Π-bond Order Research Articles

Decoupling excitons from high-frequency vibrations in organic molecules

The coupling of excitons in π-conjugated molecules to high-frequency vibrational modes, particularly carbon–carbon stretch modes (1,000–1,600 cm−1) has been thought to be unavoidable1,2. These high-frequency modes accelerate non-radiative losses and limit the performance of light-emitting diodes, fluorescent biomarkers and photovoltaic devices. Here, by combining broadband impulsive vibrational spectroscopy, first-principles modelling and synthetic chemistry, we explore exciton–vibration coupling in a range of π-conjugated molecules. We uncover two design rules that decouple excitons from high-frequency vibrations. First, when the exciton wavefunction has a substantial charge-transfer character with spatially disjoint electron and hole densities, we find that high-frequency modes can be localized to either the donor or acceptor moiety, so that they do not significantly perturb the exciton energy or its spatial distribution. Second, it is possible to select materials such that the participating molecular orbitals have a symmetry-imposed non-bonding character and are, thus, decoupled from the high-frequency vibrational modes that modulate the π-bond order. We exemplify both these design rules by creating a series of spin radical systems that have very efficient near-infrared emission (680–800 nm) from charge-transfer excitons. We show that these systems have substantial coupling to vibrational modes only below 250 cm−1, frequencies that are too low to allow fast non-radiative decay. This enables non-radiative decay rates to be suppressed by nearly two orders of magnitude in comparison to π-conjugated molecules with similar bandgaps. Our results show that losses due to coupling to high-frequency modes need not be a fundamental property of these systems.

Lewis Structures and the Bonding Classification of End-on Bridging Dinitrogen Transition Metal Complexes.

The activation of dinitrogen by coordination to transition metal ions is a widely used and promising approach to the utilization of Earth's most abundant nitrogen source for chemical synthesis. End-on bridging N2 complexes (μ-η1:η1-N2) are key species in nitrogen fixation chemistry, but a lack of consensus on the seemingly simple task of assigning a Lewis structure for such complexes has prevented application of valence electron counting and other tools for understanding and predicting reactivity trends. The Lewis structures of bridging N2 complexes have traditionally been determined by comparing the experimentally observed NN distance to the bond lengths of free N2, diazene, and hydrazine. We introduce an alternative approach here and argue that the Lewis structure should be assigned based on the total π-bond order in the MNNM core (number of π-bonds), which derives from the character (bonding or antibonding) and occupancy of the delocalized π-symmetry molecular orbitals (π-MOs) in MNNM. To illustrate this approach, the complexes cis,cis-[(iPr4PONOP)MCl2]2(μ-N2) (M = W, Re, and Os) are examined in detail. Each complex is shown to have a different number of nitrogen-nitrogen and metal-nitrogen π-bonds, indicated as, respectively: W≡N-N≡W, Re═N═N═Re, and Os-N≡N-Os. It follows that each of these Lewis structures represents a distinct class of complexes (diazanyl, diazenyl, and dinitrogen, respectively), in which the μ-N2 ligand has a different electron donor number (total of 8e-, 6e-, or 4e-, respectively). We show how this classification can greatly aid in understanding and predicting the properties and reactivity patterns of μ-N2 complexes.

Understanding Terminal versus Bridging End-on N2 Coordination in Transition Metal Complexes.

Terminal and bridging end-on coordination of N2 to transition metal complexes offer possibilities for distinct pathways in ammonia synthesis and N2 functionalization. Here we elucidate the fundamental factors controlling the two binding modes and determining which is favored for a given metal-ligand system, using both quantitative density functional theory (DFT) and qualitative molecular orbital (MO) analyses. The Gibbs free energy for converting two terminal MN2 complexes into a bridging MNNM complex and a free N2 molecule (2ΔGeq°) is examined through systematic variations of the metal and ligands; values of ΔGeq° range between +9.1 and -24.0 kcal/mol per M-N2 bond. We propose a model that accounts for these broad variations by assigning a fixed π-bond order (BOπ) to the triatomic terminal MNN moiety that is equal to that of the free N2 molecule, and a variable BOπ to the bridging complexes based on the character (bonding or antibonding) and occupancy of the π-MOs in the tetratomic MNNM core. When the conversion from terminal to bridging coordination and free N2 is associated with an increase in the number of π-bonds (ΔBOeqπ > 0), the bridging mode is greatly favored; this condition is satisfied when each metal provides 1, 2, or 3 electrons to the π-MOs of the MNNM core. When each metal in the bridging complex provides 4 electrons to the MNNM π-MOs, ΔBOeqπ = 0; the equilibrium in this case is approximately ergoneutral and the direction can be shifted by dispersion interactions.

