Bond Length Alternation Parameter Research Articles

Static NLO responses of fluorinated polyacetylene chains evaluated with long-range corrected density functionals

As an alternative to oligomeric systems with different skeleton atoms it is shown that asymmetry introduced by substitution on a symmetric π-conjugated chain can lead to molecular systems with high non-linear optical responses. First hyperpolarizability and related properties such as the bond-length alternation parameter, dipole moment and polarizability of polyfluoroacetylene (PFA) oligomers are investigated by the Hartree-Fock, DFT and MP2 approaches. Particular attention is paid to long-range corrected DFT methods (LR-DFT). Systematic behavior of the MP2/LR-DFT ratio enables to estimate Δ β L for the eicosamer to 76 × 10 3 a.u. what makes PFA oligomers attractive candidates for NLO applications.

High second-order NLO responses of dehydrogenated hydrogen cyanide borane(1) oligomers

Second-order non-linear optical (NLO) properties of dehydrogenated hydrogen cyanide borane(1) oligomers (up to dodecamers) are investigated by the Hartree–Fock, hybrid DFT (including long-range corrected functionals) and MP2 approaches. Due to one-dimensional extension of the systems the longitudinal component of the properties is addressed with focus on the electronic contributions. Direct and indirect electron correlation effects are evaluated at the MP2 level paying particular attention to the basis set effects. Unit-cell asymmetry and delocalization effects in the NLO responses are discussed in terms of the evolution of the bond-length alternation parameter, dipole moment and polarizability (reduced per unit cell) with the increasing chain length. It was found that suitable combination of the unit-cell asymmetry and electron delocalization leads to extremely large NLO response (MP2/6-311++G(d,p) value for the dodecamer is 43.7 × 10 3 a.u. per unit cell) what makes the conjugated BCN oligomers (if one takes into account their thermodynamic stability) a promising material for NLO applications.

Breakdown of the first hyperpolarizability/bond-length alternation parameter relationship

We have investigated the dependence of the static first hyperpolarizability on the bond-length alternation (BLA) parameter. Our analysis indicates that the validity of the first hyperpolarizability/BLA parameter relationship is restricted to the no-field, vacuum, limit, while it successively breaks down along with increasing polarity of a surrounding medium, becoming invalid, for instance, in an aqueous solution. This contention is based on a series of TD-DFT, TD-DFT/PCM and hybrid TD-DFT/MM calculations of the first hyperpolarizability for a set of molecular configurations generated from Car-Parrinello hybrid QM/MM simulations of the stilbazolium merocyanine chromophore in chloroform and water solvents, and on a rationalization by means of the two-state model for the first hyperpolarizability. The BLA dependence of the three parameters entering the two-state model is shown to be qualitatively different in vacuum and in solvents. Particularly, in the vacuum case, the difference between ground and excited state dipole moments goes to zero for a vanishing BLA, which is not true in the presence of an aqueous medium. In the aqueous medium, an opposing behavior of the parameters involved in the two-state model results in an almost constant first hyperpolarizability with varying BLA parameter.

Semiempirical Molecular Dynamics Study of Empty C2(3)-C82 Fullerene in Neutral and Charged Forms: Geometrical and Spectroscopic Characterization

A systematic and comparative theoretical calculation based on the Density Functional Theory and semiempirical Austin Model 1 (AM1) and Zerner’s Intermediate Neglect Overlap (ZINDO) methods have been performed on the neutral and charged states of empty C2(3)-C82 fullerene. The relations between the dynamical structure and the total molecular charge were studied using AM1 molecular dynamics (MD). The obtained results show that the shape of the fullerene ball is more-or-less periodically changed around the most probable geometry. These changes were quantified by using the averaged geometrical bond length alternation parameter. On the basis of the evaluated MD geometries and relevant ZINDO transitions, the absorption spectra were simulated. These simulations allowed us to assign individual bands in spectroelectrochemical records where the mixtures of oxidation and reduction products occurred.

