A Combination of Chemometrics and Quantum Mechanics Methods Applied to Analysis of Femtosecond Transient Absorption Spectrum of Ortho-Nitroaniline

A combination of the advanced chemometrics method with quantum mechanics calculation was for the first time applied to explore a facile yet efficient analysis strategy to thoroughly resolve femtosecond transient absorption spectroscopy of ortho-nitroaniline (ONA), served as a model compound of important nitroaromatics and explosives. The result revealed that the ONA molecule is primarily excited to S3 excited state from the ground state and then ultrafast relaxes to S2 state. The internal conversion from S2 to S1 occurs within 0.9 ps. One intermediate state S* was identified in the intersystem crossing (ISC) process, which is different from the specific upper triplet receiver state proposed in some other nitroaromatics systems. The S1 state decays to the S* one within 6.4 ps and then intersystem crossing to the lowest triplet state within 19.6 ps. T1 was estimated to have a lifetime up to 2 ns. The relatively long S* state and very long-lived T1 one should play a vital role as precursors to various nitroaromatic and explosive photoproducts.

Scientific RepoRts | 6:19364 | DOI: 10.1038/srep19364 spectroscopic mixtures in both time and spectral direction, which provides a powerful alternative way to complement the resolving of femto-TA data 18,19 . However, it is still limited for purely applying the chemometrics method to thoroughly map the photodynamic mechanism of the excited states since the method cannot characterize the structures and the transition nature of excited states, which are associated with the electronic level of the molecules. As well accepted, quantum mechanics (QM) calculation is a mature technique to study molecular properties at the electronic level 20 , including molecular structures, chemical reactions, spectral properties, and so on. Consequently, QM method has been successfully applied to study the structures and the transition natures of the excited states in nanosecond 21,22 and femtosecond TA spectra so as to explore the decay mechanism after the excitation 4, [23][24][25][26] . These previous works clearly exhibit that the chemometrics and QM methods have individual advantages in resolving the femto-TA spectrum. The chemometrics method could decompose the overlapping spectra into spectrum of pure species by means of a mathematic separation while the QM method could characterize the structure and transition nature of the excited state. Thereby, we can assume that a combination of the advantages from the two techniques should provide a more efficient and in-depth way for resolving the femto-TA spectrum. However, to the best of our knowledge, the joint method has not been proposed in previous works, which inspire our research interests. Namely, we hope to explore an effective strategy in globally resolving femto-TA data absorption spectroscopy by means of a combination of the QM and chemometrics methods.
In the work, we choose ortho-nitroaniline (ONA) as a case study, mainly based on the following two reasons. First, the interest in the ONA stems from the background of explosives with multi-nitro groups and amino groups. As revealed, the excited electronic state decay can lead to local heating effect called "hot spot" of energy materials in the energy conversion, which plays an important role in detonation course and impact sensitivity of explosives 26,27 . However, there are very limited studies on the decay of the electronically excited states of the nitro-and amino-aromatic explosives since the process is ultrafast and exothermic, involving in the safety. Only recently, with the aid of a simple singular-value decomposition (SVD) method, Chu 28 used femto-second transient absorption to study the relaxation dynamics behavior of 2, 2′, 4, 4′, 6, 6′-hexanitrostilbene (HNS) after excitation at 266 nm and proposed a relaxation process of S 2 → S * → S 1 → T 1 . Thereby, elucidation of the initial decay and the dynamics behavior of excited electronic states has been quietly absent and highly desirable for the explosives. Alternatively, there is also an effective way to access the dynamics behavior of the excited state for the applied explosives through studying their simple prototypes. The approach has been commonly adopted to assist studies on the structure and function of the explosives. For example, by means of nanosecond energy resolved and femtosecond time resolved spectroscopic techniques, E. R. Bernstein's group 29 studied some explosives model systems, such as nitromethane (NM), dimethylnitramine (DMNA) and isopropylnitrate (IPN) in order to obtain the initial decomposition of electronic excited states in the energetic materials. In fact, compared to the simple model systems above, ONA has more similar structure to the nitro aromatic explosives, such as 1,3,5-triamino-2,4,6-tr initrobenzene (TATB), 1,3-diamino-2,4,6-trinitro-benzene (DATB) and 1-amino-2,4,6-trinitrobenzene (TNA). The intramolecular hydrogen transfer of ONA, as a model system of poly-nitro aromatic explosives, was already studied by Zhang 30 using infrared spectroscopic and quantum chemistry methods. However, the dynamics behavior of the excited states has not been addressed for ONA so far. Thus, the observations from the fetmo-TA of ONA will advance understanding of the dynamics behavior of the excited states for more complicated explosives.
