Effects of dipole alignment and channel interference on two-photon absorption cross sections of two-dimensional charge-transfer systems

Impact of the Protein Environment on Two-Photon Absorption Cross-Sections of the GFP Chromophore Anion Resolved at the XMCQDPT2 Level of Theory

The search for fluorescent proteins with large two-photon absorption (TPA) cross-sections and improved brightness is required for their efficient use in bioimaging. Here, we explored the impact of a single-point mutation close to the anionic form of the GFP chromophore on its TPA activity. We considered the lowest-energy transition of EGFP and its modification EGFP T203I. We focused on a methodology for obtaining reliable TPA cross-sections for mutated proteins, based on conformational sampling using molecular dynamics simulations and a high-level XMCQDPT2-based QM/MM approach. We also studied the numerical convergence of the sum-over-states formalism and provide direct evidence for the applicability of the two-level model for calculating TPA cross-sections in EGFP. The calculated values were found to be very sensitive to changes in the permanent dipole moments between the ground and excited states and highly tunable by internal electric field of the protein environment. In the case of the GFP chromophore anion, even a single hydrogen bond was shown to be capable of drastically increasing the TPA cross-section. Such high tunability of the nonlinear photophysical properties of the chromophore anions can be used for the rational design of brighter fluorescent proteins for bioimaging using two-photon laser scanning microscopy.

Difluoroborate-based bichromophores: Symmetry relaxation and two-photon absorption

Given potential applications of multiphoton absorbers, in the present work we have studied the symmetry-relaxation effects in one- and two-photon absorption spectra in two bichromophore systems based on difluoroborate core linked by biphenylene or bianthracene moieties. We have employed a palette of experimental methods (synthesis, one- and two-photon spectroscopy, X-ray crystallography) and state-of-the-art computational methods to shed light on how symmetry relaxation, a result of twisting of building blocks, affects one- and two-photon absorption of the two studied fluorescent dyes. Electronic-structure calculations revealed that the planarity of central biphenyl moiety, as well as deviations from planarity up to 30-40 deg., ensure maximum values of two-photon transition strengths. Perpendicular arrangement of phenylene units in biphenylene moiety leads to 20% drop in the two-photon transition strengths. More detailed studies demonstrated that equilibrium structures of both compounds in chloroform solution show very different values of two-photon absorption cross sections at absorption band maxima, i.e. 224 GM for and 134 GM for biphenyle and bianthracene linkers, respectively. The latter value is in good agreement with experimental value obtained using Z-scan method. The difference in two-photon absorption cross section between both compounds can be rationalized based on equilibrium geometry differences, i.e. interplanar angle is 35 deg and 91 deg in the case of biphenylene and bianthracene moiety, respectively. It is thus not beneficial to introduce conformationally locked central linker based on bianthracene moiety.

Quantum chemistry study of the multiphoton absorption in enhanced green fluorescent protein at the single amino acid residue level

The chromophore (CRO) of fluorescent proteins (FPs) is embedded in a complex environment that is a source of specific interactions with the CRO. Understanding how these interactions influence FPs spectral properties is important for a directed design of novel markers with desired characteristics. In this work, we apply computational chemistry methods to gain insight into one-, two- and three-photon absorption (1PA, 2PA, 3PA) tuning in enhanced green fluorescent protein (EGFP). To achieve this goal, we built EGFP models differing in: i) number and position of hydrogen-bonds (h-bonds) donors to the CRO and ii) the electric field, as approximated by polarizable force  field, acting on the CRO. We  find that h-bonding to the CRO's phenolate oxygen results in stronger one- and multiphoton absorption. The brighter absorption can be also achieved by creating more positive electric field near the CRO's phenolate moiety. Interestingly, while individual CRO-environment h-bonds usually enhance 1PA and 2PA, it takes a few h-bond donors to enhance 3PA. Clearly, response of the absorption intensity to many-body effects depends on the excitation mechanism.  We further employ symmetry-adapted perturbation theory (SAPT) to reveal excellent (2PA) and good (3PA) correlation of multiphoton intensity with electrostatic and induction interaction energies. This points to importance of accounting for mutual CRO-environment polarization in quantitative calculations of absorption spectra in FPs.

