Assigning flavin's difference-FTIR spectral bands in solution: frequency and intensity shifts in flavin's 1-electron and 2-electron reduced states

Abstract

Flavins are versatile cofactors that undergo different redox, chemical, and/or photophysical transformations depending on the protein they are bound to. A powerful tool available for studying these transformations is Fourier transform infrared (FTIR) difference spectroscopy, where changes in the FTIR absorption bands relate to specific changes in flavin's bonding or interactions with its neighboring environment. While the infrared (IR) spectra of oxidized flavins are well-characterized, fewer computational and experimental studies have focused on characterizing the IR spectra of flavins in their reduced (radical semiquinone or hydroquinone) states. Here, we employ hybrid quantum mechanical/molecular mechanical (QM/MM) models with implicit solvation to compute vibrational frequencies and IR intensities for a model flavin (lumiflavin) in its oxidized, anionic semiquinone, anionic hydroquinone, and neutral hydroquinone states. The water solvent configurations around the flavin are sampled with molecular dynamics for each state. These simulations, applied with semi-empirically determined broadening and frequency-scaling factors, are used to assign the main features of experimental FTIR difference spectra in the diagnostic 1350–1750 cm⁻¹ range from a variety of sources. The calculations show distinct, redox-state-dependent frequency shifts, especially for C=O stretching bands and C=N stretching bands, consistent with changing formal bond orders in flavin's pteridine rings upon reduction. These shifts can serve as spectral fingerprints for specific radical and 2-electron reduced forms, which will aid in interpreting these bands in FTIR difference spectroscopy measurements of flavoproteins.

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I. Introduction

Flavins are essential redox-active cofactors involved in various biological processes, including electron transfer, catalysis, and photoactivation.^1–3 Flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD) are the most prevalent flavins in biological systems, playing key roles in catalysis (flavoenzymes)^1,4 and mediating response to light (photoreceptors).^5–8 Underpinning flavin's versatility is their ability to exist in multiple redox states, most prominently oxidized, one-electron reduced (semiquinone radical), and two-electron reduced (hydroquinone) states. Each of these states can adopt different protonation forms depending on pH.^9–12

Fig. 1 shows several physiologically relevant redox and protonation states of flavins, using lumiflavin (LF) as a model compound. The oxidized form (LF) undergoes one-electron reduction to form semiquinone radicals, which exist in either neutral (LFH˙) or anionic (LF˙⁻) states. Further reduction produces the hydroquinone form, which can be neutral (LFH₂) or anionic (LFH⁻).

Fig. 1 Five flavin redox and protonation states for lumiflavin (LF). The atom numbering is shown for the oxidized quinone structure.

Flavin's redox, chemical, or photophysical transformations are often followed using FTIR difference spectroscopy, which is an effective tool for probing such transformations with molecular level specificity. FTIR difference spectroscopy is typically undertaken using spectroelectrochemistry^13–15 or time-resolved (TR), step-scan FTIR difference spectroscopy methods.^16–19 The latter is widely used to study the molecular mechanisms underlying flavoprotein photoreception.^20–90 Spectroelectrochemistry and TR-FTIR experiments generate difference spectra, which highlight vibrational changes between states by subtracting one spectrum from another (Fig. 2).¹⁹ Several of the experimental studies cited above were accompanied by electronic structure calculations, or prompted independent computational studies to interpret the experiments, usually by simulating so-called light-minus-dark FTIR difference spectra.^91–95 Together, theory and experiments can construct an atomic-level picture of molecular events following a redox or photoexcitation event.

Fig. 2 Top: A schematic representation showing the principles of FTIR difference spectroscopy measurements for a redox change in a flavoprotein. The protein structure is shown for a representative flavoprotein, Arabidopsis thaliana LOV2, PDB ID 4eep.⁹⁶ The spectrum is just a cartoon and not a real spectrum. The FTIR spectrum of a protein before (red) and after (blue) a redox process are represented in the top panel. The change, shown magnified in the inset, is due to alterations in a few molecular bonds near the site of radical formation within the protein, and is normally very weak compared to the IR signals of the entire protein and solvent. Bottom: FTIR difference spectrum obtained by subtracting the red (initial) from the blue (final) spectrum. The changes due to redox processes are now clear with most of the protein and solvent absorption cancelling out.

