Measurement of Electric Fields Experienced by Urea Guest Molecules

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Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18–Crown–6:Urea (1:5) Host–Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis. Ming W. Shi, Sajesh P. Thomas, Venkatesha R Hathwar, Alison J. Edwards, Ross O. Piltz, Dylan Jayatilaka, George A. Koutsantonis, Jacob Overgaard, Eiji Nishibori, Bo B. Iversen, and Mark A. Spackman J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b12927 • Publication Date (Web): 14 Feb 2019 Downloaded from http://pubs.acs.org on February 14, 2019

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Journal of the American Chemical Society

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18–Crown–6:Urea (1:5) Host–Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis. Ming W. Shi,‡,† Sajesh P. Thomas,‡,§ Venkatesha R. Hathwar,§,¶,# Alison J. Edwards,^ Ross O. Piltz,^ Dylan Jayatilaka,‡ George A. Koutsantonis,‡ Jacob Overgaard,§ Eiji Nishibori,¶ Bo B. Iversen,§ and Mark A. Spackman*,‡ ‡ School of Molecular Sciences, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. § Center for Materials Crystallography and Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark. ¶ Division of Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan. ^ Australian Nuclear Science and Technology Organization, Australian Centre for Neutron Scattering, New Illawarra Road, Lucas Heights, New South Wales 2234, Australia. ABSTRACT: High resolution synchrotron and neutron single crystal diffraction data of 18-crown-6:(pentakis)urea measured at 30 K are combined, with the aim to better appreciate the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a co-crystal or host-guest system incorporating such a large number of unique molecules. Dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared with values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range 10 – 19 GV m–1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes, and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

INTRODUCTION Electric fields play an important role in a very broad range of noncovalent interactions, most notably the structure and function of proteins, enzyme and chemical catalysis, as well as chemical reactivity in general. Until quite recently the discussion of the nature and magnitude of electric fields in bulk matter has been more qualitative than quantitative,1 but that is rapidly changing with advances in experimental techniques and computational approaches. Foremost among these developments is the application of the vibrational Stark effect (VSE) to measure the electric field magnitude in the active sites of enzymes,2 with a particular focus on the relationship between changes induced by specific mutations and their effect on turnover rates. This technique has been applied to myoglobin,3 ketosteroid isomerase (KSI),4 a model lipid bilayer membrane,5 human aldose reductase (hALR2),6 dehalogenase and serine proteases,7 ribonuclease S,8 and green fluorescent protein (GFP).9 These experiments have been supported by computational studies of the electric field in liquids,10 and in the active sites of KSI11 and GFP.12 The VSE has also been applied to estimate local electric fields in metal-exchanged ZSM-5 zeolite,13 as well as the interface between self-assembled monolayers on metal surfaces.14

Electric-field-assisted reactions are currently a topic of vigorous research, both experimentally and computationally. Examples include fields due to electrodes,15 and those arising from STM tips.16 A number of researchers are actively exploring the potential of oriented external electric fields as ‘smart reagents’ to control important non-redox chemical reactions,17 and the role of electric fields in catalysis has been reviewed recently.18 External electric fields have also been investigated for their ability to promote nucleation and crystallization of polymorphs of molecular crystals.19 The design and synthesis of relatively simple organic compounds as models that mimic the substrate selectivity of enzymes has a long history. Particularly relevant to the present study is the work by Cram, who coined the term “host-guest chemistry” in 1974,20 and pioneered the modern field of biomimetic chemistry through the design of mimics for the active site of chymotrypsin.21 Host-guest supramolecular chemistry is now a fast-growing field of modern chemistry, in part due to the fascination of its structural variety, but also for the breadth of important potential applications in drug delivery,22 catalysis,23 gas storage and sequestration,24 electro-optics and non-linear optics.25 Although a great deal of current research focuses on the design, synthesis and characterization of novel and increasingly complex molecular aggregates, their very size and complexity can actually

