Solvatochromism and Preferential Solvation of Brooker'

WWW.C-CHEM.ORG FULL PAPER Solvatochromism and Preferential Solvation of Brooker’s Merocyanine in Water–Methanol Mixtures Yuichi Tanaka ,[a] Yukio Kawashima ,[b] Norio Yoshida ,*[a] and Haruyuki Nakano *[a] The excitation energy of Brooker’s merocyanine in water–methanol revealed preferential solvation by methanol. The free energy com- mixtures shows nonlinear behavior with respect to the mole frac- ponent analysis implied that solvent reorganization and solvation tion of methanol, and it was suggested that this behavior is related entropy drive the preferential solvation by methanol, while the to preferential solvation by methanol. We investigated the origin of direct solute–solvent interaction promotes solvation by water. The this behavior and its relation to preferential solvation using the difference in the preferential solvation effect on the ground and three-dimensional reference interaction site model self-consistent excited states causes the nonlinear excitation energy shift. VC 2017 field method and time-dependent density functional theory. The Wiley Periodicals, Inc. calculated excitation energies were in good agreement with the experimental behavior. Analysis of the coordination numbers DOI: 10.1002/jcc.24902 Introduction (QM/MM),[9] which is widely used to investigate both the electronic structure of the solvated molecule and the solvation Preferential solvation, a phenomenon whereby a solute is structure. In this method, the solvent environment is treated as an solvated more preferentially by one solvent than by others, explicit molecule with a classical force field placed around the usually occurs in a mixed solvent, and the local mole fractions solute molecule based on the configuration sampling by of a solvent around the solute differ from the bulk mole molecular dynamics simulation. Frutos-Puerto et al.[10] investi- [1] fractions. Preferential solvation has attracted the attention of gated the solvatochromic shift of p-nitroaniline in cyclohexane– researchers because many chemical reactions and biological triethylamine mixtures using a mean-field QM/MM method.[11–13] processes occur in a mixed solvent, and the environment The computed excitation energies were in good agreement with around a solute has a large influence on the reaction and the experiments, showing the nonlinear behavior of the excitation [2–6] physical properties. energy with respect to the mole fraction. The solvent composition The solvatochromic shift of absorption and emission spectra is surrounding p-nitroaniline was significantly different from that of strongly affected by preferential solvation because the solvation the bulk; this observation clearly indicates preferential solvation. structure near the solute molecules drastically changes the elec- Although the QM/MM method has been successfully applied to tronic structure of the solute molecules. A binary or multicompo- study the electronic structure of solvated molecules, QM/MM nent mixed solvent is useful to control the solvatochromic shift by studies of mixed solvents are not common. One reason is that the changing the mole fraction of the components. 1-Methyl-4-[(oxocy- QM/MM method requires extensive computational cost and time clohexadienylidene)ethylidene]-1,4-dihydropyridine, which is often for configuration sampling of a multicomponent solvent, espe- called Brooker’s merocyanine (BM, Fig. 1), is a famous and typical cially for dilute components, because the convergence of such solvatochromic dye that is used as a target to investigate the effects sampling is generally very slow. of preferential solvation on the solvatochromic shift because of its Another possible method for investigating solvatochromism [7] high responsiveness. in mixtures is a hybrid of the integral equation theory of liquids [8] Da Silva et al. measured the absorption spectra of BM in and electronic structure theory, such as reference interaction site binary mixtures comprising a protic solvent (water, methanol, model self-consistent field (RISM-SCF),[14–16] three-dimensional ethanol, 2-propanol, or 1-butanol) and aprotic solvent (acetoni- RISM-SCF (3D-RISM-SCF),[17] or Kohn–Sham density functional trile, dimethyl sulfoxide, or acetone) in various mole fractions. theory (KS-DFT)/3D-RISM methods.