(TD-)DFT Calculation of Vibrational and Vibronic Spectra of Riboflavin

Aug 3, 2010 - step of flavins is electronic and vibrational spectroscopy, both in frequency ... Further, vibronic absorption spectra for the S0 f S1 t...
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J. Phys. Chem. B 2010, 114, 10826–10834

(TD-)DFT Calculation of Vibrational and Vibronic Spectra of Riboflavin in Solution Bastian Klaumu¨nzer, Dominik Kro¨ner, and Peter Saalfrank* Institut fu¨r Chemie, UniVersita¨t Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam, Germany ReceiVed: January 22, 2010; ReVised Manuscript ReceiVed: May 18, 2010

The photophysics and photochemistry of flavin molecules are of great interest due to their role for the biological function of flavoproteins. An important analysis tool toward the understanding of the initial photoexcitation step of flavins is electronic and vibrational spectroscopy, both in frequency and time domains. Here we present quantum chemical [(time-dependent) density functional theory ((TD-)DFT)] calculations for vibrational spectra of riboflavin, the parent molecule of biological blue-light receptor chromophores, in its electronic ground (S0) and lowest singlet excited states (S1). Further, vibronic absorption spectra for the S0 f S1 transition and vibronic emission spectra for the reverse process are calculated, both including mode mixing. Solvent effects are partially accounted for by using a polarizable continuum model (PCM) or a conductor-like screening model (COSMO). Calculated vibrational and electronic spectra are in good agreement with measured ones and help to assign the experimental signals arising from photoexcitation of flavins. In particular, upon photoexcitation a loss of double bond character in the polar region of the ring system is observed which leads to vibronic fine structure in the electronic spectra. Besides vibronic effects, solvent effects are important for understanding the photophysics of flavins in solution quantitatively. 1. Introduction Riboflavin, also known as vitamin B2 and henceforth abbreviated as RF, plays a key role in many biological systems. For example, RF is the central component of the cofactors FAD (flavin adenine dinucleotide) and FMN (flavin mononucleotide), and it is contained in all flavoproteins. Flavins are the chromophores in blue-light receptors such as blue-light-sensingusing-FAD (BLUF) or light-oxygen-voltage (LOV) domains, or phototropins. The basic structural elements of RF, and related compounds such as isoalloxazine, lumiflavin, FMN, and FAD are indicated in Figure 1. In blue-light receptors, biological function is initiated by absorption of light by the chromophore. Therefore, the photophysics of flavoproteins in which both ground and excited states are involved has attracted much attention recently, both from experiment1-4 and theory.5-7 In particular, spectroscopical approaches such as vibrational spectroscopy in ground and excited states, UV/vis absorption and emission spectroscopy, and triplet-triplet absorption, either in frequency or time domains, were successfully used to unravel details of the early photophysics and photochemistry in flavins. Here we mention only contributions with direct relevance for the present work. (i) For RF (and also for the smaller lumiflavin), most quantum chemical calculations find a first UV/vis absorption maximum corresponding to an allowed π f π* transition from S0 to S1 at around 410 nm (∼3.0 eV).5,6 This transition is blue-shifted by about 0.2 eV (ca. 40 nm or 2000 cm-1) compared to experimental values for various flavins.3,8 Furthermore, experimentally in ethanol at low temperature (77 K), in BLUF domains, and also in the LOV1 domain of Chlamydomonas reinhardtii (C. reinhardtii),3 the lowest (S1) band of RF shows a well-resolved vibronic structure with three peaks grouped around the most intense central one and separated by 0.15-0.2 eV.8 Also the fluorescence spectra of RF in the LOV1 domain of C. rein* To whom correspondence should be addressed. E-mail: [email protected].

Figure 1. Chemical structure and labeling of flavins referred to in this work. R1 ) H, isoalloxazine; R1 ) CH3, lumiflavin; R1 ) ribityl, riboflavin (RF); R1 ) ribityl-5′-phosphate, FMN; R1 ) ribityl(9adenosyl)pyrophosphate, FAD.

hardtii, of RF in H2O (pH ) 7),9 and of RF in a BLUF domain10 show this fine structure. Both the fine structure and the fluorescence maximum are solvent-dependent.2 In ref 11, UV/ vis absorption spectra were measured for lumiflavin and related model compounds, in which either CH units were replaced by N or vice versa. For these model compounds also vibronic (Franck-Condon) absorption spectra for the S0 f S1 transition were calculated by selecting 30 “important” modes. The calculations were performed by (time-dependent) density functional theory [(TD-)DFT] and by DFT/MRCI (multireference configuration interaction), respectively. On the basis of the calculations, it was suggested that the fine structure observed in flavins is likely due to vibronic transitions between geometrically displaced S0 and S1 states. Due to the atom displacement in the excited state, the maximum of the S0 f S1 transition is also shifted to the red in comparison to the vertical transition (by ∼1500 cm-1 for lumiflavin). This accounts for a major portion of the blue shift in earlier theory. Other possible/ additional sources for the blue shift have been discussed elsewhere.6,12 (ii) In ref 1, femtosecond dynamics of riboflavin in dimethyl sulfoxide (DMSO) after photoexcitation was followed by broadband transient absorption. It was suggested that, on a picosecond time scale after initial photoexcitation into S1, a

