Localized molecular orbital studies of transition metal complexes. II: Simple π-accepting ligands

Localized molecular orbitals (LMOs) for several octahedral complexes are presented. Wavefunctions are calculated within the PRDDO approximations and localized by the Boys criterion. Complexes of general formula (NH₃)_x(CO)_6-xM, M = Cr⁰ or Mn⁺ and x = 1, 2, or 3 illustrate the general trends for carbonyl complexes. Weak to moderate π-bonding results in three equivalent inner shell LMOs dominantly of metal 3s, 3p and 3d character but highly delocalized to the carbonyls. These three LMOs flank the M-CO bond axis. Other π back-bonding situations result in metal-ligand double bonds which are nonequivalent and have σ-π separability [(NH₃)₅(py)Mn⁺] and also equivalent double bonds [(NH₃)₅(NO)Cr⁺].     

Localized molecular orbitals and chemical binding in five-membered heterocycles. II

The localized molecular orbitals (LMOs) of thiophene, furan, and pyrrole are derived from ab initio 4-31G wavefunctions using Boys' criteria for localization. From the transferability point of view, these LMOs are classified as (i) completely different and nontransferable LMOs (these are the lone-pair orbitals on O and N on one hand and those on S on the other hand), (ii) chemically similar lone pairs and inner shells on O and N (of furan and pyrrole, respectively), and (iii) chemically equivalent C? C, C?C, and C? H LMOs in the three heterocycles. The sp³ hybridization of the L core of sulfur, its appreciable polarization, and considerable involvement in bonding in the C? S bond region have been discussed. The present investigation indicates the limitation of the application of semiempirical MO methods to molecules that contain second-row atoms due to both the appreciable core—valence and π-σ interactions involving such atoms. Qualitative investigation of aromaticity and reactivity of the studied heterocycles agrees satisfactorily with experimental observations and shows that conclusions drawn based solely on static factor considerations (charge distribution in the noninteracting molecules) might very well be misleading and such factors determine the ease rather than the final orientation of the substituent.     

线形碳元素簇合物的成键性质

在ab initio 3-21G水平上, 用能量梯度法优化了线性碳元素簇合物C_n~e(n为成簇原子个数, e为电荷)的平衡几何结构. 所得的电离势随成簇原子个数的改变, 呈现出不同程度的奇偶交替变化趋势. 在ab initio计算基础上, 用Boys方法, 对其占据正则分子轨道进行定域化变换, 得到了它们的定域分子轨道. 对定域分子轨道性质的分析表明, 线性碳元素簇合物中, 主要键型有双中心σ和π健, 双中心弯键和三中心香蕉健, 以及多中心σ和π健. 这种键型的多样化可视为小元素簇的成健特征. 此外, 通过对其成键性质的分析, 讨论了线性碳元素簇的稳定性. 对于小碳元素簇, 化学键的共轭性对其稳定性具有十分显著的作用.     

A localized molecular-orbital assembler approach for Hartree-Fock calculations of large molecules

We describe an alternative fragment-based method, the localized molecular-orbital assembler method, for Hartree-Fock (HF) calculations of macromolecules. In this approach, a large molecule is divided into many small-size fragments, each of which is capped by its local surroundings. Then the conventional HF calculations are preformed on these capped fragments (or subsystems) and the canonical molecular orbitals of these systems are transferred into localized molecular orbitals (LMOs). By assembling the LMOs of these subsystems into a set of LMOs of the target molecule, the total density matrix of the target molecule is constructed and correspondingly the HF energy or other molecular properties can be approximately computed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations with double-zeta and polarized double-zeta basis sets demonstrate that the present approach is able to reproduce the conventional HF energies within a few millihartrees for a broad range of molecules.     

Linear scaling local correlation approach for solving the coupled cluster equations of large systems

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.     

