Why does the orientation of azulene affect the two-photon activity of a porphyrinoid-azulene system?

Attaching a dipolar molecule in a symmetric system induces a major change in the electronic structure, which may be reflected as the enhancement of the optical and charge-transfer properties of the combined system as compared to the pristine ones. Furthermore, the orientation of the dipolar molecule may also affect the said properties. This idea is explored in this work by taking porphyrinoid molecules as the pristine systems. We attached azulene, a dipolar molecule, at various positions of five porphyrinoid cores and studied the effect on charge-transfer and one- and two-photon absorption properties using the state-of-the-art RICC2 method. The attachment of azulene produces two major effects - firstly it introduces asymmetry in the system and, secondly, being dipolar, it makes the resultant molecule dipolar/quadrupolar. Porphyrin, N-confused porphyrin, sub-porphyrin, sapphyrin, and hexaphyrin are used as core porphyrinoid systems. The change in charge-transfer has been studied using the orbital analysis and charge-transfer distance parameter for the first five singlet states of the systems. The effect of orientation of azulene on the said properties is also explored. The insights gained from our observations are explored further at the dipole and transition dipole moment levels using a three-state model.

Chromophore Planarity, -BH Bridge Effect, and Two-Photon Activity: Bi- and Ter-Phenyl Derivatives as a Case Study.

In this work, we have employed electronic structure theories to explore the effect of the planarity of the chromophore on the two-photon absorption properties of bi- and ter-phenyl systems. To that end, we have considered 11 bi- and 7 ter-phenyl-based chromophores presenting a donor-π-acceptor architecture. In some cases, the planarity has been enforced by bridging the rings at ortho-positions by -CH2 and/or -BH, -O, -S, and -NH moieties. The results presented herein demonstrate that in bi- and ter-phenyl systems, the planarity achieved via a -CH2 bridge increases the 2PA activity. However, the introduction of a bridge with the -BH moiety perturbs the electronic structure to a large extent, thus diminishing the two-photon transition strength to the lowest electronic excited state. As far as two-photon absorption activity is concerned, this work hints toward avoiding -BH bridge(s) to enforce planarity in bi- and ter-phenyl systems; however, one may use -CH2 bridge(s) to achieve the enhancement of the property in question. All of these conclusions have been supported by in-depth analyses based on generalized few-state models.

First-order hyperpolarizabilities of propellanes: elucidating structure-property relationships.

Following recent experimental work demonstrating strong nonlinear optical properties, namely second harmonic generation of light, in crystals composed of 16,20-dinitro-(3,4,8,9)-dibenzo-2,7-dioxa-5,10-diaza[4.4.4]propellane molecules [A. Miniewicz, S. Bartkiewicz, E. Wojaczynska, T. Galica, R. Zalesny and R. Jakubas, J. Mater. Chem. C, 2019, 7, 1255-1262] in this paper we aim to investigate "structure-property" relationships for a series of 16 propellanes presenting a wide palette of substituents with varying electron-accepting/donating capabilities. To that end, we use electronic- and vibrational-structure theories and a recently developed generalized few-state model combined with a range-separated CAM-B3LYP functional to analyze electronic and vibrational contributions to the first hyperpolarizability for the whole series of molecules. The variations in computed properties are large among the studied set of substituents and can reach an order of magnitude. It has been demonstrated that the maximum values of frequency-independent first hyperpolarizability are expected for strong electron-accepting NO2 substituents, but only at the preferred position with respect to the electronegative oxygen atom in the 1,4-oxazine moiety. This holds for electronic as well as vibrational counterparts.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations.

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor-acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure-property studies across large series of dipolar compounds.

Much of a Muchness: On the Origins of Two- and Three-Photon Absorption Activity of Dipolar Y-Shaped Chromophores.

The molecular origin of two- (2PA) and three-photon absorption (3PA) activity in three experimentally studied chromophores, prototypical dipolar systems, is investigated. To that end, a generalized few-state model (GFSM) formula is derived for the 3PA transition strength for nonhermitian theories and employed at the coupled-cluster level of theory. Using various computational techniques such as molecular dynamics, linear and quadratic response theories, and GFSM, an in-depth analysis of various optical channels involved in 2PA and 3PA processes is presented. It is found that the four-state model involving the second and third excited singlet states as intermediates is the smallest model among all considered few-state approximations that produces 2PA and 3PA transition strengths (for S0 → S1 transition) close to the reference results. By analyzing various optical channels appearing in these models and involved in studied multiphoton processes, we found that the 2PA and 3PA activities in all the three chromophores are dominated and hence controlled by the dipole moment of the final excited state. The similar origins of the 2PA and the 3PA in these prototypical dipolar chromophores suggest transferability of structure-property relations from the 2PA to the 3PA domain.

Structure, Carbonyl Vibrational Frequencies, and Local Energy Decomposition of Binding Energy in Formaldehyde Clusters, (HCHO)n=1-10.

