Hydrogen Bonding and Electron Donor−Acceptor (EDA) Interactions

ARTICLE pubs.acs.org/crystal

Hydrogen Bonding and Electron Donor
Acceptor (EDA) Interactions Controlling the Crystal Packing of Picric Acid and Its Adducts with Nitrogen Bases. Their Rationalization in Terms of the pKa Equalization and Electron-Pair Saturation Concepts Valerio Bertolasi, Paola Gilli,* and Gastone Gilli Centro di Strutturistica Diffrattometrica and Dipartimento di Chimica, Universit
a di Ferrara, Via L. Borsari 46, 44121 Ferrara, Italy

bS Supporting Information ABSTRACT: The structures of picric acid and 14 of its adducts with N-bases were determined by X-ray diffraction. All intermolecular contacts shorter than the sum of the van der Waals radii were retrieved, classified as 81 conventional X
H 3 3 3 :Y (X,Y = N,O) and 108 weaker C
H 3 3 3 :O H-bonds and as 49 C/Nr:O π*rn or π*(k)rn and four Cr:C π*rπ electron donor
acceptor (EDA) interactions, and carefully scrutinized to single out the general rules (if any) the 242 contacts are conforming to. X 3 3 3 Y distances and related EHB energies of the 81 X
H 3 3 3 :Y bonds are found to correlate with ΔpKa = pKa(X
H)
pKa(Y
Hþ), validating the pKa equalization principle for which strong H-bonds occur only when ΔpKa tends to zero. Moreover, by redefining all X/C
H 3 3 3 :Y bonds as X/C
Hr:Y σ*rn EDA interactions, all contacts become EDA interactions, leading to formulate the electron-pair saturation rule for which “all electron donors of a closed-shell molecule (nonbonding pairs of lone pairs or π-bonding pairs of multiple bonds) become engaged in EDA interactions with the electron acceptors (X
H, C
H, π*(k), or π*) present, as far as they are available; when the acceptors are insufficient, they are saturated in order of decreasing EDA interaction strength”. It is shown that this novel rule provides a particularly easy way to look at crystal packing.

’ INTRODUCTION In van der Waals (vdW) molecular crystals molecules are bound by a diffuse net of atom
atom London’s dispersion interactions which are individually quite weak (a fraction of kcal mol
1), steeply decrease with the sixth power of the distance (EvdW µ r
6), and are essentially isotropic, that is, nondirectional. The result is that each molecule tends to become surrounded by a maximum number of other molecules, normally 12 according to the well-known rule of cubic or hexagonal closepacking.1 The net of directional (or structure-maker) nonbonded forces within the crystal is instead controlled by two specific factors: (i) molecules may possess functional groups which are either Brønsted acids (proton donors, D
H) or Brønsted bases (proton acceptors, :A) and then can interact by sharing the proton and forming D
H 3 3 3 :A hydrogen bonds (H-bonds); and (ii) in a similar way, molecules may be endowed with groups which are either Lewis bases (electron donors, :D) or Lewis acids (electron acceptors, A) which can interact by sharing a couple of electrons, so forming D:fA electron donor
acceptor (EDA) or charge-transfer (CT) interactions. H-bond properties are now known in considerable detail.2
4 At variance with vdW interactions, H-bonds feature a large r 2011 American Chemical Society

interval of individual association energies, EHB (from less than 1 to more than 30 kcal mol
1, 45 if also [F 3 3 3 H 3 3 3 F]
bonds are considered), which appear to be modulated in two ways: (i) they increase with the increasing electronegativities of both D and :A; and (ii) for any given D/A couple, they increase with the increasing D/A proton-affinity matching. The latter effect can be summarized in terms of the pKa equalization principle for which really strong bonds occur only when the difference ΔpKa = pKa(D
H)
pKa(A
Hþ) tends to zero, pKa being the cologarithm of the water acid
base dissociation constant.4
7 A second feature distinguishing H-bonds from vdW interactions is their directional character which forces the bond to be as linear as possible compatibly with the surrounding steric field. This is particularly true for strong H-bonds, which take the linear and symmetric form of proton-centered three-center-four-electron covalent bonds but also occurs in weak electrostatic δ
D
Hδþ 3 3 3 :Aδ
bonds because linearity maximizes the charge
dipole interaction even in the weakest bonds, such as the C
H 3 3 3 :O ones.8 While Received: August 1, 2010 Revised: March 24, 2011 Published: March 29, 2011 2724