Bond Ellipticity Alternation: An Accurate Descriptor of the Nonlinear Optical Properties of π-Conjugated Chromophores.

Well-defined structure-property relationships offer a conceptual basis to afford a priori design principles to develop novel π-conjugated molecular and polymer materials for nonlinear optical (NLO) applications. Here, we introduce the bond ellipticity alternation (BEA) as a robust parameter to assess the NLO characteristics of organic chromophores and illustrate its effectiveness in the case of streptocyanines. BEA is based on the symmetry of the electron density, a physical observable that can be determined from experimental X-ray electron densities or from quantum-chemical calculations. Through comparisons to the well-established bond-length alternation and π-bond order alternation parameters, we demonstrate the generality of BEA to foreshadow NLO characteristics and underline that, in the case of large electric fields, BEA is a more reliable descriptor. Hence, this study introduces BEA as a prominent descriptor of organic chromophores of interest for NLO applications.

Stability studies of double-base propellants with centralite and malonanilide stabilizers using MO calculations in comparison to thermal studies

Propellants containing nitrate esters need stabilizers to avoid early decomposition or even explosion during storage. Newly prepared malonanilides M1– M5 were tested in stabilizing double-base propellants (DBPs). Their stabilization was compared with the effect of classical stabilizer N,N′-diethyldiphenyl urea ( C1) using both practical thermal stability tests (qualitative and quantitative tests) and theoretical molecular orbital calculations. This research shows that the new stabilizers (malonanilides) have good stabilizing effects. Some of malonanilides e.g. ( M5) and ( M2) have higher stability effects. Different mechanisms were suggested to explain the role of different stabilizers. Molecular orbital calculations using the semi-empirical program AM1 are performed on the new and classical stabilizers. Correlation was made between the volume (ml) of NO x , weight loss (wt%), other thermal analyses data, calculated thermodynamic parameters like activation energy ( E a, kJ mol −1) of the decomposed propellant samples containing different stabilizers and some of their calculated properties such as HOMO, LUMO energies, the charge distribution and the π-bond order. The stabilization effect decreases with the increase in HOMO energy. The correlation between the net charge and parameters measured for the stabilization effect shows good accordance. Comparison of the results obtained show that the high electron charge on N atom of the stabilizers and on its benzene ring is the most important factor, but not the only factor governing the stabilization effect of the stabilizers.

Monocyclic Electrocyclic Transition States are Neither Favoured Nor Disfavoured if the Incipient Ring Bears More Than Two Odd Substituents

A general case is presented that supports the conclusion that incipient π-bond orders, op1,j, are approximately zero if the incipient alternant ring bears more than two odd substituents. Hence, corresponding electrocyclic transition states are neither favoured nor disfavoured. The case is made using permethylene polyenes. After presentation of the novel application of dense Sachs’ subgraphs to the problem of convenient, rapid access to permethylene polyene characteristic polynomials, permethylene polyenes are shown to belong to the newly defined Hückel symmetrenes. Employing novel expressions for permethylene polyene molecular orbital coefficients, a general relationship for pairs of terms that lead to π-bond orders, op1,j, is obtained that, in turn, allows the key generalization to be made.

An Alternative Platform for the Assessment of Hückel and Möbius Transition States in Concerted Reactions

A novel approach to the evaluation of Hückel and Möbius transition states is described. It employs incipient π-bond orders, opi,k and *pi,k. A complete analytical scheme is developed for monocyclic p-orbital arrays in both Hückel and Möbius transition states for both thermal and photochemical reactions. Assessment of monocyclic transition states does not require the calculation of explicit incipient π-bond orders. Transition states featuring polycyclic p-orbital arrays may be assessed by means of calculated opi,k and *pi,k values. A more detailed presentation is available in the Accessory Publication.

