Atomic Charges in Describing Properties of Aromatic Molecules - The

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Atomic Charges in Describing Properties of Aromatic Molecules Valia Nikolova, Diana Cheshmedzhieva, Sonia Ilieva, and Boris Galabov J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.8b02908 • Publication Date (Web): 08 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019

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The Journal of Organic Chemistry

Atomic Charges in Describing Properties of Aromatic Molecules Valia Nikolova, Diana Cheshmedzhieva, Sonia Ilieva, Boris Galabov* Department of Chemistry and Pharmacy, University of Sofia, Sofia 1164, Bulgaria Email: [email protected] Abstract The performance of four frequently employed population analysis methods is assessed by comparisons with experimentally derived properties of monosubstituted benzene derivatives. The analysis is based on the expected dependence between site reactivities and electron densities at the respective ring carbon atoms. The correspondence between charges obtained from Mulliken, NPA, Hirshfeld, and QTAIM approaches and the σ0m and σ0p aromatic substituent constants is examined. The series of molecules investigated includes benzene and 18 monosubstituted derivatives. The atomic charges are derived using the B3LYP, ωB97X-D density functional and MP2 MO methods combined with the 6-311++G(3df,2pd) basis set. A quantitative correspondence between Hirshfeld charges and σ0 constants is established. Application of Møller–Plesset second-order perturbation theory (MP2) wave functions appears to be essential in obtaining a more realistic electron density distribution. NPA and QTAIM charges provide in most cases a satisfactory description of the substituent effects. The net transfer of charges between substituents and the aromatic ring is assessed. Introduction In this research we test the applicability of several alternative theoretical methods for evaluating atomic charges in describing experimental properties of aromatic molecules. We focus on the quality of theoretical predictions by considering correlations between experimental kinetic parameters for aromatic systems and atomic charges used as descriptors of local (atomic sites) reactivities. We applied three quantum mechanical methods in deriving atomic charges: density functional theory with the B3LYP1 and ωB97X-D2 density functionals as well as the MP2 MO computations.3 Medvedev et al.4 showed recently that a number of earlier defined density functionals, including B3LYP and ωB97X-D, predict charge density distributions in good accord with state-of-the-art wave function computations, while some newly proposed functionals do 1 ACS Paragon Plus Environment

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not perform so well. We analyzed the quality of theoretical predictions of reactivity using four frequently employed atomic charges: Mulliken charges,5 natural population analysis (NPA) atomic charges of Weinhold and Reed,6 QTAIM (Quantum Theory of Atoms in Molecules) charges of Bader,7 and Hirshfeld charges.8 The Mulliken and NPA charges are defined in terms of the contributions to the molecular electron density from atom-centered basis functions. The QTAIM and Hirshfeld charges are derived from partitioning of the electron density. Extensive discussions have taken place over the years over the accuracy of definition and applicability of differently defined atomic charges.9-19 An excellent overview of the approximations involved in these procedures has been provided by Corminboeuf et al.13 Though atomic charges are not rigorously defined quantum mechanical quantities,20 the interest in these theoretical parameters is determined by their simple physical interpretation and the possibilities for applications in explaining various molecular properties, chemical reactivity trends, noncovalent interactions, as well as other chemical and physical phenomena. The charge density distribution in molecules as illustrated by the charges assigned to atomic sites has justifiably been referred to as the chemistry of the isolated molecule. As early as in 1952, Fukui, Yonezawa and Shinghu21 have shown that the π-electron densities at the carbon atoms of aromatic hydrocarbons correlate excellently with the reactivity for several electrophilic aromatic substitution reactions. A computational study of Hehre and Pople22 shows how well atomic charges obtained at the Hartree-Fock level of theory illustrate and quantify a number of basic notions in classical organic chemistry, such as inductive and mesomeric effects, hyperconjugation, reactivity trends, and the role of conformation on charge distribution. In 1993 Wiberg and Rablen10 conducted a detailed comparative computational study on the performance of a number of differently defined atomic charges using Hartree-Fock SCF wave functions, including the four procedures considered in the present research. Various types of aliphatic organic molecules have been considered. These authors found satisfactory correlations between NPA, Hirshfeld and QTAIM charges for a number of systems, though the magnitude of values may differ substantially. Overall, some preference is given to the charges derived from QTAIM population analysis. In a recent study23 the same authors reexamined the quality of theoretical predictions of the charge distribution in molecules as obtained by several different 2 ACS Paragon Plus Environment

