Vibronic coupling in molecules and in solids

We utilize the experience gained in our previous studies on the "chemistry of vibronic coupling" in simple homonuclear and heteronuclear molecules to begin assembling theoretical guidelines for the construction of potentially superconducting solids exhibiting large electron-phonon coupling. For this purpose we analyze similarities between vibronic coupling in isolated molecules and in extended solids. In particular, we study vibronic coupling along the antisymmetric stretch coordinate (Q(as)) in linear symmetric AAA molecules, and along the optical phonon "pairing" mode coordinate (Q(opt)) in corresponding one-dimensional [A]( infinity ) chains built of equidistant A atoms. This is done for a broad range of chemical elements (A). The following similarities between vibronic coupling in molecules and phonon coupling in solids emerge from our calculations: 1) The HOMO/LUMO electronic energy gap in an AAA molecule increases along Q(as), and the highest occupied crystal orbital/lowest unoccupied crystal orbital gap in [A]( infinity ) chain increases along Q(opt). 2) The maximum vibronic instability is invariably obtained for a half-filled, singly occupied molecular orbital in AAA molecules, and for a corresponding half-filled band in [A]( infinity ) chains. 3) The vibronic stability of an AAA molecule increases with a decrease of the AA bond length, as does the vibronic stability of [A]( infinity ) chains (external pressure may lead to a reversal of a Peierls distortion). 4) The high degree of s-p mixing and ionic/covalent forbidden curve crossing dramatically enhance the vibronic instability of both AAA molecules and [A]( infinity ) chains. We also introduce one quantitative relationship: The parameter log(R) (where R is molar refractivity, a parameter used by Herzfeld to prescribe the conditions for the metallization of the elements) correlates with a parameter f(AA) (defined as twice the electronegativity of A, divided by the equilibrium AA bond length), used by two of us previously to describe vibronic coupling in AAA molecules for a broad range of elements (A=halogen, H, or an alkali metal). We hope to illustrate that key chemical aspects of vibronic coupling in simple molecules may thus be profitably transferred to corresponding materials in the solid state.     

An analysis of the through bond interaction using the localised molecular orbitals—III : Long range effect of lone pair orbital to the optical rotatory strength of the carbonyl n-π* transition in 3-ketopiperidines

The optical rotatory strengths of the carbonyl n-π^* transitions of (1R)-3-ketopiperidine and (1S)-3-ketopiperidine were subjected to the analysis in terms of the through-space and the through-bond interactions according to the procedure using localised molecular orbitals we proposed in the preceding papers. As a result of the present analysis, the optical rotatory strengths of the molecules were found to be influenced by the direction of the remote nitrogen lone pair orbital. This influence was found to be illustrated by the coupling between the CO group and the nitrogen lone pair orbital as well as the N-H bond localized orbital via a path containing the through-bond and the through-space interactions. That is, the positive coupling and the negative coupling paths were determined by the present analysis and the sign of the optical rotatory strength was found to correspond to the sum of the contributions of both coupling paths.     

On obtaining localized bonding schemes from delocalized molecular-orbital wave functions

A straightforward procedure is proposed for expanding a molecular orbital determinantal wave function into a set of determinantal wave functions composed of atomic orbitals localized at the atoms of a molecule. By employing this method, atomic orbital determinants and their weights can be derived for a molecule from the computed molecular-orbital wave function. The procedure permits the interpretation of a molecular orbital determinantal wave function in terms of bonding schemes related to the classic resonance structures used by organic chemists. By using the unrestricted molecular orbital determinant, bonding schemes and their weights are obtained for butadiene, the butadiene radical cation and the acrylonitrile radical anion. Their dominant bonding schemes are in accord with the relevant resonance structures for these molecules. For the butadiene radical cation and the acrylonitrile anion they are shown to be compatible with the accepted mechanisms of the electrochemical coupling reactions of butadiene and acrylonitrile. Received: 7 August 1996 / Accepted: 18 March 1997     

Interproton coupling over dual vicinal and homoallylic paths in 4-membered rings

A study is presented of cis and trans H? H coupling over dual vicinal (H? C? C? H) and homoallylic/interbenzylic/interbenzylic (H? C? C?C? C? H) paths in the series of molecules cyclobutene and benzocyclobutanes, and a series of dihydrocyclobutacenaphthylenes. Both the experimental and calculated molecular orbital results for these molecules increase in magnitude as the π-bond order of the homoallylic (interbenzylic) path decreases. These trends appear to be consistent only with homoallylic (interbenzylic) coupling contributions of negative sign. At least qualitatively, these trends can be rationalized in terms of the increase in positive contributions associated with the π→π* transitions as the energy denominators decrease in the series.     

