Effect of Solvation on Electron Detachment and Excitation Energies of

Article pubs.acs.org/JPCB

Effect of Solvation on Electron Detachment and Excitation Energies of a Green Fluorescent Protein Chromophore Variant Samik Bose, Suman Chakrabarty, and Debashree Ghosh* Physical and Materials Chemistry Division, CSIR-National Chemical Laboratory, Pune 411008, India S Supporting Information *

ABSTRACT: Hybrid quantum mechanics/molecular mechanics (QM/MM) is applied to the fluorinated green fluorescent protein (GFP) chromophore (DFHBDI) in its deprotonated form to understand the solvatochromic shifts in its vertical detachment energy (VDE) and vertical excitation energy (VEE). This variant of the GFP chromophore becomes fluorescent in an RNA environment and has a wide range of applications in biomedical and biochemical fields. From microsolvation studies, we benchmark (with respect to full QM) the accuracy of our QM/MM calculations with effective fragment potential (EFP) as the MM method of choice. We show that while the solvatochromic shift in the VEE is minimal (0.1 eV blue shift) and its polarization component is only 0.03 eV, the effect of the solvent on the VDE is quite large (3.85 eV). We also show by accurate calculations on the solvatochromic shift of the VDE that polarization accounts for ∼0.23 eV and therefore cannot be neglected. The effect of the counterions on the VDE of the deprotonated chromophore in solvation is studied in detail, and a charge-smearing scheme is suggested for charged chromophores.

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INTRODUCTION Green fluorescent protein (GFP) and its variants have encouraged several experimental and theoretical studies over the last couple of decades.1−4 The reason behind the intense interest in these systems is their use as fluorescent probes for various phenomena in vivo.5−8 Therefore, the importance of understanding the electronic structure of the ground and excited states of GFP as well as its oxidized and reduced forms cannot be overemphasized. The main findings as well as challenges in the understanding of the photophysical properties of GFP have been extensively covered in several reviews.9−13 The chromophore in GFP is 4-hydroxybenzylidene imidazolinone (HBDI) (Figure 1a, deprotonated form). UV and

zwitterionic form of HBDI has been theoretically suggested in some cases.18,19 There have been suggestions that the mechanism of isomerization between the cis and trans configurations of the chromophore proceeds via a zwitterionic intermediate.20 The various protonation states of GFP chromophore have different spectroscopic properties.21 Recently, a halogen-substituted HBDI chromophore, 3,5difluoro 4-hydroxybenzylidene imidazolinone (DFHBDI) (Figure 1b, deprotonated form), has been used to form a fluorescent complex with RNA.22 This has opened new avenues to engineer genetically encoded fluorescent RNA, which can be used as a biomarker for information about various biochemical and biological processes both in vivo and in vitro.23−27 Using a fluorescent RNA and a fluorescent protein can be a strategy to understand protein−RNA interactions or RNA−RNA interactions in live cells.28 Also, a recent study reported that DFHBDI binds to the G-quadruplex, a region that has a major role to play in the oncogenic character of cells.29 Similar to its protein counterpart, this chromophore exhibits fluorescence only when bound to RNA and not when present in solution,22 possibly because of severe constraints on the intramolecular motion inside the RNA as well as H-bonding and efficient π−π stacking.29 DFHBDI has important properties such as resistance to photobleaching and low cytotoxicity.22,30 Therefore, understanding the photophysical properties of DFHBDI− RNA complexes is crucial.31,32 Moreover, halogenated GFP chromophores have been used to study the effects of short H-

Figure 1. Structures of the GFP chromophore HBDI and the fluorinated chromophore DFHBDI, both shown in their deprotonated form.

fluorescence spectroscopy suggest that HBDI in wild-type GFP absorbs at 395 nm (neutral protonated form) and 480 nm (anionic deprotonated form)14 and emits at 510 nm (deprotonated form).15 Picosecond spectroscopy shows that the protonated HBDI undergoes excited-state proton transfer and is transformed into the deprotonated form.16 In enhanced GFP (eGFP), HBDI is present in the anionic form only.17 A © 2016 American Chemical Society

Received: April 12, 2016 Revised: April 26, 2016 Published: April 26, 2016 4410

DOI: 10.1021/acs.jpcb.6b03723 J. Phys. Chem. B 2016, 120, 4410−4420

Article

The Journal of Physical Chemistry B

spectroscopic properties? (iii) How do fluctuations in the environment affect the distributions of VDE and VEE? (iv) What are the relative contributions of geometry and polarization to the solvatochromic shift? This last question might give us insight into how the solvatochromic shift will affect the VEE and VDE in protein or RNA environments.

