Solvent effect on the Molecular structure and Global, Local and Dual Descriptors: A Density Functional Theory Study

 

ABSTRACT:

This study aims to explore the effects of solvent polarity on the geometry, energy of solvation, dipole moment, polarizability, charge distribution, frontier molecular orbital analysis, and global, local, and dual descriptors for β Carboline. The effects of eight solvents were treated using a conductor-like polarized continuum model. Density Functional Theory calculations were performed at B3LYP level at 6-311++g (d,p) basis set. The computed results showed that the dipole moment, polarizability, the solvation free energy, and atomic charge of β Carboline increased with the increasing polarity of the solvent. Also, the solvation modified the values of the reactivity descriptors as a result of the interaction between the solvent and β Carboline. The dual descriptor provided a clearer difference between electrophilic and nucleophilic attack at specific atomic site than presented by Fukui functions of β Carboline.

 

 

 

INTRODUCTION:

Molecules often face changes in their properties when changing their state from isolation to solution. These changes usually occur because of interactions of a long range as well as the electrostatistics of solvents. The impact of solvents on those properties can be analyzed through computational chemistry. Solvent molecules play a role in the reactivity of chemical species as well¹.

 

There are two types of solvents: polar solvents and non-polar solvents. The solvent’s polarity is measured through its dielectric constant. For instance, water has a dielectric constant of 88, hence its high polarity².

 

On the contrary, any solvent that has a dielectric constant less than 15 is non-polar. The calculations of Density Functional Theory (DFT) give detailed insights on molecular characteristics and interactions and hence of molecular properties and reactivity^3-7.

 

The goal of the present work is to study the effect of solvents on the molecular structure and chemical reactivity (global, local, and dual descriptor) of β Carboline which could potentially be helpful to understand the variation in the reactivity structure using different polarity of solvents and comparing to gas phase.

 

COMPUTATIONAL DETAILS:

During this study, a package of programs were used to do the molecular modeling calculation of β Carboline. Initially, the molecules were pre-optimized using the Molecular Mechanics force field (MM⁺) with HyperChem version 8.0⁸. After that, we calculated the geometric and electronic parameters through 6-311++ G (d,p) basis set in the gas phase, and the optimized structures have been used for subsequent calculations in eight different solvents using the conductor-like polarizable continuum model (CPCM) of solvation^9,10. DFT calculations have been performed at B3LYP level of theory which is a combination of Becke’s three-parameter hybrid exchange function^11,12 and the Lee-Yang-Parr correlation function¹³. All the calculations reported here were performed with the Gaussian 09 package¹⁴, and GaussView 5.0.8 program was used to visualize the obteined theoretical data¹⁵.

 

RESULTS AND DISCUSSION:

Structural Description:

The optimized geometrical parameters such as bond lengths, bond angles, and dihedral angles of β Carboline obtained by B3LYP/6-311++G(d,p) in gas phase and in water (H₂O), Methanol (CH₃OH), Ethanol (C₂H₅OH), Acetone (CH₃COCH₃), Chloroform (CHCl₃), Diethyl ether (C₂H₅OC₂H₅), Benzene (C₆H₆), and Cyclohexane (C₆H₁₂), in order of decreasing dielectric constant (ε= 78.36, 32.61, 24.85, 20.49, 4.71, 4.24, 2.27, and 2.02, resp.) are listed in Table 1. The effect of the solvents was added using the CPCM of solvation. The labeling of atoms in β Carboline is given in Figure 1. According to the molecular structure of β Carboline, there are mainly three different bond lengths between the different atoms such as C-C, C-N, and X-H (X: C or N). All bond lengths indicate a slight variation from -0,0027Å to 0,0038Å. The most important decrease of the valence angle is the C8-C19-H20 angle of 0.2358º with the increase in the polarity of the solvent. This decrease is due to the effect of the dielectric constant of each solvent on the charges of β Carboline atoms.

