Correlations between molecular electrostatic potentials and some experimentally-based indices of reactivity

Journal of Molecular Structure (Theo&em), 256 (1992) 29-45 Elsevier Science Publishers B.V., Amsterdam

29

Correlations between molecular electrostatic potentials and some experimentally-based indices of reactivity Jane S. Murray, Tore Brinck, M. Edward Grice and Peter Politzer University of New Orleans, Department of Chemistry, New Orleans, LA 70148 (USA) (Received 29 May 1991)

The key role that electrostatics plays in molecular reactive behavior is demonstrated in this work, which surveys and further explores correlations that we found between the molecular electrostatic potential V(r) calculated by an ab initio SCF-MO approach (a gas-phase property) and experimentally-baaed indices of reactivity (derived from solution studies). In our relationships involving negative V(r), we find in all cases that spatial minima (V,,) provide correlations of higher quality than surface minima ( V,, min) . Relationships between V,, and the hydrogen-bondacceptor parameter fi, and Vs., and the hydrogen-bond-donor parameter (Y,confirm the physical validity of the empirically-derived solvatochromic parameters (Yand /I. Correlations between the V,, of NH,-X molecules and the substituent constants a,, and or+ on (when oa>O) for the substituents X show how electrostatic properties reflect the electron-attracting tendencies of substituent groups. Whereas good relationships exist between the pK, values of some limited groups of molecules and their conjugate base Vmin,we find that the average local ionization energy r(r) is better suited as a general measure of aqueous acidity.

INTRODUCTION

The electrostatic potential V(r) has emerged as an effective tool for studying the reactive behavior of molecules in both electrophilic and nucleophilic processes and in intermolecular recognition interactions [l-5]. V(r) is a real physical property which expresses the net electrical effect of the nuclei and electrons of a molecule, and is expressed rigorously by

(1) 2, is the charge on nucleus A, located at RA, and p (r ) is the electronic density function, which we compute from the molecular wave function. The first term on the right side of eqn. (1) represents the contribution of the nuclei, which is Correspondence to: P. Politzer, Orleans, LA 70148, USA

0166-1280/92/$05.00

University

of New Orleans, Department

0 1992 Elsevier Science Publishers

of Chemistry,

B.V. All rights reserved.

New

30

positive; the second term brings in the effect of the electrons,and is negative. V(r) can be determined experimentallyby diffraction methods, as well as computationally [ 3 1. The sign of V( r ) in any particularregion depends upon whetherthe effects of the nuclei or the electrons are dominant there. Thus an approachingelectrophile will initiallybe attracted to these regions in which V(r) is negative, and in particularto the points where V(r) has its most negativevalues (the local minima,or V,,) . Figure1 shows the electrostaticpotential contour map of acetone, in a plane containingthe oxygen and carbon atoms. The largenegative potential associatedwith the oxygen atom is attributedto its lone pairs; the V,, values are -56.7 kcal mole-‘, and their locations indicate favorable positions for electrophilicinteractions. Sites susceptibleto electrophilic attack can be identified and ranked quite readily by means of the local V( r ) minima [l-5], and they have been used very extensivelyfor this purpose. The situation is not as straightforwardfor nucleophilic interactions, however, owing to the fact that V(r) maxima are found only at the positions of the nuclei [ 61. These reflect the magnitudesof

Fig. 1. Calculated electrostatic potential of acetone (in kcal mol-‘) in the plane containing the carbon and oxygen atoms. Dashed contours correspond to negative potentials. The positions of the most negative potential are indicated; the value at w is -56.7.

31

the nuclear charges and therefore cannot be assumed to indicate relative susceptibilities toward nucleophilic attack. There is accordingly no criterion existing for nucleophilic interactions that corresponds directly to V,, for electrophilic ones. However, we have developed techniques that do allow the electrostatic potential to be used to interpret nucleophilic processes [ 7-131. For example, investigation of V(r) on two- or three-dimensional surfaces significantly removed from the nuclei has revealed buildups of positive potential that reflect relative affinities for nucleophiles [ 8-131. We have recently discovered some useful relationships between the calculated electrostatic potential, a gas-phase property, and some experimentallybased indices of reactivity that are determined from solution studies [5,1315]: (1) inductive and resonance substituent constants, aI and OR [ 16,171; (2) the solvatochromic hydrogen-bond donor and acceptor parameters cy and/3 [18]; (3) PK. The existence of such correlations reflects the importance of electrostatic interactions in chemical reactive behavior, and supports the physical validity of some of the indices which may have been viewed as more empirical in nature (e.g. the solvatochromic parameters (Y and /3). These previously reported relationships will be briefly described in this introduction, to lay the groundwork for the questions that we have addressed in the present work. Substituent