Jahn-Teller effect in Rydberg series: a multi-state vibronic coupling problem

Two simple limiting cases of Jahn-Teller (JT) coupling in Rydberg states of polyatomic molecules are considered, namely(i) JT coupling in Rydberg orbitals as well as in the ionization continuum (nondegenerate ion core, degenerate Rydberg series) and(ii) JT coupling in the ion core (degenerate ion core, nondegenerate Rydberg series). For both models simple and efficient algorithms for the computation of spectra (dynamical JT effect) are developed. The orbital JT effect is shown to represent a novel type of multi-state vibronic coupling, giving rise to interesting spectroscopic phenomena, among them resonant inter-Rydberg perturbations and JT induced autoionization. Particular attention is paid to the demonstration of the characteristic spectroscopic signatures of the two types of JT coupling in Rydberg states.     

Computational and experimental evidence of through-space NMR spectroscopic J coupling of hydrogen atoms

J coupling in NMR spectroscopy is conventionally associated with covalent bonds. A noncovalent contribution often called through-space coupling (TSC) has been observed for heavy atoms. In this study, the TSC was detected and analyzed for the more common (1)H-(1)H coupling as well. In synthesized model molecules the hydrogen positions could be well controlled. For several coupling constants the through-space mechanism was even found to be the predominant factor. The nature and magnitude of the phenomenon were also analyzed by density functional computations. Calculated carbon- and hydrogen-coupling maps and perturbed electronic densities suggest that the aromatic system strongly participates in the noncovalent contribution. Unlike covalent coupling, which is usually governed by the Fermi contact, TSC is dominated by the diamagnetic term comprising interactions of nuclei with the electron orbital angular momentum. The computations further revealed a strong distance and conformational dependence of TSC. This suggests that the through-space coupling can be explored in molecular structural studies in the same way as the covalent one.     

Lone-pair orbital interactions in polythiaadamantanes

The electronic structures of a series of polythiaadamantanes from thiaadamantane through 2,4,6,8,9,10-hexathiaadamantane (HTA) have been analyzed using density functional theory calculations in conjunction with Hückel and natural bond orbital analysis. The effects of multiple sulfur p-type lone-pair orbital interactions on ionization potentials, hole mobilities, and electronic coupling have been determined. An overall increase in the average energy of the lone-pair orbitals as the number of sulfur atoms increases is predicted, with the exact positioning of the HOMO depending on specific lone-pair interactions. Separation of through-bond (TB) and through-space (TS) interactions between intramolecular sulfur atoms has been performed using localized molecular orbitals and model systems based on interacting hydrogen sulfide molecules. TB interations were found to reduce orbital splitting, while TS interactions were found to increase orbital splitting. TS interactions were more or less constant from one polythiaadamantane to the next, and the contributions of TB effects to individual orbital energies vary depending on the relative orientation of sulfur atoms as determined by the sigma molecular framework. Electronic coupling between intermolecular sulfur lone-pair orbitals was determined by investigating unique dimer pairs observed in the crystal structure of HTA. Electronic coupling is not as strong as expected given the short intermolecular S-S distances observed in the crystal structure. In general, B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) give very similar orbital energies and splittings.     