Analysis of Proton NMR in Hydrogen Bonds in Terms of Lone‐Pair and Bond Orbital Contributions

NMR spectroscopic parameters of the proton involved in hydrogen bonding are studied theoretically. The set of molecules includes systems with internal resonance‐assisted hydrogen bonds, internal hydrogen bonds but no resonance stabilization, the acetic acid dimer (AAD), a DNA base pair, and the hydrogen succinate anion (HSA). Ethanol and guanine represent reference molecules without hydrogen bonding. The calculations are based on zero‐point vibrationally averaged molecular structures in order to include anharmonicity effects in the NMR parameters. An analysis of the calculated NMR shielding and J‐coupling is performed in terms of “chemist’s orbitals”, that is, localized molecular orbitals (LMOs) representing lone‐pairs, atomic cores, and bonds. The LMO analysis associates some of the strong de‐shielding of the protons in resonance‐assisted hydrogen bonds with delocalization involving the π‐backbone. Resonance is also shown to be an important factor causing de‐shielding of the OH protons for AAD and HSA, but not for the DNA base pair. Nitromalonamide (NMA) and HSA have particularly strong hydrogen bonds exhibiting signs of covalency in the associated J‐couplings. The analysis results show how NMR spectroscopic parameters that are characteristic for hydrogen bonded protons are influenced by the geometry and degree of covalency of the hydrogen bond as well as intra‐ and intermolecular resonance.     

Approximate Self-Consistent Molecular Orbital Method and Repulsive Bonding of Monocarbocyclic Π System

Zero differential overlap (ZDO) approximation^1,2) and the consideration of long range (meta and para bonds etc) bonding are applied in this semiempirical LCAO-SCF MO method. Effective Huckel type formulation and diagonalization procedure of symmetry adapted analysis simplify the computational procedure as well as give a clear and intuitive localized bonding behavior of the carbocyclic molecules. The long range repulsive bonds are defined and discussed between aromatic and non-aromatic cases. Such bonds are closely correlated to the rigidity and distortion of ring systems. Benzene is the most stable species among the 6π electron systems, and there will be some new explanation of Dewar resonance structures due to the consideration of long range para repulsive bonds in this work.     

Balancing Donor-Acceptor and Dispersion Effects in Heavy Main Group Element π Interactions: Effect of Substituents on the Pnictogen⋅⋅⋅π Arene Interaction

High-level ab initio calculations using the DLPNO-CCSD(T) method in conjunction with the local energy decomposition (LED) were performed to investigate the nature of the intermolecular interaction in bismuth trichloride adducts with π arene systems. Special emphasis was put on the effect of substituents in the aromatic ring. For this purpose, benzene derivatives with one or three substituents (R=NO₂, CF₃, OCHO, OH, and NH₂) were chosen and their influence on donor-acceptor interaction as well as on the overall interaction strength was examined. Local energy decomposition was performed to gain deeper insight into the composition of the interaction. Additionally, the study was extended to the intermolecular adducts of arsenic and antimony trichloride with benzene derivatives having one substituent (R=NO₂ and NH₂) in order to rationalize trends in the periodic table. The analysis of natural charges and frontier molecular orbitals shows that donor-acceptor interactions are of π→σ* type and that their strength correlates with charge transfer and orbital energy differences. An analysis of different bonding motifs (Bi⋅⋅⋅π arene, Bi⋅⋅⋅R, and Cl⋅⋅⋅π arene) shows that if dispersion and donor-acceptor interaction coincide as the donor highest occupied molecular orbital (HOMO) of the arene is delocalized over the π system, the M⋅⋅⋅π arene motif is preferred. If the donor HOMO is localized on the substituent, R⋅⋅⋅π arene bonding motifs are preferred. The Cl⋅⋅⋅π arene bonding motif is the least favorable with the lowest overall interaction energy.     