constant correlations

The inductive and resonance substituent parameters (ai and CR) derived from reaction rate and equilibrium studies, are accepted measures of the electron-withdrawing and electron-donating tendencies of substituents, through induction and through resonance [ 16,171. We have recently shown that the most negative lone pair potentials (V,,) of the amine nitrogens in a series of NH2-X molecules correlate well with aI or the sum of oI and on (when on is positive, i.e. electron-withdrawing), and thus provide a measure of the electron-attracting tendencies of the substituents X [5,14]. In this earlier work, we computed amine nitrogen V,, values for twentyfour NH2-X molecules [ 141. (The HNX angles in these molecules were held constant at the STO-3G values of ammonia (104.2’ ) during the STO-3G geometry optimizations, allowing us to focus solely on how the substituents influence Vminand eliminating the effect of HNX angle variation on their values [ 141.) The linear correlation coefficient between V,, and aI was found to be 0.90 [ 141.Although inductive electron-withdrawing effects are of primary importance in the NH2-X systems, the substituents with oR values greater than zero do show some electron attraction through resonance. To take into account both the inductive and the resonance electron-withdrawing tendencies of the

32

substituents in the NH2-X systems, we examined the possibility of a relationship between V,, and the sum of oI and on, when on> 0. This proved to have a good linear correlation coefficient of 0.92. These relationships provide a predictive capability for estimating aI or crl+ on, when oR> 0, for substituents for which these parameters are not available [5,14]. Hydrogen-bond-donor and -acceptor correlations Linear solvation energy relationships based upon the use of “solvatochromic parameters” have resulted from extensive efforts to quantify solvent effects on various experimentally observed quantities (e.g. rate constants, equilibrium constants and IR, NMR, ESR and UV/vis absorption maxima and intensities) [ 18-221. Two of the solvatochromic parameters, designated as CYand p, have been interpreted as providing measures of a solvent’s ability to donate or accept a proton, respectively, in solute-solvent hydrogen bonding [ 181. We have recently found that good relationships exist between B and the most negative electrostatic potentials associated with the hydrogen-bond-accepting heteroatoms in four families of compounds, taken separately: ten azines, four primary amines, four alkyl ethers and fifteen molecules containing doublebonded oxygens [ 151. The correlation coefficients were found to be 0.96,0.98, 0.94 and 0.95, respectively. These relationships between B and V,, confirm that the electrostatic potential in the space around a gas-phase molecule is a key (but not the sole) factor in determining its ability to accept a proton in a hydrogen bond, and provide a predictive capability for obtaining unknown jl values. In view of the good correlations between ~3and Vmin, it was suggested that relationships might exist between the hydrogen-bond-donor parameter a! and positive regions of V( r ) [ 231. Because there is no criterion for positive regions of potential corresponding to V,, for the negative (see above), we chose to compute V( r ) on well-defined molecular surfaces encompassing the molecules of interest. We found that good linear relationships exist between a! and the most positive surface electrostatic potential (Vs.,) for two groups of hydrogen-bond donors taken separately [ 131; the correlation coefficients were 0.96 and 0.97. The electrostatic potentials were computed on molecular surfaces defined by the 0.002 electron bohrm3 contour of the electronic density. This contour has been shown to encompass at least 95% of the electronic density of a molecule and to provide physically meaningful molecular dimensions [ 24,251. pK, correlutions We and others have shown previously that the electrostatic potential minima of series of azines [26,27], aliphatic amines, substituted pyridines and

33

aniline derivatives [ 281,taken separately, correlate well with the measured pK, values of their conjugate acids. In contrast, the conjugate base Vmi, of a group of weak hydrocarbon acids do not relate well to the respective pK, values

1291.