Solvent Dependence on Bond Length Alternation and Charge Distribution in Phenol Blue: A Car−Parrinello Molecular Dynamics Investigation

Car-Parrinello mixed quantum mechanics/classical mechanics (CP-QM/MM) calculations are performed for phenol blue (PB) in chloroform and water solvents along with Car-Parrinello molecular dynamics (CPMD) calculations on PB in the gas phase. The solvent effect on molecular geometry, particularly of bond length alternation (BLA), has been studied. As reported for similar donor-acceptor polyenic systems, a remarkable solvent effect is seen on the BLA. The calculated BLA parameter suggests that PB is in the neutral form in the gas phase and in chloroform solvent, while in water, it is cyanine-like, which is a mixture of neutral and zwitterionic resonant forms, something that clarifies the controversial reports on the structure of PB in chloroform. We have also verified that the structures obtained from CPMD and CP-QM/MM calculations are correct by calculating absorption spectra for PB in the gas phase and in chloroform solvent and compared with experimental results. To understand the structure for PB in the gas phase and in water solvent, we have carried out Mayer bond order analysis, supporting that the structure of PB in water is cyanine-like. Moreover, PB in water is found to be much more polarized than that in chloroform solvent. Overall, the present work demonstrates that CP-QM/MM calculations can be used to understand the solvent effects on polyenic and merocyanine-like systems, which are usually difficult to model.

Enhancement of the second-order NLO responses of boron–nitrogen oligomers by copolymerization with polyyne

The enhancement of the static electronic second-order NLO properties of the linear boron–nitrogen chains by copolymerization with polyyne that is related mainly to the changes in the bond length alternation (BLA) parameter has been investigated at the HF and MP2 levels using the 6-311G(d,p) and 6-311+G(d,p) basis sets. The non-zero BLA parameter combined with ununiform electron distribution along the chain yields a unit cell asymmetry necessary for large second-order NLO responses. Alternance of the single and triple bonds brings an efficient electron delocalization resulting in large polymeric electronic dipole polarizability (186 ± 1 a.u. per unit cell). The unit cell asymmetry and large delocalization lead to sizeable longitudinal first hyperpolarizability (5850 ± 100 a.u. per unit cell).

First‐principles calculation of the Peierls distortion in an infinite linear carbon chain: the contribution of Raman spectroscopy

AbstractThe modulation of the longitudinal optical (LO) phonon branch of a linear, infinite carbon chain (carbyne) by the degree of bond length alternation (BLA) is discussed in relation to the wavenumber dispersion of the strongest Raman line of oligoynes. Furthermore, the potential energy surface describing the Peierls distortion of the infinite 1D crystal has been determined theoretically through DFT calculations with periodic boundary conditions. A two‐minima potential surface has been obtained as a function of BLA parameter, under the constraint that the diatomic unit cell keeps its translational period fixed to the optimized value. In this way, it has been possible to obtain the generalized harmonic force constant associated with the LO phonon at the Γ point. The results obtained can be related to the observed behavior of the LO Raman line upon the temperature‐driven phase transition towards a cumulenic structure. Copyright © 2007 John Wiley & Sons, Ltd.

Fluorescence and solvatochromism of a merocyanine dye with a high quadratic polarizability in solutions and polymer films

The influence of medium polarity on the spectroscopic and photophysical properties of 2-[(2 E,4 E)-6-(1,3,3-trimethyl-2,3-dihydro-1 H-2-indolyliden)-2,4-hexadienyliden]malononitrile (THDM) in solutions and polymer matrices is studied at room temperature and 77 K under conditions of steady-state and pulsed laser excitation. A large bathochromic shift of the absorption spectra observed upon an increase in the solvent polarity is caused by a strong increase of the dipole moment in the ground state ( μ g = 7.6 D ) on going to an excited Franck–Condon state ( μ FC = 33.5 D ). Based on the solvatochromic data, the quadratic polarizability was calculated to be β = ( 3.2 ± 0.6 ) × 1 0 - 28 esu , which is close to the experimentally determined value β exp = ( 3.9 ± 0.2 ) × 1 0 - 28 esu . A strong narrowing of the fluorescence spectra in comparison with the absorption spectra at room temperature is observed upon an increase in the solvent polarity caused by a decrease in the bond length alternation parameter and by weakening of vibronic interactions in the singlet excited state. The mirror symmetry of the absorption and fluorescence spectra of THDM in ethanol at 77 K is explained by the increase of the electrostatic interactions between the solvent and merocyanine molecules. The dynamic fluorosolvatochromism of THDM in the picosecond range is caused by molecules reorientations of the polar environment occurring during a time period consistent with the dielectric relaxation time of these molecules.