 

Indeed, the dielectric constant ε indicates the ability of a solvent to separate the charges. The higher this constant is, the more the charges are separated, and therefore the dipole moment created will decrease the angle of valence. On the other hand, an increase in valence angle H20-C19-N21 (0.3667°) in polar solvents was observed relative to the gas phase. This increase is due to the formation of intermolecular hydrogen bonds between the polar solvent molecules and the N21 atom, which increases the polarization of the C19-N21 bond. Solvents have slightly influenced the dihedral angles.

 

Fig.1: Theoretical optimized geometric structure with atoms numbering of β Carboline

 

Table 1: Optimized geometric parameters (bond lengths, bond angles and dihedral angles) of β Carboline in the gas phase and other solvents

Bond lengths	G	W	M	E	A	C	D	B	Cy
C1-C2	1.3886	1.3893	1.3893	1.3893	1.3893	1.3892	1.3892	1.3891	1.389
C2-C3	1.4059	1.4081	1.408	1.408	1.408	1.4076	1.4075	1.407	1.4069
C3-C4	1.3896	1.3901	1.3901	1.3901	1.3901	1.3901	1.3901	1.39	1.3901
C4-C5	1.3962	1.3979	1.3979	1.3979	1.3979	1.3975	1.3975	1.3971	1.3969
C5-C6	1.4187	1.4206	1.4206	1.4206	1.4205	1.4203	1.4202	1.4199	1.4198
C5-N11	1.3857	1.3838	1.3838	1.3839	1.3839	1.3843	1.3843	1.3847	1.385
C1-C6	1.3993	1.401	1.401	1.4009	1.4009	1.4005	1.4005	1.4001	1.4000
C6-C7	1.4478	1.4465	1.4465	1.4466	1.4466	1.4468	1.4469	1.4472	1.4472
C7-C8	1.4152	1.4177	1.4176	1.4176	1.4176	1.4171	1.417	1.4165	1.4164
C7-C9	1.3967	1.3974	1.3974	1.3974	1.3974	1.3972	1.3972	1.3971	1.3972
C8-N11	1.386	1.3817	1.3818	1.3819	1.3819	1.3828	1.3829	1.3839	1.3844
C8-C19	1.3947	1.3955	1.3954	1.3954	1.3954	1.3953	1.3953	1.3951	1.3949
C9-C10	1.3905	1.3901	1.3901	1.3901	1.3901	1.3902	1.3902	1.3903	1.3902
C10-N21	1.3459	1.3498	1.3497	1.3497	1.3496	1.3489	1.3488	1.3479	1.3476
C19-N21	1.3311	1.3347	1.3346	1.3346	1.3345	1.3338	1.3337	1.3328	1.3327
N11-H12	1.0062	1.0085	1.0084	1.0084	1.0083	1.0079	1.0078	1.0073	1.0072
C1-H13	1.0843	1.0842	1.0842	1.0842	1.0842	1.0842	1.0842	1.0842	1.0843
C2-H14	1.0835	1.0836	1.0836	1.0836	1.0836	1.0836	1.0836	1.0836	1.0836
C3-H15	1.0841	1.0842	1.0842	1.0842	1.0842	1.0842	1.0842	1.0842	1.0842
C4-H16	1.0842	1.0836	1.0836	1.0836	1.0836	1.0837	1.0838	1.0839	1.0839
C9-H17	1.0838	1.0835	1.0835	1.0835	1.0835	1.0836	1.0836	1.0836	1.0837
C10-H18	1.0854	1.0853	1.0853	1.0853	1.0853	1.0853	1.0853	1.0853	1.0854
C19-H20	1.0873	1.086	1.0861	1.0861	1.0861	1.0863	1.0863	1.0866	1.0868

 

