1. Introduction

Computational Chemistry

2332-5968

Scientific Research Publishing

10.4236/cc.2017.51004

CC-73616

Articles

Chemistry&Materials Science

Quantum Chemistry Prediction of Molecular Lipophilicity Using Semi-Empirical AM1 and <i>Ab Initio</i> HF/6-311++G Levels

Ouanlo

Ouattara

¹Nahossé

Ziao

¹^*

Laboratoire de Thermodynamique et de Physico-Chimie du Milieu, UFR-SFA, Université Nangui Abrogoua, Abidjan, C&ocirc;te d’Ivoire

* E-mail:nahosse_ziao@yahoo.fr(NZ);

06122016

05013850September 19, 2016Accepted: January 15, January 19, 2017

2014

This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

Reliable prediction of lipophilicity in organic compounds involves molecular descriptors determination. In this work, the lipophilicity of a set of twenty-three molecules has been determined using up to eleven quantum various descriptors calculated by means of quantum chemistry methods. According to Quantitative Structure Property Relationship (QSPR) methods, a first set of fourteen molecules was used as training set whereas a second set of nine molecules was used as test set. Calculations made at AM1 and HF/6-311++G theories levels have led to establish a QSPR relation able to predict molecular lipophilicity with over 95% confidence.

Molecular Lipophilicity Molecular Descriptors Quantum Chemistry Statistical Analysis

1. Introduction

The informations contained in molecular structure can be accessed and described by the mean of various physicochemical quantities named descriptors. For decades, many studies have been conducted to determine empirically or compute these descriptors and it is well known that they actually can describe molecular structures [1] [2] [3] . In quantum chemistry, the computed descriptors, obviously, will be favoured. The aim of our work is to determine the molecular descriptors that can reliably predict the molecular lipophilicity by quantum chemistry methods. The suitable descriptors will be selected from an initial set of eleven, only taking into account the ones who are highly correlated with the molecular lipophilicity while being independent one from each other, in pairs. The whole process will lead to establish and validate by statistical methods, a performant QSPR model.

2. Computational Details2.1. Training and Test Sets Molecules

Both training and test sets are constituted from a sample of twenty-three aromatic compounds with known experimental values [4] of molecular lipophilicity expressed as logP_exp, where P_exp is the experimental value of octanol-water partition’s coefficient. The training set corresponds to fourteen molecules and test set, nine molecules (Table 1). All molecules are codified CAi, the i running from 1 to 23.

2.2. Computational Theories Levels and Softwares

All molecules have been fully optimized using GAUSSIAN 03 [5] software at semi-em- pirical AM1 method and ab initio HF/6-311++G method. The basis set 6-311++G is sufficient, especially, the use of both polarization and diffuse functions is not necessary since we are not in a case of intermolecular study. Two other softwares have been used, according their specificities, to do statistical analysing of the results and to plot graphics, i.e. XLSTAT [6] and EXCEL [7] .

2.3. Statistical Analysing

QSPR study needs a statistic analysis all along the validation process. In this work, we used the multiple linear regression analysis method [8] [9] , corresponding to the below general equation:

: Property studied;: explanatory variables (descriptors) of the studied property;: model regression coefficients. Excel software directly provides these linear regression equations with the regression analysis tool. The final choice of predictive descriptors is based on two fundamental criteria for selecting descriptors set, according Vessereau [10] . The first criterion requires that there must be a linear dependency between the property studied and the descriptors. For each descriptor, one must have where R is the linear correlation coefficient. The second criterion indicates that the descriptors must be independent each from other, so we must have where is the partial correlation coefficient between descriptors i and j. XLSTAT software directly provides these coefficients. In the case of simple linear regression [11] , expressions of R and are:

The determination coefficient [12] is given by the following equation:

TSS: Total Sum of Squares; ESS: Extended Sum of Squares; RSS: Residual Sum of Squares. A linear regression equation significancy is drawn from Fisher’s coefficient (F) [13] . The higher this coefficient is, the better the linear regression equation is.