bonds and their effect on proton transfer from adjacent amino acids.33 Because of the importance of the fluorescent properties of GFP, there have been extensive studies of the photophysics of the HBDI chromophore in gas phase, both experimental and theoretical.34−37 A photoelectron spectroscopy study38 of the gas-phase anionic HBDI chromophore showed that contrary to theoretical predictions,37 the first optically active S1 excited state is bound against the photodetached D0 state. However, in both the experimental observations and theoretical calculations the D0 and S1 states are very close to each other (within 0.15 eV). On the other hand, the HBDI anion in the protein environment fluoresces,15 thus eliminating any possibilities of resonance phenomena in the lowest excited state. In 2011, Bravaya et al.39 showed computationally that the vertical excitation energy (VEE) [S0 → S1] of the chromophore is almost unchanged (increased by only 0.1 eV) by the protein environment but that the vertical detachment energy (VDE) or vertical ionization energy (VIE) [S0 → D0] increases remarkably from 2.70 to 5.00 eV. This makes S1 a bound state in the protein with a significant increase in its lifetime in comparison with the gas phase. However, experimental studies of HBDI anion in the gas phase40 and in the GFP environment8 showed that the VEE is red-shifted in protein by 0.1−0.2 eV. This red shift has been notoriously difficult to predict using quantum mechanics/molecular mechanics (QM/MM) techniques.41 The major factor responsible for this failure has been the use of nonpolarizable force fields.41−43 In polar solvents such as methanol and water, experimental results have shown a small blue shift (0.1 eV) in the absorption spectra.44 The effect of the RNA environment on the VDE and VEE of DFHBDI anion has still not been explored. The excited-state decay and reactions have been very challenging to understand. Each of the excited-state processes has also shown a strong dependence on the environment.45,46 There have also been combined experimental and theoretical efforts to understand the spectroscopic properties of HBDI in a microsolvated environment.47 While there has been some work on excited-state processes in GFP, not much is known about the electron-donating properties of GFP chromophores. However, there has been interest in the use of GFP as a photoinduced electron donor.48−51 Therefore, understanding its VDE is crucial. It has been found that the VDE is much more strongly affected by the environment than the VEE.39 While studies have suggested the importance of polarization for understanding of the absorption energy and excited-state processes, it is much more important in electron detachment processes because of the change in the net charge of the chromophore. Thus, for a complete understanding of the VEE and VDE together, one needs to use polarizable force fields in the QM/MM approach. In this work, we aim to understand the solvatochromic shifts in the VEE and VDE of anionic DFHBDI in water. Hybrid equation of motion (EOM)/effective fragment potential (EFP) and density functional theory (DFT)/EFP methods are benchmarked against full EOM-based methods for microsolvated DFHBDI chromophore. The benchmark studies are followed by an exploration of the effect of bulk solvation on these properties. The questions we aim to answer are the following: (i) What are the exact red/blue solvatochromic shifts in the VEE and VDE of DFHBDI in water? (ii) How does solvation affect the ground- and excited-state potential energy surfaces and what are the consequences of this for the

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THEORY Equation of motion coupled cluster singles and doubles (EOMCCSD) is the method of choice for small- to medium-sized systems for the computation of both the VDE and VEE. It gives a similar framework for the two computations within EOM-EECCSD and EOM-IP-CCSD, i.e., one starts from the same CCSD closed-shell ground state and uses the excitation and ionization operators (R̂ EE or R̂ IP) to generate excited and ionized states, respectively. In these methods, the ground state (anionic chromophore) is computed at the coupled cluster level of theory: Ψgs = exp(T1 + T2)Ψ0

(1)

where Ψ0 refers to the uncorrelated Hartree−Fock wave function and Ψgs is the coupled-cluster-corrected wave function for the ground state (before electron detachment or excitation). The excited and electron-detached states are computed from Ψgs via the operators R̂ EE and R̂ IP, respectively, given by R̂EE =