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.

Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.

Substituted 9-Diethylaminobenzo[a]phenoxazin-5-ones (Nile Red Analogues): Synthesis and Photophysical Properties

Nile Red is a benzo[a]phenoxazone dye containing a diethylamino substituent at the 9-position. In recent years, it has become a popular histological stain for cellular membranes and lipid droplets due to its unrivaled fluorescent properties in lipophilic environments. This makes it an attractive lead for chemical decoration to tweak its attributes and optimize it for more specialized microscopy techniques, e.g., fluorescence lifetime imaging or two-photon excited fluorescence microscopy, to which Nile Red has never been optimized. Herein, we present synthesis approaches to a series of monosubstituted Nile Red derivatives (9-diethylbenzo[a]phenoxazin-5-ones) starting from 1-naphthols or 1,3-naphthalenediols. The solvatochromic responsiveness of these fluorophores is reported with focus on how the substituents affect the absorption and emission spectra, luminosity, fluorescence lifetimes, and two-photon absorptivity. Several of the analogues emerge as strong candidates for reporting the polarity of their local environment. Specifically, the one- and two-photon excited fluorescence of Nile Red turns out to be very responsive to substitution, and the spectroscopic features can be finely tuned by judiciously introducing substituents of distinct electronic character at specific positions. This new toolkit of 9-diethylbenzo[a]phenoxazine-5-ones constitutes a step toward the next generation of optical molecular probes for advancing the understanding of lipid structures and cellular processes.

What is the Optimal Size of the Quantum Region in Embedding Calculations of Two-Photon Absorption Spectra of Fluorescent Proteins?

We systematically investigate an impact of the size and content of a quantum (QM) region, treated at the density functional theory level, in embedding calculations on one- (OPA) and two-photon absorption (TPA) spectra of the following fluorescent proteins (FPs) models: Aequorea victoria green FP (avGFP) with neutral (avGFP-n) and anionic (avGFP-a) chromophore as well as Citrine FP. We find that amino acid (a.a.) residues as well as water molecules hydrogen-bonded (h-bonded) to the chromophore usually boost both OPA and TPA processes intensity. The presence of hydrophobic a.a. residues in the quantum region also non-negligibly affects both absorption spectra but decreases absorption intensity. We conclude that to reach a quantitative description of OPA and TPA spectra in multiscale modeling of FPs, the quantum region should consist of a chromophore and most of a.a. residues and water molecules in a radius of 0.30–0.35 nm (ca. 200–230 atoms) when the remaining part of the system is approximated by the electrostatic point-charges. The optimal size of the QM region can be reduced to 80–100 atoms by utilizing a more advanced polarizable embedding model. We also find components of the QM region that are specific to a FP under study. We propose that the F165 a.a. residue is important in tuning the TPA spectrum of avGFP-n but not other investigated FPs. In the case of Citrine, Y203 and M69 a.a. residues must definitely be part of the QM subsystem. Furthermore, we find that long-range electrostatic interactions between the QM region and the rest of the protein cannot be neglected even for the most extensive QM regions (ca. 350 atoms).

Nonlinear response time-dependent density functional theory combined with the effective fragment potential method

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

Donor's position-specific channel interference in substituted biphenyl molecules

Changing the relative positions of the donor group can reverse the nature of channel interference in donor–acceptor substituted biphenyls.

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.