The second reason of selecting the ONA comes from the fact that ONA is also a simple and typical nitroaromatic compounds while the photochemistry and photophysics of the nitroacromatic compounds have aroused significant attention because they are closely associated with mutagenic and carcinogenic environmental pollutants, the photodynamics of the excited states of which play an essential role in natural decay from the atmosphere through light-induced reactions 26,31-33 . As mentioned above, the transient absorption studies were already performed for some singly nitroaromatic compounds and nitro-polyaromatic ones 23,24,26,33,34 including para nitroaniline (PNA) 35,36 , an isomer of ONA. These works mainly concerned the intersystem crossing (ISC) dynamics process with help of QM calculation and revealed that the nitroacromatic compounds have significantly different ISC behaviors, dependent on their structures, the substituent types and positions as well as environments. Thus, the observations from the ONA will further extend our understanding of the photophysics of the nitroaromatics.
Based on the consideration above, we, herein, study the femto-TA spectrum of ONA by pump-probe technique in a range 400-710 nm with 35 fs resolution after excitation at 266 nm. Compared to 400 nm excitation wavelength used in PNA system, we used shorter excitation wavelength for ONA in order to gain insight into the relaxation process in higher excited levels. The short excitation wavelength close to 266 nm were adopted in the femto-TA spectra of some compounds 4,37-40 , including HNS 28 . The MCR-ALS in combination with QM calculation is for the first time adopted to explore an efficient resolving method to obtain a comprehensive description of a complete decay evolution process of the electronic excited states of ONA, which will provide valuable information for developing facile yet efficient analysis method for resolving the transient absorption spectrum used in the other fields. In addition, some novel observations were obtained from the work, which would advance understanding of electronic excited state decay for the nitro-aromatic compounds and the explosives.

Results and Discussion
In the following, we first used the steady state absorption and QM calculation to identify the electronic excited state populated by quick excitation at 266 nm. Then, SVD and the evolving factor analysis (EFA) were performed to estimate the number of significant contribution in the relaxation process of the excited state. Based on the number of significant contribution, MCR-ALS was used to decompose the time-resolved spectra into pure spectra of overlapping transient species and their corresponding time-dependent concentration. With aid of QM calculations, we interpret the dynamics profiles and the pure spectra of main excited states of ONA transient absorption. Analysis of steady state absorption assisted with quantum mechanics calculation. Steady state absorption spectrum of ONA was measured in water and displayed in Fig. 1, which exhibits three wide intense absorption peaks at 225 nm, 283 nm and 409 nm. To gain insight into the transition nature of the absorption spectrum, we optimized ONA ground S 0 structure in water at the level of B3LYP/6-311+ + G (d, p) within the framework of polarizable continuum model (PCM). Based on the S 0 optimized geometry, TD-DFT method was used to calculate the spectral properties of ONA in water at the same level. The calculated absorption spectrum is also depicted in Fig. 1 while Table 1 shows compilations of the excitation energies, oscillator strengths, transition character and dominant orbital contributions of the low-lying single excited states of ONA. As shown in Fig. 1, the calculated spectrum is very close to the experiment one, in which the three calculated absorption peaks at 210, 283 and 405 nm well reproduce the experiment ones at 225, 283 and 409 nm, respectively.