Resonance Raman study of free-base tetraphenylporphine and its dication

Resonance Raman spectra of free-base tetraphenylporphine and its dication obtained with 441.6, 476.5, 488.0 and 514.5 nm excitation lines in the frequency region 100-1625 cm(-1) are reported. Some bands due to in-plane and out-of-plane vibrational modes, which are symmetry forbidden under ideal D(2h), are also seen in the Raman spectra of these molecules. These bands arise due to dynamic and/or static coupling of out-of-plane modes with the allowed in-plane modes. Dynamic coupling may be facilitated by the proton tunneling, while static coupling is due to out-of-plane distortion in the geometrical structure of the molecule. Shift in the positions for certain bands in the Raman spectra of dication are interpreted on the basis of electronic changes due to sharing of electrons of the B(1u) orbital by the two added protons.     

Finite perturbation MCSCF and CI calculations of nuclear spin-spin coupling constants for some molecules with multiple bonds

Non-empirical finite perturbation calculations at the Hartree-Fock, multiconfigurational self-consistent field and configuration interaction levels of approximation are presented for the Fermi contact contribution in multiply-bonded molecules ethene, formimide, formaldehyde, ethyne and hydrogen cyanide. The finite perturbation-multiconfigurational SCF (FPMC) method (with few configurations) is free from the UHF triplet instabilities normally present in single configuration coupled Hartree-Fock (CHF) calculations of the Fermi contact (and spin-dipolar) contribution for π-bonded systems. The behaviour of coupling constants, calculated using FPMC for multiply-bonded systems parallels the behaviour of the CHF coupling constants in comparable systems with single bonds only. The effects of dynamic electron correlations are important and are obtained using the Cl method. After accounting for the orbital contribution by means of the single configuration CHF method, agreement with experiment is excellent for systems containing only carbon and hydrogen, when a double-zeta quality basis set is used. For systems containing nitrogen and oxygen agreement is still reasonable, but the use of larger basis sets seems to be necessary if good agreement with experiment is to be obtained.     

Thermal and solvent effects on NMR indirect spin-spin coupling constants of a prototypical Chagas disease drug

NMR J-couplings across hydrogen bonds reflect the static and dynamic character of hydrogen bonding. They are affected by thermal and solvent effects and can therefore be used to probe such effects. We have applied density functional theory (DFT) to compute the NMR (n)J(N,H) scalar couplings of a prototypical Chagas disease drug (metronidazole). The calculations were done for the molecule in vacuo, in microsolvated cluster models with one or few water molecules, in snapshots obtained from molecular dynamics simulations with explicit water solvent, and in a polarizable dielectric continuum. Hyperconjugative and electrostatic effects on spin-spin coupling constants were assessed through DFT calculations using natural bond orbital (NBO) analysis and atoms in molecules (AIM) theory. In the calculations with explicit solvent molecules, special attention was given to the nature of the hydrogen bonds formed with the solvent molecules. The results highlight the importance of properly incorporating thermal and solvent effects into NMR calculations in the condensed phase.     

Orbital localization in transition metal molecules

In multiply bonded, weakly interacting systems the excessive electron repulsion associated with the non-dynamical correlation error can be reduced within the Hartree Fock approximation by localizing the bonding orbitals. The mechanism behind this (unphysical) orbital localization is studied through calculations on a model system, and SCF and CI calculations on the MnO⁺ ion. It is shown, from a pair-population analysis of the two-particle density matrix (which is analogous to a Mulliken population analysis of the one-density) that the orbital localization is a two-electron effect. Transition metal molecules often exhibit this kind of orbital localization which may (or may not) require symmetry breaking. The special characteristics of transition metal molecules that makes them suitable candidates for orbital localization will be discussed.     

Nuclear spin–spin coupling and nuclear motion

The vibration and rotation of molecules affects nuclear spin–spin coupling constants. This manifests itself as a temperature dependence of the coupling and also as an isotope effect (after allowing, where necessary, for differing magnetogyric ratios of the two nuclei involved in the isotopic substitution). Within the Born–Oppenheimer approximation, a nuclear spin–spin coupling surface can be defined for each pair of coupled nuclei. This surface is sampled by the nuclei as they undergo the excursions about equilibrium geometry that are governed by the force field. An accurate ab initio carbon–proton spin–spin coupling surface for the methane molecule has been calculated. This was obtained by summing the surfaces for each of the four contributions—Fermi contact, spin–dipolar, orbital paramagnetic, and orbital diamagnetic—expressed as power series in terms of symmetry coordinates. Preliminary calculations for ¹³CH₄ and ¹³CD₄ give a difference of only 6% between the calculated and observed nuclear motion contributions. The observed temperature dependence is also accounted for by the calculations. For these isotopomers, bond stretching plays the dominant role. © 1994 John Wiley & Sons, Inc.     