Angles (°)	G	W	M	E	A	C	D	B	Cy
C1C2C3	120.6741	120.6975	120.697	120.6967	120.6964	120.6921	120.6916	120.6872	120.6774
C2C1C6	119.0688	118.9069	118.911	118.913	118.9149	118.9488	118.9534	118.9904	118.997
C2C3C4	121.4927	121.6075	121.6055	121.6032	121.6019	121.578	121.5748	121.5488	121.548
C3C4C5	117.6327	117.5549	117.5553	117.5579	117.5588	117.5752	117.5774	117.5948	117.6025
C4C5C6	121.6715	121.5974	121.5984	121.5997	121.6004	121.6139	121.6158	121.6323	121.6346
C4C5N11	129.6243	129.5336	129.5336	129.537	129.538	129.5564	129.5588	129.5786	129.58
C6C5N11	108.7042	108.8689	108.868	108.8633	108.8616	108.8297	108.8253	108.7891	108.8172
C1C6C5	119.4601	119.6359	119.6311	119.6296	119.6276	119.5919	119.587	119.5465	119.5404
C1C6C7	133.9753	133.9509	133.951	133.952	133.9524	133.9592	133.9602	133.9685	133.9696
C5C6C7	106.5646	106.4133	106.4133	106.4184	106.42	106.4488	106.4528	106.485	106.488
C6C7C8	106.734	106.6283	106.63	106.6318	106.6329	106.6531	106.6559	106.6793	106.6797
C6C7C9	135.5663	135.4864	135.4877	135.489	135.4899	135.5051	135.5072	135.5247	135.5251
C8C7C9	117.6997	117.853	117.8574	117.8791	117.8772	117.8418	117.8369	117.796	117.7103
C7C8N11	108.7574	108.9347	108.9311	108.9294	108.9277	108.8969	108.8926	108.8564	108.85
C7C8C19	120.3322	120.2679	120.27	120.2702	120.2709	120.2834	120.285	120.298	120.2946
N11C8C19	130.9105	130.7974	130.8	130.8004	130.8014	130.8197	130.8224	130.8456	130.8461
C7C9C10	117.7327	117.7183	117.7183	117.7186	117.7186	117.7207	117.7211	117.7249	117.73
C9C10N21	124.2534	124.1646	124.1646	124.1673	124.1682	124.1835	124.1857	124.2036	124.2253
C5N11C8	109.2398	109.1548	109.1551	109.1571	109.1578	109.1714	109.1734	109.1902	109.1908
C8C19N21	121.2291	121.0983	121.1	121.1023	121.1036	121.1276	121.131	121.1601	121.1652
C10 N21C19	118.7529	118.8655	118.863	118.8624	118.8615	118.843	118.8404	118.8174	118.8098
C2C1H13	120.4486	120.5135	120.5127	120.5107	120.5099	120.4944	120.4923	120.4754	120.4677
C6C1H13	120.486	120.5796	120.5763	120.5763	120.5752	120.5568	120.5543	120.5342	120.5323
C1C2H14	119.8907	119.857	119.857	119.8579	119.8582	119.8632	119.8639	119.8698	119.8701
C3C2H14	119.4352	119.4455	119.4455	119.4455	119.4454	119.4447	119.4445	119.443	119.4425
C2C3H15	119.322	119.2821	119.2821	119.2833	119.2837	119.2912	119.2922	119.3011	119.3063
C4C3H15	119.1853	119.1104	119.112	119.1134	119.1144	119.1308	119.133	119.15	119.1657
C3C4H16	120.9639	121.1548	121.1526	121.1478	121.1456	121.1066	121.1013	121.0586	121.0371
C5C4H16	121.4034	121.2903	121.2921	121.2943	121.2956	121.3182	121.3213	121.3466	121.3604
C7C9H17	121.8698	121.9319	121.9311	121.9299	121.9293	121.9174	121.9157	121.9007	121.9002
C10C9H17	120.3975	120.3498	120.35	120.3515	120.3521	120.3619	120.3633	120.3743	120.3755
C9C10H18	120.1206	119.9785	119.9825	119.984	119.9858	120.0168	120.021	120.0549	120.1051
H18C10N21	115.626	115.8569	115.8529	115.8486	115.8461	115.7997	115.7934	115.7415	115.7337
C5N11H12	125.3229	125.3568	125.3567	125.3567	125.3567	125.3547	125.3542	125.3481	125.3377
C8N11H12	125.437	125.4883	125.4882	125.486	125.4854	125.4738	125.4723	125.4615	125.4614
C8C19H20	121.6794	121.4436	121.4511	121.4522	121.4548	121.502	121.5083	121.5587	121.5751
H20C19N21	117.0915	117.4582	117.4552	117.4455	117.4416	117.3705	117.3607	117.2812	117.27896

