Explaining the effects of T-O-T bond angles on NMR chemical shifts in aluminosilicates: A natural bonding orbital (NBO) and natural chemical shielding (NCS) analysis

It has long been recognized that the 29Si and 27Al NMR chemical shifts for aluminosilicate crystals and glasses correlate to some extent with the T-O-T bond angle (where T is the tetrahedral atom Si or Al). With increasing T-O-T bond angle, the 29Si and 27Al NMR shieldings increase and the shifts thus become more negative. This result has been demonstrated both experimentally and through quantum computations. However, no simple qualitative explanation has ever been given for what appears to be a simple qualitative trend. We here provide such an explanation based upon quantum calculations. We have used high level ab initio NMR shielding calculations, natural bonding orbital (NBO) analysis, and natural chemical shielding (NCS) analysis, performed on model clusters with different T-O-T angles, to obtain an explanation for this trend from an electronic structure point of view. On the basis of both NBO populations and the NCS analysis, the following factors account for the correlation of shift with T-O-T angle: (1) a slight increase in population of the Al-O and Si-O bond orbital electrons and a dramatic change in bond orbital shapes and hybridization (with more s character and less bond bending as the T-O-T angle increases), (2) a movement of one of the lone pairs on O toward the vicinity of the Si or Al as the T-O-T angle increases, and (3) a change in the shielding contribution from the core 2p electrons of Al or Si. The changes in the 17O NMR shift with T-O-T angle are more complex, and the shifts are also more strongly influenced by distant atoms, but some systematic changes in O lone pair contributions can be identified.     

Unpaired electrons,spin polarization,and bond orders in radicals from the 2‐RDM in orbital spaces: Basic notions and testing calculations

Adopting the second‐order reduced density matrix level, the conventional α‐ and β‐spin populations in radicals are split into paired and unpaired or electropon (referring to the simultaneous occurrence of an electron and a hole of opposite spins in an orbital) populations. This analysis gives the possibility to distinguish the (un)favorable for chemical bonding electronic interactions by means of positive or negative Coulomb and/or Fermi correlations of two electropons. To overcome the conceptual difficulties originated from the subtle superposition of unpaired electrons due to spin density and those responsible for chemical bonding, we use the notion of properly unpaired electrons. The quantity describing this notion provides a global picture for the ability of electrons of a given orbital to form covalent bonds with the electrons of all remaining orbitals. More detailed information, concerning the behavior of electrons in two distinct target orbitals, is obtained by means of the two‐electropon correlations. As shown, the boundary values of the used quantities are physically meaningful, and the whole theory is tested from various points of view concerning: localized and delocalized radical centers, orthogonal and nonorthogonal orbitals, uncorrelated and correlated levels, Coulomb and Fermi correlations. We also check the electropon based analysis by investigating the spin polarization effects and bond orders in radicals. The tests are achieved for well‐known radicals, and to preserve the stability of the numerical results and the invariance of the obtained conceptual pictures, we used natural basis sets introduced within the natural bond orbital methodology. © 2014 Wiley Periodicals, Inc.     

取代基对N—H…O＝C氢键三聚体中氢键强度的影响

使用MP2方法研究了氢键三聚体中N-H…O=C氢键强度,探讨了氢键受体分子中不同取代基对N-H…O=C氢键强度的影响.研究表明,不同取代基对氢键三聚体中N-H…O=C氢键强度的影响是不同的:取代基为供电子基团,氢键键长r(H…O)缩短,氢键强度增强;取代基为吸电子基团,氢键键长r(H…O)伸长,氢键强度减弱.自然键轨道(NBO)分析表明,N-H…O=C氢键强度越强,氢键中氢原子的正电荷越多,氧原子的负电荷越多,质子供体和受体分子间的电荷转移越多.供电子基团使N-H…O=C氢键中氧原子的孤对电子n(O)对N-H的反键轨道σ~*(N-H)的二阶相互作用稳定化能增加,吸电子基团使这种二阶相互作用稳定化能减小.取代基对与其相近的N-H…O=C氢键影响更大.     

Correspondence on “Core Electron Topologies in Chemical Compounds: Case Study of Carbon versus Silicon”

The conclusions of a recent Communication of Yoshida, Raebiger, Shudo, and Ohno published in this journal, that varying core orbital topologies with minuscule negative tails upon bond formation determine the different chemistries of carbon and silicon and affect ionization energies, excitation energies and bond properties of molecules, are now shown to be based on computational artifacts and oversimplified models. The all‐electron wave function uniquely determines the observables, while its representation by one‐electron orbital products depends on the details of the chosen approximation and therefore need to be considered with great care.     