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population analysis procedures. The methods considered include Mulliken population analysis,5 Natural population analysis (NPA),6 Minimal Basis Set (MBS) method,24 M-K25 and ChelpG26 electrostatic potential fitting methods, Hirshfeld population analysis,8 and CM5 (charge model 5) procedure.27 Most of the reported data were obtained using the MP2/aug-cc-pVTZ method. Atomic charges in aliphatic systems were discussed with focus on the hydrogen charges. Correlations with theoretically estimated proton affinities as well as with other molecular parameters have provided a basis for comparison of the performance of the tested population analysis methods. The correspondence between charges and experimental spectroscopic data for deuterated methanes and the hydrogen bonding energy for the methanol dimer were also analyzed. The results showed that the Hirshfeld method performs most consistently in deriving atomic charges. The focus of our research is to examine how well atomic charges obtained from the Mulliken, NPA, Hirshfeld and QTAIM procedures correlate with experimentally derived properties of aromatic compounds. Computations were conducted for a series containing benzene and 18 monosubstituted derivatives. The charges at carbon atoms at meta and para positions were evaluated and juxtaposed to the experimentally evaluated σ0m and σ0p substituent constants. The σ0 constants,28 evaluated using a fitting procedure to kinetic data for nearly 80 reaction series, is considered to represent best, among differently defined substituent constants, the properties of monosubstituted benzene derivatives.29 In determining the set of σ0 constants, special attention is paid to avoid the effects of the mesomeric para interaction between substituent and reaction center.28 Altogether the correlations obtained in the present research contain 37 data points. Additionally, we also evaluated the total charge exchange between the aromatic ring and the substituents. In a recent study Liu30 conducted similar studies using M062X density functional as well as Hartree-Fock and MP2 ab initio computations for a series of benzene derivatives and reached the unexpected conclusion that, independently of the type of substituent, the overall effect is a transfer of a negative charge from the ring to the substituent group. It was of interest to follow these trends on the basis of results for an extended series of derivatives.

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Methods The computations employed the B3LYP1 and ωB97X-D2 density functionals combined with the 6-311++G(3df,2pd) basis set.31 As discussed, the theoretical methods based on these functionals provide charge density distribution in a satisfactory accord with CCSD/aug-cc-pωCV5Z computations.4 We also conducted MP2 wave function computations on the studied systems using the same basis set. Since the σ0 constants are derived from kinetic data for reactions in different solvents, the computations conducted refer to the gas phase. Harmonic vibrational frequencies verified that the optimized geometries correspond to true minima of the potential energy surfaces. The sets of Mulliken, NPA, Hirshfeld, and QTAIM charges were evaluated for the carbon atoms at meta and para positions in the aromatic ring for the monosubstituted benzene derivatives considered in the present study (Table 1). Most computations were performed with the Gaussion09 program.32 Tight SCF convergence was employed. Ultrafine integration grids were used in applying the density functional theory methods. QTAIM charges were evaluated with the Multiwfn program.33 Cartesian coordinates and energies of all optimized structures are given in the Supporting Information. Besides atomic charges, we also evaluated for comparison the electrostatic potentials (EPN) at the respective nuclei. We have shown34 that this, otherwise long known,35 theoretical quantity may be successfully employed as a reactivity index, especially for interactions (hydrogen bonding, chemical reactions) involving series of structurally related species. EPN are rigorous quantum mechanical quantities. Politzer and Truhlar36 defined the electrostatic potential VY at the nuclear position of an atom Y by the expression:

VY  V (R Y ) 



A ( Y )

ZA  (r ) dr  R A  RY r  RY

(1)

In eqn. 1, ZA is the charge on nucleus A positioned at RA and ρ(r) is the electron density function. Equation (1) contains a summation over all atomic nuclei, treated as positive point charges, as well as integration over the continuous distribution of the electronic charge.


