# QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra

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^{†}

## Abstract

**:**

## 1. Introduction

_{max}= 649 nm) and a green-absorbing photoproduct (λ

_{max}= 536 nm) resulting in a photoproduct tuning of more than 100 nm, see Scheme 1. Therefore, the lowest energy absorption maxima of both forms are found in two different regions of the visible spectrum providing a model system to assess the quality of the quantum chemical methods to model the photoproduct tuning of a specific CBCR family and phytochromes in general.

_{r}and P

_{g}forms [16]. For the latter, the PCB chromophore was isomerized manually in the P

_{r}structure to mimic the photoproduct. In the second study by Scarbath-Evers et al., the P

_{r}form was simulated with classical MD for 1 μs [17]. In both studies, no attempts were reported to simulate ultraviolet/visible (UV/Vis) absorption spectra. However, pure quantum mechanical (QM) calculations for the excited states of PCB that are related to investigations on CBCRs have been performed. These studies either used model compounds built from scratch and optimized in vacuo to mimic PCB in CBCRs [18,19] or the required atomic positions were extracted from crystallized protein structures. In case of the latter, typically only PCB without relevant, adjacent amino acids was extracted [20,21,22,23] with the exception of one study, where in addition also the conserved aspartate and some solvent molecules were included [20]. In all those studies, time-dependent density functional theory (TD-DFT) was employed for the excited state calculations. Based on calculated absorption and circular dichroism spectra conclusions about possible PCB conformations in the protein could be drawn [18,19,20,21,23]. Matute et al. found that excited state calculations based on X-ray geometries of PCB from the cyanobacterial phytochrome Cph1 yield better agreement with experimental absorption spectra than from freely relaxed PCB structures in vacuo [21]. Therefore and to the best of our knowledge, our recently published study on the photoproduct tuning of the red/green CBCR Slr1393g3 was the first one to combine the treatment of a CBCR protein via quantum mechanics/molecular mechanics (QM/MM) with the simulation of absorption spectra based on snapshots extracted from QM/MM MD [12]. In that study, we have put special emphasis on describing the difference in absorption between the dark state P

_{r}and the photoproduct P

_{g}, as our simulations were based on crystal structures for both forms from the same protein [24].

## 2. Results

#### 2.1. Chromophore Structure Optimizations with Semiempirical Methods

_{r}than for the P

_{g}form. Furthermore, modified neglect of diatomic overlap (MNDO) [66], parameterized model 3 (PM3) [67] and PM3 with pairwise distance directed Gaussian method (PM3-PDDG) [68] exhibit RMSD values of around 1 Å for P

_{r}and of at least 1.26 Å for P

_{g}, see Table S1. This also holds for parameterized model 6 (PM6) [69], but including corrections for dispersion and hydrogen bonding (DH+) [70,71] improves the agreement, in particular for P

_{g}, see Table S2. The same trend is observed in case of the Austin model 1 (AM1) methods [72], where the revised model AM1/d [73] exhibits a performance between the original AM1 method and its dispersion corrected version AM1-D. Again the best results are obtained when both dispersion and hydrogen bond corrections [70,71] are employed, see Table S3. Overall, AM1-DH+ and Recife model 1 (RM1) [74] are the two best performing semiempirical methods based on Hartree-Fock with RMSD values of around 0.66 Å (P

_{r}) and 1.00 Å (P

_{g}), followed by the PM6-DH+ method with RMSD values of 0.76 Å (P

_{r}) and 1.10 Å (P

_{g}).

_{r}is similar to the results from PM6-DH, whereas the value of 0.94 Å for P

_{g}is already lower than in case of the Hartree-Fock based methods. Furthermore, using an empirical dispersion correction (+D) [82] in combination with DFTB2 results in further improvements: the RMSD values of 0.58 Å (P

_{r}) and 0.23 Å (P

_{g}) are for each form the lowest among all evaluated methods, see Table 1. However, no dispersion correction, e.g., Grimme′s dispersion correction D3 [83], is available in the current implementation of DFTB3 in the AMBER software package. Hence, we find DFTB2+D to be the most promising SQM method for the description of the PCB chromophore based on the assessment of in vacuo optimized geometries.

