Exploring Geometrical, Electronic and Spectroscopic Properties of 2-Nitroimidazole-Based Radiopharmaceuticals via Computational Chemistry Methods

Tumor hypoxia plays an important role in the clinical management and treatment planning of various cancers. The use of 2-nitroimidazole-based radiopharmaceuticals has been the most successful for positron emission tomography (PET) and single photon emission computed tomography (SPECT) imaging probes, offering noninvasive means to assess tumor hypoxia. In this study we performed detailed computational investigations of the most used compounds for PET imaging, focusing on those derived from 2-nitroimidazole: fluoromisonidazole (FMISO), fluoroazomycin arabinoside (FAZA), fluoroetanidazole (FETA), fluoroerythronitroimidazole (FETNIM) and 2-(2-nitroimidazol-1-yl)-N-(2,2,3,3,3-pentafluoropropyl)acetamide (EF5). Conformational analysis, structural parameters, vibrational IR and Raman properties (within both harmonic and anharmonic approximations), as well as the NMR shielding tensors and spin-spin coupling constants were obtained by density functional theory (DFT) calculations and then correlated with experimental findings, where available. Furthermore, time-dependent DFT computations reveal insight into the excited states of the compounds. Our results predict a significant change in the conformational landscape of most of the investigated compounds when transitioning from the gas phase to aqueous solution. According to computational data, the 2-nitroimidazole moiety determines to a large extent the spectroscopic properties of its derivatives. Due to the limited structural information available in the current literature for the investigated compounds, the findings presented herein deepen the current understanding of the electronic structures of these five radiopharmaceuticals.


Introduction
Hypoxia is a common feature of the microenvironment of solid tumors and is associated with metastasis, recurrence and the development of resistance to radiotherapy, chemotherapy and immunotherapy [1][2][3].There is a continuous effort to develop methods able to facilitate proper oncological treatment [2].Among these methods, molecular imaging techniques like PET and SPECT, using nitroimidazole derivatives, have shown promising results [4,5].Their effectiveness is due to their ability to undergo oxygen dependent reduction specifically in hypoxic cells.A significant number of 18 F-labelled radiopharmaceuticals for hypoxia imaging have been successfully developed and evaluated in clinical trials [6].Fluromisonidazole (FMISO) was the first 2-nitroimidazole (2nim) derivative to undergo clinical testing and remains the preferred standard in clinical imaging.However, its high lipophilicity results in low uptake and low-contrast images, thereby prompting the development of more optimized radiopharmaceuticals such as fluoroazomycin arabinoside (FAZA), fluroetanidazole (FETA), fluoroerythronitroimidazole (FETNIM) and 2-(2-nitroimidazol-1-yl)-N-(2,2,3,3,3-pentafluoropropyl) acetamide (EF5) (see Figure 1) [5].
prompting the development of more optimized radiopharmaceuticals such as fluoroazomycin arabinoside (FAZA), fluroetanidazole (FETA), fluoroerythronitroimidazole (FET-NIM) and 2-(2-nitroimidazol-1-yl)-N-(2,2,3,3,3-pentafluoropropyl) acetamide (EF5) (see Figure 1) [5].The current understanding of the molecular mechanism of nitroimidazole compounds in hypoxia cells is limited.A recent study by Rashed et al. [7] investigated the mechanism of action of two nitroimidazoles (IAZA and FAZA) in a head and neck cancer model.They concluded that covalent binding of the investigated compounds to proteins can inhibit catalytic functions of critical cellular enzymes and they plan on further analyzing the proteins targeted by the nitroimidazoles.Once the targets are identified, studies of receptor-ligand binding could further advance the understanding of the mechanism of action and would require detailed structural (conformational) information of the nitroimidazole derivatives.The current understanding of the molecular mechanism of nitroimidazole compounds in hypoxia cells is limited.A recent study by Rashed et al. [7] investigated the mechanism of action of two nitroimidazoles (IAZA and FAZA) in a head and neck cancer model.They concluded that covalent binding of the investigated compounds to proteins can inhibit catalytic functions of critical cellular enzymes and they plan on further analyzing the proteins targeted by the nitroimidazoles.Once the targets are identified, studies of receptor-ligand binding could further advance the understanding of the mechanism of action and would require detailed structural (conformational) information of the nitroimidazole derivatives.
Thus, we consider that our results related to the structure and conformations of the investigated compounds could be useful for docking studies and ligand-receptor interactions [8,9].The predicted spectroscopic properties might also be of help for drug monitoring [10], for drug detection or for pharmaceutical research and development [11].
Although extensively utilized in nuclear medicine, detailed information on their molecular and electronic configurations remains limited.Therefore, in this study, we present a computational structural analysis of the aforementioned radiopharmaceuticals.Despite their development beginning in the late 1980s, a review of the current literature reveals a lack of data regarding the electronic structures of these compounds.According to the Web of Science database, only 64 papers were found when searching for the keywords "radiopharmaceuticals" AND "DFT".
Our aim was to provide a characterization of their conformational landscape and to determine the optimal structures of possible conformers, as well as to analyze their vibrational, NMR and electronic spectroscopic properties using density functional theory calculations.All these compounds show favorable properties for hypoxia imaging; however, there are still limitations in their implementation in the clinical setting [5].Furthermore, compounds such as FMISO will act as a benchmark when evaluating the performance of new imaging agents.To this extent, we consider that a thorough structural characterization of these compounds could provide information that can be useful when optimizing and developing new agents.