The IR spectra of oxidized flavins have been characterized through experimental spectro-electrochemistry and TR-FTIR difference spectroscopy experiments cited above, and through steady-state FTIR spectroscopy^97–102 and computational studies.^103–108 We also recently showed that key vibrational frequencies can be reproduced for flavin in aqueous solution using either an implicit polarizable continuum model (PCM) or explicit solvent model.^106,107 The latter often requires adequate sampling of hydrogen bonding interactions with the solvent and treatment of water molecules close to the flavin quantum mechanically. However, simulating relative band intensities remains challenging, particularly for C=C and C=N stretching vibrations. These intensities are sensitive to vibrational coupling that can be influenced by minor frequency shifts of only a few cm⁻¹.¹⁰⁷ As a result, accurate intensity predictions require advanced models that account for both short-range hydrogen bonding and long-range electrostatic interactions.^103,104,107

In contrast to studies of oxidized flavins, relatively few computational and experimental studies have focused on characterizing the FTIR spectroscopy signals of flavins in their reduced (semiquinone or hydroquinone) states, even though those reduced states are often key intermediates in the mechanisms of flavin-binding photoreceptors and (photo)enzymes. Recently, Huix-Rotllant, Schwinn and Ferré¹⁰⁸ simulated a (FADH˙–FAD) difference spectrum for cryptochrome using an efficient analytic second derivative and local normal mode analysis that they developed for hybrid quantum mechanical/molecular mechanical (QM/MM) models.^109–113 Furthermore, some of the computational QM/MM protocols developed and applied to simulate light-minus-dark signals in flavoproteins, such as those by Menucci and co-workers^91,92 and Hammes-Schiffer and co-workers,⁹³ may similarly be applied to simulate reduced-minus-oxidized signals in flavoproteins.

Because even minor deviations in vibrational frequencies or intensities can be amplified in difference spectra, the accurate simulation of difference spectra remains a challenge. In this study, we extend our previously successful computational protocol for simulating the IR spectrum of oxidized flavin¹⁰⁷ to three other redox states: the anionic semiquinone, anionic hydroquinone, and neutral hydroquinone states. We use those calculations to produce FTIR difference spectra, which we compare to spectroelectrochemistry¹⁵ and TR-FTIR experiments,⁴⁰ allowing us to identify and characterize major experimental peaks. The neutral semiquinone was not included since we could not find an experimental spectrum for this species. The assignments we suggest provide a reference for interpreting TR-FTIR data in all flavin-binding systems, which will aid in our understanding of flavin redox (bio)chemistry.

II. Computational methods

Model system selection

Since redox state changes are localized to the flavin's isoalloxazine ring, we use LF as a model system for FTIR spectral simulations instead of FMN or FAD. This approach reduces the computational cost while retaining the key structural moiety responsible for flavin's redox chemistry. Previous QM/MM vibrational frequency calculations on cryptochrome have shown that the IR spectrum of FAD in the 1350–1750 cm⁻¹ range is primarily determined by isoalloxazine vibrations, with only minor adenine contributions around 1600 cm⁻¹.¹⁰⁸ Other moieties, such as the diphosphate, ribityl, and ribose groups, exhibit negligible contributions to vibrations in that range. In difference spectra, contributions from the adenine are expected to cancel out for the different redox states. Thus, the LF model allows us to isolate essential vibrational features relevant to flavin redox behavior.

In previous work focused on the oxidized state of LF, we compared vibrational frequency calculations of gas-phase QM cluster models,¹⁰⁶ QM/PCM models,^106,107 QM/MM models,¹⁰⁷ and QM/MM/PCM¹⁰⁷ models to the experimental FTIR spectra of flavin in aqueous solution.^40,102,105 We found that QM cluster models only reproduced the relative frequencies of the most intense bands appearing in the 1400–1700 cm⁻¹ range after accounting for multiple hydrogen-bonding interactions, but could not reproduce the relative intensities of the bands.¹⁰⁶ QM/PCM better reproduced the relative positions and intensities of those bands but introduced an artifact; an additional intense band appeared computationally at 1520 cm⁻¹, although such a band did not exist in the experimental spectrum.¹⁰⁶ In ref. 107, we compared a series of QM/MM protocols for simulating the FTIR spectrum of LF in water. The first model, termed M1, treated LF quantum mechanically and the water solvent molecules all at the MM level of theory. The second protocol, M2, expanded the QM region to include water molecules near flavin's hydrophilic pyrimidine ring. The third protocol, M3, additionally incorporates long-range electrostatic effects by using a hybrid QM/MM/PCM approach through the ONIOM/PCM-X approach,^114–117 which includes a PCM¹¹⁸ environment around the entire QM/MM system. This hybrid M3 approach captures explicit local hydrogen bonding at the QM level, short and medium-range electrostatic interactions at the QM/MM level, and long-range solvation effects via implicit PCM. We found that the M3 protocol gave the best agreement with experimental spectra when adequately sampling the water environment around the flavin using molecular dynamics (MD) simulations.¹⁰⁷ The MD sampling is necessary, since a single snapshot or a few snapshots do not reproduce the experimental spectra well. We found that 100 snapshots is adequate and gave a good agreement with the experimental spectra.¹⁰⁷ These earlier benchmark studies inform the computational approach used here, which will also follow a slightly modified version of protocol M3.