10.1021/jp100642c  2010 American Chemical Society Published on Web 08/03/2010

TD-DFT for Vibrational Spectra of Riboflavin superposition of the optically active state (S1, π f π* transition) and a dark state (n f π* transition) is formed by nonadiabatic coupling. One of the arguments of ref 1 for this statement was the spectral observation of out-of-plane vibrations, which seems possible only if population is indeed transferred between the bright and dark excited states. (iii) In ref 13, vibrations of RF in DMSO in the excited (S1) state were directly measured by femtosecond time-resolved infrared (IR) spectroscopy. Also, ground-state (S0) IR spectra were recorded as well as difference spectra between both. From the time-resolved spectra, a vibrational cooling time in the S1 state of about 4 ps was determined. The experimental data were supported by theoretical calculations on the Hartree-Fock (HF) and configuration interaction singles (CIS) levels of theory, showing a loss of double-bond character between the C4a and N5 atoms in the excited state (see Figure 1). It is the purpose of the present paper to study in some detail the vibrational and vibronic spectra of riboflavin in solution, using modern computational models. In particular we will characterize the UV/vis absorption and fluorescence spectra of RF by calculating the vibronic transitions taking Duschinsky mode mixing14 into account. The vibronic transitions will be determined by a program based on a block diagonalization approach for the Duschinsky rotation matrix.15 In contrast to earlier work, all 3N - 6 ) 135 modes of RF (C17H20N4O6) will be considered. The required geometry optimization and normalmode analysis for ground (S0) and excited (S1) states will be carried out on the (TD-)DFT level of theory, using the B3LYP density functional. It has been shown elsewhere that this approach captures well the low-lying π f π* and n f π* transitions of flavins.6 The vibrational analysis also accounts for IR spectra of the S0 and S1 states. Solvent effects will be accounted for by continuum models such as PCM16 and COSMO.17 The paper is organized as follows. In the next section 2, a brief overview of the applied computational methods is given. Then, in section 3, calculated vibrational and vibronic spectra will be presented and discussed in the light of recent experiments and theory. Section 4 summarizes the present work. 2. Computational Methods 2.1. Electronic Structure Methods and Vibrational Spectra. For RF the geometries and the vibrational frequencies and normal modes of the two lowest electronic states, S0 and S1, were determined. The geometry optimization and the frequency analyses were done with DFT (for S0) and TD-DFT (for S1), respectively, using the TURBOMOLE18 and GAUSSIAN0919 program packages. For all ground-state calculations we used the B3LYP functional,20,21 and the standard TZVP22 basis set.23 To account for spectral shifts by solvents, either the PCM16 as implemented in GAUSSIAN09 (for ground and excited states) or the COSMO model17 as implemented in TURBOMOLE (for the ground state only) was used. Both are continua models for which we employed a dielectric constant of ε ) 46.68 to model DMSO, since DMSO is the solvent in most of the experiments we refer to. When considering the solvent, excitation energies, geometries, normal modes, and corresponding frequencies were recalculated. For each state SR (R ) 0, 1), we calculate an IR absorption spectrum by broadening the vibrational line spectra with Lorentzians. At an assumed temperature of T ) 0 K, the spectrum is therefore given as

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IR(ν˜ ) )

C π

M

∑ gm,R (ν˜ - ν˜ γ )2 + γ2 m

(1)

m,R

where C is a constant. Further, gm,R is the oscillator strength for the fundamental vibrational transition of the mth vibrational mode in state SR with wavenumber ν˜ m, R. In the double-harmonic approximation, we use harmonic oscillator functions obtained from normal-mode analysis and we approximate the dipole function µR,R of state SR as R R µ _R,R(Q _ ))µ _R,R(Q _0) +

M

∑

m)1

∂µ _R,R ∂QmR

|

(QmR - Q0Rm)

(2)

0

R with QmR being the mth out of M normal modes in state R. Q _0 ) (Q01, ..., Q0M) is the equilibrium geometry, at which the derivative of the dipole function is taken. In this approximation, _R,R/∂QmR |0}|2. Further, ν˜ m,R is the wavenumber for the gm, R ∝ {|∂µ fundamental 0 f 1 transition in the vibrational mode m and state SR, and γ is a global Lorentzian width parameter accounting for various broadening mechanisms. IR-difference spectra were calculated as

∆10(ν˜ ) ) I1(ν˜ ) - I0(ν˜ )

(3)

Since this difference spectrum refers to the relaxed excited state S1, it corresponds to an experimental situation with delay times between UV pump and IR probe pulses which are long compared to the vibrational relaxation time (∼4 ps) of the S1 state.13 Negative values of ∆10(ν˜ ) indicate ground-state vibrations; positive ones indicate excited-state vibrations at long delay.13 2.2. Vibronic Spectra. In most publications on flavins to date UV/vis absorption spectra were calculated from vertical transitions between electronic states, out of the ground-state geometry, without taking vibrations into account. That is, expressions similar to eq 1 were used, however with M being the number of excited electronic states and gm,R and ν˜ m,R being replaced by oscillator strengths for electronic transitions from S0 to the respective excited state and the corresponding vertical excitation wavenumber, respectively. In this work we calculate vibronic spectra instead; i.e., we take the vibrations of ground and excited states into account. In particular, we determine vibronic absorption spectra at T ) 0 K, where we start from the vibrational ground state of S0 and could reach, in principle, all the excited-state vibrational levels. We also calculate vibronic emission spectra out of the cold (T ) 0 K) excited state S1, where we start from the lowest vibrational level of S1 and could reach all vibrational levels of S0. In practice energy cutoffs (see below) and maximal vibrational quantum numbers (νmax ) 127) are defined in the numerical treatment. Since the S0 T S1 transitions are strongly dipole-allowed, we can adopt the Condon approximation; i.e., the transition dipole moment µ _ˆ |ΨS1〉 (ΨSR are electronic wave _1,0 ) 〈ΨS0|µ functions; µ ˆ_ is the molecular dipole operator) is approximated as R µ _1,0(Q _) ≈ µ _1,0(Q _0)

(4)

R where Q _ 0 is the equilibrium geometry of the state R we start from. For the vibronic spectra at T ) 0 K, we need oscillator

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strengths, or transition dipole moments, which connect the initial state to all possible final states. In the Condon approximation (4), the vibronic spectra are

IR,R′(ν˜ ) )

C π

∑ |µ_R,R′(Q_R0 )| f0,R,ν′,R′ (ν˜ - ν˜ 2

γ 2

ν,R,ν′,R′)

ν′

+ γ2 (5)

Here, f0,R,ν′,R′ is the Franck-Condon integral (FCI), i.e., the overlap of the initial ground-state vibrational level 0 in initial electronic state R, to a final vibrational level ν′ in electronic state R′. Note that ν′ is a combined index for the vibrational quantum numbers of all M modes, ν′ ) (ν′1, ν′2, ..., ν′M). The relevant FCIs are given, in harmonic normal mode approximation, as

f0,R,ν′,R′ ) R′ R′ ′ )〉 〈0R1 (Q1) 0R2 (Q2) ... 0RM(QM)|ν′R′ 1 (Q1′) ν′2 (Q2′) ... ν′M (QM

(6)

where |νRm〉 is the Vth vibrational wave function of the mth normal mode in state R. For absorption spectra, the initial electronic state is R ) 0 (i.e., S0), and the final state is R′ ) 1 (i.e., S1). For emission spectra, it is the other way around. Note that the constants C and the broadening factor γ are generally different from those in eq 1. Below, in both eqs 1 and 6 we set arbitrarily C ) 1 but select different γ’s to empirically account for different vibrational and electronic broadenings. The difficulty in calculating FCIs lies in the fact that the equilibrium geometries of ground and excited states are different, and also the normal modes of ground and excited states are not identical. This causes vibrational mode coupling. The final state modes can usually be expressed in terms of the initial state modes, using the so-called Duschinsky transformation14 