 

Dihedral angle (°)	G	W	M	E	A	C	D	B	Cy
D4 5 11 12	0.1616	0.1232	0.1235	0.1236	0.1237	0.1262	0.1262	0.1287	0.146
D6 5 11 12	-179.862	-179.889	-179.8883	-179.8882	-179.8881	-179.8856	-179.8856	-179.883	-179.8591
D19 8 11 12	-0.1728	-0.1268	-0.1271	-0.1272	-0.1273	-0.1298	-0.1298	-0.1323	-0.1471

G: gas, W: water, M: methanol, E: ethanol, A: acetone, C: chloroform, D: diethyl ether, B: benzene, Cy: cyclohexane

 

Energy:

The key properties of a solute can be accurately described through free energy variation^16,17. The solvation free energies of β Carboline calculated with the CPCM are summarized in Table 2. Eight different solvents (cyclohexane, benzene, chloroform, diethylether, acetone, ethanol, methanol, and water) were used to compute free energies of solvation for the compound, calculated according to the following equation¹⁸.

 

From Table 2, we can see that the calculated energy is dependent on the size of the dielectric constant of solvents. In the CPCM, the energies ET decrease with the increasing dielectric constants of solvents relative to the gaseous phase of β Carboline. On the other hand, ΔGsolv values indicate the increase of stability in more polar solvents than gas phase.

 

The order of absolute value of ΔGsolv for β Carboline was found to be as follows:

 

Water > Methanol > Ethanol > Acetone > Chloroform > Diedthylether > Benzene > Cyclohexane.

Dipole Moment:

Dipole moment is the result of every molecular charges in addition to the separation distance among molecules. Polarizability and dipole moment are directly related to each other. The dipole moment is considered a necessary elements to calculate the effects of different solvents having different dielectric constants, leading to high solvent polarity effects. The delocalization of molecular charges is thus improved and the dipole moments are increased, leading to a reorientation of the solvent molecules towards a bigger reaction field^19,20,21. The dipole moments of β Carboline in solvents vary exactly from 3.5941 D to 4.3045 D when the values change from ε = 2.02 to ε= 78.36. In Table 2, with increasing polarity of the solvent, the dipole moment is constantly rising. This means that increasing the polarity of the solvent causes an increase in the solubility of the compound. Whatever the calculated dipole moment (D) for the compound is, the compound is easily and quickly solved in solvents with higher polarity.

 

Polarizability:

Polarizability is the linear coefficient between an applied electric field and the induced dipole moment. Polarizability of a molecule is the realization of the global polarity of the molecular structure¹⁹ as an outcome from the uneven partial charge distribution over all the atoms of the molecule. Also, it was displayed that polarizability is important in the modeling of solubility^22,23,24. Polarizability (α) is calculated using the following equation:

 

The polarizability for β Carboline in gas and in different solvents is listed in Table 2. We observed that as the solvent dielectric constant increases, the polarizability of the molecule also increases. Therefore, for compound β Carboline, the order of polarizability is as follows:

 

Water > Methanol > Ethanol >Acetone > Chloroform > Diethylether > Benzene > Cyclohexane > Gas.

 

Atomic Charge:

Measuring the atomic charge is crucial in quantum chemistry applications to molecular systems. Atomic charges have an impact on molecular properties, that is to say, dipole moment, polarizability, and electronic structure^25,26,27. The charge distributions calculated by the chelpG method, at the B3LYP/ 6-311 ++G (d, p) level, for the optimized structures of β Carboline are listed in Table 3 and shown in Figure 2. The results show that the positive charges are mainly localized on hydrogen atoms, while the carbon atoms are found to be either positive or negative, and the nitrogen atoms show a negative charge.

 

The charges obtained in the polar solvents increase by 0.0010 to 0.036 relative to the gas phase, by the effect of solvent polarity or, more exactly, by the effect of the dielectric constant of each solvent. The higher this constant is, the higher the separation of atoms increases by its great dissociating power, and consequently the atomic charges increase relative to the gaseous phase of the β Carboline molecule.