More generally successful than Vmh,in relation to pK,, is a property that we have recently introduced and interpret as the average local ionization energy, r(r) [ 29-331.It is rigorously defined within the framework of self-consistentfield molecular orbital (SCF-MO ) theory, as given by ~(r)=CPimI i

p(r)

(2)

pi(r) is the electronic density of the ith molecular orbital at the point r, ei is the orbital energy and p(r) is the total electronic density function. r(r) can be viewed as the average energy required to remove an electron from any point r in the space of an atom or molecule [ 301. The positions at which I(r) has its lowest values (rm,) are indicative of the least tightly bound electrons, and thus are the sites expected to be the most reactive toward electrophiles. For example, we have shown for a series of monosubstituted benzenes that the surface coin (us,,,) provides a quantitative measure of the activating-deactivating and directing tendencies of the various substituents toward electrophilic aromatic substitution [ 301. We have also demonstrated that the pKa values of a wide variety of acids correlate with the lowest rs,minof the respective conjugate bases [ 29,32,33]. PRESENT OBJECTIVES

Most of the relationships between V(r) and reactivity indices that were summarized in the introduction section discussion of Vmin, the minimum (most negative) V( r ) in the three-dimensional space around a heteroatom or anionic site. However, another possibility would be to look at the most negative V(r) on the molecular surface, especially because surface maxima have already been shown to correlate well with the hydrogen-bond-donor parameter cy [ 131. In doing this, it would be useful to compare the results obtained using several different contours of the electronic density to define the molecular surfaces [34], e.g. 0.001 and 0.0005 electron bohrM3, in addition to the current 0.002. Finally, because electrostatic potential minima and Fs,min can both be regarded conceptually as reflecting reactivity toward electrophiles, it would be of considerable interest to determine which of them shows a better correlation with each specific reactivity index. Our objectives in the present work have been to explore and evaluate these possible modifications of our earlier procedures, and to look at certain aspects of them in greater detail.

34

METHODS AND PROCEDURE

We have used an ab initio SCF-MO approach (GAUSSIAN82 [ 351 and GAUSSIAN 88 [36] ) to optimize the geometries (at either the STO-3G or 3-21G level) of a large number of molecular systems of interest in our studies exploring correlations between experimentally-based indices of reactivity and V(r) . Most of these optimizations were performed in conjunction with our earlier TABLE 1 Hydrogen-bond-acceptor parameters j?” and come STG-5G/STO-3G calculated properties for come molecules containing double-bonded oxygen atoms Molecule

O=P(CH,),

e

(H,C),N’ ‘NCH,), O=S(CH,),

Y C (CH&N’

Hydrogenv,,(G)b (kcal mol-‘) bondacceptor parameter /3

(kcal mol-‘) z$rnol-‘) (%T (0.002 electron (0.001 electron (0.002 electron bohrT3) bohrm3) bohr-3)

1.02

-94.5

-72.0

-65.6

12.35

0.85

- 73.4

-49.0

-45.1

13.92

0.80

- 68.0

-44.3

-40.7

15.89

0.76

-69.5

-65.4

-59.0

11.94

0.76

-65.2

- 44.9

-40.7

15.63

0.69

- 60.5

-44.6

- 40.3

15.90

0.49

-56.4

-40.8

-36.7

16.04

0.48

-56.7

-42.1

-38.1

16.05

0.46

- 48.2

-37.4

-33.8

16.61

f

VS,,

‘H

B

0 0

%-I3

HJCH 3

3

0 e (CH&N ’

‘CF,

“The values of the hydrogen-bond-acceptor parameter p are taken from ref. 18. “The V,,(O) values, except for that ofp-nitrobenxaldehyde, were reported in ref. 15.