Q _ ) bJQ _ + d_

(7)

with Jb being the Duschinsky rotation matrix and d_ a displacement vector, denoting the difference of the equilibrium geometries of the initial and final state. Due to the normal mode mixing the multidimensional FCIs cannot be separated into onedimensional FCIs for each individual mode. This is only possible if Jb ) 1b ; i.e., the initial- and final-state modes are parallel. At least a partial separation becomes possible, however, if Jb has a block-diagonal structure.15 Here we approximate the FCIs with the help of the program FCFast24 by Dierksen. Consider a general FCI R′ R′ ′ )〉 ) 〈νR1 (Q1) νR2 (Q2) ... νRM(QM)|ν′R′ 1 (Q1′) ν′2 (Q2′) ... ν′M (QM :〈ν1ν2...νM |ν′1ν′2...ν′M〉 (8)

Within FCFast one defines a model system in which the Duschinsky rotation matrix Jb assumes a block-diagonal form, so that the FCIs of the approximate system can be computed as a simple product of individual blocks; for further details see ref 15. In each block the FCIs are calculated using a recurrence relation by Doktorov et al.25 Thereby the multidimensional FCIs 〈ν1ν2...νM|ν′1ν′2...ν′M〉 in each block are expressed as linear combinations of FCIs of lower quantum numbers until the FCI of the vibrational ground-state functions (〈01...0M|0′1...0′M〉) is reached, corresponding to the so-called 0-0 transition. The 0-0 integral

Figure 2. Highest occupied molecular orbital (HOMO, π) and lowest unoccupied molecular orbital (LUMO, π*) of the electronic ground state (S0) of RF (B3LYP/TZVP, gas phase).

TABLE 1: Selected Bond Lengths R of the Ground State S0 and the Excited State S1 of RF, Calculated with (TD-)B3LYP/TZVPa gas phase

DMSO

bond R

RS0/Å

RS1/Å

∆R/Å

RS0/Å

RS1/Å

∆R/Å

C4a-N5 C4a-C10a C4-C4a C10a-N1 C2-O2 C4-O4

1.294 1.456 1.498 1.305 1.213 1.211

1.353 1.425 1.454 1.332 1.220 1.217

0.059 -0.031 -0.044 0.017 0.007 0.006

1.299 1.448 1.490 1.315 1.225 1.219

1.345 1.426 1.452 1.320 1.227 1.230

0.046 -0.022 -0.038 0.005 0.002 0.011

∆R ) RS1 - RS0; for labeling of the atoms, see Figure 1. Left half, gas phase; right half, DMSO, treated within the PCM model. a

can be calculated analytically. The precision of this approximation is defined by two parameters: the Duschinsky threshold, which controls the similarity of the model system with the exact system, and the screening threshold, below which the corresponding FCIs are set to zero. For the 135 modes of RF we used a maximum block size of 31 modes for the Duschinsky matrix, which corresponds to a Duschinsky threshold of 0.7 and a screening threshold of 10-6, as described earlier and in ref 15. 3. Results and Discussion 3.1. Geometries. Riboflavin was optimized in its electronic ground (S0) and the lowest singlet excited state (S1) with (TD-)B3LYP/TZVP, first for the gas phase (ε ) 1), and then in DMSO modeled by the PCM (ε ) 46.68). All calculations in this subsection 3.1 were carried out with GAUSSIAN09. Here we consider only the non-hydrogen-bonded conformation in which the ribityl chain is pointing away from the isoalloxazine unit. (According to ref 13, a second stable form exists in which the ribityl chain is bent and an intramolecular hydrogen bond is formed to the isoalloxazine ring; this configuration is not considered here.) As mentioned earlier, the S0 f S1 transition is related to a π f π* (HOMO f LUMO) transition. The frontier orbitals of S0 in its optimized molecular geometry are depicted in Figure 2. We find for the S0 f S1 transition a vertical excitation energy of 3.04 eV (408 nm), which is in excellent agreement with the values of refs 5 and 6 for simpler flavins. In Table 1 we show selected bond lengths of RF in geometry-optimized S0 and S1 states, obtained for the gas phase (left) or in DMSO (right). The S0 and S1 geometries of the isoalloxazine ring are in very good agreement with those of lumiflavin in refs 5 and 26. For the gas phase, the geometries are also in qualitative agreement with those of RF found by Wolf et al.13 by Hartree-Fock (for S0) and CIS (for S1). Upon electronic excitation, several geometric variables change. The observed bond length changes are in qualitative agreement with ref 13. They can be understood by the nature of the HOMO and LUMO involved in the transition; see Figure 2. In the gas phase, a maximal elongation

TD-DFT for Vibrational Spectra of Riboflavin

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Figure 3. Calculated IR spectra of (a) the S0 state and (b) the S1 state [(TD-)B3LYP/TZVP/PCM] of RF in DMSO, both broadened with Lorentzians (see eq 1) of width γ ) 5 cm-1.

TABLE 2: Assignment of Vibrational Modes of Riboflavin in the Electronic Ground State S0 Calculated with B3LYP/TZVPa ν˜ (cm-1) (ν˜ IR/ν˜ ) DMSO ν˜ IR (exptl13)

ν˜ Raman (exptl27)

1724 (0.992) 1678 (0.999) 1662 (-) 1596 (0.992) 1553 (0.992) 1535 (0.984) 1519 (0.964) 1454 (-)

1711 1676

1709

1376 (0.946)

1362 (0.956)

1302

33.72 (0.982)

27.41 (0.985)

gas phase

PCM

COSMO

1782 (0.960) 1762 (0.951) 1668 (-) 1616 (0.980) 1573 (0.983) 1562 (0.967) 1525 (0.96) 1463 (-)

1736 (0.986) 1693 (0.990) 1663 (-) 1597 (0.992) 1554 (0.995) 1537 (0.983) 1521 (0.963) 1456 (-)

1365 (0.953) 56.35 (0.967)

1628 1584 1547 1511 1464

1550 1506 1465 1403

mode type C4-O4 str (and N3-H wag) C2-O2 str (and N3-H wag) C6-C7 str, C8-C9 str N5-C4a str, C10a-N1 str, C8-C9 str C10a-N1 str, N10-C10a str, C7-C8 str, C5a-C9a str N5-C4a str, C10a-N1 str C9-C9a str, C6-C5a str, H-C-H (CH3) bend C6-C7 str, C8-C9 str, C4-C4a str, C9a-N10 str, N5-C4a str, C4-N3 str, H-C-H (CH3) bend C8-C9 str, C5a-C9a str, C4a-C4 str root-mean-square deviation (mean quotient)

a

The gas-phase and PCM calculations were done with GAUSSIAN09; the COSMO calculation was with TURBOMOLE. In both cases DMSO was simulated with ε ) 46.68. We compare to experimental IR13 and Raman27 spectra, both in DMSO. The values in brackets give the ratio of calculated to measured values. Abbreviations: str ) stretching mode, wag ) wagging mode, and bend ) bending mode.

