Explicit Aqueous Solvation Treatment of Epinephrine from Car

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Explicit Aqueous Solvation Treatment of Epinephrine from Car-Parrinello Molecular Dynamics: Effect of Hydrogen Bonding on the Electronic Absorption Spectrum Arsenio P. Vasconcelos Neto, Daniel Francisco Scalabrini Machado, Thiago O. Lopes, Ademir J. Camargo, and Heibbe Cristhian Benedito de Oliveira J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b06110 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 14, 2018

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The Journal of Physical Chemistry

Explicit Aqueous Solvation Treatment of Epinephrine from Car-Parrinello Molecular Dynamics: Effect of Hydrogen Bonding on the Electronic Absorption Spectrum Arsênio P. V. Neto,† Daniel F. Scalabrini Machado,† Thiago O. Lopes,† Ademir J. Camargo‡ and Heibbe C. B. de Oliveira*,† ⊥ †

Laboratório de Estrutura Eletrônica e Dinâmica Molecular (LEEDMOL), Instituto de Química,

Universidade de Brasília, 70904-970, Brasília, DF, Brazil. ‡

Grupo de Química Teórica de Anápolis (GQTEA), Universidade Estadual de Goiás, 75132-903,

Anápolis, Goiás, Brazil. ⊥Laboratório

de Estrutura Eletrônica e Dinâmica Molecular (LEEDMOL), Instituto de Química,

Universidade de Brasília, 74690-900, Goiânia, GO, Brazil.

ABSTRACT The electronic absorption spectrum of the neurotransmitter epinephrine (EPN) in water solution is studied, combining ab initio Car-Parrinello molecular dynamics with a quantum mechanical approach within the framework of the time-dependent-density functional theory (TDDFT) scheme. By selecting 52 uncorrelated snapshots, the excitation modes were calculated at the LC-𝜔PBE/6-31+G(d) level of theory, using an optimal range separation parameter 𝜔, determined by means of the gap-tuning scheme in the presence of the solvent molecules. By

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comparing with static approaches (vacuum and implicit solvation), we show here that explicit solvation treatment dramatically enhances the photophysical properties of the EPN, especially due to the more realistic dynamic description of the molecular geometry. The agreement between the simulated and experimental spectra is demonstrated when TDDFT calculations are performed with the optimally-tuned version of the DFT hybrid, not only improving the relative intensities of the absorption bands but also the 𝜆𝑚𝑎𝑥 position. These results highlight that accounting for the nuclear motions, i.e., thermal effects (of both chromophore and solvent molecules), is imperative to predict experimental absorption spectra. In this paper, we have addressed the critical importance of explicit solvation effects on the photophysics of the EPN, raking in performance when the simulation is performed based on first principles molecular dynamics such as CPMD.


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1 Introduction Epinephrine (EPN), also known as adrenaline, is an important member of the cathecolamine series of neurotransmitters and neuroendocrine hormones whose action takes place in adrenergic receptors in several organs. Epinephrine was first synthesized in 19041 and displays vast clinical uses, including the treatment of myocardial infarction, bronchial asthma, hypertension and cardiac surgery.2–7 Accurate detection of EPN in biological samples is important for both clinical diagnoses and pathological studies of some diseases. EPN has been determined by several methods, such as liquid chromatography,8 chemiluminescense,9 and spectrophotometry.10,11 From a theoretical standpoint, this paper is concerned with the latter method, accounting for the solvatochromic effects on the UV-vis absorption spectra of EPN in aqueous media. In biological environments, the interaction between drugs and water is of fundamental importance to understand their absorption, transportation, and biological action. Concerning the solubility of drugs in water, the aqueous medium assists their transport from the site of administration to the site of action and is closely involved in their absorption.12 Plumridge and Waigh emphasized the importance of the aqueous medium in drug-receptor interaction. Since in most cases the drug will have a combination of hydrophilic and hydrophobic groups, it is possible that primary recognition occurs through water molecules surrounding the drug and water molecules surrounding the receptor.13 Theoretical studies in the literature seek to understand the interaction mechanism between water and epinephrine, with special attention to the hydrogen bondings.14,15 van Mourik, for example, studied the hydration of epinephrine in 1:1 and 1:2 water-epinephrine clusters through a rigid body DMA-based model for scanning the potential energy surface of the hydrates.16 However, to better understand the solvent’s effect on biomolecule structures and chemical properties, the need


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emerges for studies where water molecules are explicitly considered. In this context, ab initio molecular dynamics is a suitable approach since it performs an atomistic simulation of the solvent, capturing the real solvation effects on structural and dynamical properties of target molecules, which is not the case for static calculations.17 Car-Parrinello molecular dynamics (CPMD)18 is one such approach that has been used to study the thermodynamics and structural properties of molecules in solution.19–25 To theoretically model the solvatochromic effects on a given analyte, the inclusion of solvents becomes mandatory for better correlation with experimental measurements. Even though implicit treatments of the solvent’s influence on the electronic absorption spectra of different molecules have been routinely used,26 some solute-solvent interactions, such as local hydrogen bonding and long-range polarization effects, cannot be described by implicit solvation. Another important aspect when simulating condensed phases, as highlighted by De Mitri and co-workers, is that nuclear motions (whether solute or solvent molecules), i.e., thermal effects, must be adequately considered to reproduce the complexity of the vertical excitation energies in experimental measurements.27–30 For instance, CPMD has been employed to simulate the absorption spectra of phenol blue in chloroform solvent that is comparable with experimental results.31 Recently, one of the present authors employed CPMD simulations to elucidate the influence of methanol solvent on the intramolecular proton mobility of the curcumin molecule.32 Explicit solvated curcumin from CPMD lowered the intramolecular proton transfer barrier in one order of magnitude compared to static M062X/6-31+G* calculations, endorsing the importance of explicit solvation treatment from theoretical first principles. CPMD, therefore, provides a straightforward approach to correctly simulate the polarization of the solvent and its effect on the


