Perspective Cite This: Cryst. Growth Des. 2018, 18, 1−6
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F or O, Which One Is the Better Hydrogen Bond (Is It?) Acceptor in C−H···X−C (X− = F−, O) Interactions? Binoy K. Saha,* Arijit Saha,‡ Durgam Sharada,‡ and Sumair A. Rather‡ Department of Chemistry, Pondicherry University, Puducherry 605 014, India S Supporting Information *
ABSTRACT: Three sets of statistical analyses have been performed to evaluate whether C−F or CO is the better C−H hydrogen bond acceptor and to understand the nature and preferred geometry of the C− H···F−C interactions. The first analysis uses Hirshfeld surface of the molecules, which shows that CO is a better hydrogen bond acceptor than C−F, though C−H···F−C interactions also play an important role in crystal packing. The second analysis compares the population densities of C−H···F−C interactions at different H···F distances and at different C− H···F or C−F···H angles. This analysis shows the directional nature of this interaction. The third analysis shows which combinations of the C−H···F and C−F···H angles are preferred by the C−H···F−C interactions.
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INTRODUCTION Supramolecular interactions are at the heart of crystal engineering and solid-state chemistry.1 Conventional hydrogen bonds are at one end of the wide spectrum of these interactions and van der Waals interactions are at the other end. Conventional hydrogen bonds, such as O−H···O, O−H···N, and N−H···O, are known as directional and strong interactions, whereas the van der Waals interactions are known as nondirectional and weak interactions.2−5 There is a plethora of other interactions that bridge between these two extreme ends. Most common types of interactions in this category are C−H···O/N, N/O−H···halogen, C−H···π, halogen···O/N, halogen···halogen, etc.6,7 C−H···O/N interactions are now widely accepted as weak hydrogen bonds,8−12 but the nature of C−H···halogen−C interactions is still a matter of debate. Among the C−H···halogen−C interactions, the C−H···F−C interaction is the most debated one because of the widespread presence of F in different materials and biological systems.13 A school of thought considers this as a van der Waals interaction,9,14 whereas other groups think it should fall into the category of weak hydrogen bonding.15−17 X-ray crystal structures, theoretical calculations, charge density calculations have been the tools to assess the nature of these interactions. However, the most popular tool, in this regard, perhaps is the statistical analysis on the reported database available in Cambridge Crystallographic Data Centre (CCDC). Here we have performed statistical analyses on the C−H··· X−C (X = F, O) interactions data, retrieved from CCDC,18 to see which one, O or F, is the better hydrogen bond acceptor and to understand the nature and geometry of the C−H···F−C interactions. Because C−H···OC has been widely accepted as a hydrogen bond, if F is found to be a better acceptor than O, then the C−H···F−C interaction should also be considered as a hydrogen bond and hence an important determining factor in © 2017 American Chemical Society
crystal packing. But if it is weaker than O, then the question arises as to whether this interaction is still a significant one or merely a result of random distribution. What would be the preferred geometry of the C−H···F−C interactions if it is not an isotropic van der Waals interaction? On the basis of statistical analysis and energy calculations, Gavezotti and Lo Presti have concluded that this interaction is not more than a van der Waals interaction.9 Their energy calculations show that the Coulombic contribution in the interactions is very small. They used very strict distance cutoff criteria in their study. Similarly, on the basis of statistical analysis with the H···F distances < 2.3 Å, Dunitz and Taylor concluded that it is extremely rare for the C−F groups to act as a hydrogen bond acceptor.14 On the basis of charge density analyses, Guru Row and co-workers have found that in a few systems C−H···F interactions are as strong as C−H···O interactions, and in some other systems C−H···F interactions are found to be inferior to C−H···O interactions.19,20 On the other hand, in a seminal work, Desiraju, Nangia, and Boese showed that under certain circumstances, where the C−H hydrogen is sufficiently acidic due to the presence of a large number of F in the molecule, this interaction plays a significant structure directing role.21 On the basis of the H···F distance and C−H···F angle relationship, Brammer et al. considered C−H··· F−C as a hydrogen bond.22 Seddon and Berg applied Isotropic Density Correction on the statistical analysis of C−H···F−C interactions and showed that though the directionality of C− H···H−C and C−H···F−C interactions are very similar, the distance−population density relationship indicates a weak hydrogen bonding nature in C−H···F−C interactions.23 Taylor Received: August 20, 2017 Revised: October 25, 2017 Published: November 20, 2017 1
DOI: 10.1021/acs.cgd.7b01164 Cryst. Growth Des. 2018, 18, 1−6
Crystal Growth & Design
Perspective
molecule (i) and SX(e)...Y(i) % is the percentage contact surface area between X atoms from surrounding (e) and Y atoms from the concerned molecule (i) involved in intermolecular contact. On the basis of random distribution of the molecules, the expected contact surface area for the contacts between Y and X is calculated as
went one step further and even claimed that C−H···F−C interaction is stronger than C−H···OC interactions.16 In his study he analyzed the number of contacts on the accessible surface area of the atoms and showed that number of observed H···F contacts is a few times higher than that if the intermolecular interactions were random. The observed/ random contact numbers for H···F are higher than that for the H···O interactions, and therefore, C−H···F−C interactions are not van der Waals type but stronger than C−H···OC hydrogen bonds. In this interesting work, Taylor put the cutoff distance as the van der Waals sum of the interacting atoms +1 Å and considered only one interaction per atom irrespective of the surface area available on the atoms. He calculated the available surface area on the atoms using the RPluto program which uses the van der Waals radius of the atom.24 Though the van der Waals radius may be a good approximation for many practical purposes, it is known that the atomic radius, as defined by Bondi and some other workers, is not really rigid and constant across different crystal structures.23 In the present work we too have calculated the observed/random H···X contact, but our approach is completely different. We have here used the Hirshfeld surface25 to calculate molecular, atomic, and contact surface areas. To the best of our knowledge, this is the first report where the Hirshfeld surface area calculation has been used for this type of analysis. In this approach there is no need to define the distance cutoff and number of allowed contacts, and neither is there any need to consider van der Waals radius of the atoms.