MD simulations

For each redox state of LF, MD simulations were performed in a cubic water box with a minimum 3 Å distance between the solute atoms and the box edge. This smaller box size minimizes the computational cost of subsequent QM/MM/PCM calculations, which scale unfavorably with the size of the PCM cavity enclosing the full QM/MM system. We previously tested an expanded 12 Å solvent box for oxidized LF and found it had minimal impact on the simulated spectrum compared to the smaller solvent box generated at 3 Å from the flavin edge, which is an indication that the smaller periodic solvent box still allows for adequately sampling the water configurations around the LF.¹⁰⁷

Water was modeled using the TIP3P force field,¹¹⁹ with a sodium ion (Na⁺) replacing one water molecule to maintain overall charge neutrality for the anionic semiquinone and hydroquinone states. LF's parameters were derived from GAFF2, with RESP-assigned charges,¹²⁰ marking a slight deviation from our previous GAFF¹²¹/AM1-BCC¹²² approach for oxidized LF used previously in the M3 protocol.¹⁰⁷ Since the flavin structure is refined at the QM/MM level of theory, spectra computed using the two parameter sets were very similar (see Fig. 3B and C), suggesting that short-range water orientation around LF is not strongly dependent on the charge model. In other words, the small discrepancies from the MM force field, which may not be optimal for charged species,¹²³ are likely removed by the QM/MM optimization prior to frequency analysis. Related electrostatic potential fitting methods have also been well tested for flavins as part of a different QM/MM protocol, namely, the average protein electrostatic configuration approach for flavoproteins.^123–130

Fig. 3 Comparison between experimental (A) oxidized FMN⁹⁷ and computed FTIR spectra of LF in two different force field (parameters) and charge methods (B) GAFF/AM1-BCC (from ref. 107) (C) GAFF2/RESP (this work). The computed vibrational lines (green) were convolved with 8 cm⁻¹ wide (FWHM) Gaussian functions and summed to give the simulated spectra (purple).

Hydroquinones (LFH₂ and LFH⁻) are known to adopt a bent “butterfly” conformation in their ground state.^131–134 However, the standard GAFF2 protocol incorrectly results in a planar geometry. To address this, we manually adjusted force field assignments, redefining the central nitrogen atoms (N5 and N10) as sp³ instead of sp², yielding the expected bent geometry in MM minimizations. We note that when we use the planar force field, the QM/MM optimizations partially correct the structures by introducing some degree of bending, although this bending is sterically limited by the surrounding (frozen) solvent. This led to some worsening of the agreement between the spectrum simulated with the planar force field and the experimental difference spectrum (see Fig. S1 in the SI document). In contrast, the simulations using the modified (bent) force fields for LFH₂ give more well-defined peaks in IR difference spectra, with their calculated frequencies in better agreement with experiment. Overall, the best combination—GAFF2/RESP for LF and GAFF2/RESP with the modified bent force field for LFH₂—led to a small improvement in agreement with experimental spectra (Fig. S1).

The MD simulations began with a 5 ns gradual thermalization from 0 K to 300 K with constant volume and temperature (NVT) ensemble, followed by an equilibration at 1 bar for an additional 5 ns at the constant pressure and temperature (NPT) ensemble. Periodic boundary conditions¹³⁵ and particle-mesh Ewald^136,137 were applied, with an electrostatic interaction cutoff set to 5 Å during those steps. Next, we ran an additional 5 ns NPT equilibration where we reduced the cutoff to 4 Å out of an abundance of caution to prevent flavin interacting with itself through the periodic boundary walls. If the average pressure exceeded 3 bar or was smaller than 0.5 bar during the NPT MD, we repeated this equilibration step until the pressure gets closer to 1 bar. Lastly, we carry out an NVT production simulation for 5 ns using the average volume from the NPT equilibration run. MD simulations were conducted using AMBER 20 software package.^138,139

Quantum mechanics/molecular mechanics (QM/MM) calculations

We selected 100 snapshots from the production phase of the MD simulations for QM/MM geometry optimizations and vibrational frequency calculations. The QM/MM models were set up following the M3 protocol previously reported for oxidized LF.¹⁰⁷ For each redox state, the QM region was defined as lumiflavin plus all water molecules with at least one atom within 3.5 Å of any flavin carbonyl oxygen, identified using VMD.¹⁴⁰ The remaining solvent molecules were treated using the TIP3P MM force field. On average, the number of QM water molecules per snapshot was 10.11 for LF, 11.56 for LF˙⁻, 11.75 for LFH⁻, and 10.38 for LFH₂; these values were obtained by counting the QM waters in each of the 100 snapshots and calculating the mean for each state.

