For the first time, we report the effect of interference between different optical channels on the two-photon absorption (TPA) process in three dimensions. We have employed response theory as well as a sum-over-states (SOS) approach involving few intermediate states to calculate the TPA parameters like transition probabilities (δ(TP)) and TPA tensor elements. In order to use the limited SOS approach, we have derived a new formula for a generalized few-state-model (GFSM) in three dimensions. Due to the presence of additional terms related to the angle between different transition moment vectors, the channel interference associated with the TPA process in 3D is significantly different and much more complicated than that in 1D and 2D cases. The entire study has been carried out on the two simplest Reichardt's dyes, namely 2- and 4-(pyridinium-1-yl)-phenolate (ortho- and para-betain) in gas phase, THF, CH(3)CN and water solvents. We have meticulously inspected the effect of the additional angle related terms on the overall TPA transition probabilities of the two 3D isomeric molecules studied and found that the interfering terms involved in the δ(TP) expression contribute both constructively and destructively as well to the overall δ(TP) value. Moreover, the interfering term has a more conspicuous role in determining the net δ(TP) associated with charge transfer transition in comparison to that of π-π* transition of the studied systems. Interestingly, our model calculations suggest that, for o- and p-betain, the quenching of destructive interference associated with a particular two-photon process can be done with high polarity solvents while the enhancement of constructive interference will be achieved in solvents having relatively small polarity. All the one- and two-photon parameters are evaluated using a range separated CAMB3LYP functional.
The two-photon absorption (TPA) process is the simplest and hence the most studied nonlinear optical phenomenon, and various aspects of this process have been explored in the past few decades, experimentally as well as theoretically. Previous investigations have shown that the two-photon (TP) activity of a molecular system can be tuned, and at present, performance-tailored TP active materials are easy to develop by monitoring factors such as length of conjugation, dimensionality of charge-transfer network, strength of donor-acceptor groups, polarity of solvents, self-aggregation, H-bonding, and micellar encapsulation to mention but a few. One of the most intriguing phenomena affecting the TP activity of a molecule is channel interference. The phrase "channel interference" implies that if the TP transition from one electronic state to another involves more than one optical pathway or channel, characterized by the corresponding transition dipole moment (TDM) vectors, the channels may interfere with each other depending upon the angles between the TDM vectors and hence can either increase (constructive interference) or decrease (destructive interference) the overall TP activity of a system to a significant extent. This phenomenon was first pointed out by Cronstrand, Luo, and Ågren [Chem. Phys. Lett. 2002, 352, 262-269] in two-dimensional systems (i.e., only involving two components of the transition moment vectors). For three-dimensional molecules, an extended version of this idea was required. In order to fill this gap, we developed a generalized model for describing and exploring channel interference, valid for systems of any dimensionality. We have in particular applied it to through-bond (TB) and through-space (TS) charge-transfer systems both in gas phase and in solvents with different polarities. In this Account, we will, in addition to briefly describing the concept of channel interference, discuss two key findings of our recent work: (1) how to control the channel interference by chemical means, and (2) the role of channel interference in the anomalous solvent dependence of certain TP chromophores. For example, we will show that simple structurally induced changes in certain dihedral angles of the well-known betaine dye (TB type) will help fine-tune the constructive channel interference and hence increase the overall TP activity of molecules with this general TP channel structure. Another intriguing result we will discuss is observed for a tweezer-trinitrofluorinone complex (TS type) where, on moving from polar to essentially nonpolar solvents, the nature of the channel interference switches from destructive to constructive, leading to a net abnormal solvent dependence of the TP activity of the system. The present Account highlights the usefulness of the channel interference effect and establishes it as a new and unique way of controlling the TP transition probability in different types of three-dimensional molecules.
In the Letter, we address the question as to why larger two-photon absorption cross sections are observed in nonpolar than in polar solvents for through-space charge-transfer (TSCT) systems such as [2,2]-paracyclophane derivatives. In order to answer this question, we have performed ab initio calculations on two well-known TSCT systems, namely, a [2.2]-paracyclophane derivative and a molecular tweezer-trinitrofluorinone complex, and found that the two-photon transition probability values of these systems decreases with increasing solvent polarity. To rationalize this result, we have analyzed the role of different optical channels associated with the two-photon process and noticed that, in TSCTs, the interference between the optical channels is mostly destructive and that its magnitude increases with increasing solvent polarity. Moreover, it is also found that a destructive interference may sometimes even become a constructive one in a nonpolar solvent, making the two-photon activity of TSCTs in polar solvents less than that in nonpolar solvents.
In the present work, we have studied the two-photon absorption (TPA) properties of some selective molecules containing triarylborane and 1-naphthylphenylamine as the acceptor and donor moiety, respectively. The calculations are performed by using the state-of-the-art linear and quadratic response theory in the framework of the time dependent density functional theoretical method. The TPA parameters are calculated with CAMB3LYP functional and the cc-pVDZ basis set. The one-photon results indicate that both the electronic transitions (S(0)-S(1) and S(0)-S(2)) are associated with the charge transfer interaction between the donor and acceptor moieties along with the reorganization of the π-electron density. All these chromophores are found to have very strong two-photon active modes. In order to find out the origin of large TP transition probability of these molecules, we have performed two-state model (TSM) and sum-over-states (SOS) calculations. We have found that the TSM failed to reproduce the correct trend of the TP transition probability of the molecules obtained from the response theory, while SOS is quite successful in doing so. The whole study indicates that the transition moments between the excited states play a pivotal role in controlling the TP transition probabilities of these molecules. The role of solvent in the TP transition probability of these molecules has meticulously been scrutinized within the polarized continuum model (PCM). Further more, we have benchmarked our theoretical findings by calculating the TPA cross-section of a boron and nitrogen containing a charge transfer molecule for which the experimental result is available and we found that our theoretical result is in good agreement with the experimental one which definitely demonstrates the potential of all these light-emitting diode molecules as TP active materials too.
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.
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