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Polarizability of acetanilide and RDX in the crystal: effect of molecular geometry
Chemical Physics 305 (2004) 317–323 www.elsevier.com/locate/chemphys
Polarizability of acetanilide and RDX in the crystal: effect of molecular geometry D. Tsiaousis, R.W. Munn *, P.J. Smith, P.L.A. Popelier Department of Chemistry, UMIST, Sackville Street, Manchester M60 1QD, UK Received 7 April 2004; accepted 13 July 2004 Available online 3 August 2004
Abstract Density-functional theory with the B3LYP functional at the 6-311++G** level is used to calculate the dipole moment and the static polarizability for acetanilide and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) in their in-crystal structures. For acetanilide the dipole moment is 212% larger than for the gas-phase structure and for RDX (where there is a gross geometry change) it is 15% larger. The polarizability for the in-crystal structure is smaller than for the gas-phase structure by 3% for both species, whereas the incrystal effective optical polarizability is larger than the gas-phase static polarizability for both crystals. Hence, effects in addition to the molecular geometry change in the crystal must be considered in order to interpret the effective polarizability completely. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Acetanilide; RDX; Dipole moment; Polarizability; Crystal
1. Introduction Molecular crystal properties arise from the molecular properties, the molecular arrangement, and the molecular interactions. Hence, a proper understanding of molecular crystal properties relies in particular on knowing the molecular properties, which must be evaluated as ‘‘effective’’ properties appropriate to the crystal environment. One can then recognize a number of environmental effects that modify the properties of the ‘‘in-crystal’’ molecule from those of the free gas-phase molecule [1]. Perhaps most obvious of these is the different molecular geometry in the crystal. Nevertheless, this effect seems to have received comparatively little recognition or systematic study, so that molecular properties used for crystals have often been calculated for the gas-phase molecule geometry. There *
Corresponding author. Tel.: +44 161 200 4534; fax: +44 161 200 4584. E-mail address: [email protected] (R.W. Munn). 0301-0104/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.07.013
are exceptions, including work on phosphorobenzopyrene derivatives where the molecular geometry changes qualitatively between the gas phase and the crystal [2] and on 5-nitrouracil in two polymorphic forms [3]. There have also been attempts to calculate molecular structures in the crystal fields of surrounding molecules. However, the available studies [4,5] have tended to concentrate on the dipole moment, characteristic of the equilibrium electron density, rather than on the polarizability, characteristic of the response of the electron density to an external perturbation. We undertake here the simpler task of exploring what the properties of molecules are, given their structure in the crystal phase, with particular reference to the polarizability. Our interest in these general issues arises from work [6] on the energetics of charged states in the crystals of acetanilide (C6H5NHCOCH3, N-phenylacetamide: Fig. 1) and RDX (1,3,5-trinitro-1,3,5-triazacyclohexane or cyclotrimethylene trinitramine: Fig. 2). A link between the crystals is that acetanilide is one of the few molecular crystals for which the mechanism of optical damage has
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Fig. 1. Molecular structure of acetanilide. (a) In-crystal structure [16] and atomic numbering scheme; hydrogens not labelled. (Graphical display generated with the Materials VisualizerÔ from Accelrys Inc.) (b) Molecular skeleton in the energy-minimized gas-phase structure (black) and in the observed in-crystal structure (grey).
been reported in any detail [7], while RDX is well known as a detonator [8], and it has been remarked that the extreme conditions of optical damage in chemical materials simulate the initiation of detonation in solid explosives [9]. The processes of optical damage and the initiation of detonation in the two crystals therefore have some conceptual similarities, and we are exploring mechanisms for both based on the trapping of charged states near vacancies [6,10]. Our calculations require effective dipole moments and polarizabilities in the crystals. The polarizabilities can be obtained by analysing measured crystal refractive indices or the dielectric tensor [11], but we have to derive the dipole moments of the individual molecules from theoretical calculations. Analysis of high-precision electron densities derived from diffraction measurements can give in-crystal dipole moments [3,12], but these are total moments including contributions induced by the electric field of the surrounding dipoles through the molecular effective polarizability. Elsewhere, we calculate these induced contributions from the interactions between molecules that have the permanent dipole moment of an isolated molecule with the in-crystal geometry [10,13]. Similarly, cluster calculations [14] also give the total in-crystal dipole moment. Here, we present calculations of the dipole moments and polarizabilities of acetanilide and RDX in both the gas-phase and the in-crystal geometries, in order to explore the effect of the geometry changes while generating
Fig. 2. Molecular structure of RDX. (a) In-crystal structure [29] and atomic numbering scheme; hydrogens not labelled. (Graphical display generated with the Materials VisualizerÔ from Accelrys Inc.) (b) Molecular skeleton in the gas-phase structure obtained from electron diffraction [30] (black) and in the in-crystal structure (grey).