[18] These methods have In water–methanol mixtures, they obtained a nonlinear excitation energy behavior with respect to the mole fraction and [a] Y. Tanaka, N. Yoshida, H. Nakano concluded that the origin for the nonlinearity was preferential Department of Chemistry, Graduate School of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan solvation by methanol. Although the experimental observa- E-mail: [email protected], E-mail: [email protected] tions suggested a phenomenological relation between the sol- [b] Y. Kawashima vatochromic shift and the preferential solvation, the molecular- RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima- level understanding of this process is still insufficient. minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan Contract grant sponsor: JSPS KAKENHI; Contract grant numbers: Theoretical approaches are desirable to understand the 15J04698, 16K05676, 16K05519, and 15K05392; Contract grant sponsor: detailed solvation structure at a molecular level. One effective MEXT KAKENHI; Contract grant number: 16H00842 theoretical approach is quantum mechanics/molecular mechanics VC 2017 Wiley Periodicals, Inc. Journal of Computational Chemistry 2017, 38, 2411–2419 2411 FULL PAPER WWW.C-CHEM.ORG function of the solute and the distribution of the solvent (spatial distribution function [SDF], gcðÞr ; c indicates the solvent site) around the solute are determined simultaneously. The Helmholtz free energy (A) of a system is defined as the sum of the solute electronic energy (Esolute) and the excess chemical potential (Dl): A5Esolute1Dl: (1) Esolute is calculated from an electronic structure calculation: Figure 1. The molecular structure of Brooker’s merocyanine. [Color figure can be viewed at wileyonlinelibrary.com] solv solv Esolute5 < W jH^ 0jW >; (2) been successfully applied to the solvatochromism of dyes in vari- [19–22] ^ ous single component solutions. An advantage of the where H0 is the Hamiltonian of the isolated solute molecule solv hybrid method is that it is easily applicable to multicomponent and W is the electronic wave function of the solute mole- solutions because the integral equation theory of liquids allows cule in solution. Dl is calculated from the following equation: one to obtain the solvation structure of multiple components ð X X ÀÁÀÁ 1 2 1 from the complete ensemble average based on statistical Dl5kBT q dr hcðÞr H 2hcðÞr 2ccðÞr 2 hcðÞr ccðÞr ; m m c2m 2 2 mechanics. Pioneering work to investigate the electronic structure of molecules in a mixed solvent using the hybrid methods (3) was done by Hayaki et al.[23]; they performed a theoretical analy- where kB and T indicate the Boltzmann constant and the abso- sis of a Diels–Alder reaction in ionic liquids. Following their work, lute temperature, respectively, and q is the number density of many works have been devoted to chemical reactions in ionic m solvent species m. The functions hcðÞr 5gcðÞr 21 and ccðÞr are liquids,[24–28] electrolyte solutions,[29–31] and water–organic the 3D total and direct correlation functions of solvent site c, mixed solvents.[32] For all these studies, the RISM/3D-RISM-SCF respectively, and HðÞx is the Heaviside step function. To derive and extended hybrid methods gave reasonable results and eq. (3), we applied the Kovalenko–Hirata (KH) closure[18]: reproduced the nature of the chemical reactions in mixed ( ÀÁ solvents. exp 2ucðÞr =kBT1hcðÞr 2ccðÞr 21forhcðÞr 0 In the present study, we investigated the solvatochromism hcðÞr 5 ; of BM in water–methanol mixtures using the 3D-RISM-SCF 2ucðÞr =kBT1hcðÞr 2ccðÞr for hcðÞr > 0 method and TD-DFT to clarify the details of preferential solva- (4) tion of BM (as suggested by Da Silva et al.[8]) at the molecular where u ðÞr is the interaction potential between the solute level. Although both water and methanol are protic solvents, c molecule and solvent site c. 3D correlation functions can be their abilities to form hydrogen bonds are different because obtained by solving the 3D-RISM equation [eq. (5)] coupled water has two hydroxyl hydrogen atoms while methanol has with the KH closure [eq. (4)]: one hydroxyl hydrogen atom and one methyl group. We performed 3D-RISM-SCF calculations and obtained the excitation vv vv h ðÞr 5c 0 ðÞÃr x 0 ðÞr 1q h 0 ðÞr ; (5) energy changes for BM as well as the spatial distribution of c c c c m c c the solvent in various mole fractions of water–methanol mix- vv vv where x 0 ðÞr and h 0 ðÞr are the site–site intramolecular and tures. From the results, we examined the relation between the cc cc total correlation functions of the solvent, respectively (super- solute–solvent interactions and coordination numbers (CNs) to script “v” denotes the solvent). The symbol * indicates convo- theoretically clarify the origin of the excitation energy behavior lution in direct space and summation over repeated site (i.e., preferential solvation or not). A free energy component indices. Before the 3D-RISM calculation, we need to solve the analysis for the solvation structure was also performed to dis- (1D) RISM equation between the solvent molecules [eq. (6)] cuss the mechanism of preferential solvation. vv and obtain hcc0 ðÞr in eq. (5): Computational Methods vv vv vv vv vv

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