Valence-bond Charge-transfer Model Research Articles

Two States Are Not Enough: Quantitative Evaluation of the Valence‐Bond Intramolecular Charge‐Transfer Model and Its Use in Predicting Bond Length Alternation Effects

The structural weights of the canonical resonance contributors used in the Two-state valence-bond charge-transfer model, neutral (N, R1) and ionic (VB-CT, R2), to the ground states and excited states of a series of linear dipolar intramolecular charge-transfer chromophores containing a buta-1,3-dien-1,4-diyl bridge have been computed by using the block-localized wavefunction (BLW) method at the B3LYP/6-311+G(d) level to provide the first quantitative assessment of this simple model. Ground- and excited-state analysis reveals surprisingly low ground-state structural weights for the VB-CT resonance form using either this Two-state model or an expanded Ten-state model. The VB-CT state is found to be more prominent in the excited state. Individual resonance forms were structurally optimized to understand the origins of the bond length alternation (BLA) of the bridging unit. Using a Wheland energy-based weighting scheme, the weighted average of the optimized bond lengths with the Two-state model was unable to reproduce the BLA features with values 0.04 to 0.02 Å too large compared to the fully delocalized (FD) structure (BLW: ca. -0.13 to -0.07 Å, FD: ca. -0.09 to -0.05 Å). Instead, an expanded Ten-state model fit the BLA values of the FD structure to within only 0.001 Å of FD.

Solvent effects on the static nuclear relaxation and the curvature hyperpolarizabilities of push-pull polyenes

The influence of the solvent on the nuclear relaxation and curvature contributions to the first, β, and second, γ, hyperpolarizability, of push-pull molecules has been investigated within the framework of the valence-bond charge-transfer model and the analytical evaluation of electrical properties method. It was found that the solvent effect on the β and γ values is very pronounced, where increases of a factor as great as 15 for cyanine resonance form and 30 for zwitterionic and neutral resonance forms, were calculated upon changing from gas phase to an aqueous environment. The general trends of β and γ in different environments may be estimated roughly by adding the harmonic terms of the nuclear relaxation to the electronic contribution because the anharmonics terms of the nuclear relaxation and the contribution of curvature tend to cancel one another.

Computational insight into relations between electronic and vibrational polarizabilities within the two-state valence-bond charge-transfer model

In this paper, the relationship between static vibrational and electronic hyperpolarizabilities of a series of push–pull molecules within the two-state valence-bond charge-transfer model are reinvestigated computationally at the Møller–Plesset level of theory. Although the level of theory employed here gives significantly different results for electronic and vibrational counterparts than those obtained by Bishop et al. [D. Bishop, B. Champagne, B. Kirtman, J. Chem. Phys. 109 (1998) 9987] at the RHF level, the overall conclusions remain unchanged: The comparison of ab initio computations with the predictions of the VB–CT model gives a little confidence in the latter.

Analytic expressions of the curvature contribution to the static electrical properties of push–pull conjugated systems within the VB–CT model and the AEEP method

We have derived analytic expressions of the curvature contribution to the dipole moment as well as to the static polarizability and hyperpolarizabilities of push–pull π-conjugated systems. These expressions were obtained from harmonic zero-point energy using the analytical evaluation of electrical properties method and the valence-bond charge-transfer model. We have found that the curvature contribution can be expressed in terms of the electronic hyperpolarizabilities. On the other hand, the curvature contribution can be as important as—or even more important than—electronic contribution.

Relaxation times effects on the four wave-mixing signal for π-conjugated push-pull molecules within the two-state valence-bond charge-transfer model

We have theoretically studied the four wave-mixing signal for π-conjugated push-pull molecules in the context of the simple valence-bond charge-transfer model. In particular, we address the effect of modify the rate between the longitudinal and transversal relaxation times on this signal considering the variation of the parameter f (fraction of the charge-transfer resonance structure of the ground state). Our results show notable changes in intensity of the peaks of the four wave-mixing (FWM) spectrum with relation to the variation in the ratio of the relaxation times.

