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In this study, Density Functional Theory including a dispersion correction is employed to model and analyze the structural, electronic and local reactivity of the (100) surface of felodipine. The surface energy calculated at the Generalized Gradient Approximation ( GGA) level, along with plane waves as basis set and ultrasoft pseudopotentials, shows that the (100) surface is the most stable as compared to the (010) and (110) ones. In particular, we have focused on performing a quantitative study of the reactivity of the surface by means of the Fukui function and through the HOMO and LUMO populations. Our results can be related to some applications in the pharmaceutical chemistry of this compound.

The chemical reactivity of a compound can be interpreted as the resistance or ease with which it attracts or gives away electrons under the action of an external potential v(r). In this sense, there are global parameters that allow us to characterize this electron transfer from a theoretical point of view, such as the electronic chemical potential (μ) [

Felodipine (FD), (methyl-4-(2,3-dichlorophenyl)-1,4-dihydro-2,6-dimethyl- 3,5-pyridinedicarboxylate), shown in

Four crystalline forms of FD have been reported [

of the system to a simultaneous disturbance in the number of electrons N, may be useful to characterize the reactivity of crystals with respect to crystal packing [

The compounds of the group of 1,4-DHP drugs undergo hepatic metabolization (by which the oxidation of 1,4-dihydropyridines in pyridines occurs) catalyzed by the CYP3A enzyme of cytochrome P450 [

There are many computational approaches that attempt to explain the process of metabolism. Some of them use statistical models in molecular descriptors [

Felodipine shows a particularly rich variety of metabolites [

In this report we investigate how crystal morphology can relate to properties of FD. The novelty of this work lies in studying the surfaces (100), (010) and (001), especially the first one, with supercells to model the periodic systems, based on DFT with the Generalized Gradient Approximation (GGA) and a dispersion correction as formulated by Tkatchenko and Scheffler (TS). By using the FF the most reactive sites of the surfaces to electrophilic species are described.

We will lay the basic definitions of the global descriptors according to DFT. The energy E is expressed in terms of the number of electrons N and an external potential v(r), so that E [ ρ ( r ) ] ≡ E [ N , v ( r ) ] , where ρ ( r ) is the electronic density [

f ( r ) = ( δ μ δ v ( r ) ) N = ( ∂ ρ ( r ) ∂ N ) v ( r ) = ( ∂ 2 E ∂ N ∂ v ( r ) ) (1)

Equation (1) presents a discontinuity problem in atoms and molecules when combined with the finite difference approximation, resulting in expressions of the FF [

f + ( r ) = ( ∂ ρ ( r ) ∂ N ) v ( r ) + ≈ [ ρ N + 1 ( r ) − ρ N ( r ) ] ≈ ρ L ( r ) ,

f − ( r ) = ( ∂ ρ ( r ) ∂ N ) v ( r ) − ≈ [ ρ N ( r ) − ρ N − 1 ( r ) ] ≈ ρ H ( r ) (2)

when a molecule accepts electrons, they tend to move around places where f + ( r ) is large because at these locations the molecule is most likely to stabilize additional electrons, and therefore, it is susceptible to nucleophilic attack at such sites. Likewise, a molecule is susceptible to electrophilic attack at sites where f − ( r ) is large, since these are the regions where electron removal least destabilizes the molecule. In chemical density functional theory, the FF are the key of region selectivity indicators for electron-transfer controlled reactions. The function quantification is possible through a system of condensation on an atomic region, where FF can be written by using population analysis techniques [

f k + = ∫ k [ ρ N + 1 ( r ) − ρ N ( r ) ] = [ q k ( N + 1 ) − q k ( N ) ] ,

f k − = ∫ k [ ρ N ( r ) − ρ N − 1 ( r ) ] = [ q k ( N ) − q k ( N − 1 ) ] (3)

where q k ( N ) denotes the electronic population of atom k of the reference system, more correctly called q k ( N 0 ) .

The Fukui functions favourably determinate the reactive sites for most chemical systems. However, the values of the FF rely upon the scheme chosen to calculate the charges and the accuracy of the population analysis used. In this study the Hirshfeld method was used [

The evaluation of the surface energies of the crystalline faces can be useful to compare how the resistance of different surfaces affects the kinetics of the reaction. As often observed, a solid state reaction can proceed in a specific crystallographic direction. Therefore, the study of mechanical properties on different faces can give some insight into the solid state reaction. The surface energy can be calculated as [

E s u r f = 1 2 ( E s l a b − n E b u l k ) S (4)

where E_{slab} and E_{bulk} are total energies of the surface and crystal in bulk, respectively, and n is the thickness (or layers of unit cells) of the surface, and S is the surface area. In the present study, the surface energies, the electronic structures, and Fukui nuclear functions of three surfaces of the crystal form I of FD were calculated.

The crystal structure of FD, form I, was obtained from the Cambridge Structural Database (CSD) (ref code: DONTIJ). FD crystallizes in an orthorhombic lattice with space group P2(1)/c, and cell parameters a = 12.086 Å, b = 12.077 Å, c = 13.425 Å and β = 116.13˚, packed with four molecules [

A periodic solid state program was used, with DFT-D (dispersion correction) [^{−6} eV/atom. Vanderbilt pseudopotentials [^{1}, C: 2s^{2}2p^{2}, N: 2s^{2}2p^{3}, O: 2s^{2}2p^{4}, Cl: 3s^{2}3p^{5}. Surface (100) (a = 12.077 Å, b = 13.425 Å, c = 32.736 Å and α = β = γ = 90˚), Surface (010) (a = 13.425 Å, b = 12.086 Å, c = 43.082 Å and α = β = 90˚, γ = 116.13˚) and Surface (001) (a = 12.086 Å, b = 12.077 Å, c = 42.005 Å and α = β = γ = 90˚) of form I were modeled (

The electronic structure of the three surfaces of Form I of FD was studied. Also, the FF and the surface energy for each were calculated. The bulk crystal structure was optimized with the same methods that were used to calculate the FF. The network parameters were set during the optimization. Surface models of (100), (010) and (001) faces, of two unitary cells of thickness were thus constructed. On the (100) and (001) faces the rings of the pyridine are exposed on the surface unlike the face (010) where the benzyl ring together with the methyl ether group are more exposed.