Table 1 Training setand test set samples molecules and theirli pophilicities

Training set
Molecule	Code	logP_Exp
	CA1	2.13 ± 0.10
	CA2	3.12 ± 0.20
	CA3	3.15 ± 0.20
	CA4	3.69 ± 0.15
	CA5	3.63 ± 0.15
	CA6	3.53 ± 0.30
	CA7	4.00 ± 0.20
	CA8	4.10 ± 0.20
	CA9	4.00 ± 0.20
	CA10	3.22 ± 0.20
	CA11	2.27 ± 0.20
	CA12	2.73 ± 0.10

	CA13	3.35 ± 0.10
	CA14	3.87 ± 0.20
	CA15	3.98 ± 0.10
	CA16	3.66 ± 0.20
	CA17	3.60 ± 0.20
	CA18	3.63 ± 0.40
	CA19	3.05 ± 0.30
	CA20	3.20 ± 0.20
	CA21	4.10 ± 0.10
	CA22	3.15 ± 0.20
	CA23	4.10 ± 0.20

n: number of molecules; p: number of explanatory variables.

The predicting power of a model can be obtained from five Tropsha’s criteria [14] [15] . If at least three of the criteria are satisfied, then the model will be considered efficient in predicting the property studied. These criteria are:

Criterion 1:; Criterion 2:; Criterion 3: and

Criterion 4: and; Criterion 5:

2.4. Molecular Descriptors Selection

There are thousands of molecular descriptors from the literature and quantum chemical calculations. For our study, we considered eleven quantum descriptors (Table 2).

Table 3 and Table 4 give the values of the quantum descriptors at AM1 and HF/ 6-311++G levels respectively. These values were used to calculate correlation linear coefficient R, the partial coefficient correlation and to establish regression models.

According to Table 5, the rejected descriptors have a correlation coefficient value less than 0.50 and those selected have a coefficient greater than 0.50. We hold the following results. At semi-empirical level, AM1, the selected descriptors are and. At ab initio level HF/6-311++G, the selected descriptors are

and. The last step is to verify the criterion 2 (Table 6 and Table 7). According to Table 6, the descriptors and are dependent. This leads us to consider two groups of descriptors at AM1 level. In the group 1, the selected de-

Table 2 List of eleven quantum descriptors

Quantum descriptors	Notation	Expression
Dipolar moment
Energy of the HOMO
Energy of the LUMO
Acidity by hydrogen bonding [16]
Basicity by hydrogen bonding [16]
Chemical elecrtonegativity [17]
Chemical hardness [17]
Chemical softness [17]
Smallestnegative charge of the molecule
Larger positive charge of the hydrogenatoms of the molecule
Sum of absolutes values of net electrical charges of Mulliken

Table 3 Values of the training set quantum descriptors at AM1 level

CODE
CA1	0.0009	−0.3547	0.0204	0.0048	0.0052	−0.1672	0.1876	5.3319	−0.1301	0.1301	1.5614
CA2	0.4692	−0.3375	0.0192	0.0048	0.0050	−0.1592	0.1784	5.6070	−0.1775	0.1296	2.0264
CA3	0.2453	−0.3444	0.0194	0.0048	0.0051	−0.1625	0.1819	5.4975	−0.2072	0.1304	2.0942
CA4	0.2589	−0.3441	0.0192	0.0048	0.0051	−0.1625	0.1817	5.5051	−0.2119	0.1306	2.4142
CA5	0.2977	−0.3298	0.0186	0.0048	0.0049	−0.1556	0.1742	5.7405	−0.1777	0.1296	2.2557
CA6	0.4228	−0.3382	0.0195	0.0048	0.0050	−0.1594	0.1789	5.5913	−0.2067	0.1297	2.3258
CA7	0.4717	−0.3277	0.0199	0.0048	0.0049	−0.1539	0.1738	5.7537	−0.1796	0.1289	2.4884
CA8	0.0000	−0.3246	0.0182	0.0048	0.0049	−0.1532	0.1714	5.8343	−0.1760	0.1292	2.4782
CA9	0.3123	−0.3173	−0.0086	0.0045	0.0048	−0.1630	0.1544	6.4788	−0.1795	0.1321	2.3463
CA10	1.5121	−0.2948	−0.0319	0.0043	0.0046	−0.1634	0.1315	7.6075	−0.1880	0.1410	2.0976
CA11	1.5754	−0.3508	0.0060	0.0046	0.0051	−0.1724	0.1784	5.6054	−0.1657	0.1479	1.5913
CA12	0.2652	−0.3429	0.0191	0.0048	0.0051	−0.1619	0.1810	5.5249	−0.1792	0.1301	1.7976
CA13	0.0003	−0.3201	−0.0098	0.0045	0.0048	−0.1650	0.1552	6.4454	−0.1278	0.1321	2.1093
CA14	0.2741	−0.3155	−0.0098	0.0045	0.0048	−0.1627	0.1529	6.5424	−0.1811	0.1325	2.3500

