Electronegativity Scaled as a Average Attracting Energy of Valence‐Shell Electrons in a Ground‐State Free Atom

The total capability of an atom attracting valence electrons can be measured by the sum of ionization energies of valence electron in a ground‐state free atom plus its electron affinity called Total Attracting Energy, TAE = Σn_iE_i + EA, where, E_i is the ionization energy of the ith valence‐shell electron in a ground‐state free atom, n_i is the number of valence‐shell electron bearing energy E_i, and EA is the electron affinity. And the electronegativity χ_CL is proportional to the average of TAE, AAE = TAE_av, divided by Σn_i, the number of atomic valence‐shell electrons. χ_CL = 0.1813 TAE_av = 0.1813 AAE = 0.1813 TAE/Σn_i, = 0.1813 (Σn_iE_I + EA)/Σn_i. Further, the atomic valence orbital electronegativity can be also obtained from the TAE value of an atom. Some discussions were made on several special aspects such as scale of rare gases, comparisons with Pauling's and Allen's scales, etc.     

原子价壳层电子量子拓扑指数与元素电负性的关系

在基态原子价壳层电子隐核图的基础上, 基于拓扑化学原理以及原子价壳层电子结构特征, 构建了原子价壳层电子量子拓扑指数(AEI), 它对基态原子实现唯一性表征, 结合原子价壳层电子平均化能(∑n_iE_i/∑n_i)等参数, 建立了一套新的元素电负性标度: X_N＝－0.588710AEI₁＋0.761214AEI₂＋0.154982(∑n_iE_i/∑n_i)－0.080929. 该式给出了周期表中氢至镅共95种元素的电负性, 结果表明新电负性标度X_N与Pauling电负性标度颇为一致. 进一步从原子价轨道量子拓扑指数确定了sp, sp², sp³杂化轨道的电负性. 新标度在元素和物质的结构-性质研究中具有一定的适用性.     

Charge transfer and dispersion interaction stabilization of the D2h isomer of O4

The results of some minimal basis set valence bond calculations, with an antibonding midbond molecular orbital (π_m*) included, are reported for the D_2h isomer of O₄. The in-plane π_m*←π* excitations describe the charge transfer from each monomer, while the π*←π excitations on each monomer partially describe the intermolecular dispersive attractions. It is found that the charge-transfer interactions by themselves are insufficient to stabilize the S=0 spin D_2h dimer of O₄ relative to two O₂ monomers when a correction is included for basis set superposition error. The inclusion of both the charge transfer and dispersion terms yields an estimate of 14 cm⁻¹ for the binding energy (D_e) at an equilibrium separation (R_e) of 3.29 Å. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 129–134, 1998     

Theory of chemical bonds in metalloenzymes IV: Hybrid‐DFT study of Rieske‐type [2Fe?2S] clusters

The Rieske‐type [2Fe? 2S] cores of electron‐transfer (ET) proteins in the mitochondrial respiratory chain have unusual properties, such as redox potentials and spectroscopy. In this study, part IV of a series, the inherent molecular structures and characteristic electronic structures of the Rieske‐type [2Fe? 2S] clusters are investigated using broken‐symmetry hybrid density functional theory (BS‐HDFT). Geometry optimizations for the oxidized and reduced states were performed and their characteristic vibrational modes are assigned. Magnetic properties are investigated using model Hamiltonians to describe the electron delocalization and the unsymmetric property. The parameters of the model Hamiltonian, such as exchange coupling J, valence delocalization B, and potential energy difference Δ, are evaluated from the BS‐HDFT calculations. The valence localization and excitation energy (ΔE) of the Rieske‐type [2Fe? 2S] cluster are discussed. The chemical bond nature is characterized by chemical indices from natural orbital analysis. Our theoretical results are reasonably consistent with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The nature of the chemical bond in UO2

The nature of the chemical bond in UO₂ was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO₈ (D_4h) cluster, reflecting uranium's close environment in UO₂, and the U₁₃O₅₆ and U₆₃O₂₁₆ clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO₂ single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO₂ are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO₂ was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO₈ and by 25% in U₆₃O₂₁₆.     