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hinder research aimed at a detailed understanding of their formation, interaction and electrostatic nature. As one of the earliest and most prominent classes of host in hostguest chemistry, crown ethers have been studied extensively thanks to their broad applications in metal cation transport and separation.26 Compared with other organic hosts, crown ether complexes usually have simpler structures in the solid state and exhibit less disorder and air-sensitivity, making them more amenable to the detailed experimental investigation of their geometric and electronic structure in the solid state. Although 18-crown-6 (18C6) is well known for its binding affinity to various metal and ammonium cations, the nature and strength of its binding with neutral guest molecules remains relatively unexplored.27 18C6:(neutral molecule) complexes commonly occur as trimers in the solid state, with two guest molecules bound above and below the 18C6 macrocycle. Because of the strength of the host:guest interaction, the host:guest trimer can often be considered to be the fundamental structural unit in 18C6:(neutral molecule) crystal structures.28 The title host:guest complex, 18-crown-6 pentakis(urea) (18C6:5U), was first reported in 1981;27a a subsequent study compared 18C6:5U with the isostructural, but disordered, aza-18crown-6 pentakis(urea) complex.29 These studies were motivated by the possibility that a complex between 18C6 and urea might be suitable for removing urea molecules in dialysis, mimicking the enzyme urease. As a result, their emphasis was on the mode of binding between 18C6 and guest molecules, and in particular the conformations of the crowns. Surprisingly, the unusually large number of unique urea molecules in these crystal structures did not elicit any comment. Co-crystals of urea are many and varied,30 and may be divided into those where the molecules are all involved in a hydrogen bonded network, and urea inclusion compounds (UICs) where urea acts as a crystalline ‘host’ forming tunnels in which ‘guest’ molecules are located, weakly bound to the ‘host’ network. The crystal structure of 18C6:5U is a hybrid of these, as it incorporates two examples of the centrosymmetric 1:2 trimer, as well as a separate hydrogen bonded network of urea molecules. This offers the opportunity to explore the electrostatic environment, intermolecular interactions and their influence on the properties of five different urea mole-

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cules, and in two distinctly different environments. Here we present results from single crystal diffraction experiments at 30 K on 18C6:5U, obtained using both synchrotron and neutron radiation. This represents the first combined X-ray/synchrotron and neutron experimental charge density analysis on a co-crystal or hostguest system incorporating such a large number of unique molecules. The synchrotron data contains details of the electron distribution in the crystal, and the neutron experiment provides intimate structural information on hydrogen atoms and especially the numerous hydrogen bonds in this crystal. In combination, the two experiments afford an unusually high-quality model of the electron distribution in the crystal. As all molecular properties are derived from the same experimental observations and modeling procedure, the systematic errors that are unavoidable when comparing properties of molecules derived from different crystals and different experiments are completely absent. Importantly, this model of the electron distribution can be used to map the electrostatic potential (ESP) and electric field (EF)31 experienced by each of the urea molecules in the crystal, enabling a detailed comparison between their electrostatic environments, and the effect these environments have on derived molecular properties such as dipole moments. This is part of an ongoing study aimed at demonstrating that experimental charge density analysis can reliably measure the magnitude and direction of the electric field experienced by molecules in crystals, and correlate this with molecular polarization and dipole moment direction and enhancement.32 We first present the structural information on 18C6:5U with an emphasis on the supramolecular environment of the distinct urea molecules in the unit cell. From the multipole-refined model of the electron distribution we map the ESP and EF experienced by each urea molecule, and explore the relationship between these EFs and the experimentally derived enhancement of their molecular dipole moments. Finally, we compare the average EFs experienced by the urea molecules in 18C6:5U with other relevant experimental results, in particular those obtained for small chromophores in enzyme environments using the VSE. These results corroborate the conclusions of Boxer et al. regarding the magnitude of internal EFs

Figure 1. Packing diagrams for 18C6:5U with molecules colored and labeled by symmetry equivalence. (a) viewed along a, and (b) viewed along b.


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in the active sites of enzymes.2a,4b They also provide an important independent experimental point of reference for recent discussions focused on electric-field-assisted chemical reactions.

RESULTS AND DISCUSSION Crystal structure overview. The crystal structure of 18C6:5U was described succinctly when it was first reported: “The crystal structure contains two crystallographically different rings, both containing a centre of symmetry. The urea molecules in the structure can be divided into two different types. The first one consists of urea molecules not bonded to the crown ether molecules. These urea molecules are arranged in layers held together by a two-dimensional hydrogen bonding network. The urea molecules of the second type are bonded to crown ether molecules by means of two N–H···O bonds to adjacent oxygen atoms of the ring”.27a Figure 1 provides two views of the structure, with labels that will be used in all subsequent discussion. The three urea molecules that form separate folded layers are urea2, urea3 and urea4; urea1 and urea5 also interact with the two distinct 18C6 macrocycles, forming 1,2 bridges with adjacent oxygen atoms of the crowns (crown1 and crown2, respectively). The projection of the 18C6:5U structure along a in Figure 1 resembles the urea host hydrogen bonding network in UICs, the so-called b-urea structure. This important relationship is discussed in more detail in the Supporting Information, where the folded urea layer in 18C6:5U is compared with similar features in three UICs for which neutron diffraction structures were recently reported:33 hexadecane (U:HEX), 1,6-dibromohexane (U:DBH) and 2,7-octanedione (U:OCT) (see Figures S5 and S6). The two independent 18C6 molecules have identical ‘biangular’ Ci conformations and the two structures are almost superimposable (the root-mean-square difference for all atoms is only 0.094 Å). Although the crown conformation observed in the majority of crystalline complexes with neutral molecules approximates D3d symmetry,27g,34 the present Ci conformation is also relatively common, and typically observed in complexes where –NH2 groups form 1,335 or 1,436 bridges.

