bond: A theoretical study of RhCO and PdCO

The electronic structure of linear RhC0 and PdCO molecules has been studied by means of effective core potential calculations including configuration interaction. The study of the ⁴Δ and ²Σ⁺ states of RhCO and the ³Σ⁺ and ¹Σ⁺ states of PdCO has shown that their low-spin states are bound and their high-spin states are repulsive. The binding energies of RhCO and PdCO are 4.0 and 7.2 kcal/mol, for the equilibrium bond lengths of 3.87 and 4.03 au, respectively. The interaction between the diffuse 5s metal orbital and the carbon lone pair produces a repulsion in the α-space, as depicted by the negative region along the metal-carbon axis in the electron density difference contour maps. The bonding in low-spin states of RhCO and PdCO is due to the metal-CO π “backdonation”. The present investigation on RhCO and PdCO, preliminary results on ScCO, as well as published results on FeCO, NiCO, CuCO and PtCO allows us to make a general conjecture that a low occupancy of the outer s atomic orbital of the transition metal atom in the complex favours the bonding interaction with the CO moiety. The analogy with properties of LiCO and NaCO systems is pointed out.     

The electronic structure of borabenzene: Combination of an aromatic π-sextet and a reactive σ-framework

The electronic structure of borabenzene (C₅H₅B, known also as borinane, borinine, borine) is studied using modern valence bond theory in its spin-coupled (SC) form. Three different types of SC wave functions—with six active π orbitals and with four and eight active σ orbitals—are used to describe the π system of the molecule and the σ-bond framework around the boron atom. It is demonstrated that the SC picture of the π space in borabenzene is very similar to that in benzene: The spins of six distorted nonorthogonal 2p_π orbitals are combined in a spin-coupling pattern involving two dominating Kekulétype and three less important Dewar-type Rumer spin functions. This indicates that it is appropriate to consider the π-electron sextet in borabenzene as aromatic and that the reason for the reactivity of this molecule should lie with its σ framework. The two SC models of the σ bonding around B show that the boron-carbon σ bonds in borabenzene involve orbitals are “bent” to the outer side of the six-membered ring. This creates an orbital “hole” at the boron, which should represent the preferred attachment site for Lewis acids. © 1997 John Wiley & Sons, Inc.     

Conformational control of oxidation sites, spin states and orbital occupancy in nickel porphyrins

Ni(II) porphyrin π cation radicals are known to undergo an internal electronic isomerization to L₂Ni(III) cations upon complexation with ligands (L). Additional examples of the Ni(II) to Ni(III) conversion are presented for flexible, 'planar' NiOEP (2,3,7,8,12,13,17,18-octaethylporphyrin) and NiT(Pr)P (5,10,15,20-tetra-n-propylporphyrin) in which the Ni(III) orbital occupancy, d _z2 or d _x2-y2, is determined by the ligand field strength of the axial ligands (pyridine, imidazole, or cyanide). In contrast to these results, the nonplanar NiOETPP (2,3,7,8,12,13,17,18-octaethyl-5,10,15,20-tetraphenylporphyrin), which is easily oxidized because of its saddle-shape, yields a complex postulated to be a high spin Ni(II) π cation radical, based on crystallographic and optical data for (imidazole)2NiOETPP⁺ClO^4-, in which the electron of high spin Ni(II) in the d _x2-y2 orbital is antiferromagnetically coupled to the unpaired electron of the porphyrin radical leaving one electron in the Ni(II) d _z2 orbital, i.e. a pseudo Ni(III). The sterically encumbered, nonplanar NiT(t-Bu)P (5,10,15,20-tetra-tertiary-butylporphyrin) yields Ni(III) complexes when ligated by pyridine, imidazole or cyanide, but in all cases only the Ni(III) d _z2 orbital is occupied as evidenced by EPR spectroscopy. This anomalous chemistry is attributed to the fact that the macrocycle of NiT(t-Bu)P is so sterically constrained that it cannot readily expand to accommodate the longer equatorial Ni—N distances required by population of the d _x2-y2 orbital in Ni(III) or high spin Ni(II). Further support for this postulate derives from NiD(t-Bu)P (5,10-di-tertiary-butylporphyrin) which is less sterically constrained and in which the Ni(III) d _x2-y2 orbital is indeed occupied upon complexation with cyanide. These results thus illustrate the significant effects that the conformations, plasticity or rigidity of Ni porphyrin macrocycles can have on sites of oxidation (metal or porphyrin), spin states (low spin Ni(III) or high spin Ni(II)), and orbital occupancies (d _z2 or d _x2-y2 in Ni(III)).     