_{r}and P

_{g}, respectively. In addition, the deviations in excitation energies from the RI-CC2 optimized reference structures for the first excited state, which is the origin of the lowest energy absorption band, are shown in Figure 1. Overall the excitation energies from the SQM optimized geometries are higher than those from RI-CC2. The smallest differences are found for DFTB2+D, therefore the good agreement for the P

_{g}form could have already been expected based on its low RMSD value. This method is followed by DFTB2 and DFTB3 optimized structures, which exhibit RI-CC2 excitation energies somewhat lower than in case of the SQM methods based on Hartree-Fock, even though the RMSD values are comparable. The deviations for the three Hartree-Fock based methods are nearly the same for P

_{r}with a difference of ca. 0.23 eV, but increase from 0.24 eV (AM1-DH+) to 0.28 eV (PM6-DH+) to 0.29 eV (RM1) in case of P

_{g}. We want to point out that the deviations in terms of RMSD values and excitation energies for the in vacuo optimized structures are expected to be significantly higher than in case of the protein-embedded chromophore, as the protein environment introduces additional constraints on the PCB geometry.

#### 2.2. Spectrum Simulations Based on Sampling from Molecular Dynamics

_{g}divided by P

_{r}remains close to 0.9 and is therefore hardly affected. Employing a larger cutoff of 24 Å for the point charges from the environment leads to a slightly smaller photoproduct tuning, but the absorption shifts are only around 0.01 eV for both forms and therefore the smaller cutoff of 12 Å appears to be sufficient. Employing a larger basis set including diffuse functions red shifts the absorption maxima of both forms to nearly the same extent, ca. 0.06 eV, leaving the photoproduct tuning virtually unchanged. The same holds for the ratio of absolute absorption intensities, where the larger basis set leads to a similar decrease for both forms.

_{g}form close to the RI-ADC(2) calculations, whereas the absorption of the P

_{r}form is significantly blue shifted leading to a relatively small photoproduct tuning of 0.08 eV. To better describe the absorption of the latter form, one could for example employ the GGA functional BLYP, but this functional exhibits a negligible tuning caused by the red-shifted absorption of the photoproduct.

_{r}than for P

_{g}resulting in an increased difference in absorption of 0.26 eV. Similar shifts are also found when comparing 10 snapshots for both QM regions. In addition, also the ratio in peak heights goes down from ca. 0.90 to 0.80, closer to the experimental ratio of 0.56. So the deviations for the positions of the absorption maxima are more symmetric and the peak heights are also more similar to the experiments. In case of TD-DFT calculations with B3LYP, the absorption maxima of both forms are shifted by nearly the same amount of ca. 0.06 eV, hence the difference in absorption is again underestimated. For the ratio in absorption height, we observe a similar decrease by around 0.1 as for RI-ADC(2). The shifts towards lower energies for ZINDO/S are less prominent, but as in case of the RI-ADC(2) calculations, they are more pronounced for P

_{r}than for P

_{g}leading to larger differences between the absorption maxima of both forms. Also the ratio in peak heights decreases by around 0.05. This holds also for sTD-DFT calculations, but the shifts in positions are less systematic, whereas the difference in absorption remains around the same in the comparison of the two QM regions.

_{g}form for SC-NEVPT2 is in close agreement with the experimental value, whereas PC-NEVPT2 leads to a slight red shift. However, the absorption of P

_{r}is blue shifted by 0.20 eV and 0.32 eV for PC- and SC-NEVPT2, respectively. This leads to a photoproduct tuning of only 0.07 eV (PC-NEVPT2) and 0.08 eV (SC-NEVPT2). Also the absorption intensities are now interchanged, i.e., the P

_{g}absorption maximum is slightly higher than the one of P

_{r}. In particular the blue shifted absorption for P

_{r}might indicate that a larger active space is required to better describe the more conjugated structures of this form.