Figure 2. Local hydrogen bond environments for the five urea molecules in 18C6:5U compared with that in the UIC with hexadecane, U:HEX (bottom right). Supramolecular environment of the urea molecules. The local hydrogen bond environments for the five urea molecules in 18C6:5U are depicted in Figure 2. All urea hydrogen atoms are involved in hydrogen bonds, and it is readily seen from the figure how they comprise two distinct groups. Molecules urea2, urea3 and urea4

all exhibit the same hydrogen bonding pattern, with the oxygen accepting three hydrogen bonds from three separate ureas, two of which are also hydrogen bonded to the central molecule’s syn hydrogens forming a ring of eight atoms, with two donors and two acceptors (𝑅"" (8) in graph set notation37). The anti hydrogens of these three ureas all form single hydrogen bonds to two separate ureas, which in turn are linked together via a cyclic 𝑅"" (8) motif. The other two urea molecules, urea1 and urea5, display a similar hydrogen bond arrangement around the carbonyl oxygens and syn hydrogens (except that the urea5 oxygen accepts four hydrogen bonds from four other ureas), but the anti hydrogens are linked to two adjacent 18C6 ring oxygen atoms. Figure 2 also depicts the hydrogen bond environment for the urea host in U:HEX, revealing its close similarity with those for urea2, urea3 and urea4 in 18C6:5U. Intermolecular interaction energies, estimated by our CE-B3LYP model,38 are given in Table S2 for all unique pairwise nearest neighbour interactions depicted in Figure 2, including those for U:HEX (Table S2 also provides separate electrostatic, polarization, dispersion and repulsion contributions to these energies). The cyclic 𝑹𝟐𝟐 (𝟖) motif with two hydrogen bonds involves interaction energies in the range –58 to –68 kJ mol-1 in 18C6:5U and –60 kJ mol-1 in U:HEX, while pairwise interactions involving a single hydrogen bond are approximately half this value (–25 to –33 kJ mol-1 in 18C6:5U and –30 kJ mol-1 in U:HEX). Urea···crown interactions in 18C6:5U are stronger at –79 kJ mol-1, but nevertheless less than estimated for the 18C6:urea dimer at its optimized geometry in the gas phase, –114 kJ mol-1.27g The present neutron structure of 18C6:5U also reveals the deviation of urea nitrogen atoms from the structure found in urea itself, where the molecule has ideal planar C2v symmetry.39 Using the angle between C–N–Hsyn and C–N–Hanti planes as a measure of pyramidalization for each N atom, values obtained range from 2.5° to 17.9°, with a mean of 10.1° (Table S5). In all cases inspection of the structure reveals that the deviation of each H atom from the plane of the heavy atoms in each urea molecule correlates with a close approach to an acceptor carbonyl oxygen atom. Electrostatic potential and electric field experienced by the urea molecules. A primary objective of this experimental charge density study is the mapping of the ESP and EF experienced by each of the five urea molecules in different environments, with a particular focus on the effect on their electron distributions, as summarized by their dipole moments. These properties are computed directly from the experimentally-derived molecular electron distributions, as described in detail elsewhere,31 and hence depend intimately on the quality of the MM-NEUTRON electron density model. The static deformation electron density maps for the five urea molecules in 18C6:5U (Figure S4) demonstrate the high quality of the MMNEUTRON electron densities. (It is important when comparing those maps with one another to bear in mind that the five urea molecules are completely independent, possess no symmetry elements, and the multipole parameters in the model were not constrained in any way). Contour maps of the ESP and the magnitude of the EF, in the plane of each of the urea molecules, are given in Figures 3 and 4, with a superposition of each urea molecular skeleton on the mapping plane. The two sets of maps provide related information, as the EF is the negative gradient of the ESP. These maps have been obtained by the summation of contributions from a cluster of nearest neighbor