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Results and Discussion Table 1 and Table 2 contain the computed values of shifts (with respect to values for benzene) of NPA, Mulliken, Hirshfeld, and QTAIM atomic charges for the carbon atoms of benzene and for carbons at the meta and para ring positions of 18 monosubstituted derivatives. In the penultimate column of the tables the electrostatic potentials at nuclei for the same carbon positions are presented. The last columns in Table 1 and Table 2 contain the respective σ0m and σ0p substituent constants.29 The benzene derivatives considered contain both electron withdrawing and electron donating substituents, thus forming a representative set. From a theoretical perspective, kinetic data for reactions of aromatic systems are frequently interpreted in terms of computed charges for atoms in the respective reaction centers.37-40 As mentioned, the atomic charges provide a physically plausible approach in interpreting chemical reactivity for many interactions of aromatic compounds. Although a number of alternative theoretical indexes have been proposed, atomic charges are often the first to consider as potential reactivity descriptors. The physical basis for such an approach is the fundamental importance of the electron densities at reaction centers in determining the rates of many chemical reactions as well as of most types noncovalent interactions. We, therefore, correlated atomic charges derived using several popular procedures with the σ0 substituent constants. In determining the set of σ0 constants,28,29 special care has been taken to avoid the para mesomeric interaction between electron donating and electron withdrawing groups. This type of intramolecular effect may significantly influence the substituent constant values and also depends on the type of interacting groups involved. Such effects are, obviously, not present in monosubstituted benzene derivatives. We have, therefore, correlated the set of σ0m and σ0p substituent constants with the theoretically evaluated atomic charges at the respective aromatic ring carbon atoms to verify how well the differently defined charges characterize the local reactivities of the derivatives investigated. To secure consistency in the evaluated charges for the meta carbons in derivatives with unsymmetrical substituents, we used the following approach: for -OCH3, -NHCH3, and -OH substituents, the charges taken are for the meta carbons that are situated at greater distances to the CH3 group (in -OCH3 and -NHCH3) and the H atom (in –OH); for substituents containing a 5 ACS Paragon Plus Environment


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carbonyl group, the charges included in the tables are for the meta carbons on the side of the C=O moiety. In order to define more clearly the effects of substituents, the entries in Table 1, 2 and 3 contain the shifts of charges compared to the benzene values. ΔqX = qX – qbenzene

(2)

qX and ΔqX refer to charges for derivatives with substituent X. The last rows in the table contain the linear regression correlation coefficients for the relationships between shifts of charges and σ0 constants. The evaluated atomic charges for carbon atoms in benzene (qC) using NPA, Mulliken, Hirshfeld and QTAIM procedures with the B3LYP, ωB97X-D, and MP2 methods are given in Table S1 of the Supporting Information. Table 1: Shifts of chargesa (see Eqn. 2, in electron units) from different methods (NPA, Mulliken, Hirshfeld, and QTAIM) for the carbon atoms at meta and para positions in monosubstituted benzenes, shifts of EPN valuesa (ΔV, in a. u.) for the same carbon positions, and σ0 substituent constants. The theoretical quantities are from B3LYP/6-311++G(3df,2pd) computations. Substituent & Charge H CH3 OCH3 OH NH2 NHCH3 N(CH3)2 F Cl Br CHF2 COMe CO2CH3 CHO CF3

meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta

ΔqNPA

ΔqMulliken

ΔqHirsh

ΔqQTAIM

ΔV

σ0

0.0000 0.0081 -0.0093 0.0186 -0.0336 0.0230 -0.0337 0.0223 -0.0438 0.0202 -0.0485 0.0219 -0.0468 0.0200 -0.0176 0.0169 -0.0041 0.0175 -0.0021 0.0079 0.0113 -0.0029 0.0269 -0.0025 0.0253 -0.0036 0.0332 0.0084

0.0000 -0.0494 -0.1495 0.1960 -0.2905 -0.1454 0.0237 0.2120 -0.2615 0.0995 -0.2382 0.2368 -0.1862 0.0167 -0.1413 0.1578 -0.2969 0.3105 -0.4775 0.0634 -0.1861 -0.0249 -0.1961 0.0661 -0.2381 0.0679 -0.2219 0.1177

0.0000 -0.0015 -0.0063 0.0017 -0.0169 0.0041 -0.0160 -0.0011 -0.0227 -0.0029 -0.0254 -0.0040 -0.0258 0.0077 -0.0059 0.0077 0.0006 0.0085 0.0021 0.0058 0.0071 0.0017 0.0133 0.0030 0.0125 0.0050 0.0177 0.0092

0.0000 -0.0052 0.0018 0.0095 0.0020 -0.0065 0.0120 0.0057 -0.0027 0.0075 -0.0036 0.0065 -0.0057 0.0189 0.0097 0.0057 0.0101 0.0026 0.0123 0.0074 0.0106 0.0051 0.0052 0.0061 0.0090 0.0017 0.0124 0.0303