Conformers and Boltzmann Population Analysis
The conformers of the five compounds in the gas phase were generated from the 2D relaxed potential energy surfaces (PES) defined by the dihedral angles shown in Table 1.In the case of FAZA, because of its low structural flexibility we investigated only the 1D PES generated by scanning the C4-N3-C9-C10 dihedral angle.The scanned dihedrals were incremented 24 times in steps of 15 • over the 360 • interval.

Compound
Dihedral Angle ( We identified 9 local minima for FMISO, 11 for FETNIM, 3 for FAZA and 2 for FETA and EF5.The geometries of the minima for each compound were further fully optimized at the B3LYP/6-311+G(d,p) level of theory, both in gas phase and water.These new geometry optimizations revealed a lower number of unique conformations for FMISO and FETNIM (5 and 7, respectively).The relative Boltzmann populations were calculated using the following formula: where ∆G i are the relative (Gibbs) free energies, k B is the Boltzmann constant, and T is the temperature (T = 298 K) [12][13][14].The Gibbs free energy was used for Boltzmann population calculations as recommended in ref. [12].The structures of the most stable conformers in the gas phase and water are shown in Figure S1, while Boltzmann populations are presented in Table 2. Geometry re-optimizations in water show small changes in the structures of the conformers.On the other hand, as can be seen in Table 2, important changes are noted between the Boltzmann populations of the conformers when passing from the gas phase to the liquid state.Regarding the energetic order of the conformations for the five investigated compounds, the following matchings were observed: As an example, the above mentioned correspondences for FMISO means that the conformer 1g is the most stable in the gas phase.It exhibits structural similarity with the conformer 1w, which attains maximal stability in an aqueous environment.The 3g conformer, which ranks as the third most stable in the gas phase, experiences a decrease in relative stability in water, where it is ranked as the fifth most stable, denoted as 5w.
According to data collected in Table 2, in the case of FMISO, the most stable conformer in the gas phase remains the most stable in water as well, with a similar relative population 62.15% vs. 65.91%.The conformers 2g and 3g suffer a destabilization due to solvation and they transform into the 3w and 5w conformers in water, with the relative population of 7.59% and 2.33%, respectively.On the other hand, the conformer 4g shows an increase in relative population to 20.56% in water, becoming the second most stabilized.
For FETNIM, most conformers suffer a slight destabilization due to solvation effects; however, the conformer 3g shows an increase in relative population in water from 8.22% to 23.16%, becoming the second most stabilized in the aqueous environment.
Significant solvent destabilization effects can be observed for FAZA 1g and FETA 1g, while a large increase in relative population can be seen for the conformer FAZA 3g from 0.29% in gas phase to 28.46% in water.This change from the gas phase to water comes with a structural reconfiguration, mainly in the dihedral angles related to the oxolane group.
The two conformers of EF5 show negligible solvation effects and retain the same energetic order in the gas phase and water.

Vibrational Properties 2.2.1. 2-Nitroimidazole
The theoretical IR and Raman spectra of 2nim in the harmonic (scaled frequencies) and anharmonic approximations in the gas phase and water are presented in Figure 2. The assignments of the most representative bands are given in Table 3.
0.29% in gas phase to 28.46% in water.This change from the gas phase to water comes with a structural reconfiguration, mainly in the dihedral angles related to the oxolane group.
The two conformers of EF5 show negligible solvation effects and retain the same energetic order in the gas phase and water.