Simulation of scanning tunneling microscope images of 1,3-cyclohexadiene bound to a silicon surface

Scanning tunneling microscope (STM) images of 1,3-cyclohexadiene bound to silicon are interpreted using a nonequilibrium Green's function method. The resolution of the carbon-carbon double bond for positive bias voltages but not for negative bias voltages is explained using a quasiprobability density analysis. The asymmetry in the images arises from the system's voltage dependent electronic structure. A pi* orbital is found to be responsible for the empty state STM images of the carbon-carbon double bond, which is observed experimentally. The pi orbital relevant for the opposite bias does not produce an STM image sharply localized in the bond region because the molecule induces a Si-surface dipole dependent on the bias. The dipole voltage dependence arises from molecular charging. This result emphasizes the importance of simulating the molecule as an element in an open quantum system.     

Removing electrons can increase the electron density: a computational study of negative Fukui functions

Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.     

Hydrogen bond and halogen bond inside the carbon nanotube

The hydrogen bond and halogen bond inside the open-ended single-walled carbon nanotubes have been investigated theoretically employing the newly developed density functional M06 with the suitable basis set and the natural bond orbital analysis. Comparing with the hydrogen or halogen bond in the gas phase, we find that the strength of the hydrogen or halogen bond inside the carbon nanotube will become weaker if there is a larger intramolecular electron-density transfer from the electron-rich region of the hydrogen or halogen atom donor to the antibonding orbital of the X-H or X-Hal bond involved in the formation of the hydrogen or halogen bond and will become stronger if there is a larger intermolecular electron-density transfer from the electron-rich region of the hydrogen or halogen atom acceptor to the antibonding orbital of the X-H or X-Hal bond. According to the analysis of the molecular electrostatic potential of the carbon nanotube, the driving force for the electron-density transfer is found to be the negative electric field formed in the carbon nanotube inner phase. Our results also show that the X-H bond involved in the formation of the hydrogen bond and the X-Hal bond involved in the formation of the halogen bond are all elongated when encapsulating the hydrogen bond and halogen bond within the carbon nanotube, so the carbon nanotube confinement may change the blue-shifting hydrogen bond and the blue-shifting halogen bond into the red-shifting hydrogen bond and the red-shifting halogen bond. The possibility to replace the all electron nanotube-confined calculation by the simple polarizable continuum model is also evaluated.     

取代基对N-H…O=C氢键三聚体中氢键强度的影响

使用MP2方法研究了氢键三聚体中N—H…O=C氢键强度, 探讨了氢键受体分子中不同取代基对N—H…O=C氢键强度的影响. 研究表明, 不同取代基对氢键三聚体中N—H…O=C氢键强度的影响是不同的: 取代基为供电子基团, 氢键键长r(H…O)缩短, 氢键强度增强; 取代基为吸电子基团, 氢键键长r(H…O)伸长, 氢键强度减弱. 自然键轨道(NBO)分析表明, N—H…O=C氢键强度越强, 氢键中氢原子的正电荷越多, 氧原子的负电荷越多, 质子供体和受体分子间的电荷转移越多. 供电子基团使N—H…O=C氢键中氧原子的孤对电子n(O)对N—H的反键轨道滓*(N—H)的二阶相互作用稳定化能增加, 吸电子基团使这种二阶相互作用稳定化能减小. 取代基对与其相近的N—H…O=C氢键影响更大.     

Classical chemical concepts from ab initio SCF calculations

Alternative definitions of bond order, valency, gross orbital populations and total atomic charge for SCF wavefunctions are compared. It is found that there are sound theoretical and numerical reasons for preferring definitions based on the Löwdin density matrix.     

Bond types of molecular orbitals and the photoelectron spectrum

The vibrational structures of the photoelectron spectra for diatomic molecules can be accounted for in terms of the slope of the orbital energy curve in the conventional correlation diagram with respect to internuclear distance. The vibrational structures of the photoelectron spectra for simple polyatomic molecules HCN, C₂H₂, and AH₂ type of hydrides can also be accounted for in terms of the slopes of the orbital energy curves in the correlation diagrams with respect to angles, as well as distances. Among all correlation diagrams, the slopes in the distance correlation diagram are related to the criterion for bond type—the positive for “bonding,” the negative for “antibonding,” while slopes with small magnitudes for “nonbonding.” The Fock matrix elements within the bond orbital basis provide heuristic and systematic rationalization of the slopes for the orbital energy curves. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 53–65, 2001     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Substituent effects and the role of negative hyperconjugation in siloxycarbene rearrangements