molecules, but omitting the contribution from the central urea molecule in each case.31b This procedure amounts to computing these properties in a cavity formed by the cluster of surrounding molecules, and in this sense it may be considered as a simple model for the binding site of a protein. From Figure 3 we see that the urea molecules are situated in regions of relatively constant EF, and the contour maps for urea2, urea3 and urea4 are distinctly different from those for urea1 and urea5 (which are hydrogen bonded to the crowns). The mean EFs experienced by the urea molecules (from the vector average over the eight nuclei) fall into two distinct categories: the mean field for urea1 and urea5 of 17.7 GV m–1 is greater than the mean for the other three molecules, 10.1 GV m–1 (Table 2).40 Even in the absence of experimental error estimates we believe this large and systematic difference is real, and reliably reflects the difference between the hydrogen bonding environment of the UIC network and the stronger host-guest interaction experienced by the two molecules forming hydrogen bond bridges across the 18C6 rings. The contour maps of the ESP in Figure 4 also include red arrows to indicate the strength and direction of the projection in the mapping plane of the EF at the nuclei of each urea molecule, as well as a blue arrow indicating the magnitude and direction of the molecular dipole moment. The EF is not depicted directly, but as the negative gradient of the ESP its field lines are perpendicular to the contours on these maps. In this manner the electric field direction and magnitude can be inferred from Figure 4 by the separation between contours and their number over the extent of each urea molecule. Note that the EF points from positive ESP (red) to negative ESP (blue) in Figure 4, and we are using the dipole moment convention that is consistent with fundamental electrostatics but at odds with conventional chemistry texts41 [i.e., the dipole moment vector for urea points from oxygen (d–) to carbon (d+)]. For urea2, urea3 and urea4 all N–H bonds are oriented towards identifiable local (negative) ESP minima in the mapped planes, with the C=O bonds oriented towards localized regions of positive ESP. The situation is clearly different for urea1 and urea5, where the molecules lie between two quite broad regions of significantly greater positive (red) and negative (blue) ESP. Standard deviations of 2.4 to 4.0 GV m–1, derived from the range of EFs across each molecule (Table 2), indicate that the EF across each urea molecule is not homogeneous, and the EF vectors at the nuclei (red arrows in Figure 4) give some insight into how different nuclei experience quite different EFs, in both magnitude and direction. As a major effect of the EF upon molecules is the perturbation and polarization of their electron density distribution, we also investigated the variations in the electron density for the chemical bonds of different urea molecules. Bader’s quantum theory of atoms in molecules42 (QTAM) has been widely used to characterize the nature of chemical bonds and intermolecular interactions on the basis of experimental electron distributions.43 In the present study these quantities highlight the close similarity of the electron distributions for the five urea molecules. The electron density topological parameters at the bond critical points (bcps) of the same bond types in different urea molecules vary slightly and reveal significant distance-dependent trends. Table S4 summarizes geometric data, the electron density at the bcp, rbcp, and its Laplacian, ∇2rbcp, for all covalent bcps in 18C6:5U along with estimated standard deviations (esds) derived from experiment, and scatter plots for each of the six bond types are given in Figures S7 and S8. Figure S9 condenses that data into

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scatter plots for each of rbcp and ∇2rbcp and Table S3 summarizes a linear regression analysis of the distributions of rbcp and ∇2rbcp for each of the different bond types, as well as the mean values of experimental esds. The large number of bonds of each type, combined with neutron-derived H atom positions, yield valuable insight into the quality and reproducibility of intra- and intermolecular bond critical point properties derived from the experimental electron density. As the deviations in rbcp and ∇2rbcp over the five urea molecules are comparable to the mean values of experimental esds, it is not possible to draw direct correlations between the EFs experienced by individual molecules and their electron density topological parameters. Urea dipole moments and their relationship with the surrounding electric field. We have had a long-standing interest in dipole moment enhancement for molecules in crystals.44 Table 2 summarizes experimental molecular dipole moments and the magnitude and direction of the mean EF experienced by each urea molecule in 18C6:5U, derived from the model charge distribution. The dipole moments have been obtained in the usual way from the atomic net charges and dipoles for each molecule, derived from the experimental electron density. The esds indicated for the dipole moment magnitudes are based on propagation of errors from esds of monopole and dipole multipole populations, and are likely to slightly underestimate more rigorous values that would be derived from a full covariance matrix. To estimate the enhancement of urea dipole moments from experiment we use as a benchmark the experimental gas phase result from the microwave Stark effect, 3.83(4) D,45 in preference to the value of 4.56 D obtained for urea in dilute dioxane solution.46 Urea is known to be non-planar in the gas phase,47 and calculated dipole moments at the CCSD(T)/aug-cc-pVQZ level48 are 4.58 D for a planar C2v geometry, falling to 3.87 D for the C2 geometry observed in the gas phase. The present zero-field MP2/aug-ccpVDZ calculation yields a non-planar C2 optimized geometry (albeit with greater pyramidalization at the nitrogen atoms than observed in 18C6:5U), and a dipole moment of 3.57 D (Table 2). Table 2 also summarizes dipole moments computed for molecules subjected to experimentally observed electric fields (obtained at optimized geometries), and the enhancement relative to the zero-field result at the same level of theory. The experimental urea dipole moments are all aligned strongly with the mean EF experienced by the molecules; the angle between the two vectors lies between 10° and 19° (Table 2). Although this is unsurprising from basic electrostatics, we believe this is the first direct experimental demonstration of this relatively simple principle in molecular crystals.49 The urea dipole moments are even more closely aligned with the molecular C→O vectors, the approximate symmetry axis of the molecules; the angle between the two vectors lies in the narrow range of 2.7° to 4.3°. Although the average observed dipole moment for the two ureas bound to crowns is greater than for those forming the hydrogenbonded urea network, the difference between the two is not significant (6.74(40) D and 6.43(43) D, respectively; the estimated uncertainties derive from the sample variances). The mean dipole moment of 6.55(40) D for all five ureas in 18C6:5U agrees with the corresponding experimental value of 6.2(5) D obtained for crystalline urea.50 The present experimental estimates of dipole moment enhancement vary between 2.2(2) D and 3.2(2) D for the five ureas, with no clear correlation with the mean electric field they experi-


