Abstract

Ten density functionals that include CAM-B3LYP, LC-wPBE, M11, M11L, MN12L, MN12SX, N12, N12SX, wB97X and WB97XD in connection with the Def2TZVP basis set and the SMD solvation model (water as a solvent) have been assessed for the calculation of the molecular structure and properties of seven key chromophores formed by nonenzymatic browning of hexoses and L-alanine. The chemical reactivity descriptors for the systems are calculated via the Conceptual Density Functional Theory. The choice of active sites applicable to nucleophilic, electrophilic as well as radical attacks is made by linking them with Fukui functions indices, electrophilic Parr functions, and condensed dual descriptor ∆f(r). The study found the MN12SX and N12SX density functionals to be the most appropriate in predicting the chemical reactivity of this molecule.

Keywords:Key chromophores; Conceptual DFT; Chemical reactivity; Colored maillard reaction Products; Parr functions; Dual descriptor

Introduction

As pointed out by Rizzi [1] “Visual color in processed foods is largely due to colored products of Maillard or nonenzymic browning reactions. In spite of the longstanding aesthetic and practical interest in Maillard derived food coloring materials, relatively little is known about the chemical structures responsible for visual color”. These chemical structures are known as Colored Maillard Reaction Products and can be isolated at intermediate stages during the melanoidin formation process. Besides their interest as dye molecules which may be useful as food additives, but also as dyes for dye-sensitized solar cells (DSSC), these compounds have also antioxidant capabilities. Thus, they are amenable to be studied by analyzing their molecular reactivity properties. Some of these isolated molecules are called key chromophores which are formed by nonenzymatic browning of hexoses and L-alanine [2], and we believe that it could be of interest to study their molecular reactivity by using the ideas of Conceptual DFT, in the same way of our previous works [3-33]. Thus, in this computational study we will assess ten density functionals in calculating the molecular properties and structures of the seven key chromophores. Following the same ideas of previous works, we will consider fixed RSH functional instead of the optimally-tuned RSH density functionals that have attained great success [34-53].

Theoretical Background

The theoretical background of this study is similar to the previous con- ducted research presented [3-33], and will be shown here for complete purposes, because this research is a component of a major project that it is in progress. If we consider the KID procedure presented in our previous works [3-33] together with a finite difference approximation, then the global reactivity descriptors can be written as:

Table 1 : where εH and εL are the energies of the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO), respectively.

Table 2 : Applying the same ideas, the definitions for the local reactivity descriptors are:

where ρN+1(r), ρN(r), and ρN-1(r) are the electronic densities at point r for the system with N+1, N, and N−1 electrons, respectively, and ρsrc(r) and ρsra(r) are related to the atomic spin density (ASD) at the r atom of the radical cation or anion of a given molecule, respectively [68].

Settings and Computational Methods

Following the lines of our previous work [3-33], the computational studies were performed with the Gaussian 09 [69] series of programs with density functional methods as implemented in the computational package. The basis set used in this work was Def2SVP for geometry optimization and frequencies, while Def2TZVP was considered for the calculation of the electronic properties [70, 71]. All the calculations were performed in the presence of water as the solvent by doing Integral Equation Formalism-Polarized Continuum Model (IEF-PCM) computations according to the solvation model density (SMD) solvation model [72].

For the calculation of the molecular structure and properties of the studied systems, we have chosen ten density functionals which are known to consistently provide satisfactory results for several structural and thermodynamic properties

Table 3 : In these functionals, GGA stands for generalized gradient approximation (in which the density functional depends on the up and down spin densities and their reduced gradient) and NGA stands for non-separable gradient approximation (in which the density functional depends on the up/down spin densities and their reduced gradient, and also adopts a non-separable form).

Results and Discussion

The molecular structure of the seven key chromophores were built with the aid of a graphical molecular viewer starting from their IUPAC names. The pre-optimization of the systems was done using random sampling that involved molecular mechanics techniques and inclusion of the various torsional angles via the general MMFF94 force field [82-86] through the Marvin View 17.15 program that constitutes an advanced chemical viewer suited to multiple and single chemical queries, structures and reactions (https://www.chem axon.com). Afterwards, the structures that the resultant lower-energy conformers assumed for these molecules were re-optimized using the ten density functionals mentioned in the previous section together with the Def2SVP basis set as well as the SMD solvation model using water as the solvent. A graphical representation of these molecular structures is presented in [Figure 1].