∑ rijai†aj + ∑ i,j

R̂IP =

rijklai†aj†ak al

i ,j,k ,l

∑ rjaj + ∑ rjkla†j akal j

j,k ,l

(2)

a†j

where ai and refer to the destruction and creation operators for orbitals i and j, respectively. Thus, R̂ EE is the operator for the generation of the excited state, where the number of particles is conserved, while R̂ IP is the operator for the generation of an ionized or electron-detached state and therefore effectively destroys a particle. EOM-CCSD is a preferred method because it can treat charge-transfer states accurately and does not give rise to spin contamination or unphysical symmetry breaking. However, EOM-CCSD is computationally expensive, scaling with system size as O(N6). While there are perturbative methods for approximate EOM-IP-CCSD that have lower scaling (N5), these approximations for EOM-EE-CCSD are still plagued with the N6 scaling.52 The system size increases significantly when bulk solvation of chromophore is considered. Therefore, hybrid QM/MM methods are used.53−57 Our MM method of choice was EFP58−61 since it contains an accurate electrostatic potential (up to octupoles using a distributed multipole analysis) as well as polarization. The dispersion and exchange-repulsion components are seen only for the EFP− EFP interactions. EOM/EFP techniques have been developed to understand accurate solvatochromic shifts of large systems, and the details can be found in refs 56 and 60−62. We used EOM/EFP versus full EOM for microsolvated systems to verify the accuracy of EFP theory in our system. Time-dependent DFT (TDDFT) or DFT were benchmarked with respect to EOM-CCSD and used for the bulk solvation studies. We employed the QM/EFP technique over a number of configurations obtained from classical molecular dynamics (MD) simulations. In the case of charged species, the situation was complicated by the need to neutralize the system to 4411


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Table 1. VEEs and VDEs (in eV) of the HBDI and DFHBDI Chromophores in Their Protonated and Deprotonated Forms Calculated at Various Levels of Theory HBDI method

DFHBDI

deprot

prot

deprot

prot

4.18 4.02 3.82 3.80 3.84 3.82 3.60−3.70b

3.05 3.12 3.09 3.09 3.13 3.12 −

3.99 3.96 3.51 3.50 3.53 3.51 3.65−3.75b

7.37 7.43 7.46 7.49 7.44 7.47 7.51 −

2.81 2.90 3.07 3.12 3.06 3.09 3.15 −

7.47 7.53 7.53 7.56 7.48 9.12d 7.60 −

VEE EOM-EE/6-31+G* EOM-EE/6-311++G* CAM-B3LYP/6-31+G* CAM-B3LYP/6-311++G* ωB97x-D/6-31+G* ωB97x-D/6-311++G* expt

3.11 3.15 3.17 3.16 3.17 3.16 2.59−2.84a

EOM-IP/6-31+G* EOM-IP/6-311++G* ωB97x-D/6-31+G* ωB97x-D/6-311++G* ωB97x-D/aug-cc-pVDZ CAM-B3LYP/6-31+G* CAM-B3LYP/6-311++G* expt

2.46 2.53 2.74 2.78 2.76 2.76 2.81 2.7−2.9c

VDE

a

Taken from refs 40, 44, 71, and 72. bTaken from ref 73. cTaken from ref 74. dConverged to the incorrect ionized state. Convergence to the correct ionized state was achieved with a secondary basis set (6-31G), and the ionization energy in that case was 7.55 eV. Details are given in the SI.

6-31+G* levels of theory to compute values of ΔVDE and ΔVEE (solvatochromic shifts), respectively. The water molecules directly H-bonded to the chromophore were included in the QM region. To understand the distance dependence of the effect of solvation on the VDE and VEE, calculations were performed with water shells of varying radii. Since the Na+ ion from the MD snapshot was not always present within the nearby solvation shells, the extra charge, when applicable, was smeared equally in the MM region. The effect of charge smearing was estimated. The importance of various components of the electrostatic interactions (charges, dipoles, quadrupoles, and octupoles) and polarization interactions were studied for the bulk-solvated system. The ground-state polarization was calculated by allowing the induced dipole moments to converge selfconsistently in the field generated by the rest of the EFP region as well as the QM part. Furthermore, since the charge density of the QM part was different for the ground and excited states, a one-shot perturbative correction was added to incorporate this effect. Details of the polarization correction are given in refs 56, 60, and 62.

employ periodic boundary conditions (PBCs) with Ewald summation. We studied the average effect of the charge (smeared over the environment) versus specific counterions in order to extend our formalism to highly charged systems.

