Quasi－aromaticity in Cluster Chemistry Ⅲ． Localized Molecular Orbital Study on Electron－rich Cobalt－sulfur Cluster Compounds ［Co_6（μ_3－X）_8L_6］~（n＋） （X＝S，Se；L＝PPh_3，PEt_3，CO；n＝0，1）

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用分子片轨道逐步剔除法研究电子离域

估计分子中不同类型的电子离域作用（如p-π → d-π和p-π → σ~*）的相 对强弱对理解分子中化学键的本质有关键的作用。剔除某一分子片轨道（d-π或σ ~*）后分子体系能量的改变可用来计算电子离域到该轨道的离域能。由于轨道之间 的相互作用,使离域能的计算与轨道剔除的次序有关。为克服这种不确定性,可以 逐步轮流增加某一对特定轨道（d-π和σ~*）的库仑积分,以使这对轨道在分子波 函数中的比重逐步减少,即将这对轨道轮流逐步剔除。这样可将轨道间的相互影响 减小以至消除,从而得到各轨道的精确的离域能。以H_3PO中P-O键为例说明了轨道 逐步剔除方法的应用。     

Frontier Orbital Control of Molecular Conductance and its Switching

For transmission of electrons through a π system, when the Landauer theory of molecular conductance is viewed from a molecular orbital (MO) perspective, there obtains a simple perturbation theoretic dependence, due to Yoshizawa and Tada, on a) the product of the orbital coefficients at the sites of electrode attachment, and b) the MO energies. The frontier orbitals consistently and simply indicate high or low transmission, even if other orbitals may contribute. This formalism, with its consequent reinforcement and/or interference of conductance, accounts for the (previously explained) difference in direct vs. cross conjugated transmission across an ethylene, as well as the comparative ON/OFF ratios in the experimentally investigated dimethyldihydropyrene and dithienylethene‐type single‐molecule switches. A strong dependence of the conductance on the site of attachment of the electrodes in a π system is an immediate extrapolation; the theory then predicts that for some specified sites the switching behavior will be inverted; i.e. the “open” molecular form of the switch will be more conductive.     

QR‐SCMEH‐MO calculations on the complex [Pt (SnCl3)5]3−: Electronic structure,UV–visible spectrum,magnetic properties,and bond energy

A molecular orbital study via the QR‐SCMEH‐MO (quasi‐relativistic self consistent modified extended H?ckel molecular orbital) method has been carried out on the unusual Pt 5‐ coordinated complex Pt (SnCl₃). The computed UV–Visible spectral data and NMR parameters are found to be in good agreement with the reported experimental values. In addition, the magnetic susceptibility and Pt? Sn bond energy have been calculated, although there are no reported experimental data with which to compare these results. Pt? Sn bond energies of other Pt‐SnX₃ (X = Cl, Br) systems and are compared with proposed bond energy trends based on NMR and observed bond distances. © 2012 Wiley Periodicals, Inc.     

Maximum Overlap Symmetry Molecular Orbital Calculation under CNDO／2 Approximation

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Localized molecular orbital studies on B_4C1_4,1,5-C_2B_3H_5 and B_nH_n~(2-)(n = 6-10, 12)

The wave functions, level energies and Mulliken population analysis of localized molecular orbitals (LMO's) for B4Cl4, 1,5-C2B3H5 and the closo-BnHn2- (n = 6-10, 12) are calculated by using the Edmiston-Reudenberg energy localization scheme under the CNDO/2 approximation in order to reveal the nature of quasi-aromaticity of the closo-BnHn2- (n > 5). It has been found that all the B-H or B-Cl LMO's are highly localized between the B and H (or Cl) atoms, corresponding to B-H or B-Cl o-bond, while the Bn framework bonding is formed mainly by the three-centered two-electron B-B-B bonds on the polyhedral faces. In the cases of B4Cl4 and 1,5-C2B3H5, these three-centered B-B-B bonds just fill their polyhedral faces; however, for the framework bonding of the closo-BnHn2- (n > 5), the valence electron deficiency leads to the delocalization of their three-centered B-B-B bonds, and as delocalizability of this three-centered B-B-B bond increases, some three-centered B-B-B bonds are further delocalized to become a f     