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solute molecules, relying on some averaging of electronic structure calculations for a significant number of unbiased dynamics snapshots. Time-dependent density functional theory (TD-DFT) is today the best choice for a description of the ground and excited states of molecular systems containing thousands of electrons.33 Optical absorption and emission spectra of organic molecules can be calculated by TDDFT, with a major drawback that conventional hybrid DFT functionals (such as the “de facto standard” B3LYP functional34) poorly describe such excited state properties, especially charge-transfer excitations.35 Tuned range-separated hybrid (LC-RSH) functionals36 have the ability to provide a description of the excited states, leading to better agreement with experimental optical absorption spectra.37 The central premise of LC-RSH hybrids is to include a distance-dependent fraction of exact HartreeFock exchange through a splitting of the Coulomb operator into a long range (LR) and a short range (SR) term, and is given by: 1 erf⁡(𝜔𝑟) 𝑒𝑟𝑓𝑐(𝜔𝑟) = + , 𝑟 𝑟 𝑟

(1)

where 𝜔 is the range-separation parameter. The SR part (first term in eqn (1)) is described by a local or a semi-local functional and the LR part (second term in eqn (1)) fully includes the exact exchange. However, for many instances, the default range-separation parameter 𝜔 has been shown to be inadequate, overestimating the energies of charge transfer states, and more importantly, it is system-dependent.38 Non-empirical tuning of the range-separation parameter has been shown to alleviate this problem, improving the TD-DFT description of the absorption spectra of organic molecules.39 Here, to better correlate with experimental measurements, we employ the so-called gap tuning scheme40 (vide infra) to optimize the chosen LC-RSH functional (LC-𝜔PBE) in order to describe the UV-vis spectrum of an explicitly solvated EPN neurotransmitter in water from CPMD


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simulations. This non-empirical tuning procedure relies on the ionization potential (IP) theorem, which states that the negative HOMO eigenvalue (−𝜀𝐻 ) in exact Kohn-Sham theory is equal to the vertical ionization energy, i.e., the difference between the neutral and cationic forms with fixed geometry.41 Boruah et al. studied the performance of LC-RSH functionals in the presence of implicit solvation, resorting to the computationally less expensive polarizable continuum model (PCM), and observed that LC-RSH functionals are not capable of reproducing the HOMO and LUMO energies in PCM, although the non-equilibrium PCM method is better.42 Furthermore, when it comes to optimization of the range-separation parameter, the investigations of Rubešová et al.43 and De Queiroz et al.44 drew attention to the performance of tuned LC-RSH functionals for a solute embedded in a dielectric continuum as well as extended systems of solvating molecules. In such contexts, the 𝜔 parameter can be so small that the LC-RSH hybrid becomes essentially its GGA counterpart, which strongly underestimates HOMO-LUMO gaps.43 To circumvent these problems, in the case of explicitly solvated molecules, the suggestion of De Queiroz and Kümmel44,45 indicates that the solvent molecules should be included during the tuning process, which is the methodology adopted herein. In the context of explicit solvation approaches, several studies have examined the solvation effects on the excitation energies of organic molecules combining TD-DFT calculations with the QM/MM approach, due to the simplicity in considering the outer solvation shell to behave classically.46–48 In these investigations, the distribution of solvent molecules in the surroundings of the solute molecules is treated by classical mechanics, and the spectroscopic properties are further calculated from the classical configurations. In the present study, however, the novelty comes from the fully quantum-mechanical treatment of the solute-solvent, and solvent-solvent interactions, i.e., they are


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considered at the same level of accuracy by means of the ab initio molecular dynamics of CarParrinello. Guided by our interest in ab initio molecular dynamics,49–51 the solvent’s effects on optical52 and spectroscopic properties53–55 prompted us to investigate these subjects in the case of the neurotransmitter EPN in aqueous medium. In this paper our goal is to account for the effects of the explicit water solvation on EPN’s geometry and absorption spectrum to highlight the importance of an atomistic treatment of the solvent when the accuracy of continuum approximations is not attainable. A second goal here was to provide good agreement with the experimental absorption spectrum when EPN from MD simulations is considered by tuning the LC-𝜔PBE functional.

2 Computational Details

2.1 Car-Parrinello Molecular Dynamics of EPN in Water. To quantify the effect of the aqueous solvent on the geometric parameters of epinephrine, we computed the trajectory formed by one EPN molecule and 104 water molecules in a cubic box with edges of L=15 Å (Figure 1), chosen to reproduce the water density at 300K. The CPMD program package version 3.17.156 was used to perform the ab initio molecular dynamics simulation in the canonical ensemble NVT with periodic boundary conditions.


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Figure 1. Epinephrine molecular structure and atomic labels used for the molecular dynamics analyses (left); Epinephrine molecule solvated by 104 water molecules in a cubic box with edges of 15 Å (right).