Nature of Bonding in Bowl‐Like B36 Cluster Revisited: Concentric (6π+18π) Double Aromaticity and Reason for the Preference of a Hexagonal Hole in a Central Location

The bowl‐shaped C_6v B₃₆ cluster with a central hexagon hole is considered an ideal molecular model for low‐dimensional boron‐based nanosystems. Owing to the electron deficiency of boron, chemical bonding in the B₃₆ cluster is intriguing, complicated, and has remained elusive despite a couple of papers in the literature. Herein, a bonding analysis is given through canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The concerted computational data establish the idea of concentric double π aromaticity for the B₃₆ cluster, with inner 6π and outer 18π electron counting, which both conform to the (4n+2) Hückel rule. The updated bonding picture differs from existing knowledge of the system. A refined bonding model is also proposed for coronene, of which the B₃₆ cluster is an inorganic analogue. It is further shown that concentric double π aromaticity in the B₃₆ cluster is retained and spatially fixed, irrespective of the migration of the hexagonal hole; the latter process changes the system energetically. The hexagonal hole is a destabilizing factor for σ/π CMOs. The central hexagon hole affects substantially fewer CMOs, thus making the bowl‐shaped C_6v B₃₆ cluster the global minimum.     

The interaction of chemical bonds. III. Perturbed strictly localized geminals in LMO basis

The formalism of strictly localized geminals (SLGs ) is summarized. It is shown that the SLG wave function serves as an appropriate multiconfigurational reference state that can easily be improved by perturbational, CI - or coupled cluster-type procedures. The possibility of expanding the geminals in the basis set of localized Hartree-Fock molecular orbitals (LMOs ) is discussed. Sample calculations on H₄, CH₄, H₂O, and He…?He systems are reported. © 1994 John Wiley & Sons, Inc.     

Density functional study of platinum polyyne monomer,oligomer, and polymer: Ground state geometrical and electronic structures

Geometries of monomers and oligomers of a platinum polyyne and its free ligands were optimized using density functional theory with B3LYP hybrid functional. The LANL2DZ basis set was used for Pt and the 6‐31G* for other atoms in geometry optimizations. The electronic structures of these compounds were analyzed using Stuttgart/Dresden ECPs (SDD) basis set for metal atoms and 6‐311G* for others. The polymerization has very little effect on the bond lengths and by introducing the metal, the acetylide bond length increases slightly. The strong overlap between metal sp_x orbitals and σp_x orbitals of acetylides results in localized σ bonding. The hybridization between the ligand pπ orbitals and the platinum dπ orbital resulted in the π‐conjugation enhancement. This conjugation enhancement causes some effects such as the highest‐occupied molecular orbital–lowest‐unoccupied molecular orbital gap reduction and charge transfer characteristic of low‐energy vertical transitions. © 2013 Wiley Periodicals, Inc.     

含三重键有机小分子定域分子轨道的理论研究

为了能够应用定域分子轨道(LMO)模型计算链状有机大分子的光电子能谱,我们已做了一系列工作。本文是用STO-3G基组和Foster-Boys LMO程序,采用文中的计算方法,对含H、C、N和O原子及单,双和叁键的近20个有机小分子进行研究,得到了它们     

Efficiency of perturbation‐selection and its orbital dependence in the SAC‐CI calculations for valence excitations of medium‐size molecules

The efficiency and accuracy of the perturbation‐selection used in the symmetry‐adapted cluster‐configuration interaction (SAC‐CI) calculations are investigated for several low‐lying valence excited states of 21 medium‐size molecules, including typical chromophores with heterocyclic macrocycles (free‐base porphine, coumarin, indole, and BODIPY), nucleobases, amino acids (tyrosine and tryptophan), polycyclic aromatic hydrocarbons, and organometallics (ferrocene and Re(bpy) ). Benchmark SAC‐CI calculations with up to 110 million operators are performed. The efficiency of the perturbation‐selection depends on the molecular orbitals (MOs); therefore, the canonical MO and localized MO (LMO) obtained by Pipek‐Mezey's method are examined. Except for the highly symmetric molecules, using LMOs improves the efficiency and accuracy of the perturbation‐selection. With using LMOs and perturbation‐selection, sufficiently reliable results can be obtained in less than 10% of the computational costs required for the full‐dimensional calculations. The perturbation‐selection with LMOs is suggested to be a promising method for excited states in larger molecular systems. Copyright © 2014 Wiley Periodicals, Inc.     