 

In apolar solvents, there is a small change in values from 0.0006 to 0.014, due to the interaction between the permanent β Carboline dipole and the non-polar molecules of the solvent considered as induced dipole. These results clearly indicated that the presence of solvent increases the value of charge of the atoms: N21, H12, C9, C10, and C19.

 

Table 2: Energy totale (E_T), salvation energy (ΔG_solv), Dipole moments (μ) and molecular Polarizabilities (α) for β Carboline in gas phase and different solvents

Solvent (Dielectric constant)	ET (a.u)	ΔGsolv ( kcal/mol )	μ (D)	α (a.u)
Gas	-533,6399141	-	3.0880	145.086
Water (78.36)	-533,6511001	-7.0193	4.3045	207.946
Methanol (32.61)	-533,6508569	-6.8667	4.2744	206.268
Ethanol (24.85)	-533,6507285	-6.7861	4.2556	205.416
Acetone (20.49)	-533,6506136	-6.7140	4.2407	204.641
Chloroform (4.71)	-533,6484967	-5.3857	3.9752	190.948
Diethyl ether (4.24)	-533,6482026	-5.2011	3.9401	189.130
Benzene (2.27)	-533,6457611	-3.6690	3.664	174.775
Cyclo hexane (2.02)	-533,6451289	-3.2723	3.5941	171.268

 

Table 3: Chelpg charge distribution for β Carboline in gas phase and different solvents.

Atoms	G	W	M	E	A	C	D	B	Cy
C1	-0.11	-0.120	-0.12	-0.12	-0.119	-0.118	-0.119	-0.118	-0.114
C2	-0.144	-0.158	-0.158	-0.158	-0.158	-0.155	-0.154	-0.15	-0.152
C3	-0.03	-0.045	-0.044	-0.044	-0.044	-0.042	-0.042	-0.04	-0.037
C4	-0.302	-0.310	-0.31	-0.31	-0.31	-0.309	-0.308	-0.306	-0.306
C5	0.408	0.419	0.418	0.418	0.418	0.416	0.414	0.412	0.412
C6	-0.116	-0.142	-0.14	-0.141	-0.141	-0.134	-0.132	-0.126	-0.127
C7	0.26	0.276	0.273	0.275	0.275	0.27	0.269	0.265	0.266
C8	0.039	0.029	0.033	0.029	0.029	0.034	0.035	0.037	0.036
C9	-0.415	-0.442	-0.44	-0.441	-0.441	-0.435	-0.434	-0.428	-0.428
C10	0.362	0.389	0.388	0.389	0.388	0.383	0.382	0.376	0.375
C19	0.304	0.349	0.346	0.348	0.347	0.337	0.335	0.325	0.323
N11	-0.656	-0.658	-0.659	-0.658	-0.658	-0.66	-0.66	-0.659	-0.659
N21	-0.629	-0.741	-0.738	-0.737	-0.736	-0.713	-0.71	-0.685	-0.68
H12	0.405	0.442	0.442	0.441	0.441	0.434	0.433	0.425	0.423
H13	0.116	0.131	0.131	0.13	0.13	0.128	0.128	0.125	0.123
H14	0.09	0.101	0.101	0.101	0.101	0.099	0.099	0.096	0.096
H15	0.088	0.100	0.1	0.1	0.1	0.098	0.097	0.095	0.094
H16	0.136	0.157	0.156	0.156	0.156	0.152	0.151	0.147	0.145
H17	0.15	0.173	0.172	0.172	0.172	0.167	0.167	0.162	0.161
H18	0.014	0.013	0.013	0.013	0.013	0.014	0.014	0.014	0.014
H20	0.03	0.036	0.037	0.036	0.036	0.035	0.035	0.034	0.034

 

Fig.2: The atomic charges for β Carboline in gas phase and different solvents

G: gas, W: water, M: methanol, E: ethanol, A: acetone, C: chloroform, D: diethyl ether, B: benzene, Cy: cyclohexane

 

 

Frontier Orbitals Energy:

The effect of the solvent is reflected not only in the geometric parameters of the molecules, but also in the energies of frontier orbitals. It is known that the frontier orbitals energy and Egap values are closely related to the electronic property^28-31.