Figure 1 illustrates the epinephrine atomic numbering adopted in this paper. The systems were simulated for 28 ps and the wave function fictitious mass (𝜇) was set to be 400 a.u. The electronic structure of the valence electrons was described within the DFT framework using the PBE functional.57 The interaction between the valence structure is based on the expansion of the valence electronic wave functions into a plane wave basis set, with an energy cutoff of 25 Ry; a cutoff energy of 100 Ry was set for the charge density expansion and the size step was set to 5 a.u. (0.121fs). The Nosé-Hoove thermostat58,59 was used to control the temperature, which was maintained at around 300 K. Vanderbilt ultrasoft pseudopotentials were employed for the corevalence electron interactions.60,61 The aqueous solvation of EPN was analyzed in terms of radial


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distribution (PRDF, g(r)), mean residence time (MRT) and hydrogen bonds in the first solvation shell. 2.2 Excitation Energies Calculations. As a reliable model system for the EPN solution, we considered 52 equally-spaced uncorrelated snapshots (vide infra) of explicitly solvated EPN dynamics to determine the average UV-vis absorption spectrum. To do so, we computed the electronic spectrum of EPN from TD-DFT calculations using the long-range corrected DFT functional LC-𝜔PBE along with the Pople-type 6-31+G(d) basis set. The geometries of aqueous EPN solution were those of the 52 uncorrelated configurations. We systematically optimized the 𝜔 parameter following the suggestion of Livshits and Baer,62 that LC-DFT functionals can be improved by demanding that the molecule, and its corresponding anionic form, satisfy Koopman's theorem (which states that the HOMO eigenvalue is equal to the negative sign of the ionization potential, -IP).63 Because Koopman’s theorem does not apply to electron affinity (EA), the rangeseparation parameter 𝜔 becomes an independent variable, modified to minimize the target function 𝐽𝑔𝑎𝑝 (𝜔), the so-called gap-fitting procedure:39,40

2

2

𝐽𝑔𝑎𝑝 (𝜔) = √(𝐽𝐼𝑃 (𝜔)) + (𝐽𝐸𝐴 (𝜔)) ,

(2)

with 𝐽𝐼𝑃 (𝜔) = |𝜀𝐻𝜔 (𝑁) + 𝐸𝜔 (𝑁 − 1) − 𝐸𝜔 (𝑁)|

(3)

𝐽𝐸𝐴 (𝜔) = |𝜀𝐻𝜔 (𝑁 + 1) + 𝐸𝜔 (𝑁) − 𝐸𝜔 (𝑁 + 1)|

(4)

where 𝜀𝐻𝜔 is the energy of the HOMO and 𝐸𝜔 (𝑁) the total energy for the 𝑁-electron molecule. For the sake of comparison, we additionally tuned the LC-DFT functional for both isolated (gas phase) and the well-known PCM implicit solvation method. The optimally-tuned (OT) LC-DFT functional was then used for TD-DFT calculations of the isolated and PCM solvated EPN,


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employing the same level of theory as in the case of the explicitly solvated EPN. Regarding the optimization of the range separation parameter, we spanned and selected the 𝜔 value that minimizes eq (2) within the range of 𝜔(𝑏𝑜ℎ𝑟 −1 ) = 0.01 − 0.6, with increments of 0.01𝑏𝑜ℎ𝑟 −1. All electronic structure calculations were carried out using the Gaussian 09 suite of programs.64 Charge-transfer indices of Le Bahers et al.65 were computed using the wavefunction analysis program Multiwfn.66 To obtain the final form of the spectrum from CPMD simulations, the transition energies in each snapshot were convoluted with Gaussian functions with half width at half maximum (HWHM, ∆1⁄2 𝜈) of 0.4eV. The spectrum is then computed for the 𝑠-th snapshot as67 𝜖𝑠 (𝜈) ∝ ∑ 𝑠

2 2.175 × 108 𝐿 ∙ 𝑚𝑜𝑙 −1 ∙ 𝑐𝑚−2 ∙ 𝑓 ∙ 𝑒 −2.772(𝜈−𝜈𝑖→𝑓 ⁄∆1⁄2 𝜈) , ∆1⁄2 𝜈

(5)

where 𝑓 is the dimensionless oscillator strength, and 𝜈 − 𝜈𝑖→𝑓 stands for the excitation energy corresponding to the electronic state of interest. The broadening of the spectrum for the 52 uncorrelated snapshots was then convoluted over all Gaussian functions including each snapshot in a single spectrum, thus averaging the absorption spectrum in an unbiased way. For further comparison with experimental results, the spectra were plotted in the wavelength domain (𝜖𝑠 (𝜆)).

3 Results and Discussion 3.1 Radial Distribution Function (RDF). Figure 2 shows the RDF of water molecules surrounding the EPN molecule with respect to the following specific atomic sites of EPN: N4, O3, H6, and H7 atoms. These sites were chosen to assess the solvation shells most likely to establish hydrogen bonding between solute and solvent. Black curves stand for the hydrogen atoms’


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distribution, and red curves for the oxygen atoms’ distribution of the water molecules embedding the aforementioned EPN atomic sites.