The good consistency between the calculated data and the experimental one confirms the reliability of the computational level adopted in the work. An inspection of Table 1 clearly shows that S 0 → S 3 transition has much stronger oscillator strength with f = 0.22 than the other transitions and its transition energy is calculated to be 4.38 eV, corresponding to the adsorption wavelength of 283 nm with π → π * transition character. The calculated wavelength of 283 nm is close to the pumping wavelength at 266 nm used in the transient absorption spectrum. Taking together, it is convincing to confirm that the ONA molecular most probably be excited to the electronic excited S 3 state after quick excitation at 266 nm.

Conventional Analysis of Femtosecond transient absorption. Two-dimensional transient absorp-
tion spectrum of ONA was determined at various time delays after the 266 nm excitation pulse with 35 fs time resolution in water at room temperature. Figure 2 shows 2D plot of the spectrum, which covers the range from 400 nm to 710 nm and possess a long delay time of 400 ps. The negative signals (blue region) in the 400-460 nm range should correspond to the ground state bleaching (GSB) or stimulated emission (SE) 28,41 . The positive signals in the region of 460-710 nm should involve in excited state absorption mixed with the simulated emission from the high vibration excited states to the low ones. In addition, as shown in Fig. 2, the persistence absorption in the positive signal region is still strong without fading out even in a long delay time of 400 ps, implying an existence of long-lived triplet state absorption. Figure 3 further displays the representative transient absorption spectra within the first 20 ps decay time scale after 266 nm excitation. As can be seen from Fig. 3a, after quick excitation (viz., 38 fs), one relatively broad negative signal appeared at less than 460 nm region should be mainly ascribed to the transition in the electronic ground state absorption and partly mixed with stimulated emission from S 3 excited state since the region almost corresponds to the band peaked at 409 nm of the steady state absorption (see Fig. 1). Within the time delay of  38-500 fs, the negative signal in the range of less than 420 nm gradually decay concomitant with the growth of the negative signal at 420-460 nm region, which should arise from the weakness of the ground state absorption and the increase of the stimulated emission. In addition, the broad positive absorption band between 460 nm and 710 nm gradually rises within first 500 fs (see Fig. 3a), implying appearance of some new excited states. After 500 fs, the positive absorption band gradually drop due to depopulation of the singlet electronic excited state. It is interesting to note that a sharp and positive peak appears near 675 nm at the 20 ps time delay (see Fig. 3b), implying a possibility of formation of one new excited state at 20 ps.

MCR-ALS of Time-Resolved Spectra.
In order to further identify the specific temporal evolution of the spectrum and dynamics behavior for the main excited states involved in the femtosecond transient absorption data, we used MCR-ALS method to decompose the transient absorption spectra of multiple components into pure spectra of the transient species and their time-dependent concentrations. As described in method part, EFA calculation was first performed to estimate the number of significant contributions for the S 3 state relaxation process. To reduce computing time of EFA calculation, we only took the first 60 row into accounts, which corresponds to 30 ps. Figure 4 plots the principal component eigenvalues (in log units) obtained from the forward and backward analysis versus the delay time. A threshold separating major contributions from noise is set at log  (eig) = − 2.8, which leads to four significant contributions observed. As reflected by Fig. 4, in the forward direction, the first contribution and the second one emerges very quickly. The third and the fourth components appear a bit delayed. The analysis on the backward direction give similar result. Thereby, we could draw such a conclusion that there are four significant contributions in the relaxation process.
Based on the number of main excited states derived from the EFA analysis, the soft-modeling MCR-ALS analysis was applied to resolve the transient absorption spectra during 0-30 ps time range and obtain the initial estimates of time dependent concentration profiles C for sequential process. Figures 5 and 6 display the pure spectra of the four components (S T ) and the corresponding time-dependent concentrations (C) obtained from the MCR-ALS analysis, respectively. A lack of fit was estimated to be 2.8% from the experimental matrix, indicating the reasonability of the MCR-ALS results.
