One-electron versus electron-electron interaction contributions to the spin-spin coupling mechanism in nuclear magnetic resonance spectroscopy: analysis of basic electronic effects

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. (1)J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas (2)J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of (1)J(C,H) and (2)J(H,H), respectively, for hydrocarbons.     

Orbital magnetism in finite size systems

The orbital magnetism in atoms is described in terms of Larmor diamagnetic and van Vleck paramagnetic contributions. The orbital magnetism in metals is described by Landau diamagnetism. Here, a discussion of the intermediate, mesoscopic regime is presented using a simple free-particle-in-a-box approximation. It is argued that, in general, one cannot separate Larmor and van Vleck contributions, and that the total susceptibility is expected to be small. The conclusions are illustrated on some experimental results.     

Natural J-coupling analysis: interpretation of scalar J-couplings in terms of natural bond orbitals.

The natural J-coupling (NJC) method presented here analyzes the Fermi contact portion of J-coupling in the framework of finite perturbation theory applied to ab initio/density function theory (DFT) wave functions, to compute individual and pairwise orbital contributions to the net J-coupling. The approach is based on the concepts and formalisms of natural bond orbital (NBO) methods. Computed coupling contributions can be classified as Lewis (individual orbital contributions corresponding to the natural Lewis structure of the molecule), delocalization (resulting from pairwise donor-acceptor interactions), and residual repolarization (corresponding to correlation-like interactions). This approach is illustrated by an analysis of the angular and distance dependences of the contributions to vicinal (3)J(HH) couplings in ethane and to the long-range (6)J(HH) couplings in pentane. The results indicate that approximately 70% or more of the net J-coupling is propagated by steric exchange antisymmetry interactions between Lewis orbitals (predominantly sigma bonding orbitals). Hyperconjugative sigma to sigma delocalization interactions account for the remainder of the coupling. Calculated pairwise-steric and hyperconjugative-delocalization energies provide a means for relating coupling mechanisms to molecular energetics. In this way, J-coupling contributions can be related directly to the localized features of the molecular electronic structure in order to explain measured J-coupling patterns and to predict J-coupling trends that have yet to be measured.     

Ca2B2O5的电子结构和能带结构

合成了标题化合物,在已测晶体结构的基础上,利用含组态作用的INDO/S方法计算了其他电子能带结构;利用态求和方法计算了微结构分子的线性极化率及其晶体的平均折射率。分析结果表明,价带主要由B^3^+和O^2^-离子的价轨道的贡献,导带底部主要由Ca^2^+离子轨道的贡献,从O^2^-离子到Ca^2^+离子的电荷转移对线性极化率起主要贡献。     

Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.     

Floating spherical Gaussian orbital model study of average electric polarisabilities and magnetic susceptibilities: Some aliphatic hydrocarbons

Floating spherical Gaussian orbital model is used to discuss the average electric polarisabilities and magnetic susceptibilities of a series of hydrocarbons. It has been noticed that the core contributions are negligibly small and these quantities (average electric polarisabilities and magnetic susceptibilities) can be well estimated from contributions localised on bond Gaussians.     

Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis

We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.     

What do kinetic-energy anisotropies tell us about chemical bonding? I. Diatomic hydrides

The kinetic-energy anisotropies of fifteen diatomic hydrides AH with A = H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl are calculated from self-consistent-field wave functions constructed from extended basis sets of Slater-type orbitals. It is found that there is no consistent ordering of the bond-parallel and bond-perpendicular components of the kinetic energy with respect to separated atom values. An analysis of the orbital contributions reveals that nonbonding π orbitals make large contributions to the total kinetic-energy anisotropy. This makes it difficult, if not impossible, to deduce anything about the nature of the chemical bond from the total anisotropy. However, certain dimensionless orbital kinetic-energy anisotropies are useful for interpretative studies because, in free atoms, these quantities have fixed values that depend only on the symmetry of the orbital.     