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Figure 3. Contour maps of the magnitude of the electric field (EF) in the plane of the urea molecules in 18C6:5U. Legend at bottom right has units of e Å–2, and contour intervals are 0.02 e Å–2 (0.02 e Å–2 = 2.88 GV m–1). The color scale ranges from red (large EF) to blue (small EF); the large red areas are due to the closest atoms in neighboring molecules.

Figure 4. Contour maps of the electrostatic potential (ESP) in the plane of the urea molecules in 18C6:5U. Legend at bottom right has units of e Å–1, and contour intervals are 0.02 e Å–1 (0.02 e Å–1 = 0.288 V). The color scale ranges from red (electropositive region) through green (near zero ESP) to blue (electronegative region). Red arrows depict the magnitude and direction of the electric field at each nucleus, and the blue arrow indicates the magnitude and direction of the molecular dipole moment. The large red areas are due to the closest atoms in neighboring molecules.



Table 2. Molecular dipole moments, magnitude and direction of the average electric field experienced by each urea molecule in 18C6:5U.a urea1

urea2

urea3

urea4

urea5

6.45(21)

6.37(18)

6.88(17)

6.03(17)

7.02(20)

angle between µ and C→O vector

177.3

176.1

177.1

177.0

175.7

b

16.5

10.1

10.6

9.7

18.8

s() c

2.7

4.0

3.0

2.9

2.4

angle between F and µ

4.2

16.5

10.1

12.2

7.2

enhancement relative to gas phase, D|µ|expt d

2.62(25)

2.54(22)

3.05(21)

2.20(21)

3.19(24)

zero-field |µ|

3.57

3.57

3.57

3.57

3.57

|µ| with applied field

8.13

6.62

6.84

6.58

8.64

enhancement relative to zerofield, D|µ|theor

4.56

3.05

3.27

3.01

5.07

Experiment |µ|

Theory

a

All dipole moments are in D, angles in degrees and electric fields in GV m–1. ‘Experiment’ results are computed directly from the experimental electron density; ‘Theory’ results from MP2/aug-cc-pVDZ calculations at geometries optimized with experimental EFs applied. b

is the mean electric field experienced by each urea molecule, estimated as a vector average of the fields determined at the eight nuclei. c

Standard deviation of the distribution of electric fields at the eight nuclei of each urea molecule, from the mean value, .

d

Dipole moment enhancement relative to value of 3.83(4) D in the gas phase.45

ence (although the largest enhancement is found for urea5, which experiences the greatest EF, and the smallest enhancement for urea4, which experiences the smallest EF). As expected from the two different categories of EFs, computed dipole moments obtained by applying the experimentally-derived EF (magnitude and direction) to each urea molecule result in two distinctly different sets of results: an average value of 8.39 D is computed for urea1 and urea5, compared with an average of 6.68 D for the other three ureas. These results imply mean computed enhancements of 4.82 D and 3.11 D, respectively, for the two sets. The latter value is in line with the present mean experimental dipole enhancement for all five ureas, 2.7(4) D, but it is evident that the observed enhancements for urea1 and urea5 are less, by amounts that exceed several esds, than those anticipated from a straightforward polarization due to stronger mean EFs in Table 2. It is important to recognize that the comparison between experiment and theory pursued here involves many simplifications and assumptions. The application of a uniform EF ignores the fact that the urea molecules clearly experience directional interactions in the crystal as noted earlier (Figure 3) – not just a simple applied electric field; inhomogeneity and electric field gradient terms are likely to be important, but they have been neglected in these calculations.