the necessary inputs for our work on the energetics of charged states. We find that for both systems the static polarizability for the in-crystal geometry aC is smaller than the gas-phase polarizability aG, whereas the observed effective optical polarizability in the crystal environment aE is larger than aG. Hence, the enhancement required to give aE is larger than might have been suspected, because it has to overcome the reduction from aG to aC in addition to accounting for the increase from aG to aE. The mechanism for such an enhancement is explored elsewhere in work on the C60 crystal [15], where the geometry issue is not significant and there is direct experimental evidence for the enhancement.
2. Acetanilide 2.1. Structure The acetanilide crystal has attracted attention because the molecule contains the peptide linkage
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–CONH– and takes part in an extended hydrogenbonded network in the crystal. As such, the crystal has features that make it a plausible model for biological systems. The crystal lacks a centre of symmetry, although there appear to have been no proposals to exploit the resulting quadratic non-linear optical behaviour. However, acetanilide differs from most organic crystals with non-linear optical potential because it has been the subject of rather detailed investigation of the mechanism of optical damage [7], which is an important limitation for practical applications in nonlinear optics. We take the in-crystal molecular structure from single-crystal neutron diffraction measurements [16]. The molecule is found to adopt the amide form rather than its imidol tautomer; the phenyl ring deviates significantly from C2v symmetry, with the carbon atoms adopting the boat conformation B14 . There appears to be no suitable molecular structure available for the gas phase, but the conformations and relative stabilities of acetanilide in the vapour phase have been determined from vibrationally resolved electronic spectra obtained by resonant two-photon ionization in a supersonic jet expansion [17]. These experiments show that the molecule exists as the trans geometrical isomer, having the phenyl ring oriented anti to the methyl group, the same as found in the crystal. We have therefore used the crystal-phase structure as the starting point for full geometry optimization to obtain the gas-phase structure, within the same theoretical approach that we use to calculate the molecular properties, namely using density functional theory with the B3LYP hybrid functional [18–20] at the 6-311++G** level within the Gaussian 98 software package [21]. This approach should take sufficient account of correlation to yield a realistic geometry and properties. The molecular skeletons in the gas-phase and in-crystal structures are shown superimposed in Fig. 1, which shows relatively modest changes. The most noticeable change in the crystal is a twisting seen most clearly in the methyl group but actually involving a rather pronounced twist about the bond connecting the acetamido substituent to the phenyl ring. This presumably serves to relieve some of the steric repulsion between the acetamido group and the hydrogen atom nearest it on the benzene ring [22]. Acetanilide lacks molecular symmetry in either phase, but in order to compare detailed results in the two phases we need to define molecular axes that should be comparable in both. For this purpose we adopt the atomic numbering scheme used in reporting the crystal structure [16] (see Fig. 1). We define the long L-axis to coincide with the vector from the carbon atom C4 to the carbon atom C1 that carries the acetamido substituent in the para position to it; the normal N-axis to be perpendicular to the L-axis and the vector from the car-
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bon atom C3 to carbon atom C5 (both meta to C1), so that the axis is roughly normal to the mean plane of the ring; and the medium M-axis to be perpendicular to L and N. 2.2. Dipole moment Our results are given in Table 1. The change in structure in the crystal induces a significant component of the dipole moment out of the LM plane, but the M component falls slightly and as a result the magnitude changes rather little. Our values lie among those reported from numerous measurements, mostly in benzene solution, as shown in the Table. Values measured in dioxane solution are mostly significantly higher, presumably because of the effect of the polar solvent, and are not shown. 2.3. Polarizability Our results are given in Table 2. The pattern of changes from the gas phase to the crystal structure differs from those in the dipole moment. The changes are fairly small, but in each case the polarizability is reduced in the crystal structure, by 412% for the LL component and over 3% in the MM component, but essentially zero in the NN component, so that the mean polarizability decreases by something over 3%. The value calculated for the crystal structure can be compared with the effective polarizability in the crystal environment calculated [10] from the crystal refractive indices, which is thus the optical rather than the static polarizability. There is considerable enhancement over the static polarizability for the in-crystal structure, to the extent that aE exceeds aG by 412% even though aG exceeds aC by 3%. This is attributable mainly to the 30% enhancement in the NN component, since the LL components are much the same and the MM component is actually the smallest of those reported here, at some 5% smaller than in the gas-phase molecule. For comparison, calculations using bond and group polarizabilities [23] gave a mean polarizability that corre˚ 3. sponds to 15.3 A