Substituent effects and the role of negative hyperconjugation in 1,2-silyl migration and decarbonylation of methoxy(substituted-siloxy)carbenes have been investigated using quantum chemical calculations and natural bond orbital analysis. It has been found that sigma-electron-withdrawing substituents generally lower the barriers for 1,2-silyl migration and decarbonylation, consistent with symmetry-forbidden concerted rearrangements involving intramolecular front-side nucleophilic attack by the carbene lone pair at silicon and by the methoxy oxygen at silicon, respectively. However, while good linear Hammett correlations are obtained for 1,2-silyl migration, those obtained for decarbonylation are poor. In addition, there appears to be a relationship between the extent of pertinent hyperconjugative interactions in the siloxycarbene conformers and the ease of intramolecular reactivity. As a matter of fact, the finding that 1,2-silyl migration is more favorable than decarbonylation seems to be primarily related to stronger negative hyperconjugation between the carbene lone pair and the O-Si antibonding orbital, compared to that between the methoxy oxygen n(sigma) lone pair and the O-Si antibonding orbital. Moreover, the activation enthalpies for 1,2-silyl migration decrease linearly with stronger negative hyperconjugation, although no such correlation could be established for decarbonylation.     

An Insight of the Results Provided by Color‐Tuning Studies Made on Ir(III) Complexes: A pi‐Neutral CF3 Group Viewed by Adjusting Energies of pi‐type Molecular Orbitals

The pi‐nature of a CF₃ group can be understood through analysis of its bond orbitals (BOs) mixed into the pi‐type molecular orbitals of CF₃‐substituted Ir(ppy)₂MDPA⁺ complexes (ppy=2‐phenyl‐pyridine and MDPA=methylated 2,2′‐dipyridyl amine). It has been found that, through this natural bond orbital analysis, the parent’s molecular orbitals (MOs) can be stabilized by χρ^*_CF BO via negative hyperconjugation and, simultaneously, destabilized by electron lp(F) BO. Since these two competing pi‐effects are virtually counterbalanced as indicated by the vanishing values of crystal orbital overlap populations, the chemical substitution strategy originated from lowering of HOMO by using this electron‐withdrawing CF₃ group has been found effective in color‐tuning to blue region. Based on reduced shielding effect due to de‐ creased χρ‐electron density, the reported position dependent CF₃‐substitution effects on pi‐type MOs can also be understood through HOMO/LUMO wavefunction analysis.     

Valency and molecular structure

Valency is defined for each molecular orbital. The molecular orbital valency values are shown to be a good measure of the bonding nature of the molecular orbital. Comparisons are made with photoelectron spectral studies and Mulliken overlap population analysis.The variation of molecular valency and molecular orbital valency with bond angle is studied. It is found that for all the molecules presently considered, energy is linearly related to valency and that the molecular valency reaches a maximum at the equilibrium bond angle. It is also shown that the molecular orbital valency can serve as a quantitatively reliable ordinate for Mulliken-Walsh diagrams.     

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding,and coulomb and fermi correlations in closed shell systems

The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.     

On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

氯化钕异丙醇配合物的电子结构与络合活化的研究

本文用INDO方法计算了氯化钕异丙醇配合物的电子结构。计算结果指出, 配位后, 与Nd-Cl键对应的分子轨道能量升高, Nd-Cl键级降低, Nd的正电荷降低, Cl的负电荷增多。从而表明。由于配位发生轨道重迭, 使得异丙醇氧的孤对电子移向钕离子的空价轨道。钕离子上的电子云密度增高加强了对Nd—Cl键的价电子的推斥作用, 使Nd-Cl间的价电子密度减小, 导致Nd-Cl键的削弱, 降低了键的能量, 有效地活化了Nd-Cl键,有利于生成活性物种的烷基化反应的进行。同时表明, 对Nd-Cl的络合催化有某种选择性。     

元素掺杂对VH2解氢性能的影响

采用密度泛函理论（DFT）的第一性原理的平面波超软赝势方法,研究了Zr、Cu、Zn掺杂对VH2的电子结构和解氢性能的影响．计算结果显示Zr掺杂VH2后晶体模型的负合金形成热增加和费米能级目处电子浓度N（Ef）的减少,体系结构稳定性增强;V—H之间重叠集居数和电子密度计算也显示V-H之间相互作用增强;表明在VH2中掺杂Zr以后吸放氢最大容量增加,但解氢能力减弱．而Cu或Zn掺杂VH2以后晶体模型的负合金形成热减少和费米能级Ef处电子浓度N（Ef）增加,体系结构稳定性减弱;V-H之间重叠集居数和电子密度计算也显示V-H之间相互作用减弱;表明在VH2中掺杂Cu或Zn以后吸放氢最大容量降低,但解氢能力增强．与实验结论相符．同时Mulliken集居数计算结果还显示V-d轨道MuUiken集居数与掺杂有关,掺杂Zr以后V—d轨道Mulliken集居数减少;掺杂Cu或Zn以后V—d轨道Mulliken集居数增加．