# Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3

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## Abstract

**:**

## 1. Introduction

## 2. Computational Methods

**Classical Ensemble:**The Cy3-DNA system shown in Figure 1 was built using Chimera [44] version 1.14. The system is adapted from the experimental work of Heussman et al. [5], but a shorter sequence was used to reduce the computational cost. The MD setup and simulation was handled by Gromacs/2018.8. [45]. The force field parameters of Cy3 were derived from Amber99SB-dyes force field [46]. The missing linker parameters were obtained from the general Amber force field [47] (GAFF). The electronic density matrix of Cy3 optimized with B3LYP/6-31G(d) and the Gaussian16 package [48] was used to obtain the restrained electrostatic potential [49] (RESP) charges. The RESP charges fitting was undertaken using the Antechamber [50] package. The DNA part of the system was treated by Amber99SB-ILDN force field [51,52]. The system was solvated with TIP3P water [53], 100 mM NaCl, 6 mM MgCl${}_{2}$, and neutralized by Na${}^{+}$ in a cubic box of length 84.90 Å, resulting in a total number of 60,432 atoms. The energy of the system was minimized in vacuo using a steepest descent algorithm for 1000 steps. For initial equilibration, the temperature was gradually increased to 298 K in an NVT ensemble for 1 ns using a velocity-rescaling thermostat [54,55]. Further equilibration to reach a constant pressure of 1 bar was run for 1 ns in an NPT ensemble using a Parrinello–Rahman barostat [56,57]. For the MD production, the system was propagated using the leapfrog integration scheme [58] for 200 ns in an NPT ensemble. The equilibrations and the MD-production with periodic boundary conditions were propagated using a step size of 2 fs. The cutoff distance for the non-bonded interactions was set to 15 Å, and the long-range electrostatic interactions were accounted for by the particle mesh Ewald summation method [59].

**Quantum Ensemble:**A Wigner distribution within the harmonic approximation, as implemented in Newton-X V-2.2. [74], was used for the quantum sampling. In total, 200 configurations were generated from a Cy3 molecule with N-methyl group optimized with $\omega $B97XD/Def2SVP in implicit solvent (methanol) via polarizable continuum model (PCM). Methanol was used as an implicit solvent due to its negligible effect on Cy3’s spectra when compared to DNA [5,75]. For the vertical excitations, Newton-X was paired with Turbomole [72] V6.5 for the ADC(2) calculations and it was paired with Gaussian09 [76] for the TD-DFT calculations. The TD-DFT vertical excitations were performed in implicit solvent (methanol). ADC(2) vertical excitations were undertaken in a vacuum because there is no implicit solvation in the Turbomole version we have, and as we will discuss later, the solvent does not seem to have much of an effect. The Wigner absorption spectrum is obtained using summation over all the vertical excitations convoluted with Gaussian functions, and smooth spectra were obtained using spectral width of 500 cm${}^{-1}$ [18].

**Franck–Condon Calculations:**All the Franck–Condon calculations were run using Gaussian16 [73]. The ground and excited state optimizations and frequency calculations were obtained in the gas-phase as well as in implicit solvent (methanol) via PCM. The performance of the harmonic approximations, adiabatic Hessian, adiabatic shift, vertical Hessian, and vertical gradient, were tested. Since we are only considering the first excited state which is known to be a strongly allowed transition, the use of the FCHT [77] approximation is not necessary. Hence, through the study, we only use the FC approximation where the electric transition dipole moment is truncated at the zeroth-order of the Taylor expansion. For completeness, FCHT is compared to FC in the supplementary material Section 3.1, where it is confirmed that it is not important. The absorption spectrum is obtained using the time-independent and the time-dependent approaches. The Gaussian16 package’s default spectral width of 150 cm${}^{-1}$ at half maximum was used for all the FC calculations, and it resulted in a satisfactory broadening. Lastly, all the optimization calculations in the ground and excited state through the whole study were performed using the equilibrium linear response solvation formalism [78,79].

## 3. Results and Discussion

#### 3.1. Classical Ensemble: QM/MM-MD

#### 3.1.1. Electronic Structure Effect

#### 3.1.2. Sampling Effect

#### 3.1.3. Force Field Effect

#### 3.2. Quantum Ensemble: Wigner-Distribution

#### 3.3. Franck-Condon Approach

#### 3.3.1. Spectra at 0 K

#### 3.3.2. Origin of the Vibronic Structure

#### 3.3.3. Temperature Effect

#### 3.3.4. Environment and Functional Effects

#### 3.4. Comparing the Ensemble and Franck–Condon Approaches

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**

**Left**: The Cy3-DNA sequence studied [5].

**Middle**: Snapshot from the molecular dynamics equilibrated structure.

**Right**: Cy3 ground state structure optimized using $\omega $B97XD/Def2SVP showing the polymethine chain atoms numbered from 1 to 5.

**Figure 2.**(

**a**) Unnormalized absorption spectra from QM/MM-MD calculations using four wavefunction-based methods and six TD-DFT functionals using the same set of configurations (301 configurations). (

**b**) Normalized QM/MM-MD absorption spectra shifted so that all the maxima are centered at the experimental maximum of 18,194 cm${}^{-1}$ (some methods are omitted for clarity). The shift direction and magnitude is included in parentheses. All the spectra were plotted using standard deviation of 250 cm${}^{-1}$. The experimental spectrum from the work of Heussman et al. [5] is also shown.