Table 4 Values of the test set quantum descriptors at HF/6-311++G level

CODE
CA1	0.0000	−0.3409	0.0424	0.0055	0.0038	−0.1493	0.1917	5.2178	−0.3387	0.3387	4.0650
CA2	0.6870	−0.3202	0.0394	0.0055	0.0036	−0.1404	0.1798	5.5617	−1.6167	0.3402	13.3364
CA3	0.4144	−0.3273	0.0387	0.0055	0.0037	−0.1443	0.1830	5.4645	−1.1851	0.3616	7.9439
CA4	0.4319	−0.3266	0.0391	0.0055	0.0037	−0.1438	0.1829	5.4690	−1.1932	0.3730	9.4211
CA5	0.4248	−0.3104	0.0397	0.0055	0.0035	−0.1354	0.1751	5.7127	−1.8709	0.3375	18.3793
CA6	0.7839	−0.3187	0.0395	0.0055	0.0036	−0.1396	0.1791	5.5835	−1.6439	0.3713	15.3392
CA7	0.6708	−0.3076	0.0396	0.0055	0.0035	−0.1340	0.1736	5.7604	−1.8444	0.3554	21.3145
CA8	0.0000	−0.3026	0.0401	0.0055	0.0034	−0.1313	0.1714	5.8360	−2.8671	0.3183	24.3437
CA9	0.5046	−0.2909	0.0392	0.0055	0.0033	−0.1259	0.1651	6.0588	−1.5820	0.3619	10.2537
CA10	1.7852	−0.2624	0.0366	0.0055	0.0030	−0.1129	0.1495	6.6890	−0.5776	0.3718	6.2841
CA11	2.5200	−0.3536	0.0383	0.0055	0.0040	−0.1577	0.1960	5.1033	−0.5641	0.3546	3.6156
CA12	0.4218	−0.3274	0.0397	0.0055	0.0037	−0.1439	0.1836	5.4481	−1.3335	0.3521	8.7112
CA13	0.0000	−0.2948	0.0387	0.0055	0.0034	−0.1281	0.1668	5.9970	−0.4731	0.3394	5.4112
CA14	0.3839	−0.2894	0.0384	0.0055	0.0033	−0.1255	0.1639	6.1013	−1.7341	0.3853	10.2685

scriptors are Energy of the HOMO (), Basicity by hydrogen bonding () and Sum of absolutes values of net electrical charges of Mulliken (). For the group 2, the selected descriptors are Basicity by hydrogen bonding (), Chemical electronegativity () and Sum of absolutes values of net electrical charges of Mulliken ().