Assignment of the excited states significantly contributed to the Femtosecond transient absorption spectrum. S 2 state. As revealed by QM calculation above, the ONA molecular most probably be excited to S 3 state at 266 nm excitation. However, there were few experimental evidences for the S 3 → S 2 relaxation time, which may be resulted from the ultrafast internal conversion between the two singlet excited states. Only recently, theoretical observations from ab initio molecular dynamics simulation predicted that the internal conversion from S 3 to S 2 occur within 200 fs time scale for uracil 42 and 25 fs time scale for DNA nucleobase cytosine 43 , providing a thereotical support for the ultrafast relaxation of S 3 → S 2 . For ONA, the internal conversion from S 3 state to S 2 may be beyond the ~200 fs time resolution of the work. Consequently, we could not definitely identify the decay dynamics of S 3 state from the fetmo-TA spectrum. Thereby, the spectrum of the first species was assigned to be S 2 state. The corresponding time-dependent concentration gives a lifetime of 0.9 ps for the S 2 state in terms of the global fitting.
Although there also have been absent of the experimental evidence regarding the lifetime of S 2 state for nitroaniline so far, previous TRPES (time-resolved photoelectron imaging) works on the benzene derivatives [44][45][46][47] such as benzene, toluene, indene, styrene, o-xylene, and phenylacetylene, indicated that the internal conversions from S 2 state to S 1 one are commonly ultrafast within 100 fs, much shorter than 0.9 ps derived from our work. However, some experiments on the aromatic hydrocarbon benzophenone with excitation at 266 nm reported that the lifetime of the S 2 → S 1 transition is between 0.1-0.2 ps in gas phase 40 and 0.53 ps in acetonitrile solvent 37 . In addition, 0.59 ps lifetime of S 2 → S 1 was reported for a benzophenone derivative (p-iodobenzophenone) in acetonitrile media 37 . Longer relaxation time with 0.8 ps lifetime was observed from the femto-TA transient absorption spectrum of HNS for its S 2 → S 1 decay in acetontrile media 28 . The ab initio MD study on the uracil in solution 42 , which exhibited good consistency with the experimental observations, also found that 50% of the excited trajectories are still trapped in S 2 after 1 ps, indicating that the depopulation of the S 2 state slowly occur due to internal conversion to the S 1 . Recently, longer relaxation time within a few picoseconds from the S 2 state to the S 1 one was reported by Crespo-Herná ndez, 4 who used femto-TA experiment in combination with quantum chemistry calculation (CASSF and ab initio surface-hopping simulation) to study the excited-state dynamics of the purine free base and 9-methylpurine. Their results indicated that the excitation of these purine derivatives in aqueous solution at 266 nm results primarily in fast conversion of the S 2 (π , π * ) state to the vibrational excited S 1 (n, π * ) state within a few picoseconds and then an intersystem crossing occur within hundreds of picoseconds. Thus, combined with our work, it can be drawn that the S 2 → S 1 internal conversion would take place in the time range between a few femtosecond and a few picosecond, depending on the structures of various molecules and the environments used. S 1 state. The spectrum of the second species with a sharp negative signal peaked at 660 nm is assigned to the S 1 state and its lifetime is estimated to be 6.4 ps by the global fitting, similar to results from 4-nitrated polyaromatic, 2-nitrated polyaromatic and 11-nitrated polyaromatic, S 1 lifetimes of which were reported to be 4.4 ps, 10 ps and 3 ps, respectively 21 . Due to the vital role of the S 1 decay in controlling the performance of the photochemical and photobiological systems, previous works in the fields mainly focused on the subject, in particular for the intersystem crossing (ISC).
