Illuminating the origins of two-photon absorption properties in fluorescent protein chromophores

We provide here a structural impact on two-photon absorption cross-section (σ^TPA) for 22 distinct fluorescent protein (FP) chromophores. By employing time-dependent density functional theory, we gain insight into two-photon absorption (TPA) process by investigating relationship between σ^TPA and one-photon electronic transition dipole moment and permanent dipole moment change (Δμ) upon transition. Our results reveal that for the S₁ excited state, σ^TPA is proportional to (Δμ)² in agreement with two-state model of TPA process. On the contrary, the TPA spectroscopy of higher excited states (S _n, n > 1) is much more complex. We do not find a main driving force of large σ^TPA that would be common for investigated chromophores. Instead, it seems that channel interference between one-photon transition dipole moment vectors is responsible for enhancement or diminishment of σ^TPA. Our in vacuo results may serve as a benchmark to investigate a role of chromophore-protein interaction in shaping TPA spectra of FPs.     

Electronic and vibronic contributions to two-photon absorption in donor-acceptor-donor squaraine chromophores

Many squaraines have been observed to exhibit two-photon absorption at transition energies close to those of the lowest energy one-photon electronic transitions. Here, the electronic and vibronic contributions to these low-energy two-photon absorptions are elucidated by performing correlated quantum-chemical calculations on model chromophores that differ in their terminal donor groups (diarylaminothienyl, indolenylidenemethyl, dimethylaminopolyenyl, or 4-(dimethylamino)phenylpolyenyl). For squaraines with diarylaminothienyl and dimethylaminopolyenyl donors and for the longer examples of 4-(dimethylamino)phenylpolyenyl donors, the calculated energies of the lowest two-photon active states approach those of the lowest energy one-photon active (1B(u)) states. This is consistent with the existence of purely electronic channels for low-energy two-photon absorption (TPA) in these types of chromophores. On the other hand, for all squaraines containing indolinylidenemethyl donors, the calculations indicate that there are no low-lying electronic states of appropriate symmetry for TPA. Actually, we find that the lowest energy TPA transitions can be explained through coupling of the one-photon absorption (OPA) active 1B(u) state with b(u) vibrational modes. Through implementation of Herzberg-Teller theory, we are able to identify the vibrational modes responsible for the low-energy TPA peak and to reproduce, at least qualitatively, the experimental TPA spectra of several squaraines of this type.     

Two-photon excitation of substituted enediynes

Electronic spectroscopy of nine benzannelated enediynes and a related fulvene was studied under one-photon and two-photon excitation conditions. We utilize measured absorbance and emission spectra and time-resolved fluorescence decays of these molecules to calculate their radiative lifetimes and fluorescence quantum yields. The fluorescence quantum yields for the other compounds were referenced to the fluorescence quantum yield of compound 3 and used to determine relative two-photon absorption cross-sections. Further insight into experimental studies has been achieved using time-dependent density functional (TD-DFT) computations. The probability of two-photon absorption (TPA) increases noticeably for excitation to the higher excited states. The photophysical properties of benzannelated enediynes are sensitive to substitutions at both the core and the periphery of the enediyne chromophore. Considerably enhanced two-photon absorption is observed in an enediyne with donor substitution in the middle and acceptor substitution at the termini. Excited states with B symmetry are not active in TPA spectra. From a practical point of view, this study extends the range of wavelengths applicable for activation of the enediyne moiety from 350 to 600 nm and provides a rational basis for future studies in this field. Our theoretical computations confirmed that lowest energy TPA in benzannelated enediynes involves different orbitals than lowest energy one-photon absorbance and provided further support to the notion that introduction of donor and acceptor substituents at different ends of a molecule increases TPA.     

A new series of two-photon polymerization initiators: Synthesis and nonlinear optical properties

Four photopolymerization initiators with D-π-D (D, donor; π, conjugation system) structure have been synthesized by solvent-free reaction and characterized by ¹H NMR spectroscopy, IR and elemental analysis. The one-photon and two-photon excited fluorescence have been investigated in different solvents. Experimental results of the one-photon and two-photon absorption cross sections show different trends in OPA and TPA ability with different substitution groups in donor units.     

A Relative Study on Two-photon Absorption Properties of C60 and C70

We have theoretically investigated the one- and two-photon absorption properties of C60 and C70 using the ZINDO method. From the results it is suggested that the one-photon absorption spectra are in agreement with the experimental observations. It is found that the maximum TPA cross section of C70 is more than twice that of C60,which is consistent with the experimental results. A notable point is that the TPA process of C60 is different from that of C70 as well as other ordinary conjugated molecules.     