2-Nitroimidazole
The theoretical IR and Raman spectra of 2nim in the harmonic (scaled frequencies) and anharmonic approximations in the gas phase and water are presented in Figure 2. The assignments of the most representative bands are given in Table 3.In the fingerprint region of the IR spectrum, we note the most intense calculated bands at 1330 and 1546 cm −1 , both involving the vibrations of the nitro group, assigned to the ν(C-N) + ν sym (NO 2 ) and ν asym (NO 2 ) normal modes.On the other hand, the most Raman active predicted mode (ν(C-N) + ν(C=C)) is calculated at 1318 and 1345 cm −1 by the harmonic and anharmonic approximations, respectively (see Figure 2b).This mode, together with those calculated at 1059/1206 and 1143/1162 cm −1 form the set of characteristic Raman bands for 2nim.
At high wavenumbers, the three observed bands were assigned to a ν(NH) mode at 3512 cm −1 and two ν(CH) modes at 3165 and 3141 cm −1 .
Experimental data for the IR spectrum of 2nim were obtained from references [15,16].As seen in Table 3, there is a good agreement between the experimental and computed IR wavenumbers.Expectedly, the experimental bands are generally better described by the anharmonic approximation with the exception of some observed bands at 623, 944, 3146 and 3164 cm −1 which are more closely reproduced by the scaled harmonic data.