2-氢吡喃分子光激发开环反应机理的理论研究

用完全活性空间多组态(CASSCF)方法对2-氢吡喃分子光激发开环反应机理进行了研究。利用价键理论(VB)和自然键道分析(NBO)探究了沿能量最低反应途径电子的重新分布情况。计算结果表明从S0-Min p®p*垂直激发到Franck-Condon点后很容易弛豫到S1-Min,经较低的势垒到达圆锥交叉点S1/S0。而S1/S0与S1-Min相比能量低0.63eV。这样体系沿非绝热最低反应途径从激发单重态经交叉点S1/S0很容易得到产物S0-Prod。     

Theoretical study of bifurcated hydrogen bonding effects on the 1J(N,H), 1hJ(N,H), 2hJ(N,N) couplings and 1H, 15N shieldings in model pyrroles

According to the density functional theory calculations, the X···H···N (X?N, O) intramolecular bifurcated (three‐centered) hydrogen bond with one hydrogen donor and two hydrogen acceptors causes a significant decrease of the ^1hJ(N,H) and ^2hJ(N,N) coupling constants across the N? H···N hydrogen bond and an increase of the ¹J(N,H) coupling constant across the N? H covalent bond in the 2,5‐disubsituted pyrroles. This occurs due to a weakening of the N? H···N hydrogen bridge resulting in a lengthening of the N···H distance and a decrease of the hydrogen bond angle at the bifurcated hydrogen bond formation. The gauge‐independent atomic orbital calculations of the shielding constants suggest that a weakening of the N? H···N hydrogen bridge in case of the three‐centered hydrogen bond yields a shielding of the bridge proton and deshielding of the acceptor nitrogen atom. The atoms‐in‐molecules analysis shows that an attenuation of the ^1hJ(N,H) and ^2hJ(N,N) couplings in the compounds with bifurcated hydrogen bond is connected with a decrease of the electron density ρ_H···N at the hydrogen bond critical point and Laplacian of this electron density ?²ρ_H···N. The natural bond orbital analysis suggests that the additional N? H···X interaction partly inhibits the charge transfer from the nitrogen lone pair to the σ*_{N? H} antibonding orbital across hydrogen bond weakening of the ^1hJ(N,H) and ^2hJ(N,N) trans‐hydrogen bond couplings through Fermi‐contact mechanism. An increase of the nitrogen s‐character percentage of the N? H bond in consequence of the bifurcated hydrogen bonding leads to an increase of the ¹J(N,H) coupling constant across the N? H covalent bond and deshielding of the hydrogen donor nitrogen atom. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

The bonding picture in hypervalent XF3 (X = Cl,Br, I,At) fluorides revisited with quantum chemical topology

Hypervalent XF₃ (X = Cl, Br, I, At) fluorides exhibit T‐shaped C_2V equilibrium structures with the heavier of them, AtF₃, also revealing an almost isoenergetic planar D_3h structure. Factors explaining this behavior based on simple “chemical intuition” are currently missing. In this work, we combine non‐relativistic (ClF₃), scalar‐relativistic and two‐component (X = Br − At) density functional theory calculations, and bonding analyses based on the electron localization function and the quantum theory of atoms in molecules. Typical signatures of charge‐shift bonding have been identified at the bent T‐shaped structures of ClF₃ and BrF₃, while the bonds of the other structures exhibit a dominant ionic character. With the aim of explaining the D_3h structure of AtF₃, we extend the multipole expansion analysis to the framework of two‐component single‐reference calculations. This methodological advance enables us to rationalize the relative stability of the T‐shaped C_2v and the planar D_3h structures: the Coulomb repulsions between the two lone‐pairs of the central atom and between each lone‐pair and each fluorine ligand are found significantly larger at the D_3h structures than at the C_2v ones for X = Cl − I, but not with X = At. This comes with the increasing stabilization, along the XF₃ series, of the planar D_3h structure with respect to the global T‐shaped C_2v minima. Hence, we show that the careful use of principles that are at the heart of the valence shell electron pair repulsion model provides reasonable justifications for stable planar D_3h structures in AX₃E₂ systems. © 2017 Wiley Periodicals, Inc.     

Tetracyclopenta[def,jkl,pqr,vwx]tetraphenylene: A Potential Tetraradicaloid Hydrocarbon

A tetramesityl derivative of hitherto unknown tetracyclopenta[def,jkl,pqr,vwx]tetraphenylene (TCPTP), which is a potential tetraradicaloid hydrocarbon, was synthesized. Theoretical calculations based on spin‐flip time‐dependent density functional theory predict that the closed‐shell D_2h form of TCPTP is more stable than the open‐shell D_4h form with its slightly tetraradical character. The tetramesityl derivative (Mes)₄‐TCPTP exhibits remarkable antiaromaticity as a result of the peripheral 20‐π‐electron circuit, which causes an absorption maximum at a long wavelength and a small HOMO–LUMO gap. In solution, (Mes)₄‐TCPTP most likely adopts rapidly equilibrating D_2h structures that interconvert via the D_4h transition state. X‐ray crystallographic analysis showed (Mes)₄‐TCPTP as an approximate D_2h structure.     