New Element-Carbon (p-p)π Bonds

Recent years have seen the preparation of π systems containing novel (p-p)π bonds between carbon and elements from the third, fourth, and fifth Main Groups of the Periodic Table; most of these compounds are predicted to be incapable of existence according to the classical concepts of the double bond. (p-p)π. Bonds between carbon and phosphorus, arsenic, and antimony have been successfully stabilized in resonance-stabilized colored compounds of the cyanine and triphenylmethane type, and also in aromatic systems deriving from benzene, naphthalene, and anthracene. Bismuth-carbon and boron-carbon (p-p)π bonds have likewise been confirmed in aromatic systems. Silicon-carbon and germanium-carbon (p-p)π bonds have been detected in extremely reactive derivatives of silaethylene and germaethylene, respectively. The present report describes characteristic reactions of the new π systems. Their bonding follows from X-ray structure analysis, from photoelectron, UV, and NMR spectra, and from calculations. Criteria for the existence of π systems which are not allowed by the classical double bond rule are discussed; these criteria remain valid on generalization.     

Nature of the chemical bonding in D3h [MH3M]+ cations (M = Be,Mg)

Motivated by the particularly short metal-metal distance that has been predicted for the D_3h [BeH₃Be]⁺ cation, comparable to those anticipated for triple bonds, we investigate the nature of the bonding interactions in the D_3h [MH₃M]⁺ cations (M = Be, Mg). CCSD(T)/cc-pVQZ calculations are used to determine optimized geometries for all of the various species, including those “capped” by He or Ne atoms (as proxies for an inert gas matrix). The primary tools that are then used to investigate the nature of the chemical bonding are spin-coupled generalized valence bond calculations and the analysis of localized natural orbitals and of domain-averaged Fermi holes. The various results for all of the systems considered indicate the presence of highly polar three-center two-electron M─H─M bonding character instead of any significant direct metal-metal bonding.     

Derivation of ligand σ- and π-bonding parameters from density functional theoretical calculations and Bursten ligand additivity relationships

New ligand additivity equations, based on the Bursten model, describing dπ orbital energies in square-planar and square–pyramidal complexes are proposed and tested for hypothetical binary Cr(0) and Mn(I) complexes of CO and CNMe. Density functional theory calculations are used to calculate the energies of dπ orbitals of binary octahedral, square–planar, and square–pyramidal d⁶ complexes of Mn(I) and Cr(0). Combination of the modified equations for unsaturated species with Bursten’s original equations for octahedral species allows for calculation of individual ligand bonding parameters and the separation of σ- and π-bonding effects. The calculated parameters provide interesting insight into the nature of metal–ligand bonding in the species studied. The method of separating σ- and π-bonding effects, applied here to CO and CNMe, is proposed as general method for solution of the Bursten equations for low-spin d⁶ octahedral systems.     

The nido‐Cage⋅⋅⋅π Bond: A Non‐covalent Interaction between Boron Clusters and Aromatic Rings and Its Applications

Non‐covalent interactions involving multicenter multielectron skeletons such as boron clusters are rare. Now, a non‐covalent interaction, the nido‐cage???π bond, is discovered based on the boron cluster C₂B₉H₁₂^? and an aromatic π system. The X‐ray diffraction studies indicate that the nido‐cage???π bonding presents parallel‐displaced or T‐shaped geometries. The contacting distance between cage and π ring varies with the type and the substituent of the aromatic ring. Theoretical calculations reveal that this nido‐cage???π bond shares a similar nature to the conventional anion???π or π???π bonds found in classical aromatic ring systems. This nido‐cage???π interaction induces variable photophysical properties such as aggregation‐induced emission and aggregation‐caused quenching in one molecule. This work offers an overall understanding towards the boron cluster‐based non‐covalent bond and opens a door to investigate its properties.