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RAY − X =
If the
SX(e) =
∑
SAll(e)...X(i)% 100
× SM....
(1)
× SM ...
(2)
SX(e)...All(i)% 100
⎡⎛ S Y(e)...X(i)%
∑ ⎢⎜ ⎣⎝
100
+
⎤ SX(e)...Y(i)% ⎞ ⎟ × SM ⎥... 100 ⎠ ⎦
OB Y − X RAY − X
OB Y − X% =
100
+
S Y(e)...All(i)% 100
(4)
ratio is >1 then the interaction is more than what
OB Y − X × 100... SX(i) + SX(e)
(5)
and based on random orientation of the molecules, the % surface area of X covered by Y is given by RAY − X% =
RAY − X × 100... SX(i) + SX(e)
(6)
Therefore, the excess surface area on X occupied by Y is given by
EXY − X% = OB Y − X% − RAY − X%...
(7)
Distance-Cone and Double Area Corrections. CCDC database was searched (version 5.38, November 2016) for the structures containing the H···F distance range 2.00−4.00 Å, C−H···F and C−F··· H angles in the C−H···F−C interactions 90−180°, 3D coordinates available, neutron normalized, R-factor ≤10%, Only organic. This data set comprised a total of 24 439 structures with 433 499 H···F contacts. Distance-Cone Correction. The equation of volume of space confined within the angle range θ1 → θ2 and distance range r1 → r2 (Scheme 1) is given by Vθ1θ2 , r1r2 =
2 3 (r2 − r13)(cos θ1 − cos θ2) 3
Scheme 1. Volume of Space (Ring) Confined within the Distance Range r1 to r2 from X Atom and Angle Range θ1 to θ2 around the C−X Bond Is Shown Here
where SAll(e)···X(i) % is the percentage contact surface area between all the atoms from surrounding and the atom X within the concerned molecule and SX(e)...All(i) % is the percentage contact surface area between all the atoms within the molecule and the atom X from the surrounding molecules, SM is the molecular surface area, e = external or outside the molecule and i = internal or inside the molecule. The observed intermolecular contact surface area between atom type Y and atom type X is calculated as OB Y − X =
100
SAll(e)...Y(i)%
would have been expected from just a random distribution and hence it is stabilizing. We also have calculated the % surface area on X covered by the interacting atom Y as actually observed and based on random distribution. The observed % area on X covered by Y is given by
Hirshfeld Surface Area Analysis. The CCDC database was searched (version 5.38, November 2016) for the structures containing only C, H, F, and O atoms, where O is present only as the CO group so that O, similar to F, is also present as a terminal group, no other elements are allowed, 3D coordinates available, R-factor ≤5%, Z′ ≤ 1, no disorder, no error, no polymers, no powder-diffraction structures, no ions. For those structures with multiple refcodes available, only one refcode with the lowest R factor was considered. This data set comprised a total of 132 structures. Calculation of the Hirshfeld surface area and fingerprint plot on the Crystal Explorer program26 provides the total molecular surface area (SM) under the “surface” → “info” option and % contact areas between different atoms under the “finger-print plot” option. The total observed surface areas on a particular type of atom X present within the concerned molecule (SX(i)) and in the surrounding molecules (SX(e)) have been calculated as
∑
⎣⎝
×
⎤ SAll(e)...X(i)% ⎞ × ⎟ × SM ⎥... ⎠ 100 ⎦
EXPERIMENTAL SECTION
SX(i) =
⎡⎛ SX(e)...All(i)%
∑ ⎢⎜
The population density or distance-cone corrected population is given by Ndis − cone =
Nθ1θ2 , r1r2 Vθ1θ2 , r1r2
.... (8)
Nθ1θ2,r1r2 is the number of H or F atoms present within the volume of space, Vθ1θ2,r1r2 around the C−F or C−H groups respectively, participating in C−H···F−C interaction. % of Ndis‑cone values have been tabulated in Table 1 and Table 2. Double Area Correction. The double area corrected population27 has been calculated as OP/CP, where OP and CP are the observed population and calculated population based on random distribution
(3)
where SY(e)...X(i) % is the percentage contact surface area between Y atoms from surrounding (e) and X atoms from the concerned 2
DOI: 10.1021/acs.cgd.7b01164 Cryst. Growth Des. 2018, 18, 1−6
Crystal Growth & Design
Perspective
Table 1. % Populations of C−H···F−C after Distance-Cone Correction at Different Combinations of θH and H···F Distance (dHF)a
Table 2. % Populations of C−H···F−C after Distance−Angle Correction at Different Combinations of θF and H···F Distance (dHF)a
a Populations in the ranges 3.68−4.00 and 2.00−2.16 Å are very small (
