Towards understanding proton affinity and gas-phase basicity with density functional reactivity theory

Chemical Physics Letters 527 (2012) 73–78

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Towards understanding proton affinity and gas-phase basicity with density functional reactivity theory Ying Huang a,⇑, Lianghong Liu a, Shubin Liu b,⇑ a b

School of Pharmacy, Hunan University of Chinese Medicine, Changsha Hunan 410208, China Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA

a r t i c l e

i n f o

Article history: Received 21 October 2011 In final form 6 January 2012 Available online 13 January 2012

a b s t r a c t The proton affinity and gas-phase basicity of 14 heterocyclic aromatic compounds containing two or more nitrogen atoms are investigated in this work. Strong linear correlations of these quantities with the molecular electrostatic potential on the nitrogen nuclei and natural valence orbital energies were observed. We justified the relationships under the framework of density functional reactivity theory as the first-order approximation. These linear relationships suggest that the associating proton prefers to bind with the basic atom with the lowest electrostatic potential value. Different density functional formulas and basis sets have been employed to verify the validity of these results. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction There have been tremendous recent interests in the literature to accurately predict the molecular acidity for Brønsted acids using ab initio or density functional theory approaches [1–5]. The reaction in concern is the proton dissociation reaction of acids, HA , A + H+, and molecular acidity denoted by the pKa value is defined as the negative logarithm, pKa = log10 Ka, of the equilibrium constant Ka of this reaction with Ka = [A][H+]/[HA]. In thermodynamics, the equilibrium constant Ka is related to the standard Gibbs free energy change DG° of the above reaction, DG° = 2.303 RT pKa, where R is the gas constant and T is the temperature in Kelvin. This free energy change can be computationally simulated by using ab initio and DFT methods through a thermodynamic cycle, which is often not only computationally demanding but also numerically inaccurate because of the errors introduced in the implicit solvent model and proton hydration calculations. Recently, we employed two quantum descriptors, the molecular electrostatic potential (MEP) on the nucleus of either the acidic atom or the leaving proton and the natural atomic orbital (NAO) on each of the above two atoms, to predict pKa values [6–9]. We justified the usage of these quantities under the framework of density functional reactivity theory (DFRT) [10–12]. This approach has been applied to a number of organic [6] and inorganic systems [7] and, very recently, we compared its prediction accuracy with the method using Hammett constants for singly, doubly, and multiply

⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Huang), shubin@email. unc.edu (S. Liu). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2012.01.014

substituted benzoic acids [9]. Other computational approaches aiming at interpreting basicity are available in the literature [13–16]. In this work, we consider the proton affinity and gas-phase basicity of Brønsted bases. The gas-phase basicity, also called absolute or intrinsic basicity, is defined as the negative of the Gibbs free energy change (DG) in the gas phase associated with the following proton dissociation reaction,

BHþ () B þ Hþ :

ð1Þ

The proton affinity is the negative of the enthalpy change (DH) of this same reaction in the gas phase. The main purpose of this work is to understand the proton affinity and gas-phase basicity of a base by correlating these quantities with its electronic properties. To that end, we consider its reverse reaction, B + H+ , BH+, where the base B binds to an incoming proton to form its conjugate acid HB+. We will show that the two quantum descriptors, MEP and NAO, of the base can also be used to predict its gas-phase basicity and proton affinity. We justify this observation by the DFRT framework as a result of the first-order approximation of the total energy expansion in Taylor series. As a demonstration, we apply the approach to 14 heterocyclic aromatic compounds containing two or more basic (nitrogen) atoms. With MEP and NAO quantities, we can not only correctly predict which nitrogen atom the incoming proton will be bonded to, but also observe a strong linear relationship between the MEP on the basic atom and the energy change in Eq. (1), confirming the validity of our present approach. These and other results from this work will be tested using different basis sets and density functionals.