Figure 2. The hydrogen (in black) and oxygen (in red) RDF of the water molecules in the N4, O3, H6, and H7 solvation layers. By analyzing Figure 2, it becomes evident that the hydrogen atoms of the water molecules are oriented to N4 and O3, just as the oxygen atoms of water molecules are pointed to H6, and H7 atoms, suggesting the formation of hydrogen bonds. Concerning the first solvation shell of N4, there is a well-defined peak at 1.64 Å. The integration of the RDF at the first shell relating to the water oxygen shows that this layer is formed by 1.5 water molecules, on average. It is expected that subsequent layers become diffuse if the simulation time is extended. The first solvation sphere of O3 lies between 1.46 Å and 2.42 Å, showing a well-defined peak at 1.86 Å. The integration of the


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RDF at the second layer shows that there are 2.71 water molecules, on average. The first, second and third hydration shells centered on oxygen atoms are well defined and have the same width in the case of the O3---Hw interaction. The first hydration shell of H6 has a well-defined peak at 1.56 Å. The integration of the RDF at this layer shows that there are 1.29 water molecules on average. The first hydration sphere of H7 shows a well-defined peak at 1.64 Å, situated between 1.23 Å and 2.53 Å. The radial distribution function integration shows that this layer is formed by 1.29 water molecules, on average. However, to confirm the validity of the solvation shells it is necessary to analyze the mean residence time at which the water molecules remain in these sites and how water molecules approach these atoms (hydrogen bond analysis). 3.2 Mean Residence Time (MRT). The water molecules’ mean residence time and the coordination number in the first solvation shell of the O1, O2, O3, N4, H5, H6 and H7 EPN atomic sites are presented in Table 1. MRT were calculated according to Impey’s method, which defines a “survival function” defining the number of solvent molecules remaining in a given coordination shell after a time 𝑡 and estimating the MRT by an exponential fit, extrapolating to the time when all molecules have.68 “Real exchanges” are taken to be those whose ligand has to cross the shell boundary for a time span ≥ 𝑡 ∗ , which was set to 0, thus counting every solvent exchange irrespective of their duration, similar to other biomolecular systems.69 In Figure 3, the hydrogen coordination number of water molecules in the solvation shells of the N4, O3, H6 and H7 EPN atoms during the simulation time is shown.

Table 1. Mean residence time and the coordination number of water molecules at the EPN O1, O2, O3, N4, H5, H6, and H7 atomic sites.


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EPN shell O1 O2 O3 N4 H5 H6 H7

𝜏 (ps) 0.02 0.08 0.50 2.20 0.08 2.92 3.20

Coordination Number 2.96 2.65 2.71 1.54 1.29 1.28 1.39

Figure 3. Coordination number of water molecules in the first solvation shell for the N4, O3, H6 and H7 EPN atomic sites. Analyzing Figure 3, we note that water molecules remained within the N4 solvation shell (upper left panel) during all the simulation time, and at least a single water molecule remained within this


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layer during all 28.87 ps, indicating a strong hydrogen bond between these atoms. Another factor endorsing this event is the MRT value on this site at 2.2 ps, which was much higher than the adopted reference value (0.5 ps) for the hydrogen bonds.70,71 It is also noted, in the lower right panel of Figure 3, that the number of water molecules in the H7 first solvation shell range from one to four and, on average, this shell has 1.39 water molecules. The MRT of the surrounding water molecules in the first layer of the H7 site is 3.20 ps, with at least one water molecule attached to this site during all the simulation time, thus resulting in MRT of 28.87 ps, indicating that this is one of the main factors involved in the high MRT at the H7 site. Looking at the right upper panel of Figure 3, it is observed that the first solvation layer of the O3 site interacted with water molecules during nearly the entire simulation time. This site has on average two to three water molecules, and sometimes reaches seven. One water molecule remained in the O3 first solvation shell for all 28.87 ps, but its exchange number (number of molecule leaving and entering a given shell) equals 6, resulting in a MRT of 4.8 ps. Another water molecule also remained within this solvation shell for 24.14 ps. In this case, however, the exchange number was even greater, and this molecule visited this shell 21 times, which gave rise to a MRT of 1.1 ps. For the O3 site the MRT is only 0.5 ps; it therefore corresponds to the minimum value for the average hydrogen bond lifetime. The MRT for the H6 first solvation shell is 2.92 ps and its coordination number is 1.28, i.e., within this site the average number of water molecules lies between one and two. Looking at the lower left panel of Figure 3, it is readily noted that this site did not run out of water molecules and that after 23 ps the number of solvent molecules increased up to four. One water molecule remained in this site during the entire simulation time; it therefore has a MRT of 28.9 ps, which is also evidence that explains the high value of MRT for this site. In Table 1 the MRT for the H5 first


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layer is shown, which has a value of 0.08 ps. This value is much lower compared to the MRT value for the H6 first layer. When studying systems formed by an epinephrine molecule and one water molecule, Wang et al.14 and van Mourik16 indicated the formation of a bridge between the water molecule and the two catecholic hydroxyl fragments. Thus, according to these studies, such discrepant MRT values should not exist for the H5 and H6 atoms. However, for clusters formed by EPN interacting with two water molecules, van Mourik16 found that the two water molecules form a ring structure involving only one of the catechol hydroxyls. In this work, the obtained MRT values do not support the formation of such an intramolecular bridge formed between a water molecule and the catecholic group hydroxyls, and it is more likely that the ring formation involves one of the catecholic hydroxyls. 3.3 Hydrogen Bonds. Considering the MRT of water molecules discussed in the previous section, the hydrogen bonds (HB) between water molecules and EPN N4, O3, H6 and H7 atoms are now discussed in detail. The N4 and the O3 sites were analyzed with the water hydrogen atoms that remained for longer times within the first solvation layer in these sites; the H6 and H7 sites were analyzed with the water oxygen atom that was present for longer times in the first solvation shell in these sites. Jeffrey72 suggested a classification of the strength of hydrogen bonds, aiding the interpretation of the nature of the intermolecular forces of the type D-H-A (D=hydrogen donor, and A=hydrogen acceptor). The author deemed interactions with H-A distances greater than 2.2 Å and angle greater than 90 ° as weak; distances between 1.5 Å and 2.2 Å and angle greater than 130 ° as moderate, and distances between 1.2 Å and 1.5 Å and angle between 170 ° and 180 ° as strong. Figure 5 shows the distribution function of the bond length between the epinephrine H6, H7, N4, and O3 atoms and water atoms, respectively. Considering the bond length values, we note that


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moderate HB takes place, since there is a significant occurrence of bond lengths ranging from 1.4 up to 2.0 Å for all interactions considered. The angles formed between the epinephrine H6, O4 and O3 atoms and water molecules atoms also confirm the formation of HBs at these sites, as shown in Figure 4.