 

The HOMO (the highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) computed at the B3LYP/6-311++G(d,p) level are shown in Table 4. The values of the HOMO-LUMO energy gap in various solvents are presented in Figure 3. The difference of energy between HOMO and LUMO was calculated by the following equation:

 

Table 4 shows the calculated electronic properties of β Carboline in different dielectric media. When Table 4 is examined, it is seen that HOMO and LUMO energy decreases with increasing the dielectric constant of the solvent compared to the gas phase. Moreover, it is clear that the HOMO-LUMO energy gap increases on going from polar to non-polar solvent. That makes β Carboline more reactive in polar solvents compared to the gas phase.

 

Table 4: HOMO, LUMO and Egap calculated in gas phase and different solvents

Solvent (Dielectric constant)	EHOMO (eV)	E LUMO (eV)	Egap (eV)
gas	-6.1030	-1.5652	4.5378
Water (78.36)	-6.1141	-1.6496	4.4646
Methanol (32.61)	-6.1144	-1.6476	4.4667
Ethanol (24.85)	-6.1141	-1.6466	4.4676
Acetone (20.49)	-6.1139	-1.6455	4.4684
Chloroform (4.71)	-6.1122	-1.6283	4.4839
Diethyl ether (4.24)	-6.1122	-1.6259	4.4863
Benzene (2.27)	-6.1095	-1.6068	4.5027
Cyclo hexane (2.02)	-6.1098	-1.6019	4.5078

 

 

Fig.3: The HOMO- LUMO orbitals and the energy gap of β Carboline in gas and different solvent phases.

 

Global Reactivity Descriptors:

To describe a more reliable chemical reactivity, some descriptors, such as Ionization Potential (IP), Electron Affinity (A), Electronegativity (x) (or Chemical Potential (μ)), Electrophilicity Index (w), Hardness (η), and Softness (S), are given by the following expressions^32-38.

 

Ionization Potential

 

Electron Affinity

 

IP and A are obtained from total electronic energy calculations on the N-1, N, N+1-electron systems at the neutral molecule geometry.

Electronegativity (or Chemical Potential)   

 

Chemical Hardness    

 

Electrophilicity

 

Softness       

Table 5 shows the values for the global-reactivity descriptors calculated: ionization potential (IP), electronegativity (x), electrophilicity (ω), hardness(η), and softness (S). From this table, we observe that β Carboline has a small value for IP in water, while in the other solvents and in vaccum it has larger values. In the analysis of the electron affinity, in gas phase, β Carboline gives results with a negative value; this means that β Carboline with this value does not have the capability to accept one electron and bond to form an anion³², while in different polarity of solvents, a positive value is shown which increases when increasing the polarity. This indicates that the solvent has an effect on this system to form an anion. On the other hand, when moving from non-polar to polar solvents, the electronegativity, electrophilicity, and chemical softness increased, while chemical hardness decreased. These results may suggest that global hardness reflects the ability of charge transfer inside the molecule which decreases when the solvent effect is considered^39,40,41. Also note that β Carboline possesses stronger electrophilicity⁴² when solvated in solvents: water, methanol, ethanol, acetone, chloroform, and diethyl ether (see Table 6).

 

Local Reactivity Descriptors of β Carboline:

Local reactivity descriptors have been used to understand the chemical reactivity and site selectivity^43,44. To analyze selective site in a molecule, Parr and Yang⁴⁵ define the local descriptors such as the Fukui function. Thus, calculating Fukui functions helps us explore which atoms are potential reactive sites for electrophilic, nucleophilic or radical attacks, respectively. Fukui functions f ⁺(r), f ^–(r) and f ^°(r) are calculated using the following equations^34,46:

 

Where q_k(N) is electron population of the atom k in the neutral molecule, q_k (N +1) is electron population of the atom k in the anionic molecule, and q_k (N −1) is electron population of the atom k in the cationic molecule.

 

Figure 4, shows graphical representations of the condensed Fukui function obtained from chelpg charges in the gas and different solvents and at the B3LYP/6-311++ G(d, p) level of theory.