35

Molecule

HydrogenVmh(0)b (kcal mol-‘) bondacceptor parameter p

Vs,, VS,ill z,iIl (kcal mol-‘) (kcal mol-‘) (eV) (0.002 electron (0.001 electron (0.002 electron bobre3) bohre3) bohr-3)

0.44

-53.5

-39.1

-35.2

16.68

0.42

-46.6

- 34.6

-31.3

16.97

0.40

-54.0

-39.9

-36.1

16.31

0.37

-52.5

-31.1

-28.1

17.61

-45.0

-33.7

0.32

-44.1

-31.1

- 27.6

16.98

0.14

- 13.0

-23.3

- 20.9

17.77

0 %

H3C' 'OCH,

CH,CH,@' ‘H 0

d

%‘ocHH3

R

CM,CCCH,CI

H&C,

3

3

work [13-l&33]. Using these structures, we have computed electrostatic potential minima, surface electrostatic potentials and average local ionization energies (as appropriate) via eqns. (1) and (2)) at the STO-5G level for neutral molecules and 6-31G* level for anions. The results are given in Tables 1-5. RESULTS AND DISCUSSION

Hydrogen-bond-acceptor correlations We showed earlier, for a group of molecules containing double-bonded oxygen atoms, that the most negative value of the electrostatic potential near that oxygen ( Vmin(0) ) correlates well with the parameter p that reflects its hydrogen-bond-accepting tendency [ 151. These molecules are listed in Table 1, augmented byp-nitrobenzaldehyde. It is noteworthy that they include S-O, P=O,

36

N-oxide and a variety of acyl groups, e.g. aldehydes, ketones, amides, esters and ureas, with Bvalues spanning a wide range, from 0.14 to 1.02. The Vmi, (0) values are in all instances associated with the double-bonded (or zwitterionic in the case of pyridine N-oxide) oxygen atom. The relationship between V,, (0) and /3 for the sixteen molecules in Table 1 is best described as exponential; it has a correlation coefficient of 0.95, which is the same as that obtained without the inclusion of p-nitrobenzaldehyde. Our first objective was to determine whether a better correlation might be obtained by using the most negative potential on the molecular surface ( Vs,min) or, alternatively, the lowest value of the local ionization energy on the surface (&,,). All of these data, including V,,(O) and p, are given in Table 1. We find that the surface electrostatic potential minima ( Vs,min) do not correlate as well with p as do V,,(O) values. The relationships between /? and Vs,+, computed at the 0.002 and 0.001 electron bohrm3 contour of p (r) are best described as linear, with correlation coefficients of 0.88 and 0.89, respectively. The relationship between &,i, and /? is even poorer, with a linear correlation coefficient of 0.84. It is interesting that in all instances the position of Vmin(0) is closer to the hydrogen-bond accepting oxygen than is Vs,min.For the thirteen acyl-containing compounds in Table 1, the oxygen-Vmi, (0) distance is approximately 1.0 A, while the oxygen-VS,min distances for potentials computed at the 0.002 and 0.001 electron bohrm3 contour of the electronic density are about 1.4 and 1.5 4, respectively. The latter are closer to the van der Waals radius of oxygen (1.5 A) [ 371, and thus it might be anticipated that eVS,min correlations would be the more effective ones. However, our results show clearly that Vminprovides the best /3-V< r ) correlation for the molecules in Table 1. Hydrogen-bond-donor correlations

In Table 2 are listed the hydrogen-bond-donor parameters cy and the most positive surface electrostatic potentials V,,, for eleven molecules containing OH groups. We have demonstrated that there is a close relationship between them when the molecular surface is defined by the 0.002 electron bohrm3 contour of the electron density; we now wish to examine how this is affected by using other reasonable contours, the 0.001 and the 0.0005. Figure 2 shows the surface electrostatic potential of ethanol computed at the 0.001 electron bohre3 contour of p (r ), and illustrates our approach for obtaining V,,,, on a welldefined molecular surface. The V,,, value (28.6 kcal mol-‘) is within the range of V(r) shown in darkest shading, and is associated with the hydroxyl hydrogen atom. The linear correlation coefficient for the relationship between a! and V,,, improves from 0.96 to 0.98 in going from the 0.002 to the 0.001 electron bohrm3 contour of the electronic density, then it decreases again to 0.97 at p ( r) = 0.0005

37 TABLE 2 Hydrogen-bond-donating parameters a” and calculated surface electrostatic potential maxima V,,, for some molecules containing -OH groups Molecule

Hydrogen-bond donating parameter o?