The QM/MM calculations were carried out using the ONIOM/PCM-X approach.^114–117 Geometry optimizations and harmonic frequency calculations for each snapshot were performed at the B3LYP/6-31+G* level using electrostatic embedding in Gaussian 16.¹⁴¹ Geometry optimizations were terminated when a maximum RMS gradient of 0.003 atomic units or lower was achieved. We then repeated the calculations for 10 of the 100 LF structures using the B3LYP-D3 functional to examine the influence of dispersion interactions on the computed vibrational frequencies.¹⁴²

The reference experimental data used here were obtained in aqueous solution, but some of the experiments were recorded in deuterated solvent (D₂O). When comparing against experimental data in D₂O, we replace the exchangeable protons on flavin with deuterium—specifically, those on N1, N3, and N5 (if protonated for a given redox state). That said, we opted to treat all quantum and molecular mechanical waters as deuterated in this work, regardless of the experimental conditions. This choice is advantageous as it excludes H₂O bending modes that typically appear near 1630 cm⁻¹. While these modes should cancel out in difference spectra between redox states, perfect cancellation would require extensive sampling of water configurations, which is computationally impractical. By deuterating these waters, their bending modes shift to lower frequencies (∼1200 cm⁻¹) and thus appear outside the diagnostic window. Deuteration of the solvent, while maintaining isotope consistency with the experiment for flavin's exchangeable protons, is expected to have a minimal effect on the spectrum in the region 1350–1750 cm⁻¹, as suggested by previous experiments¹⁵ and our calculations reported below.

To complement these QM/MM M3 simulations, we optimized LF in each redox state and computed their vibrational frequencies in an exclusively implicit IEF-PCM solvent model,¹⁴³ providing a secondary reference for comparison with QM/MM-computed difference spectra.

Spectral simulations

Computed vibrational frequencies and intensities were broadened with Gaussian functions (typically, full-width at half-maximum FWHM = 8 cm⁻¹ for ONIOM/PCM-X and FWHM = 16 cm⁻¹ for IEF-PCM, unless indicated otherwise) and scaled by a constant factor. These FWHMs and scaling factors were chosen empirically to improve agreement with experimental data. Scaling vibrational frequencies is standard practice to account for anharmonicity; the Computational Chemistry Comparison and Benchmark DataBase (CCCBDB)¹⁴⁴ recommends a scaling factor of 0.964 for B3LYP with a double-zeta Pople basis set including diffuse functions, with an uncertainty of ±0.023. A more recent benchmark study suggests a scaling factor of 0.980 ± 0.007 for B3LYP/double-ζ calculations in the mid-IR (1000–2000 cm⁻¹) range.¹⁴⁵ Our previous benchmarks indicated 0.988 as optimal for oxidized LF.^106,107

The reason for using different FWHM values for PCM and M3 calculations is because, for ONIOM/PCM-X, we convolve spectra from 100 individual calculations (each with slightly different solvent configurations), which naturally introduces some statistical broadening. Therefore, a smaller FWHM (8 cm⁻¹) suffices to reproduce experimental line widths. In contrast, for IEF-PCM, only a single calculation is performed for each model, so we use a larger FWHM (16 cm⁻¹) to approximately capture broadening that would arise from ensemble averaging.

Here, we apply tailored scaling factors (ranging from 0.965–1.01) for each redox state to maximize agreement with experimental data while remaining close to the CCCBDB uncertainty range. Once the spectra for the oxidized and reduced state are broadened and scaled, the oxidized spectrum (LF) was subtracted from the reduced state spectra to simulate IR difference spectra.

Vibrational mode assignment

Vibrational modes were characterized using vibrational energy distribution analysis (VEDA) for the IEF-PCM computed frequencies.¹⁴⁶ VEDA employs internal coordinates optimized to represent theoretical normal modes, to help quantify the contribution of molecular movements associated with specific vibrational frequencies. This process involves decomposing vibrational normal modes into contributions from stretching, bending, torsional, and out-of-plane motions.