Theoretical study of LiK and LiK+ in adiabatic representation

The potential energy curves have been calculated for the electronic states of the molecule LiK within the range 3 to 300 a.u., of the internuclear distance R. Using an ab initio method, through a semiempirical spin-orbit pseudo-potential for the Li (1s ²) and K (1s ²2s ²2p ⁶3s ²3p ⁶) cores and core valence correlation correction added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The core valence effects including core-polarization and core-valence correlation are taken into account by using an l-dependent core-polarization potential. The molecular orbitals have been derived from self-consistent field (SCF) calculation. The spectroscopic constants, dipole moments and vibrational levels of the lowest electronic states of the LiK molecule dissociating into K (4s, 4p, 5s, 3d, and 5p) + Li (2s, 2p, 3s, and 3p) in ^{1, 3}Σ, ^{1, 3}Π, and ^{1, 3}Δ symmetries. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiK⁺ dissociating into Li (2s, 2p, 3s, and 3p) + K⁺ and Li⁺ + K (4s, 4p, 5s, 3d, and 5p). The comparison of the present results with those available in the literature shows a very good agreement in spectroscopic constants of some lowest states of the LiK and LiK⁺ molecules, especially with the available theoretical works. The existence of numerous avoided crossing between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

Electronic transition moment of the AΠr-XΣ system of TiN

The A²Π_r-X²Σ⁺ transition of TiN was observed by the dispersed laser induced fluorescence (DLIF) spectroscopy. The relative intensities of the DLIF spectra were analyzed to determine the dependence of the electronic transition moment, R_e(r), on the internuclear distance, r, as R_e(r)∝{1−0.281(26)r} (1.380 Å≤r≤1.823 Å). This r-dependence was analyzed simultaneously with the reported values of the spin-orbit constants for A²Π_r and the hyperfine-coupling constants for X²Σ⁺ to evaluate the ionic character of the TiN bond, the 4s atomic character in the 9σ orbital of X²Σ⁺, and the 4p atomic character in the 4π orbital of A²Π_r. These characters were confirmed to be in accordance with the reported theoretical prediction. A strong r-dependence was indicated for the 3d-4p mixing in the A²Π_r state due to the configuration mixing of the Ti(3d⁴) and Ti(3d³4p) states at a large internuclear distance.     

A Valence Bond Model for Electron‐Rich Hypervalent Species: Application to SFn (n=1, 2, 4), PF5, and ClF3

Some typical hypervalent molecules, SF₄, PF₅, and ClF₃, as well as precursors SF (⁴Σ^? state) and SF₂ (³B₁ state), are studied by means of the breathing‐orbital valence bond (BOVB) method, chosen for its capability of combining compactness with accuracy of energetics. A unique feature of this study is that for the first time, the method used to gain insight into the bonding modes is the same as that used to calculate the bonding energies, so as to guarantee that the qualitative picture obtained captures the essential physics of the bonding system. The ⁴Σ^? state of SF is shown to be bonded by a three‐electron σ bond assisted by strong π back‐donation of dynamic nature. The linear ³B₁ state of SF₂, as well as the ground states of SF₄, PF₅ and ClF₃, are described in terms of four VB structures that all have significant weights in the range 0.17–0.31, with exceptionally large resonance energies arising from their mixing. It is concluded that the bonding mode of these hypervalent species and isoelectronic ones complies with Coulson’s version of the Rundle–Pimentel model, but assisted by charge‐shift bonding. The conditions for hypervalence to occur are stated.     

Electro-structural correlations,elastic and optical properties among the nanolaminated ternary carbides Zr2AC

We have performed ab initio calculations for the nanolaminates Zr₂AC (A = Ti, In, Tl, Si, Ge, Sn, Pb, P, As, S) ceramics to study their electronic structure, elastic and optical properties. In this work, we used the accurate augmented plane wave plus local orbital method with density functional theory to find the equilibrium structural parameters, dielectric functions and to compute the full elastic tensors. The obtained elastic constants were used to quantify the stiffness of the Zr₂AC phases and to appraise their mechanical stability. The relationship between elastic, electronic and valence electron concentration is discussed. Our results show that the bulk modulus and shear modulus increase across the periodic table for Zr₂AC. Furthermore, trends in elastic stiffness are well explained in terms of electronic structure analysis, as occupation of valence electrons in states near the Fermi level of Zr₂AC. We show that increments of bulk moduli originate from additional valence electrons filling states involving Zr d–A p. We show also that Zr d–A p hybridizations are located just below the Fermi level and are weaker bonds than the Zr d–C p hybridizations, which are deeper in energy. As a function of the p-state filling of the A element the Zr d–A p bands are driven to deeper energy. The optical spectra were analyzed by means of the electronic structure, which provides theoretical understanding of the conduction mechanism of these ceramics.     

An Isolable Radical Anion Featuring a 2-Center-3-Electron π-Bond without a Clearly Defined σ-Bond

Featuring an extra electron in the π* antibonding orbital, species with a 2-center-3-electron (2c3e) π bond without an underlying σ bond are scarcely known. Herein, we report the synthesis, isolation and characterization of a radical anion salt [K(18-C-6)]⁺{[(HCNDipp)₂Si]₂P₂}⋅⁻ (i.e. [K(18-C-6)]⁺ 3 ⋅⁻) (18-C-6=18-crown-6, Dipp=2,6-diisopropylphenyl), in which 3 ⋅⁻ features a perfectly planar Si₂P₂ four-membered ring. This species represents the first example of a Si- and P-containing analog of a bicyclo[1.1.0]butane radical anion. The unusual bonding motif of 3 ⋅⁻ was thoroughly investigated via X-ray diffraction crystallography, electron paramagnetic resonance spectroscopy (EPR), and calculations by density functional theory (DFT), which collectively unveiled the existence of a 2c3e π bond between the bridgehead P atoms and no clearly defined supporting P−P σ bond.