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Comparison of the observed electric fields with other experiments. The EFs measured across the urea molecules in 18C6:5U provide an important point of reference for related experimental and computational studies that include emphasis on the magnitude of the EF experienced by molecules in bulk matter, and its effect on molecular properties and chemical reactions, especially with respect to enzyme activity and electric-field-assisted reactions. The average EF magnitudes in Table 2 (10 – 19 GV m–1) are comparable with values of 11.9 ± 0.4 to 14.4 ± 0.6 GV m–1 reported by Boxer and co-workers for the EF exerted on a probe C=O moiety in the active site of KSI and several of its mutants, using vibrational Stark spectroscopy.4b,c They also provide an extremely useful context for other experimental measurements obtained using the VSE. Similar large EFs have been reported for the active sites in wild-type 4-chlorobenzoylCo-A dehalogenase (11.5 GV m–1) and serine proteases (6.6 and 8.7 GV m–1),7 while smaller EFs of 1.0 GV m–1 were obtained for the Xe4 cavity in a myoglobin mutant,3b and 1.9 GV m–1 in ribonuclease S.2a,8 EF strengths in the range 2 – 7 GV m–1 have also been measured at the CO molecule adsorbed in metal-exchanged ZSM-5 zeolites using the VSE.13 Using a series of nitrile-modified KSI variants the inhomogeneity of the EF in the active site of KSI has been estimated to be 0.8 ± 0.4 GV m–1.4a EFs obtained from VSE measurements at metal-monolayer interfaces are reported to be relatively weak, and in the range 0.1 – 1.0 GV m–1.14b,c Recent computational studies have yielded varying estimates of the EF in the active site of KSI : 15.2 ± 0.4 GV m–1 for a KSI analogue,11a and 16.0 to 22.5 GV m–1 for various steps in the reaction path.11b Computational studies have shown that ‘moderate’ external EFs, appropriately oriented, can affect the outcome of non-redox chemical reactions by stabilizing (or de-stabilizing) transition states, and significantly changing reaction barriers. These studies typically apply oriented EFs up to 0.0125 au (6.4 GV m–1) in positive and negative orientations.17b,51 This was recently demonstrated in a single-molecule experiment for a Diels-Alder reaction, using the STM breakjunction technique, which showed that acceleration of the reaction is dependent on the strength and polarity of an applied EF.16b We estimate the EF strength in that experiment to be ~0.8 GV m–1 (from Figure 2 in that work the maximum applied potential difference was 0.75 V over ~1 nm – the extent of the product molecule between the STM tip and metal surface). Our earlier charge density studies on hydroquinone clathrates mapped the ESP and EF in the cage of the apohost and its clathrate with acetonitrile.32 In those studies the EF in the cage was found to be as much as 2.7 GV m–1 in the apohost, almost doubling to 5.2 GV m–1 in the acetonitrile clathrate, a result that indicated polarization of the host by the polar guest molecule. The EFs in Table 2 are also entirely consistent with our earlier estimates of the EF experienced by molecules in organic molecular crystals, using a self-consistent dipole lattice sum approach.44e EF magnitudes obtained in that work are in the range 0.8 to 15.9 GV m–1, with the magnitude depending on both the molecular dipole moments and their arrangement in the crystal. It is useful to contrast EF strengths of this magnitude inside molecular crystals (i.e. 109 – 1010 V m–1) with the EF strength that can be applied to bulk materials in a laboratory. The resistance of bulk materials to an applied electric field is measured by their dielectric strength or breakdown field, the maximum electric field that can be applied before electric breakdown. Actual measurements depend on sample thickness, defects and impurities, field inhomogeneity and


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temperature, but representative values for thin films range from 2 ´ 107 V m–1 for sodium tartrate tetrahydrate52 and 4 ´ 107 V m–1 for barium titanate,53 up to ~109 V m–1 for mica54 and diamond.55 The upper limit of the EF that can be applied to a crystal is estimated to be only ~107 V m–1 before electric breakdown occurs,56 and piezoelectric constants have been quantitatively measured for a 0.59 mm thick crystal of Li2SO4.H2O from the change in X-ray amplitudes in an applied electric field of ~5 ´ 106 V m–1.57