Figure 4. (left) Distance distribution between epinephrine H6 and water O atoms (in blue); epinephrine N4 and water H atoms (in red); and epinephrine O3 and water H atoms (in green). (right). Angle distribution of the H6---(O-H)w angle (in blue); H7---(O-H)w (in black); N4--(H-O)w (in red) and O3---(H-O)w (in green).

We note that there is no pattern in the studied angulations since, according to Jeffrey’s classification, the angles formed by H6---(O-H)w and H7---(O-H)w are characteristic of weak HBs, and the angles formed by N4---(H-O)w and O3---(H-O)w are characteristic of moderate HBs. This result can be explained by steric effects on the epinephrine solvation zone, which make the water molecules approach with an adverse angle compared with conventional angles observed in hydrogen bonds.


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Regarding intramolecular hydrogen-bonding, for the CPMD results of the EPN solvated by water molecules, it was found that the average bond length between the H7 and N4 atoms is 3.16 Å, and the H7 MRT in the N4 solvation shell is 0.06 ps, showing that there is no clear evidence of intramolecular hydrogen bonding during the simulation time. It is therefore expected that the absorption spectrum of EPN should be significantly different when the solute is in aqueous solution or in gas phase, because the latter is more favorable to establish intramolecular hydrogen bonding. To get a deeper insight into the nature of the possible interactions between the water molecules and the EPN sites most likely to establish intermolecular HBs with the solvent, we used Barder’s quantum theory of “atoms in molecules” (QTAIM). In the QTAIM framework, topological and energetic properties are evaluated at the point at which the electron density distribution, 𝜌(𝒓), reaches a minimum, termed as the “bond critical point” (BCP). The nature of the interatomic interactions, i.e., van der Waals and hydrogen bonds, can be rationalized at the BCP, relying on QTAIM properties such as the magnitude of 𝜌(𝒓), the Laplacian of 𝜌(𝒓), and the bond ellipticity 𝜀, as described elsewhere.73,74 Figure 6 depicts the QTAIM molecular graph as obtained from an uncorrelated snapshot taken from the CPMD simulation of aqueous EPN (we selected a snapshot where the arrangement of water molecules resembled the “protonated” form of EPN in the N4 atomic site according to Jeffrey’s classification of HBs), highlighting the BCPs across the whole supramolecular system. Note, however, that since our objective in this section concerns possible intermolecular HBs among the EPN molecule and approaching water molecules, the following results are devoted only to the BCPs 33, 41, 49, 63 and 69 (see Figure 5). The Laplacian of the electron density, ∇2 𝜌(𝒓), provides a measure of either charge concentration (∇2 𝜌(𝒓) < 0) or depletion (∇2 𝜌(𝒓) > 0) of the electron density distribution, the latter being


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characteristic of closed-shell interactions such as H-bonding when 𝜌(𝒓) is relatively small.75 ∇2 𝜌(𝒓) values at the BCP ranging from 0.024 to 0.139 (atomic units), ellipticity values 𝜀 < 0.1, and 𝜌(𝒓) in the range of 0.002-0.040 (atomic units) are commonly associated with HB-type interactions.76–79 Looking at Table 2, the ellipticity criterion is retained for all HB BCPs, whereas for the ∇2 𝜌(𝒓) and 𝜌(𝒓), values were not strictly within the literature classification.78 Nonetheless, the aforementioned classification was established by Koch and Popelier for C-H-O hydrogen bonds, whereas in the present work we focus only on conventional HBs. The total electronic energy density at the BCP, 𝐻𝐶𝑃 = 𝐺𝐶𝑃 + 𝑉𝐶𝑃 (the sum of the local kinetic energy density and potential energy density), was proposed as an index to describe the HB strength, seemingly because it is a more reliable parameter than ∇2 𝜌(𝒓).80 Rozas et al. found that both ∇2 𝜌(𝒓) and 𝐻𝐶𝑃 > 0 is a good indication of weak HBs, and that ∇2 𝜌(𝒓) > 0 and 𝐻𝐶𝑃 < 0 are associated with moderate HBs.81 The results for 𝐻𝐶𝑃 in Table 2 therefore indicate that all EPN HB sites interact moderately with water molecules and could be the reason why not all criteria proposed by Koch and Popelier were met, resulting from some covalent degree in the HB interactions. The landmark work of Espinoza et al. provided a good estimation of the hydrogen bonding energy (𝐸𝐻𝐵 ) from the local electronic potential density (𝑉𝐶𝑃 ), based on 83 experimental hydrogen bonds (HBs) [𝑋 − 𝐻 ⋯ 𝑂 (𝑋 = 𝐶, 𝑁, 𝑂)].82 The authors found a nearly linear relationship between 𝐸𝐻𝐵 and 𝑉𝐶𝑃 , written as 𝐸𝐻𝐵 = 1⁄2 𝑉𝐶𝑃 , as shown in the last column of Table 2. From Table 2, it is noteworthy that this approximate relationship shows that the HBs between the EPN O3H7 hydroxyl group and solvent molecules are the weakest observed, with 𝐸𝐻𝐵 values approximately 50% smaller with respect to the other HB sites. More importantly, all 𝐸𝐻𝐵 values indicate that all studied HB interaction sites fall in the range of moderate-strong HBs.80 Hence, the previous discussion


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about Jeffrey’s classification of the strength of HB is in tune with the QTAIM descriptors of intermolecular interactions.