III Results and discussion

Fig. 4–7 present the computed IR difference spectra for deuterated [LFD₂–LF], protonated [LFH₂–LF], [LFH⁻–LF], and [LF˙⁻–LF], respectively. The computed spectra are compared to the corresponding experimental spectra of [FADD₂–FAD] in D₂O, [FADH₂–FAD] in H₂O, [FMNH⁻–FMN] in H₂O, and [FMN˙⁻–FMN] in H₂O. In each of the four figures, we present the experimental difference spectra at the top, M3-calculated spectra in the middle, and IEF-PCM-calculated spectra at the bottom. The positive bands correspond to the reduced states (LFD₂, LFH₂, LFH⁻, or LF˙⁻), while negative bands represent the oxidized LF state.

Fig. 4 Comparison between experimental (A) FADD₂–FAD¹⁵ in D₂O and computational FTIR difference spectra of deuterated LFD₂–LF using (B) protocol M3, and (C) IEF-PCM. The horizontal black line within each panel helps distinguish positive from negative peaks. The green impulse lines indicate computed frequencies and intensities and the purple plots in panels B and C are generated by adding Gaussian broadening functions to each transition (8 cm⁻¹ FWHM in panel B and 16 cm⁻¹ FWHM in panel C). The band assignments, based on QM/PCM VEDA calculations, are indicated in red font for LFD₂ and blue font for deuterated LF. The normal modes corresponding to negative and positive bands in panel C are shown in Fig. S3 and S5, respectively, while the percentage contributions of specific modes used to assign the bands are provided in Tables S2 and S4.

Fig. 5 Comparison between experimental (A) FADH₂–FAD¹⁵ in H₂O and computational FTIR difference spectra of LFH₂–LF redox transition using (B) protocol M3, and (C) IEF-PCM. Only hydrogen atoms in water molecules were replaced with deuterium. The horizontal black line within each panel helps distinguish positive from negative peaks. The green impulse lines indicate computed frequencies and intensities and the purple plots in panels B and C are generated by adding Gaussian broadening functions to each transition (8 cm⁻¹ FWHM in panel B and 16 cm⁻¹ FWHM in panel C). The band assignments, based on QM/PCM VEDA calculations, are indicated in red font for LFH₂ and blue font for protonated LF. The normal modes corresponding to negative and positive bands in panel C are shown in Fig. S2 and S4, respectively, while the percentage contributions of specific modes used to assign the bands are provided in Tables S1 and S3.

Fig. 6 Comparison between experimental (A) FMNH⁻–FMN⁴⁰ in H₂O and computational FTIR difference spectra of LFH⁻–LF redox transition using (B) protocol M3, and (C) IEF-PCM. Only hydrogen atoms in water molecules were replaced with deuterium. The horizontal black line within each panel helps distinguish positive from negative peaks. The green impulse lines indicate computed frequencies and intensities and the purple plots in panels B and C are generated by adding Gaussian broadening functions to each transition (8 cm⁻¹ FWHM in panel B and 16 cm⁻¹ FWHM in panel C). The band assignments, based on QM/PCM VEDA calculations, are indicated in red font for LFH⁻ and blue font for protonated LF. The normal modes corresponding to negative and positive bands in panel C are shown in Fig. S2 and S6, respectively, while the percentage contributions of specific modes used to assign the bands are provided in Tables S1 and S5.

Fig. 7 Comparison between experimental (A) FMN˙⁻–FMN⁴⁰ in H₂O and computational FTIR difference spectra of LF˙⁻–LF redox transition using (B) protocol M3, and (C) IEF-PCM. Only hydrogen atoms in water molecules were replaced with deuterium. The horizontal black line within each panel helps distinguish positive from negative peaks. The green impulse lines indicate computed frequencies and intensities and the purple plots in panels B and C are generated by adding Gaussian broadening functions to each transition (6 cm⁻¹ FWHM in panel B and 16 cm⁻¹ FWHM in panel C). The band assignments, based on QM/PCM VEDA calculations, are indicated in red font for LF˙⁻ and blue font for protonated LF. The normal modes corresponding to negative and positive bands in panel C are shown in Fig. S2 and S7, respectively, while the percentage contributions of specific modes used to assign the bands are provided in Tables S1 and S6.

Overall, the computations reproduce well the frequencies of the main spectral features observed experimentally, though intensity mismatches remain. Before proceeding with comparing the computed and experimental spectra, it is useful to discuss sources of errors and uncertainties in comparing computed vibrational simulations and experiments. As discussed in the Introduction section, difference spectra emphasize spectral changes rather than absolute IR intensities, making them sensitive to computational parameters such as broadening and even small frequency and intensity shifts. Therefore, the same level of agreement between calculations and experiments as obtained, for instance, when simulating a steady-state FTIR spectra (e.g., Fig. 3) is not expected. Accurate simulation of difference spectra also requires that the electronic structure calculations treat the different redox states on an equal footing so that systematic errors cancel out. However, this is not always guaranteed. While B3LYP has been shown to provide reasonable harmonic frequencies for molecular radicals,^147,148 systematic errors may vary between radical semiquinones and closed-shell oxidized LF species.¹⁴⁹ The empirically determined scaling factors mitigate such errors but may not fully eliminate them. Additionally, as discussed in the Materials and methods section, the hydroquinone species exhibit non-planar distortions at the central ring, with the extent of bending dependent on the electronic structure method used.¹⁵⁰ This non-planarity may introduce an additional error for the difference spectra between the (non-planar) hydroquinone and (planar) quinone states.