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Crystal Growth & Design the crystal packing is generally tightened by greater H-bond energies, it may sometimes be weakened by its increasing directionality which may hinder close-packing and cause small voids in the structure, the most famous example being ordinary ice Ih, which increases its density when its H-bonded structure collapses into liquid water.2 The properties of EDA (or CT) interactions are less known, though an overall classification9,10 and some comprehensive surveys11
13 are available. They are normally described in terms of directional overlapping of the highest occupied MO of the donor (HOMO) with the lowest unoccupied MO of the acceptor (LUMO) inducing a HOMO lowering (bonding orbital) and a LUMO raising (antibonding orbital) which are the greater the more the two MOs are energetically alike. In other words, good donors and acceptors are characterized by a high-lying HOMO and a low-lying LUMO, respectively. The most common electron donors are (i) n donors: neutral lone-pair donors such as N/O/P/S/halogen atoms present in, for example, ethers, amines, phosphines, ketones, thioketones, amides, anilines, nitriles, N- and P-oxides, as well as in halogenated and nitro compounds; (ii) n
donors: negatively charged lone-pair donors, such as halogenide, cianide, and hydroxyl anions; and (iii) π donors: neutral π bonding-pair donors, associated with localized CdC or CC multiple bonds or delocalized C 3—3 3 C aromatic bonds in molecules with electron-donating substituents, such as alkylic, aminic, or hydroxylic groups. There are considerably more classes of electron acceptors and a selection of the most important may include (i) v acceptors: neutral acceptors with vacant AOs able to expand their coordination by dative bonding, such as sp2 trigonal planar AX3 (A = B, Al, Ga; X = R, halogen) or sp3d trigonal bipyramidal AX5 molecules (A = Sb; X = R, halogen) which, by binding a :Y electron donor, become the sp3 tetrahedral AX3Y or sp3d2 octahedral AX5Y species; (ii) vþ acceptors: positively charged acceptors with vacant AOs typical of small ions of high electric field tending to form covalent (coordinative) instead of ionic bonds, such as the Hþ, Agþ, Hg2þ ions or the :NO:þ nitrosyl cation; (iii) π* acceptors: neutral acceptors with empty π* antibonding MOs associated with localized CdC or CC multiple bonds or delocalized C 3—3 3 C aromatic bonds in molecules having electron-attracting substituents, such as nitro or cyano groups; (iv) π*(k) acceptors: neutral acceptors with π* antibonding MOs localized on a heteronuclear A=X double bond (A = C, N; X = O, S, NR; k = ketonic); X being more electronegative than A, the bonding π and antibonding π* MOs are mostly localized on X and A, respectively, making A the preferred site of attack by n donors (SN2 nucleophilic addition) increasing from sp2 to sp3 the A hybridization and so disrupting the π component of the AdX double bond; and finally (v) σ* acceptors: neutral acceptors with σ* antibonding MOs; typically, in a generic X
Y molecule the σ bonding MO is concentrated between X and Y, while the σ* antibonding one has two lobes of opposite signs protruding collinearly outside the X
Y bond with a larger weight on the less electronegative atom, which becomes the best acceptor for a donor approaching collinearly with the X
Y bond itself. The most studied σ* acceptors are, by far, the halogen X
X and the interhalogen X
Y molecules, together with the organic halogenated compounds R
X. The CT bonds formed by these acceptors with N/O/S/halogen n donors are often referred to as halogen bonds,14
18 in strict analogy with the hydrogen bonds where the σ* acceptor is now the hydrogen of the D
H bond.9 This incidentally shows that also H-bonds can be well treated as

ARTICLE

CT or EDA interactions (as explicitly suggested by Mulliken and Person,10 and Ratajczak and Orville-Thomas19) and the fact that this is not routinely done, at least so far, arises from the circumstance that H-bonds are also proton-transfer (PT) interactions, a second and more traditional approach that opens direct access to the acid
base theory and more easily leads to an overall interpretation of H-bond phenomena. In this paper, H-bonds will be indifferently treated as normal X
H 3 3 3 :Y H-bonds or as σ*rn (or X
Hr:Y) EDA interactions, respectively, in the second and first part of the discussion. So far, these three classes of interactions (vdW, H-bond, and EDA) have been treated in a quite uneven way in connection with the packing of molecular crystals. VdW crystals have been the object of hundreds of publications having shown that they can be efficiently rationalized in terms of atom
atom potentials, EDA forces have never been treated systematically, and H-bond effects have been frequently considered, though in a mostly qualitative way. Since H-bonds are normally more energetic than any other interactions occurring in neutral molecular crystals, it has been maintained20,21 that the main rule H-bonded crystals are conforming to is that “all acidic H atoms available in a molecule will be used in H-bonding in the crystal structure of that compound” (of course, if there are enough acceptors). Later, it was remarked22 that this definition may hold only when C
H 3 3 3 O/N H-bonds are not taken into account but that, if such a rather obsolete position is dismissed, this “H-bond donor saturation rule” is more properly reversed into a “H-bond acceptor saturation rule” stating that “all H-bond acceptors available in a molecule will be engaged in H-bonding as far as there are available H-bond donors; these acceptors will be saturated in order of decreasing H-bond strength”. In other words, the packing is first determined by the network of the most energetic H-bonds and then completed by the maximum number of weaker interactions such as C
H 3 3 3 O/N bonds. This rule has been checked in a number of organic cocrystals23,24 and is in touch with previous suggestions that crystal packing shows “a preference for including as many acceptors as possible”.8

Since H-bond acceptors are essentially electron pairs (nonbonding pairs or, less frequently, π-bonding pairs of multiple bonds), we may speak of an electron-pair saturation rule, expression which goes beyond simple H-bonds to include also EDA (or CT) interactions with other charge-transfer acceptors, so allowing us to treat both types of interaction at a same time. The problem is now to find a suitable set of crystal structures where most of these interactions are well represented, that is, H-bonds from strong to very weak, coupled with the maximum possible number of EDA interactions. To this aim, we have chosen to study the crystal packing of picric acid (PAc, I) and of its H-bonded complexes with nitrogen bases (NB), a class of mixed crystals allowing us to monitor a wide spectrum of different molecular interactions. First, PAc is an almost ideal candidate for studying the relationships between ΔpKa and H-bond strength, and this because (i) the O
H group is a very strong acid [pKa(O
H) = 0.36] forming relatively weak 2725

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ARTICLE

Figure 1. ORTEP33 views of molecules 1
15 with thermal ellipsoids at 30% probability.