_{g}matches its experimental counterpart at 2.31 eV and the P

_{r}absorption maximum is blue-shifted by 0.23 eV. Selecting only 10 occupied and 10 unoccupied orbitals that possess a certain amount of π orbital character leads to further blue shifts of both absorption bands but leaves the photoproduct tuning virtually unchanged. However, this smaller active space allows to include triples, which decrease the energy for the lowest energy absorption maximum of both forms by nearly 0.08 eV. Overall, the employed semiempirical multi-reference calculations always yield a photoproduct tuning that is slightly higher than for the wavefunction-based calculations and somewhat lower than for the corresponding sTD-DFT calculations. However, as for the ab initio multi-reference calculations there is a tendency to overestimate the excitation energies in particular for P

_{r}. Furthermore, absorption intensities are found to be around the same for both forms within each of the three employed MRCI settings, placing the OM2-MRCI results between the ones from NEVPT2 and single-reference methods in this regard.

#### 2.3. Spectrum Simulations Based on QM/MM Geometry Optimizations

_{r}and 0.29 Å for P

_{g}relative to RI-CC2. This is also reflected in pronounced red shifts of the lowest energy absorption band for each form, see Figure 3. In case of optimizations with DFTB2+D, we have employed several approaches to optimize the structures as shown in Table S12 and Figure S2. The differences between them are relatively small and therefore, in the main text we just show the results of the initial structure optimization with 100,000 steps of steepest descent starting from the last snapshot of the production run, which was also the starting point for the BLYP+D3/AMBER and pure AMBER force field optimizations. DFTB2+D exhibits RMSD values of 0.12 Å (P

_{r}) and 0.19 Å(P

_{g}) placing it in between the pure force field treatment and the ab initio methods for QM/AMBER calculations, see Table 3. In addition, the spectra resulting from the DFTB2+D optimized structures are closer to the ones from ab initio QM/MM optimizations than from pure force field optimizations, see Figure 3. However, the absorption maximum for the P

_{g}form is red-shifted relative to the ab initio methods resulting in a photoproduct tuning that is similar to the ones based on force field optimized structures and somewhat smaller than for QM/AMBER optimized ones. Nonetheless, the accuracy of DFTB2+D is reasonably close to the ab initio methods, but it has the advantage of being ca. 2 orders of magnitude faster than RI-BLYP+D3/def2-SV(P), thus allowing more extended MD for sampling. Due to the relatively poor description of the geometry and red-shifted absorption for the protein-embedded PCB chromophore by force field optimization, care should be taken when sampling from classical MD without any further refinements. A similar conclusion has been reported by González and coworkers in a QM/MM study of the temoporfin absorption spectrum [88].

#### 2.4. Comparison of Absorption Spectra: Sampling versus Optimized Structures

_{r}form the maximum is shifting towards longer wavelengths when going from optimized structure, to 10 and 100 snapshots. However, for P

_{g}the maximum first red shifts, but then moves back close to its original position. In contrast to this, the more structures are considered, the broader and less intense this first absorption band becomes for both forms.

## 3. Discussion

_{r}and P

_{g}forms from the same CBCR protein Slr1393g3. First, we have assessed the description of the in vacuo optimized PCB geometries using semiempirical methods by comparing them with structures optimized with the ab initio RI-CC2 method. The best performing method, DFTB2+D, was used to simulate QM/MM MD trajectories with a simulation time of 1 ns and snapshots were extracted for excited state calculations with electrostatic embedding. For this purpose, we recommend the use of wavefunction-based methods, as these methods result in similar photoproduct tunings. In particular RI-ADC(2) has proven to work well with the structures that were generated via DFTB2+D/AMBER MD, resulting in positions of the lowest energy absorption maxima close to the experimental counterparts.