B3LYP does not include a proper accounting of dispersion corrections, which may be relevant to describing the hydrogen-bonding interactions between the QM-treated waters and LF. Therefore, we reran the M3 protocol for 10 LF snapshots using B3LYP-D3. The dispersion correction resulted in an overall modest upfield shift relative to the original B3LYP results, with average errors of 4.3, 5.8, 2.2, and 2.5 cm⁻¹ for the C₄=O, C₂=O, C=C, and C=N stretching modes, respectively. (Table S7). Since this change is systematic, we expect that the use of dispersion corrections will only lead to a modest change in the overall simulated spectrum.

A third source of error arises from comparing LF QM/MM calculations to experimental spectra of FMN and FAD in complex media. Experimental spectro-electrochemistry and TR-FTIR experiments rely on signal subtraction to isolate small vibrational changes associated with redox transitions, often requiring the removal of large solvent and protein signals. As shown in Fig. 2, the full FTIR spectra before (red) and after (blue) a redox or photochemical event differ only slightly. These subtle changes become clear only after generating a FTIR difference spectrum (Fig. 2, bottom panel), where subtraction isolates redox-associated spectral features. However, the process of generating a difference spectrum by subtracting two nearly identical spectra can amplify measurement noise and small baseline variations, making the detection of subtle redox-associated features more challenging compared to direct FTIR measurements of samples. Achieving complete redox conversion is another experimental challenge; reaction kinetics and equilibrium conditions often result in mixed states, further complicating spectral interpretation. For example, the semiquinone state is unstable in solution, forming only transiently, while additional side reactions with the solvent may introduce secondary species. Experimental conditions, such as the presence of buffer components (e.g., EDTA in ref. 40) that may interact differently with the reduced and oxidized flavin states, can alter the observed spectra. In contrast, computational models assume complete redox transitions and pure states, which may not fully represent the experimental complexities reflected in FTIR difference spectra.

The use of a few empirical parameters (e.g., scaling factors and broadening) in these simulations means that the computational models may not yet be suitable for predictive simulations of FTIR difference spectra in the absence of an experimental reference. This is especially true for spectra of states with a different charge, since the scaling factor for the negatively charged LF˙⁻ and LFH⁻ states are significantly different (0.99–1.01) than the scaling factor for the neutral LF state (0.985–0.988). However, we note that for the M3 protocol, the scaling factor used for the neutral LFH₂ state (0.984–0.985) is comparable to the LF one. Despite these limitations in absolute frequency prediction, calculated difference spectra are particularly valuable for identifying systematic trends across redox states. For example, the computed bands of oxidized, semi-reduced, and fully reduced flavins (or quinones) often shift in frequency or change in intensity in a consistent and recognizable pattern as the oxidation state changes. Such trends, even if not quantitatively exact, can provide critical guidance for interpreting experimental FTIR difference spectra and for assigning bands to specific redox transitions. Thus, while empirical adjustment is required for direct comparison with experiment, the computational approach remains a powerful tool for revealing qualitative trends and mechanistic insights.

To assign the peaks to specific vibrations, we visualized the normal modes and characterized them using VEDA on the IEF-PCM calculations. We use the singular IEF-PCM calculation since it is easier to carry out the analysis compared to the M3 protocol which involves 100 QM/MM vibrational frequency calculations. The difference spectra in Fig. 4–7 indicate that the IEF-PCM model on its own introduces artifacts (e.g., a spurious negative band near 1520 cm⁻¹) and does not capture solvent-induced broadening. In contrast, the M3 (QM/MM/PCM) protocol recovers both realistic line widths and experimentally observed band shapes, while still being consistent with frequency assignments made from the simpler QM/PCM model. Thus, while QM/PCM is suitable for assignments, the M3 protocol provides the more accurate description of experimental IR difference spectra.