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COMPUTATIONAL DETAILS Deprotonated and protonated structures of both DFHBDI and HBDI were optimized at the ωB97x-D/6-31+G* level of theory. VEEs for these structures in the gas phase were computed at the EOM-EE-CCSD/6-31+G*, EOM-EE-CCSD/ 6-311++G*, CAM-B3LYP/6-31+G*, and CAM-B3LYP/6311++G* levels of theory. VDEs were computed with the EOM-IP-CCSD method and ωB97x-D functional using the 631+G* and 6-311++G* basis sets. The theory and accuracy of these functionals have already been well-documented.63−66 The microsolvated chromophores were optimized at the ωB97x-D/6-31+G* level of theory. The QM/EFP hybrid method was benchmarked against the parent QM method to understand the accuracy of the hybrid treatment for microsolvated structures. The EFP parameters for water were taken from the Q-Chem library.61 All of the QM and QM/MM calculations were performed using Q-Chem.67 The geometries are given in the Supporting Information (SI). An ensemble of configurations for the chromophore in bulk solvation was generated by classical MD simulations in Gromacs 5.0.568 using the TIP4P model of water.69 Force field parameters for the DFHBDI anion were generated by the RED Server facility70 using restrained electrostatic potential (RESP) fit charges. A docedahedral box containing 8245 water molecules and one Na+ ion to neutralize the chromophore was used. Prior to the production run, the system was allowed to relax (using the steepest-descent algorithm) followed by NVT equilibration at 300 K for 100 ps and NPT equilibration at 1 bar for 600 ps. The MD production run was done at 300 K for 5 ns. The trajectory frames were saved every 20 ps of the production run and used for further QM/EFP calculations. QM/EFP calculations with the MD-generated configurations were performed at the ωB97x-D/6-31+G* and CAM-B3LYP/

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RESULTS AND DISCUSSION HBDI and DFHBDI in the Gas Phase. The CAM-B3LYP and ωB97x-D functionals were benchmarked against the EOMCCSD method for the VEE and VDE calculations, respectively. Table 1 shows a comparison of the VEEs and VDEs calculated with these functionals for deprotonated and protonated HBDI and DFHBDI against those obtained using the EOM-CCSD method. As expected from previous studies, CAM-B3LYP was found to be in good agreement with EOM-EE calculations of the VEE,63,64 and ωB97x-D gave good agreement with EOM-IP calculations of the VDE.65,66 However, when we tested CAMB3LYP for the VDE calculations, we obtained large errors. On the other hand, in the case of VEEs of the chromophores calculated with ωB97x-D, the errors were comparable to those with CAM-B3LYP. However, when we benchmarked for the solvatochromic shifts in the VEEs of the microsolvated 4412


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Figure 2. Microsolvated structures of deprotonated DFHBDI that were considered in this study.

Table 2. ΔVDEs (in eV) of the Mono- and Dihydrated Structures of Anionic DFHBDI at Various Levels of Theory (The EOM/ 6-311++G* Calculations Could Not Be Run for the Larger (Dihydrated) Systems) method

DH1

DH2

DH3

DH4

D2H1

D2H2

D2H3

D2H4

D2H5

EOM(6-31+G*) EOM(6-31+G*)/EFP EOM(6-311++G*) EOM(6-311++G*)/EFP ωB97x-D(6-311++G*) ωB97x-D(6-311++G*)/EFP ωB97x-D(6-31+G*) ωB97x-D(6-31+G*)/EFP