An energy-decomposition technique for the analysis of band structure and its application to polyphosphazene and its halogenated derivatives

An energy-decomposition technique is presented for the analysis of band structures of polymers and is applied to the π orbitals of polyphosphazene and its halogenated derivatives. In this treatment the orbital energy is decomposed into the contributions from individual atoms and bonds in the structure. Thereby, the shape of the energy band is elucidated as a function of atomic orbital interactions as well as structures of polymers. The trends of the k dependences for the individual contributions thus analyzed are consistent with those to be expected from the characters of the crystal orbitais. This method seems to be suitable for determining the effects of various substituents on the shape of the energy bands of polymers.     

Fluorine nuclear spin coupling constants in fluoro-substituted furans

In order to assist experimental assignments in olefinic and aromatic fluorine compounds, fluorine nuclear coupling constants have been obtained from the first-order self-consistent perturbation theory equation with the INDO molecular orbital approximation in a series of fluoro-substituted furans. There is a clear distinction between the magnitudes and signs for the four fluorine coupling positions; the importance of the orbital and spin-dipolar contributions is very clear. Tentative signs are suggested for all the coupling constants.     

Nature of M-Ga Bonds in cationic metal-gallylene complexes of iron, ruthenium, and osmium, [(η5-C5H5)(L)2M(GaX)]+: a theoretical study

Density Functional Theory calculations have been performed for the cationic half-sandwich gallylene complexes of iron, ruthenium, and osmium [(η(5)-C(5)H(5))(L)(2)M(GaX)](+) (M = Fe, L = CO, PMe(3); X = Cl, Br, I, NMe(2), Mes; M = Ru, Os: L = CO, PMe(3); X = I, NMe(2), Mes) at the BP86/TZ2P/ZORA level of theory. Calculated geometric parameters for the model iron iodogallylene system [(η(5)-C(5)H(5))(Me(3)P)(2)Fe(GaI)](+) are in excellent agreement with the recently reported experimental values for [(η(5)-C(5)Me(5))(dppe)Fe(GaI)](+). The M-Ga bonds in these systems are shorter than expected for single bonds, an observation attributed not to significant M-Ga π orbital contributions, but due instead primarily to high gallium s-orbital contributions to the M-Ga bonding orbitals. Such a finding is in line with the tenets of Bent's Rule insofar as correspondingly greater gallium p-orbital character is found in the bonds to the (more electronegative) gallylene substituent X. Consistent with this, ΔE(σ) is found to be overwhelmingly the dominant contribution to the orbital interaction between [(η(5)-C(5)H(5))(L)(2)M](+) and [GaX] fragments (with ΔE(π) equating to only 8.0-18.6% of the total orbital contributions); GaX ligands thus behave as predominantly σ-donor ligands. Electrostatic contributions to the overall interaction energy ΔE(int) are also very important, being comparable in magnitude (or in some cases even larger than) the corresponding orbital interactions.     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

On the transferability of Fock matrix elements

The transferability of Fock matrix elements in the linear combination of atomic orbitals molecular orbital scheme is analysed using localized orbitals. It is shown that this transferability is dependent on the transferability of these localized orbitals and the neglect of long-range contributions from partially cancelling Coulomb nuclear attraction and electron repulsion terms. A theoretical basis is thus provided for the simulated ab initio molecular orbital and related methods. Various corrections previously introduced in an ad hoc manner are shown to be justified. Transferability in both the closed shell and open shell schemes is analysed.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

Counter‐Rotating Spin‐Polarised Ring Currents in Odd‐Electron Carbocycles

We propose a molecular‐orbital model to explain how majority and minority spins in odd‐π‐electron carbocycles sustain counter‐rotating magnetic‐field‐induced ring currents. The model is based on the ipsocentric approach to magnetic response, in which ring currents are dominated by frontier‐orbital contributions obeying angular‐momentum selection rules. Coupled unrestricted Hartree–Fock ab initio calculations of the ring‐current responses for singly charged benzene and planarised cyclo‐octatetraene ions confirm the predictions of the qualitative model, and are consistent with correlated MP2 spin‐polarised current calculations.     