Simulated ab initio molecular orbital calculations of large polynuclear aromatic hydrocarbons

Molecular orbital electronic structure calculations for twelve polynuclear aromatic hydrocarbons were performed by the samo method. Results indicate that the carcinogenicity of such aromatic hydrocarbons is related to a K-region π-bond order greater than 0.340. There is no correlation with δ-bond order or overall charge density, perhaps accounting for the success of earlier theoretical treatments based on the π-electron model. Exceptions to a simple K-region treatment are discussed in terms of other models for carcinogenic activity.

The electrical transport properties of C60 treated by argon plasma

C60 was fused by sublimation in argon plasma. The material shows optical absorption in the visible region because the degree of delocalization of the charge of C60 cages was changed by fusion of the cages. The conduction mechanism in the solid state was explained by the multi-phonon assisting model, discussing it based on the temperature dependence of the electrical conductivity. To investigate the conduction between C60 cages in fused C60s brought on by plasma treatment, the π-bond orders in peanut-shaped inter C60 crosslink structures and cyclo-addition type crosslinks in C60 dimers were examined using the semi-empirical MNDO/AM-1 and PM-3 method. We found that the π-bond order of the dimmers of fused C60 is higher than that of C60.

Clar's Sextet Rule Is a Consequence of the σ-Electron Framework

A number of condensed PAHs are examined to identify the underlying reasons governing empirical Clar's rule taking benzene as a limiting case. It is found that the so-called Clar's structures are the only minima on the MP2(fc) potential energy hypersurfaces, meaning that other conceivable valence isomers are nonexistent. The influence of the electron correlation energies to the stability of Clar's structures is substantial with predominating influence of the sigma-electrons. However, the contributions arising from the sigma- and pi-electron correlation energies are approximately the same, if Clar's structures are compared with some artificial pi-electron localized or graphite-like delocalized planar systems. Analysis of the Hartree-Fock (HF) energies provides a compelling evidence that the origin of stability of Clar's structures lies in a decrease of the positive T, V(ee) and V(nn) energy terms relative to some characteristic virtual "delocalized" or "localized" model geometries. Partitioning of the mixed and terms in the sigma- and pi-type contributions, by using the stockholder (SHR), equipartitioning (EQP) and standard pi (SPI) schemes, unequivocally shows that the driving force leading to Clar's structures are more favorable sigma-type interactions. All these conclusions hold for the archetypal benzene too, which could be considered as a limiting Clar system. Finally, the boundaries of Clar's hypothesis and some common misconceptions are briefly discussed. Perusal of the geometric parameters and pi-bond orders reveals that there are no benzene rings completely "vacant" or "fully occupied" by the pi-electrons, envisaged by Clar in his picture of condensed benzenoid compounds. Instead, there are six-membered rings with higher and lower total pi-electron density. The bond length anisotropy of the former rings is smaller. It is concluded that Clar's proposition is a useful rule of thumb providing qualitative information on the stability of the PAH systems, which in turn should not be overinterpreted.

Electronic properties of polymethine systems. 6. Bond order and bond length changes upon excitation

The dependence of bond order and bond length changes upon the excitation on the molecular topology of linear conjugated systems has been investigated using quantum-chemical methods. It has been found that the molecular geometry and π-bond orders in the excited state of polymethine dyes (odd ionic π-systems) and substituted polyenes (even neutral π-systems) containing residues with their localized MOs differ significantly from that in the typical π-systems having a totally delocalized HOMO and LUMO. Also, the extraordinary π-bond order changes upon excitation have been shown to exist in relatively long polymethine dyes when the symmetry breaking occurs. These results are consistent with spectral data.

Ab initio study of the electronic structures and conduction properties of some donor-acceptor polymers and their copolymers

The electronic structures and conduction properties of four donor-acceptor polymers containing alternating electron-donating group SiF2 and electron-accepting group Y [Y=>C=CH2 in PSIFCH, >C=O in PSIFCO, >C=CF2 in PSIFCF, and >C=C(CN)2 in PSIFCN] along the conjugated trans-cisoid polyacetylene backbone, obtained on the basis of the ab initio Hartree-Fock crystal orbital method are compared. All the polymers are predicted to have band gap values ranging between 1 and 2 eV. The calculated band gap values are found to decrease in the order PSIFCO>PSIFCH>PSIFCF>PSIFCN. PSIFCO is predicted to be the strongest candidate for oxidative (p) doping while PSIFCN is found to have the greatest capacity for reductive (n) doping. The π-bond order data as well as the geometric structures of these polymers show them to have aromaticlike electronic structures. Using the ab initio band structure results of PSIFCO (A)x and PSIFCN (B)x, the electronic density of states of various quasi-one-dimensional compositional superlattices (copolymers) (AmBn)x, belonging to the type-II-staggered class have been determined using the negative-factor counting method, taking multineighbor interactions (up to six neighbors) into account. The trends in the electronic structures and conduction properties of these copolymers as a function of (i) block sizes m and n, (ii) composition (m/n), and (iii) arrangement of blocks (periodic or aperiodic) in the copolymer chain are discussed. The results are important guidelines for molecular designing of copolymers with tailor-made conduction properties.