2-Nitroimidazole Derivatives
The theoretical harmonic IR (gas-phase) and Raman (water) spectra of the five nitroimidazole derivatives are presented in Figure 3 (spectra of 2nim are included for comparison purposes).The assignments of the most representative bands for each compound are available in the Supplementary Materials (Tables S1-S5).
We can distinctly observe characteristic spectral bands associated with 2nim in the spectra of all five compounds.Such calculated bands include the ν(C-N) imidazole + ν sym (NO 2 ) mode at ~1330 cm −1 , the ν(C-N) imidazole + β(NH) + β(CH) mode at ~1456 cm −1 , ν asym (NO 2 ) at ~1546 cm −1 and two ν(CH) modes at ~3141 and 3165 cm −1 .The specific wavenumbers for these bands can be found in Table 3.It is noteworthy that the first three bands exhibit a red-shift, whereas the second ν(CH) mode in FAZA experiences a blue-shift of 23 cm −1 .Notably, the spectral bands at 997 and 1056 cm −1 do not have a corresponding mode in the calculations for the 2nim derivatives.
The Boltzmann-weighted spectra presented in Figure 3 take into account the conformers with a Boltzmann population higher that 5%.Comparative figures illustrating the spectral variances among different conformers for each compound can be found in the Supplementary Materials (Figures S2-S6).We observe that the composite spectra are following the spectral landscape of the spectrum for the most stable conformer.For FMISO and FETNIM, significant differences in the spectral bands of the predicted conformers are observed, particularly in the lower fingerprint region.However, as the Boltzmann population for the most stable conformer is much larger, its contribution to the composite spectra outweighs that of the other conformers.A notable exception is evident in the com-posite spectra of FMISO where one can observe two distinct ν(OH) bands: at 3696 cm −1 originating from the conformers 1g and 2g, and at 3621 cm −1 attributed to the contribution of the conformer 3g (IR harmonic gas phase).In the case of FETA, both conformers exhibit similar vibrational patterns, without any obvious individual contributions.Finally, for EF5, where the Boltzmann populations of the two most stable conformers are very close, three doublets are discerned in the composite spectra which are due to the contributions of both conformers: 383 (1g)/371 (2g), 651 (1g)/675 (2g) and 3418 (1g)/3444 (2g) cm −1 .
Supplementary Materials (Figures S2-S6).We observe that the composite spectra are following the spectral landscape of the spectrum for the most stable conformer.For FMISO and FETNIM, significant differences in the spectral bands of the predicted conformers are observed, particularly in the lower fingerprint region.However, as the Boltzmann population for the most stable conformer is much larger, its contribution to the composite spectra outweighs that of the other conformers.A notable exception is evident in the composite spectra of FMISO where one can observe two distinct ν(OH) bands: at 3696 cm −1 originating from the conformers 1g and 2g, and at 3621 cm −1 attributed to the contribution of the conformer 3g (IR harmonic gas phase).In the case of FETA, both conformers exhibit similar vibrational patterns, without any obvious individual contributions.Finally, for EF5, where the Boltzmann populations of the two most stable conformers are very close, three doublets are discerned in the composite spectra which are due to the contributions of both conformers: 383 (1g)/371 (2g), 651 (1g)/675 (2g) and 3418 (1g)/3444 (2g) cm −1 .
(a) (b) Conformer analysis and Boltzmann population analysis show an energetic reordering of the most stable conformers for each compound when considering water as a solvent.Radiopharmaceuticals are usually administered to patients through intravenous injections of aqueous solutions.Figure 3b presents the calculated harmonic Raman spectra for 2nim and the Boltzmann-weighted averages of the most stable conformers for the five Conformer analysis and Boltzmann population analysis show an energetic reordering of the most stable conformers for each compound when considering water as a solvent.Radiopharmaceuticals are usually administered to patients through intravenous injections of aqueous solutions.Figure 3b presents the calculated harmonic Raman spectra for 2nim and the Boltzmann-weighted averages of the most stable conformers for the five derivatives in water.In the case of FETNIM, FETA and FAZA, no specific conformer contributions can be observed due the similarities of the corresponding spectra for the conformers with the highest predicted populations.For EF5, one doublet can be discerned at 3469 (1w)/3446 (2w) and two conformer-specific bands at 203 (2w) and at 180 (1w) cm −1 .In the case of FMISO, calculations predict significant conformer-specific characteristics in the averaged Raman spectrum weighted by the three most stable conformers in water: two doublets at 3693 (1w)/3650 (2w) and at 1272 (1w)/1253 (2w + 3w) cm −1 , as well as the band at 1065 cm −1 arising due to the contributions of the conformers 1w and 3w and the band at 632 cm −1 due to the conformers 2w and 3w.
There are no significantly intense overtones or combination modes calculated for the anharmonic spectra.Figures presenting the comparison between the IR and Raman harmonic and anharmonic spectra of the most stable conformer in the gas phase are available in the Supplementary Materials for all compounds (Figures S7-S11).Calculated anharmonic wavenumbers are shown in the assignment tables in the Supplementary Materials Tables S1-S5.
In Table S1, we provide a tentative comparison with experimental IR data from Ref. [17] for FMISO.It is important to note that the reference only provides IR wavenumbers, without IR intensity.Therefore, our assignment in Table S1 is based solely on the positions of the bands in the spectrum.We observe a good agreement with the calculated anharmonic spectra of FMISO for most of the bands, particularly in the fingerprint region.However, the harmonic bands at 786, 1121 and 1535 cm −1 were found to be in better agreement with the experimental band at 795, 1116 and 1534 cm −1 .Such discrepancies can be due to intermolecular interactions but also to differences in the anharmonicity of the normal modes.
Next, we analyzed the calculated IR and Raman spectra (Figures S12-S16) for the five compounds in which the 19 F atom was replaced by the 18 F radioisotope.The calculations were performed for the most stable conformers in each case.The harmonic spectra for FMISO, FETNIM, FETA and FAZA exhibit a distinct ν(CF) mode at 977, 992, 997 and 991 cm −1 .In all four cases, this band suffers a blue-shift of 5, 6, 11 and 9 cm −1 in the 18 F spectra with respect to the 19 F spectra.When comparing anharmonic frequencies, this difference decreases for FETNIM (3 cm −1 ), remains the same for FETA and increases for FMISO (6 cm −1 ) and FAZA (13 cm −1 ).No other significant differences were observed in the calculated harmonic bands of the IR and Raman spectra of these compounds.
In the case of EF5, spectroscopic calculations reveal the presence of multiple bands involving ν(CF) and ν(CF 2 ) vibrations.Based on the results of the conformational analysis, we considered both conformers as the relative Boltzmann populations were very similar 55.05% for 1g and 44.95% for 2g.Upon substituting one fluorine atom with the 18 F isotope we have not noticed any significant shifts in the 18 F harmonic spectra for these bands in either conformer, as all differences were less than 5 cm −1 .
To conclude this section, it is worth noting that all five investigated radiopharmaceuticals maintain the vibrational characteristics of the 2nim template, both in terms of band positions and intensities.Furthermore, the computed anharmonic frequencies generally exhibit better agreement with experimental data.However, in some instances, the scaled harmonic frequencies have also proven to be useful for reliable assignments of vibrational spectra.

