Impacts of Solvent Effect on Descriptors in Density Functional Reactivity Theory: The Case of Coumarin

RONG Chun-ying, LIAN Shi-xun, LIU Shu-bin,2

(1. Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), National and Local Joint Engineering Laboratory for New Petro-Chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha 410081, China;2. Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, United States)

Impacts of Solvent Effect on Descriptors in Density Functional Reactivity Theory: The Case of Coumarin

RONG Chun-ying1, LIAN Shi-xun1, LIU Shu-bin1,2*

(1. Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), National and Local Joint Engineering Laboratory for New Petro-Chemical Materials and Fine Utilization of Resources, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha 410081, China;2. Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, United States)

Behaviors of the coumarin molecule in non-polar and polar solvents were investigated in this work from the perspective of density functional reactivity theory (DFRT). It was revealed that its structure and reactivity properties are directly related to the dielectric constant correlative factor (ε-1)/(2ε+1), where ε is the dielectric constant. A few structural properties and charge distributions are linearly correlated with this factor in both non-polar and polar solvents. However, completely different relationships for the DFRT descriptors have been discovered in non-polar and polar solvent. Linear correlations were unveiled in non-polar solvents, but these relationships become quadratic in polar solvents. The possible underlying causes for these behavior differences were discussed. This work should shed light on understanding the overall impact of solvent effects on reactivity descriptors.

density functional reactivity theory; solvent effect; coumarin; dielectric constant

It is well known that reactivity indices from density functional reactivity theory (DFRT) are conceptually insightful, and have been widely used to study the structural and electronic properties molecules. The electron distribution of a molecule in gas phase will be markedly altered by the presence of solvent surroundings when the molecule is placed into a solvent with a different polarity. Iida et al.[1]investigated systematically the orbital energy shift in polar solvent. Sanjukta et al. studied the unusual behaviors of photophysical properties for coumarin in nonpolar and polar solvents[2-3]. Chang[4]discussed the DFT-based linear salvation energy relationships for the infrared spectral shifts of aceton in polar and nonpolar organic solvents. Kar et al.[5]studied the influence of aprotic and protic solvents with different dielectric constants on the reactivity of model systems. Recent reviews by Tomasi and Reichardt[6-7]are available in the literature. However, a systematic study on the changing behaviors of DFRT descriptors in different solvents with different polarity is still lacking.

Scheme 1 The structure of the couramin molecule and the serial number of atoms. Carbon, hydrogen and oxygen atoms are denoted by gray, white and red colors, respectively

In this work, we will look into the different behavior of DFRT descriptors in different solvents with different polarity. We choose coumarin as the system to be investigated, which serves as the prototype for aromatic systems with varied dipole moments, as shown in Scheme 1.

Coumarin is of medical importance in clinics as the precursor for several anticoagulants, notably warfarin, and is used as a gain medium in some dye lasers as well. It has a typically conjugated structure, in which the bigπstructure could be readily polarized by surrounding solvent molecules. We will consider two kinds of solvents, non-polar and polar. The main goal of this work is to compare different behaviors of DFRT indices in different solvents for coumarin from the conceptual DFT viewpoint, where we will show that significantly different behaviors are observed.

In DFRT, well-known reactivity indices include the chemical potentialμ[8-10], global hardnessη[11-12], and electrophilicity indexω.[13]In chemical language, chemical potentialμmeasures the escaping tendency of electrons from a system, and the chemical hardnessηis resistance of the chemical potential to change in the number of electrons. The corresponding analytical definitions are defined as follows:

(1)

(2)

whereEis the total energy of the system,Nis the number of electrons in the system,vis the external potential, andIandAis the first ionization potential and electron affinity, respectively.χis another widely used chemical concepts, called electronegativity, which quantifies the intrinsic capability of an atom or a functional group to attract electrons towards itself. Here, the first ionization potentialIcan be obtain byI=EN-1-ENand electron affinityAbyA=EN+1-ENwithEN+1,EN-1, andENdenoting the total energies of the system withN+1,N-1 andNelectrons, respectively. In addition, using Koopmans’ theorem as an approximation, the ionization energy and the electron affinity can be replaced by the frontier molecular orbital energies HOMO (EHOMO) and LUMO (ELUMO) respectively, within the single-determinant wave-function approximation such as the Hartree-Fock theory or Kohn-Sham scheme, yielding[14]

(3)

η=ELUMO-EHOMO.

(4)

In 1999, prompted by an earlier proposal by Maynard et al. the concept of electrophilicity indexωwas quantitatively introduced by Parr, Szentpaly, and Liu[13]as the stabilization energy when atoms or molecules in their ground states acquire maximal electronic charge from the environment. Electrophilicity indexωwas proposed in terms ofμandηto measure of the electrophilicity of an electrophile:

(5)

Reviews about these quantities are available in the literature[14-17].

From the polarity perspective, there are two categories of solvents, polar and nonpolar. In a polar solvent, the solvent effect is mainly caused by the change for the charge density of the solute, which can subsequently polarize the solvent with this polarization effect feeding back onto the solute. In a non-polar solvent, solvent molecules have no permanent dipole moments, but their fluctuating dipole moment can polarize its neighbor, giving rise to the so-called inductive interaction. Besides, the dispersive solute-solvent interaction becomes important in non-polar solvent. When we talk about the solvent effect, the quantity that matters the most is the dielectric constantεof a solvent. The dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space. The quantity that measures of the effective impact of different dielectric constants of a solvent is (ε-1)/(2ε-1). We will employ this quantity in this work to investigate the different behavior of DFRT descriptors in both polar and nonpolar solvents. We use water as the example of the polar solvent and hexane as the example of a nonpolar solvent.