0.35 0.36 0.36 0.35 0.36 0.35 0.36 0.35

0.31 0.30 0.31 0.29 0.31 0.29 0.30 0.28

0.19 0.20 0.20 0.20 0.20 0.21 0.20 0.20

0.19 0.19 0.20 0.19 0.19 0.19 0.19 0.18

0.74 0.75 − 0.75 0.75 0.73 0.74 0.74

0.57 0.59 − 0.58 0.59 0.58 0.59 0.58

0.54 0.55 − 0.55 0.56 0.55 0.55 0.55

0.65 0.66 − 0.65 0.66 0.63 0.64 0.64

0.42 0.43 − 0.43 0.43 0.43 0.43 0.42

structures (see the SI), the errors with ωB97x-D were consistently larger than those with CAM-B3LYP. Therefore, for bulk solvation we used these functionals (CAM-B3LYP for VEEs and ωB97x-D for VDEs) with an added correction (given in eqs 3 and 4). The rest of this paper deals with only the deprotonated DFHBDI chromophore.29,30 Effect of Microsolvation on Deprotonated DFHBDI. The effect of microsolvation on the VEE and VDE was studied for the deprotonated DFHBDI chromophore. Four monohydrated structures (DH1, DH2, etc.) and five dihydrated structures (D2H1, D2H2, etc.) were considered for microsolvation, where the water molecule(s) are H-bonded to the DFHBDI anion (Figure 2). Table 2 shows the effect of the method (EOM vs ωB97x-D), basis set (6-31+G* vs 6-311+ +G*), and QM versus QM/EFP scheme. We notice that while the ΔVDEs (solvatochromic shifts in the VDE) are strongly dependent on the extent and site of microsolvation, they are insensitive to the method, basis set, and hybrid scheme. ωB97xD/EFP shows errors of up to 0.02 eV, especially for the structures with water H-bonded to the phenolic O−. For the bulk-solvation calculations, we considered such H-bonded water molecules in the QM region to avoid such errors. The relative insensitivity of ΔVDE to the method was used to

calculate best estimates of the VDEs in bulk solvation using eq 3 (see below). The major effect of hydration is preferential stabilization of the anionic ground state by the polar environment, thereby increasing the VDE. Figure 3 shows the effect of the electrostatic component of the interaction energy between the chromophore and water calculated by energy decomposition analysis (EDA)75−77 on ΔVDE for the monohydrated structures. As expected, it is

Figure 3. Relationship between the electrostatic component of the interaction energy between DFHBDI and water (in kcal/mol) and ΔVDE (in eV) for the monohydrated structures. 4413


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Figure 4. Lowest few VDEs (in eV) for gas-phase deprotonated DFHBDI (denoted by DF) along with the most important MOs involved in those electron-detached states. The ΔVDEs for monohydrated DH1 and DH2 for both the EOM and EOM/EFP methods are shown for comparison. The solid black lines denote the VDEs calculated at the EOM-IP-CCSD/6-31+G* level of theory, and the red dashed lines denotes the VDEs calculated with the hybrid EOM(6-31+G*)/EFP scheme.

Table 3. ΔVEEs (Solvatochromic Shifts in the VEE, in eV) of the Mono- and Dihydrated Structures of Anionic DFHBDI at Various Levels of Theory (The Geometries (DH1, DH2, etc.) Are Given in the SI) method

DH1

DH2

DH3

DH4

D2H1

D2H2

D2H3

D2H4

D2H5

EOM(6-31+G*) EOM(6-31+G*)/EFP CAM(6-311++G*) CAM(6-311++G*)/EFP CAM(6-31+G*) CAM(6-31+G*)/EFP

0.05 0.06 0.05 0.05 0.05 0.06

0.05 0.06 0.05 0.05 0.05 0.06

−0.02 −0.02 0.00 −0.01 0.00 0.01

−0.04 −0.04 0.01 0.01 0.01 0.02

0.16 0.17 0.10 0.11 0.10 0.11

0.05 0.06 0.04 0.05 0.04 0.05

−0.02 −0.01 0.03 0.04 0.03 0.04

0.14 0.16 0.09 0.10 0.09 0.10

−0.04 −0.03 0.00 0.01 0.01 0.02

noticed that ΔVDE is strongly dependent on the electrostatic interaction between the chromophore and water molecules. We notice from Figure 4 that the VDEs are reproduced quite well in the EOM-IP-CCSD/EFP scheme (red dotted lines) compared to EOM-IP-CCSD (black line) up to 7.5 eV. Around 7.5 eV we notice a missed electron-detached state in the EOMIP-CCSD/EFP scheme since this ionization occurs from water (as can be seen from the MO from which the electron detachment predominantly occurs). It is known that the gasphase water molecule ionizes at 12.60−12.80 eV78 and that its dimers and other clusters ionize at ≥10.58 eV.79 However, since the waters present in DH1 and DH2 are strongly Hbonded to an anionic species, the ionized state of water is significantly stabilized, and therefore, electron detachment predominantly from water starts at around 7.5 eV. All of the other electron-detached states are localized completely on the DFHBDI chromophore and are therefore accurately reproduced by the QM/EFP calculation. This is the rationale for the use of the hybrid QM/EFP technique for bulk solvation. We also included the water molecules directly H-bonded to the chromophore in the QM region so that electron detachments from nearby water molecules (electron-rich) would not be overlooked. Table 3 shows the solvatochromic shifts in the VEE of DFHBDI anion due to microsolvation. As expected, the effect of solvation on the VEE is significantly smaller than the effect on the VDE (0.05 vs 0.26 eV on average for the monohydrated structures). This is due to the comparable stabilization of both the ground and excited states (negatively charged) in solvation