Effect of solvent-induced coil to helix conformational change on the two-photon absorption spectrum of poly(3,6-phenanthrene)

This paper investigates the effect of solvent-induced conformational changes of poly(3,6-phenanthrene) on their two-photon absorption (2PA). Such effect was studied employing the wavelength-tunable femtosecond Z-scan technique and modeled using the sum-over-essential states approach. We observed a strong reduction of the 2PA cross-section when the sample was prepared in hexane (poor solvent) in comparison to chloroform (good solvent), which is related to the conformation adopted by the polymer in each case. In chloroform it adopts a random coil conformation, as opposed to the one-handed helix conformation in hexane. Our results pointed out that the coil to helix conformation change decreases the degree of molecular planarity of the polymer π-conjugated backbone, which is primarily responsible for their optical nonlinearity, contributing to diminishing the effective transition dipole moments and, consequently, the 2PA cross-section. Moreover, by studying the nonlinear response with different light polarization, we showed that, although the solvent-induced conformational change does not alter the molecular symmetry of the polymer, it modifies considerably the direction of the transition dipole moments between the excited states.

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.

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 (δTP) of o-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 o-betaine has larger δTP value than any other substituted or pristine o-betaine. The twist angle dependent variation of δTP 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 δTP 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 δTP 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 n-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 o-betaine.

High-Polarity Solvents Decreasing the Two-Photon Transition Probability of Through-Space Charge-Transfer Systems - A Surprising In Silico Observation

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.

Solvent induced channel interference in the two-photon absorption process--a theoretical study with a generalized few-state-model in three dimensions

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.

A critical theoretical study on the two-photon absorption properties of some selective triaryl borane-1-naphthylphenyl amine based charge transfer molecules

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.

Strong coupling in macrocyclic thiophene investigated by time-resolved two-photon excited fluorescence

We report the femtosecond dynamics of fluorescence anisotropy excited through the two-photon absorption (TPA), which provides direct signatures of delocalized electronic excitations for symmetrical macromolecular architectures. Two-photon excited fluorescence anisotropy is strongly correlated with the orientation and value of the transition moment from the excited state to the second and higher lying states. For macromolecular systems it leads to a relatively low initial fluorescence anisotropy and specific femtosecond anisotropy dynamics. We have experimentally demonstrated qualitatively different anisotropy dynamics for two- and one-photon absorption excitations for strongly coupled ring architecture prospective for artificial-light-harvesting applications and possessing an enhanced TPA-absorption cross section.

Theoretical study of the two-photon absorption properties of several asymmetrically substituted stilbenoid molecules

Two-photon absorption (TPA) properties of noncentrosymmetric pi-conjugated stilbenoid molecules with D-pi-A structures, TPA spectra of which have been reported [L. Antonov et al., Phys. Chem. Chem. Phys. 5, 1193 (2003)], have been investigated theoretically by ab initio molecular orbital methods. The difference in the observed one-photon absorption and TPA spectra among compounds with the same donor (D) and acceptor (A) units is well reproduced by the present calculations, although the calculated excitation energies are overestimated by the configuration interaction with single excitation method used. It was found that the spectral differences among the compounds were mainly due to the deviation from the planar structure by intramolecular rotation around the N[Single Bond]C (phenyl) bond of the N-benzilideneanilines having the C[Double Bond]N linkage as the central pi bridge. Substitution of the end donor or acceptor groups with weaker ones leads to a decrease in the TPA intensity of the lowest pi-pi(*) TPA states, resulting mainly from the decrease in the dipole moment of the excited states. The total TPA cross section spectra have been separated into contributions of the dipolar term, which appear only in noncentrosymmetric systems, and the three-state term, which appear in any systems irrespective of symmetry. The dipolar term predominates only for the lowest pi-pi(*) state, while for the higher excited states the three-state terms become predominant. An analysis employing the index R(f) defined with the transition polarizability shows that the TPA properties of the higher excited states are well described by the three-state approximation mediated by the lowest pi-pi(*) state. The differences found between the centrosymmetric and dipolar molecules in the enhancement mechanism of the TPA intensity by substituting the end groups with strong donors are discussed by comparison with the TPA properties of azobenzenes symmetrically substituted with the same donors.