0.0000 -0.0032 -0.0052 -0.0012 -0.0084 0.0023 -0.0052 -0.0054 -0.0145 -0.0080 -0.0180 -0.0102 -0.0196 0.0135 0.0070 0.0142 0.0107 0.0149 0.0118 0.0126 0.0127 0.0129 0.0151 0.0098 0.0128 0.0187 0.0217 0.0196

0 -0.07 -0.12 0.06 -0.13 0.04 -0.13 -0.14 -0.38 -0.09 -0.33 -0.15 -0.44 0.33 0.2 0.38 0.24 0.38 0.26 0.32 0.35 0.34 0.46 0.36 0.46 0.41 0.47 0.47


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COF CN NO2 COOH r (corr. with σ0) a

para meta para meta para meta para meta para

0.0192 0.0003 0.0379 0.0066 0.0255 0.0084 0.0340 -0.0021 0.0292 0.649

-0.2795 0.0788 -0.1291 0.0168 -0.1251 0.3571 -0.4299 0.0349 -0.1498 0.026

0.0128 0.0089 0.0216 0.0155 0.0173 0.0132 0.0213 0.0047 0.0153 0.920

0.0153 0.0131 0.0151 0.0217 0.0163 0.0167 0.0181 0.0054 0.0035 0.681

0.0203 0.0242 0.0283 0.0270 0.0285 0.0304 0.0326 0.0137 0.0170 0.990

0.53 0.55 0.70 0.65 0.71 0.71 0.81 0.37 0.45

With respect the values in benzene.

Table 2: Shifts of chargesa (Eqn. 2, in electron units) from different methods (NPA, Mulliken, Hirshfeld and QTAIM) for the carbon atoms at meta and para positions in monosubstituted benzenes, shifts of EPN valuesa (ΔV, in a. u.) for the same carbon positions, and σ0 substituent constants. The theoretical quantities are from ωB97X-D/6-311++G(3df,2pd) computations. Substituent & Charge H CH3 OCH3 OH NH2 NHCH3 N(CH3)2 F Cl Br CHF2 COMe CO2CH3 CHO CF3 COF CN

meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para meta para

ΔqNPA

ΔqMulliken

ΔqHirsh

ΔqQTAIM

ΔV

σ0

0.0000 0.0090 -0.0104 0.0221 -0.0368 0.0263 -0.0373 0.0261 -0.0468 0.0247 -0.0511 0.0267 -0.0519 0.0217 -0.0204 0.0174 -0.0042 0.0174 -0.0017 0.0077 0.0106 -0.0039 0.0261 -0.0036 0.0252 -0.0047 0.0320 0.0076 0.0190 -0.0024 0.0372 0.0058 0.0261

0.0000 -0.0149 -0.1230 0.2473 -0.2704 -0.0543 0.0027 0.2681 -0.2564 0.3747 -0.2191 0.2756 -0.1532 0.0850 -0.1483 0.2306 -0.3072 0.3829 -0.4704 0.1150 -0.1645 0.0383 -0.1591 0.1417 -0.2185 0.0119 -0.1039 0.1791 -0.2558 0.1042 -0.1115 0.0642 -0.1311

0.0000 -0.0012 -0.0066 0.0029 -0.0177 0.0051 -0.0171 0.0003 -0.0233 -0.0008 -0.0258 -0.0022 -0.0265 0.0081 -0.0070 0.0080 0.0008 0.0085 0.0024 0.0055 0.0068 0.0012 0.0128 0.0025 0.0124 0.0043 0.0170 0.0087 0.0125 0.0079 0.0210 0.0113 0.0176

0.0000 -0.0086 -0.0039 0.0090 -0.0037 0.0198 -0.0032 0.0023 -0.0079 0.0097 -0.0101 0.0023 -0.0027 0.0234 0.0039 0.0256 -0.2511 0.0261 0.0059 0.0290 0.0043 0.0480 -0.0328 0.0065 0.0040 0.0090 0.0074 0.0051 0.0101 0.0136 0.0104 0.0065 0.0115

0.0000 -0.0031 -0.0052 -0.0006 -0.0085 0.0025 -0.0057 -0.0045 -0.0144 -0.0069 -0.0175 -0.0091 -0.0194 0.0134 0.0063 0.0143 0.0108 0.0148 0.0119 0.0121 0.0121 0.0123 0.0145 0.0095 0.0126 0.0178 0.0208 0.0190 0.0197 0.0232 0.0273 0.0271 0.0288