 

Table 5: Reactivity descriptor calculated in gas phase and different solvents

Solvent (Dielectric constant)	Ionisation Potential (eV)	Electron Affinity (eV)	Electronegativity (eV)	Hardness (eV)	Electrophilicity index (eV)	Softness (eV-1 )
gas	7.7881	-0.0232	3.8824	7.8114	0.9648	0.1280
Water (78.36)	5.9792	1.8265	3.9028	4.1527	1.8340	0.2408
Methanol (32.61)	6.0127	1.7920	3.9023	4.2208	1.8040	0.2369
Ethanol (24.85)	6.0303	1.7734	3.9019	4.2570	1.7882	0.2349
Acetone (20.49)	6.0463	1.7568	3.9016	4.2894	1.7744	0.2331
Chloroform (4.71)	6.3492	1.4433	3.8962	4.9059	1.5472	0.2038
Diethyl ether (4.24)	6.3927	1.3984	3.8955	4.9944	1.5192	0.2002
Benzene (2.27)	6.7688	1.0117	3.8903	5.7572	1.3144	0.1737
Cyclo hexane (2.02)	6.8714	0.9076	3.8895	5.9638	1.2683	0.1677

 

 

Table 6: Variation of electrophilicity of β Carboline relative of polarity of solvent

Strong electrophiles ω > 1.5 eV	Moderate electrophiles 0.8 < ω < 1.5 eV
Water
Methanol	Benzene
Ethanol
Acetone	Cyclohexane
Chloroform
Diethylether

 

Fig.4: Bar chart showing the condensed Fukui functions for nucleophilic (f⁺), electrophilic (f^-) and radical (f°) attacks in gas phase and different solvents.

 

Table 7 shows the sites with the maximum values of the Fukui functions. It is possible to observe in the gas phase that the most electrophilic active site is located on N11. In the case of nucleophilic attacks, the most active site is on N21. For a free radical attack, the most reactive site is on N11. In the solvents media, the reactivity order is N11, N21, and N11 for electrophilic, nucleophilic, and free radical attacks, respectively.

Moreover, it is also observed that the condensed Fukui function for electrophilic attack for N11 atom increases as we move on from gas phase to solvent medium with increasing the dielectric constant. The change in polarity of solvent (different dielectric constant) does not affect the nucleophilicity of atom N21.

 

Table 7: Values of the Fukui function of reactive atoms for β Carboline in gas phase and different solvents.

G: gas, W: water, M: methanol, E: ethanol, A: acetone, C: chloroform, D: diethyl ether, B: benzene, Cy: cyclohexane

 

Dual Descriptor:

Martínez-Araya pointed out in a recent study⁴⁷ that the condensed expression for dual descriptor (DD) as Δfk is more beneficial for predicting of the preferred reaction sites compared to the condensed Fukui functions.  A key advantage of Δfk is its ability to uncover most nucleophilic and electrophilic sites on a molecule at the same time ^48,49,50,51. This is given by:

 

There are two situations that need to be considered:

If Δf(r) > 0, then the site is favored for a nucleophilic attack, whereas if Δf (r) < 0, then the site may be favored for an electrophilic attack.

 

The calculation of dual descriptor of the β Carboline molecule obtained from chelpG charges in the gas phase and different solvents at the level B3LYP/6-311++G (d, p) is shown in Table 8 and depicted by Figure 5. From the values of dual descriptor in the gas phase, it can be stated that the most electrophilic active site is located on N11, C10 and C2. Further, the active sites susceptible to nucleophilic attacks are C3, N21, and C1. In the solvents phases, one can see a slight increase of the dual descriptor, also located on N11, C10, and C2 for the electrophilic attack. Again, C3, N21, and C9 are favorite sites for the nucleophilic attack. These results manifest a strong influence of solvents on the reactivity of the compound considered.

 

It can be concluded that the dual descriptor provides a clearer difference between electrophilic and nucleophilic attack at a specific atomic site than presented by Fukui functions. Also, the presence of a polar solvent increases the sites of reactivity inside the molecule.