As revealed, there are usually rapid S 1 decays for most nitroaromatics as short as a few hundred femtoseconds due to a strong coupling of the S 1 state with T 1 state 23,24,26,48 . For example, the femtosecond-resolved experiments on 2-nitrofluorene shows ultrafast intersystem crossing which depopulates the S 1 emissive state within less than a picosecond. However, introduction of NH 2 to 2-nitrofluorene leads to a much longer lifetime of 100 ps in non-polar cyclohexane solvents 48 . In addition, S 1 decays of the singly nitrated pyrenes (NP) was reported to be strongly dependent on the position of NO 2 , leading to that the decay of the fluorescence states can be of several hundred picoseconds or even enter the nanosecond scale in acetonitrile 23,49,50 . For example, S 1 in 1-nitropyrene is short-lived (up to 3 ps) while, due to the lack of an appropriate receiver triplet state, S 1 states of 4-nitropyrene and 2-nitropyrene have 0.41 ns and 1.2 ns lifetimes, respectively 23 . For 3-nitropyrene, it took place on a 100 ps time scale 50 .
Intermediate state S* in the intersystem crossing. Since the fluorescence emission is absent for ONA, there should exist a significant nonradioactive decay pathway in its S 1 excited state. Thus, we focused on its ISC pathway. As revealed, the intersystem crossing channels would become highly efficient when the singlet and upper triplet states have similar energies and appropriate electronic configurations 51-53 , while ISC would be suppressed by symmetry when the participating singlet and triplet states are composed of essentially same orbitals 54 in terms of EI-Sayed rules 55 .
Thereby, we analyzed the energy levels and electronic nature for some low-lying single and triple excited states of ONA (see Fig. 7) through TD-DFT calculations at the level of B3LYP/6-31+ + G (d, p), based on the optimized S 1 and T 1 structures. The calculation result indicates that the two optimized structures have same (π , π *) characters. In addition, the energy gap between the S 1 state and the T 1 one is also significant (Δ E = 0.96 eV). As a result, the direct transition from S 1 (π , π * ) to T 1 (π , π * ) should be prohibited according to EI-Sayed rules. Then, it is reasonable to assume that the occurrence of ISC transition should be mediated by one intermediate state for the ONA. The assumption is also supported by the observation from Fig. 3 that a sharp peak abruptly appear at near 675 nm at the 20 ps time delay. Consequently, the third spectrum can be assigned to be the intermediate state (termed as S * ) and its lifetime is estimated to be 19.6 ps by the global fitting analysis, close to 20 ps shown in Fig. 3.
The intermediate states in the ISC process were previously reported for some systems. For example, Aloise 56 proposed an intermediate state (termed as IS) existed in the ISC process for benzophenone through the pump-probe subpicosecond absorption experiments in combination with multivariate curve resolution, in which the transition lifetimes of S 1 → IS and IS → T 1 were estimated to be ~6.5 ps and 10 ps, respectively. The intermediate states S * were observed for the ISC processes of carotenoid 39 , spheroidene 57 and 1-nitronaphthalene 53 lifetimes of which were estimated to be 30 ps, 5.5 ps and the time scales of 1-16 ps, respectively. In addition, previous works on some nitroaromatics 24,33,58,59 and purine nucleobase derivatives 4 further proposed that the indirect ISC pathway from S 1 to T 1 states can be performed through one particular upper triplet states. The specific upper triplet state has isoenergetic energy and appropriate spin-orbit coupling character, leading to ultrafast ISC times as short as a few hundred femtoseconds. Whereas for some nitroaromatics, there are lack of the appropriate receiver  triplet state upper the T 1 energy. Consequently, their ISCs occur on a much longer time scale of hundreds of picosecond, even up to nanosecond 46 .
As shown in Fig. 7, no any triplet state is placed below the S 1 state energy level with exception of T 1 for ONA, implying that there is no an appropriate "receiver" triplet state required for the fast ISC process. However, different from the time scale within femtosecond and nanosecond of S 1 lifetime reported, the S 1 state of ONA has the lifetime of 6.4 ps, derived from the MCR-ALS and the global fit analysis. Thus, it is reasonable to conjecture that the intermediate mediating the ISC pathway of ONA is different from the character of the upper triplet state, maybe mixed with the singlet state character and the triplet one. Further aspects of addressing the nature of intermediate state are beyond the work.