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2. Theoretical framework and computational details In DFRT [10–12], for the proton to dissociate from an acid, because the total number of electrons N does not change during the process, up to the second order, the total energy change DE of the proton dissociation reaction can be approximated by the following Taylor expansion [7,9],

DE ¼

Z

qðrÞDmðrÞdr þ

1 2

ZZ

vðr; r0 ÞDmðrÞDmðr0 Þdrdr0

ð2Þ

Z

qðrÞDmðrÞdr

ð3Þ

where the external potential change due to the proton dissociation can simply be expressed as

DmðrÞ ¼

X Z i dðr  Ri Þ 1  jR jr  RH j  R j H i i–H

ð4Þ

Put together, as the first-order approximation, the total energy change is simply the molecular electrostatic potential (MEP) on the leaving proton, MEPH, [7]

DE  MEPH 

X i–H

Zi  jRi  RH j

Z

qðrÞ ds jr  RH j

ð5Þ

Also, we found that MEP on the leaving proton nucleus, MEPH, is intrinsically related to the valence natural atomic orbital (NAO) energy of the leaving proton, NAOH. This strong correlation can be readily understood because the quantity of MEPH is generated by the charge density distribution mostly from the orbital contribution from the proton, i.e., NAOH [7]. Meanwhile, we have also disclosed that the MEP on the nucleus of the acidic atom, e.g., oxygen atom for the carboxyl acid, is another reliable descriptor of the pKa value, i.e.,

pKa / MEPA 

X i–A

DE / MEPN 

X i–A

where q(r) is the electron density, v(r,r0 ) denotes the linear response function defined by the second-order derivative [d2E/ dm2(r)]N, and dm(r) stands for the change in the external potential due to the rearrangement of atomic nuclei before and after the reaction. Moreover, if only the first-order term is considered in Eq. (2), an even simpler relationship can be obtained [7]

DE 

longer befitting. Nevertheless, Eq. (6) should still be applicable for the basic atoms. Employing the same approximations we used elsewhere, in this work, we propose that the total energy difference DE of the proton association reaction, Eq. (1), can be utilized to predict the proton affinity and molecular basicity in gas phase. With this, for nitrogen-containing species as an example, we henceforth propose that

Zi  jRi  RA j

Z

qðrÞ ds; jr  RA j

ð6Þ

and the sum of valence natural atomic orbitals (i.e., 2px, 2py, and 2pz valence atomic orbitals of the same oxygen atom) has been shown to be strongly correlated with the MEP on the acidic nucleus as well [6]. We have demonstrated the validity of these correlations elsewhere in different systems [6–9]. Notice that to arrive to Eqs. (5) and (6), following approximations have been made. We have (i) neglected the thermodynamic contribution from solvent and temperature effects, (ii) truncated the Taylor expansion series in Eq. (2) to the first order, and (iii) omitted the relaxation in the external potential before and after the proton is dissociated. Notice that contributions from the linear response function in the second-order term in Eq. (2) could be important for the systems where polarization effects play an important role. Neglecting these contributions is the source of errors in our present approach. For Brønsted bases, in the proton association reaction in Eq. (1), the total number of electrons is also unchanged. For the same reason, Eqs. (2) and (3) as the second and first order approximations, respectively, should still be valid. The only difference between the acid and base cases is the external potential change before and after the reaction, Dm(r). In the acid case, we found that Dm(r) can simply be approximated by the MEP on the leaving proton, MEPH. In the base case, however, we do not know which basic atom the incoming proton will be bonded to, so Eqs. (4) and (5) are no

Zi  jRi  RN j

Z

qðrÞ ds; jr  RN j

ð7Þ

where the letter N stands for the basic nitrogen atom of the systems in concern. Since MEP is a negative quantity, Eq. (7) implies that the more negative the MEP value, the stronger the molecular basicity, the larger the proton affinity and gas-phase basicity. Another consequence of this formula is that for systems with multiple sites of the same basic element type, the most basic site (largest energy decrease) has the most negative MEP value. To verify this formalism, we employ 14 heterocyclic aromatic compounds containing two or more nitrogen atoms. To calculate the proton affinity and gas-phase basicity for each nitrogen atom in these species we bind a proton to each of the nitrogen atoms, one at a time according to Eq. (1), and then calculate the total energy (DE), enthalpy (DH) and free energy (DG) differences of the reaction in gas phase. At first, we will show that there exist strong linear correlations among DE, DH, and DG for these species. We will then demonstrate that the most negative MEP site is indeed the most basic nitrogen atom in a system with Eq. (7) held true. In addition, we will reveal that there exists a strong linear correlation between the MEP difference and the total energy difference DE of Eq. (1) between two basic sites, i.e.,

DDE / DMEPB :