0 -0.07 -0.12 0.06 -0.13 0.04 -0.13 -0.14 -0.38 -0.09 -0.33 -0.15 -0.44 0.33 0.20 0.38 0.24 0.38 0.26 0.32 0.35 0.34 0.46 0.36 0.46 0.41 0.47 0.47 0.53 0.55 0.70 0.65 0.71



NO2 COOH r (corr. with σ0) a

meta para meta para

0.0072 0.0329 -0.0036 0.0290 0.608

0.4351 -0.3952 0.1025 -0.1380 0.017

0.0125 0.0206 0.0040 0.0150 0.896

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0.0065 0.0127 0.0140 0.0111 0.111

0.0297 0.0318 0.0130 0.0165 0.990

0.71 0.81 0.37 0.45

With respect the values in benzene. As a theoretical verification approach, we evaluated also the electrostatic potentials at

nuclei for the considered meta and para carbon atoms in the ring. As discussed, EPN are rigorously defined quantities. Nonetheless, because of the complex contributions from nuclear charges and electron densities (Eqn. 1), EPN may only provide approximate information on the electron density distribution. Still, for sufficiently distant from the substituent groups ring positions, the major contributions to EPN for the ring carbons come from the electron densities and positive charges around the respective sites. Since the nuclear charges in the ring have almost identical geometric placement for all derivatives, the shifts of EPN for the meta and para carbons upon substitutions depend strongly on the variations of the local electron densities at the respective ring sites.34,41 The two density functional theory methods employed [(B3LYP/6-311++G(3df,2pd) and ωB97X-D/6-311++G(3df,2pd)] provide quite similar results for the effects of substituents on the intramolecular charge distribution as reflected in the computed shifts of atomic charges (Tables 1, 2). Overall, the results from the NPA, Hirshfeld and QTAIM computations may be regarded as satisfactory. For instance, the values for charge shifts (in electron units) from NPA analysis at the para carbons in the series of electron-donating substituents -CH3 (-0.0093), -OCH3 (-0.0336), OH (-0.0337), -NH2 (-0.0438), -NHCH3 (-0.0485), and -N(CH3)2 (-0.0486) vary in full accord with the expected influence of the substituents as reflected in the σ0p constants (Table 1). Similarly, the shifts of QTAIM charges for the para carbons provide good results. Inversely, the electronwithdrawing groups always produce positive charge shifts in very good accord with the variations in the σ0 constants. There are, however, some disaccords with the σ0 constants for the predicted charge shifts for the meta carbons from NPA and QTAIM computations. For charge variations induced by strong electron-donating groups, such as -NH2 (0.0223), -NHCH3 (0.0202), and N(CH3)2 (0.0219), the NPA methods predicts positive charge shifts not corresponding to the respective negative σ0m constant values. The Mulliken charges clearly do not perform well. The 8 ACS Paragon Plus Environment

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correlation coefficients for the relationships with σ0 are very low, 0.026 and 0.017 using both B3LYP and ωB97X-D methods (Tables 1,2). Among the three tested methods, the Hirshfeld charges produce better correlations with the σ0 constants. The correlations coefficients are r = 0.920 [for charges from B3LYP/6-311++G(3df,2pd) computations] and r = 0.896 [from ωB97XD/6-311++G(3df,2pd)]. Notably, the Hirshfeld charges predict correctly the charge shifts (in electron units) for the meta position in benzene derivatives containing electron-donating groups. Table 3: Shifts of chargesa (Eqn. 2, in electron units) from different methods (NPA, Mulliken, Hirshfeld and QTAIM) for the carbon atoms at meta and para positions in monosubstituted benzenes, shifts of EPN valuesa (ΔV, in a. u.) for the same carbon positions, and σ0 substituent constants. The theoretical quantities are from MP2/6-311++G(3df,2pd) computations. Substituent & Charge H CH3 OCH3 OH NH2 NHCH3 N(CH3)2 F Cl Br CHF2 COMe CO2R CHO CF3 COF CN

ΔqNPA

ΔqMulliken

ΔqHirsh

ΔqQTAIM

meta para meta para meta para meta para meta para meta para meta

0.0000 0.0029 -0.0028 0.0067 -0.0193 0.0098 -0.0190 0.0049 -0.0225 0.0025 -0.0249 0.0049 -0.0252 0.0142