Revitalizing Spin Natural Orbital Analysis: Electronic Structures of Mixed-Valence Compounds,Singlet Biradicals,and Antiferromagnetically Coupled Systems

Chemical systems with open-shell electronic structure have been gaining attention these days. Their potential applications in first-row transition metal catalysis, molecular wires, photovoltaics and other potential applications have urged the adoption of a simple analysis tool to better understand their open-shell electronic structures, especially the role played by the unpaired electrons. Despite its lack of popularity, spin natural orbital (SNO) analysis is a tool we found to well-suit this purpose. We have therefore re-examined how the SNO could help us analyze some interesting open-shell systems, including mixed-valence compounds, singlet biradicals, and antiferromagnetically coupled systems. We found that some interesting patterns emerge from SNO analysis, especially those associated with exchange interaction. © 2019 Wiley Periodicals, Inc.     

Internal conrotation and disrotation in H2BCH2BH2 and diborylmethane 1,3 H exchange

The paths of correlated internal disrotation (barrier less than 0.4 kcal/mol) and conrotation (barrier around 1.9 kcal/mol) of the two BH₂ groups in H₂BCH₂BH₂ have been computed employing ab initio [MP2(full)/6–31G**] and density functional theory (Becke3LYP/6–311+G**) methods. Two B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative interactions stabilize the C_s symmetric H₂BCH₂BH₂ isomer ( 1 ). The B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative stabilization, evaluated by homodesmotic reactions and using the orbital deletion procedure (which “deactivates” the “vacant” born p orbital), is less than 6 kcal/mol in diborylmethane. The B(SINGLE BOND)C(DOTTED BOND)B(p) stabilization is shown to be remarkably large in C₄B₆H₁₀ (Td). At MP2(fu)/6–31G**, disproportionation into 1 and methane is only 5.6 kcal/mol exothermic. The 1,3 H exchange in diborylmethane is an asynchronous process and proceeds via a doubly bridged cyclic intermediate with 9.3 kcal/mol barrier. Structures with “planar tetracoordinate” carbon are stabilized considerably by BH₂ substituents, but they are still high in energy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1792–1803, 1997     

Transition‐Metal–Boron Intermetallics with Strong Interatomic d–sp Orbital Hybridization for High‐Performance Electrocatalysis

A theoretical and experimental study gives insights into the nature of the metal–boron electronic interaction in boron‐bearing intermetallics and its effects on surface hydrogen adsorption and hydrogen‐evolving catalytic activity. Strong hybridization between the d orbitals of transition metal (T_M) and the sp orbitals of boron exists in a family of fifteen T_M–boron intermatallics (T_M:B=1:1), and hydrogen atoms adsorb more weakly to the metal‐terminated intermetallic surfaces than to the corresponding pure metal surfaces. This modulation of electronic structure makes several intermetallics (e.g., PdB, RuB, ReB) prospective, efficient hydrogen‐evolving materials with catalytic activity close to Pt. A general reaction pathway towards the synthesis of such T_MB intermetallics is provided; a class of seven phase‐pure T_MB intermetallics, containing V, Nb, Ta, Cr, Mo, W, and Ru, are thus synthesized. RuB is a high‐performing, non‐platinum electrocatalyst for the hydrogen evolution reaction.     

原子轨道的函数表示及可视化

量子化学中,Gaussian型函数是常用的一种基组函数。但最初原子核外单电子波函数的解析解是Slater型函数。介绍了2者之间的差异,以及Gaussian型函数被广泛采用的原因。在介绍这些概念的同时,作者将所涉及的函数形式使用免费的绘图软件gnuplot进行可视化,并给出相应代码,以助于学生更好地理解物理概念以及抽象的数学形式。     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance‐dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short‐range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O???C=O interactions.     