NMR Data
Given the lack of structural information for the radiopharmaceuticals, we compiled in this section the available experimental NMR data for the investigated compounds and compared the observed values with those predicted by quantum chemical calculations carried out at the PCM-B3LYP/6-311+G(d,p) level of theory (see Tables 4-8).
For all compounds the geometries have been fully optimized prior to NMR calculation at the same level of theory.Atom numbering schemes for all compounds are given in Figure 1.The computed NMR data were determined using the appropriate solvent specified in the respective available experimental works.Tetramethylsilane (TMS) was used as an NMR reference standard for FMISO (both for 1 H and 13 C spectra), FAZA (both for 1 H and 13 C spectra), FETA (for 1 H spectrum), EF5 (for 1 H spectrum) and for 2nim (both for 1 H and 13 C spectra), whereas the CFCl 3 or CF 3 COOH standards have been employed for 19 F nuclei, according to the experimental conditions.The calculated spin-spin couplings are reported merely where experimental values are available.No scaling procedure was applied for any type of nuclei.
First, we have to note that in the case of the FETNIM compound, NMR experimental data have only been documented for one of its precursors, as reported by Yang et al. [18].
To our knowledge, NMR data for the compound itself are not available and it will be excluded from the following discussion.However, we have provided computational data for the chemical shifts and spin-spin couplings in Table S6 in the Supplementary Material for future reference.On the other hand, for the FMISO and FAZA compounds, a more substantial body of experimental NMR data has been amassed for the 1 H, 13 C and 19 F nuclei and therefore allow for a more detailed analysis.
As seen in Tables 4-8, the overall agreement between the experimental and calculated NMR data is good, both for chemical shifts and J coupling constants.Significant discrepancies are evident for the chemical shifts associated with the 13 C nuclei, which is a common behavior (see, for instance, ref. [19]) and it has not prevented the assignments for these nuclei.For the chemical shifts of the 19 F nuclei, large deviations between experiment and theory have been observed (e.g., −230.70 ppm experimental vs. −266.16ppm calculated, in DMSO for FMISO).In order to mitigate systematic errors for these nuclei, we employed a linear regression approach, a common practice found in the literature [20][21][22].Thus, we fitted the calculated shifts against the experimental values (see Figure S17), resulting in the following equation for the scaled 19 F chemical shifts at the B3LYP/6-311+G(d,p) level of theory: The goodness of fit is supported by the value of R 2 = 0.9992, as well as the statistical parameters of mean absolute error (MAE = 1.486 ppm) and root mean square deviation (RMSD = 1.713 ppm).
Based on this scaling procedure, we can predict the chemical shifts for 19 F nuclei in FETA and FETNIM at −225.08 and −232.69 ppm, respectively.
For FMISO, one can note a much lower value of the calculated chemical shift for the H19 nucleus with respect to its experimental counterpart (see Table 4).This discrepancy may be attributed to intermolecular hydrogen bonding (HB) interactions involving this particular atom.We note that the optimized conformer with intramolecular HB O12-H19-O7 still does not replicate successfully the observed chemical shift.
For each compound, J couplings have been predicted by calculations at least in qualitative agreement with experimental results.Largest deviations between experiment and theory are observed for 1 J C11H21 and 3 J F13H18 in case of FMISO, and 2 J F19C12 and 1 J F19C18 for FAZA.a Atom numbering can be seen in Figure 1.b from refs.[24] (in CD 3 OD) and [25] (in CD 3 OD); Experimental values in italics for 1 H and 13 C are from ref. [25].c not available.d solvent: methanol; reference standards: TMS for 1 H and 13 C, CFCl 3 and CF 3 COOH for 19 F; e Values in italics for 19 F refer to CF 3 COOH reference standard.

TD-DFT Data 2.4.1. 2-Nitroimidazole
In the following, we were interested in the electronic absorption properties of the compounds under examination.Particularly, we focused on calculating the absorption wavelengths and the nature of the involved transitions, as well as the electronic density changes triggered by the electronic excitation of these radiopharmaceuticals.For the following discussion, we considered only the electronic transitions with λ abs ≥ 200 nm and f ≥ 0.01.
The three singlet-singlet electronic transitions of 2nim in water, with oscillator strengths larger than 0.01, are listed in Table 9.According to quantum chemical calculations, the transition to the first singlet excited state has a very low oscillator strength and the λ max band in the UV-Vis, predicted at 315 nm, is mainly due to the HOMO → LUMO excitation with a contribution of 99.12%.The other two significantly intense bands appear as a result of S0 → S5 and S0 → S5 transitions (see Table 9).
The low probability of the S0 → S1 excitation is due to a poor overlap of the orbitals involved in this electronic transition, and consequently, a low transition dipole moment.The corresponding natural transition orbitals (NTOs) [29] HOTO and LUTO for this transition are depicted in Figure S18.On the other hand, for the transition to the second excited state the HOTO and LUTO NTOs suggest a good overlap, particularly on the nitro group, which confirms the high intensity of the S0 → S2 excitation.
It is worth mentioning that the transition to the lowest excited state does not involve the HOMO → LUMO excitation for 2nim, while for its derivatives, the same excitation contributes to a lesser extent.Such behaviors have been noted very recently by Kimber and Plasser [30].These authors concluded that the interplay of the terms corresponding to the dynamic electron−hole binding energy, exchange repulsion between electron and hole and/or to the response of the exchange-correlation potential govern the different types of excited states like locally excited or charge-transfer character and influence the pairs of occupied and unoccupied molecular orbitals involved in particular transitions.
To the best of our knowledge, there are no experimental UV-Vis data for 2nim, but Yu and Bernstein [31] reported such data for the 4nim isomer.
To validate the computed data for 2nim, we also calculated the absorption spectrum of 4nim, being able to quantitatively reproduce the experimental data.That is, the three main peaks observed at 311, 287 and 203 nm were calculated at 300, 274 and 201 nm, respectively.Our calculated data for 4nim agree very well with the computationally predicted values at the CASSCF(10,7)/6-31G(d) level of theory [31].Based on the agreement between experiment and theory for 4nim, we estimate that the calculated data for 2nim will also demonstrate a high degree of reliability, thus providing confidence in the validity of our computational results for this compound.
The PBE0 [32] and ωB97XD [33] density functionals are also frequently employed for the calculation of electronic transitions.Both predict UV-Vis spectra shapes similar to that obtained by using the B3LYP functional, with zero intensity for the S0 → S1 transition.Within the 200-350 nm wavelength range, these functionals yield band positions at 306 nm, 234 nm and 200 nm for PBE0 and 293 nm, 222 nm and 197 nm for ωB97XD, respectively.