_{r}form in agreement with previous benchmark studies [44,51]. Furthermore the root mean square electron hole separation, which can be interpreted as exciton size [92], for the first excited state S

_{1}obtained as an average over 10 snapshots for P

_{r}increases from CAM-B3LYP (5.06 Å) to B3LYP (5.90 Å) to BLYP (6.16 Å), whereas the corresponding result for RI-ADC(2) is 5.11 Å, see Table S15. So the size of the exciton is similar for CAM-B3LYP and RI-ADC(2), but this functional results in an overestimation of excitation energy, as can be seen by the simulated spectra as well as by the averaged energies of the first excited state. In contrast to this, the first excitation energies and the corresponding lowest energy absorption band from BLYP are closer to the RI-ADC(2) results, but it is on the expense of the correct exciton description. Similar conclusions were also reached in a study by Mewes et al. investigating the absorption of Magnesium(II)porphyrin [93]. This deficiency in the description of the exciton properties is also found for the P

_{g}form and might be the underlying reason for the failure of the employed GGA functional to yield a reliable photoproduct tuning. It might be possible to improve the quality of the TD-DFT results by employing optimally tuned range-separated hybrid functionals [94].

_{g}form appears to be challenging. To improve the quality of the sampled structures, one may either resort to more recent semiempirical methods based on tight binding, like extended Tight Binding (xTB) [98,99] or DFTB3 with Grimme′s dispersion correction D3 [83]. In addition, xTB could also be employed to speed up the sTD-DFT calculations [100]. As an alternative approach for sampling, one may use structures sampled from DFTB2+D/AMBER MD as starting points for more accurate QM/MM MD. In case of the latter, RI-BLYP+D3/def2-SV(P) appears promising as the structures and excitation energies are close to the computationally more demanding RI-MP2 and RI-CC2 calculations. We expect that this approach will increase the simulated photoproduct tuning, but for computational reasons the corresponding trajectories might only be computed for several ps. In addition, further deviations of the simulated absorption spectra from the experimental ones might be caused by the setup of the system. For example, this study was performed with a doubly protonated HIS-529, similar to previous studies on the related red/green CBCR AnPixJ, in which the analogue histidine was also assumed to be in this protonation state [16,17]. However, simulations with a singly protonated HIS-529 lead to absorption spectra in better agreement with experiments, see the Supplementary Materials of reference [12]. Furthermore, sampling of different PCB conformations might be required to improve the agreement with experiments, as Scarbath-Evers et al. have shown that in case of the P

_{r}form of the closely related red/green CBCR AnPixJg2 two substates are found in classical MD simulations [17]. These substates differ in the orientation of the D ring, however, switching between both forms happens on a time scale of hundreds of nanoseconds.

## 4. Materials and Methods

#### 4.1. Chromophore Structure Optimizations with Semiempirical Methods

_{r}and 5M82 for P

_{g}[24]. Missing hydrogen atoms were added via GaussView [101] and side chains as well as methyl groups were replaced with hydrogen atoms with the same program resulting in truncated chromophores with 42 atoms for both forms. These structures were optimized with the SQM module of the AMBER software suite [59] until the default convergence criteria were reached and with all implemented semiempirical quantum chemical methods that are parameterized for the elements H, C, N, O, and S. For the same structures, RI-CC2/cc-pVDZ optimizations [60,61,62,63] were also performed with Turbomole 7.0 [64,65] to provide a benchmark for comparison of the differently optimized structures. For this purpose, the optimized geometries were aligned via PyMOL [102] including all atoms. Furthermore, excited state calculations were also performed with RI-CC2/cc-pVDZ [103,104] for the differently optimized structures to assess their influence on excitation energies and oscillator strengths. The RI-CC2 calculations employed frozen core orbitals and in case of the excited state calculations, a threshold of 10

^{−8}in atomic units for the SCF calculations was used. Otherwise, the default values were taken.

#### 4.2. Spectrum Simulations Based on Sampling from Molecular Dynamics

_{r}and 5M82 for P

_{g}[24]. The structures were solvated with TIP3P water molecules [106] in rectangular boxes with a distance of at least 15 Å between any atom of the protein and the boundary. Standard protonation states were employed with the exception of HIS-529, which is assumed to be doubly protonated. For the non-bonded interactions, a cutoff of 12 Å was chosen. Initial optimizations consisted of three stages:

- (i)
- Optimization via AMBER ff14SB force field [107] of the environment employing harmonic restraints of 500 kcal/(mol Å
^{2}) on the atoms of the protein with respect to their crystallographic positions. - (ii)
- Optimization via AMBER of the whole system with restraints on the atoms of the modified residue, i.e., on the PCB chromophore and CYS-528, which binds PCB.
- (iii)

- (i)
- Thermalization with classical MD with stepwise increase of the temperature from 0 to 300 K within 1 ns employing restraints of 10 kcal/(mol Å
^{2}) on the modified residue to keep the geometry close to the DFTB2+D/AMBER optimized one. - (ii)
- Equilibration via classical MD for 100 ns at 300 K to allow backbone relaxation employing the same restraints as before.
- (iii)
- Production run with DFTB2+D/AMBER for 1 ns at 300 K without any restraints.