In this work, structures, vibrational frequencies, and binding energies of formaldehyde clusters, (HCHO)n=1-10, are investigated by using global optimization genetic algorithm followed by density functional theory calculations and local energy decomposition (LED) analysis at the high-end DLPNO-CCSD(T) level of theory. With the use of genetic algorithm, different structures of all clusters are generated, which are further refined by the quantum chemical geometry optimization technique. From those structures, the conformer with the lowest energy is chosen and used for further analysis. The variation in carbonyl stretching frequency with change in cluster size is discussed and compared with available experimental data. Furthermore, by using standard and advanced LED analysis, different components of the binding energy are studied in all clusters and their variations with cluster size are also discussed.

Anisotropic and Self-Healing Copolymer with Multiresponsive Capability via Recyclable Alloy-Mediated RDRP.

A novel triple stimuli sensitive block copolymer is prepared by magnetically separable and reusable (up to multiple cycles) Ni-Co alloy nanoparticles mediated reversible deactivation radical polymerization (RDRP) at 25 °C, that responds to changes in temperature, pH, and light. Design of this block copolymer constitutes a temperature-sensitive N-isopropylacrylamide (NIPAM), an acid-sensitive lysine methacrylamide (LysMAM), and a light responsive umbelliferone (UMB) end group. The stimuli response, in response to one stimulus as well as combinations of stimuli, has been evaluated. Responsiveness to light allows the construction of self-healing materials. Density functional theory calculations rationalize the underlying mechanism of the polymerization.

Two-Photon Absorption Activity of BOPHY Derivatives: Insights from Theory.

We present a theoretical study of a two-photon absorption (2PA) process in dipolar and quadrupolar systems containing two BF2 units. For this purpose, we considered 13 systems studied by Ponce-Vargas et al. [ J. Phys. Chem. B 2017, 121, 10850-10858] and performed linear and quadratic response theory calculations based on the RI-CC2 method to obtain the 2PA parameters. Furthermore, using the recently developed generalized few-state model, we provided an in-depth view of the changes in 2PA properties in the molecules considered. Our results clearly indicate that suitable electron-donating group substitution to the core BF2 units results in a large red-shift of the two-photon absorption wavelength, thereby entering into the desired biological window. Furthermore, the corresponding 2PA strength also increases significantly (up to 30-fold). This makes the substituted systems a potential candidate for biological imaging.

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 ß, 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 ß and can hence be used to fine-tune the magnitude of ß in a molecule.

Tuning of hyperpolarizability, and one- and two-photon absorption of donor-acceptor and donor-acceptor-acceptor-type intramolecular charge transfer-based sensors.

The present work aims to study the effect of solvent as well as arrangement of donor-acceptor groups on linear and non-linear optical (NLO) response properties of two experimentally studied intramolecular charge-transfer (ICT)-based fluorescent sensors. One of them (molecule 1) is a donor-acceptor (D-A) system with hemicyanine and dimethylanilino as electron withdrawing and donating groups, respectively, while the other one (molecule 3) is molecule 1 fused with a boron-dipyrromethene (BODIPY) moiety. BODIPY acts as the electron acceptor group of molecule 2 that as well consists of dimethylanilino as the electron donor. Density functional theory (DFT) as well as time-dependent DFT has been employed to optimize the geometry of the molecules, followed by computation of dipole moment (µ), static first hyperpolarizability (ßtotal), and one- and two-photon absorption (TPA) strengths. The results reveal that dipole moment as well as total static first hyperpolarizability (ßtotal) of the studied molecules is dominated by the respective components in the direction of charge transfer. The ratio of vector component of first hyperpolarizability (ßvec) to ßtotal also supports the unidirectional charge transfer in the studied systems. In molecule 3, which is a donor-acceptor-acceptor (D-A-A)-type system, the BODIPY moiety is found to play a major role in controlling the NLO response over the other acceptor group. Solvents are also found to play an important role in controlling the linear as well as NLO response of the studied systems. A significant increase in the first hyperpolarizability as well as TPA cross-section of the studied molecules is predicted due to an increase in the dielectric constant of the medium. The results presented are expected to provide a clue in tuning the NLO response of many ICT-based chromophores, especially those with D-A-A arrangements.

Intersystem crossing rate dependent dual emission and phosphorescence from cyclometalated platinum complexes: a second order cumulant expansion based approach.

Rates of intersystem crossing (kISC) of two platinum(ii) complexes containing acetylacetonate (acac) and extended cyclometalated ppy (Hppy = 2-phenylpyridine) (1) and thpy (Hthpy = 2-(2' thienyl)pyridine) (2) ligands are calculated using the Condon approximation to the Golden Rule and employing the second-order cumulant expansion method. The emission wavelengths obtained at the RI-CC2 level for the lowest excited singlet (S1) and triplet (T1) states of the two complexes are well in agreement with the experimental results. Our analysis based on kISC evinces that the major pathway involved with the phosphorescence process in complex 1 arises from the S1 → T2 intersystem crossing while the S1 → T1 intersystem crossing is the key step towards the commencement of dual emission in complex 2. Furthermore, it is found that the different pathways are mostly guided by two factors namely, the energy gap and the spin-orbit interaction between the concerned states. Interestingly, the calculated kISC for complex 1 is found to be 107 times larger than that of complex 2, which suggests a rapid depletion of the S1 state population vis-à-vis radiative emission only by phosphorescence from the internally converted lowest excited triplet state while for complex 2, the relatively lower kISC is attributed to the dual emission from this complex.