Table 1 Dipole moments for acetanilide; all values in D Source
Phase
lL
lM
Present calculations Present calculations Experiment
Gas
0.717
3.455
0.018
3.529
Crystal
0.784
3.397
0.974
3.620
Experiment
Benzene solution CCl4 solution
lN
l
3.41–4.01 3.5 [22]
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Table 2 ˚3 Polarizability components aAB and mean polarizabilities for acetanilide in different phases; all values in A Type of polarizability aG: gas aC: crystal aE: effective
Mean ð13Tr aÞ
AB LL
LM
LN
MM
MN
NN
22.09 21.14 22.23
1.31 1.05 2.24
0.01 0.74 0.55
16.33 15.80 15.55
0.01 0.62 0.58
9.21 9.17 12.04
3. RDX 3.1. Structure RDX is an energetic material used as a secondary explosive or detonator. It owes its sensitivity to the N– NO2 bonds [24], which are strongly polar and appear to be highly sensitive to the molecular environment [25,26]. There are suggestions that the physical state of an explosive affects its pyrotechnic sensitivity [25,27], so that studies of the properties of the molecule in different phases are of direct practical importance. RDX crystallizes in a, b, and c polymorphic forms [28], the first being stable at room temperature [29]. In the a-form crystal, the molecule adopts a chair conformation, with two of the NO2 groups occupying axial (A) positions and one occupying a pseudo-equatorial (E) position (the AAE conformer, site symmetry C1); there is an approximate mirror plane passing through the latter group, which makes the other two nearly equivalent (pseudo-Cs symmetry, see Fig. 2). On the other hand, electron diffraction indicates that the gasphase RDX molecule adopts the AAA conformer of the chair structure with C3 symmetry [30,31]. Questions remain as to whether this is the equilibrium structure or a time average over different conformers [32–36], but we adopt it here for studying the effect of the change of structure from the gas phase to the crystal. In the a polymorph the crystal forces cause a significant qualitative change from this molecular structure [37]. The molecular skeletons in the gas-phase and in-crystal structures are shown superimposed in Fig. 2. It can be seen that the change in conformation in the crystal is accompanied by a bending of the ring into a more upright chair, consistent with the picture that in the crystal a somewhat strained structure is stabilized by the crystal forces. The deviation of the ring from planarity can be described by a single angle h = 33.9° in the gas phase but in the crystal by angles h1 = 53.3° and h2 = 43.7° at the opposite ends of the chair [35]. The more flattened chair in gaseous RDX agrees with the hypothesis that the strain on the molecule is relieved upon vaporization [33]. The inequivalence of the nitro groups in the crystal also allows them to twist by different amounts about the N–N axes, whereas in the gas phase they all rotate to the same extent (u = 19.1°), giving rise to the C3 symmetry
15.88 15.37 16.61
deduced from the electron diffraction measurements [30]. As for acetanilide, to compare detailed results in the gas and (a-form) crystal phases we need to define a set of molecular axes that should be comparable in either phase. This is obviously complicated by the different conformers. In the gas-phase molecule, the threefold axis is one natural choice, and then we can choose the other pair of axes perpendicular to it. In the crystal, we make use of the approximate mirror plane running through the pseudo-equatorial NO2 group. We adopt the atomic numbering scheme used in reporting the crystal structure [29] (see Fig. 2), where this group contains nitrogen N1, and choose an auxiliary point Y midway between the other two nitro group nitrogens (N2 and N3). Then we define the long L-axis parallel to the vector Y–N1; the normal N-axis perpendicular to the L-axis and the vector N3–N2 (and hence roughly normal to some mean plane of the ring); and the medium M-axis perpendicular to L and N. Thus, in the gas-phase molecule the N-axis is the threefold symmetry axis, which we use explicitly in defining the molecular structure for our calculations (see [38]). 3.2. Dipole moment Our results are given in Table 3. The change in structure in the crystal increases the magnitude of the dipole moment in the normal direction while also inducing components perpendicular to this direction, as expected by the lowering of symmetry. As a result, the magnitude of the dipole moment increases by over 15%. Measurements of the dipole moment of RDX are scarce, but the values measured in a range of solvents [39] bracket our calculated values. Values measured in dioxane solution are significantly smaller.