In Fig. S2–S7, the atomic motions within the normal modes are shown for protonated LF, deuterated LF, protonated LFH₂, deuterated LFD₂, protonated LFH⁻ and protonated LF˙⁻, respectively. Displacement vectors illustrate the atomic motions while the labels identify the dominant molecular group vibrations assigned using VEDA. Further details about the decomposition of each normal mode to internal coordinates are presented in Tables S1–S6 in the SI. In Tables S1–S6, the percentage values indicate each molecular groups contribution to a given vibrational mode frequency: positive values denote direct contributions, while negative values reflect out-of-phase contributions.

A vibrational mode is considered dominant when it is the only mode listed by VEDA, or when its contribution exceeds 50%, indicating minimal mixing with other modes. For example, the C₄=O stretching mode in LFH₂ (1629 cm⁻¹, 23% contribution, Table S3) is classified as mixed in Fig. 5C due to its contribution being below the 50% threshold. In contrast, the C=C stretching mode of LF (1650 cm⁻¹, 55% contribution, Table S1) is dominant, with smaller overlap with other modes, and so is labeled just as C=C.

PCM introduces a pronounced negative band near 1520 cm⁻¹ (e.g., compare panel C in Fig. 4–6 to panel A in the same figures), previously identified as an artifact caused by coupling of vibrational modes when using PCM with a high dielectric constant.^106,107 This artifact is mitigated in the M3 protocol (see panel B in Fig. 4–6).

Several spectral features are consistent across all redox states (Fig. 4–7). The most prominent bands include C=O stretching vibrations at the highest frequencies (∼1650–1750 cm⁻¹), with C=C and C=N stretching and bending vibrations at lower frequencies. Both the PCM and M3 models successfully capture these frequency trends, though the PCM model often yields spectra with better-defined C=O peaks that are more in line with experiments. The M3 model predicts broader and lower intensity C=O bands. As noted in previous studies, intensity predictions are challenging even for the oxidized form (LF),¹⁰⁷ and this issue is shown to persist across the other redox states here. Conversely, in the lower frequency regions, the M3 calculated spectra generally align better with experimental spectral data; PCM calculated spectral data can either overestimate or underestimate bending mode band intensities, while M3 models provides spectral profiles more consistent with experiments. Together, the M3 and PCM models offer a complementary approach to spectral band analysis in this work: the M3 model aids in assigning lower-frequency bands alongside the PCM model, while the PCM model helps better discern higher-frequency (especially C=O) bands.

While general trends are similar across redox states, some key differences emerge, which we discuss below in light of the spectral band assignments made based on our computations.

C=O stretching modes

Table 1 summarizes some of the shifts observed for a few key C=O, C=N, and C=C stretching modes upon the reduction of the flavin cofactor. The C₂=O band of LF upshifts 4/25 cm⁻¹ upon LFH₂/LFD₂ formation, respectively. The C₄=O band of LF downshifts over 80 cm⁻¹ upon LFH₂ formation independent of deuteration/protonation. This reverses the relative ordering of the C₄=O and C₂=O mode frequencies for the reduced form compared to the oxidized form. This redox-induced reorganization of modes likely results from conjugation between C₄=O and the adjacent C=C bond, leading to mode mixing (see Tables S3 and S4), while protonation of the N1 atom reduces the conjugation of C₂=O with other double bonds, resulting in the small upshift in its frequency.

Table 1 IR spectral shifts (in cm⁻¹) of five vibrational bands upon reduction of the oxidized flavin species computed at the QM/PCM level of theory. Shifts are shown for both radical (semiquinone) and 2e-reduced (hydroquinone) forms. Negative values indicate downshifts (to lower frequency), and positive values indicate upshifts (to higher frequency) relative to the oxidized state. Band assignments are based on QM/PCM VEDA calculations

	C4=O	C2=O	C=C	C=C(mixed)	C=N
Deuterated LF → LFD2	−83	25	−29/−49	−18	−56
Protonated LF → LFH2	−85	4	—	−22	−54
Protonated LF → LFH^−	−49	−48	—	85	—
Protonated LF → LF˙^−	−82	−59	−84	—	—

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In the case of the anionic hydroquinone, we see a very different trend, where both the C₄=O and C₂=O downshift ∼50 cm⁻¹ upon LFH⁻ formation. Somewhat similarly, for the anionic semiquinone state (LFH⁻, Fig. 7), the C₄=O/C₂=O mode downshifts ∼80/60 cm⁻¹, respectively. The difference spectrum of FMN˙⁻ in Fig. 7 is also quite interesting; the bands appear to be somewhat narrower and there is an apparent splitting of the bands associated with the carbonyl stretching vibrations. Fig. 7B demonstrates that the M3 model can reproduce this splitting when a reduced convolution factor is used (FWHM of 6 cm⁻¹ rather than 8 cm⁻¹). The PCM model does not exhibit the same C=O band splitting (Fig. 7C). This latter observation indicates that the C=O peak splitting may originate from solvent hydrogen bonding configurations rather than from the electronic structure of flavin. Both M3 and PCM models, however, predict C=O band positions (frequencies) consistent with the experimental spectra.