as opposed to the relatively low stabilization of the electrondetached state (neutral). In this case, the QM/EFP errors in comparison to the parent QM method are ≤0.02 eV. The solvatochromic shifts in the VEE calculated with EOM and CAM-B3LYP methods are qualitatively similar, with a difference of less than 0.06 eV. For the computation of bulk solvation, we used hybrid QM/EFP with CAM-B3LYP/631+G* as the QM level of theory. Solvatochromic Shift Due to Bulk Solvation. Since electrostatic interactions are long-range in nature, solvent molecules far from the chromophore can affect the spectroscopic properties. Therefore, to predict these properties in bulk solvation correctly, the convergence of the average ΔVEE and ΔVDE was calculated with respect to the radius of the hydration shell (Figure 5). The first hydration shell contains the water molecules that are directly H-bonded to the chromophore. As expected, the solvatochromic shift in the VDE is much higher than that in the VEE. Solvation stabilizes the anionic species preferentially, thus giving rise to the large solvatochromic shift in the VDE. ΔVDE monotonically increases before converging (error ≤0.01 eV) at 4.11 eV. On the other hand, ΔVEE is slightly negative initially (for a shell radius of 7 Å) and then becomes positive and converges at 0.10 eV. The initial decrease in ΔVEE is due to structural changes in the chromophore, as discussed later. Both ΔVDE and ΔVEE converge (error ≤0.01 eV) within 18 Å. The convergence radius is longer for the anionic species than for neutral species such as thymine.62 4414


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thus reducing the chance for autodetachment that is possible in gas phase.37 The small blue shift in the VEE for DFHBDI (0.1 eV) is in good agreement with the experimental blue shift for HBDI in water.44 On the other hand, there is a large blue shift in the VDE (3.85 eV). From Figure 7b, we also notice that the full width at half maximum (fwhm) is 0.30 eV for the VEEs and 1.14 eV for the VDEs in bulk solvation. Thus, while the average VDE in bulk solvation is 6.75 eV, electron detachment can start occurring at ∼5.5 eV. This large spread of the spectroscopic properties (especially the VDE) is due to the thermal motion of the solvent molecules, which causes a fluctuating field on the chromophore. Since the VDE is more sensitive to the field, it shows a larger fwhm than the VEE. Therefore, QM/MM calculations based on only a few structures or a single globally optimized structure would provide rather limited information about the spread of the excitations. The configuration corresponding to the global minimum would have given only the VDE and VEE values corresponding to the maximum probability (near the average) and would have missed the onset of the excitations. A pertinent question at this point has to do with the effect of the QM-optimized chromophore structure versus the structures obtained from classical MD simulations. In the snapshots taken from classical MD, we optimized the chromophore at the ωB97x-D/6-31+G* level. We find that the effect of this QM reoptimization of the chromophore on the VEE is 0.01−0.07 eV (average effect of 0.04 eV blue shift). The effect of QM optimization on the VDE is 0.08−0.25 eV (average effect of 0.18 eV blue shift). Effects of Various Energy Components on the VEE and VDE. Since the effect of solvation on the VDE is much larger than that on the VEE, we studied the effect of various components of the electrostatic interactions (charge, dipole, quadrupole, octupole) and the polarizability on the solvatochromic shift in the VDE. Figure 8 shows the effects of the various electrostatic components on ΔVDE for the MD snapshots. We clearly notice that the octupole is not important in capturing the correct solvatochromic shift for this system (the error due to neglect of octupoles is ≤0.01 eV). However, if one considers only the charges there is a significant error in the ΔVDE (≤0.4 eV). The error caused by consideration of only the charges and dipoles (neglecting quadrupoles and octupoles) is about 0.2 eV. Thus, while the error decreases, one needs to use up to quadrupoles for accurate estimates.

Figure 5. Convergence of solvatochromic shifts (ΔVEE and ΔVDE) with varying size of the spherical solvation shell included in the MM region.