H-bonds with normal amines [pKa(N
Hþ) around 9
11] but increasingly stronger ones with aromatic bases of decreasing pKa values (from 9.5 down to nearly 2); (ii) PAc nitro groups are bad

H-bond acceptors because their pKa is nearly
12 and does not match that of any known organic H-bond donor; and finally, (iii) the two C
H groups in position 3 and 5 are considerably 2726

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Table 1. Approximate Geometric and Energetic Parameters for Some Typical X
H 3 3 3 Y Bonds Discussed in the Text: Sums of van der Waals Radii, ΣvdW(X 3 3 3 Y) and ΣvdW(H 3 3 3 Y); H-bond Distances, d(X 3 3 3 Y) and d(H 3 3 3 Y); H 3 3 3 Y Shortening with Respect to ΣvdW, vdWSH(H 3 3 3 Y) and vdWSH%(H 3 3 3 Y); and Estimated H-bond Energies, EHBa ΣvdW

ΣvdW

(X 3 3 3 Y; Å)

(H 3 3 3 Y; Å)

O
H 3 3 3 O
strongest ordinaryb
maximum strengthc

3.70

2.72

N
H 3 3 3 N
strongest ordinary
maximum strengthd N
H 3 3 3 O
strongest ordinary

3.76

X
H 3 3 3 Y

d(H 3 3 3 Y) (Å)

vdW

SH

(H 3 3 3 Y; Å)

vdW

SH%

(H 3 3 3 Y)

EHB (kcal mol
1)

2.70

1.70

1.02

37.5

5
6

2.38

1.19

1.53

56.3

27
32

2.75

3.05

2.02

0.73

26.5

≈3

3.73

2.72

2.59 2.87

1.56 1.84

1.19 0.88

43.3 32.4

26 4
5

2.51

1.48

1.24

45.6

15
16

3.80

2.72

3.40

2.32

0.40

14.7

0.5
1.0

2.94

1.86

0.80

29.4

≈2


maximum strengthe

C
H 3 3 3 O
strongest ordinary
maximum strengthf

d(X 3 3 3 Y) (Å)

a

Data are taken from refs 4 and 6 and refer to nearly linear bonds having X
H
Y g 164°. b Ordinary H-bonds (OHBs) are defined4,6,7 as the H-bonds which are neither charge-assisted (CAHBs) nor resonance-assisted (RAHBs). c In negative [O 3 3 3 H 3 3 3 O]
or positive [O 3 3 3 H 3 3 3 O]þ chargeassisted H-bonds. d In positive [N 3 3 3 H 3 3 3 N]þ charge-assisted H-bonds of proton sponges. e In charge-assisted organic acid
nitrogen base complexes with full pKa matching. f Occurring in relation to C
H groups of particularly high acidity, such as in (NO2)3C
H 3 3 3 O.38

acidic because of the presence of the three nitro groups and then suited to form C
H 3 3 3 O/N bonds. Moreover, PAc displays a number of interesting EDA properties: (i) it is a quite good n donor through the 14 lone pairs its seven oxygens are endowed with; (ii) because of its strongly electron-attracting substituents, the aromatic ring (including the three N atoms) becomes an efficient π* acceptor which can form delocalized π*rπ adducts with aromatic π donors or more localized π*(k)rn ones with lone pairs approaching perpendicularly the partially positive Cδþ or Nδþ atoms of the aromatic ring. Accordingly, the following study is focused on three main topics: (i) crystal-packing description for the 15 structures studied; (ii) analysis of the role played by conventional H-bonds, C
H bonds, and EDA interactions in the crystal packing, intended to verify their steering role in the crystallization process according to the previously formulated “electron-pair saturation rule”; (iii) analysis of the relationships among d(D 3 3 3 A), EHB, and ΔpKa in the conventional H-bonds connecting PAc to the NB moiety, aimed to verify the validity of the pKa equalization principle.

’ EXPERIMENTAL SECTION Crystal Structure Determination. Reflection intensities of compounds 1
15 were collected on a Nonius Kappa CCD diffractometer with graphite monochromated Mo-KR radiation, integrated with the Denzo-SMN package,25 and corrected for Lorentz and polarization effects. Data collections were performed at room temperature except for PAc (1) that was studied at 120 K to locate the proton missing in the previous room-temperature determinations.26,27 All structures were solved by direct methods (SIR97)28 and refined by full-matrix leastsquares with anisotropic non-H and isotropic H atoms, with the following exceptions. In structure 7 the disordered atoms of the O2A
N1A
O3A nitro group and the disordered oxygens of the O4B
N2B
O5B one were refined isotropically over two positions with final occupancies of 63 and 37% and 51 and 49%, respectively; H atoms were included in calculated positions, riding their carrier atoms. In structure 10 the disordered oxygens of the O2A
N1A
O3A nitro group were refined isotropically over two positions with 50% occupancies; H atoms linked to O8A and O8B atoms were included in calculated positions riding on their carrier atoms. In structure 13 H atoms of the cation were included in calculated positions riding on their carrier atoms.