Endohedral and Exohedral Metalloborospherenes: M@B40 (M=Ca,Sr) and M&B40 (M=Be,Mg)

The recent discovery of the all‐boron fullerenes or borospherenes, D_2d B₄₀^?/0, paves the way for borospherene chemistry. Here we report a density functional theory study on the viability of metalloborospherenes: endohedral M@B₄₀ (M=Ca, Sr) and exohedral M&B₄₀ (M=Be, Mg). Extensive global structural searches indicate that Ca@B₄₀ ( 1 , C_2v, ¹A₁) and Sr@B₄₀ ( 3 , D_2d, ¹A₁) possess almost perfect endohedral borospherene structures with a metal atom at the center, while Be&B₄₀ ( 5 , C_s, ¹A′) and Mg&B₄₀ ( 7 , C_s, ¹A′) favor exohedral borospherene geometries with a η⁷‐M atom face‐capping a heptagon on the waist. Metalloborospherenes provide indirect evidence for the robustness of the borospherene structural motif. The metalloborospherenes are characterized as charge‐transfer complexes (M²⁺B₄₀^2?), where an alkaline earth metal atom donates two electrons to the B₄₀ cage. The high stability of endohedral Ca@B₄₀ ( 1 ) and Sr@B₄₀ ( 3 ) is due to the match in size between the host cage and the dopant. Bonding analyses indicate that all 122 valence electrons in the systems are delocalized as σ or π bonds, being distributed evenly on the cage surface, akin to the D_2d B₄₀ borospherene.     

Structure and Bonding in Cyclic Sulfur-Nitrogen Compounds—Molecular Orbital Considerations

The molecular structures of monocyclic sulfur-nitrogen ring systems, such as S₂N₂, S₃N, S₄N and S₅N, can be considered as examples of electron rich (4n + 2)π systems. The structures of S₄N₄, S₄N, P₄S₄, As₄S₄ and the bicyclic structures S₄N, S₄N as well as S₅N₆ can be rationalized on the basis of a planar tetrasulfur tetranitride with 12π electrons.     

聚磷链和聚氮链的自洽场晶体轨道研究

利用自治场全略微分重叠晶体轨道方法(SCFCNDO/2-CO)对聚磷链和聚氮链的各种可能构型的稳定性、能带结构和电子特性进行了研究.结果表明,本征聚磷链为半导体,而本征聚氮链为绝缘体.     

Theoretical Definition of a Functional Group and the Molecular Orbital Paradigm

It is the purpose of this review to demonstrate that the empirical classification of the observations of chemistry in terms of the properties assigned to functional groups is a consequence of and is predicted by physics. This is accomplished by showing that the atoms and functional groups of chemistry can be identified with bounded space-filling objects whose properties are defined by quantum mechanics. The quantum mechanical definition of a group is combined with a new pictorial representation of its form to obtain a unified picture which should make it eminently recognizable to chemists. This picture, when combined with the demonstrated ability of these groups to recover the measured properties of atoms in molecules, is offered as one which meets the expectations a chemist associates with the concept of a functional group. The manner in which this physical definition of a group differs fundamentally from models of functional groups based upon molecular orbital theory is discussed.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

A further study on closo boron hydrides B16H2−16 (D2) and B16H16Td) using ab initio molecular orbital theory

Ab initio molecular orbital calculations of doubly negative charged B₁₆H^2?₁₆(D₂) and neutral B₁₆H₁₆(Td) have been done at the HF/6-31G level. They are predicted to be chemically and kinetically stable by vibrational analyses on their respective energy hypersurface of the HF/6-31G level. The geometrical structure of the species B₁₆H²₁₆ (D₂) was discussed.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

A further study on closo boron hydrides B_(16)H_(16)~(2-)(D_2) and B_(16)H_(16)(Td) using ab initio molecular orbital theory

Ab initio molecular orbital calculations of doubly negative charged B16H162-(D2) and neutral B16H16(Td) have been done at the HF/6-31G level.They are predicted to be chemically and kinetically stable by vibrational analyses on their respective energy hypersurface of the HF/6-31G level.The geometrical structure of the species B16H1622-(D2) was discussed.     

铌团簇和配合物的多面体分子轨道理论研究

应用多面体理论方法研究铌纯金属团簇和配合物的电子结构成键性质,并将理论预测结果用密度泛函方法验证.证实多面体理论是简便预测过渡金属簇,尤其是簇骨架电子结构的有效方法.铌的小团簇总是以低自旋密堆积结构为稳定构型,当体系的价电子数满足轨道成键数时,用该方法可较准确地推断成键性质(如Nb₄和[Nb₆Cl₁₂]⁺⁴);而对于不满足成键数的体系(如Nb₅和Nb₆),则可利用该理论分析畸变趋势.