ð8Þ

These 14 heterocyclic aromatic nitrogen-containing species are adenine, benzimidazole, caffeine, cinnoline, cytosine, guanine, imidazole, indazole, pruine, pyrazole, quinazoline, thymine, tioguanine, and uracil. Scheme 1 includes these 14 systems studied in this work, where the numbering of the basic nitrogen atoms is also exhibited. A full structure optimization for each of these model structures in gas phase at 0 K was first carried out at the DFT B3LYP/6-311++G(d,p) level of theory [17,18]. We also considered another density functional, M06-2X [19], and another basis set, aug-CC-pvTZ, with which both structure optimization and singlepoint calculations were performed separately. When a molecule has more than one stable conformation, all conformers will be examined and the one with the lowest energy will be picked for the subsequent calculations. After the structure optimization, a frequency calculation for each of the systems was carried out to check that the optimized structure was indeed a minimum (i.e., with no imaginary frequency). A single point calculation was ensued to compute the molecular electrostatic potential on each of the nuclei followed by a full NBO (Natural Bonding Orbital) analysis to obtain the natural atomic orbital energies. All calculations were performed with the GAUSSIAN 09 package Version B01 [20] with tight self-consistent field convergence and ultrafine integration grids. 3. Results and discussion Table 1 shows the numerical data of the total electronic energy difference DE, enthalpy change DH, entropy contribution TDS for the proton association reaction of the systems studied in this work, Eq. (1), from which one obtains the proton affinity and gas-phase basicity. Also shown in the table are the experimental proton affinity and gas-phase basicity values for a few systems [21]. Under the standard state conditions, the values of the enthalpy and entropy of the gas-phase proton are H(H+) = 1.48 kcal/mol and S(H+) =

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Scheme 1. A total of 14 heterocyclic aromatic compounds containing two or more nitrogen atoms studied in this work.

Table 1 Calculated total electronic energy difference DE, enthalpy change DH, entropy contribution TDS for the proton association reaction of the systems studied in this work, Eq. (1), from which one computes and obtains the proton affinity and gas-phase basicity. Also shown are the experimental proton affinity values for a few systems. All units in kcal/mol.

Adenine Benzimidazole Caffeine Cinnoline Cytosine Guanine Imidazole Indazole Purine Pyrazole Quinazoline Thymine Tioguanine Uracil a

DE

TDS

Proton affinity

Gas-phase basicity

Proton affinity (exp)a

Gas-phase basicity (exp)a

229.57 232.56 221.38 231.06 232.99 232.52 230.88 219.73 224.90 218.13 224.75 181.50 232.61 179.15

0.81 0.06 0.37 0.09 0.34 0.43 0.05 0.56 0.10 0.27 0.24 0.96 0.48 0.32

222.61 225.31 214.79 223.52 225.19 225.61 223.56 213.00 217.85 211.34 217.76 175.18 225.97 173.48

214.04 217.60 206.67 215.84 217.77 218.29 215.85 205.80 210.19 203.85 210.24 168.38 218.69 165.40

223.50 – – 223.20 223.80 222.30 219.80 – 218.30 209.90 – – – –

215.7 – – 215.4 – 215.0 212.0 – 211.5 – – – – –

Experimental data from Ref. [21].

26.02 cal/(mol K), respectively, and lead to a gas-phase Gibbs freeenergy value of G(H+) = H(H+)  TS(H+) = 6.28 kcal/mol [22]. From the table, one can see that our calculated results are in good agreement with the experimental data. Also, the enthalpy (proton affinity) and Gibbs free energy (gas-phase basicity) differences are close to each other in value, because the entropy contribution for these species is relatively small, as witnessed by the TDS values in the table. Plotting the total energy difference DE vs. either the enthalpy difference DH or the Gibbs free energy difference DG (not shown), we find that the correlation coefficient is larger than 0.999, indicating that there exists a near perfect correlation between DE and DH (proton affinity) or between DE and DG (gas-phase basicity) for the systems studied in this work. These strong correlations among the three quantities, DE, DH, and DG, suggest that the proton affinity and gas-phase basicity of these species are linearly correlated and they can be represented by the total energy difference DE, if one only cares the trend, not their absolute values. Because of this