Role of donor-acceptor strengths and separation on the two-photon absorption response of cytotoxic dyes: a TD-DFT study

Time-dependent density functional theory (TD-DFT) is applied to model one-photon (OPA) and two-photon (TPA) absorption spectra in a series of conjugated cytotoxic dyes. Good agreement with available experimental data is found for calculated excitation energies and cross sections. Calculations show that both OPA and TPA spectra in the molecules studied are typically dominated by two strong peaks corresponding to different electronic states. We find that donor-acceptor strengths and conjugated bridge length have a strong impact on the cross-section magnitudes of low- and high-frequency TPA maxima, respectively. These trends are analyzed in terms of the natural transition orbitals of the corresponding electronic states. Observed structure-property relationships may have useful implications on design of organic conjugated chromophores with tunable two-photon absorption properties for photodynamic therapy applications.     

Theoretical investigation of two-photon absorption allowed excited states in symmetrically substituted diacetylenes by ab initio molecular-orbital method

Symmetrically substituted diacetylene compounds, which shows large two-photon absorption (TPA) cross sections, have been theoretically investigated by the ab initio molecular-orbital method employing several theoretical models including the configuration interaction with single excitation (CIS), random phase approximation (RPA), and time-dependent density-functional theory (TDDFT) methods. The calculated excited energies are overestimated by CIS or RPA, whereas underestimated by TDDFT with the B3LYP parametrization for both one-photon absorption (OPA) and TPA allowed states. The lowest OPA state is well described by the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) transition. On the other hand, lower TPA allowed states can be represented as the superposition of the HOMO-LUMO+1 and HOMO-1-LUMO transitions, giving rise to two TPA allowed states. The absorption intensity for the lower TPA state of the diacetylenes molecules is discussed in terms of the alternancy symmetry and its breaking. The symmetry property is differently manifested for neutral and dicationic diacetylenes. Introduction of charges breaks the alternancy symmetry, which gives rise to an increase in the TPA cross sections at the lower frequency. The upper TPA state is calculated to show huge TPA cross sections, which reproduces the enhancement of the TPA cross section experimentally observed for one of the diacetylenes at the higher-frequency region. The enhancement is discussed employing an index defined as the ratio of the transition polarizability and its static limit, which represents the degree of influence of one-photon resonance on the TPA intensity. The huge TPA cross sections are found to be due to a near-resonance effect. The present theoretical calculation approves the previously proposed assumption based on the four-state (dual three-state) model, which consists of the ground, one OPA allowed, and two TPA allowed states.     

Laser two-photon ionization spectroscopy of molecules in liquids

A two-photon lonization technique has been developed and applied to determine the photoionization threshold of a molecule in liquid solution. The photoionization of pyrene in n-pentane was studied by monitoring the photocurrent of an≈ 10^?6 M solution as a function of the laser wavelength in the region 360–530 nm, corresponding to two-photon, transition in the region 180–265 nm. The photoionization threshold thus determined is 4.80 ± 0.02 eV. Resonances were observed in the two-photon ionization spectrum which are tentatively ascribed to preionization of one-photon forbidden transitions to states energetically degenerate with the continuum, reached via two-photon absorption.     

Two-photon absorption properties of proquinoidal D-A-D and A-D-A quadrupolar chromophores

We report the synthesis, one- and two-photon absorption spectroscopy, fluorescence, and electrochemical properties of a series of quadrupolar molecules that feature proquinoidal π-aromatic acceptors. These quadrupolar molecules possess either donor-acceptor-donor (D-A-D) or acceptor-donor-acceptor (A-D-A) electronic motifs, and feature 4-N,N-dihexylaminophenyl, 4-dodecyloxyphenyl, 4-(N,N-dihexylamino)benzo[c][1,2,5]thiadiazolyl or 2,5-dioctyloxyphenyl electron donor moieties and benzo[c][1,2,5]thiadiazole (BTD) or 6,7-bis(3',7'-dimethyloctyl)[1,2,5]thiadiazolo[3,4-g]quinoxaline (TDQ) electron acceptor units. These conjugated structures are highly emissive in nonpolar solvents and exhibit large spectral red-shifts of their respective lowest energy absorption bands relative to analogous reference compounds that incorporate phenylene components in place of BTD and TDQ moieties. BTD-based D-A-D and A-D-A chromophores exhibit increasing fluorescence emission red-shifts, and a concomitant decrease of the fluorescence quantum yield (Φ(f)) with increasing solvent polarity; these data indicate that electronic excitation augments benzothiadiazole electron density via an internal charge transfer mechanism. The BTD- and TDQ-containing structures exhibit blue-shifted two-photon absorption (TPA) spectra relative to their corresponding one-photon absorption (OPA) spectra, and display high TPA cross sections (>100 GM) within these spectral windows. D-A-D and A-D-A structures that feature more extensive conjugation within this series of compounds exhibit larger TPA cross sections consistent with computational simulation. Factors governing TPA properties of these quadrupolar chromophores are discussed within the context of a three-state model.     

