Experimental and computational data on two-photon absorption and spectral deconvolution of the upper excited states of dye IR780

Evaluating candidates for novel materials with high nonlinear absorption properties for applications as biomarkers is a very important field of research. In this context, experimental and computational information on the two-photon absorption (TPA) properties of the dye IR780 is shown. The two-photon absorption data from 850 to 1000 nm for IR780 and other two well-known dyes, taken as reference, are presented. The experimental data were collected via an implementation of the two-photon induced fluorescence technique, while the quantum chemical data were produced by implementing DFT (Density-functional theory) methods. The data presented here supplement the paper “Two-photon absorption spectrum and characterization of the upper electronic states of dye IR780” by Guarin et al. (2021).

Physical Sciences. Specific subject area Two-photon absorption, ultrafast spectroscopy, dyes as biomarkers. Type of data Tables and figures. How data were acquired A two-photon induced fluorescence (TPIF) scheme was implemented: an excitation beam was produced by an optical parametric amplifier UV-vis and luminescence spectra for IR780 in methanol were recorded in Perkin-Elmer spectrometers.

Description of data collection
The logarithm of the intensity of the fluorescence was plotted vs. the logarithm of the peak intensity of the excitation light.

Value of the Data
• These data show a measurement of the two-photon absorption band of the dye IR780.
• The data and associated calculations are useful for researchers interested in the nonlinear properties of cyanines as well as users looking into the potential of these substances as biomarkers excitable via IR radiation. • The fits of the UV bands in the 1PA (one-photon absorption) spectrum can serve as reference for the fitting of the absorption spectra of other cyanines.

Data Description
The data presented here are experimental results to better understand the twophoton absorption processes involved in cyanine IR780 (2-[2-[2-Chloro-3-[(1,3-dihydro-3,3dimethyl-1-propyl-2H-indol-2-ylidene)ethylidene]-1-cyclohexen-1-yl]ethenyl]-3,3-dimethyl-1-pr opylindolium iodide). Fig. 1 shows the quadratic dependence of the logarithm of the integrated fluorescence vs. the logarithm of the peak intensity of the pump beam for IR780, rhodamine B and rhodamine 6G; this is done for several wavelengths ranging from 850 to 10 0 0 nm. Figs. 2-6 show each of them successive 5-Gaussian peak, 6-Gaussian peak, 7-Gaussian peak, 8-Gaussian peak and 9-Gaussian peak fits of the 1PA spectrum of IR780 in the spectral range 18350-35980 cm −1 , respectively. Fig. 7 shows the optimized structure of the molecule IR780 after applying three functionals.       Tables 1-5 feature the results of the Gaussian-peak fitting procedures. Table 6 reports on the area under the curve (AUC) pertaining to the Gaussian fitting procedure. Table 7 shows the calculated oscillator strengths of the excited states S n of IR780 in methanol. Table 8 contains results furnished from the data and the energy gap law formalism. Tables 9-11 show the results of vertical transition calculations with different functionals and, finally, Table 12 reports the TPA cross-sections of IR780 estimated via quantum chemical calculations and three functionals.
Supporting files in [1] contain the raw data that substantiate Figs. 1-6 . Peak  Peak Peak Peak   Peak