Curvature contributions to the static electrical properties of push-pull molecules

Abstract Calculations of the curvature contribution to the diagonals components of the static dipole moment (μ), polarizability (α), first (β) and second (γ) hyperpolarizability of push-pull molecules are presented. This contribution was obtained from the analytical evaluation of electrical properties method using the harmonic zero-point energy. The valence-bond charge-transfer model was employed to obtain the field-dependent force constant and their derivates with respect to electric field. Our results show a relationship between the curvature and electronic contributions. We have also found that the curvature contribution is important in a numerical estimation of β and γ.

Simple parameter-dependent relations for the maximum value of the optical activity of push—pull molecules in solution

Based on the valence bond-charge transfer model for push-pull polyenes and reaction field theory, several parameter-dependent relations for selecting the molecule-solvent pair that produces a maximum value of the nonlinear optical response have been established. From these relations, we have determined a limit to the value of the dielectric constant of the solvent (above ε = 9) and effectiveness of the donor-acceptor pairs (between 5 and 6eV) beyond which the (hyper)polarizabilities of push-pull molecules in solution do not exhibit any significant change in magnitude.

Inclusion of non-orthogonality on the valence bond charge-transfer model for nonlinear optical properties of push—pull molecules

In models based on valence bond theory for predicting nonlinear optical properties of push-pull molecules, the wave functions representing resonance structures are assumed to be orthogonal. We have extended the two-state valence bond charge-transfer model to include non-zero overlap integrals. The resulting model leads to analytic formulae for the polarizability and hyperpolarizabilities, which are related to the overlap and other molecular parameters. In particular we report, as a function of the overlap: (i) relatively weak dependence of the first-order polarizability; (ii) significant variations in both the magnitude and the shape of the response curves corresponding to the second- and third-order polarizabilities. This result may be of relevance in the context of optical switching effects induced by chemical changes (related to the overlap) rather than the more conventional field-induced effect.

Large Off-Diagonal Contribution to the Second-Order Optical Nonlinearities of Λ-Shaped Molecules

The diagonal and off-diagonal tensor components of the first hyperpolarizability of a series of A-shaped molecules are compared by means of ab initio and semiempirical molecular orbital calculations. The calculated results are rationalized using expressions derived from a simple valence-bond charge-transfer model in which one ground and two excited state are described as a combination of one valence-bond (VB) and two charge-transfer (CT) states. In addition to the CT character, the angle (2θ) between the two donor (D)/acceptor (A) branches is a key parameter to determine the relative magnitudes between the β x x z and β z z z components. In the VB-2CT model, β x x z presents a maximum value for 2θ = 109.47°, whereas β x x z and μ z have the same sign. On the other hand, β z z z decreases monotonically with θ, and its variations with the CT character follow a curve with two extrema like for one-dimensional D/A chromophores. The ab initio and semiempirical calculations as well as the VB-2CT model show that A-shaped molecules with large first hyperpolarizability and specific η = β x x z /β z z z can be designed in order to build phase-matchable second-harmonic generation crystals.

Relationship between static vibrational and electronic hyperpolarizabilities of π-conjugated push–pull molecules within the two-state valence-bond charge-transfer model

The two-state valence-bond charge-transfer (VB-CT) model for π-conjugated push–pull molecules is analyzed to yield several parameter-independent relations between vibrational and electronic hyperpolarizabilities. Ab initio computational tests show that these relations are not satisfied. As a byproduct of the ab initio calculations, we have found cases where the static vibrational first hyperpolarizability is much larger than the static electronic first hyperpolarizability. Our results also shed light on a controversy regarding normal coordinate polarizability derivatives.

Vibrational contributions to the molecular first and second hyperpolarizabilities of a push–pull polyene

The vibrational contributions to the first and second hyperpolarizabilities of a push–pull polyene are theoretically studied by using the valence-bond charge-transfer model. The formal relationships between the vibrational and electronic contributions to the hyperpolarizabilities are derived. It is found that there exist strong correlations between the vibrational contributions and bond length alternation of a push–pull polyene. By calculating these contributions numerically, it is proven that the vibrational contributions, estimated from the IR, Raman, and hyper-Raman measurements, to the hyperpolarizabilities can also provide a measure of the nonlinear optical property.