The solvatochromic shift in the VDE is strongly dominated by the electrostatic stabilization of the anionic ground state. We notice a linear dependence of ΔVDE on R−3 or R−4, where R is the radius of the solvation shell (see Figure 6). For the computation of the best-estimate values of the VEE and VDE in bulk solvation, we utilized the relative insensitivity of the ΔVEE and ΔVDE values with respect to the level of theory. For the computation of VDE, we used the equation VDE best est = VDE EOM‐IP/6‐311++G*(gs) + ⟨ΔVDEωB97x‐D/6‐31+G* /EFP(bulk)⟩av

(3)

where ⟨ΔVDEωB97x‑D/6‑31+G*/EFP(bulk)⟩av refers to the average ΔVDE computed at the lower level of theory (ωB97x-D/631+G*/EFP) for the bulk system and VDEEOM‑IP/6‑311++G*(gs) refers to the VDE of gas-phase DFHBDI at a more rigorous level of theory. Similarly, we computed the best estimate of VEE using VEE best est = VEE EOM‐EE/6‐311++G*(gs) + ⟨ΔVEECAM‐B3LYP/6‐31+G* /EFP(bulk)⟩av

(4)

Figure 7a shows the VDEs and VEEs of the equally spaced snapshots obtained from MD and their running averages for the full box (radius of 35 Å). These results show that the average value is converged within 25−30 snapshots. The spread of the VDEs and VEEs are shown in Figure 7b. The VEE and VDE are extremely close to each other in the gas phase, but they are clearly separated in the solvent phase. A similar effect in biological media is expected to shift the VDEs from the VEEs,

Figure 6. Dependences of the solvatochromic shift in the VDE on 1/R3 and 1/R4, where R denotes the radius of the solvation shell. 4415


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Figure 7. Effect of bulk solvation on VEE and VDE. (a) Instantaneous and running average of the solvatochromic shifts in VEE and VDE for the full dodecahedron of water on DFHBDI (snapshots obtained from MD simulation). (b) Simulated peak shapes corresponding to the lowest VDE and the π−π* excitation energy for DFHBDI in bulk solvation compared with the lowest VDE and VEE in the gas phase.

Figure 8. Effect of multipoles (charges, dipoles, quadrupoles, and octupoles) on ΔVDE in bulk solvation. (a) ΔVDEs calculated with multipoles up to charges (black), dipoles (blue), quadrupoles (red), and octupoles (green). The red and green lines overlap almost completely, thus denoting the small error due to neglect of octupoles. (b) Errors in the ΔVDEs considering multipoles up to charges (black), dipoles (blue), and quadrupoles (red). The errors were calculated with respect to full EFP multipoles (up to octupoles).

Figure 9. Effect of polarization on the ΔVDE in bulk solvation. (a) The ΔVDEs calculated with and without polarization. (b) Error in ΔVDE due to neglect of polarization.

The effect of polarization on ΔVDE is also quite significant (Figure 9). The absolute errors due to polarization are in the range of 0.01−0.7 eV (average 0.23 eV) for the 20 snapshots considered. This shows that for such systems the polarizable QM/EFP scheme is significantly more accurate than the nonpolarizable QM/MM scheme. The effect of polarization on the VEE is ∼0.03 eV (blue shift), as shown in the SI. The polarization component of ΔVEE in water is thus significantly different from that in the protein environment (red shift).41,42

We tested the effect of charge smearing of the counterion (Na+) versus the explicit use of point charges from the MD snapshot. The overall effect of charge smearing on ΔVDE was found to be approximately −0.1 eV. As expected, the maximum errors due to charge smearing (marked by the large black circles in Figure 10a) are seen in the snapshots where the Na+ is nearer to the chromophore. We also notice that the error in ΔVDE due to charge smearing is negative in these cases. This is due to partial neglect of the effect of a nearby counterion, which would have otherwise increased the VDE appreciably by 4416


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Figure 10. Effect of charge smearing on ΔVDE (in eV) in bulk solvation. The large black circles mark the snapshots where the error due to charge smearing is maximum.

Figure 11. Effect of structure (configuration of the chromophore in the MD snapshot) on the VEE and VDE (in eV). The VEE and VDE calculations used the geometries of the chromophores from the MD snapshots in the gas phase (without environment/water).

stabilizing the charged ground state. Thus, the average VDE with charge smearing always underestimates the total VDE compared with the average VDE calculated without charge smearing. The effect of charge smearing on ΔVEE is minimal (Figure 10b), which suggests that we can use the chargesmearing scheme for evaluation of ΔVEE for charged systems. Effect of Geometry on VEE and VDE. The major difference between the geometry of the gas-phase DFHBDI anion and the conformations of the chromophore in the MD snapshots is in the torsion angle between the phenolic and imidazolinone rings (details are given in the SI). In the MD snapshots, the torsion angles ranges between 130° and 230°. Figure 11a,b show the effects of conformational changes in the chromophore on the VEE and VDE, respectively. The average effects of conformation are −0.23 eV on the VDE and −0.13 on the VEE. Nonplanarity in the structure effectively reduces the energy gap between the HOMO and LUMO, thus reducing the VEE as well as the VDE. However, since the total ΔVDE and ΔVEE values are very different, the percentage effect of the structural factors is higher in the case of the VEE. This structural effect of the VEE predominates the ΔVEE value when the solvation shell is smaller, as shown in Figure 5, and ΔVEE becomes less than zero. In order to estimate the effects of geometry and solvation on the ground and few lowest excited states of the chromophore, we varied the torsion angle for the gas-phase DFHBDI anion and microsolvated structure D2H1. In Figure 12 we have plotted the energies of the ground and lowest few excited states