 

Fig.5: Graphical representation of the Dual Descriptor (DD) of the β Carboline. (a) in gas phase, (b) in water. Red: DD > 0; Yellow: DD < 0. In all cases the isosurfaces were obtained at 0,009 a.u.

 

Table 8: Dual Descriptor Δƒ of β Carboline in gas phase and different solvents, where bold number is the significance values in table.

Atoms	G	W	M	E	A	C	D	B	Cy
C1	0.051	0.042	0.043	0.041	0.044	0.047	0.046	0.049	0.049
C2	-0.134	-0.138	-0.138	-0.139	-0.139	-0.137	-0.136	-0.135	-0.135
C3	0.118	0.131	0.131	0.131	0.131	0.130	0.130	0.127	0.126
C4	-0.089	-0.110	-0.109	-0.109	-0.109	-0.103	-0.101	-0.097	-0.095
C5	0.069	0.068	0.067	0.066	0.066	0.068	0.067	0.069	0.068
C6	-0.035	-0.023	-0.024	-0.024	-0.024	-0.027	-0.027	-0.031	-0.030
C7	0.002	-0.008	-0.008	-0.009	-0.008	-0.004	-0.003	-0.002	0.000
C8	0.034	0.037	0.039	0.037	0.036	0.037	0.036	0.036	0.033
C9	0.048	0.084	0.084	0.083	0.081	0.073	0.072	0.064	0.061
C10	-0.136	-0.141	-0.141	-0.139	-0.141	-0.139	-0.139	-0.138	-0.138
C19	-0.010	0.009	0.009	0.009	0.008	0.004	0.003	-0.003	-0.003
N11	-0.146	-0.166	-0.164	-0.164	-0.164	-0.160	-0.160	-0.154	-0.153
N21	0.084	0.106	0.106	0.105	0.105	0.100	0.099	0.094	0.092
H12	0.002	-0.005	-0.004	-0.004	-0.003	-0.004	-0.003	-0.001	-0.001
H13	0.016	0.015	0.015	0.014	0.014	0.015	0.016	0.016	0.015
H14	0.018	0.010	0.010	0.011	0.011	0.012	0.013	0.013	0.014
H15	0.013	0.005	0.006	0.006	0.007	0.008	0.007	0.009	0.010
H16	0.029	0.022	0.021	0.021	0.022	0.023	0.022	0.026	0.024
H17	0.020	0.019	0.019	0.019	0.019	0.018	0.019	0.019	0.019
H18	0.024	0.022	0.021	0.021	0.022	0.022	0.022	0.022	0.022
H20	0.021	0.018	0.019	0.018	0.018	0.018	0.018	0.019	0.020

G: gas, W: water, M: methanol, E: ethanol, A: acetone, C: chloroform, D: diethyl ether, B: benzene, Cy: cyclohexane

 

CONCLUSION:

This work is focused on the study of the influence of solvents having different dielectric constants on the molecular structure and chemical reactivity of β Carboline as compared to the gas phase, using the DFT. It has been concluded that there were small changes in bond lengths and angles, which means that the introduction of a solvent reaction field has a slight effect on the geometry of the β Carboline structure. The solvation free energy is the highest in the polar solvent. The dipole moment, polarizability, and atomic charge of β Carboline increase with the increase in the polarity of the solvent. We found that the solvation modifies the values of the reactivity descriptors as a result of the interaction between the solvent and the β Carboline molecule. The HOMO-LUMO energy orbital, electronegativity (or chemical potentiel), electrophilicity index, and softness increase with the increase of solvent polarity, unlike hardness which decreases with the increase of solvent polarity. On the other hand, the electrophilicity of the reactive atom increases while going from the gas phase to polar solvents and for nuclephilicity the change in the polarity of the solvent does not have an effect on the reactive atom. Finally, the dual descriptor provides a clear difference between electrophilic and nucleophilic attack at the specific atomic site of β Carboline in both cases (gas and solvents) compared to what is presented by Fukui functions.

 

CONFLICT OF INTEREST:

The authors declare no conflict of interest.

 

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Received on 03.04.2021                    Modified on 19.06.2021

Accepted on 22.07.2021                   ©AJRC All right reserved