We examined the following 8 non-polar solvents, including toluene (C6H5-CH3), benzene (C6H6), carbontetrachloride (CCl4), cyclohexane, heptane (C7H16), xenon (Xe), krypton (Kr) and argon (Ar). We take water as the example of a polar solvent, and designed its dielectric constant to vary from 2.0 to 79.0. We optimized the structure of coumarin in various solvents at the B3LYP/6-311+G(d) level of theory. The polarizable continuum model (PCM) of Tomasi[16]was employed as the continuum solvent self-consistent reaction field methods. All calculations were conducted using Gaussian 09 package version D01[18], with tight SCF convergence and ultra-fine integration grids. Atomic units are used throughout if unspecified.

Shown in Tab.1 are dipolar moments and frontier orbitals of coumarin in different solvents, polar and nonpolar, with different dielectric constants. As we can see from the Table, in the nonpolar solvents, as the dielectric constant becomes smaller, the dipole moment also decreases, and the HOMO/LUMO energy values become lower (with larger absolute values) as well. The same trend is true for polar solvents (e.g., water in this study), where, as the dielectric constant decreases, so do the dipole moment and frontier orbitals. This is because as the dielectric constant becomes smaller, the interaction of solvent molecules with coumarin will decrease, thus rendering a smaller dipole moment. The dielectric constant is a quantity measuring the ability of a substance to store electrical energy in an electric field, which is represented by the ratio of the permittivity of a substance to the permittivity of free space. As the dielectric constant decreases, the electric flux density also decreases. This enables objects of a given size to hold their electric charge for shorter periods of time, and/or to hold smaller quantities of charge, leading to the decrease in dipole moments and frontier orbital energies.

Tab.1 A few selected electronic properties of coumarin in different nonpolar and polar solvents with different dielectric constants

Fig.1 Relationships of couramin’s structure properties vs (ε-1)/(2ε+1) in nonpolar solvents (plot a and b) and in polar water solvent (c and d)

However, there are other properties, which are heavily dependent on the solvent type and whose behaviors could be significantly different in different solvents. Fig.2 shows the profiles of 4 different electronic properties of coumarin in the cyclohexane solvent, including (a) HOMO, (b) LUMO, (c) hardnessηand (d) electrophilicity indexω. We find that HOMO, LUMO and electrophilicity index are positively proportional to the (ε-1)/(2ε+1) factor. The larger this factor, the larger these reactivity descriptors. For the electrophilicity index, however, it decreases as the factor becomes larger. Since hardness is an indicator of chemical stability and the electrophilicity index is a descriptor of chemical reactivity, these results suggest that as the (ε-1)/(2ε+1) factor increases, the molecule becomes more stable and less reactive.

Fig.2 Linear relationships of couramin’s DFRT index vs (ε-1)/(2ε+1) in nonpolar solvents

In polar solvents, these four electronic properties demonstrate completely different behaviors, as shown in Fig.3. As we can see from the Figure, all linear relationships are gone. Instead, quadratic relationships are observed. As the (ε-1)/(2ε+1) factor increases, HOMO, LUMO and hardness initially increases, reaches to a maximum value, and then starts to decrease. For the electrophilicity index, it decreases first, reaches to a minimum, and then bounces back. These behaviors are qualitatively different from those observed in the nonpolar solvent shown in Fig.3. The reason behind these markedly different behaviors comes from the different electrostatic interaction nature between the solute and solvent molecules in polar and nonpolar solvent environments.

Fig.3 Quadratic relationships of DFRT indexes vs (ε-1)/(2ε+1) in water

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(编辑 杨春明)

2014-05-15

湖南省自然科学基金资助项目(12JJ2029); 湖南省高校创新平台开放基金资助项目(12K030); 湖南省高校科技创新团队支持计划资助项目(湘教通[2012]318号)

O211.62

A

1000-2537(2014)05-0031-06

溶剂效应对香豆素模型分子中密度泛函活性指标的影响

荣春英1，廉世勋1，刘述斌1,2*

(1.湖南师范大学化学化工学院，化学生物学及中药分析教育部重点实验室，石化新材料与资源精细利用国家地方联合工程实验室，中国 长沙 410081； 2.北卡罗来纳大学超算中心，美国 北卡罗来纳州教堂山市 27599-3420)

运用密度泛函活性理论研究了香豆素在非极性和极性溶剂中的行为和规律．结果表明香豆素的分子结构和活性指数与溶剂介电常数ε相关因子 (ε-1)/(2ε+1)直接关联．在非极性和极性溶剂中一些结构参数和电荷分布数与该因子成良好的线性关系，但密度泛函活性指标与相关因子却存在完全不同的相关性．在非极性溶剂中它们是线性相关关系，而在极性溶剂中它们表现出二次方的相关性．本文讨论了这种行为差异存在的可能内在原因，为理解溶剂效应对活性指数的全面影响提供理论依据．

密度泛函活性理论；溶剂效应；香豆素；介电常数

*

,E-mail：shubin@email.unc.edu