2-Nitroimidazole Derivatives
As shown in Figure 4, the calculated λ max bands for the derivatives display remarkable similarity, with each of them closely following the pattern observed for 2nim.Table 10 lists the calculated excitation energies of the most stable conformers in water for the five 2-nitroimidazole derivatives.In contrast to the results obtained for the 2nim molecule, the transition to the S1 excited singlet state is allowed for all five compounds.Furthermore, the largest contributions to the S1 excited state are HOMO-2 → LUMO (60%) predicted at 331 nm for FMISO, HOMO-3 → LUMO (59%) at 332 nm for FETNIM, HOMO-4 → LUMO (58%) at 328 nm for FAZA, HOMO-1 → LUMO (78%) at 328 nm for FETA and HOMO-3 → LUMO (41%) at 335 nm for EF5.The contribution of the HOMO → LUMO transition to the S1 excited state is less than 10% in each case.
As seen in Table 10, the largest contribution for the S2 singlet excited state, corresponding to the most intense band, is due to the HOMO → LUMO transitions for all five compounds: 89% for FMISO predicted at 315 nm, 76% for FETNIM at 318 nm, 73% for FAZA at 317 nm, 60% for FETA at 323 nm and 54% for EF5 at 322 nm.Table 10 lists the calculated excitation energies of the most stable conformers in water for the five 2-nitroimidazole derivatives.In contrast to the results obtained for the 2nim molecule, the transition to the S1 excited singlet state is allowed for all five compounds.Furthermore, the largest contributions to the S1 excited state are HOMO-2 → LUMO (60%) predicted at 331 nm for FMISO, HOMO-3 → LUMO (59%) at 332 nm for FETNIM, HOMO-4 → LUMO (58%) at 328 nm for FAZA, HOMO-1 → LUMO (78%) at 328 nm for FETA and HOMO-3 → LUMO (41%) at 335 nm for EF5.The contribution of the HOMO → LUMO transition to the S1 excited state is less than 10% in each case.As seen in Table 10, the largest contribution for the S2 singlet excited state, corresponding to the most intense band, is due to the HOMO → LUMO transitions for all five compounds: 89% for FMISO predicted at 315 nm, 76% for FETNIM at 318 nm, 73% for FAZA at 317 nm, 60% for FETA at 323 nm and 54% for EF5 at 322 nm.
For FMISO, the band predicted at 316 nm appears as a result of the joint contributions of the transitions to the S1 and S2 excited states.For FETNIM and FAZA, the λ max bands at 319 nm are again attributed to the transitions to the S1 and S2 states.However, for FETNIM we observe an additional band at 286 nm, while for FAZA a shoulder is seen at 297 nm.They are assigned to the transitions to the S3 excited states with the main contributions being HOMO-1 → LUMO, 92.78% for FETNIM and HOMO-2 → LUMO, 68.72%, for FAZA (see Table 10).
The band at 314 nm in the spectrum for FETA is due to the joint transitions to the S2, S3 and S4 states.In contrast to the other investigated compounds where the S2 transition was calculated with the highest oscillator strength, the transition to the S4 excited state of FETA, predicted at 312 nm, has the largest value for the oscillator strength and is mainly due to HOMO → LUMO (54.27%) and HOMO-1 → LUMO (37.03%) transitions.
A distinct characteristic for the UV-Vis spectrum of EF5 is the broadness of the 317 nm band.The main contributions to it comes from transitions to the S2 and S3 states, predicted at 322 and 307 nm, respectively, and mainly due to the HOMO → LUMO (for S2) and HOMO-1 → LUMO (for S3) transitions.
An elegant and useful way to describe how the electronic density changes as a result of excitation is by plotting the difference between the electronic densities of the two states involved in the transition.In Figure 5 are illustrated the electronic density differences (EDDs) between the state of interest for 2nim and the five derivatives.In the case of 2nim, we note a charge transfer from the imidazole ring to the nitro group during the transition to the excited state.All the other derivatives show basically the same pattern for EDDs, excepting the FETA and EF5 compounds for which the carbonyl group acts together with the imidazole group as a donor of electronic density to the nitro group.A distinct characteristic for the UV-Vis spectrum of EF5 is the broadness of the 3 nm band.The main contributions to it comes from transitions to the S2 and S3 states, pr dicted at 322 and 307 nm, respectively, and mainly due to the HOMO → LUMO (for S and HOMO-1 → LUMO (for S3) transitions.
An elegant and useful way to describe how the electronic density changes as a resu of excitation is by plotting the difference between the electronic densities of the two stat involved in the transition.In Figure 5 are illustrated the electronic density differenc (EDDs) between the state of interest for 2nim and the five derivatives.In the case of 2nim we note a charge transfer from the imidazole ring to the nitro group during the transiti to the excited state.All the other derivatives show basically the same pattern for EDD excepting the FETA and EF5 compounds for which the carbonyl group acts together wi the imidazole group as a donor of electronic density to the nitro group.