T 1 state. The fourth spectrum should be assigned to be T 1 state. A detail comparison of T 1 time-dependent concentration with that of S * state clearly shows that there is an opposite trend between the two states (vide Fig. 5). Namely, depopulation of S * corresponds to repopulation of T 1 state, similar to the population relationship between S 1 state and S * one. The lifetime of T 1 is estimated to be 2 ns by the global fitting analysis, significantly exceeding the experimental time range of 400 ps relaxation. The conclusion is consistent with the finding above that the persistence of the positive absorption at long wavelengths still exists even at 400 ps delay time (vide Fig. 2), which imply the formation of a new long-lived state. It was reported that the absorption of the triplet state of the benzophenone 56,57 , HNS 28 and 9-methylpurine 4 could persist up to the maximum delay of 1.6 ns, ~4 ns and > 3 ns time scale, respectively, which are in line with the nanosecond time scale of the triplet state derived from our work.

Conclusion
By introducing advanced chemometric method (MCR-ALS) and quantum mechanics calculation, we proposed a joint strategy to resolve the femtosecond transient absorption for ONA. The results revealed that the ultraviolet excitation populates primarily the S 3 (π , π * ) state in the Franck-Condon region. The internal conversion from S 3 to S 2 should be too ultrafast to be identified from our femtosecond spectrum with 200 fs resolution time. However, the decay from S 2 state to S 1 one was determined to be within 0.9 picosecond. It is noteworthy that one intermediate was detected in the ISC pathway from the S 1 state to T 1 one and the existence of the intermediate results in fast decay of S 1 → S * within 6.4 ps, which should contributed to the absence of fluorescence for ONA. The 6.4 ps lifetime of S 1 state is different from some previous observations concerning ultrafast S 1 deactivation within femtosecond time scale resulted from the existence of appropriate upper triplet state strong coupling with S 1 , and also distinguished from ultraslow decay on the nanosecond time scale due to the absence of appropriate upper receiver triplet state in the ISC pathways reported for some nitroaromatics. The decay time from the intermediate S * state to the T 1 one was estimated to be 19.6 ps. The following T 1 was populated and its lifetime was estimated to be up to be 2 ns. Based on the observations, it can be assumed that relatively long-lived S * and very long-lived T 1 states, in particular for T 1 state, should play a dominant role as precursors to various nitroaromatic and explosive photoproducts because they cannot directly compete with the other possible deactivation process with shorter or similar lifetimes.
To the best of our knowledge, it is for the first time to combine the advanced chemometrics method (MCR-ALS) with quantum chemistry calculation to explore an efficient and facile way to thoroughly resolve the femtosecond transient adsorption. More importance, some novel observations were obtained from ONA and extend knowledge's regarding the photophysics of the nitroaromatics, which in turn is helpful for the understanding of photoinduced reactive channels of nitroaromatics and the initial ignition process of explosives like TATB, DATB and TNA.