Figure 5. (A) Molecular graph from the theory of “atoms in molecules” obtained for an uncorrelated snapshot from EPN CPMD simulation, highlighting the most likely intermolecular hydrogen bond-type interaction between EPN and water molecules. Bond critical points (BCP, shown as small green spheres) determine the point on the electron density 𝜌(𝒓) surface at which 𝜌(𝒓) reaches a minimum value along the bond paths (shown as black curves). (B) Laplacian of the electron density isosurface, including all water molecules in the first solvation shell. The wavefunction was obtained at the OT-LC-𝜔PBE/6-31+G(d) level, with 𝜔 = 0.25𝑏𝑜ℎ𝑟 −1 .

Table 2. Topological and energetic properties of the electron density 𝜌(𝒓), Laplacian of 𝜌(𝒓), ellipticity 𝜀, local potential energy density 𝑉𝐶𝑃 , and hydrogen bonding interaction energy 𝐸𝐻𝐵 , calculated at the bond critical point (BCP) of possible intermolecular hydrogen bonding


19


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interactions for an uncorrelated snapshot of the CPMD trajectory.a The QTAIM calculations were performed at the OT-LC-𝜔PBE/6-31+G(d) level, with 𝜔 = 0.25𝑏𝑜ℎ𝑟 −1.

a

BCP

𝜌(𝒓)

∇2 𝜌(𝒓)

𝜀

𝐻𝐶𝑃

𝑉𝐶𝑃

𝐸𝐻𝐵 = 𝑉𝐶𝑃 ⁄2 (𝑘𝐽 ∙ 𝑚𝑜𝑙 −1 )

49

0.078

0.162

0.0053

-0.01721

-0.07485

-98.26

41

0.052

0.156

0.0480

-0.00268

-0.04444

-58.34

33

0.034

0.110

0.0734

-0.0009

-0.02935

-38.53

44

0.026

0.080

0.0360

-0.0012

-0.02241

-29.42

63

0.079

0.208

0.0435

-0.01391

-0.07986

-104.84

69

0.092

0.194

0.0380

-0.02662

-0.10164

-133.43

all properties in atomic units unless otherwise specified. 𝐷 and 𝐴 stand for the hydrogen donor and

acceptor, respectively.

3.4 Velocity Autocorrelation Function (VACF). The velocity autocorrelation function expresses the correlation function dependence with velocity and provides important information about the dynamic processes that may be occurring in molecular systems. The VACF provides insights into the microscopic dynamics of a given solute, defined as68 𝑉𝐴𝐶𝐹(𝑡) = 〈𝒗(𝑡0 + 𝛿𝑡) ∙ 𝒗(𝑡0 )〉⁄〈|𝒗(𝑡0 )|2 〉,

(6)

where 𝒗(𝑡0 + 𝛿𝑡) is the velocity of the solute at time 𝑡 + 𝛿𝑡. In the EPN’s aqueous dynamics there are interactions between the atoms of the system, so it is expected that there will be changes in the magnitude and direction of the atoms’ velocities, i.e., we expect the scalar product between 𝒗(𝑡0 ) and 𝒗(𝑡0 + 𝛿𝑡) to decrease as the velocity changes. Figure 6 represents the VACF analysis for the studied dynamics, where twenty repetitions were analyzed in a range of 500 frames.


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1.2

Velocity Correlation Function

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.9

0.6

0.3

0.0

-0.3

0

100

200

300

400

500

Sample Frames Figure 6. Velocity Correlation Function of epinephrine’s aqueous solvation dynamics. As seen in Figure 6, the velocity correlation is lost approximately at frame 200. Therefore, to prevent biasing in the calculation of UV-vis excitation energies of the EPN embedded in water, we selected 52 equally-spaced frames starting from frame number 1000 up to frame 45000. In doing so, it is guaranteed that these frames are not correlated, and taking the average over these 52 uncorrelated frames, the reliability of the UV-vis simulation is attained.

3.5 𝝎 Optimization. Optimal tuning of the LC-𝜔PBE functional using the 𝐽𝑔𝑎𝑝 method was performed for one of the uncorrelated snapshots from explicitly solvated EPN CMD simulation. The optimization function, eq (2), is shown, respectively, in Figures S1, S2 and S3 (see SI file) for the explicitly solvated, implicitly solvated using PCM, and gas phase EPN. To best appreciate the optimal 𝜔 parameter values, we summarized these results in Table 3. From Table 3, there is a