Experimental Design, Materials and Methods
In the experiment, dyes IR780, rhodamine B and rhodamine 6G were irradiated with a beam produced in an optical parametric amplifier (OPA) within a wavelength range of 850-10 0 0 nm and the two-photon induced fluorescence was recorded to measure the two-photon absorption cross-section of IR780. The molecular structure of the cyanine IR780 is shown in Scheme 1 .
The dyes and the methanol (HPLC-grade) used for the solutions employed in the measurements were purchased from Sigma-Aldrich. The concentrations utilized for the experiments were 2.25 × 10 −5 M for IR780, 7.65 × 10 −6 M for rhodamine B and 8.06 × 10 −5 M for rhodamine 6G. The solutions were used immediately after preparation and, while the experiment was carried out, the temperature of the laboratory was kept at 20 ± 0.6 °C and the relative humidity at 45 ± 5%.
The laser system consists of a Ti:Sapphire mode-locked laser (Vitara-T, Coherent) seeding a regenerative amplifier (Legend-Elite DUO, Coherent) which, in turn, pumps an optical parametric amplifier (TOPAS OPA, Light Conversion). The output of the Legend (4.5 mJ per pulse, 1 kHz repetition rate, 80 fs, and pulse centered at 800 nm) is fed to the TOPAS where, in this case, radiation from 850 to 10 0 0 nm is obtained. The power of the output beam from the OPA is controlled via OD filters and the polarization of the light at the sample is always vertical.
The excitation beam was expanded by a telescope and then steered to a microscope objective (Rossbach Kyowa) with NA = 0.1, 4x which focuses the light into the sample container, a sealed quartz cuvette with a 10 mm-optical path. The focal point was placed approximately 1 mm from the side wall of the cuvette. The pulse energy was varied between 0.002 and 0.35 μJ, producing peak intensities of ≈ 5.0 × 10 10 to ≈ 7.9 × 10 12 W cm −2 and controlled so the peak power never exceeded 8 × 10 12 Wcm −2 . The fluorescence from the dyes was collected at right angles with respect to the propagation vector of the excitation beam by an f = 50 mm, 1 in. diameter biconvex lens and focused to the entrance slit of an f = 300 mm Czerny-Turner monochromator coupled to a photomultiplier tube (PMT) (R12896, Hamamatsu Photonics). The output signal of the PMT was monitored with an oscilloscope (Tektronix 1102B-EDU). The peak power of the OPA was also independently monitored with a high-speed Si photodetector (DET110, 17.5 MHz bandwidth, 350-1100 nm, Thorlabs) also connected to the Tektronix oscilloscope and set to average over 64 samples.
Steady-state (linear) absorption and fluorescence spectra of the dyes were recorded for calibration purposes and were carried out in a Lambda-40 VU/vis and LS50B Luminescence spectrophotometers, both apparatus from Perkin-Elmer.

Quadratic dependence of the fluorescence for all the excitation wavelengths
In this section, a linear relationship between the Logarithm of the Integrated Fluorescence and the Logarithm of the peak intensity with slope 2 for each of the three compounds of interest (Rhodamine 6G, Rhodamine B and IR780) is shown. See Fig. 1 . The raw data of the plots in Fig. 1 can be found in [1] .

Deconvolution of the spectral bands of the states S n
The spectral bands were fitted using Gaussian functions described by the following equation where y 0 is the offset, x c is the centroid, w is the width and A is the amplitude of each peak. Tables 1-5 and Figs. 2-6 show the parameters of the fit for the upper sates and the gaussian functions in the spectral range 18350 -35980 cm −1 , respectively. A 10-peak fit of the spectral bands of the states S n can be found in [2] .

Experimental oscillator strength derived from the fitting of the upper excited states S n
The following equation was used to calculate the oscillator strength (O.S.) [3,4] : where ε 0 is the vacuum permittivity (in C 2 /Nm 2 ), m is the electron mass (in kg), c is the speed of light (in m/s), N a is Avogadro's number (6.02214076 × 10 23 mol −1 ), e is the electron charge (in C) and the integral of ε( v ) is the area under the curve (AUC) of the peak-fitting by gaussian functions [5,6] . The AUC is to be multiplied by a factor of 10 [3] . Tables 6 and 7 show the calculated AUC and O.S.'s of the excited states S 2 , S 3 , S 4 , S 5 and S 6 of IR780 in methanol, respectively.

Non-radiative decay properties of IR780 within the framework of the energy gap law
In this section, parameters γ (Potential Energy Surfaces shift), the matrix element of the vibrational coupling between electronic states ( C ) and the preexponential factor ( A ) from the energy gap law [2] are calculated (taking into account several vibrational modes ( h ω in Eq. (3) ) of the cyanines).   Table 8 shows these results for γ , C and A .