Figure 1 : A graphical representation of the optimized molecular structures of the seven key chromophores: a) Key1, b) Key2a, c) Key2b, d) Key3, e) Key4a, f) Key4b, and g) Key5.

The analysis of the results obtained in the study aimed at verifying that the KID procedure was fulfilled. On doing it previously, several descriptors associated with the results that HOMO and LUMO calculations obtained are related with results obtained using the vertical I and A following the ∆SCF procedure. A link exists between the three main descriptors and the simplest conformity to the Koopmans’ theorem by linking with -I, εLwith -A, and their behavior in describing the HOMO-LUMO gap as JI = |εH+Egs(N-1) - Egs(N)|, JA = |εL+Egs(N) - Egs(N+1)|, and JHL = √(JI2+JA2 ) . Notably, the JA descriptor consists of an approximation that remains valid only when the HOMO that a radical anion has (the SOMO) shares similarity with the LUMO that the neutral system has. Consequently, we decided to design another descriptor ∆SL, to guide in verifying how the approximation is accurate.

The results of the calculation of the electronic energies of the neutral, positive and negative molecular systems (in au) of PPA, the HOMO, LUMO and SOMO orbital energies (also in au), JI, JA, JHL and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as a solvent simulated with the SMD parametrization of the IEF-PCM model for the seven key chromophores are presented in [Tables 1 to 7] of the Supplementary Materials. As presented in previous works [3-33], we consider four other descriptors that analyze how well the studied density functionals are useful for the prediction of the electronegativity , the global hardness , and the global electrophilicity , and for a combination of these Conceptual DFT descriptors, considering only the energies of the HOMO and LUMO or the vertical I and A: Jχ = |χ-χK|, Jη = |η-ηK|, Jω= |ω-ωK|, and JCDFT = √(Jχ2+Jη2+Jω2) , where CDFT stands for Conceptual DFT. The results of the calculations of Jχ,Jη,Jω and JCDFT for the low-energy conformers of the seven key chromophores in water are displayed in [Tables 8] to 14 of the Supplementary Materials.

Table 1 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key1 chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 2 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key2a chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 3 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key2b chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 4 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key3 chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 5 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key4a chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 6 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key4b chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

As [Tables 1 to 14] of the Supplementary Materials provide, the KID procedure applies accurately from MN12SX and N12SX density functionals that are range-separated hybrid meta-NGA as well as range-separated hybrid NGA density functionals respectively. In fact, the values of JI, JA, JHL are actually not zero. Nevertheless, the results tend to be impressive especially for the MN12SX density functional. As well, the ∆SL descriptor reaches the minimum values when MN12SX and N12SX density functionals are used in the calculations. This implies that there are sufficient justifications to assume that the LUMO of the neutral approximates the electron affinity. The same density functionals follow the KID procedure in the rest of the descriptors such as Jχ,Jη,Jω and JCDFT. As a summary of the previous results, the global reactivity descriptors for the seven key chromophores calculated with the MN12SX/Def2TZVP model chemistry in water are presented in [Table 15].

Table 7 : Electronic energies of the neutral, positive, and negative molecular systems (in au) of the Key5 chromophore, the HOMO, LUMO, and SOMO orbital energies (also in au); and JI, JA, JHL, and ∆SL descriptors calculated with the ten density functionals and the Def2TZVP basis set using water as solvent simulated with the SMD parametrization of the IEF-PCM model.

Table 8 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key1 chromophores in water.

Table 9 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key2a chromophore in water.

Table 10 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key2b chromophores in water.

Table 11 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key3 chromophores in water.

Table 12 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key4a chromophores in water.

Table 13 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key4b chromophore in water.

Table 14 : J𝜒, J𝜼, J𝜔 and JCDFT for the Key5 chromophore in water.