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significant departure from the OT-⁡𝜔 parameter, whether in the gas phase or explicitly solvated EPN, with respect to the default parametrized value 𝜔 = 0.4𝑏𝑜ℎ𝑟 −1 , respectively, 0.270 and 0.250𝑏𝑜ℎ𝑟 −1 . Since predicted molecular properties are arguably insensitive to changes in the 𝜔 values, which differ by about ±0.01𝑏𝑜ℎ𝑟 −1,40 we might expect that the calculated electronic properties of EPN will not be affected by this particular choice of OT-⁡𝜔. Consequently, changes in the calculated absorption spectrum are primarily dominated by the molecular geometric structure in a specific environment over the electronic structure. Of course, the molecular geometry alone is not sufficient to predict molecular properties.83 When the solvent is treated by polarizable continuum models, the OT-⁡𝜔 value obtained from implicit treatment of the solvent (PCM) is very small (𝜔 = 0.019𝑏𝑜ℎ𝑟 −1 ) and far from the default benchmarked value 𝜔 = 0.4𝑏𝑜ℎ𝑟 −1; thus a tiny fraction of exact exchange is included in the LCRSH. As highlighted by Garza et al., in such a circumstance it is expected that the GGA functional (PBE) will be more adequate than the present LC-GGA counterpart (LC-⁡𝜔PBE).63 As has been shown by Rubešová et al., fulfilling Koopmans’ theorem for a molecule embedded in a dielectric constant yields artificially low 𝜔 values, suppressing the amount of exact Hartree-Fock exchange of the functional.43 As a result, the remaining functional will inherit all the drawbacks of pure GGA functionals.

Table 3. Optimal Range Separation Parameters (𝑏𝑜ℎ𝑟 −1 ) for EPN as obtained at the OT-LC𝜔PBE/6-31+G(d) level of theory. Gasa

0.270

Water (PCM)a

0.019

Water (CPMD)b

0.250


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a

Geometries optimized at the default LC-𝜔PBE/6-31+G(d), then the 𝜔 parameter is subsequently

tuned using this geometry. bGeometry taken from an uncorrelated snapshot of the EPN CPMD simulation.

3.6 Absorption spectra. In Figure 7, a comparison between the spectra calculated using both the default LC-𝜔PBE and OT-LC-𝜔PBE averaged over 52 uncorrelated CMPD snapshots is presented. Before inspection of the electronic spectra depicted in Figure 7, it is important to bear in mind that it does not represent the average over all oscillator strengths for each excitation mode; instead, it is a Gaussian convolution for all oscillators in each configuration (52 snapshots), so that the final spectrum explicitly accounts for every TD-DFT excitation of the uncorrelated snapshots (see the Methodology section). The first striking difference in the electronic spectra of aqueous EPN is the influence of the range separation parameter in the LC-RSH hybrid. From Figure 7, it is noted that not only is the spectral shape moderately altered, but also the maximum absorption band is red-shifted towards larger 𝜆 values when calculated using the optimal 𝜔 parameter; the first absorption band peaks at nearly the same wavelength of 219 nm and 223 nm, using LC-𝜔PBE and OT-LC-𝜔PBE, respectively, whereas for the second band the OT-LC-𝜔PBE 𝜆𝑚𝑎𝑥 is shifted by 15 nm with respect to the 𝜆𝑚𝑎𝑥 value, using LC-𝜔PBE (250 nm and 265 nm). The 𝜆𝑚𝑎𝑥 red-shift resulting from the tuning-scheme employed here has also been reported for other organic molecules, and this effect has been attributed to the larger amount of Hartree-Fock exchange in the default LC-RSH functional with respect to the tuned-RSH (recall that the obtained optimal 𝜔 parameter is ~60% of the benchmarked value).39 In terms of accuracy, the calculated absorption at 219nm and 223 nm matches the measured spectrum of EPN in water by Siva et al (220 nm).84 On the other hand, for


23


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the weakest excitation band, the maximum absorption wavelength of 265 nm is in better agreement with the experimentally measured band (280nm) than with the default DFT hybrid, thus a clear improvement of the simulated spectrum is aided by the gap-tuning scheme. Still in Figure 7, the calculations indicate that the absorption of EPN is due to the local transition in the catechol moiety, because the HOMO-1 -> LUMO+1 (both showing 𝜋 symmetry) transition is involved in the 𝑆1 state. As shown in Figure 7, the dominating character in this transition is of 𝜋 → 𝜋 ∗ nature, i.e., a local excitation in tune with the experimental characterization of this absorption band.85

Figure 7. (left) UV-vis spectrum of the EPN explicitly solvated in water (first solvation shell) as obtained at the OT-LC-𝜔PBE/6-31+G(d) level. Optimally-tuned range separation parameter value


24

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is 0.27𝑏𝑜ℎ𝑟 −1 . (right) Schematic energy diagram for the dominating molecular orbitals involved in the vertical excitation 𝑆0 → 𝑆1, highlighting the 𝜋 → 𝜋 ∗ nature of this band as obtained at the OT-LC-𝜔PBE/6-31+G(d) level.

To disclose the CPMD capability of modeling solvatochromic effects on the electronic optical properties of EPN more clearly, we now compare the TD-DFT results calculated for an uncorrelated snapshot of the CPMD simulation to usual static approaches: isolated (“Gas phase”) and implicitly solvated (PCM) treatments. For that purpose, we also performed geometry optimizations followed by TD-DFT calculations of EPN in both gas phase and embedded in a dielectric continuum under integral equation formalism (IEF-PCM), using the dielectric constant of water. These additional calculations were performed under the same level of theory employed for the CPMD configurations, differing only in the tuned-𝜔 parameter (see Table 3). Figure 8 shows the electronic absorption spectra as obtained for the isolated (Gas), implicitly solvated (PCM) and explicitly solvated (Water) EPN molecule, all obtained at the OT-LC-𝜔PBE/631+G(d) using the environment-specific 𝜔 parameter.