Tunable resonance hyper-Raman spectroscopy of second-order nonlinear optical chromophores

Two-photon-resonant hyper-Raman spectra are reported for three "push-pull" conjugated organic chromophores bearing -NO(2) acceptor groups, two dipolar and one octupolar. The excitation source is an unamplified picosecond mode-locked Ti:sapphire laser tunable from 720 to 950 nm. The linear resonance Raman spectra of the same molecules are measured using excitation from the laser second harmonic. Excitation on resonance with the lowest-lying band in the linear absorption spectrum yields nearly identical resonance Raman and resonance hyper-Raman spectra. However, excitation into a region that appears to contain more than one electronic transition gives rise to different intensity patterns in the linear and nonlinear spectra, indicating that different transitions contribute differently to the one-photon and two-photon oscillator strength. The promise of the hyper-Raman technique for examining electronic transitions that are both one- and two-photon allowed is discussed.     

The polarised two-photon excitation spectrum of benzene monocrystals at 6 eV

The two-photon excitation spectrum of a benzene single crystal at 4.2 K has been recorded in the region of the second absorption system. The onset of two-photon absorption occurs near 46 500 cm^?1 (quoted as a two-photon frequency). The spectrum has the appearance of a forbidden transition in that the system begins with weak lines which become dominated by an intense continuum at higher energies. The two-photon cross section at 55 000 cm^?1 (the limit reached in this study) is about 200 times greater than at 47 490 cm^?1 although the peak of this strongly allowed system has not yet been reached. The fwhm of the bands near 47 000 cm^?1 is 280 cm^?1, the same as in the one-photon spectrum at these energies. The polarisation ratio is much the same over the entire energy range, and is consistent with the two-photon operators (xz, yz) or (zz). An analysis of all the data available from the one- and two-photon spectra suggests that the transition is ¹B_1u ← ¹A_1g in which the vibronic intensity is derived from the ¹E_1u state in the one-photon and ¹E_1g in the two-photon spectrum.     

Two-photon spectroscopy of dipole-forbidden transitions

We have investigated the applicability of CNDO/S-type methods for the calculation of optical spectra of molecules with the special implication that the calculations should not only describe the intense, dipole-allowed transitions which dominate the one-photon absorption spectrum but also those transitions which are one-photon forbidden in first-order approximation. We show that such a method is well suited to predict dipole allowed and dipole forbidden transitions at a similar level of accuracy if double excited configurations are taken into account. In spite of the lack of perfect pairing in NDO methods there are still two types of states which exhibit a different sensitivity towards correlation effects. Therefore, the approximation by which we describe the R-dependence of the Coulomb repulsion gains much more importance than in cases where mainly dipole allowed transitions are of interest. These findings confirm results obtained earlier from theories for which the pairing theorem is valid. The calculated data show an excellent stability with respect to further increase of the number of configurations if at least about 200 energy selected configurations are taken into account.     

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.     

Experimental and Theoretical Investigation of the 3sp(d) Rydberg States of Fenchone by Polarized Laser Resonance-Enhanced-Multiphoton-Ionization and Fourier Transform VUV Absorption Spectroscopy

The VUV absorption spectrum of fenchone is re-examined using synchrotron radiation Fourier transform spectrometry, revealing new vibrational structure. Picosecond laser (2+1) resonance enhanced multiphoton ionization (REMPI) spectroscopy complements this, providing an alternative view of the 3spd Rydberg excitation region. These spectra display broadly similar appearance, with minor differences that are largely explained by referring to calculated one- and two-photon electronic excitation cross-sections. Both show good agreement with Franck-Condon simulations of the relevant vibrational structures. Parent ion REMPI ionization yields with both femtosecond and picosecond excitation laser pulses are studied as a function of laser polarization and intensity, the latter providing insight into the relative two-photon excitation and one-photon ionization rates. The experimental circular-linear dichroism observed in the parent ion yields varies strongly between the 3s and 3p Rydberg states, in good overall agreement with the calculated two-photon excitation circular-linear dichroism, while corroborating other evidence that the 3p_z sub-state plays no more than a very minor role in the (2+1) REMPI spectrum. Vibrationally resolved photoelectron spectra are recorded with picosecond pulse duration (2+1) REMPI at selected intermediate vibrational excitations. The 3s intermediate state displays a very strong Δv=0 propensity on ionization, but the 3p intermediate evidences more complex vibronic dynamics, and we infer some 3p→3s internal conversion prior to ionization.     