Core excitation in O3 localized to one of two symmetry-equivalent chemical bonds: molecular alignment through vibronic coupling

Core excitation from terminal oxygen OT in O3 is shown to be an excitation from a localized core orbital to a localized valence orbital. The valence orbital is localized to one of the two equivalent chemical bonds. We experimentally demonstrate this with the Auger-Doppler effect which is observable when O3 is core excited to the highly dissociative OT1s(-1)7a1 1 state. Auger electrons emitted from the atomic oxygen fragment carry information about the molecular orientation relative to the electromagnetic-field vector at the moment of excitation. The data together with analytical functions for the electron-peak profiles give clear evidence that the preferred molecular orientation for excitation only depends on the orientation of one bond, not on the total molecular orientation. The localization of the valence orbital "7a1" is caused by mixing of the valence orbital "5b2" through vibronic coupling of antisymmetric stretching mode with b2 symmetry. To the best of our knowledge, it is the first discussion of the localization of a core excitation of O3. This result explains the success of the widely used assumption of localized core excitation in adsorbates and large molecules.     

以笼烯为接头的球棒式碳纳米管的电子结构

按照Hamada构造一维至三维球棒式碳纳米管,构造了一些球棒式的笼烯接头的具有C₃/C₅旋转轴的单层碳纳米管.在Hückel近似下,利用群论约化定理计算了它们的π电子结构,并对其稳定性进行了探讨.     

Three-dimensional through-space/through-bond delocalization in cyclophane systems: a molecule-in-molecule approach

In this article, we propose a simple strategy to identify the nature of excitonic couplings in a series of cyclophanedienes based on the "molecule-in-molecule" (MIM) theory. The contributions of charge-transfer (CT) exciton, unavailable by the commonly used supermolecular approach due to the inadequate basis set, can be unambiguously identified within this methodology. Combining the CT contributions calculated on the cyclophanedienes and the corresponding hypothetical molecules with tethers removed, one can infer the information on the relative importance of through-bond and through-space contributions in the low-lying excited states. Particularly, we discovered that the tether effect for the meta-linkage cyclophanedienes is crucial, whereas those for para-linkage cyclophanedienes are vanishingly small. The changes in the coupling between two moieties for both the six-membered meta-linkage and five-membered cyclophanedienes arise primarily from an increase in the through-bond charge-transfer component of the coupling (>70%). Within the MIM model, the delocalization pathway of the dimer in the excited state can be explained quantitatively by a CT exciton, which differs from the approach based on the conventional orbital interaction analysis.     

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.     

UV-vis, IR and 1H NMR spectroscopic studies of some mono- and bis-azo-compounds based on 2,7-dihydroxynaphthalene and aniline derivatives

The absorption spectra of mono- and bis-azo-derivatives obtained by coupling the diazonium salts of aromatic amines and 2,7-dihydroxynaphthalene have been studied in six organic solvents. The different absorption bands have been assigned and the effect of solvents on the charge transfer band is also discussed. The diagnostic IR spectral bands and 1H NMR signals are assigned and discussed in relation to molecular structure. Also, semi-empirical molecular orbital calculations using the atom superposition and electron delocalization molecular orbital (ASED-MO) theory have been performed to investigate the molecular and electronic structures of these compounds. According to these calculations, an intramolecular hydrogen bonding is essential for stabilization of such molecules.     

Bond orbital analysis of the deuteron quadrupole coupling constants in MD4 molecules

The deuteron quadrupole coupling constants were used as constraints on the bond orbital functions of a series of MD₄ molecules (M=B, C, N, Al, Si, P). It was demonstrated that a minimal basis set may be sufficient to describe first row deuterates, but not for second row deuterates, where double zeta orbitals are needed.This work was started when the author was a post doctoral fellow at Battelle Memorial Institute, Columbus, Ohio.