0.0000 -0.0237 -0.0332 0.2098 -0.1291 -0.0551 0.0733 0.2113 -0.1420 0.1374 -0.0852 0.2463 -0.0078 0.0689

0.0000 -0.0032 -0.0039 -0.0024 -0.0120 -0.0006 -0.0108 -0.0063 -0.0147 -0.0079 -0.0164 -0.0085 -0.0167 0.0050

0.0000 -0.0006 0.0005 0.0069 0.0087 0.0011 0.0106 0.0153 0.0061 0.0077 0.0047 0.0062 0.0040 0.0078

para meta para meta para meta para meta para meta para meta para meta para meta para meta

-0.0121 0.0170 -0.0040 0.0198 -0.0037 0.0124 0.0076 0.0124 0.0116 0.0159 0.0073 0.0129 0.0158 0.0177 0.0107 0.0199 0.0160 0.0212

-0.0835 0.1782 -0.2442 0.3115 -0.3695 0.0662 -0.0640 0.0488 -0.0866 0.1517 -0.1899 -0.0171 -0.0385 0.1391 -0.1834 0.0561 -0.0439 0.0420

-0.0042 0.0071 0.0008 0.0084 0.0018 0.0068 0.0059 0.0060 0.0080 0.0082 0.0065 0.0091 0.0114 0.0116 0.0098 0.0144 0.0138 0.0154

0.0142 0.0229 0.0131 0.0023 0.0127 -0.0096 0.0054 0.0096 0.0143 0.0142 0.0026 0.0137 0.0020 0.0114 0.0101 0.0189 0.0048 0.0266


ΔV 0.0000

-0.0033 -0.0041 -0.0017 -0.0064 0.0014 -0.0033 -0.0054 -0.0107 -0.0075 -0.0133 -0.0092 -0.0145 0.0126 0.0073 0.0139 0.0107 0.0144 0.0114 0.0125 0.0118 0.0135 0.0127 0.0106 0.0102 0.0188 0.0185 0.0197 0.0188 0.0241 0.0243 0.0275

σ0 0 -0.07 -0.12 0.06 -0.13 0.04 -0.13 -0.14 -0.38 -0.09 -0.33 -0.15 -0.44 0.33

0.20 0.38 0.24 0.38 0.26 0.32 0.35 0.34 0.46 0.36 0.46 0.41 0.47 0.47 0.53 0.55 0.7 0.65


para meta para meta para

NO2 COOH r (corr. with σ0) a

0.0105 0.0328 0.0071 0.0169 0.0100 0.792

-0.0863 0.3721 -0.3249 0.0999 -0.1111 0.058

0.0120 0.0191 0.0114 0.0101 0.0087 0.959

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0.0103 0.0302 0.0111 0.0142 0.0026 0.394

0.0262 0.0303 0.0274 0.0144 0.0141 0.980

0.71 0.71 0.81 0.37 0.45

With respect the values in benzene.

The charge shifts [ωB97X-D/6-311++G(3df,2pd)] induced by the strong electron donor substituents -NH2 (-0.0063), -NHCH3 (-0.0079), and -N(CH3)2 (-0.0085) are negative and change in harmony with the respective σ0m constant values. The conducted density functional theory computations suggest some preference for the the Hirshfeld charges in describing properties of aromatic compounds. Krygowski et al.42,43 have successfully applied Hirshfeld charges in analyzing the nature of substituent effects in aromatic systems. Liu et al.44 employed Hirshfeld charges in quantifying reactivity in electrophilic aromatic substitution reactions. A good confirmation of these findings comes from applying MP2 computations employing the same 6-311++G(3df,2pd) basis set. The obtained results are presented in Table 3. The correlation between ΔqHirsh charges and of σm0 and σp0 values is very good, especially considering the expected only qualitative relationship between charges and substituent constants.