Vsmb (kcal mol- ’ ) (0.002 electron bohrm3)

VS.msX (kcal mol-‘) (0.001 electron bohre3)

V (l%Ymol-‘) (0.0005 electron bohrm3)

F,CCH(OH)CF, F,CCH,OH Hz0 CH,COOH CH30H HOCHzCHzOH CH&H,OH CH3CH&H&H20H CH&H,CH,OH CH3CH(OH)CH3 (CHACOH

1.96 1.51 1.17 1.12 0.93 0.90 0.83 0.79 0.78 0.76 0.68

49.6

43.1 40.3 32.4 30.2 29.8 29.4 28.6 28.2 27.8 27.8 26.1

37.8 34.7 28.2 24.0 24.7 25.2 23.5 23.2 23.1 22.8 21.1

48.6 38.0 39.0 37.3 37.1 35.6 34.6 35.6 35.0 31.4

“The values of the hydrogen-bond-donating parameter (Yare taken from ref. 18. These V,,, values were reported in ref. 13.

Fig. 2. Calculated electrostatic potential on the 0.001 electron bohrm3molecular surface of ethanol. The hydroxyl group is facing the viewer. Four ranges of V(F) aredepicted, in kcal mol-‘. In order ofincreasinglydarkshading,theserangesare:V(~)~0;O~V(~)~10;10~V(~)c:27;27~V(~). is indicated by an asterisk; its value is 28.6 kcal mol-‘. The VS.,

Vs,max (kcallmole) Fig. 3. Correlation between V,,, (computed on a 0.001 electron bohre3 molecular surface) and cx for the group of molecules containing OH groups listed in Table 2. The correlation coefficient is 0.98.

electron bohre3. a! is plotted against V,,, computed on the 0.001 contour in Fig. 3. In light of the slight improvement in the relationship between cx and Vs,, when V(r) is computed at the 0.001 electron bohrv3 contour of the electronic density, it is interesting to compare the distances between the positions of the and the OH hydrogen atoms. These distances are relatively constant for VS,mar any one particular contour of the electronic density upon which V(r) is computed. For the 0.002, 0.001 and 0.0005 electron bohrB3 contours of p(r), the hydrogen- Vs,,, separations range in general from 1.11-1.13, 1.26-1.28 and 1.41-1.44 A, respectively. The 0.001 electron bohrs3 distances fall well within the range reported for the van der Waals radius of hydrogen (1.20-1.45 A) [37,38]. It appears that this contour provides what may be considered to be close to an optimum distance for computing Vs_ in our hydrogen-bond donating correlations. (It should be pointed out, however, that we find our relationship between cy and Vs,_ for the group of molecules without OH groups to be equally good for V(r) computed at all three contours of p (r). ) Substituent

constant correlations

In Table 3 are listed V,,, Vs,,, and &,s.min for nine of the NH,-X molecules included in our earlier work [ 141, along with their inductive and resonance substituent constants [ 16,171. In contrast to our previous study, however (see Introduction), the calculated properties for these molecules were now obtained using fully optimized STO-3G structures.

39 TABLE 3 Calculated STO-BG/STO-3G proper&a for come substituted amines, and inductive end resonance substituent constants for the substituenta” Substituent Xfor NH*-

VS,i.

VS.&

(kcal mol-‘)

(kcal mol-‘) (0.002 electron bohr-3)

(kcal mol-‘) (0.001 electron bohr-3)

(0.002 electron bohr-3)

-63.0 -60.3 -47.7 -45.7 - 49.5 -44.2 -43.8 -36.0 -34.7

-55.1 -52.6 -41.3 - 39.1 -43.1 -37.5 - 38.0 -30.1 -31.2

11.91 11.88 12.53 12.85 13.06 13.18 13.82 14.15 14.47

X H

CHs NH, OH F CFs Cl CN NO,

r,,.

VmiruW)

- 109.3 - 105.9 -91.5 -84.8 -85.1 -82.3 - 75.9 -64.8 -59.9

u1+%l (u&-O)

(eV)

0.00

-0.01 0.17 0.35 0.54 0.40 0.47 0.57 0.67

0.00

-0.16 -0.80 -0.67 -0.48 0.11 -0.25 0.08 0.10

0.00

-0.01 0.17 0.35 0.54 0.51 0.47 0.65 0.77

“The substituent constanta are taken from ref. 16.