of 0.059 Å is found for the C4a-N5 bond; here the HOMO of S0 has bonding character while the LUMO (HOMO of S1) is antibonding. In analogy the C4a-C10a and the C4-C4a bonds have more binding character in S1 (see LUMO of S0 in Figure 2). For the C10a-N1 bond more nonbonding character, i.e., a longer bond length, can be observed when exciting from S0 to S1; see Table 1. Therefore, the C4a-C10a and C4-C4a bonds shorten while the C4a-N5 and C10a-N1 bonds elongate, due to the gain or loss of double-bond character. In summary, we find that the major geometry changes take place in rings II and III of Figure 1. In DMSO, the minimum geometries are not much affected by the solvent compared to the gas phase (see right half (DMSO) of Table 1): Solvent-induced bond length changes are only on the order of 0.01 Å, both for S0 and S1. The largest changes are found for the polar bonds, C2-O2 and C4-O4, as expected, which both are slightly elongated in DMSO. With and without the solvent, the C-O bonds are slightly elongated in the excited state because the LUMO is always C-O antibonding. 3.2. Vibrational Spectra. 3.2.1. Ground State S0. In Figure 3a we show the calculated, broadened IR vibrational spectrum of the electronic ground state of RF [B3LYP/TZVP/PCM(DMSO)]. A more detailed assignment of vibrations in the “fingerprint region” from about 1300 to 1800 cm-1 is given in

Table 2, where also a comparison to the experimental IR spectrum of RF by Wolf et al.,13 and the experimental Raman spectrum by Lustres27 is made. DMSO was the solvent in both experiments. The vibrational modes for the electronic ground state of RF were not only calculated for DMSO with the PCM (and GAUSSIAN09) but also with COSMO (and TURBOMOLE). Also, gas-phase calculations were made for comparison. It is found that the calculated spectra and band assignments are in good agreement with the experimental IR spectra of ref 13, at least when solvent effects are accounted for. For instance, the two carbonyl vibrations of the isoalloxazine ring are found at 1782 (C4-O4) and 1762 cm-1 (C2-O2) in the gas phase; see Table 2. The experimental values for DMSO from ref 13 are 1711 and 1676 cm-1. To compare with the tabulated data of ref 13, we also calculated the ratio of the measured IR frequencies in DMSO with respect to the (unscaled) gas-phase values. They are on the order of 0.95-0.96, as shown in parentheses in the first column of Table 2. (The universal scaling factor for B3LYP/6-311G(d,p) is also 0.96.28) Including DMSO via PCM, we obtain frequencies of 1736 and 1693 cm-1, respectively; i.e., clear red shifts occur in the polar solvent which bring theory and experiment in close agreement, even without scaling: The ratios ν˜ IR/ν˜ are now ∼0.99. Adopting the COSMO model, we obtain wavenumbers of 1724 and 1678 cm-1,

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TABLE 3: Assignment of Selected Vibrations of RF in the Electronic Excited State S1, Calculated with TD-B3LYP/TZVP, and Comparison to Experimental IR Spectra13 ν˜ (cm-1) (ν˜ IR/ν˜ ) gas phase

DMSO (PCM)

ν˜ IR (exptl13)

mode type

1739 (0.987) 1644 (1.005) 1609 (0.976) 1531 (1.010) 1519 (0.988) 1505 1503 (0.969) 1493 (0.975) 1489 1474 1461 1429 1372

1674 (1.025) 1659 (0.996) 1621 (0.969) 1534 (1.008) 1504 (0.998) 1503 1499 (0.970) 1493 (0.975) 1481 1479 1458 1429 1374

1716 1652 1571 1546 1501

C4-O4 str C2-O2 str C6-C7 str, C8-C9 str C10a-N1 str, C7-C8 str, C4a-C10a str, C5a-C6 str, C9-C9a str C4a-C10a str, C5a-C9a str, C7-C8 str, C10a-N1 str H-C-H bend in ribityl H-C-H bend, C9-C9a str, C5a-C6 str, C6-C7 str H-C-H bend, C7-C8 str, C5a-C9a str, C9-C9a str, C10a-N1 str H-C-H bend H-C-H bend, C10a-N1 str, C9a-N10 str, N5-C4a str H-C-H bend, C5a-N5 str, C10a-N1 str H-C-H bend, C4-C4a str, C4a-N5 str, C8-C9 str C4a-C10a str, C5a-C9a str, C6-C7 str, N1-C2 str

30.49 (0.987)

33.83 (0.992)

1454 1454

respectively, in even slightly better agreement with experiment. It should be noted, however, that both solvent models are approximate and no scaling of the harmonic frequencies has been made; i.e., the observed accuracy of the COSMO model of a few wavenumbers is somewhat fortuitous. Below 1650 cm-1 the vibrational spectrum is dominated by other in-ring vibrations, such as C-C and C-N stretching modes, with intensity similar to the C-O stretches. Here agreement between theory and experiment is again best for the COSMO DMSO model, with errors slightly larger than for the C-O stretches, however: The ν˜ IR/ν˜ ratios are on the order of 0.96-0.99. It is also observed that for these less polar in-ring vibrations, the influence of the polar solvent is generally small. In the experimental Raman spectrum one finds in addition to the IR spectrum of ref 13, a band at 1628 cm-1. We assign this signal to the C6-C7 and C8-C9 stretch, for which 1662 cm-1 is calculated with COSMO. We note that in earlier IR spectra of RF a peak at 1621 cm-1 was found.29 Note that according to Table 2, the deviation between IR and Raman frequencies is typically on the order of a few wavenumbers, where a comparison was possible. Finally, in the region below about 1100 cm-1 we have inplane or out-of-plane vibrations of the ribityl chain or the ring system, which extend down to very low frequencies of a few hundred wavenumbers and below (not shown). In Table 2, also the root-mean-square deviations between calculated and measured vibrational frequencies are shown, both for the gas-phase and the continuum models. For the unscaled values in Table 2, the rmsd decreases when including solvent effects, from about 56 to about 34 cm-1 (PCM), and 27 cm-1 (COSMO), respectively, again demonstrating the better agreement in the solvent case. In passing we note that the rmsd from experiment for gas-phase frequencies is 21.77 cm-1, when frequencies are multiplied with a recommended scaling factor of 0.96.28 Our assignments of the vibrational frequencies are also consistent with theoretical and experimental investigations for the BLUF4 and LOV domains.30 In refs 4 and 30 lumiflavin and riboflavin chromophore models were used, respectively, and water4 and amino acid environments were explicitly included.30 Within these models a downshift of the highest five frequencies was found, relative to the gas phase. We observe the same trend when modeling DMSO via continuum models. 3.2.2. Excited State S1. Figure 3b shows the calculated vibrational spectrum of the electronic excited state S1 [TD-

root-mean-square deviation (mean quotient)