CONCLUSIONS We have described in this work one of the most ambitious experimental charge density studies on a co-crystal undertaken to date. Measurement of extremely high-quality synchrotron and neutron single crystal diffraction data at 30 K has afforded detailed information on the crystal structure, the geometries of all seven unique molecules in the unit cell, and the closest intermolecular interactions between them. In particular, the neutron diffraction data gave important insight into the pyramidalization of the urea nitrogen atoms, and its correlation with hydrogen atoms oriented towards nearby oxygen acceptor atoms. These structural details have also highlighted the relationship between 18C6:5U and urea inclusion compounds more generally. The neutron experiment was also vital in providing independent position and thermal parameters for the 44 unique hydrogen atoms in this structure, which in turn facilitated construction of a detailed and high-quality model of the molecular electron distributions in the crystal from multipole modeling of the synchrotron data. Although the 18C6:5U crystal includes common covalent and noncovalent interactions, the very large number of examples of different interactions, and the range of outcomes from the topological analysis of the experimental electron distribution, has yielded important insight into the reliability of error estimates computed from the inverse least-squares covariance matrix, especially for the Laplacian at bond critical points. Based on the experimental electron density, molecular dipole moments and EFs experienced by the urea molecules reveal important information on dipole moment enhancement as a consequence of the local EF, and especially the close alignment of molecular dipoles with the EF direction across each of the ureas. Perhaps the most important – and robust – outcome of this work is the very clear demonstration that this combination of high-quality single-crystal diffraction experiments, and relatively standard modeling techniques, can yield accurate, quantitative, three-dimensional information on the ESP and EF experienced by molecules in molecular crystals. Mapping these properties across a cavity formed by a cluster of molecules surrounding the molecule of interest represents a useful model for the binding site of a protein. EF strengths measured in this way for the five urea molecules in 18C6:5U are in accord with the VSE measurements of Boxer et al. in the active sites of various enzymes. Although the 2014 report on KSI referred to 14.4 GV m–1 as an “extreme electric field”, the present work suggests that fields of this magnitude are neither extreme, nor unusual, in organized matter.

EXPERIMENTAL METHODS Synthesis. Colorless single-crystals of 18C6:5U are readily obtained from various choices of solvents; suitably-sized block crystals were grown from slow evaporation by stoichiometrically mixing 18C6 in ethyl acetate with 5 equivalents of urea in ethanol.

Single crystal synchrotron diffraction. The weak diffracting power of the crystals at 100 K limited investigation with our in-house X-ray diffractometer, which is not equipped with a low-temperature cryostat or an X-ray micro-source. Excellent high-resolution diffraction data was subsequently measured using synchrotron radiation at beamline BL02B1, SPring-8 in Japan. Synchrotron X-ray data were collected to a resolution of 0.35 Å at 30 K using a wavelength of 0.24783 Å. The BL02B1 beamline is equipped with a Rigaku kappa diffractometer and a cylindrical image-plate detector. Integration of all Bragg reflections, Lorentz–polarization corrections and scaling of the frames were carried out using the on-site software RAPIDAUTO.58 Due to the weak intensity of the reflections in the resolution range 0.35 to 0.40 Å, the final dataset was re-integrated to a maximum resolution of 0.40 Å ((sinq/l)max = 1.25 Å–1). An empirical absorption correction, sorting and merging were carried out using SORTAV,59 and the structure was solved and refined applying the independent-atom model (IAM) using the SHELX suite60 in Olex2.61 Single crystal neutron diffraction. The neutron diffraction experiment was performed at the OPAL Research Reactor of the Australian Nuclear Science and Technology Organization using the singlecrystal quasi-Laue diffractometer (KOALA). After several attempts at flash cooling the crystals to 50 K resulted in crystal cracking, a block-sized single crystal was folded in a thin aluminum foil in order to maximize the contact surface area and minimize the thermal shock effect, and mounted on the φ axis of the Laue diffractometer. The crystal in aluminum foil was flash cooled by means of a CF-2 cryofurnance to 50 K and then slowly cooled to 30 K. 13 images were collected at the first orientation with an exposure time of 5000s, separated by sequential φ rotations of 14°. The orientation was then adjusted manually and 28 images were collected at the new orientation with the same exposure time and increments of 7° about φ. The 41 images yielded 11494 unique reflections62 for structure refinement,63 using cell constants from the synchrotron experiment. Crystallographic details and refinement results using synchrotron and neutron data are summarized in Table S1. Multipole refinement. Two multipole models were refined against the synchrotron data using the Hansen-Coppens formalism64 in XD2016.65 One is based on the current charge density model of choice when neutron data is unavailable (MM-SHADE) and the other incorporates hydrogen atom positions and anisotropic displacement parameters (ADPs) from the neutron structure refinement (MM-NEUTRON). Although the refinement statistics and residual density maps are very similar for these two models (see Table S1 and Figure S3), the hydrogen atom positions and unscaled ADPs from the neutron experiment provide a better fit to the X-ray diffraction data. (Comparison between X-ray and neutron ADPs66 for the 36 heavy atoms in 18C6:5U showed a mean absolute difference of 0.00095(106) Å2, and a mean ratio of diagonal terms, Uii(synchrotron)/Uii(neutron) = 1.04(8). These values are comparable with those for other high-quality combined X-ray and neutron studies,67 and serve as an important indicator of the high accuracy of both of the present diffraction experiments.68) All results presented and discussed in this work derive from the MM-NEUTRON experimental electron distribution. For the MM-NEUTRON model the scale factor, atomic positions and anisotropic displacement parameters (ADPs) of non-hydrogen atoms were initially refined against high angle synchrotron data (sinq/l > 0.7 Å–1). Hydrogen atom positions and ADPs from the neutron structure refinement were then incorporated with no