The calculations of
are done by using the Chemcraft molecular analysis program to extract the Mulliken and NPA atomic charges [87] beginning with single-point energy calculations involving the MN12SX density functional that uses the Def2TZVP basis set in line with the SMD solvation model, and water utilized as the solvent. Considering the potential application of the key chromophores as antioxidants, it is of interest to get insight into the active sites for radical attack. A graphical representation of the radical Fukui function f0 for the seven key chromophores calculated with the MN12SX/Def2TZVP model chemistry in water is presented in [Figure 2].

Figure 2 : A graphical schematic representation of the radical Fukui function f0 over the atomic sites of the seven key chromophores: a) Key1, b) Key2a, c) Key2b, d) Key3, e) Key4a, f) Key4b, and g) Key5.

The condensed electrophilic and nucleophilic Parr functions Pk- and Pk+ over the atoms of the seven key chromophores in water have been calculated by extracting the Mulliken and Hirshfeld (or CM5) atomic charges using the Chemcraft molecular analysis program [87] starting from single-point energy calculations of the ionic species with the MN12SX density functional using the Def2TZVP basis set in the presence of the solvent according to the SMD solvation model. The results for the condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) are displayed in [Tables 16 to 22] for the seven key chromophores in water. The results from [Tables 16 to 22] show that the MN12SX/Def2TZVP/SMD(water) model chemistry is
able to predict accurately the electrophilic and nucleophilic sites of the seven key chromophores studied here. Moreover, there is a nice match between the predictions coming from the Dual Descriptor and from the Parr functions.

Table 15 : Global reactivity descriptors for the seven key chromophores calculated with the MN12SX density functional using water as the solvent simulated with the SMD solvation model.

Table 16 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key1 chromophore in water.

Table 17 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key2a chromophore in water.

Table 18 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key2b chromophore in water.

Table 19 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key3 chromophore in water.

Table 20 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key4a chromophore in water.

Table 21 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key4b chromophore in water.

Table 22 : The condensed dual descriptor calculated with Mulliken atomic charges ∆fk(M), with NPA atomic charges ∆fk(N), the electrophilic and nucleophilic Parr functions with Mulliken atomic charges Pk-(M) and Pk+(M), and the electrophilic and nucleophilic Parr functions with Hirshfeld (or CM5) atomic charges Pk-(H) and Pk+(H) for the Key5 chromophore in water.

Conclusion

Ten fixed RSH density functionals, including CAM-B3LYP, LC-wPBE, M11, N12, M11L, MN12L, N12SX, MN12SX, wB97X and wB97XD, were examined to determine whether they fulfill the empirical KID procedure. The assessment was conducted by comparing the values from HOMO and LUMO calculations to those generated by the ∆SCF technique for the seven key chromophores derived from the reaction between hexoses an L-alanine in water. This is a compound which is of academic as well as industrial interest. The study has observed that the range-separated and hybrid meta-NGA density functionals tend to be the most suited in meeting this goal. Thus, they can be suitable alternatives to density functionals where the behavior of the same are optimally tuned using a gap-fitting procedure. They also exhibit the desirable prospect of benefiting future studies aimed at understanding the chemical reactivity of colored melanoidins with larger molecular weights when reducing sugars react with proteins and peptides. From the results of this work, it becomes evident that it is easy to predict the sites of interaction of the seven key chromophores under study. This involves having DFT-based reactivity descriptors, including Parr functions and Dual Descriptor calculations. Evidently, the descriptors are useful in characterizing and describing the preferred reactive sites. They are also useful in comprehensively explaining the reactivity of the molecules.

Acknowledgement

This work has been partially supported by CIMAV, SC and Consejo Nacional de Ciencia y Tecnología (CONACYT, Mexico) through Grant 219566-2014 for Basic Science Research. Daniel Glossman-Mitnik conducted this work while a Visiting Lecturer at the University of the Balearic Islands from which support is gratefully acknowledged. This work was cofunded by the Ministerio de Economía y Competitividad (MINECO) and the European Fund for Regional Development (FEDER) (CTQ2014-55835-R).