Table 3 Dipole moments for RDX; all values in D Source
Phase
Present calculations Present calculations Experiment
Gas Crystal Various solutions
lL
lM
0
0
1.930
0.163
lN
l
6.404
6.404
7.147
7.405 6.0–7.5 [39]
D. Tsiaousis et al. / Chemical Physics 305 (2004) 317–323
At first sight our results appear counter-intuitive. The dipole moments of the axial nitro groups in the gasphase molecule all contribute equally to the total moment by symmetry, and therefore it might seem that changing one group to equatorial would reduce the total rather than increasing it. We have therefore explored how far this effect can be reproduced in a pure bond-dipole model, as follows. From the calculated total dipole moment in the gas-phase molecule and the angle between the N–NO2 bond and the threefold axis, we deduce a bond dipole of 3.11 D parallel to the N–NO2 bond. We then take this value and apply it unchanged to calculate the total dipole moment for the in-crystal molecular structure, which we find to be 6.69 D, some 412% larger than the value calculated directly. In fact, the ‘‘intuitive’’ argument is misleading in this case, because the outcome depends critically on the angle between the N–NO2 bond and the threefold axis. For example, if the three N–NO2 bonds in the gas-phase molecule were coplanar, their bond dipoles would cancel by symmetry, and then any deviation from planarity in the crystal would necessarily change the total moment to a larger value. However, comparison of the structures in Fig. 2 suggests that the geometry changes in the crystal increase the contributions of the axial N–NO2 groups by more than they decrease that of the equatorial one. 3.3. Polarizability Our results are given in Table 4. For the gas-phase molecule, the polarizability anisotropy aNN < aMM = aLL is consistent with the negative Kerr coefficient measured for RDX in dioxane solution [40]. In the crystal, the LL component increases slightly, consistent with the greater spatial extension along this direction towards the pseudo-equatorial nitro group. At the same time, the MM component decreases by over 10%, with the NN component little changed, with the result that the mean value decreases by a little over 3%. In the effective polarizability there is a 10% average enhancement over the polarizability for the in-crystal structure: a 5% increase in the LL component, a 1212% increase in the MM component, and a 13% increase in the NN component. As a result, aE exceeds aG by 6%. For comparison, an additiv˚ 3 for the ity scheme gave a mean polarizability of 15 A gas-phase molecule [41]; ab initio calculations gave ˚ 3 for a geometry-optimized AAE structure [42]; 12.3 A
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˚ 3 deduced from the and a group polarizability of 5.5 A Clausius–Mossotti equation for the crystal assuming that only the N–NO2 group is responsible for the polar˚3 izability gave a mean molecular polarizability of 16.5 A [24]. The values of the polarizability anisotropy c deduced ˚3 from the present calculations are 4.55, 3.88 and 3.30 A for the gas-phase, crystal-phase and effective polarizabilities, respectively, so that the crystal environment decreases the anisotropy. The anisotropy deduced from the depolarization of Rayleigh scattering in different solvents has been quoted [39] as c2 35, whence c is some ˚ 3; this is larger than our calculated anisotropies, 6.0 A but refers to RDX in solution, where polarographic studies indicate that all nitro groups are inequivalent [43].
