A generalized few-state model for the first hyperpolarizability

The properties of molecules depend on their chemical structure, and thus, structure–property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure–property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule

Channel interference in multiphoton absorption

We extend the theory of channel interference to higher-order multiphoton absorption processes. We derive an explicit expression for channel interference in a three-photon absorption process and propose a general scheme for deriving such expressions for multiphoton absorption processes of any order. Based on this general scheme, we derive and analyze the simplest few-state models for multiphoton absorption in centrosymmetric molecules and discuss the criteria for maximizing the corresponding multiphoton absorption strengths

Interplay of twist angle and solvents with two-photon optical channel interference in aryl-substituted BODIPY dyes

Channel interference plays a crucial role in understanding the physics behind multiphoton absorption processes. In this work, we study the role of channel interference and solvent effects on the two-photon absorption in aryl-substituted boron dipyrromethene (BODIPY) dyes, a class of intramolecular charge-transfer (ICT) molecules. For this purpose, we consider fourteen dyes of this class with various donor/acceptor substitutions at the para position of the phenyl ring and with or without methyl (–CH3) substitution on the BODIPY moiety. The presence of a methyl group on the BODIPY moiety affects the dihedral angle significantly, which in turn affects the one- (OPA) and two-photon absorption (TPA) properties of the molecules. Among the molecules studied, the one having the strong electron-donating dimethylamino group and no methyl substitution at the BODIPY moiety is found to have the highest TPA cross section. Our few-state model analysis shows that the large TPA activity of this molecule is due to the all positive contributions from different channel interference terms. Change in dielectric constant of the medium is found to have a profound impact on both the magnitude and sign of the channel interference terms. The magnitude of destructive channel interference gradually decreases with decreasing solvent polarity and becomes constructive in a low-polarity solvent. We also study the effect of rotating the phenyl ring with respect to the BODIPY moiety on the TPA activity. In the gas phase and in different solvents, we found that channel interference is changed from destructive to constructive on twisting the molecule. These results are explained by considering different dipole-, energy- and angle-terms appearing in the expression of a two-state model

Effect of donor–acceptor orientation on solvent-dependent three-photon activity in through-space charge-transfer systems – case study of [2,2]-paracyclophane derivatives

We study the effect of donor–acceptor orientation on solvent-dependent three-photon transition probabilities (δ3PA) of representative through-space charge-transfer (TSCT) systems, namely, doubly positively charged [2,2]-paracyclophane derivatives. Our cubic response calculations reveal that the value of δ3PA may be as high as 106 a.u., which can further be increased by a specific orientation of the donor–acceptor moieties. To explain the origin of the solvent cum orientation dependency of δ3PA, we have calculated different three-photon tensor components using a two-state model, noting that only a few tensor elements contribute significantly to the overall δ3PA value. We show that this dependence is due to the large dipole moment difference between the ground and excited states of the systems. The dominance of a few tensor elements indicates a synergistic involvement of π-conjugation and TSCT in the large δ3PA of these systems

Tuning of Hyperpolarizability, One- and Two-Photon Absorption of D-A and D-A-A Type Intramolecular Charge Transfer Based Sensors

Solvents play an important role in shaping the intramolecular charge transfer (ICT) properties of π-conjugated molecules, which in turn can affect their one-photon absorption (OPA) and two-photon absorption (TPA) as well as the static (hyper)polarizabilities. Here, we study the effect of solvent and donor-acceptor arrangement on linear and nonlinear optical (NLO) response properties of two novel ICT-based fluorescent sensors, one consisting of hemicyanine and dimethylaniline as electron withdrawing and donating groups (molecule 1), respectively and its boron-dipyrromethene (BODIPY, molecule 2)-fused counterpart (molecule 3). Density functional theoretical (DFT) calculations using long-range corrected CAM-B3LYP and M06-2X functionals, suitable for studying properties of ICT molecules, are employed to calculate the desired properties. The dipole moment (µ) as well as the total first hyperpolarizability (βtotal) of the studied molecules in the gas phase is dominantly dictated by the component in the direction of charge transfer. The ratios of vector component of first hyperpolarizability (βvec) to βtotal also reveal unidirectional charge transfer process. The properties of the medium significantly affect the OPA, hyperpolarizability and TPA properties of the studied molecules. Time dependent DFT (TDDFT) calculations suggest interchanging between two lowest excited states of molecule 3 from the gas phase to salvation. The direction of charge polarization and dominant transitions among molecular orbitals involved in the OPA and TPA processes are studied. The results presented are expected to be useful in tuning the NLO response of many ICT-based chromophores, especially those with BODIPY acceptors.<br /

Enhancement of Twist Angle Dependent Two-Photon Activity through the Proper Alignment of Ground to Excited State and Excited State Dipole Moment Vectors

Herein, we show that the two-photon (TP) transition probability (δ_TP) of <i>o</i>-betaine system will reach its maximum value at a twist angle around 65°. However, the potential energy scan with respect to the twist angle between its two rings indicates that the molecule in its ground state is quite unstable at this twist angle. Out of the different possibilities, the one having a single methyl group at the ortho position of the pyridinium ring is found to attain the optimum twist angle between the two rings, and interestingly, this particular substituted <i>o</i>-betaine has larger δ_TP value than any other substituted or pristine <i>o</i>-betaine. The twist angle dependent variation of δ_TP has been explained by employing the generalized-few-state-model formula for 3D molecules. The results clearly reveal that the magnitude of ground to excited state and excited state dipole moment vectors as well as the angle between them are strongly in favor of maximizing the overall δ_TP values at the optimum twist angle. The constructive interference between the optical channels at the optimum twist angle also plays an important role to achieve the maximum δ_TP value. Furthermore, to give proper judgment on our findings, we have also performed solvent phase calculations on all the model systems in nonpolar solvents, namely, cyclohexane and <i>n</i>-hexane, and the results are quite consistent with the gas phase findings. The present study will definitely offer a new way to synthesize novel two-photon active material based on <i>o</i>-betaine

On the Origin of Large Two-Photon Activity of DANS Molecule

In this work, using the quadratic response theory and two-state model approach, we have explained the origin of high two-photon activity and the corresponding solvent dependence of 4,4′-dimethyl-amino-nitro-stilbene (DANS) molecule. For this purpose, we have made two structural modifications in the DANS molecule (1) at the donor–acceptor part and (2) at the unsaturated bridge between the two rings and calculated the one- and two-photon (OP and TP) absorption parameters of all the systems in gas phase and in three different solvents, viz., MeCN, THF, and toluene. We found that the removal of donor–acceptor groups from the original DANS molecule vanishes the transition moment between the ground and excited states and also the corresponding dipole moment difference, and the saturation of the π-conjugation bridge between the two rings keeping the donor–acceptor groups intact causes a large decrease in the ground to excited state transition moment. These changes, in turn, decrease the overall TP activity of the molecules as compared to DANS. On the basis of our analysis, we have concluded that neither the donor–acceptor pair nor the π-conjugation bridge between the two, rather their cooperative involvement leads to a large overlap between the ground and virtual and also the virtual and charge-transfer states, which are eventually responsible for the very large TP activity of DANS