Ab initio study of the electronic structures and conduction properties of some novel low band-gap donor–acceptor polymers

The results of the electronic structures and conduction properties of four novel donor–acceptor polymers based on polysilole, obtained on the basis of ab initio Hartree–Fock crystal orbital method using their optimized geometries, are reported. The repeat unit of these polymers consists of bicyclopentadisilole unit bridged by an electron-accepting group Y(Y=CCH 2 in PSICH, CO in PSICF, CCF 2 and CC(CN) 2 in PSICN). All the polymers on the basis of their geometries and π-bond order values are found to have benzenoid-type electronic structures. Comparison of the important electronic properties such as ionization potential, electron affinity and band-gap of these polymers indicates PSICN to be the best candidate for intrinsic conductivity and reductive (n-) doping while PSICH is predicted to be the best candidate for oxidative (p-) doping. All these polymers are estimated to have band-gap values ranging between 1 and 2 eV. The low band-gap values of these polymers are rationalised on the basis of the patterns of their frontier orbitals.

Molecular and electronic structure of some silacyclopropabenzenes: the reversed Mills–Nixon effect

Molecular and electronic structure of silacyclopropabenzenes are examined by the MP3(fc)/6-31G* theoretical model. The salient feature of these compounds is alternation of bond distances of the aromatic fragment in the reversed Mills–Nixon sense i.e. the annelated CC bonds are shortened, whilst the ortho bonds are stretched. This is in harmony with the π-electron partial bond localization as evidenced by the π-bond order analysis, which in turn indicates that the π-effect dominates over the σ-electron rehybridization effect. Concentration of the π-density in the ipso bond(s) seems to be triggered by hyperconjugation with SiH 2 group(s). The latter mode of interaction is responsible for a decrease in the strain energy of silacyclopropabenzenes relative to the corresponding cyclopropabenzenes. It is shown that the total strain energy is a simple additive function of the number and types of the fused small rings involving SiH 2 group(s).

Theoretical design of donor-acceptor polymers with low bandgaps

The electronic and geometric structures of some novel hypothetical donor-acceptor polymers containing alternating electron-donating group X (X = CF 2, SiF 2, or GeF 2) and electron-accepting group Y y = CCH 2, C CCF 2 C(CN 2 or GeF 2) and electron-accepting group Y (Y = CCH 2, CO, CCF 2 or C(CN) 2) obtained on the basis of the one-dimensional tight-binding self-consistent field-crystal orbital (SCFCO) method at the MNDO-AM1 level of approximation are reported. Polymers derived from X = CF 2, SiF 2 or GeF 2 and Y = CC(CN 2) are predicted to have stable quinoid-like electronic structures with bandgap values of less than 1 eV. All other polymers are found to have benzenoid-like electronic structures. The smaller bandgap values of the quinoid-like polymers in contrast to the benzenoid-like polymers are rationalized on the basis of their π-bond order data and the patterns of their frontier orbitals.

Vibrational analysis of infrared spectra of matrix-isolated transient silenes on basis of density functional theory calculations

The infrared spectra of matrix-isolated transient silenes, R 2SiC R 2, with the substituents R such as H, D, Cl, CH 3, CD 3 at Si and H, D, CH 3 at C, have been interpreted by comparison with the density functional theory (DFT) B3LYP/6-311G(d,p), calculated harmonic vibrational frequencies and infrared intensities and additional computation of potential energy distribution for normal modes. The calculated unscaled frequencies deviate only by 2%–3% from the experimental ones and thus demonstrate the high reliability of the DFT approximation in predicting the spectra of silenes, out-performing the ab initio methods in accuracy. The DFT-based vibrational analysis confirms the previous CI/DZ + P normal mode description given for parent silene H 2SiCH 2 by Schaefer, and substantially changes the MNDO or force field approximated assignments for observed IR absorptions in all other studied silenes, in particular, those of the CH 2 (CD 2) wagging modes. These “olefinic” frequencies are found to be red-shifted by 200–250 cm −1, relative to those in corresponding alkenes. The SiC force constants in internal coordinates and π-bond orders, calculated to be within 5.36–5.75 and 1.62–1.71 mdyn/Å, respectively, are in line with the changes in the SiC bond lengths depending on the substituents.