reason, in our later discussion, we employ DE as the representative of these three quantities. When a good relationship is found for DE, so will be it for DH and DG. Figure 1 plots the relationship at the DFT M06-2X/60311++G(d,p) level of theory between the molecular electrostatic potential on the nitrogen atoms, MEPN, of the 14 heterocyclic aromatic nitrogen-containing compounds and above three quantities, i.e., gas-phase basicity in Figure 1a, total energy difference in Figure 1b, and the proton affinity in Figure 1c. As can be seen from the figure, there exists a strong linear correlation between MEPN and DG with the correlation coefficient R2 = 0.927, between MEPN and DE with R2 = 0.932, and between MEPN and DH with R2 = 0.931. These linear relationships confirm what we have observed above that these three quantities (DE, DH, and DG) are strongly correlated. More importantly, they confirm that as the first-order approximation from Eq. (2) in DFRT, Eq. (7) is indeed still valid, for the systems investigated in this work. The negative

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Figure 1. The strong linear correlation of (a) the gas-phase basicity, (b) the total energy difference of Eq. (1), and (c) proton affinity represented with the molecular electrostatic potential (MEP) on all nitrogen atoms of the 14 heterocyclic aromatic nitrogen-containing compounds. All calculations were done at the DFT M06-2X/6311++G(d,p) level of theory.

of the table is the comparison of the total energy difference, DDE, for each of the 14 species between the two reactions in Eq. (1) where the proton binds to the site with the lowest and second lowest MEPN values, i.e., DDE = DE2nd_lowest_MEP  DElowest_MEP. The fact that all DDE in the table is always positive, DDE > 0, indicates that when the proton binds to the nitrogen atom with the lowest MEPN (i.e., the underlined in Table 2) the total energy difference of Eq. (1), DE, will be invariably the lowest. That is to say, thermodynamically speaking, for a proton in Eq. (1) to bind to the basic site with a lower MEP is more likely to occur because it possesses a lower DE. On the other hand, since DE strongly correlates with the proton affinity and gas phase basicity, a larger DE suggests a larger proton affinity and stronger gas-phase basicity. In addition, from the DDE data in Table 2, we can see that our current approach is applicable to a wide range of DDE value predictions and the smallest DDE

slope of the linear correlations in the figure shows that the more negative the MEP value on the basic nucleus, the stronger basicity of the nitrogen atom. This result predicts that if a molecule contains more than one basic site of the same element type, e.g., the nitrogen element in this study, the atom with the smallest MEP (i.e., the biggest in magnitude) should be the site to preferably bond with the incoming proton. To verify the above prediction, Table 2 shows the MEP values on the nucleus of all nitrogen atoms in the 14 systems studied at the M06-2X/6-311++G(d,p) level of theory. The number underlined denotes the smallest MEPN value for each of the 14 species and its corresponding nitrogen atom is predicted to be the binding site in Eq. (1) for the proton. We predict that N4 is the proton binding site for adenine and purine (Scheme 1), N1 is the binding site for quinazoline, and N2 is the site for others. Shown in the last column

Table 2 The molecular electrostatic potential on the nucleus of all nitrogen atoms in the 14 systems studied at the M06-2X/6-311++G(d,p) level of theory (in a.u.). The underlined number represents the smallest MEPN value in a molecule and its corresponding nitrogen atom is predicted to be the binding site in Eq. (1) for the proton association. Shown in the last column is the comparison of the total energy difference, DDE, between the two reactions in Eq. (1) where the proton binds to the site with the lowest and second lowest MEPN values. That is, DDE = DE2nd_lowest_MEP  DElowest_MEP. The unit of DDE is in kcal/mol. N1

