Ab initio calculations of three-photon absorption

Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements

We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.

Three-photon circular dichroism: towards a generalization of chiroptical non-linear light absorption

We present the theory of three-photon circular dichroism (3PCD), a novel non-linear chiroptical property not yet described in the literature. We derive the observable absorption cross section including the orientational average of the necessary seventh-rank tensors and provide origin-independent expressions for 3PCD using either a velocity-gauge treatment of the electric dipole operator or a length-gauge formulation using London atomic orbitals. We present the first numerical results for hydrogen peroxide, 3-methylcyclopentanone (MCP) and 4-helicene, including also a study of the origin dependence and basis set convergence of 3PCD. We find that for the 3PCD-brightest low-lying Rydberg state of hydrogen peroxide, the dichroism is extremely basis set dependent, with basis set convergence not being reached before a sextuple-zeta basis is used, whereas for the MCP and 4-helicene molecules, the basis set dependence is more moderate and at the triple-zeta level the 3PCD contributions are more or less converged irrespective of whether the considered states are Rydberg states or not. The character of the 3PCD-brightest states in MCP is characterized by a fairly large charge-transfer character from the carbonyl group to the ring system. In general, the quadrupole contributions to 3PCD are found to be very small.

Benchmarking two-photon absorption cross sections: performance of CC2 and CAM-B3LYP

We investigate the performance of CC2 and TDDFT/CAM-B3LYP for the calculation of two-photon absorption (TPA) strengths and cross sections and contrast our results to a recent coupled cluster equation-of-motion (EOM-EE-CCSD) benchmark study [K. D. Nanda and A. I. Krylov, J. Chem. Phys., 2015, 142, 064118]. In particular, we investigate whether CC2 TPA strengths are significantly overestimated compared to higher-level coupled-cluster calculations for fluorescent protein chromophores. Our conclusion is that CC2 TPA strengths are only slightly overestimated compared to the reference EOM-EE-CCSD results and that previously published overestimated cross sections are a result of inconsistencies in the conversion of the TPA strengths to macroscopic units. TDDFT/CAM-B3LYP TPA strengths, on the other hand, are found to be 1.5 to 3 times smaller than the coupled-cluster reference for the molecular systems considered. The unsatisfactory performance of TDDFT/CAM-B3LYP can be linked to an underestimation of excited-state dipole moments predicted by TDDFT/CAM-B3LYP.

Five-Photon Absorption and Selective Enhancement of Multiphoton Absorption Processes

We study one-, two-, three-, four-, and five-photon absorption of three centrosymmetric molecules using density functional theory. These calculations are the first ab initio calculations of five-photon absorption. Even- and odd-order absorption processes show different trends in the absorption cross sections. The behavior of all even- and odd-photon absorption properties shows a semiquantitative similarity, which can be explained using few-state models. This analysis shows that odd-photon absorption processes are largely determined by the one-photon absorption strength, whereas all even-photon absorption strengths are largely dominated by the two-photon absorption strength, in both cases modulated by powers of the polarizability of the final excited state. We demonstrate how to selectively enhance a specific multiphoton absorption process.

Impact of electron acceptor on three-photon absorption cross-section of the fluorene derivatives

Small three-photon absorption (3PA) cross-section values of present nonlinear organic molecules limit their practical applications. Although electron donors and electron acceptors have a great effect on 3PA cross-section, little is known about how the strength and situation of electron acceptors influence the 3PA cross-section value of a compound. The present work reports 3PA effects of two fluorene derivatives with symmetric D-π-π(A)-π-D archetype, which are named as 2,7-bis(4-methoxyphenylacetylene)-9-fluorenone (FATT) and 2,7-bis(4-methoxyphenylacetylene)-9-thoine-fluorene (TSATL). Large 3PA cross-section and ideal 3PA-induced optical limiting effects have been found in the two fluorene derivatives. The two molecules both have a different electron acceptor on the fluorene core, by which the 3PA cross-section value for FATT is enhanced by nearly 3-fold compared with that for TSATL. The mechanism of this significant enhancement in 3PA cross-section has been investigated by density functional theory (DFT) and configuration interaction singles (CIS) method with use of 6-311+G basis set in combination with conductor polarizable continuum model (CPCM). The theoretical results show that increase of electronegative character of the electron acceptor on the core is responsible for the increase of 3PA cross-section values of the two molecules.