Few-states models for three-photon absorption

Few-states models are derived for the calculation of three-photon absorption matrix elements. Together with earlier derived few-states models for two-photon absorption, the models are evaluated against results from response theory calculations that provide the full sum-over-states values. It is demonstrated that not even for systems with charge-transfer character, where few-states models for two-photon absorption are in excellent agreement with response theory, do the models provide a quantitatively correct description for three-photon absorption. The convergence behavior, merits, and shortcomings of the models are elucidated in some detail. The role of various characteristics of the electronic structure, such as symmetry, charge transfer, and conjugation--important for the formation of a large three-photon cross section--is analyzed. As for two-photon absorption cross sections, it is essential to consider generalized few-states models also for three-photon absorption, that is, to account for dipolar directions and laser beam polarization. Despite their poor quantitative performance, it is argued that few-states models at times can be useful for interpretation purposes when applied to three-photon absorption.

Two-photon absorption cross sections: An investigation of solvent effects. Theoretical studies on formaldehyde and water

The effects of a solvent on the two-photon absorption of microsolvated formaldehyde and liquid water have been studied using hybrid coupled-cluster/molecular mechanics (CC/MM) response theory. Both water and formaldehyde were considered solvated in water, where the solvent water molecules were described within the framework of molecular mechanics. Prior to the CC/MM calculations, molecular dynamics simulations were performed on the water/formaldehyde and water/water aggregates and many configurations were generated. By carrying out CC/MM response calculations on the individual configurations, it was possible to obtain statistically averaged results for both the excitation energies and two-photon absorption cross sections. For liquid water, the comparison between one- and two-photon absorption spectra is in good agreement with the experimental data available in the literature. In particular, the lowest energy transition occurring in the one-photon absorption spectrum of water only occurs with a relatively small strength in the two-photon absorption spectrum. This result is important for the interpretation of two-photon absorption data as these results show that in the absence of selection rules that determine which transitions are forbidden, the spectral profile of the two-photon absorption spectrum can be significantly different from the spectral profile of the one-photon absorption spectrum.

Strong Two-Photon Absorption in New Asymmetrically Substituted Porphyrins: Interference between Charge-Transfer and Intermediate-Resonance Pathways

We study two-photon absorption (2PA) in two series of new free-base porphyrins with 4-(diphenylamino)stilbene or 4,4'-bis-(diphenylamino)stilbene (BDPAS) attached via pi-conjugating linkers at the porphyrin meso-position. We show that this new substitution modality increases the 2PA cross section in the Soret band region (excitation wavelength 750-900 nm) of the core porphyrin by nearly 2 orders of magnitude, from sigma(2) approximately 10 GM for the meso-phenyl-substituted analogue to sigma(2) approximately 10(3) GM for the ethynyl-linked BDPAS-porphyrin dyad. The 2PA properties are quantitatively described by considering two different and interfering 2PA quantum transition pathways. The first path involves virtual transition via intermediate one-photon resonance. The second path bypasses the intermediate resonance and occurs due to a large permanent dipole moment difference between the ground and the final electronic states. To our best knowledge, this is the first experimental observation of the combined effect of these two pathways on one particular two-photon transition, resulting in quantum-interference-modulated 2PA strength.

Two-photon absorption cross sections: An investigation of the accuracy of calculated absolute and relative values

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple zeta level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.

Effects of conjugation length, electron donor and acceptor strengths on two-photon absorption cross sections of asymmetric zinc-porphyrin derivatives

Exceptionally large two-photon absorption cross sections at the infrared region have been revealed by time-dependent density functional theory calculations for asymmetric charge-transfer conjugated zinc-porphyrin derivatives. The largest two-photon cross section is found to be more than one order of magnitude larger than for the conventional two-photon active organic molecules. The calculations show that the formation of strong charge-transfer states depends on the length of the conjugation bridge between the zinc-porphyrin core and the electron donor/acceptor. The two-photon absorption cross section can be greatly enhanced by increasing the strengths of the electron donor/acceptor.