In structure 15 the disordered oxygens of the O6
N3
O7 nitro group were refined over two positions with final occupancies of 51 and 49%. Calculations were performed by SHELXL-97,29 PARST,30 and PLATON31 programs implemented in the WINGX32 system. Crystallographic details for compounds 1
15 (excluding structure factors) have been deposited as Supporting Information in the form of crystallographic information files (CIF files). Crystal data, selected bond distances and angles, and H-bond and EDA contact distances have been deposited, respectively, as Tables S1, S2, S3, and S4 of the Supporting Information. ORTEP33 views of all molecules are displayed in Figure 1. Data Treatment. Since the present analysis needs to intercompare different classes of H-bonded and EDA interactions, it is important to assess a common scale of the interactions. This is tentatively achieved in two ways: 1 The geometric vdW-shortening scale (vdWSH, in Å) holds equally for all X
H 3 3 3 Y, C
H 3 3 3 Y, and X 3 3 3 :Y interactions and is based on the shortening of the contact distances with respect to the sum of the vdW radii (ΣvdW) or, sometimes, on its percent value, vdW SH% = 100 3 vdWSH/ΣvdW. Isotropic vdW radii were taken from Bondi.34 To correct for the well-known X-ray protonpositioning errors, all H-bonds have been renormalized by setting the O
H, N
H, and C
H distances to their standard 0.94, 1.03, and 1.08 Å values30 whenever shorter than them. 2 The energetic EHB scale relies on the D
H 3 3 3 A bond dissociation energies, EHB in kcal mol
1, evaluated by the Lippincott and Schroeder (LS) method35
37 as a function of the d(D 3 3 3 A) distance and D
H
A angle or, alternatively, of the related quantity d’(D 3 3 3 A) = d(D
H) þ d(H 3 3 3 A) (renormalized D
H) which automatically accounts for the effect of the D
H
A angle. Both methods give very close and realistic energy estimates for conventional O
H 3 3 3 O, N
H 3 3 3 O, N
H 3 3 3 N bonds but not for EDA interactions and neither for the C
H 3 3 3 O/N bonds for which no reliable LS parametrization is available. By making use of a number of recent tabulations,4,6 the energy scale can be tentatively joined to the scale of geometrical shortening as shown in Table 1 for the most common H-bond types. Another important parameter used to evaluate H-bond strengths according to the pKa equalization principle4
7 is ΔpKa, the difference of the water acid
base dissociation constants. Since H-bonds can be equally formed by an acid and a base (D
H 3 3 3 A a
D 3 3 3 H
Aþ), by two acids (D1
H 3 3 3 D2
a
D1 3 3 3 H
D2), or by two bases (þA1
H 3 3 3 A2 a Α1 3 3 3 H
A2þ), there are three different ways for 2727

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Table 2. Numbers of Interatomic Contacts Shorter than ΣvdW, the Sum of van der Waals Radii, Occurring in Compounds 1
15 (Data from Table S5)a COMP.b

ΣINT

ΣINT/D

d (g/cm3)

11

21

1.50

1.822

7 (2)

16 12

1.60 1.20

1.682 1.653

D:

UNS(D)

A

A
D

X
Hr:D H-bond

UNS(XH)

C
Hr:D H-bond

UNS(CH)

Ar:D EDA

1

14

2

6

-8

4

0

6

0

15 6

10 10

0 0

7 8

-3 -2

2 5

0 0

7 5

0 0

2

8

1

7

-1

8

0

2

2

(1)