N2

N3

N4

N5

18.39 716

18.40 306

18.35 900

Adenine

18.31 632

18.38 870

Cenzimidazole

18.32 440

18.40 750

Caffeine

18.29 645

18.38 558

18.35 559

18.35 741

Cytosine

18.32 916

18.41 187

18.35 176 18.38 424

Guanine

18.31 772

18.39 870

18.32 507

18.41 566

Indazole

18.31 176

Purine

18.30 605

18.36 479 18.38 281

Pyrazole

18.30 749

Quinazoline Thymine

18.38 670 18.31 153

Tioguanine

18.29 980

18.39 322

Uracil

18.30 562

18.32 563

1.7 41.0

Cinnoline

Imidazole

DDE

18.32 851

18.32 193

24.3 1.0 31.8

18.32 359

18.34 165

16.8 52.4 20.9

18.37 474

6.5

18.38 816

34.8

18.37 799 18.38 529

0.1 0.6

18.32 804 18.37 780

18.30 434

18.34 201

16.1 3.5

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Figure 2. Strong linear correlations (a) between molecular electrostatic potential (MEP) and the natural atomic orbital (NAO) of all the nitrogen atom with the correlation coefficient R2 = 0.977; and (b) between total energy difference and MEP difference between two systems with the correlation coefficient R2 = 0.90, for the 14 heterocyclic aromatic species containing two or more nitrogen atoms. All calculations were done at the DFT M06-2X/6-311++G(d,p) level of theory.

Table 3 Comparison of DMEPN and DDE results in Eq. (8) with different approximate exchange–correlation energy density functionals and basis sets. Units in kcal/mol. B3LYP/6-311++G(d,p)

Adenine Benzimidazole Caffeine Cinnoline Cytosine Guanine Imidazole Indazole Purine Pyrazole Quinazoline Thymine Tioguanine Uracil

M06-2X/6-311++G(d,p)

M06-2X/aug-CC-pvTZ

DMEP

DDE

DMEP

DDE

DMEP

DDE

3.0 53.2 36.9 0.8 39.2 10.0 56.9 35.1 3.2 44.8 0.9 11.2 9.3 13.1

1.4 41.3 24.3 1.2 31.0 17.9 51.5 20.6 6.7 34.0 0.2 2.1 15.5 5.0

3.7 52.1 35.8 1.1 37.7 9.1 56.8 33.3 3.4 44.2 0.9 10.4 9.7 12.6

1.7 41.0 24.3 1.0 31.8 16.8 52.4 20.9 6.5 34.8 0.1 0.6 16.1 3.5

3.3 51.5 36.7 0.2 51.6 7.9 55.9 31.8 2.7 43.5 1.6 10.0 9.4 12.1

1.5 45.6 24.6 0.8 32.8 16.3 52.5 21.4 6.4 35.0 0.4 0.1 15.3 3.0

value is only 0.1 kcal/mol, for which our approach is still able to predict the correct proton binding site. These results validate that our present approach is able to predict both large and small energy differences, and it is a sensitive and reliable method to predict molecular basicity in gas phase. Notice that the difference in basicities between two nitrogen atoms in thymine is just 0.6 kcal/mol, while in a very similar compound, uracil, it is six times larger, 3.5 kcal/mol. This result suggests that though thymine and uracil are structurally similar, they are biologically quite different. Our results may be an indication of their substantial differences in biological reactivity. Figure 2a shows the strong linear correlation between MEPN and NAON of all nitrogen atoms in the 14 species with R2 = 0.977, confirming what has been known in other systems, i.e., the equivalence of these two quantum descriptors, MEP and NAO. Figure 2b

is based on Table 2, where we plot the relationship in Eq. (8), for the DDE in Table 2 vs. the MEPN difference, DMEPN, between the lowest and second lowest MEP values in the table. Again, a strong linear correlation is observed with R2 = 0.90. This latter correlation can be seen as a consequence of Eq. (7), which is one of the main results of this work. To check the impact of the density functional and basis set on the validity of Eqs. (7) and (8), we have performed structure optimization and single point calculations with two exchange–correlation energy density functionals, B3LYP and M06-2X, and two basis sets, 6-311++G(d,p) and aug-CC-pvTZ. Table 3 shows the comparison of DMEPN and DDE results from the three sets of independent calculations. Generally speaking, we do not observe substantial differences from one method to another, and the calculated values of these two quantities are consistent with each