Influence of the polarity of a medium on the photonics of a merocyanine dye with a high quadratic polarizability

The influence of the polarity of a medium on the spectral and luminescent properties of 2-[(2E,4E)-6-(1,3,3-trimethyl-2,3-dihydro-1H-2-indolyliden)-2,4-hexadienyliden]malononitrile (THDM) in solutions and polymer matrices is studied at room temperature under conditions of steady-state and pulsed laser excitation. A large bathochromic shift of the absorption spectra observed upon an increase in the polarity of a solvent is caused by a strong increase in the molecular dipole moment μ due to a transition of molecules from the ground state (μg = 7.6 D) to an excited Franck-Condon state (μFC = 33.5 D). Based on the solvatochromic data, the quadratic polarizability was calculated to be β = (3.2 ± 0.6) × 10−28 esu, which is close to the experimentally determined value βex = (3.9 ± 0.2) × 10−28 esu. A strong narrowing of the fluorescence spectra in comparison with the absorption spectra is observed upon an increase in the solvent polarity. This narrowing is explained by a decrease in the bond length alternation parameter and by weakening of vibronic interactions in the singlet excited state. The dynamic solvatofluorochromism of THDM in the picosecond range is caused by reorientations of molecules of the polar environment occurring during a time period consistent with the dielectric relaxation time of these molecules.

Hyperpolarizability of novel carbo-meric push-pull chromophores

A systematic carbo-meric comparison of geometrical and NLO properties of push-pull aromatic NLO chromophores is undertaken at the B3PW91/6-31G* level and the INDO-SOS level respectively. In a first approach, merocyanine-like chromophores all containing a p-oxyphenyl donor and a N-methyl-4-pyridyl acceptor with various conjugated hydrocarbon bridges are considered. Carbo-merization of ethylene, 2,5-thiophenylene or 1-oxo-2,5-cyclopentadienylene bridges results in a ca ten times exaltation of static hyperpolarizability (β$_{0}$). Surprisingly, carbo-merization of the p-phenylene unit of $^{-}$O-C$_{6}$H$_{4}$-C$_{6}$H$_{4}$-C$_{5}$H$_{4}$N$^{+}$-Me results in a three-fold decrease of β$_{0}$. The negative carbo-meric is even more pronounced for the $^{-}$O-C$_{6}$H$_{4}$-C$_{6}$H$_{4}$-C≡C-C$_{5}$H$_{4}$N$^{+}$-Me ethynylogue. This is however relative to the exceptional value of the latter parent molecule (β$_{0}$ = 825 × 10$^{-30}$ cm$^{5}$esu$^{-1})$. The $^{-}$O-C$_{6}$H$_{4}$-C≡C-C$_{6}$H$_{4}$-C$_{5}$H$_{4}$N$^{+}$-Me isomer exhibits a similar hyperpolarizability (β$_{0}$ = 774 × 10$^{-30}$ cm$^{5}$ esu$^{-1})$. Inserting an additional $_{2}$ unit results in the double ethynylogue structure $^{-}$O-C$_{6}$H$_{4}$-C≡C-C$_{6}$H$_{4}$-C≡C-C$_{5}$H$_{4}$N$^{+}$-Me, for which β$_{0}$ = 1982 × 10$^{-30}$ cm$^{5}$esu$^{-1}$. The phenylethynylene effect becomes dramatic in the $^{-}$O-C$_{6}$H$_{4}$-C≡C-(C$_{6}$H$_{4}$-C≡C)$_{2}$-C$_{5}$H$_{4}$N$^{+}$-Me homologue which exhibits an unprecedented calculated value among small organic chromophores, namely: β$_{0}$ = 33856 × 10$^{-30}$ cm$^{5}$ esu$^{-1}$. A generalized absolute bond length alternation parameter (ABLA) is propounded and calculated for a homogeneous family of merocyanine-like chromophores. An astonishing regular variation of β$_{0}$ vs ABLA is empirically observed: drawing nearer to a critical value ABLA° a 0.040 A results in a steep increase of β$_{0}$. A Lorentzian-based fit is empirically found (R > 0.999) and heuristically derived from simple approximations in a two-level model. The curve interpolates points corresponding to all kinds of chromophores bearing p-C$_{6}$H$_{4}$O and 4-C$_{5}$H$_{4}$N termini, including the non-zwitterionic isomer MeO-C$_{6}$H$_{4}$-C$_{18}$H$_{4}$-C$_{5}$H$_{4}$N, the experimental synthesis of which is addressed. As in the case of p-nitroaniline, a positive carbo-meric on β$_{0}$ is restored upon carbo-merization of the p-phenylene bridge of the non-zwitterionic Me$_{2}$N-C$_{6}$H$_{4}$-C$_{6}$H$_{4}$-C$_{6}$H$_{4}$-NO$_{2}$ congener of $^{-}$O-C$_{6}$H$_{4}$-C$_{6}$H$_{4}$-C$_{5}$H$_{4}$N$^{+}$-Me. It is also shown that β$_{0}$ exaltation is larger when carbo-merization is applied to the terminal benzene ring of 4-nitro-biphenyl derivatives, thus confirming the excellent intrinsic donor properties of the carbo-benzene ring.