B3LYP/TZVP/PCM(DMSO)]. Table 3 compares our calculated vibrations [gas phase and DMSO (PCM)] to the ultrafast infrared spectroscopy experiments for RF by Wolf et al.13 In the theoretical gas-phase spectrum, we find intense peaks at 1739 and 1644 cm-1,31 which belong to the carbonyl stretching modes of C4-O4 and C2-O2, respectively. The corresponding DMSO (PCM) values are 1674 and 1659 cm-1. In experimental IR spectra, two intense peaks were found at 1716 and 1652 cm-1, which were assigned to the C2-O2 and C4-O4 stretching mode, respectively.13 Our assignment is opposite, i.e., the higher frequency band corresponds to the C4-O4 and the lower one to the C2-O2 stretch. The energetic ordering of ref 13 was also based on CIS calculations, with computed vibrational energies of 1988 cm-1 for C2-O2 and 1966 cm-1 for C4-O4. Note that the CIS frequencies overestimate the experimental values by about 300 cm-1, while on the TD-B3LYP/TZVP/PCM level of theory the deviation between computed and measured frequencies is -42 cm-1 for C4-O4 and 7 cm-1 for C2-O2 for the new assignment of experimental values (cf. Table 3). If we were to assign the carbonyl stretching modes in accordance with ref 13, we would obtain a difference between the calculated and measured frequencies of -57 cm-1 for the C2-O2 and 22 cm-1 for the C4-O4 modes. In fact, also as far as ν˜ IR/ν˜ values are concerned, our alternative, “new” picture fits better. On the other hand, assuming that the new assignment is correct, then experimentally a small blue shift of the C4-O4 band from 1711 to 1716 cm-1 would be observed when exciting from S0 to S1. In contrast in calculations one sees a red shiftsin our case from 1736 to 1674 cm-1 (in DMSO). A clear red shift is also seen in experiment if the “old” assignment is made (from 1711 to 1652 cm-1). Given the fact that the LUMO is C4-O4 antibonding with slightly elongated bond length in S1 compared to S0 (see above), it is hard to understand why a blue shift of the C4-O4 vibration should occur in S1. Therefore, a conclusive statement about the energetic ordering of the two carbonyl stretches, and in particular about the assignment of the experimental 1716 cm-1 peak to the C4-O4 vibration, cannot be made at present. The C2-O2 bond slightly stretches in the excited state according to Table 1. One therefore expects a red shift of the C2-O2 stretching mode in S1, which is indeed found. On the (TD-)B3LYP/TZVP/PCM level of theory, the frequency shifts from 1693 to 1659 cm-1. A similar shift occurs according to experiment, when taking our new assignment as a basis. In

TD-DFT for Vibrational Spectra of Riboflavin contrast with the “old” assignment of ref 13, one would observe a blue shift of 40 cm-1 (from 1676 to 1716 cm-1). In summary, we suggest for the carbonyl stretching modes in the S1 state the same energetic order as in the S0 state. The question remains, why a small blue shift of the C4-O4 vibration was reported in experiment, despite its more antibonding character of C-O bonds in the LUMO (see above). The calculated bands at 1621, 1534, 1504, 1499, and 1493 cm-1 and some other lower lying signals [all for DMSO (PCM)] refer mostly to C-C and C-N stretching vibrations of the isoalloxazine ring. The band at 1621 cm-1 corresponds to C6-C7 and C8-C9 stretching vibrations. This band is the analog of the ground-state vibration with a calculated frequency of 1663 cm-1 (PCM), and the experimental Raman peak at 1628 cm-1 (see Table 2 and ref 27). This mode is assigned to the band at 1571 cm-1 in the experimental excited-state spectrum by Wolf et al.13 Thus, in S1 the mode is red-shifted both in experiment (by ∼57 cm-1) and in our theory (by ∼42 cm-1), in agreement with an increasing antibonding character of the C6-C7 in the excited state (see Figure 2). The peak at 1534 cm-1 (1546 cm-1 experimentally) originates mainly from C10a-N1 and C7-C8 stretching vibrations, with contributions from other ring stretches. It can be related to the 1597 (experiment, 1584 cm-1) and the 1537 cm-1 (experiment, 1511 cm-1) bands in the ground state [see Table 2, all calculated values for DMSO (PCM)]. Again, both in theory and experiment a red shift occurs in S1 which can be understood, e.g., from the elongated, weakened C10a-N1 bond (Table 1). The 1504 cm-1 peak (experiment, 1501 cm-1) is correlated to the 1554 cm-1 (experiment, 1547 cm-1) band in the ground state, also arising from in-ring C-C and C-N vibrations. Again, a red shift on the order of 50 cm-1 occurs in the excited state due to, e.g., the bond weakening and stretching of the C10a-N1 bond in S1. Note that there is also a shift of the individual (C-C or C-N) contributions to the various modes when exciting from S0 to S1. All the discussed assignments and shifts reflect the change in the single and double bonds in the conjugated ring system upon electronic transition. Finally, the bands between 1481 and down to about 1100 cm-1 belong to bending vibrations coupled to C-C and C-N stretching modes within the isoalloxazine ring system. These framework modes are delocalized over the whole molecule and therefore difficult to assign. Modes below about 1100 cm-1 correspond to the in-plane or out-of-plane vibrations of the ribityl chain or the ring system. As for the ground-state vibrational spectrum we also computed the root-mean-square deviation (rmsd) for the excited vibrational spectrum; see Table 3. Here, the rmsd for the gas phase is about 30 cm-1 and does not further improve upon inclusion on solvent effects, at least if no rescaling of frequencies was performed. All assignments of vibrational transitions for S1 are in qualitative agreement with those of ref 13 by Wolf et al., except for the carbonyl stretches as mentioned earlier. 3.2.3. IR Absorption Difference Spectrum. The changes in vibrational spectra due to electronic excitation can best be visualized by showing the IR-difference spectrum as defined in eq 3. When calculated at the (TD-)B3LYP/TZVP/PCM(DMSO) level of theory, one obtains, in the interval [1500,1800] cm-1, the broadened difference spectrum shown in Figure 4. Apart from a small general blue shift of the theoretical spectrum, it is in good qualitative agreement with the experimental spectrum of ref 13 (see Figure 1 of ref 13). It shows bleaching regions indicative of ground-state vibrations, e.g., at

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Figure 4. Calculated IR absorption difference spectrum between S1 and S0 states [(TD-)B3LYP/TZVP/PCM(DMSO)], Lorentzian broadening γ ) 5 cm-1.