Materials and Methods
For this work, we used state-of-the-art, yet confident, density functional theory (DF methods to obtain the calculated properties of the investigated compounds.All calcu tions were performed with the Gaussian 16, revision C.01 software package [34] by usin

Materials and Methods
For this work, we used state-of-the-art, yet confident, density functional theory (DFT) methods to obtain the calculated properties of the investigated compounds.All calculations were performed with the Gaussian 16, revision C.01 software package [34] by using the B3LYP hybrid exchange-correlation functional [35][36][37][38] in conjunction with Pople's style split-valence basis sets [39].
Tight and very tight criteria were employed to define the convergence of the molecular geometries and SCF convergence.The ultrafine grid was applied for the numerical integration of the electronic density.All geometry optimizations were followed by vibrational frequency calculations in order to check and validate the minima on the potential energy surfaces (PES) of the investigated molecules.Gibbs free energies were calculated using the standard thermochemistry model (T = 298.15K).
Relaxed PESs in the gas phase were calculated at the B3LYP/3-21G level of theory.Geometry optimization and IR and Raman spectra calculations were performed at the B3LYP/6-311+G(d,p) level of theory for all the minima found on the PES.Solvent effects in water have been accounted for by using the implicit polarizable continuum model [40] within the integral equation formalism [41].We chose water as a solvent because radiopharmaceuticals are usually administered intravenously to patients in an aqueous saline solution.
Both harmonic and anharmonic approximations were used to calculate the IR and Raman spectra.The harmonic spectra were scaled by a factor of 0.9668 [42], and the anharmonic wavenumbers were calculated using the vibrational second-order perturbation theory (VPT2) [43], as implemented in the Gaussian software package.The anharmonic IR and Raman spectra were simulated using the computed anharmonic wavenumbers.The IR intensities and Raman activities were those obtained within the harmonic approximation.Because of their very low calculated intensities, the overtones and the combination modes were not included in the simulation.
This approach was chosen because the anharmonic calculations can result in spurious very large activities [44,45].Pure Lorentzian band shapes with a half-width at half maximum of 4 cm −1 were used for the plots of the calculated IR and Raman spectra.
NMR spectra calculations were performed using the GIAO (gauge-including atomic orbital) method [46,47] as implemented in the Gaussian software package, at the B3LYP/6-311+G(d,p) level of theory.The computed NMR shielding tensors were converted into chemical shifts using the standard referencing method to tetramethylsilane (TMS) for 1 H and 13 C, and to trichloro-fluoro-methane (CFCl 3 ) for 19 F. The TMS and CFCl 3 shielding tensors were calculated at the same level of theory as that used for the 2nim derivatives, after geometry optimization of the reference molecules.
To assess the absorption properties of the compounds, time-dependent density functional theory (TD-DFT) methods [48] were employed, as implemented in the Gaussian software package.Single-point calculations on the excitation energies to singlet excited states were carried out at the TD-B3LYP/6-311+G(d,p) level of theory.The simulated UV-Vis spectra were obtained by convoluting the calculated vertical transitions with Gaussian functions with a half-width at half maximum of 0.15 eV.