For the subgroup of NH,-X molecules in Table 3, good correlations exist between Vminand aI, V,, and oI + on when OR> 0, &,i, and oI and &min and aI + ORwhen on z=-0. The correlation coefficients range from 0.94 to 0.95. The surface electrostatic minima ( Vs,min) yield corresponding relationships of poorer quality, with linear correlation coefficients ranging from 0.63 to 0.91. As was found earlier [ 141, fluorine is the substituent that shows the greatest deviations in these relationships. When fluorine is eliminated from the data set, the correlations involving V,, and 1S,minimprove to correlation coefficients of 0.98 and 0.99, respectively. A plot of Vminversus aI for the systems in Table 3 excluding NH2-F is shown in Fig. 4. This plot predicts aI of fluorine to be 0.35, whereas the literature value is 0.54 [ 16,171. Although fluorine is regarded as the most electronegative element, there is considerable experimental and theoretical evidence indicating that it is limited in the total amount of electronic charge that it is able to accept [ 11,39-461. For example, the delocalization of the negative charge in the trihaloacetate and the trihalomethanide anions decreases as the halogen changes from bromine to fluorine [ 39,411. These and other analogous observations have been interpreted in terms of anomalously strong repulsive interactions between the electrons already associated with the small fluorine atom and any additional electronic charge [41,42]. In earlier studies of halogenated epoxides, dibenzo-p-dioxins and naphthalenes, we have found chlorine to be more effective than fluorine in withdrawing electronic charge from other portions of the molecules [ 11,45,46] ; this has been attributed to the greater charge capacity of chlorine [40,44]. Our results for NH2-F are consistent with these earlier experimental and theoretical findings [ 141, and support the view that fluorine has a limited capacity for accepting additional electronic charge, despite an initial strong attraction for

-0.2 ! -110

.

I -100

.

I -90

.

, -00

.

, -70

.

, -60

. .

0

Vmln(N) [kcalhnole]

Fig. 4. Correlation between V,, and q for the NH2-X systems listed in Table 3, excluding NH2F. The linear correlation coefficient is 0.99.

it. The high aI value that has been reported in the literature for fluorine may reflect anomalous solution effects associated with the reactions upon which this value is based (e.g. the ionization of substituted acetic acids [ 16,171) . It is interesting again to note the distances between the positions of the V,, these are consistently around or Vj,,i, and the amine nitrogen atoms. For Vmin, 1.0 A, whereas for Vs,mh they are in the regions of 1.56 and 1.66 A for the 0.002 and 0.001 surfaces, respectively. As was found in our correlation between V(r) and the hydrogen-bond acceptor parameter /3, the V,,-heteroatom distances are approximately two thirds of the Vs,,ti-heteroatom distance?. Although the latter are close to the van der Waals radius of nitrogen (1.55 A) [37], and it might be anticipated that the surface minima would therefore provide the better correlations with substituent constants, we again find that the best relationships are obtained with the spatial electrostatic potential minima, Vmin.

ThepK, correlations Calculated Vmh,Vs,min and Fs,minfor two families of anions are given in Tables 4 and 5, together with the pK, values of their conjugate acids [ 47-501. We have recently shown that there exist excellent correlations between the experimentally determined pK, values and the calculated conjugate base [s,min values for these and other acids [33], in separate groups and together. Is,min can both be regarded conceptually as indicating reactivity and Vmi, (or V~,~ti) toward electrophiles, so it is of interest to examine the relationships between Vmin(or Vs,min) and pK, for these systems.

41 TABLE 4 Experimentally determined substituted methanes Conjugate base

pK, values and some calculated

Conjugate acid

25 11.2 10.2 3.6 0.1 -5.od

properties

for some

VUlill (kcal mol-‘)

Vs.mill (kcal mol-‘) (0.002 electron bohF’)

&.,minb (eW (0.002 electron bohr-3)

- 182.3 - 135.1 - 129.2 -92.1 - 76.3 - 100.8

- 147.8 - 119.7 - _= -91.1 - 74.9 -96.3

2.906 5.475 5.630 7.622 8.917 7.712

PK,”

CH&NCH(CN), CH, NO; CH(NO,), C(NO& C(CN),

6-31G*/3-21G

“The pK, values are taken from ref. 47. These Gemin values were reported in ref. 33. “No calculated surface minimum was found. dMeasured in aqueous sulfuric acid.