1736 and 1693 cm-1 (the two C-O stretches) and at 1597 and 1554 cm-1 (C-N and C-C ring stretches); cf. Table 2. The positive regions indicate the shift of the corresponding vibrations in the excited state; e.g., the double-peak centered around 1670 cm-1 originates from the red-shifted carbonyl vibrations, and the peak at around 1620 cm-1, from the C6-C7 and C8-C9 stretches (cf. Table 3). 3.3. Vibronic Spectra. 3.3.1. Vibronic Absorption Spectrum. The vibronic absorption spectrum of RF was computed by taking all 135 modes of both the ground and the excited states into account. For the absorption spectrum, we assume that the molecule is in the ground vibrational state of S0 initially; i.e., T ) 0 K. In the calculation, an energy cutoff of 0.99 eV (125 nm) above the 0-0-transition was used. Both gas-phase and PCM (DMSO) calculations were carried out. The gas-phase vibronic absorption spectrum obtained in this way is shown in Figure 5a. The resulting line spectrum shows the 0-0 transition as the most intense peak, indicating that the overall geometric changes after electronic excitation are not large. The computed gas-phase 0-0-transition energy is 458 nm (2.71 eV). This compares well with recent low-temperature, He droplet measurements by Dick who determined, albeit for lumiflavin, a 0-0 transition energy of 465 nm (2.67 eV).32 Note that the 0-0, nonvertical transition energy deviates substantially from the vertical transition energy which is the electronic energy difference of S0 and S1 states, at the S0 equilibrium geometry. For gas-phase RF, we find a vertical excitation energy of 408 nm (3.04 eV), which is strongly blue-shifted relative to 0-0 and shown as a vertical dashed line in the figure. Neither the 0-0 nor the vertical transitions are good models to compare with experimental UV/vis absorption spectra, as will be outlined below. Before doing so, we mention a few further details of the line spectrum of Figure 5a. There one finds in addition to the 0-0 transition two other high-intensity peaks, namely, an out-of-plane (oop) vibration at 456 nm and an inplane (ip) motion of the isoalloxazine ring at 454 nm. The oop mode is related to a 86 cm-1, and the ip modes are to a 176 cm-1 peak in the excited-state vibrational spectrum. At higher energies (smaller wavelengths) one also finds, besides combinations of the oop and the ip vibrations, some contributions (relative intensity > 0.2) of the stretching modes C4a-C10a, C5a-C9a, C7-C8, and C10a-N1. The C4a-C10a/C5a-C9a stretching mode, which is at 1375 cm-1, appears at 431 nm in the vibronic absorption spectrum. The peak at 427 nm arises from a combination of the C5a-C9a, C7-C8, and C10a-N1 stretching vibration (1504 cm-1), the oop mode, and the C6-C7 and C8-C9 stretching mode (1621 cm-1). Thus, the vibronic line spectrum

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Figure 5. Calculated vibronic absorption spectrum (a) and emission spectrum (b) of gas-phase RF [(TD-)B3LYP/TZVP, T ) 0 K]. The line spectra are shown, along with spectra that were broadened with Lorentzians of γ ) 250 cm-1. Several signals of the line spectrum are marked. The dashed vertical lines define the vertical excitation (a) and deexcitation (b) energies, respectively.

represents the change in the bonding character of rings II and III of isoalloxazine. In solution and in particular at higher temperatures the line spectra will be broadened. A convolution of the line spectrum with Lorentzians of width γ ) 250 cm-1 gives the smooth absorption signal in Figure 5a. The smoothed spectrum shows three distinct bands, one of them, at the high-energy side, being visible as a shoulder only. (In general, the width, shape and intensity of the bands depends on the broadening parameter γ of course.11) The three bands, which are visible already in the line spectrum, occur at 448 nm (2.77 eV), 425 nm (2.91 eV), and 404 nm (3.08 eV) in the gas phase, with the middle peak being the most intense in this case. We can now compare the broadened spectrum to the experimental absorption spectrum of RF which was measured in ethanol at a temperature at 77 K.8 In the experimental spectrum, the most intense vibronic peak is at 443 nm (2.79 eV). The maximum of our calculated vibronic spectrum (peak 2) at λ ) 425 nm (2.91 eV) is thus blue-shifted relative to experiment, by 19 nm (0.12 eV). If the vertical or 0-0 transition energies are taken as measures for the experimental S0 f S1 signal instead, these are even more strongly blue-shifted relative to experiment for the vertical transition (by 35 nm or 0.25 eV), or red-shifted in the case of the 0-0 transition (by 15 nm or 0.08 eV). A more meaningful comparison between theory and the experimental values of ref 8 should account for solvent effects. We do so by considering DMSO. [Of course, for comparison with ref 8, ethanol, which is less polar (ε ≈ 25), would be a better model.] When doing so, we find a vibronic fine structure similar to the one of Figure 5a, however, with shifted energies (and intensities) of the individual peaks. In this case, the computed central peak (2) appears at 453 nm (2.73 eV); i.e., the DMSO solvent shifts this peak by 28 nm (or 0.18 eV) to the red. When compared to the position of the central peak of RF in ethanol according to ref 8, the corresponding theoretical peak is now even slightly red-shifted by 10 nm, or 0.06 eV. In contrast, the vertical and 0-0 transition energies of RF in DMSO are 423 nm (2.93 eV) and 488 nm (2.54 eV), respectively; i.e., they are too blue- and too red-shifted when compared to experiment. Therefore, for a good agreement between theory (central peak) and experiment (central peak), both vibronic and solvent effects need to be accounted for. For DMSO, both are about equally important and both lead to a red-shift of the vertical gas-phase spectrum. The importance of the vibronic effects both for the fine structure and the position of the absorption signal has recently been mentioned, for smaller