Relation between bond-length alternation and two-photon absorption of a push–pull conjugated molecules: a quantum-chemical study

Abstract The results of the semiempirical study of the structure/property relationships for the two-photon absorption cross-section ( δ ) of a series of prototypical π-conjugated push–pull molecules are presented. The calculations of δ for the first charge-transfer (CT) excited state were performed as a function of the bond length alternation (BLA). The molecular hyperpolarizabilities ( β and γ ) were calculated using the finite-field (FF) method. The obtained data were analyzed based on the simple two-state models. A strong dependence of δ on the BLA parameter was noticed.

A theoretical study of second hyperpolarizabilities for donor–acceptor–donor molecules

The linear polarizabilities α and second hyperpolarizabilities γ of molecules with donor–acceptor–donor (D–A–D) motifs were calculated by a semi-empirical molecular orbital method through the finite-field approach. The bond-length alternation (BLA) parameter was used to consider the structure–property relationship for this class of molecule. By tuning the molecular ground-state geometries with the applied electric field, the dependence of the longitudinal components, αxx and γxxxx, on the BLA parameter is obtained, differing from those for push–pull chromophores. With the reduction of BLA, the value of αxx increases monotonously, while γxxxx is firstly positive and increases, reaches a maximum, then decreases and crosses through zero, ultimately approaching a negative maximum. The extension of the conjugation paths connecting the acceptor and the two donors leads to a rapid increase in αxx and γxxxx values for short oligomers, accompanied by a sign reversion (from positive to negative) in γxxxx for some oligomers with highly polarized structures. A strategy for designing and synthesizing D–A–D-like molecules with large positive or negative third-order optical non-linearities is suggested based on the calculated results.

Effect of bond length alternation and of bond length alternation oscillations on the molecular nonlinear optical response of push pull polyenes

Quantum chemical ab initio calculations have been performed on a model push–pull polyene. In these calculations the mean bond length alternation of the chain has been constrained to specific discrete values so as to yield various structures ranging from a polyenelike geometry to a zwitterionic geometry. It is shown that this purely geometric distortion of the nuclei induces relevant changes of the electronic properties such as molecular dipole moment, molecular polarizabilities, and hyperpolarizabilities. Also, simulated vibrational spectra are heavily affected by changes in geometry. By changing the molecular environment (solvent effect) the theoretically predicted molecular nonlinear optical behavior parallels the trends observed experimentally, thus showing the key role played by the bond length alternation parameter. In Appendix A the derivative relationship among hyperpolarizabilities at various orders as a function of the bond length alternation parameter is discussed.

First hyperpolarizabilities of some push-pull olefins measured by the hyper-Rayleigh scattering technique

First hyperpolarizabilities of a series of donor-acceptor substituted ethylenes and butadienes have been measured using the hyper-Rayleigh scattering technique. Keeping the donor group fixed as dimethylamino, the second-order nonlinear coefficient β in these aliphatic systems has been measured and is shown to increase as a function of the acceptor strength with the exception of the cyano group, β values of the substituted butadienes are correlated with their bond length alternation parameter 〈 δr〉 obtained from semi-empirical calculations. It is shown that even in these small push-pull olefins, it is possible to generate a variety of ground state structures by choosing a suitable acceptor with a fixed donor.

The vibrational properties and defect structures in vinylene-linked low-band-gap conducting polymers

We have performed a normal mode analysis and used a newly developed vibrational analysis method for polymers, based on ab initio calculations for large oligomers, to determine the valence force field of poly(p-phenylene vinylene) (PPV), poly(thienylene vinylene) (PTV) and related polymers, and to calculate theoretical IR and Raman spectra of these oligomers and polymers. The calculated C-C stretch constants are used to describe the structure of neutral and doped PPV in terms of bond lengths r and Δr, the bond length alternation parameter. The results are compared to bond length alternation patterns from MNDO for cations (polarons) and dications (bipolarons) of large model oligomers. The results favor the formation of bipolarons in PPV.