Three-photon-absorption-induced optical stabilization effects in a bifluorenylidene derivative

A bifluorenylidene derivative with extended π-conjugated system has been designed and successfully synthesized. The compound displays strong three-photon absorption effect. The obtained three-photon absorption cross section is as high as 81.3 × 10(-76) cm(6)s(2). Distinguished 3PA-induced optical limiting and optical stabilization performances have been achieved. The on-axis transmitted intensity approached a constant even though the incident laser pulse fluctuation was 300%.

Two- and three-photon absorption of organic ionic pyrylium based materials

Pyrylium dyes having the same basic chemical structure, differing only to a specific substituent, have been used as novel materials for multiphoton three-dimensional data storage. Electronic absorption spectra, two-photon and three-photon absorption properties of this class of pyrylium dyes, have been studied theoretically and compared to experimental results. The effects of the counteranion, the surrounding solvent, and electron releasing and electron withdrawing groups in specific positions of the basic structure have been explored in detail. It is argued that on grounds of the quality of experimental spectroscopic agreement, the computed two- and three-photon data may be used in pulse propagation simulations of three-dimensional recording in optical memories.

Three-Photon Absorption Cross-Section Enhancement in Two Symmetrical Fluorene-Based Molecules

In this article, we report the pure three-photon absorption effects of two novel symmetrical fluorene-based molecules with 2D-pi-2D [9,9-diethylhexyl-2,7-bis-(N,N-diphenylamine)fluorene] and 2D-D-pi-D-2D [5,5'-(9,9-bis-(2-ethylhexyl)-9H-fluorene-2-yl)bis(N,N-diphenylthiophen-2-amine)] structural motifs. The obtained three-photon absorption cross sections, (4.74 +/- 0.01) x 10(-76) and (6.77 +/- 0.02) x 10(-76) cm(6) s(2) for the 2D-pi-2D and 2D-D-pi-D-2D archetypes, respectively, are rather high. The geometries and electronic excitations of the two molecules were systematically studied by the PM3 and ZINDO/S methods. The influence of the different molecular structures on the three-photon absorption cross section is discussed micromechanically. The experimental and theoretical results demonstrate that the transition dipole moment between the ground and final states is the most definitive factor. A new fitting method that is more accurate than those reported previously was used to obtain the 3PA coefficient.

Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores

Based on essential-state models for three-photon absorption (3PA), we have investigated the structure-property relationships for stilbene-based dipolar and quadrupolar chromophores. The emphasis lies on the evolution of the 3PA cross section with the degree of ground-state polarization. For dipolar systems, we find a dominant role played by Deltamu, which expresses the change in dipole moment between the ground state and the 3PA active excited state. Thus, the strategies usually applied to maximize the second-order polarizability beta are also applicable to optimize the 3PA cross section. For quadrupolar systems, the 3PA response is dominated by contributions from channels including various low-lying two-photon allowed states, which limits the applicability of essential-state models. Optimization strategies can be proposed but vary for different ranges of ground-state polarization.

Structure to property relationships for multiphoton absorption in covalently linked porphyrin dimers: a correction vector INDO/MRDCI study

The correction vector method has been used to investigate structure to property relationships for multiphoton absorption properties in covalently linked porphyrin dimers. The electronic structure of the system is described within the multireference single and double configuration interaction (MRDCI) method coupled with the intermediate neglect of differential overlap (INDO) Hamiltonian. We find a strong increase in the two-photon absorption (2PA) and three-photon absorption (3PA) cross sections when going from an isolated porphyrin to the dimers. The nature of the 2PA and 3PA active states as well as the cross sections show a strong but not straightforward dependence on the length of the bridge between the two porphyrins. Our theoretical results are in very good agreement with experimental data for 2PA. The resulting structure to property relationships are analyzed on the basis of essential-state models, where it turns out that a three-state model considering only the Q(x) intermediate state proposed in literature does not provide a full description of the actual situation.