We focus our attention on the (100) surface model which turned out to be the most stable, in which there are intermolecular hydrogen bonds formed by N-H-O located on the normal plane of the surface (see

Once the optimization of the geometry of the surface model (100) was carried out, it was observed that the hydrogen bonds lying on the surface tend to move downwards, along the z-axis. The above can be seen in

(100) opt Å | (100) Å | |||||
---|---|---|---|---|---|---|

Hbond | X | Y | Z | ΔX | ΔY | ΔZ |

1 | −19.040 | −2.761 | 20.663 | −0.042 | 0.092 | −0.347 |

2 | −18.892 | 4.204 | 20.663 | 0.044 | 0.093 | −0.347 |

3 | −19.041 | 11.168 | 20.663 | −0.043 | 0.092 | −0.347 |

4 | −7.072 | 2.414 | 11.860 | −0.019 | −0.031 | −0.010 |

5 | −13.092 | 3.037 | 10.810 | −0.024 | 0.006 | 0.029 |

6 | −12.807 | 10.002 | 10.810 | 0.024 | 0.025 | 0.029 |

7 | −18.826 | 9.379 | 11.860 | 0.020 | −0.030 | −0.010 |

8 | −13.092 | 16.966 | 10.810 | 0.006 | 0.029 | 0.029 |

9 | −19.107 | 16.343 | 11.860 | 0.020 | −0.031 | −0.010 |

10 | −24.842 | 10.002 | 10.810 | 0.023 | 0.025 | 0.029 |

z-axis lower than those on the surface. From the above it can be observed that surface molecules, having no interaction with other molecules in the upper part, tend to flatten the surface. This displacement of the hydrogen bonds causes an activation of the carbon atoms C2 and C4, which favors the reactivity of these atoms as shown by Fukui functions (

The FF of each atom was obtained from the calculations of the neutral and anionic forms of the surface models. The molecular structure of the anionic form remained the same as its neutral counterpart. The quantitative results of the FF for faces (100), (010) and (001) are listed in

Fukui Indices for Electrophilic Attack (Fukui ( f − )) | |||||||
---|---|---|---|---|---|---|---|

Molecule | Slab (001) | Slab (010) | Slab (100) | ||||

atom | f − | atom | f − | atom | f − | atom | f − |

C2 | 0.080 | C2 | 0.017 | C4 | 0.028 | N1 | 0.014 |

N1 | 0.079 | Cl1 | 0.016 | N1 | 0.023 | C2 | 0.014 |

C4 | 0.078 | C4 | 0.014 | C2 | 0.022 | C4 | 0.014 |

O3 | 0.055 | N1 | 0.013 | O3 | 0.021 | Cl1 | 0.010 |

O1 | 0.054 | O1 | 0.012 | Cl2 | 0.017 | O3 | 0.007 |

C1 | 0.039 | Cl2 | 0.010 | Cl1 | 0.015 | C9 | 0.007 |

the atoms N1, C1 and C4 of the pyridinic ring and the atoms O1 and O3 of the carbonyls groups in the three surfaces are larger than those of other atoms. These results agree with those reported by Michael E. Beck [

In

To elucidate the influence of mechanical resistance on chemical reactivity, the surface energies of the surface models of Form I were calculated by the DFT-D with the functional GGA, obtaining the following E_{surf}: −0.2303 eV/Å2 for (100), 0.0222 eV/Å2 for (010) and 0.0302 eV/Å2 for (001) surfaces. The latter energies remain significantly above the one for (100) surface, thus indicating a closer bond between the molecules on the faces (010) and (001). As the reaction begins on the surfaces, it is expected that their propagation and penetration in the bulk are limited by forces of intermolecular nature. The surface energy characterizes the intermolecular interactions within a crystallographic plane, specifying the mechanical resistance. Therefore, the lower surface energy of (100) may facilitate a faster reaction rate than the other two surfaces

The reaction capacity of the three analyzed surfaces of form I of felodipine was investigated by studying their electronic structures, nuclear Fukui functions and their surface energies. The present findings show that Fukui nuclear functions constitute a useful tool in the analysis of surface reactivity for a crystal such as FD. In addition, due to the highly heterogeneous nature of a molecular crystal reaction, the surface intermolecular forces ought to be taken into account to elucidate chemical reactions occurring on this type of crystals.

These results can provide information on experimental work in surface catalysis as based on theoretical knowledge of local reactivity of the compound here analyzed, thereby saving efforts when selecting the best sites a priori. Our findings may also be useful in some pharmaceutical applications of felodipine.

One of us (CTC) gratefully acknowledges a PhD fellowship granted by CONACyT (Mexico). JFRS and AFR are grateful to Sistema Nacional de Investigadores (SNI, Mexico) for provision of funds.

The authors declare no conflicts of interest regarding the publication of this paper.

Tepech-Carrillo, C., Licona-Ibarra, R., Rivas-Silva, J.F. and Flores-Riveros, A. (2019) Study of the Reactivity of (100) Felodipine Surface Model Based on DFT Concepts. Open Journal of Physical Chemistry, 9, 1-12. https://doi.org/10.4236/ojpc.2019.91001