TABLE 4: Comparison of the Calculated Vibronic Absorption Bands (for Gas Phase and DMSO, T ) 0 K) to the Experimental UV/vis Spectrum (for Ethanol, T ) 77 K)8 a nm (eV) theory, gas phase

theory, DMSO

experiment, “solution” (ethanol, 77 K 8)

experiment, “gas” (He droplets32)

peak 1 peak 2 peak 3 ∆12 ∆23 0-0 vertical peak 1 peak 2 peak 3 ∆12 ∆23 0-0 vertical peak 1 peak 2 peak 3 ∆12 ∆23 0-0

448 (2.77) 425 (2.91) 404 (3.08) 23 (0.14) 21 (0.17) 458 (2.71) 408 (3.04) 479 (2.59) 453 (2.73) 424 (2.92) 26 (0.14) 29 (0.19) 488 (2.54) 423 (2.93) 468 (2.65) 443 (2.79) 415 (2.99) 25 (0.14) 28 (0.20) 465 (2.67)

a The central peak (2) is indicated in bold. Peak spacings ∆ij ) Ei - Ej are also given. Further, computed vertical and 0-0 transition energies for RF are shown and compared to the experimental 0-0 line for lumiflavin.32

flavins, by Salzmann et al.11 The red shift of the S0 f S1 absorption band in polar environments can be traced back to a slightly reduced HOMO-LUMO gap as explained in ref 12. There, for lumiflavin in various solvents an increasing red shift of the vertical transition energy was observed when increasing the solvent polarity. The red shift did not change anymore significantly, however, beyond ε ∼ 25 and was also slightly smaller than the shift observed here for RF in DMSO. In Table 4 we summarize computed vibrational peaks as well as vertical and 0-0 transitions for RF in the gas phase and in solution, along with selected experimental data. From the table we note that also experimentally determined energy spacings between the vibronic subbands of ∼0.15 - 0.2 eV is wellreproduced by (TD-)B3LYP/TZVP/(PCM). In summary, the overall agreement between theory and experiment for RF in a polar solvent is very good and in fact better than expected given the limitations of the electronic structure method and solvent models which we use. In passing we note that the fact that out-of-plane vibrations contribute to the vibronic S0 f S1 absorption signal of RF in

TD-DFT for Vibrational Spectra of Riboflavin DMSO suggests that this alone cannot be used as an argument for nonadiabatic transitions between S1 and dark (n f π*) states. This argument would only hold for a system with higher symmetry than RF, such as lumiflavin. In fact, other arguments are needed in addition to support the role of dark states.1 3.3.2. Vibronic Fluorescence Spectrum. We also calculated the vibronic S1 f S0 emission spectrum. Again, the gas phase and DMSO (PCM) were considered. The spectrum was calculated up to an energy cutoff of 7000 cm-1 above the 0-0 transition, starting from the vibrational ground state of S1 (T ) 0 K). The gas-phase line spectrum in Figure 5b shows four dominant peaks (with relative intensity >0.3). The first one at 458 nm is the 0-0 transition again; the next one at 462 nm signifies in-plane-modes, now of the ground state, at 179 cm-1. The third high-intensity peak at 495 nm is assigned to the N5-C4a and the C10a-N1 stretching mode, corresponding to the 1616 cm-1 band of the gas-phase S0 vibrational spectrum (see Table 2). The fourth dominant peak is at 499 nm, originating from a combination of the 1616 cm-1 mode and the in-plane vibration at 179 cm-1. As for the vibronic absorption spectrum, we also observe significant contributions of out-of-plane and in-plane vibrations, for example in the 460 nm peak. After convolution with Lorentzians, the vibronic emission spectrum shows three main bands (one of them being a shoulder) and two smaller shoulders at longer wavelengths. The strongest band is at 498 nm (2.49 eV). Experimentally, the fluorescence maximum is at 542 nm (2.29 eV) for RF in water (pH ) 7).9 Therefore, our calculated emission spectrum is blue-shifted by 44 nm (0.20 eV) with respect to RF in water, comparing only the fluorescence maxima. Taking the vertical transition at 487 nm (2.55 eV) for gas-phase RF according to theory as a reference instead, the blue shift relative to experiment is 55 nm (0.26 eV). The two other main bands appear in the calculated spectrum at 471 nm (2.63 eV) and 539 nm (2.30 eV), respectively. Experimentally one finds two shoulders around the main peak at 523 nm (2.37 eV) and 565 nm (2.19 eV) for RF in water.9 These two theoretical bands are therefore also blueshifted, by 0.26 and 0.11 eV, respectively. At 593 and 660 nm two weak shoulders are found in the calculated gas-phase spectrum. For RF in water, Islam et al.9 find two lower bands at 638 and 691 nm. The theoretical emission spectrum is shifted toward the red in DMSO (not shown), bringing theory and experiment in better quantitative agreement for the main position of the S1 f S0 emission signal. In particular, the vertical deexcitation energy from S1 to S0 at the S1 equilibrium geometry shifts from 487 nm (2.55 eV) to 506 nm (2.45 eV). Similarly, the main peak of the vibronic fluorescence occurs now at 521 nm (2.38 eV), resulting in a deviation from the experimental maximum for water of 21 nm (0.09 eV). In passing we note that recent emission spectra of RF in DMSO find a maximum at 516 nm (2.40 eV); i.e., in this case the deviation to experiment is even smaller. The spectra in ref 2 are less fine-resolved than those of ref 9, however, which is why we do not discuss them in detail here. In summary, given the level of theory and the simplified treatment of the solvent, the agreement between theory and experiment is again very good. The calculations show that also for the emission spectra of RF both vibronic and solvent effects are important. Calculated and measured emission maxima, along with calculated vertical transition energies, are summarized in Table 5.

J. Phys. Chem. B, Vol. 114, No. 33, 2010 10833 TABLE 5: Comparison of the Calculated Vibronic Emission Maxima (for Gas Phase and DMSO, T ) 0 K) to the Experimental Emission Maximum of RF in Solution29 a nm (eV) theory, gas phase theory, DMSO experiment, solution (water9) experiment, solution (DMSO2)

maximum 0-0 vertical maximum 0-0 vertical maximum maximum

peak peak peak peak

498 458 487 521 488 506 542 516

(2.49) (2.71) (2.55) (2.38) (2.54) (2.45) (2.29) (2.40)

a Computed vertical and 0-0 transition energies for RF are also shown.