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other. In all the cases, we only observe one exception, the B3LYP/6311++G(d,p) method for quinazoline, whose DDE becomes negative. Since the energy differences in Eq. (1) for the two nitrogen sites in this system are small (less than 1 kcal/mol), this result suggests that for systems like this where the basicity of the two sites is not adequately separated, a better-quality density functional (such as hybrid or double hybrid GGA formulas) and larger basis set are required to obtain reliable predictions of the proton association site in Eq. (1). Finally, we would like to mention in passing that it appears to be more natural to evaluate the MEP and NAO at the proton in the conjugate acid, in agreement with our previous applications to acidity evaluations. We did such evaluations for the conjugate acids and observed the same trends (results not shown). Also, a more intriguing question is whether or not our current approach is applicable to systems containing more than one type of acidic or basic elements, e.g., N and O atoms in thymine and uracil. In our previous work, we considered different acidic elements (e.g., O for carboxyl acid and alcohols, N for amines and anilines, and S for sulfonic acids and thiols) in different systems and obtained the same linear correlation [6]. For different elements in one molecule, it remains to be seen how our present work within the DFRT framework is to be generalized. Studies along this line are in progress. 4. Concluding remarks In this work, the proton affinity and molecular basicity in gas phase are considered from the viewpoint of density functional reactivity theory (DFRT). The proton affinity and gas-phase basicity are defined as the negative of the total enthalpy and Gibbs free energy differences, respectively, of the proton dissociation reaction for a base. Using a total of 14 heterocyclic aromatic compounds containing two or more nitrogen atoms as examples, we have demonstrated that the proton affinity and gas-phase basicity are closely related to the total energy difference. We found that there exists a strong linear correlation between the molecular electrostatic potential (MEP) on the nucleus of a basic atom and the proton affinity or molecular basicity in gas phase. We have justified this correlation from the DFRT point of view as a result of the first-order approximation. The negative slope of this linear relationship predicts that the associating proton prefers to bind with the basic atom with the lowest MEP value. We have also exhibited that when the lowest MEP atom is compared with the second low-

est MEP atom, there exists a strong linear relationship across the entire set of the systems studied in this work between the differences of their total energy difference and the MEP value. In agreement with our earlier studies, the equivalence between MEP and natural atomic orbital energies of the basic atoms as the two reliable quantum descriptors of molecular basicity has been obtained. Different density functionals and basis sets have been employed to verify the validity of these results in this work. Acknowledgments Y.H. acknowledges financial support from the Natural Science Foundation of Hunan Province (Grant No. 11JJ5065), Hunan College Student Research Study and Innovative Experiments (Grant No. Xiang Jiao Tong [2011] 272), and Hunan Teaching Reform Project (Grant No. Xiang Jiao Tong [2009] 321) for this study. S.B.L. was supported as part of the UNC EFRC: Solar Fuels, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DESC0001011.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

W.L. Jorgensen, J.M. Briggs, J. Gao, J. Am. Chem. Soc. 109 (1987) 6857. C. Lim, D. Bashford, M. Karplus, J. Phys. Chem. 95 (1991) 5610. M.J. Potter, M.K. Gilson, J.A. McCammon, J. Am. Chem. Soc. 116 (1994) 10298. A. Klamt, F. Eckert, M. Diedenhofen, M.E. Beck, J. Phys. Chem. A 107 (2003) 9380. G. da Silva, E.M. Kennedy, B.Z. Dlugogorski, J. Phys. Chem. A 110 (2006) 11371. S.B. Liu, L.G. Pedersen, J. Phys. Chem. A 113 (2009) 3648. S.B. Liu, C.K. Schauer, L.G. Pedersen, J. Chem. Phys. 131 (2009) 164107. S.K. Burger, S.B. Liu, P.W. Ayers, J. Phys. Chem. A 115 (2011) 1293. Y. Huang, L.H. Liu, W.H. Liu, S.G. Liu, S.B. Liu, J. Phys. Chem. A 115 (2011) 14697. R.G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev. 103 (2003) 1793. S.B. Liu, Acta Phys. Chim. Sin. 25 (2009) 590. Z.B. Maksic, R. Vianello, Pure Appl. Chem. 79 (2007) 1003. C.A. Deakyne, Int. J. Mass Spectrosc. 227 (2003) 601. P.K. Chattaraj, U. Sarkar, D.R. Roy, Chem. Rev. 106 (2006) 2065. R. Vianello, Acta Chim. Slov. 58 (2011) 509. A.D. Becke, J. Chem. Phys. 104 (1996) 1040. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. Y. Zhao, D.G. Truhlar, Theor. Chem. Acc. 120 (2008) 215. M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al., GAUSSIAN 09, Revision B.01, Gaussian, Inc., Wallingford CT, 2009. S.G. Lias, J.F. Liebman, R.D. Levin, J. Phys. Chem. Ref. Data 13 (1984) 695. A. Moser, K. Range, D.M. York, J. Phys. Chem. B 114 (2010) 13911.