According to Table 7, the descriptors and are dependent. This leads us to consider two groups of descriptors for the level calculation HF/6-311++G. So, we can

Table 5 Selection of quantum descriptors according criterion 1 [<xref ref-type="bibr" rid="scirp.73616-ref10">10</xref>] at AM1 and HF/6-311++G levels

Niveau AM1		Niveau HF/6-311++G
Correlation coefficient	Rejected	Correlation coefficient	Rejected


0.3173	Rejected	0.3551	Rejected
0.5727	Selected	0.6186	Selected
0.1127	Rejected	0.2126	Rejected
0.0600	Rejected	0.2126	Rejected
0.5641	Selected	0.6186	Selected
0.7228	Selected	0.6241	Selected
0.3572	Rejected	0.6122	Selected
0.2980	Rejected	0.5522	Selected
0.4134	Rejected	0.7340	Selected
0.4414	Rejected	0.1300	Rejected
0.9818	Selected	0.7060	Selected

Table 6 Selection of quantum descriptors according criterion 2 [<xref ref-type="bibr" rid="scirp.73616-ref10">10</xref>] at AM1 level

Correlation between	AM1 level
Correlation between	Coefficient	Criterion 2: Independent descriptors if
and	−97.3800	Independent
and	0.8450	Dependent
and	0.0269	Independent
and	−0.0078	Independent
and	−0.0003	Independent
and	0.0124	Independent

settled two groups. For the first group 3, descriptors selected are Energy of the HOMO (), Basicity by hydrogen bonding (), Chemical hardness (), Chemical softness (), Smallest negative charge of the molecule (), Sum of absolutes values of net electrical charges of Mulliken (). For the last group 4, the selected descriptors are Basicity by hydrogen bonding (), Chemical electronegativity (), Chemical hardness (), Chemical softness (), Smallest negative charge of the molecule () and Sum of absolutes values of net electrical charges of Mulliken ().

3. Results and Discussion3.1. Prediction of Lipophilicity at Semi-Empirical Level AM1 (Model 1)

Figure 1 shows that the group 2 quantum descriptors retained are linearly dependent on molecular lipophilicity. The actual plot on Figure 1 is. Indeed, there are several descriptors corresponding to a single value of, and it has

Table 7 Selection of quantum descriptors according criterion 2 at HF/6-311++G level

Correlation between	HF/6-311++G level
Correlation between	Coefficient Criterion 2 Independent descriptorsif
and	−100.00	Independent
and	2.0533	Dependent
and	−1.9416	Independent
and	0.0572	Independent
and	−0.0065	Independent
and	0.0007	Independent
and	−0.0205	Independent
and	0.0194	Independent
and	−0.0006	Independent
and	0.00006	Independent
and	−0.000007	Independent
and	−0.9416	Independent
and	0.0277	Independent
and	−0.0034	Independent
and	0.0004	Independent
and	−0.0295	Independent
and	0.0031	Independent
and	−0.0003	Independent
and	−0.0676	Independent
and	0.0078	Independent
and	−0.0985	Independent

Figure 1 Graphs <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/4-1710063x185.png" xlink:type="simple"/></inline-formula> at semi-empirical AM1 level

been impossible with the software Excel to plot on a same graph.

The quantum descriptors of group 2 were used for the establishment of Model 1 because they give a more significant regression equation in the sense of Fisher than group 1.

Model 1:

According to the statistical t_test, the importance of quantum descriptors in Model 1 is in the following descending order:. In Table 8 are various statistical parameters for Model 1 validation. Table 8 shows that the Model 1 has a very high predictive capability, since up to 95.60%, of the test molecules have their game lipophilicities predicted. This means that Model 1 can be used to reliably predict the aromatic compounds unavailable lipophilicities.

Verification of Tropsha criteria for Model 1.

1); 2); 3)

4); 5) and

All values satisfy Tropsha’s criteria. Model 1 is retained as predictive model of molecular lipophilicity. Statistical parameters are gathered in Table 8.

3.2. Prediction of Lipophilicity at Ab Initio Level HF/6-311++G (Model 2)

Figure 2 shows that there is indeed a linear dependence between the quantum descriptors of group 4 and the molecular lipophilicity. The quantum descriptors of group 4 were used for the establishment of Model 2 as they give a more significant regression equation in the sense of Fisher than group 3.