4. Summary and Outlook We calculated the vibrational spectra of the singlet ground S0 and the lowest singlet excited state S1 of riboflavin. Our findings for the S0 state are in good agreement with previous gas-phase calculations13 regarding the geometry and the vibrational spectrum. The ground-state vibrational spectrum fits also well with experimental IR and Raman spectra by Wolf et al.13 and Lustres.27 Also for the excited-state vibrations our calculations match well with experiment13 with respect to the employed quantum chemical models. However, we suggest an assignment of the C4-O4 stretching and C2-O2 stretching modes in the excited state S1 opposite to the assignment of Wolf et al.13 The vibronic UV/vis absorption spectrum of RF shows three peaks within the lowest band, with small deviations from experiment,8 if both vibronic effects and solvent shifts are considered. The same holds true for vibronic emission spectra. The vibrational fine structure was analyzed in terms of groundand excited-state vibrations, respectively, which are different due to a change of the bonding character in the isoalloxazine ring. This work can be extended in several ways. (i) The inclusion of vibronic structure in absorption and emission spectra opens also the way to treat resonance Raman spectra for systems as large as riboflavin. (ii) For flavins, the proximity of S1 to dark or weakly allowed singlet states (of the n f π* type), but also the possibility that the S0 f S1 transition dipole moment varies spatially, may require going beyond the Condon approximation (4). (iii) Besides (nearly) dark states, also higher excited, bright singlet states and triplet states should be included to cover a larger spectral width of the absorption (emission) spectra. In general, nonadiabatic (spin-orbit or non-Born-Oppenheimer) couplings between the various electronic states will be of interest in unravelling details of singlet and triplet spectra. (iv) Finally, a more realistic solvent model, e.g., of the microsolvation plus continuum type, will be a useful intermediate toward the treatment of flavoproteins. Preliminary results of calculations of riboflavin with four surrounding water molecules (microsolvatation) show that the vibrational frequencies of the “polar” modes are downshifted, in the ground as well as in the excited state. Further investigations, including amino acids representing a BLUF domain, are in progress. Acknowledgment. We thank Luis Lustres (Berlin), for supplying the Raman spectrum of RF in DMSO, Bernhard Dick (Regensburg), for sharing results prior to publication, and Tatjana Domratcheva (Heidelberg) and Jan Go¨tze (Potsdam) for stimulating discussions. We gratefully acknowledge financial support from the Cluster of Excellence 304 “Unifying Concepts in Catalysis” coordinated by the Technical University Berlin and funded by the Deutsche Forschungsgemeinschaft.

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References and Notes (1) Weigel, A.; Dobryakov, A. L.; Veiga, M.; Lustres, J. L. P. J. Phys. Chem. A 2008, 112, 12054–12065. (2) Zirak, P.; Penzkofer, A.; Mathes, T.; Hegemann, P. Chem. Phys. 2009, 358, 111–122. (3) Kottke, T.; Heberle, J.; Hehn, D.; Dick, B.; Hegemann, P. Biophys. J. 2003, 84, 1192–1201. (4) Unno, M.; Sano, R.; Masuda, S.; Ono, T.; Yamauchi, S. J. Phys. Chem. B 2005, 109, 12620–12626. (5) Salzmann, S.; Tatchen, J.; Marian, C. M. J. Photochem. Photobiol., A 2008, 198, 221–231. (6) Neiss, C.; Saalfrank, P.; Parac, M.; Grimme, S. J. Phys. Chem. A 2003, 107, 140–147. (7) Dittrich, M.; Freddolino, P. L.; Schulten, K. J. Phys. Chem. B 2005, 109, 13006–13013. (8) Sun, M.; Moore, T. A.; Song, P.-S. J. Am. Chem. Soc. 1972, 94, 1730–1740. (9) Islam, S. D. M.; Penzkofer, A.; Hegemann, P. Chem. Phys. 2003, 291, 97–114. (10) Yousefabadi, P. Z. Photodynamics of BLUF domain proteins: A new class the biological blue-light photoreceptors. Thesis, University of Regensburg, Germany, 2007. (11) Salzmann, S.; Martinez-Junza, V.; Zorn, B.; Braslavsky, S.; Mansurova, M.; Marian, C.; Gärtner, W. J. Phys. Chem. A 2009, 113, 9365– 9375. (12) Zenichowski, K.; Gothe, M.; Saalfrank, P. J. Photochem. Photobiol., A 2007, 190, 290–300. (13) Wolf, M. M. N.; Schumann, C.; Gross, R.; Domratcheva, T.; Diller, R. J. Phys. Chem. B 2008, 112, 13424–13432. (14) Duschinsky, F. Acta Physicochim. URSS 1937, 7, 551–566. (15) Dierksen, M.; Grimme, S. J. Chem. Phys. 2004, 120, 3544–3554. (16) Mertusˇ, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117– 129.

Klaumu¨nzer et al. (17) Klamt, A.; Schürmann, G. J. Chem. Soc., Perkin Trans. 1993, 2, 799–805. (18) Ahlrichs, R.; Turbomole (Version 6.0); University of Karlsruhe: Karlsruhe, Germany, 2009. (19) Frisch, M. J.; Gaussian 09, Revision A.02; Gaussian: Wallingford, CT, 2009. (20) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (21) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (22) Godbout, N.; Salahub, D. R. J. A.; Wimmer, E. Can. J. Chem. 1992, 70, 560–571. (23) (the implementation of the B3LYP functional in Turbomole and in GAUSSIAN differs slightly and therefore minor differences in the results occur). (24) Dierksen, M. FCFast; University of Mu¨nster: Mu¨nster, Germany, 2004-2006. (25) Doktorov, E. V.; Malkin, I. A.; Man’ko, V. I. J. Mol. Spectrosc. 1977, 64, 302–326. (26) Hasegawa, J.; Bureekaew, S.; Nakatsuji, H. J. Photochem. Photobiol., A 2007, 189, 205–210. (27) Lustres, J. L. P. Private communication. (28) Andersson, M. P.; Uvdal, P. J. Phys. Chem. A 2005, 109, 2937– 2941. (29) Abe, M.; Kyogoku, Y.; Kitagawa, T.; Kawano, K.; Ohishi, N.; Takai-Suzuki, A.; Yagi, K. Spectrochim. Acta, Part A 1986, 42, 1059– 1068. (30) Kikuchi, S.; Unno, M.; Zikihara, K.; Tokutomi, S.; Yamauchi, S. J. Phys. Chem. B 2009, 113, 2913–2921. (31) With TURBOMOLE, we find 1672 cm-1 instead for this mode. The difference from GAUSSIAN09 of 28 cm-1 is much larger than for all other modes (typically only 1 or 2 wavenumbers). However, the geometries used in GAUSSIAN09 and TURBOMOLE differ, as N1 is much more displaced out of the isoalloxazine plane in the GAUSSIAN09 geometry than in the Turbomole geometry. (32) Dick, B. Private communication.

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