Trans-hydrogen-bond (h2)J(NN) and (h1)J(NH) couplings in the DNA A-T base pair: natural bond orbital analysis

Natural bond orbital (NBO) analysis described here demonstrates that trans-hydrogen-bond (trans-H-bond) NMR J couplings in the DNA A-T base pair, h2JNN and h1JNH, are determined largely by three terms: two Lewis-type contributions (the single-orbital contribution from the adenine lone pair and the contribution from the sigmaN3H3 natural bond orbital of the thymine ring) and one contribution from pairwise delocalization of spin density (between the lone pair in adenine and the sigma* antibonding orbital linking N3 and H3 of thymine). For h2JNN coupling, all three contributions are positive, whereas for h1JNH coupling, the delocalization term is negative, and the other two terms are positive, resulting in a small net positive coupling constant. This result rationalizes the experimental findings that the two-bond coupling (h2JNN approximately 9 Hz) is larger than the one-bond coupling (h1JNH approximately 3 Hz) and demonstrates that the same hyperconjugative and steric mechanisms that stabilize the H-bond are involved in the transmission of J coupling information. The N1...H3-N3 H-bond of the DNA A-T base pair is found to exhibit significant covalent character, but steric effects contribute almost equally to the trans-H-bond coupling.     

Why do the heavy-atom analogues of acetylene E2H2 (E = Si-Pb) exhibit unusual structures?

DFT calculations at BP86/QZ4P have been carried out for different structures of E(2)H(2) (E = C, Si, Ge, Sn, Pb) with the goal to explain the unusual equilibrium geometries of the heavier group 14 homologues where E = Si-Pb. The global energy minima of the latter molecules have a nonplanar doubly bridged structure A followed by the singly bridged planar form B, the vinylidene-type structure C, and the trans-bent isomer D1. The energetically high-lying trans-bent structure D2 possessing an electron sextet at E and the linear form HEEH, which are not minima on the PES, have also been studied. The unusual structures of E(2)H(2) (E = Si-Pb) are explained with the interactions between the EH moieties in the (X(2)Pi) electronic ground state which differ from C(2)H(2), which is bound through interactions between CH in the a(4)Sigma(-) excited state. Bonding between two (X(2)Pi) fragments of the heavier EH hydrides is favored over the bonding in the a(4)Sigma(-) excited state because the X(2)Pi --> a(4)Sigma(-) excitation energy of EH (E = Si-Pb) is significantly higher than for CH. The doubly bridged structure A of E(2)H(2) has three bonding orbital contributions: one sigma bond and two E-H donor-acceptor bonds. The singly bridged isomer B also has three bonding orbital contributions: one pi bond, one E-H donor-acceptor bond, and one lone-pair donor-acceptor bond. The trans-bent form D1 has one pi bond and two lone-pair donor-acceptor bonds, while D2 has only one sigma bond. The strength of the stabilizing orbital contributions has been estimated with an energy decomposition analysis, which also gives the bonding contributions of the quasi-classical electrostatic interactions.     

Tuning Solid-State Luminescence in Conjugated Organic Materials: Control of Excitonic and Excimeric Contributions through π Stacking and Halogen Bond Driven Self-Assembly

Two polymorphs with distinctly different fluorescence emission (green and yellow; G, Y) emanating from excitonic and excimeric contributions were prepared from solution as well as by using physical vapour transport. Based on crystal structure investigations, the vibrationally-resolved excitonic emission is found to originate from a β-Sheet arrangement (G), whereas a sandwich herringbone structure is responsible for the excimer emission (Y). The intermolecular interactions and energies were quantified to have a complete picture of the decisive factors that controls the self-assembly. Halogen-bond directed self-assembly was explored to fine-tune the intermolecular interactions through co-crystallization as well as a commercially viable liquid assisted grinding method. A smooth fluorescence shift from G to Y was achieved by co-assembly due to substantial differences in the π orbital overlap in the molecular packing. Our investigation provides a comprehensive understanding of the origin of excitonic and excimeric contributions of emission behaviour in conjunction with the molecular packing and π–π orbital overlap, and might provide a directive towards the engineering of fluorescent functional molecular materials.