Benchmarking the Performance of Exchange-Correlation Functionals for Predicting Two-Photon Absorption Strengths.

The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.

Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states.

The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as µ-2 in the large range-separation-parameter µ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as µ-3) towards their pure wavefunction theory values (µ → +∞ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) µ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz., H2, HeH+, and LiH), thus considering different types of excitations such as Rydberg, charge transfer, and double excitations. Potential energy profiles of the first three and four singlet Σ+ excitation energies in HeH+ and H2, respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.

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.

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.

Solvent effects on static polarizability, static first hyperpolarizability and one- and two-photon absorption properties of functionalized triply twisted Möbius annulenes: a DFT study.

The present work aims to study solvent effects on the polarizability (α), static first hyperpolarizability (ß) and one- and two-photon absorption (OPA and TPA) properties of a new class of molecules viz. triply twisted Möbius annulenes, recently studied by us in vacuum phase [Kundi et al., Phys. Chem. Chem. Phys., 2015, 17, 6827]. We have employed linear and quadratic response theories within the framework of time-dependent density functional theory with the CAM-B3LYP functional and a cc-pVDZ basis set to calculate different parameters. The microscopic details of the said properties have been studied using a two-state model (2SM) approach, which performs very well in the case of ß and TPA of the first excited state of all the systems. However for the second excited state, the 2SM results are far from those of response theory. In fact, in comparison to response theory, 2SM predicts an opposite trend for the TP activity of some of the model systems, indicating a significant contribution from the other higher excited states. The anomaly between the 2SM approach and response theory has been resolved by incorporating three states in the calculations.

Triply twisted Möbius annulene: a new class of two-photon active material--a computational study.

In the present work, we have studied the gas phase one- and two-photon absorption (OPA and TPA) properties of the first two excited states of the triply twisted Möbius annulene molecule (G. R. Schaller, et al., Nat. Chem. 2014, 6, 608) and five model systems substituted with different donor and acceptor groups. The main purpose of this study is to explore the OPA and TPA properties of this newly synthesized molecule and the unique π-conjugation provided by it. We have used the linear and quadratic response theory methods with the CAMB3LYP functional and the cc-pVDZ basis set for calculating the required parameters. Our results indicate that in the absence of any directive force (i.e. the donor-acceptor groups) the unsubstituted molecule is completely TP inactive. However, as soon as we insert the donor-acceptor group the system becomes TP active which can further be enhanced (up to 3640 GM in our case) by changing the donor-acceptor groups. We have explained the results by performing a two-state model calculation and by analyzing the TP tensor elements and the orbitals involved in the transition processes.

Donors contribute more than acceptors to increase the two-photon activity--a case study with cyclopenta[b]naphthalene based molecules.

In the present work, we address the question -"which among the electron donors and the electron acceptors contribute more to the two-photon (TP) activity of a donor-π-acceptor type of molecule?" For this purpose we have performed ab initio calculations to calculate the TP transition probability (δTP) of a recently synthesized (Benedetti et al., J. Am. Chem. Soc., 2012, 134(30), 12418-12421) cyclopenta[b]naphthalene based chemo-sensor and its derivatives containing different electron donor and acceptor groups. Our study revealed that both under vacuum and in solvent phases, an increase in electron donor strength (-OMe, -NH2, -NMe2) increases the δTP value up to five times, whereas, an increase in the acceptor group strength (-COCH3, -NO2, -CN) increases it by a factor of two only. The highest δTP value is obtained for the molecule having the strongest donor-acceptor pair (-CN, -NMe2) considered in this work. We have also noted that, the removal of the cyclopentane ring from the original system increases the δTP value by ∼20% and the replacement of the naphthyl group by the benzene ring decreases it by ∼70%. All these results are explained by inspecting different TP tensor elements and different transition moment vectors involved in a two-state model approach. A close scrutiny of different parameters in 2SM clearly reveals that upon increasing the strength of either the donor or the acceptor group the parameters change in favour of increasing the overall δTP values but in the case of donors this effect is much larger.

Electrically controlled eight-spin-qubit entangled-state generation in a molecular break junction.

The generation of spin-based multi-qubit entangled states in the presence of an electric field is one of the most challenging tasks in current quantum-computing research. Such examples are still elusive. By using non-equilibrium Green's function-based quantum-transport calculations in combination with non-collinear spin density functional theory, we report that an eight-spin-qubit entangled state can be generated with the high-spin state of a dinuclear Fe(II) complex when the system is placed in a molecular break junction. The possible gate operation scheme, gating time, and decoherence issues have been carefully addressed. Furthermore, our calculations reveal that the preservation of the high spin state of this complex is possible if the experimentalists keep the electric-field strength below 0.78 V nm(-1). In brief, the present study offers a unique way to realize the first example of a multi-qubit entangled state by electrical means only.

Chemical control of channel interference in two-photon absorption processes.

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.