Resonance hyper-Raman excitation profiles of a donor-acceptor substituted distyrylbenzene: one-photon and two-photon states

Resonance Raman and resonance hyper-Raman spectra of the "push-pull" conjugated molecule 1-(4'-dihexylaminostyryl)-4-(4"-nitrostyryl)benzene in acetone have been measured at excitation wavelengths from 485 to 356 nm (two-photon wavelengths for the nonlinear spectra), resonant with the first two bands in the linear absorption spectrum. The theory of resonance hyper-Raman scattering intensities is developed and simplified using assumptions appropriate for intramolecular charge-transfer transitions of large molecules in solution. The absorption spectrum and the Raman, hyper-Rayleigh, and hyper-Raman excitation profiles, all in absolute intensity units, are quantitatively simulated to probe the structures and the one- and two-photon transition strengths of the two lowest-energy allowed electronic transitions. All four spectroscopic observables are reasonably well reproduced with a single set of excited-state parameters. The two lowest-energy, one-photon allowed electronic transitions have fairly comparable one-photon and two-photon transition strengths, but the higher-energy transition is largely localized on the nitrophenyl group while the lower-energy transition is more delocalized.     

Time-dependent density functional theory studies of the photoswitching of the two-photon absorption spectra in stilbene, metacyclophenadiene, and diarylethene chromophores

Photochromophores such as cis-stilbene (1a), metacyclophenadiene (2a), and the diarylethene 3a undergo photoinduced conrotatory opening and closing of a central bond and are currently being sought out as potential candidates for media within 3D optical information storage devices. Strong molecular two-photon absorption (inducing the reversible photoisomerization) is a necessary feature for this application due to the need for high 3D spatial resolution. Here, the one- and two-photon absorption (OPA and TPA) characteristics of the open- and closed-ring isomers of 1-3 have been investigated using time-dependent density functional theory. It was determined that the excited states populated by two-photon absorption were nearly 1 eV higher in energy than the lowest energy excited state populated by one-photon absorption. The electronic structures of the TPA and OPA accessed states were then compared utilizing natural transition orbital analysis. There, it was found that states excited by OPA had pipi* character about the C-C framework associated with the bond formation/scission of the central C-C bond. In contrast, the states populated by TPA have pipi* character along the C-C skeletal periphery, including phenyl excitations. It is postulated that these differences in excited state electronic structure may lead to reaction pathways alternative to photoisomerization about the central C-C bond, impacting the utility of these compounds as 3D information storage media.     

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.     

Nonlinear optical and two-photon absorbtion properties of 1,3,5-tricyano-2,4,6-tris(styryl)benzene-containing octupolar oligomers

Octupolar oligomers containing 2-12 molecules of 1,3,5-tricyano-2,4,6-tris(styryl)benzene derivatives have been synthesized and their nonlinear optical and two-photon absorption (TPA) properties were determined. The beta(0) values are in the range of (85-1219) x 10(-30) esu and increase monotonically with the increasing number of the octupolar units within the molecule. The two-photon-induced fluorescence excitation spectra are quite similar to the single-photon absorption spectra except that the wavelength is doubled, indicating that the one- and two-photon allowed excited states are the same. The peak TPA cross-section values (delta(max)) measured with nanosecond pulses by the two-photon-induced fluorescence method are in the range (3010-62, 930) x 10(-50) cm(4)s photon(-1). The delta(max) increases as the number of the octupolar units in the molecules increases. A linear relationship is observed between delta(max) and beta, and this delta-beta relationship serves as a useful design strategy for the synthesis of novel octupolar oligomers and polymers with large TPA and beta.     

Two photon absorption of extended substituted phenylenevinylene oligomers: A TDDFT study

Time dependent density functional theory has been applied to analyze the effect of substituent groups on one-photon (OPA) and two-photon (TPA) absorption properties of extended amine-terminated phenylenevinylene oligomers. All investigated molecules are characterized by increased TPA activity. Calculated TPA cross-sections for these compounds do not show TPA enhancements observed in experimental measurements. Stabilization of the TPA active excited state in these chromophores leads to the small (0.2 eV) energy separation between the OPA and TPA allowed excited states, which agrees well with experimental data and may lead to the enhancement of the TPA response due to the strong vibronic couplings.     

Diaza-18-crown-6 based chromophores for modulation of two-photon absorption cross-section by metal ions

Two chromophores with diaza-18-crown-6 as receptor have been synthesized in high yields. The electronic structure, one-photon absorption (OPA) spectra, and two-photon absorption (TPA) properties have been studied in detail. When no metal ion is added as input, both show negligible TPA cross-section (σ₂). However, in the presence of Zn(II)/Cd(II)/Mg(II)/Ca(II) ion, each exhibits large TPA cross-section value. Binding of metal ion in the receptor increases the symmetric charge transfer leading to large σ₂ values. Theoretical calculations at the B3LYP functional with 6-31G^∗ and LanL2DZ mixed basis set under DFT formalism support experimental results.