Model 2:

According to the statistical t_test, the importance of quantum descriptors in Model 2 is in the following descending order:. Table 9 shows the various statistical parameters for validating the Model 2. Table 9 shows that the Model 2 has a low predictive ability (), since only 59.71%, of the test molecules have their game lipophilicities predicted. This means that the Model 2 cannot be used to reliably

Table 8 Statistical parameters of the Model 1 (Semi-empirical level AM1)

	Internal validation LOO (Training set)		External validation (Test set)
14		14		9
0.9729 (97.29%)	PRESS	0.3716		0.9900 (99%)
0.9647		0.9265 (92.65%)	PRESS	0.1429
119.4556		0.9265 (92.65%)		0.9560 (95.60%)
0.1171		0.1928		0.1691

predict the aromatic compounds unavailable lipophilicities.

Verification of Tropshacriteria for Model 2.

1); 2); 3)

4); 5) and

All Tropsha criteria, excepted criterion 4, are not satisfied. Model 2 established at HF/6-311++G level is validated, since, but is not efficient in predicting the lipophilicity. He is dismissed as a model for lipophilicity prediction. This unsuitable prediction of lipophilicity is certainly due to the use of an extended basic function, taking into account the diffuse functions on all atoms. The use of diffuse functions seems unefficient when calculating lipophilicity. Statistical parameters are gathered in Table 9.

Figure 2 Graphs <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/4-1710063x220.png" xlink:type="simple"/></inline-formula> at ab initio HF/6-311++G level

Table 9 Statistical parameters of the Model 2 (ab initio level HF/6-311++G)

	Internal validation LOO (Training set)		Validation externe (Test set)
14		14		9
0.8724 (87.24%)	PRESS	2.5848		0.4006 (40.06%)
0.6677		0.4884 (48.84%)	PRESS	1.3086
10.9402		0.4884 (48.84%)		0.5971 (59.71%)
0.2839		0.5684		0.6605

3.3. Correlation between the Predicted and Experimental Values of Lipophilicity

Figure 3 and Figure 4 represent the following graphs depending for internal validation (LOO) and external of our models.

Figure 3 Graph <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/4-1710063x236.png" xlink:type="simple"/></inline-formula> of Model 1Figure 4 Graph <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/4-1710063x238.png" xlink:type="simple"/></inline-formula> of Model 2

Figure 3 shows that there is, indeed, a strong correlation between the predicted and the experimental lipophilicity according Model 1. The contrary is observed at Figure 4, for Model 2. In the latter case, it can be seen a large dispersion of the points cloud and no linear plot could be obtained. Here is the confirmation that Model 1 is highly performant, but not Model 2.

4. Conclusion

QSPR methodology and quantum chemical methods were used to establish predictive models of molecular lipophilicity. In this work, we identified four groups of quantum descriptors according to the basic criteria usually used for descriptors selection. The results showed that many descriptors strongly correlate lipophilicity. From these descriptors, we have established two lipophilicity prediction models. The statistical analysis led us to select only the semi-empirical (AM1) based model. On the other hand, ab initio (HF/6-311++G) based model was rejected because of its low predictive power. Furthermore, the main descriptors that strongly influence the lipophilicity are, from of the selected model, the Basicity by hydrogen bonding (), Chemical electonegativity () and the Sum of absolutes values of net electrical charges of Mulliken (). The ab initio based model unefficiency could be due to the use of high theory level, and tends to indicate that high theory levels, and specifically diffuse functions addition, are not suitable for molecular lipophilicity calculation. The performance of the semi-empirical based model could indicate that lipophilicity property is not strongly linked to electronic effect in molecules.

Cite this paper

Ouattara, O. and Ziao, N. (2017) Quantum Chemistry Prediction of Molecular Lipophilicity Using Semi-Empirical AM1 and Ab Initio HF/6- 311++G Levels. Computational Chemistry, 5, 38-50. http://dx.doi.org/10.4236/cc.2017.51004

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