further corrections and kept fixed throughout the refinement. Charge neutrality constraints were employed for each of the seven molecular fragments, but no local symmetry constraints were imposed on multipole populations. Core and valence monopole scattering factors were from Hartree-Fock wavefunctions,69 and single exponential functions described the radial part of higher multipoles. The multipole expansion for non-hydrogen atoms extended to the hexadecapole level, while that for hydrogen atoms was limited to the quadrupole level. κ and κ’ parameters were refined for non-hydrogen atoms, and a fixed κ value of 1.2 used for H atoms. In order to estimate standard deviations for molecular dipole moments, a final refinement cycle was performed using a global coordinate system, adjusting only the multipole populations. For the MM-NEUTRON model a normal probability plot and a plot of the distribution of scale factors vs data resolution are shown in Figure S1, and a fractal dimension plot70 in Figure S2. The MM-SHADE model employed a similar multipole expansion, but with N–H and C–H bond distances fixed to literature neutron values obtained for 18C6:(cyanamide)271 and urea,39 and hydrogen atom ADPs were estimated using SHADE3.72 Residual electron density maps for both MMNEUTRON and MM-SHADE models are compared in Figure S3. Theoretical calculations. Intermolecular interaction energies between neighboring molecular pairs in 18C6:5U and U:HEX, were calculated using an efficient energy estimation procedure designed to obtain accurate model energies for intermolecular interactions in molecular crystals.38 These CE-B3LYP energies use electron densities of unperturbed monomers to estimate electrostatic, polarisation, and repulsion energies, which are combined with Grimme’s D2 dispersion corrections,73 with the separate energy components fitted to B3LYP-D2/6-31G(d,p) counterpoise-corrected energies for molecule/ion pairs extracted from a large number of crystal structures. The mean absolute deviation (MAD) of these CE-B3LYP model pairwise energies from the DFT benchmark values is 2.4 kJ mol−1 for energies of molecule/ion pairs that span a range of 3.75 MJ mol−1.38a Fixed neutron geometries were used to determine CEB3LYP interaction energies, but MP2/aug-cc-pVDZ calculations of urea dipole moment enhancements were based on optimized geometries. CrystalExplorer1774 was used to compute CE-B3LYP energies, and Gaussian0975 for all calculations on isolated molecules (including the B3LYP/6-31G(d,p) monomer wavefunctions in the CEB3LYP model).

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Crystallographic and refinement details; normal probability and fractal dimension plots; residual electron density maps; static deformation density maps. Discussions of the relationship between 18C6:5U and urea inclusion compounds (UICs), the conformation of the crown molecules and the pyramidalization of the urea nitrogens. CE-B3LYP energy decomposition for unique nearest neighbor interactions. Topological properties at bond critical points for the covalent bonds and noncovalent interactions; scatter plots of electron density and its Laplacian at bcps for covalent bonds and noncovalent interactions. (PDF)

AUTHOR INFORMATION Corresponding Author * [email protected]

Page 8 of 12

Present Address # V.R.H.: Department of Physics, Goa University, Goa 403206, India

Notes † Deceased.

ACKNOWLEDGMENTS This work has been supported by the Australian Research Council (DP130103304) and the Danish National Research Foundation (Center for Materials Crystallography, DNRF-93).

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Measurement of Electric Fields Experienced by Urea Guest Molecules

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