#### 4.3. Spectrum Simulations Based on QM/MM Geometry Optimizations

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Sample Availability: Not Available. |

**Scheme 1.**Schematic representation of the PCB structures in the red- and green-absorbing forms. The differences between the two forms are highlighted in red and green for P

_{r}and P

_{g}, respectively. The wavelengths refer to the lowest energy absorption maxima of the measured spectra [13,14]. The QM region consisting of 42 atoms (QM42) is shown in blue, whereas the atoms of the QM region with 66 atoms (QM66) are shown accentuated in black.

**Figure 1.**Deviations of the excitation energies for the first excited state based on differently optimized structures for QM42. The energies are calculated via the RI-CC2/cc-pVDZ level of theory for P

_{g}(green) and P

_{r}(red). The reference values from RI-CC2/cc-pVDZ optimizations are 2.01 eV and 2.00 eV for P

_{r}and P

_{g}, respectively, see also Tables S5 and S6.

**Figure 2.**Absorption spectra for the P

_{r}(red) and P

_{g}(green) forms calculated with RI-ADC(2)/cc-pVDZ for QM66. The spectra are either based on 10 snapshots from a QM/MM MD trajectory taken every 100 ps (solid) or on 100 snapshots taken every 10 ps from the same trajectory (dotted). The sticks represent the positions and relative intensities of the two lowest energy absorption maxima for each form extracted from the measured spectra [14].

**Figure 3.**QM/MM absorption spectra for structures optimized at different levels of theory with QM66 for (

**a**) the P

_{r}and (

**b**) the P

_{g}form. The method for the treatment of the QM atoms is stated in the legend, while AMBER denotes pure force field calculations. Excitation energies are obtained using sTD-DFT calculations for QM106. The sticks represent the positions and relative intensities of the two lowest energy absorption maxima for each form extracted from the measured spectra [14].

**Figure 4.**Absorption spectra for the P

_{r}(red) and P

_{g}(green) forms calculated with sTD-DFT for QM106. The spectra are either based on one singly optimized structure (solid), 10 snapshots from a QM/MM MD trajectory taken every 100 ps (dashed) or 100 snapshots taken every 10 ps from the same trajectory (dotted). The sticks represent the positions and relative intensities of the two lowest energy absorption maxima from experiment [14].

**Table 1.**Root mean square deviations of geometries in Å. Comparisons are given for methods in the corresponding column and row for P

_{r}(first value) and P

_{g}(second value, shown in parenthesis).

P_{r} (P_{g}) | RM1 | AM1-DH+ | DFTB2+D | RI-CC2 |
---|---|---|---|---|

PM6-DH+ | 0.18 (0.35) | 0.35 (0.25) | 0.29 (0.96) | 0.76 (1.10) |

RM1 | - | 0.32 (0.23) | 0.31 (0.90) | 0.65 (1.02) |

AM1-DH+ | - | 0.39 (0.81) | 0.67 (0.96) | |

DFTB2+D | - | 0.58 (0.23) |

**Table 2.**Lowest energy absorption maxima of P

_{r}and P

_{g}. Wavelengths (λ), energies (E

_{max}), energy differences in parenthesis and absolute absorption (ε

_{Pr}and ε

_{Pg}) as well as photoproduct tuning (ΔE

_{max}) and ratio of absorption intensities (ε

_{Pg}/ε

_{Pr}) are tabulated. The QM region consisted of 66 atoms and if not stated otherwise, the results are based on 10 snapshots taken every 100 ps. The cc-pVDZ basis set was utilized and a cutoff of 12 Å to any of the QM atoms was employed to take the environment as point charges into account.