11

1.38

1.562

8

9

0

9

0

6

0

6

1

2

14

1.56

1.556

10

14

0

14

0

10

0

9

0

5

24

1.71

1.644

11

8

0

8

0

4

0

7

0

0

11

1.38

1.694

9

8

0

9

1

4

0

7

2

8

19

2.38

1.676

12

7

2

8

1

4

0

6

1

1

11

1.57

1.601

5 4

8 7

1 1

9 9

1 2

5 5

0 0

4 5

3 1

4, (1) 2

14 12

1.75 1.71

1.599 1.662

13

14

1

16

2

8

0

12

4

3

23

1.64

1.612

14

9

0

13

4

4

0

11

2

1

16

1.78

1.496

3

7

0

12

5

2

0

9

5

2

13

1.86

1.516

7

14

0

22

8

10

0

12

6

3

25

1.79

1.599

147

8

157

81

0

108

27

100%

5.4%

sum %

33.5%

44.6%

53 21.9%

242 100%

mean 1.65

mean 1.625

a

D: = electron donors, UNS(D) = unsaturated donors; A = electron acceptors; A
D = acceptors minus donors; X
Hr:D (X = N, O) = conventional H-bonds, UNS(XH) = unsaturated X
H acceptors; C
Hr:D = C
H H-bonds, UNS(CH) = unsaturated C
H acceptors; Ar:D = charge-transfer or EDA interactions (normally π*rn or π*(k)rn; π*rπ in parentheses); ΣINT = total number of interactions; d = calculated crystal density in g/cm3. b Chemical names: 1: picric acid (PAc); 2: acetamidinium picrate (1:1); 3: 4-phenylpyridinium picrate (1:1); 4: 3-aminopyridinium picrate (1:1); 5: 4-aminopyridinium picrate (1:1); 6: 2-Aminopyrimidinium picrate (1:1); 7: 8-aminoquinazolium picrate (1:1); 8: 2,6-dimethyl-4-oxo-3,4-dihydropyrimidinium picrate 3 H2O (1:1:1); 9: 4-oxo-3,4-dihydroquinazolinium picrate (1:1); 10: 3-hydroxy-5-methyl-1H-pyrazolium picrate (1:1); 11: 2-hydroxypyridinium picrate (1:1); 12: 6-methyl-2-hydroxypyridinium picrate (1:1); 13: 4-methyl-2-hydroxypyridinium picrate (1:1); 14: 4-methyl2-hydroxypyridinium picrate 3 4-methylpyridine-2(1H)one (1:1:1); 15: 4-nitropyridine-N-oxide 3 picric acid (1:1). calculating such a ΔpKa difference. Only in the first case this difference can be univocally calculated as ΔpKa = pKa(acid)
pKa(base) = pKa(D
H)
pKa(H
Aþ), while in the two other cases the equation becomes ΔpKa = pKa(acid)
pKa(acid) = ( |pKa(D2
H)
pKa(D1
H)| or ΔpKa = pKa(base)
pKa(base) = ( |pKa(A2
Hþ)
pKa(A1
Hþ)|, where the sign of the results is lost because the order of the two bases, or of the two acids, is actually irrelevant. Following our previous classification,6,7,4 the three classes of H-bonds above are sometimes indicated by the acronyms (()CAHB, (
)CAHB, and (þ)CAHB, respectively, double, negative, and positive charge-assisted H-bond. Structure Description. A complete discussion on the crystal packing in structures 1
15 (including a full set of color figures) is included in Appendix 1 (pp S21
S36) of the Supporting Information. It reports the detailed analysis of all the interatomic H-bond and EDA contacts shorter than ΣvdW occurring in the 15 structures, whose distances are listed in Table S5 of the Supporting Information. Table 2 summarizes, for each structure, the number of the electron donors (D:) and acceptors (A) present, the number of the intermolecular contacts they form (subdivided in the three classes of X
Hr:Y (X,Y = O,N), C
Hr:Y (Y = O) H-bonds, and Xr:Y (X = C,N; Y = C,O) EDA interactions), and the total number of interactions formed, ΣINT. All crystals are packings of discrete molecular units, consisting of PAc molecules in 1 and of PAc-NB H-bonded adducts in 2
15. Because of that, the crystal packing has been analyzed as a two-step process, the first involving the H-bonding within the PAc-NB complexes and the second the packing of such complexes within the crystals. Chemical sketches of PA and of the 14 PAc-NB complexes are depicted in Chart 1, where the numbers in color indicate (when accessible from the literature) the pKa of acids (in red) and bases (in blue) involved in H-bond formation, while the numbers in black adjacent to each D
H 3 3 3 A bond represent its

H-bond energy, EHB in kcal mol
1, as calculated by the LS method (C
H 3 3 3 O energies are missing because they cannot be evaluated for lack of the corresponding LS parameters). As discussed in more detail below, the 15 structures contain a total of 242 short contacts which are not uniformly distributed within the crystals. The strong X
Hr:Y (X,Y = O,N) H-bonds are mostly localized in between the picrate and the protonated nitrogen base to form the essentially planar PAc-NB adducts (Figure 1) whose C
H groups are also in a plane and thus have the correct orientation for linking other adducts in planes or supramolecular islands by a net of C
Hr:Y (Y = O) bonds, a situation exemplified in Figure 2 for the compounds 6, 11, and 15. These planes are kept together, besides van der Waals forces and electrostatic attractions between PAc anions and NB cations, by a net of perpendicular EDA interactions belonging to the three π*rn, π*(k)rn, and π*rπ classes, which are all shorter than ΣvdW and are illustrated in the examples of Figure 3 (the reader interested to a more detailed description is referred to the full Figures S1
S15 reported in Appendix 1 of the Supporting Information).

’ RESULTS AND DISCUSSION A Verification of the Electron-Pair Saturation Rule. It has been suggested in the introduction that the packing of molecular crystals can be plausibly rationalized in terms of the electron-pair saturation rule, stating that all electron donors of a molecule (either donors of nonbonding pairs or donors of π-bonding pairs of multiple bonds) have a definite tendency to become engaged in EDA interactions with electron acceptors and, whenever these acceptors are not enough, to be saturated in order of decreasing 2728

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Chart 1. Chemical Sketches of the H-bond Patterns in the Structures of Picric Acid (1.1) and of its 14 Adducts with Nitrogen Bases (1.2
1.15)a

a Color figures report (when accessible from the literature) the pKa of the acids (in red) and bases (in blue) involved in H-bond formation, while figures in black adjacent to any X
H 3 3 3 Y bond indicate its binding energy, EHB in kcal mol
1, as calculated by the LS method.35
37

interaction strength. A verification of this assumption is attempted here by a full packing analysis of structures 1
15. The list of all intermolecular contacts shorter than ΣvdW has been deposited as Table S5 and summarized in Table 2. All together, the 15 compounds contain 147 electron donors D: (counting OH, O
, NO2, CdO, NfO oxygens, imino nitrogens, and only the effective ring C π-donors) and 157 electron acceptors A (counting C
H and X
H (X = N,O) groups but not the many potential ring C/N π-acceptors) with a donor/acceptor ratio of 0.94, which is considerably larger than usual in view of the great

number of PAc nitro groups, and then suited to study how acceptors can saturate the maximum number of donors. In the table, the 15 structures are ordered for increasing value of the A
D difference, which is seen to undergo large fluctuations for the different structures, ranging from
8 (large excess of donors) to 8 (large excess of acceptors). In spite of these large variations, the number of unsaturated electron donors, UNS(D), remains always very low, not exceeding, on average, the 5.4% of the 147 donors present. For reasons of homogeny, all intermolecular contacts of this paragraph, including H-bonds, are treated as EDA interactions, 2729