Effects of Donor/Acceptor Strengths on the Multiphoton Absorption: An EOM-CCSD Correction Vector Study

We have developed a correction method (CV) to calculate the single- and multiphoton absorption (MPA) spectra of organic pi-conjugated systems within the equation of motion coupled-cluster method with single and double excitations (EOM-CCSD). The effects of donor/acceptor strengths on the multiphoton absorption in a series of symmetrically substituted stilbene derivatives have been reinvestigated at both the ab initio and the semiempirical intermediate neglect of differential overlap (INDO) Hamiltonian levels. Both ab initio and INDO calculations show that the electron-donating or electron-withdrawing substituents lead to enhancements of two- and three-photon absorption cross sections, more pronounced for two-photon absorption than for three-photon absorption. The ab initio calculations usually produce larger excitation energies than the semiempirical, which lead to lower MPA cross sections.

The correction vector method for three-photon absorption: the effects of pi conjugation in extended rylenebis(dicarboximide)s

A correction vector method within the multireference determinant single and double configuration interaction approximation coupled with the semiempirical intermediate neglect of differential overlap Hamiltonian has been developed for the computation of single and multiphoton absorption spectra of conjugated molecules. We study the effect of pi conjugation on these properties in the extended rylenebis(dicarboximide)s. The one-, two-, and three-photon absorption cross sections of the lowest-lying excited states show a power law dependence on the conjugation length, with exponents of about 1.3, 2.6, and 5.6, respectively. The maximum value of the three-photon absorption cross section in these molecules is calculated to be 1.06x10(-78) cm6 s2photon2 for photon energy at 0.57 eV.

Solvent effects on the three-photon absorption cross-section of a highly conjugated fluorene derivative

Herein, we report the study of the three-photon absorption cross-section dependence on solvents parameters for a highly conjugated organic dye, 2,2'-(4,4'-(1E,1'E)-2,2'-(9,9-didecyl-9H-fluorene-2,7-diyl) bis(ethene-2,1-diyl)bis(4,1-phenylene))dibenzo[d]thiazole (A-pi-pi-pi-A). The three-photon absorption cross-section was measured for this organic dye in solution in four different solvents with polarity function, Deltaf between 0.162 and 0.247. The experiments show how the solvent's reorientation of the electrons and polarity contribute to the 3PA cross-section. Multiphoton-absorption experiments of A-pi-pi-pi-A in all four different solvents were performed with a tunable OPG pumped by a 25 picosecond Nd-YAG laser.

Experimental and Quantum Chemical Studies of Cooperative Enhancement of Three-Photon Absorption, Optical Limiting, and Stabilization Behaviors in Multibranched and Dendritic Structures

This paper reports on cooperative enhancement of three-photon absorption (3PA) cross section, studied by nonlinear transmission method, in going from a one-branched to a three-branched and then to a dendritic structure. Experimentally, we observe a 72% enhanced 3PA cross-section value in going from the one-branched chromophore to the dendritic chromophore, and a 49% enhanced 3PA cross-section value in going from the one-branched chromophore to the three-branched chromophore, when the 3PA cross-section values are normalized per structure unit. Quantum chemical calculation for the one- and three-branched structures, using the cubic response (CR) theory applied to a single determinant self-consistent field (SCF) reference state, also predicts such an enhancement. Two-dimensional pi-delocalization, resulting in extended charge-transfer network in the case of the multibranched structures, is the main cause of the cooperative enhancement. Owing to the increased 3PA cross-section value for the dendritic chromophore, improved optical limiting performance at an optical communication wavelength of 1310 nm was observed, compared with the one-branched (or three-branched) chromophore, using comparable structure-unit-based concentrations. Optical stabilization capability of the dendritic chromophore was also observed at this wavelength.

The impact of the π-electron conjugation length on the three-photon absorption cross section of fluorene derivatives

The three-photon absorption cross sections of three different fluorene derivatives, with extended pi-electron conjugation lengths was experimentally measured and compared with shorter pi-electron conjugation length analogs. The effect of the conjugation length on the three-photon absorption cross section sigma(3) (') of this family of molecules has been elucidated. It is demonstrated that sigma(3) (') of the asymmetric compound D-pi-pi-pi-A is 6.6 times larger than its shorter configuration D-pi-A, while for the symmetric compounds D-pi-pi-pi-D and A-pi-pi-pi-A a two-fold enhancement was found relative to their shorter conjugation length analogs. Measurements of the three-photon excitation of these compounds in THF solution (10(-3)M) were accomplished with a tunable optical pulse generation pumped by a 25 ps Nd-YAG laser.

Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules

In this paper, the equilibrium geometries, one-, two-, and three-photon absorption properties, and the transition nature of a series of Y-shaped molecules which possess an imidazole-thiazole core have been theoretically studied by using the parametrization model 3 and Zerner's intermediate neglect of differential overlap methods. Our calculated results have confirmed the experimental findings that the investigated molecules are all promising multiphoton absorption materials and both the two-photon absorption and the three-photon absorption cross sections are seriatim increscent along with the increase of the electron-donor strength. The nonlinear optical phenomenon originates from the intramolecular charge transfer within the pi-conjugated system. The calculated results indicate that the heterocyclic core increases the two- and three-photon absorption cross sections due to its pi-excessive nature. So it can provide more free electrons to enlarge the charge transfer within the molecule system. In addition, the design of Y shape and the sulfonyl-based electron-accepting group play a part in the enhancement of multiphoton absorption. It is notable that molecules with heterocyclic core will provide favorable condition for multiphoton absorption applications.

Quantum Chemical Studies of Three-Photon Absorption of Some Stilbenoid Chromophores

Three-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to the third-order response function and its residues. The results obtained by using different functionals are compared with experimental data for similar systems obtained from the literature. With a Coulomb attenuated, asymptotically corrected functional, the excitation energy to the first resonance state is much improved. Comparison with experiment indicates that this is the case for the three-photon cross section as well. In particular, the overestimation of the cross sections and underestimation of excitation energies offered by the density functional theory using common density functionals is corrected for. It is argued that a reliable theory for three-photon absorption in charge transfer and other chromophore systems thereby has been obtained. Further elaboration of the theory and its experimental comparison call for explicit inclusion of solvent polarization and pulse propagation effects.

Density functional response theory calculations of three-photon absorption

Three-photon absorption probabilities delta(3PA) have been calculated through application of a recently derived method for cubic response functions within density functional theory (DFT). Calculations are compared with Hartree-Fock (HF) and with a coupled cluster hierarchy of models in a benchmarking procedure. Except for cases having intermediate states near resonance, density functional theory is demonstrated to be in sufficient agreement with the highly correlated methods in order to qualify for predictions of delta(3PA). For the larger systems addressed, a set of acceptor A and donor D substituted pi-conjugated systems formed by trans-stilbene and dithienothiophene (DTT), we find noticeable differences in the magnitude of delta(3PA) between HF and DFT, although similar trends are followed. It is shown that the dipolar structures, TS-AD and DTT-AD, have substantially larger delta(3PA) than other types of modifications which is in accordance with observations for two-photon absorption. This is the first application of density functional theory to three-photon absorption beyond the use of few-state models.

The effects of oxygenation on the optical properties of dimethyl-dithienothiophenes: Comparison between experiments and first-principles calculations

Modifications of the optical properties of dimethyl-dithienothiophenes due to the oxygen functionalization of the central sulfur atom are investigated. We have measured the absorption, photoluminescence (PL) and PL excitation spectra, the PL quantum efficiencies, and the PL decay times. These experimental results are interpreted and compared with first-principles time-dependent density-functional theory calculations, which predict, for the considered systems, excitation and emission energies with an accuracy of 0.1 eV. It is found that the oxygenation strongly changes optical and photophysical properties. These effects are related to the modifications of the energetically lowest-unoccupied molecular orbital and the energetically second highest occupied one, which change the relative position of the two lowest singlet and triplet excited states.

Three-photon absorption in anthracene-porphyrin-anthracene triads: A quantum-chemical study

We have applied correlated quantum-chemical methods to investigate the three-photon absorption (3PA) response of a porphyrin triad derivative, where the central macrocycle is linked in mesopositions to two anthracene units via acetylenic bridges. The 3PA frequency-dependent spectrum of this derivative is dominated by a single resonance feature in the transparent region, associated with charge-transfer states between porphyrin and anthracene. The calculations indicate a two order of magnitude enhancement in the 3PA cross section in the triad molecule with respect to the individual entities, which is attributed to close one-, two-, and three-photon resonances together with strong electronic couplings among the units.