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Figure 1. Correlation between shifts of Hirshfeld charges (ΔqHirsh) for carbon atoms at meta and para position calculated at MP2/6-311++G(3df,2pd) and σm0 and σp0 substituent constants. The plot between ΔqHirsh and σ0 is illustrated in Figure 1. The MP2 wave functions are expected to provide more realistic charge density distribution in molecules and better correspondence with experiment. The individual entries for the Hirshfeld charges on meta and para ring carbons follow quite nicely the sign and magnitude of the respective substituent constants. The obtained correlation coefficient for the relationship between ΔqHirsh for the meta and para ring carbons and σ0 constants (r = 0.959) reveals a good correspondence between the induced by substituents variations in charges and site reactivities. The computed NBO charges also provide a satisfactory qualitative description of the site properties of the studied benzene derivatives (Table 3). As already emphasized, electrostatic potentials at nuclei (EPN) have been successfully employed in rationalizing reactivity trends for both noncovalent interactions and chemical reactions.34,41 The penultimate columns of Tables 1-3 contain the shifts of EPN values (ΔV, with respect to values in benzene) for the meta and para carbon positions in the aromatic derivatives investigated. As expected, quite good correlations between ΔV and σ0 are established. The data in Tables 1-3 show that the electrostatic potentials at nuclei provide better correlations with the σ0 constants than the atomic charges considered in the present research. It should be emphasized, nonetheless, that the EPN values depend on both the electron density and the 11 ACS Paragon Plus Environment


positive nuclei charges. (Eqn. 1). Thus, because of the inverse relationship to distance, good correlations between EPN values and kinetic parameters may only be expected when the structural variations (e. g. changes of substituents) are at distance to the reaction center. This is the case for the series treated in the present study. No such limitations exist when atomic charges are applied. The good correlations with the gas-phase EPN values show also that the relationships established between atomic charges and the σ0 constants are similarly reliable. The application of EPN values in characterizing properties of aromatic derivatives was examined in detail in an earlier study.41 As mentioned in the introductory section, an interesting point with respect to the substituent effects in benzene derivatives has been raised in a theoretical study of Liu.30 This author reported RHF/aug-cc-pVDZ computational data, which revealed that for a series of seven benzene derivatives containing both electron-donating and electron-withdrawing groups, the overall charge shifts is always a transfer of a negative charge from the ring to the substituent. This result is supported by atomic charges obtained from five alternative population analysis methods. In the present research we examined the charge transfer between substituents and the aromatic ring over an extended series of benzene derivatives. Our analysis is based on results from the four alternative population analysis methods employed in this study. B3LYP, ωB97X-D density functional and MP2 ab initio methods combined with the 6-311++G(3df,2pd) basis set were used. Table 4 presents the results of the conducted computations for the Δq(C6H5) = [q(C6H5X) – q(C6H5H)] charge transfers. The series of substituents includes additionally three negatively charged groups: Oˉ, Sˉ, and COOˉ. All four population analysis methods predict a negative charge transfer from the Oˉ, Sˉ, and COOˉ substituents to the ring (Table 4). The wellestablished electron-donating CH3, OCH3, and OH groups, which are known to enhance the reactivity in electrophilic aromatic substitution reactions, are predicted to extract electronic density from the ring. The electronwithdrawing inductive effects along the sigma bonds, appear to overcome the electron-releasing resonance effect along the π-electron system. For the stronger electron-donating NH2, NHCH3, and N(CH3)2 groups, only the Hirshfeld charges predict correctly the expected transfer of a negative charge from the substituents to the ring. In a recent study, we discussed the charge transfer and methyl hyperconjugative effects in a theoretical and spectroscopic investigation of π-hydrogen bonding complexes between substituted phenols and hexamethylbenzene.45


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Table 4. Total charge shifts in the C6H5 moiety (in electron units) induced by substituents [q(C6H5X) - q(C6H5H)] in monosubstituted benzenes from theoretical computations. Substituent & charges

qNPA

qMulliken

qHirsh

qQTAIM

qNPA

B3LYP/6-311++G(3df,2pd) H CH3 OCH3 OH NH2 NHCH3 N(CH3)2 F Cl Br CHF2 COCH3 COOCH3 CHO CF3 COF CN NO2 COOH Oˉ Sˉ COOˉ

qMulliken

qHirsh

qQTAIM

qNPA

wB97XD/6-311++G(3df,2pd)

qMulliken

qHirsh

qQTAIM

MP2/6-311++G(3df,2pd)