Experimental Method
Transient Absorption Measurements. The typical transient absorption experimental setup were described in detail before 60,61 . Briefly, a regenerative amplified laser system was used to generate fundamental pulse of duration of 35 fs centered at 800 nm, with an energy per pulse of 1 mJ and repetition rate of 1 kHz. Another harmonics fundamental pulse centered at 400 nm was obtained by a 1 mm thick BBO crystal. The 266 nm pump beam attenuated to ~5 μ J as excitation pulse was obtained by sum frequency mixing of the first and the second pulses. The white-light-continuum pulses obtained from CaF 2 crystal were spilt into the experimental probe beam with the range of 400-710 nm and the reference one by a beam-splitter. The probe pulse passed through an optical delay line and overlapped with the pump in sample cell at an intersection angle of 5˚. And the polarization angle between pump and probe beams was set at a magic angle of 54.7˚. The fundamental, pump and the probe pulses were controlled by three optical shutters. The probe and the reference pulses were detected by a two dimensional CCD detector (PI-MAX, 1024 × 256 pixel array) equipped with a grating inside spectrometer (Princeton, SpectraPro 2500i). The probe and the reference image signals from CCD were sent to computer by a 16-bit analog-to-digital converter (ADC). The experiment control and data acquisition were performed using a labview program. By means of averaging approximately 1600 pulses, the noise level lower than 2 mOD could be achieved. The instrumental response of the system was determined to be ~200 fs by cross-section measurement between pump and probe pulses, which was also used to measure the precise zero time-delay at each probe wavelength. The chirp of white-light-continuum pulse was measured at the position of the sample cell by the use of the optical Kerr effect of solvent and was used to correct the dispersion of relative delay time in the time-resolved data. The 0.7 mmol/L of ONA in water was prepared under dark room and circulated flow by a device to avoid re-excitation. The cross-correlation function was also used to determine the precise zero time-delay at each probe wavelength.
Scientific RepoRts | 6:19364 | DOI: 10.1038/srep19364 Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS). In general, the experimental matrix D of femtosecond-TA can be described by a bilinear model given in Eq. (1) Where the matrix C (m × k) contains the time dependent concentration profiles of k pure contribution at m delays and matrix S T (k × n) contains the corresponding transient spectra at n wavelengths. The error matrix E (m × n) contains the residuals not explained by the k components. Multivariate curve resolution-alternating least squares (MCR-ALS) 17,62 was applied to resolve Eq.(1) in order to select the real contributions of the pure components represented by the concentration profiles C and spectra profiles S T from the mixed nonselective information. The first step of MCR-ALS algorithm is to estimate the appropriate number of components composing the experimental matrix D, which is usually obtained by singular-value decomposition (SVD) 63,64 . However, the SVD alone cannot settle correctly threshold that separates chemical contributions from noise. Thus, instead of SVD analysis on the full data matrices, evolving factor analysis (EFA) 65,66 was used to perform successive SVD analysis on the gradually increasing submatrics by means of adding a row at a time from the top of the matrix to the bottom (forward EFA). The emergence and evolution of the singular values can be followed individually with increasing time. Also, EFA from bottom to top (backward EFA) was carried out using the same approach, in which the emergence and evolution of the singular values can be followed in reverse sequence and their disappearance can be observed with the increasing time. Taken the forward EFA result together with the backward EFA one, estimation of the profiles C and S T can be obtained and input as initial solution in the MCR-ALS procedure. The ALS algorithm is used to fit iteratively the C and S T matrices to the experimental matrix D. At each iterative cycle of the optimization, matrices C and S T are calculated under constraints minimizing the reproduction error E. Non-negativity and unimodality constraints for concentration profiles were applied during the ALS optimization order to get meaningful results 41,56 . The lack of fit (Eq. 2) can be used as global estimator of the fitting error of the transient spectra data. where d ij is an element of the experimental data matrix and (d ij -d ij * ) 2 is the related residual value obtained from the difference between the experimental matrix D and the reproduced matrix CS T derived by MCR-ALS.
Quantum Mechanics Calculation. The equilibrium geometries of the ground state S 0 and the triplet excited state T 1 were optimized using density function theory (DFT) 67 method at the level of B3LYP 68 /6-311+ + G(d, p) while the optimization of the S 1 state was carried out using time-dependent density functional theory (TDDFT) 69 at the same level. The vibrational frequency calculations confirm that the optimized structures are true minimum on the potential energy surfaces. Based on the optimized geometries, TD-DFT calculations were carried out to obtain the transition properties at the level of B3LYP/6-311+ + G (d, p). All calculations above included the water environment using the polarizable continuum model (PCM) 70,71 . The Gaussian 09 suite of programs 72 was used for all calculations.