Ab initio study of novel low-band-gap donor–acceptor polymers based on poly(cyclopentadienylene)

Ab initio determinations of the band structures of two novel donor–acceptor polymers, PPDCN and PPDCO, based on poly(cyclopentadienylene) (PPD) are reported. The repeat unit of these polymers is a bicyclopentadienylene unit bridged by an electron-accepting group Y (Y = CO in PPDCO and CC(CN)2 in PPDCN). Both PPDCO and PPDCN, on the basis of their geometries and π-bond orders, are found to have benzenoid-like structures, as do the corresponding thiophene analogues poly-4H-cyclopenta-dithiophene-4-one (PCDT) and polydicyanomethylene-cyclopenta-dithiophene (PCNTh). However, the band-gap values of PPDCO and PPDCN are smaller than those of the thiophene analogues owing to the weak electronic effects of the CH2 bridging group. The smaller band-gap values of PPDCO and PPDCN are rationalised on the basis of the patterns of their frontier orbitals.

Properties of Some Condensed Aromatic Systems

The structures, energies, and other properties of a series of linearly annelated arenes, and of a corresponding series annelated in the fashion of phenanthrene, were examined at the B3LYP/6-311G** level of theory. The compounds in the latter series were uniformly found to have a lower energy than their isomers in the former series. In both series, the C−C bond lengths were found to be correlated with the charge density at the bond critical point, the ellipticity at that point, and with the π-bond order. This indicates that the π-electron distribution is the dominant factor in determining the bond lengths. The resonance energies were estimated and were found to increase linearly with the number of rings with the [n]phenacenes, but at a slower rate with the linearly annelated benzenes. The ionization potentials were calculated, and the change in electron density on ionization was examined. It was found that the radical cations formed via ionization have the positive charge mainly located at the π-orbitals t...

Ab initio study of the electronic structures of polycyclopentadithiophene-4-one and polydicyanomethylene-cyclopentadithiophene: Two conjugated polymers with small band gaps

Quantum chemical results of the electronic structures of polycyclopentadithiophene-4-one (PCDT) and polydicyanomethylene-cyclopentadithiophene (PCNTh), (the two known conjugated polymers consisting of successive bithiophene units bridged by an electron accepting carbonyl group in PCDT and a dicyanomethylene group in PCNTh), obtained with the aid of ab initio Hartree-Fock crystal orbital method are reported. Both polymers on the basis of their geometries as well as their π-bond orders are found to have benzenoid-like structures. It is shown that the small band gap values of these polymers as compared with polythiophene (PTP) arise mainly due to the strong bonding interaction between the LUCO of the bithiophene skeleton and the LUMO of the electron accepting group.

A density functional study of the bonding in tertiary phosphine chalcogenides and related molecules

The nature of the phosphorus–tellurium bond in tertiary phosphine tellurides is not well understood. There is also controversy over the nature of multiple bonding in the lighter chalcogenides and the related ylides and imides. Density functional theory (DFT) was used to investigate the interactions in the molecule, Me3PE (E = O, S, Se, Te, BH3, CH2, NH). The calculated PE bond energies and orbital populations reveal contributions from both σ donation from the phosphine and π back-donation to the phosphine in all of the above cases. Down the group from oxygen to tellurium, the PE bond weakens from 544 kJ mol−1 to 184 kJ mol−1, but multiple bonding becomes more significant with respect to the single bond. For E = BH3, the PB bond energy is 166 kJ mol−1. Trimethylphosphine ylide was found to have a π-bond order of 0.5, while that of trimethylphosphine imine is 0.6. For comparison, the oxides of trimethylamine and trimethylarsine were also calculated to examine the pnictogen–oxygen bond; Me3N does not participate in multiple bonding with oxygen, while the π-bond orders for Me3PO and Me3AsO were calculated as 0.7 and 0.6, respectively. Key words: phosphine chalcogenides, phosphine ylides, phosphine imides, DFT calculations