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.1665

0.1554

0.0166

-0.0458

0.1696

0.1064

0.0174

-0.0206

0.1649

-0.0199

0.0187

-0.0747

0.4240

0.4080

0.0533

0.5469

0.4298

0.3813

0.0582

0.5727

0.4188

0.4520

0.0569

0.6511

0.4143

0.4211

0.0652

0.5526

0.4183

0.3868

0.0683

0.5778

0.4123

0.4841

0.0700

0.6550

0.2539

0.4472

-0.0135

0.3415

0.2637

0.4035

-0.0073

0.3610

0.2663

0.4914

-0.0004

0.4650

0.2525

0.3178

-0.0313

0.3243

0.2645

0.2984

-0.0229

0.3501

0.2665

0.3800

-0.0145

0.4587

0.2615

0.2890

-0.0393

0.3100

0.2729

0.2917

-0.0321

0.3327

0.2762

0.3470

-0.0207

0.4425

0.5589

0.5631

0.1518

0.6742

0.5594

0.5267

0.1535

0.6897

0.5491

0.6105

0.1522

0.7549

0.1968

0.2548

0.1288

0.2498

0.2002

0.2484

0.1337

0.0050

0.1762

0.2424

0.1232

0.3030

0.1390

0.2289

0.1660

0.1198

0.1350

0.2472

0.1667

0.1235

0.1066

0.1963

0.1565

0.1247

0.1858

0.1094

0.0675

0.1148

0.1825

0.0853

0.0653

0.1076

0.1754

0.0145

0.0608

0.1141

0.1997

0.4597

0.0898

0.0694

0.1915

0.3526

0.0860

0.0638

0.1791

0.2941

0.0761

0.0561

0.2091

0.2836

0.0890

0.1384

0.2033

0.7947

0.0878

0.1343

0.1974

0.0982

0.0750

0.1546

0.2054

0.3706

0.1228

0.0971

0.1954

0.3551

0.1168

0.0895

0.1837

0.2162

0.1040

0.0848

0.1994

0.0963

0.0964

0.1960

0.1949

0.0867

0.0937

0.1865

0.1902

0.0137

0.0869

0.2207

0.2204

0.3771

0.1490

0.2220

0.2097

0.3254

0.1428

0.2086

0.2008

0.2523

0.1290

0.2500

0.2270

0.7199

0.1940

0.2842

0.2279

0.6616

0.1971

0.2890

0.2147

0.3555

0.1828

0.3626

0.4695

0.8908

0.1944

0.5375

0.4606

0.8714

0.1910

0.5437

0.4372

0.9623

0.1663

0.6961

0.1788

0.4496

0.1192

0.1153

0.1732

0.4046

0.1169

0.1092

0.1987

0.2413

0.0934

0.1787

-0.0031

-0.0678

-0.4844

0.2749

0.0115

-0.1051

-0.4739

0.3107

-0.0195

-0.0270

-0.4866

0.4356

-0.7301

-0.2155

-0.4112

-0.9914

-0.2593

0.1253

-0.3029

-0.4778

-0.2953

0.0754

-0.3152

-0.6869

-0.4132

-0.1241

-0.1923

-0.1832

0.0094

-0.1384

-0.1835

-0.1900

-0.0005

-0.1813

-0.1864

-0.2525



The approach adopted in the present research of correlating atomic charges with substituent constants derived from kinetic experiments appears to offer a realistic assessment of the performance of different population analysis methods. As already emphasized, theoretically evaluated atomic charges are invaluable tool for understanding various processes in chemistry, physics, and biology. Thus, finding a good correlation between charges and experimental quantities at an appropriate level of theoretical computations, provides a clear support for the use of these quantities in theoretical modeling research as well as in understanding experimental findings. Summary The performance of Mulliken, NPA, Hirshfeld, and QTAIM population analysis methods in predicting the site reactivities at the meta and para ring carbons for a series comprising benzene and 18 monosubstituted derivatives is examined. A quantitative correspondence between atomic charges from Hirshfeld population analysis and the σ0 substituent constants is established. The application of Møller–Plesset second-order perturbation theory (MP2) computations appear to be essential in obtaining a satisfactory accord between predicted trends of variation of atomic charges for the ring carbons and the experimental σ0m and σ0p constants. NPA and QTAIM atomic charges provide in most cases a satisfactory qualitative description of substituent effects in the monosubstituted benzenes. The overall charge transfers between substituents and the aromatic ring is determined with the aid of theoretically evaluated atomic charges. Acknowledgements. Financial support from the National Science Fund (Bulgaria), Grant DN 09/4, and EU Grant „Materials Networking“ is gratefully acknowledged. Supporting Information. Charges of the carbon atoms in benzene from different theoretical methods, Cartesian coordinates and energies of all optimized structures.

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Atomic Charges in Describing Properties of Aromatic Molecules - The

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