Figure 12. Energies (in Eh) of gas-phase and microsolvated (D2H1) DFHBDI plotted vs the torsion angle (τI), which is the dihedral angle between the bridge atoms and the imidazolinone ring. The energies of the ground and lowest three excited states of the DFHBDI chromophore in the gas phase are shown as solid lines, while the energies of the microsolvated structure are depicted with dashed lines. The black, blue, violet, and red lines correspond to the ground, S1, S2, and S3 states, respectively. The y axis to the left corresponds to the microsolvated structure, while that to the right corresponds to the gasphase structure.

(S1, S2, S3) of both gas-phase and microsolvated D2H1 along this coordinate (τI). The D2H1 microsolvated structure was used because it shows the maximum overall ΔVEE. The CCSD ground-state and EOM-CCSD excited-state energies were used 4417



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for DFHBDI, while the CCSD/EFP and EOM-CCSD/EFP energies were used for D2H1. We notice that with the change in geometry from planar to nonplanar, the ground-state energy increases while that of the S1 state is relatively flat. As shown by previous work, this is also the direction in which the minimumenergy conical intersection (MECI) lies.80 However, it is important to note that our potential energy is not the minimum-energy path. The S2 and S3 surfaces, while less flat than the S1 surface, are still less affected by the geometry than the ground-state surface, and therefore, all of the low-lying excited states are red-shifted as a result of geometry changes (changes in τI). On the other hand, the effects of electrostatics and polarization on the D2H1 structure show that near equilibrium the ground state is preferentially stabilized with respect to S1, thus causing a blue shift. The changes in structure (change in dihedral angle) and environment electrostatics give rise to opposite effects (red vs blue shift) on the lowest ΔVEE near the equilibrium torsion angle. It is the delicate balance of these two opposing effects that gives rise to the overall ΔVEE.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91 20 2590 3052. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank CSIR for the XIIth Five Year Plan on Multiscale Modelling for funding. D.G. thanks DST-SERB (SB/FT/CS090/2013) and DAE-BRNS for additional funding. S.C. is thankful for a DST-Ramanujan Fellowship. S.B. thanks CSIR for a Junior Research Fellowship and the Ph.D. Program of AcSIR.

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REFERENCES

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CONCLUSION We have investigated the effect of solvation on the VEE and VDE of the deprotonated DFHBDI chromophore. The VDE is strongly blue-shifted while the VEE shows a slight blue shift in the solvent. The VDE and VEE, which are very close to each other in the gas phase (2.90 vs 3.12 eV, respectively), move apart in the solvent phase (6.75 and 3.22 eV, respectively), and thus, the autodetachment processes that are predominant in the gas phase do not occur in solvent. While ΔVDE increases monotonically with the size of the solvation shell, the dependence of ΔVEE on the solvent shell radius is more complex because of the opposing effects of structure (geometry) and electrostatics. The predominant factor in the solvatochromic shift in the VDE is electrostatic in nature (Coulomb and polarization), while both structural and electrostatic factors are important in ΔVEE. The structural and electrostatic components act in opposite directions (red vs blue shift) in the polar water medium, and this causes the nonmonotonic dependence of ΔVEE with the size of the solvation shell. In this work, we have ascertained that polarization is important for the exact estimation of effects of the environment on spectroscopic properties such as the VDE and VEE of the GFP chromophore variant. We have used this work to build a methodology to compute these properties in protein or RNA environments. The effect of charge smearing was found to be minimal, and therefore, this technique might be used for complex environments. The specific interactions cause large changes in the VDE and VEE, and therefore, an explicit solvation method is crucial for the exact estimation of the solvatochromic shifts. Work on estimating the average VDE and VEE (and their spread) for the chromophore in complex environments is in progress.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b03723. Geometries of all the systems used in this work, radial distribution functions, distribution of torsion angles in the MD configurations, and effect of polarization on the VEE (PDF) 4418


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