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S2N2 and Related 6π‐Electron Four‐Membered Rings E2N2 and E42+ (E=S,Se, Te)

A series of 6π‐electron 4‐center species, E₂N₂ and E₄²⁺ (E=S, Se, Te) is studied by means of ab initio valence bond methods with the aims of settling some controversies on 1) the diradical character of these molecules and 2) the radical sites, E or N, of the preferred diradical structure. It was found that for all molecules, the cumulated weights of the two possible diradical structures are always important and close to 50 %, making these molecules comparable to ozone in terms of diradical character. While the two diradical structures are degenerate in the E₄²⁺ dications, they have on the contrary strongly unequal weights in the E₂N₂ neutral molecules. In these three molecules, the electronic structure is dominated by one diradical structure, in which the radical sites are the two nitrogen atoms, while the other diradical structure is much less important. The ordering of the various VB structures in terms of their calculated weights is confirmed by the relative energies of individual VB structures. In all cases, the major diradical structure (or both diradical structures when they are degenerate) is (are) the lowest one(s), while the covalent VB structures lie higher in energy. The vertical resonance energies are considerable in S₂N₂ and S₄²⁺, about 80 % of the estimated value for benzene, and diminish as one goes down the periodic table (S→Se→Te). This confirms the aromatic character of these species, as already demonstrated for S₂N₂ on the basis of magnetic criteria. This and the high weights and stabilities of one or both diradical structures in all systems indicates that aromaticity and diradical character do not exclude each other, contrary to what is usually claimed. Furthermore, it is shown that the diradical structures find their place in a collective electron flow responsible for the ring currents in the π system of these species.     

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.     

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.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis

We provide a didactic introduction to 2nd-quantized representation of complex electron–hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance “weighting” that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φ_λ → φ_ν (creating an e/h excitation with h in φ_λ and e in φ_ν) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron “to be” or “not to be” in φ_ν must be rigorously linked to the complementary h-probabilities in φ_λ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.     

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.     

A New Conformation With an Extraordinarily Long, 3.04 Å Two‐Electron,Six‐Center Bond Observed for the π‐[TCNE]22− Dimer in [NMe4]2[TCNE]2 (TCNE=Tetracyanoethylene)

[NMe₄]₂[TCNE]₂ (TCNE=tetracyanoethenide) formed from the reaction of TCNE and (NMe₄)CN in MeCN has ν_CN IR absorptions at 2195, 2191, 2172, and 2156 cm^?1 and a ν_CC absorption at 1383 cm^?1 that are characteristic of reduced TCNE. The TCNEs have an average central C?C distance of 1.423 Å that is also characteristic of reduced TCNE. The reduced TCNE forms a previously unknown non‐eclipsed, centrosymmetric π‐[TCNE]₂^2? dimer with nominal C₂ symmetry, 12 sub van der Waals interatomic contacts <3.3 Å, a central intradimer separation of 3.039(3) Å, and comparable intradimer C???N distances of 3.050(3) and 2.984(3) Å. The two pairs of central C???C atoms form a ?C?C???C?C of 112.6° that is substantially greater than the 0° observed for the eclipsed D_2h π‐[TCNE]₂^2? dimer possessing a two‐electron, four‐center (2e^?/4c) bond with two C???C components from a molecular orbital (MO) analysis. A MO study combining CAS(2,2)/MRMP2/cc‐pVTZ and atoms‐in‐molecules (AIM) calculations indicates that the non‐eclipsed, C₂ π‐[TCNE]₂^2? dimer exhibits a new type of a long, intradimer bond involving one strong C???C and two weak C???N components, that is, a 2e^?/6c bond. The C₂ π‐[TCNE]₂^2? conformer has a singlet, diamagnetic ground state with a thermally populated triplet excited state with J/k_B=1000 K (700 cm^?1; 86.8 meV; 2.00 kcal mol^?1; H=?2 JS_a?S_b); at the CAS(2,2)/MBMP2 level the triplet is computed to be 9.0 kcal mol^?1 higher in energy than the closed‐shell singlet ground state. The results from CAS(2,2)/NEVPT2/cc‐pVTZ calculations indicate that the C₂ and D_2h conformers have two different local metastable minima with the C₂ conformer being 1.3 kcal mol^?1 less stable. The different natures of the C₂ and D_2h conformers are also noted from the results of valence bond (VB) qualitative diagram that shows a 10e^?/6c bond with one C???C and two C???N bonding components for the C₂ conformer as compared to the 6e^?/4c bond for the D_2h conformer with two C???C bonding components.