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Figure 2. Typical H-bond patterns observed in the structures of (a) 2-aminopyrimidinium picrate (6), (b) 2-hydroxypyridinium picrate (11), and (c) 4-nitropyridine-N-oxide 3 picric acid (15). Strong X
Hr:Y (X,Y = O,N) H-bonds join the picrate and the protonated nitrogen base in PAc-NB adducts which are essentially planar and whose C
H groups are then in the correct orientation for linking other adducts in planes or supramolecular islands by a net of weak C
Hr:Y (Y = O) bonds.

that is, (i) X
H 3 3 3 :Y and C
H 3 3 3 :Y (X,Y = N,O) H-bonds (lying in the mean PAc ring plane) as X
Hr:Y and C
Hr:Y σ*rn interactions; (ii) C/Nr:O contacts (nearly perpendicular to the PAc ring) as π*rn, that is, as lone-pair addition to the aromatic ring, or π*(k)rn interactions, that is, as lone-pair addition to NdO or CdN double or partially double bonds; and (iii) Cr:C contacts (nearly perpendicular to two mutually parallel aromatic rings and occurring only in 2, 5, and 6) as π*rπ interactions between the two aromatic rings. The total number of contacts (ΣINT = 242) can be partitioned in 81 X
Hr:D, 108 C
Hr:D, 49 π*rn or π*(k)rn, and only four π*rπ interactions. Another important parameter is the number of electron acceptors not saturated by donors: Table 2 shows that, while UNS(XH) is identically zero, UNS(CH) is considerably larger (27), and the number of unsaturated π* carbons or

nitrogens (not considered in the statistics of Table 2) is even larger, only a limited number of them being actually involved in π*rn/π EDA interactions. The full saturation of all the X
H groups seems to confirm, at least in the series studied, the Donahue and Etter tenet20,21 that, in molecular crystals, all the conventional H-bond donors are normally used in H-bond formation. Moreover, the increasing unsaturation level of the three interaction types definitely suggests that they must be endowed with decreasing interaction energies. Though we are presently unable to quantitatively estimate the energies involved in most of the cases treated, the problem can be dealt with at a reasonable level of approximation making use of vdWSH%, the percent van der Waals shortening. Figure 4 reports the histograms of this quantity, showing that π*rn, π*(k)rn and π*rπ EDA interactions are considerably weaker than C
H 3 3 3 :Y bonds which, in turn, are much weaker than a substantial fraction 2730

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Crystal Growth & Design

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Figure 3. Patterns of EDA contacts shorter than ΣvdW connecting perpendicularly the planes of H-bonded molecules exemplified in Figure 2, as observed in the most characteristic crystal packings. The classes of EDA interactions the different contacts belong to are marked in red.

of the X
H 3 3 3 :Y ones (with plausible energy ranges of 0
1, 0
2, and 0
10 kcal mol
1, respectively). In conclusion, the results of this analysis are not such to falsify the initial hypothesis that crystal packing is widely determined by the need to saturate the maximum number of electron donors by using, as acceptors, all conventional X
H groups first, then the weaker C
H ones, and finally the even weaker π* acceptors. This is especially apparent in compounds 1 and 15 (first two lines of Table 2) which, having the lowest A
D difference of
8 and
3, do not possess enough X/C
H groups to saturate all the PAc oxygens and, to do so, must resort to form 11 and 7 π*rn or π*(k)rn EDA interactions, respectively. If the lack of X/C
H acceptors can increase the number of π* EDA contacts, the converse is not true because their excess does not exclude the possibility that weaker π* EDA interactions will be caused by other specific chemical factors. This is particularly evident in

compounds 10, 9, 5, and 13 which, even having a sufficient number of X/C
H acceptors (A
D difference = 0, 1, 1, and 2), also form 5, 8, 5, and 3 EDA interactions, respectively, linking the planes of the layered PAc sublattice. This fits the PAc feature of being, besides an efficient n donor through its oxygens, a quite efficient π* acceptor at the C/N ring atoms because of its many electron-attracting substituents. A Verification of the pKa Equalization Principle. As remarked in the introduction, the formation of strong D
H 3 3 3 :A bonds of prevalent covalent nature requires a substantial protonaffinity matching between H-bond donor, D, and acceptor, :A. In less qualitative terms, this condition can be reduced to the socalled pKa equalization principle4
7 for which strong bonds appear only when the difference ΔpKa = pKa(D
H)
pKa(A
Hþ) tends to zero, pKa being the cologarithm of the acid
base dissociation constant. 2731

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Crystal Growth & Design

Figure 4. Distribution of the vdW shortenings (expressed as vdWSH%) for the 242 contacts shorter than the ΣvdW observed in the crystal structures of compounds 1
15. The three histograms refer to the different classes of donor
acceptor contacts (a) X
Hr:Y σ*rn EDA interactions (or X
H 3 3 3 :Y H-bonds; X,Y = N,O); (b) C
Hr:Y σ*rn EDA interactions (or C
H 3 3 3 :Y H-bonds; Y = O); (c) C/Nr:O π*rn and π*(k)rn, or Cr:C π*rπ EDA interactions.