Method | P_{r} | P_{g} | Comparison | |||||
---|---|---|---|---|---|---|---|---|

λ (nm) | E_{max} (eV) | ε_{Pr}^{3} | λ (nm) | E_{max} (eV) | ε_{Pg}^{3} | ΔE_{max} (eV) | ε_{Pg}/ε_{Pr} | |

Exp.^{1} | 649 | 1.91 | - | 536 | 2.31 | - | 0.40 | 0.562 |

RI-ADC(2) | ||||||||

100 geom.^{2} | 609 | 2.04 (+0.13) | 8.37 | 548 | 2.26 (−0.05) | 7.52 | 0.23 | 0.898 |

10 geom. ^{2} | 600 | 2.07 (+0.16) | 10.27 | 559 | 2.22 (−0.10) | 9.47 | 0.15 | 0.922 |

24 Å cutoff | 596 | 2.08 (+0.17) | 9.32 | 561 | 2.21 (−0.10) | 9.13 | 0.13 | 0.979 |

cc-aug-pVDZ^{2} | 616 | 2.01 (+0.10) | 9.83 | 575 | 2.16 (−0.16) | 9.03 | 0.14 | 0.918 |

WF-based | ||||||||

RI-CC2 | 560 | 2.21 (+0.30) | 12.77 | 524 | 2.37 (+0.05) | 11.56 | 0.15 | 0.905 |

RI-CCS | 448 | 2.77 (+0.86) | 14.24 | 423 | 2.93 (+0.62) | 11.39 | 0.16 | 0.800 |

CIS | 448 | 2.77 (+0.86) | 14.45 | 423 | 2.93 (+0.62) | 11.47 | 0.17 | 0.794 |

TD-HF | 493 | 2.52 (+0.61) | 12.59 | 461 | 2.69 (+0.37) | 9.99 | 0.17 | 0.793 |

DFT-based | ||||||||

CAM-B3LYP | 538 | 2.31 (+0.40) | 11.98 | 504 | 2.46 (+0.15) | 10.70 | 0.15 | 0.893 |

B3LYP | 569 | 2.18 (+0.27) | 10.98 | 548 | 2.26 (−0.05) | 8.68 | 0.08 | 0.790 |

B3LYP (TDA) | 500 | 2.48 (+0.57) | 17.38 | 497 | 2.49 (+0.18) | 11.48 | 0.01 | 0.661 |

BLYP | 609 | 2.03 (+0.12) | 9.00 | 609 | 2.04 (−0.28) | 5.68 | 0.00 | 0.631 |

**Table 3.**Root mean square deviations of geometries in Å. Comparisons are given for methods in the corresponding column and row for P

_{r}(first value) and P

_{g}(second value, shown in parenthesis). For alignment, the geometries were reduced to 42 atoms as in case of the optimizations in vacuo. They were obtained from QM/AMBER optimized structures with QM66, while AMBER denotes pure force field calculations.

P_{r} (P_{g}) | DFTB2+D | RI-BLYP+D3 | RI-MP2 | RI-CC2 |
---|---|---|---|---|

AMBER | 0.14 (0.24) | 0.16 (0.27) | 0.16 (0.30) | 0.16 (0.29) |

DFTB2+D | - | 0.12 (0.15) | 0.12 (0.19) | 0.12 (0.19) |

RI-BLYP+D3 | - | 0.06 (0.07) | 0.05 (0.07) | |

RI-MP2 | - | 0.01 (0.01) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wiebeler, C.; Schapiro, I. QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra. *Molecules* **2019**, *24*, 1720.
https://doi.org/10.3390/molecules24091720

**AMA Style**

Wiebeler C, Schapiro I. QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra. *Molecules*. 2019; 24(9):1720.
https://doi.org/10.3390/molecules24091720

**Chicago/Turabian Style**

Wiebeler, Christian, and Igor Schapiro. 2019. "QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra" *Molecules* 24, no. 9: 1720.
https://doi.org/10.3390/molecules24091720