Conclusions
The present study offers a detailed structural investigation of the most successful PET imaging agents for evaluating tumor hypoxia based on 2nim.To our knowledge, this is one of the very few works available in the current literature that provide a thorough characterization of the electronic structures and spectroscopic properties of radiopharmaceuticals.
Conformational analysis, vibrational and NMR spectra were obtained by means of quantum chemical DFT calculations.We have determined the structures of all unique conformers in the gas phase and water.Apart from the EF5 compound, important changes are observed in the conformers' stabilities when going from the gas phase to the liquid state for all the other compounds.The available experimental data were accurately repro-duced by the computational results obtained in this work.Anharmonic calculations proved to be more consistent in predicting the experimental IR spectrum for 2nim.Both calculated chemical shifts and spin-spin couplings were in good agreement with the available experimental data.
The photophysical properties of the compounds were predicted by means of TD-DFT calculations.UV-Vis spectra were obtained for all investigated compounds; however no such experimental data were available for validation.The migration of the electronic density during transitions was explained based on the electronic density differences between the ground and the excited states.
Our findings contribute to a deeper understanding of the spectroscopic properties of the five investigated radiopharmaceuticals.Moreover, the obtained results in this study can prove useful in further understanding the receptor binding mechanism of current and prospective 2-nitroimidazole based radiopharmaceuticals. Computational data indicate that the electronic excitation energies of all examined compounds fall outside the NIR spectral range, rendering them unsuitable as optical imaging probes.
In the development of multimodal agents based on 2-nitroimidazole, particularly for applications in nuclear medicine and optical imaging/photodynamic therapy, it would be imperative to incorporate a functional group that is compatible with both radiofluorination and the requisite absorption/emission characteristics.This dual functionality is essential to ensure the efficacy and versatility of these agents in their respective diagnostic and therapeutic applications.

Figure 2 .
Figure 2. Theoretical IR spectrum in the gas phase (a) and Raman spectrum in water (b) for 2nim in the harmonic (red) and anharmonic (black) approximation, at the B3LYP/6-311+G(d,p) level of theory.

Figure 2 .
Figure 2. Theoretical IR spectrum in the gas phase (a) and Raman spectrum in water (b) for 2nim in the harmonic (red) and anharmonic (black) approximation, at the B3LYP/6-311+G(d,p) level of theory.

Figure 3 .
Figure 3.The harmonic (scaled) IR (gas-phase) (a) and Raman (water) (b) spectra for 2nim and the five derivatives.The spectra for the derivatives are the Boltzmann-weighted averages of the most stable conformers.

Figure 3 .
Figure 3.The harmonic (scaled) IR (gas-phase) (a) and Raman (water) (b) spectra for 2nim and the five derivatives.The spectra for the derivatives are the Boltzmann-weighted averages of the most stable conformers.

Figure 5 .
Figure 5.The total SCF electronic density isosurfaces (0.02 a.u.) mapped with electronic dens differences between the S2 singlet excited state and the ground state for 2nim (a) and between t S1 singlet excited state and the ground state for FMISO (b), FETNIM (c), FAZA (d), FETA (e) a EF5 (f), calculated at the B3LYP/6-311+G(d,p) level of theory in water.The blue (red) areas deno an increase (depletion) in electronic density in the excited state.

Figure 5 .
Figure 5.The total SCF electronic density isosurfaces (0.02 a.u.) mapped with electronic density differences between the S2 singlet excited state and the ground state for 2nim (a) and between the S1 singlet excited state and the ground state for FMISO (b), FETNIM (c), FAZA (d), FETA (e) and EF5 (f), calculated at the B3LYP/6-311+G(d,p) level of theory in water.The blue (red) areas denote an increase (depletion) in electronic density in the excited state.

Table 1 .
Dihedral angles used to generate the relaxed PESs for the five investigated molecules.

Table 2 .
Calculated relative free energies and Boltzmann populations of conformers in the gas phase and water, at the B3LYP/6-311+G(d,p) level of theory.

Table 3 .
B3LYP/6-311+G(d,p) calculated wavenumbers of 2nim in the gas phase alongside the corresponding wavenumbers of the same modes in the five derivative compounds.

Table 3 .
B3LYP/6-311+G(d,p) calculated wavenumbers of 2nim in the gas phase alongside the corresponding wavenumbers of the same modes in the five derivative compounds.

Table 4 .
Experimental and calculated NMR data for FMISO.

Table 5 .
Experimental and calculated NMR data for FAZA.

Table 6 .
Experimental and calculated NMR data for FETA.

Table 7 .
Experimental and calculated NMR data for EF5.

Table 8 .
Experimental and calculated NMR data for 2nim.