Figure 5a,b displays the plots of d’(D 3 3 3 A) = d(D
H) þ d(H 3 3 3 A) (in Å) and LS-computed35
37 H-bond energies (EHB in kcal mol
1) versus ΔpKa for all the 81 O
H 3 3 3 :O and N
H 3 3 3 :O bonds of structures 1
15 (Table S5 and Table 2), whose EHB versus d’(D 3 3 3 A) plot is shown in Figure 5c. The strongest occurrences (compounds 11, 14, 15) are O
H 3 3 3 O bonds with d’(D 3 3 3 A) of 2.53
2.56 Å and EHB of 8.80
10.60 kcal mol
1 for ΔpKa values ranging from
1 to 2 pKa units. The strongest N
H 3 3 3 :O bond [compound 8; d’(D 3 3 3 A) = 2.670 Å; EHB = 6.11 kcal mol
1; ΔpKa =
1.59] is rather weaker than the O
H 3 3 3 O ones in spite of its good pKa matching, suggesting a some sort of rule in the order of strength of the two bonds (see below). The weakest bonds (0 e EHB e 0.99 kcal mol
1) are those donated by N
Hþ, N
H, and O
H groups to the PAc nitro oxygens whose pKa(nitro) ≈
11.5 does not match that of any other functional group. All other H-bonds of intermediate strengths are arranged in between these two extremes in an approximately linear fashion.

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Figure 5. Correlations for the 81 X
H 3 3 3 O (X = N,O) H-bonds of structures 1
15: (a) d’(D 3 3 3 A) = d(D
H) þ d(H 3 3 3 A) distances (Å) versus ΔpKa = pKa(D
H)
pKa(A
Hþ) scatter plot; (b) H-bond dissociation energies, EHB in kcal mol
1, versus ΔpKa scatter plot; and (c) dependence of the H-bond dissociation energies, EHB in kcal mol
1, on d’(D 3 3 3 A). All H-bond energies were computed by the LS method35
37 starting from the molecular geometries.

Figure 5a,b shows that present data comply rather well with the pKa equalization model, even taking into account that some pKa values were unknown and should be extrapolated from similar compounds. The main discrepancy with the literature is that the maximum N
H 3 3 3 O and O
H 3 3 3 O energies (6.11 and 10.60 kcal mol
1) are considerably smaller than those normally accepted for bonds at this level of pKa matching (respectively, 15.2 and 27.0 kcal mol
1).4,6 Since these stronger bonds are associated with PAc hydroxyls linked to cumbersome N-bases, it may be supposed that this general wakening is due to the steric repulsion exerted by the two o-nitro groups. This is supported by the fact that PAc itself is known to form stronger O
H 3 3 3 O bonds with smaller ligands, such as 1,3-dimethylurea [d’(O 3 3 3 O) = 2.518 Å, EHB = 11.24 kcal mol
1, ΔpKa ≈ 0.25], 3-methylpyridine-N-oxide [d’(O 3 3 3 O) = 2.499 Å, EHB = 12.53 kcal mol
1, ΔpKa =
0.73] and, in particular, with H2O [d’(O 3 3 3 O) = 2.397 Å, EHB = 23.71 kcal mol
1, ΔpKa = 2.09).39
41 On the other side, also N-bases of suitable acidity are known to form stronger N
H 3 3 3 O bonds with less hindering phenols, such as pentachlorophenol with 4-methylpyridine [d’(N 3 3 3 O) = 2.515 Å, 2732

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Crystal Growth & Design EHB = 14.37 kcal mol
1, ΔpKa =
1.26] and 2,6-dichloro-4nitrophenol with 3-methylpyridine [d’(N 3 3 3 O) = 2.566 Å, EHB = 11.09 kcal mol
1, ΔpKa =
2.14].42,43 Concluding Remarks. In this paper, the authors report and analyze the crystal structures of picric acid (PAc) and of 14 of its complexes with different nitrogen bases (NB). In the 15 resulting structures, all the 242 intermolecular contacts shorter than ΣvdW have been retrieved, quantified in terms of their vdW shortening (in Å), and found to be classifiable in the following four classes: (i) conventional X
H 3 3 3 :Y (X,Y = N,O) H-bonds (81 cases), (ii) weaker C
H 3 3 3 :Y (Y = O) C
H bonds (108 cases), (iii) C/Nr:O EDA interactions of the π*r n or π*(k)r n type (49 cases), and (iv) Cr:C EDA interactions of the π*rπ type (4 cases), whose relative vdW shortenings are in the order i > ii > iii, iv (Figure 4) with respective estimated energies of 0
10, 0
2, and 0
1 kcal mol
1. A rationalization of such a complex interaction pattern is not a simple task. A fortunate exception is the so-called pKa equalization principle for which strong H-bonds may take place only when the ΔpKa = pKa(D
H)
pKa(A
Hþ) difference comes close to zero.4
7 First applications of this rule date back to the 60s and, over the years, it has been successfully used in a remarkable list of cases.44
51 In touch with these previous results, the present application to the full set of 81 O
H 3 3 3 :O and N
H 3 3 3 :O conventional H-bonds (Figure 5) confirms the strict intercorrelation among ΔpKa, H-bond geometry and H-bond binding energy, so validating the equalization rule over a ΔpKa range of wideness (from
24 to nearly þ2) has never been experienced before. To go further in understanding the interaction net, it has been necessary to remove the dichotomy between proton exchange (the way by which H-bonds are interpreted) and charge transfer (the way adopted for EDA interactions). This can be easily achieved because X
H 3 3 3 :Y bonds can be alternatively accounted for as X
Hr:Y bonds, that is, as σ*rn EDA interactions.9,10 In this way, all intermolecular interactions but London’s dispersion ones turn into EDA interactions, the electron becomes the unified particle (or token) of exchange, and we may start to wonder which rules this electron exchange will follow. Of course, there may be several of such rules acting at the same time, but the only one we have been able to find out so far, hopefully for the prominent role it plays, is the electron-pair saturation rule which can be formulated as “all the electron donors of a closed-shell molecule, either nonbonding pairs of lone pairs or π-bonding pairs of multiple bonds, will display a definite tendency to become engaged in EDA interactions with all electron acceptors present as far as these are available; if acceptors are insufficient to saturate all donors, the latter will be saturated in order of decreasing EDA interaction strength”. The detailed analysis of the 242 short contacts occurring in these structures (Table 2) confirms that the rule is actually obeyed whenever not too severely hindered by steric factors, achieving a rather impressive level of n- or π-donor saturation (ΣINT/D) amounting, on average, to 1.65 surrounding acceptors per donor. Moreover, the interaction energy (and then the order of preference by which electron acceptors are saturated by donors) is found to be X
H > C
H > π* (Figure 4), which can help explain why, over the 15 structures studied, the acceptor unsaturation fraction is 0/81 and 27/108 for X
H and C
H,