**Figure 3.**Normalized absorption spectra from the same MD ensemble (50 configurations) using the ADC(2) method in gas phase (GS-MD) and with QM/MM (QM/MM-MD).

**Figure 4.**Comparing the spectra as a function of the number of configurations sampled (100 frames, 200 frames, 300 frames) obtained using (

**a**) CC2, (

**b**) ADC(2), and (

**c**) $\omega $B97XD. All the spectra have been normalized and shifted by the same shift as that used for the spectra obtained from 300 configurations to match the experimental maximum. The shift value and direction is included in parentheses in the charts titles.

**Figure 5.**Comparison of the spectra obtained from the unmodified force field [46] (unmodified FF) and after adjusting the polymethine bond length using parameters obtained from $\omega $B97XD/Def2SVP Cy3 optimized structure. Spectra are normalized relative to the modified one.

**Figure 6.**Normalized absorption spectra from an ensemble of 200 geometries generated using Wigner distribution and the harmonic approximation.

**Figure 7.**Spectra at 0 K obtained using the Franck–Condon adiabatic (AH and AS) and vertical (VH and VG) approaches. The time-independent (TI) approach at 0 K was used. The spectra are normalized and shifted to match the maximum of the experimental peak.

**Figure 8.**The vibronic spectrum obtained from structures optimized with $\omega $B97XD/Def2SVP in gas phase at 0 K using the AH approach. The red sticks correspond to the vibrational excitations. The labels on the sticks are selected transitions.

**Figure 9.**Temperature effect in the time-independent (TI) and time dependent (TD) schemes. The adiabatic Hessian (AH) approach at 0 K and 298 K was used along with structures optimized using $\omega $B97XD/Def2SVP in the gas-phase. The spectra are normalized and shifted to match the maximum of the experimental peak.

**Figure 10.**(

**a**) FC spectra obtained from $\omega $B97XD in gas-phase (ground and excited state optimized in the gas-phase) and methanol/MeOH (ground and excited state optimized in implicit solvent methanol via PCM) (

**b**) Comparing the performance of B3LYP, CAM-B3LYP, and $\omega $B97XD using methanol as an implicit solvent. All the spectra were obtained at 298 K using TD and were plotted using standard deviation of 150 cm${}^{-1}$.

**Figure 11.**Comparing the spectra obtained from the Franck–Condon (FC), quantum sampling (Wigner), and classical sampling (QM/MM-MD) using $\omega $B97XD/Def2SVP. The spectra here are shifted so that the first peak is matching the first experimental peak.

**Table 1.**Comparison of the polymethine equilibrium bond lengths (${R}_{0}$) in Å obtained from: the equilibrium structures of the ground ($\omega \mathrm{B}97\mathrm{XD}$$\left({S}_{0}\right)$) and the first excited ($\omega \mathrm{B}97\mathrm{XD}$$\left({S}_{1}\right)$) state optimized using $\omega $B97XD/Def2SVP; and the equilibrium bonds from Amber99SB-dyes force field (FF) [46]. k/FF is the force constant in kJ mol${}^{-1}$ nm${}^{-2}$ obtained from Amber99SB-dyes force field (FF) [46]. The polymethine bonds are defined in Figure 1. The newly used equilibrium C-C bond length is 1.3970 Å and the force constant is 389,275 kJ mol${}^{-1}$ nm${}^{-2}$. These values correspond to cag-cag bond parameters as implemented in the Amber99SB-dyes force field [46]. The newly used equilibrium N-C bond length is 1.3550 Å and the force constant is 387,100 kJ mol${}^{-1}$ nm${}^{-2}$, which corresponds to c2g-nhg [46] bond parameters. cag, c2g, and nhg are the atom-type [46]. The FF parameters are adapted with permission from Ref. [46]. Copyright 2014 American Chemical Society.

${\mathit{R}}_{0}$/$\mathit{\omega}$B97XD(${\mathit{S}}_{0}$) | ${\mathit{R}}_{0}$/$\mathit{\omega}$B97XD(${\mathit{S}}_{1}$) | ${\mathit{R}}_{0}$/FF [46] | k/FF [46] | |
---|---|---|---|---|

R(N${}_{1}$,1) | 1.3435 | 1.3712 | 1.391 | 343760 |

R(1,2) | 1.3966 | 1.3960 | 1.4510 | 326770 |

R(2,3) | 1.3938 | 1.4071 | 1.3379 | 470620 |

R(3,4) | 1.3938 | 1.4071 | 1.4511 | 326770 |

R(4,5) | 1.3966 | 1.3960 | 1.3390 | 469030 |

R(5,N${}_{2}$) | 1.3435 | 1.3712 | 1.355 | 387100 |

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## Share and Cite

**MDPI and ACS Style**

Sorour, M.I.; Marcus, A.H.; Matsika, S.
Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3. *Molecules* **2022**, *27*, 4062.
https://doi.org/10.3390/molecules27134062

**AMA Style**

Sorour MI, Marcus AH, Matsika S.
Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3. *Molecules*. 2022; 27(13):4062.
https://doi.org/10.3390/molecules27134062

**Chicago/Turabian Style**

Sorour, Mohammed I., Andrew H. Marcus, and Spiridoula Matsika.
2022. "Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3" *Molecules* 27, no. 13: 4062.
https://doi.org/10.3390/molecules27134062