25


186

202

220

OT-LC-PBE (PCM) OT-LC-PBE (Gas) OT-LC-PBE (Water) Experimental

236

Normalized intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 43

280

276 251

175

200

225

250

275

300

 (nm) Figure 8. Absorption spectra obtained at the OT-LC-𝜔PBE/6-31+G(d) level for EPN in gas phase (Gas), implicitly in aqueous solution (PCM), and explicitly in aqueous solution (water). Gas and PCM geometries of EPN were optimized at the same level of theory, whereas in-water was selected as the configuration from an uncorrelated CPMD snapshot. EPN experimental absorption maximum values in water are 280 and 220 nm.84 Inspection of Figure 8 shows that the static Gas phase (PCM) spectrum strongly under(over)estimates the absorbance intensity at the longest wavelength band, and PCM did not properly represent the global spectral shape that almost merges (the longer wavelength band is only a shoulder) the two characteristic absorption bands. For the calculated spectrum in water, however, the CPMD simulation reproduces the relative intensity of both absorption bands quite well. Additionally, the relative intensities of the two characteristic bands resemble the experimental spectrum, and the position of the 𝜆𝑚𝑎𝑥 obtained from the CPMD simulation is also


26

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very close (𝜆𝑚𝑎𝑥 = 276𝑛𝑚) to the experimentally measured one, especially for the longest wavelength band (𝜆𝑚𝑎𝑥 = 280𝑛𝑚), even though it is only a particular snapshot taken from Figure 7. In Figure S4 we overlay the EPN geometries in gas phase as well as with explicit water to highlight the most striking difference in each environment. It turns out that in the atomistic solution, specific solute-solvent interactions do not favor the intramolecular hydrogen bond between the two catechol hydroxyls, which evidently takes place in isolated single molecule calculations. These results suggest that the geometry in a complex environment such as explicit solvent has a strong influence, in addition to the electronic polarization effects, which shows the ability of CPMD to foreshadow real solvent effects on the optical properties of organic chromophores. To investigate the nature of the 𝑆0 → 𝑆1 vertical excitation even further, we analyzed the charge transfer properties of the EPN in water by calculating the indices of Le Bahers et al.65 and Cortona et al.,86 𝐷𝐶𝑇 , 𝑆, 𝑡(𝑥, 𝑦, 𝑧), and ∆𝑟, which measure, respectively, the distance between the two centroids (hole and electron), overlap between hole and electron distributions, the separation degree of hole and electron densities, and the charge-transfer length during electron excitation. For the best appreciation of the electron-hole distribution, see Figure S5 in the SI file. These indices were calculated with the optimally tuned value of the 𝜔 parameter (from CPMD solvated EPN) at the OT-LC-𝜔PBE/6-31+G(d) level, to be, respectively, 𝐷𝐶𝑇 = 0.71⁡Å, 𝑆 = 0.36, 𝑡(𝑥, 𝑦, 𝑧) = −0.76Å, −1.04Å, −1.37Å, and ∆𝑟 = 1.58Å. Clearly, there is some spatial extent in which hole and electron densities overlap (𝑆 = 0.36), indicating that 𝑆0 → 𝑆1 mode is a local excitation (LE) and, as shown in Figure S5, both hole and electron densities are essentially located over the catechol moiety in EPN. The remaining quantities also point to the same direction, with significantly small 𝐷𝐶𝑇 and ∆𝑟 < 2Å (this threshold was suggested in the original paper)86, and the


27


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𝑡(𝑥, 𝑦, 𝑧) index is negative in all directions, so the separation of electron and hole is not clear (LE excitation). 4. Conclusions In this study we have drawn attention to the explicit solvation treatment of an aqueous solution of the neurotransmitter epinephrine, aiming at improving the description of the electronic absorption spectrum. To achieve this goal, Car-Parrinello Molecular Dynamics of one epinephrine molecule solvated by 104 water molecules was performed. By means of the pair radial distribution function, we obtained well-defined solvation shells, especially in the surroundings of EPN’s atomic sites that are more favorable to establishing intermolecular hydrogen bonds. The mean residence time was also determined and showed that every hydroxyl and aminic fragment is significantly surrounded by water molecules, showing a coordination number of at least 1, i.e., the water molecules interact appreciably. From the CPMD results, we carefully selected 52 uncorrelated snapshots to average the absorption spectrum of EPN in water, by superimposing all excitation modes on a single spectrum, which was then convoluted by a Gaussian function with HWHM of 0.4eV. The excitations were calculated at the LC-𝜔PBE/6-31+G(d) level of theory, and the range separation parameter for EPN was optimized in the presence of the solvent molecules using the gap-tuning scheme. We demonstrated that the use of the optimally-tuned LC-𝜔PBE improved the overall performance of the simulated spectrum with respect to the experimentally determined results. We note that not only the relative intensities between the bands was reproduced, but also the 𝜆𝑚𝑎𝑥 position. Moreover, we observed that this improvement of the photophysical properties can be attributed to the more realistic geometry of the EPN in solution, which reflects the strong thermal spectroscopic conformational dependence. Finally, we conclude that our fully ab initio


28

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statistical approach considers thermal effects retrieved from CPMD simulations, enhancing the UV-vis spectrum of EPN over any static approach (vacuum or implicit solvation).

ASSOCIATED CONTENT Supporting Information. Graphical information about the optimization of the LC-𝜔PBE in gas phase, water PCM, and explicitly solvated EPN. Overlay of the optimized EPN geometry in gas phase and explicitly solvated in water. Hole and electron densities of the 𝑆0 → 𝑆1 excitation for EPN in water. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions All authors contributed equally. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The work at the Universidade de Brasília was funded by Conselho Nacional de Desenvolvimento Cientifíco e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento Pessoal de Nível Superior (CAPES), and Fundação de Apoio à Pesquisa do Distrito Federal (FAP-DF). The work at the


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