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respectively, in perfect agreement with the Donahue and Etter tenet20,21 that, in the crystallization process, all conventional H-bond donors are normally involved in H-bond formation. Though based on a purely empirical crystal packing analysis, the electron-pair saturation rule has a number of interesting theoretical implications. The main point is that the assessing of the rule itself requires the preliminary separation of the attractive London’s forces from the more properly chemical ones (H-bond and charge-transfer) for the latter may become apt to be analyzed in the unified form of EDA interactions. This separation, which was rather arbitrarily adopted at the beginning of our analysis, has recently found a valid theoretical justification in a number of DFT studies of ab initio molecular dynamics52 and crystalstructure prediction53,54 which have shown that DFT methods can account for all interaction forces except attractive dispersion ones, a fact mostly interpreted by saying that DFT, being a monodeterminantal technique, necessarily neglects the molecular excited states determining the polarizability of the molecular electron clouds which are at the very root of London’s dispersion forces.55,56 As a self-explaining example, in the most recent blind test of crystal-structure prediction,53 all four structures submitted were successfully predicted54 by a hybrid method combining crystal-state DFT simulation57 with an empirical C6r
6 vdW term expressed in the form of isotropic atom
atom pair potentials.58 On these grounds, a reclassification of the attractive intermolecular forces determining the packing of molecular crystals in two groups may be proposed: (i) physical interactions, which are essentially due to atomic dispersion forces and are widely independent of molecular constitution; (ii) chemical interactions (including EDA interactions, C
H 3 3 3 :Y and X
H 3 3 3 :Y H-bonds), which can be intended as holistic properties of whole molecules reacting among themselves by incipient (molecular interaction) or full (dative bond) nucleophilic addition to fulfill the saturation rule, that is, to remove from the external molecular surface all points of residual reactivity associated with bonding or nonbonding unsaturated electron pairs. It is our belief that the particular approach to molecular interactions arising from the present analysis deserves to be further investigated by analogous systematic studies carried out on suitable ensembles of molecular crystals, as well as by more sophisticated techniques particularly suited to study this class of phenomena on smaller sets of well-selected molecules. In this second respect, the methods of election may be traced back to electrostatic potentials and electron densities,59,60 quantities derivable from both quantum-mechanical calculations and multipolar refinements of accurate diffraction data,61,62 and for which a number of valuable methods of analysis have been well established, such as the AIM Bader’s topological analysis,63 the source function,64,65 or the electron localization function (ELF).66,67 It is interesting to remark that the present approach to molecular interactions seems to provide a particularly easy way to look at the crystal packing. Alkanes contain only bondsaturated sp3 carbons and represent the paradigmatic compounds that are packed by purely physical interaction forces accountable in terms of atom
atom potentials only. Introduction of double, triple, or aromatic C
C bonds in the molecule, however, induces some new specific features (free π-bonding electron pairs and more acidic C
H groups at the sp2 carbons) which will cause an increase of intermolecular residual reactivity: in addition to the background of London’s dispersion attractions, molecules start to interact among themselves by what we are used to calling 2733

dx.doi.org/10.1021/cg101007a |Cryst. Growth Des. 2011, 11, 2724–2735

Crystal Growth & Design C
H 3 3 3 :π H-bonds or σ*rπ EDA interactions. While molecules are becoming more and more complex and the ever new chemical functionalities introduced (CdO, CdS, OH, NH2 functional groups, ring-included N, O, and S atoms, etc.) will add ever new unsaturated electron donors and acceptors to the molecular surface, the chemical interaction net will become more and more complex, but the rules that govern its formation will remain that simple.

’ ASSOCIATED CONTENT

bS

Supporting Information. Tables of crystal data, selected bond distances and angles, and H-bond and EDA contact distances for compounds 1
15 (Tables S1
S4). Full list of the geometric (vdWSH and vdWSH%) and energetic (EHB) parameters for H-bonds and EDA interactions are collected in Table S5. Complete discussion of the crystal packing of structures 1
15 including a full set of color figures (S1
S15) is given in Appendix 1. X-ray crystallographic information files (CIF) for structures 1
15 (deposited at the CCDC with deposition numbers 787071
787085). This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] Tel. þ39-0532 455141. Fax þ390532 240709.

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