We also note that bands due to C=O stretching modes of LF˙⁻ are more intense than that observed for the other reduced states. Note that intensity here is discussed relative to the oxidized form, which is constant reference state in all spectra. This (relative) high intensity of the C=O stretching modes of LF˙⁻ is observed also in the experimental spectra.

C=N and C=C stretching modes

In all difference spectra (Fig. 4–7), the pronounced negative C=N band of LF near 1550 cm⁻¹ becomes significantly weaker upon flavin reduction. In other words, there is no intense, positive band in the difference spectra corresponding to a pure C=N stretching vibration in any of the reduced states. This is consistent with the change in electronic structure of flavin upon reduction where the formal C=N double bonds are converted to single bonds (see Fig. 1).

Multiple (positive) C=C bands appear in each of the FTIR difference spectra, and those bands are calculated to have mixed character. Due to the number of these mixed C=C bands and their relatively low intensity, they may be difficult to ascertain experimentally and are of less diagnostic utility. However, we note the presence of a C=C band appearing at an unusually low frequency at around 1420 cm⁻¹ for LFH⁻ (Fig. 6C). The low frequency of this mode may be associated with bending of the flavin at the central ring and coupling to HNC bending modes appearing in the other hydroquinone states (Fig. 4 and 5) around the same frequency. While VEDA does not identify a strong HNC contribution in the case of LFH⁻, it can be seen visually in Fig. S6 for this mode.

IV. Conclusions and future directions

We extended our previous work on assigning bands in FTIR spectra of oxidized flavin to other flavin redox forms. Specifically, we applied the hybrid QM/MM/PCM approach, following a protocol (M3) that previously was successful in reproducing the FTIR absorption spectrum of oxidized flavin. The M3 simulations are compared to a simple QM/PCM model where the solvent is treated only as a dielectric, and against experimental spectroelectrochemistry and step-scan FTIR difference spectra for flavin in three redox states. While empirical parameters—such as frequency scaling and broadening factors—are necessary, the M3 model effectively captures the general features of the of the FTIR difference spectra and reduces artifactual contributions that arise when using the PCM model alone, such as the negative band near 1520 cm⁻¹. The scaling factors used for the M3 protocol were in the range of 0.984–0.987 for neutral redox states of flavin and 0.990–1.010 for anionic redox states. For PCM, a wider range of scaling factors were needed to obtain reasonable agreement with experiment: 0.965–0.988 for the neutral redox states and 0.9925–1.010 for the anionic states.

For both the M3 and QM/PCM models, discrepancies in predicted intensities compared to the experimental spectra highlight the need for further benchmarking and methodological refinements, including improvements in the quantum chemical level of theory, enhancements in the QM/MM model, and the incorporation of anharmonic corrections. Nonetheless, the PCM and M3 calculations presented here are of sufficient quality for assigning and interpreting bands in the experimental difference spectra. The relatively simple QM/PCM approach alone was useful for assigning most of the experimental bands, but the QM/MM/PCM M3 protocol resulted in several improvements by better capturing frequency shifts and solvent broadening effects. Importantly, of the two methods tested (PCM and M3), only the latter can potentially be applied for simulating FTIR difference spectra associated with flavins in proteins. Therefore, the simulated spectra and band assignments reported here can serve as a reference for future QM/MM FTIR calculations, and/or for TR-FTIR and spectroelectrochemistry experiments of flavin-mediated biological redox reactions.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). The supplementary information includes optimized coordinates of lumiflavin in different redox states computed using the IEF-PCM solvation model, figures representing normal modes of vibrational bands discussed in the manuscript, tables of computed vibrational frequencies and VEDA analysis, simulated difference IR spectra obtained with planar and bent force fields, and mean signed errors between B3LYP and B3LYP-D3 frequency calculations. See DOI: https://doi.org/10.1039/d5cp02306h.

Acknowledgements

This material is based upon work supported by the National Science Foundation (NSF) under Grant CHE-2047667 (S. G.). D. P. N. L. acknowledges a fellowship from the Molecular Basis of Disease Program at Georgia State University. This work used Expanse at SDSC through allocation CHE180027 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services and Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. We also acknowledge the use of Advanced Research Computing Technology and Innovation Core (ARCTIC) resources at Georgia State University's Research Solutions, made available by the NSF Major Research Instrumentation (MRI) grant number CNS-1920024.

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