TABLE 5 Experimentally of oxoacids Conjugate base

determined

pK, values and some calculated 6-31G*/3-21G

Conjugate acid

11.65b 7.20” 3.75d 3.40d 2.0’

for a series

V,, (kcal mol-‘)

Vs.Ulill (kcal mol-‘) (0.002 electron bohre3)

&&U&la (ev) (0.002 electron bohrd3)

-

-

5.014 6.399 7.250 7.626 8.139

PK,

HOOOCIHCOOONOOClO-

properties

246.6 203.4 205.0 205.5 194.5

197.8 168.8 166.5 154.7 166.0

‘These &min values were reported in ref. 33. ‘The PK. value is taken from ref. 48. “The pK, values are taken from ref. 49. dThe pK, values are taken from ref. 50.

A plot of pKa vs. V,, for the molecules listed in Table 4, excluding C (CN); , is shown in Fig. 5. The exponential and linear correlation coefficients are 1.00 and 0.99, respectively. These decrease to 0.92 when C(CN); is included. Similar results have been found for pK, vs. &min [ 331, as would be predicted from the excellent relationship existing between Vminand &,min(correlation coefficient= 1.00). Both V,, and Is,minpredict HC (CN), to be less

42

20

-200

-180

-160

-140

-120

-100

-80

-60

Vmin (kcallmole) Fig. 5. Correlation between V,, and pK, for the systems listed in Table 4, excluding HC ( CN)3. The linear correlation coefficient is 0.99.

acidic than HC (NO,),, contrary to their reported pKa values [47]. This disagreement may reflect anomalous solvation effects involving C (CN) 3 . For the compounds in Table 4, both including and excluding HC (CN),, our V,,-pK, relationships are found to be slightly better than the corresponding ones for

VS,min-P K 8.

For the group of oxoacids listed in Table 5, an excellent correlation has been reported between pK, and &min, with a linear correlation coefficient of 0.99 [ 331. For this group of acids, V(r) is significantly less effective; the correlation coefficients for the corresponding Vm,-pKa and Vs,min-pK, relationships are 0.93 and 0.88, respectively. It should be pointed out that there is no general correlation between pK, and Vminfor the molecules in Tables 4 and 5. The different families of compounds must be treated separately. In contrast, we have shown that a general correlation between pK, and Fs,,in does exist for a large variety of carbon, oxygen and nitrogen acids [ 29,331, including those in Tables 4 and 5 [ 331. SUMMARY AND CONCLUSIONS

We have discussed and explored some relationships that had been developed earlier between the calculated molecular electrostatic potential and several experimentally based indices of reactivity: the solvatochromic hydrogen-bond donor and acceptor parameters Q!and 8, the inductive and resonance substit-

43

uent constants, aI and aR, and pK, values. One of our objectives was to determine whether these relationships could be improved through certain modifications. For the correlations involving negative electrostatic potentials, we found that spatial V(r) minima ( V,,), which we originally used for this purpose, give better results than do the surface minima ( Vs,min),even though the latter are located at distances closer to the van der Waals radii of the respective heteroatoms. Vminalso correlates quite well with pK,, but the average local ionization energy (f((r) ) appears to be better suited than V(r) as a general measure of aqueous acidity. For the correlation between V,,,, and cx,which involves positive potentials, we compared three possible choices for defining the molecular surface. For OHcontaining molecules, the p (r) = 0.001 electron bohr3 surface is slightly more effective than either the 0.0005 or the usual 0.002 electron bohrm3. The key role of electrostatics in hydrogen-bonding interactions is reflected in our correlations between V,, and /3,and Vs,, and a; indeed these provide support for the physical validity of the empirically derived solvatochromic parameters. Our relationships between the Vminvalues of NH,-X molecules and aI or aI + on, when on > 0, show how the electrostatic properties of molecules reflect the electron-attracting tendencies of substituents. In the case of pK,, however, electrostatic considerations prove to be less effective. ACKNOWLEDGMENTS

We greatly appreciate the support of this work by the Office of Naval Research through contract #N00014-85-K-0217. A portion of this research was conducted using the Cornell National Supercomputer Facility, a resource of the Center for Theory and Simulations in Science and Engineering (Cornell Theory Center), which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of the Corporate Research Institute.

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