4. Discussion and conclusions We have calculated the changes in molecular dipole moment and polarizability between gas-phase and incrystal structures of acetanilide and RDX. In each case, what we have taken as the gas-phase structure cannot be considered as definitive, for acetanilide because we have obtained it theoretically and for RDX because there is continuing discussion over the role of conformers in the gas phase other than the one we have taken, though it was derived to fit experimental measurements. On the other hand, in each case the in-crystal structure, which is our primary concern, can be regarded as established experimentally. We have used the same method of calculation for each pair of structures, and hence our results should provide at least a good semi-quantitative representation of how the geometry change affects the dipole moment and polarizability. The calculated changes are noticeable but quite small in acetanilide (212% or 0.1 D increase in the dipole moment and 3% decrease in the polarizability), and even in the case of RDX where there is a gross change in geometry between the two structures, the changes are not as large as might have been expected (15% or 1 D increase in the dipole moment and 3% decrease in the polarizability). In both cases the dipole moment increases and the polarizability decreases. Hence, as the molecule becomes more polar it becomes less polarizable. Comparable conclusions emerge from other
Table 4 ˚3 Polarizability components aAB and mean polarizabilities for RDX in different phases; all values in A Type of polarizability G
a : gas aC: crystal aE: effective
Mean ð13Tr aÞ
AB LL
LM
LN
MM
MN
NN
17.70 17.83 18.77
0 0.04 0.01
0 0.71 0.90
17.70 15.71 17.68
0 0.01 0.42
13.15 13.35 15.08
16.18 15.63 17.18
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work – for the constituent molecules in the water dimer [44], for molecules in an environment of discrete solvent molecules studied by direct reaction-field calculations [45], and for three squaric acid conformers [46]. A decrease in polarizability is also compatible with the principle that systems tend to change naturally towards a state of minimum polarizability [47]. As noted in Section 1, there are various factors that change the crystal polarizability from the gas-phase static polarizability aG, of which the change in structure is only one [1]. For each molecule we have therefore compared the static polarizability aC calculated for the crystal structure not only with aG but also with the total effective optical polarizability aE in the crystal environment obtained [10,13] by analysis of the crystal refractive indices. In each case, we find aE > aG > aC. Crystal effective polarizabilities are commonly found to be greater than gas-phase polarizabilities, but we have shown directly that in the two cases studied here the change of geometry in going from the gas-phase molecule to the crystal actually works in the opposite direction, to reduce the polarizability. Some of the net increase in the effective polarizability can be attributed to the fact that, being derived from the refractive indices, it refers to the relevant optical frequency, where it should be larger than the zero-frequency static polarizability calculated here, but away from absorption bands the increase with frequency is not expected to be large. We therefore conclude that using the in-crystal structure for calculations of molecular properties in the crystal phase is necessary as a correct approach. However, it is not sufficient for the polarizability because additional environmental effects can have larger effects than the geometry change, and in the opposite direction. Thus, our results show the value of theoretical calculations in allowing one to disentangle different contributions to the effective polarizability. The increase in the effective polarizability over that calculated for the in-crystal structure indicates a particularly important role for other environmental effects. The environmental origin of enhanced effective polarizability is taken up in work on the C60 crystal [15], for which the enhancement over the gas-phase polarizability is deduced directly from experimental data rather than from theoretical computations. For C60 the geometry issue is not significant, and the effective polarizability is reduced or affected negligibly by other environmental effects considered hitherto (orbital confinement; the effect of the large permanent electric fields in the crystal caused by the dipole moments of the molecules; and the marked non-uniformity of these fields over molecular dimensions [1]). In that case, the observed enhancement is ascribed to the effect of crystal charge-transfer configurations in which an electron is not confined to a single molecule (in the sense of the tight-binding approximation). Such configurations are analogous to
the unbound states in the gas-phase molecule, but their energy is lowered in the dielectric medium provided by the other molecules and so their contribution to the polarizability is raised. This mechanism is sufficiently general to apply to all molecular crystals, and estimates for C60 indicate that the enhancement via this mechanism is sufficient to outweigh the reduction from the other environmental effects. For the more complicated molecules of acetanilide and RDX, the enhancement found in the effective polarizability is then presumably the resultant of the increase caused by this mechanism and the decrease caused by the changes of molecular structure in the crystal and other environmental factors; it has been suggested that hydrogen bonding and polarizability are intimately connected [48], and so in acetanilide hydrogen bonding may also play a role. Evidence for other molecular crystals indicates that the effective polarizability is generally enhanced over the gas-phase polarizability. If acetanilide and RDX are reasonably representative molecular crystals, in the sense that in-crystal geometry changes typically reduce the effective polarizability, then the enhancement to be explained by environmental effects such as charge-transfer is larger than hitherto suspected.
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Polarizability of acetanilide and RDX in the crystal: effect of molecular geometry D. Tsiaousis, R.W. Munn *, P.J. Smith, P.L.A. Popelier Department of Chemistry, UMIST, Sackville Street, Manchester M60 1QD, UK Received 7 April 2004; accepted 13 July 2004 Available online 3 August 2004
Abstract Density-functional theory with the B3LYP functional at the 6-311++G** level is used to calculate the dipole moment and the static polarizability for acetanilide and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) in their in-crystal structures. For acetanilide the dipole moment is 212% larger than for the gas-phase structure and for RDX (where there is a gross geometry change) it is 15% larger. The polarizability for the in-crystal structure is smaller than for the gas-phase structure by 3% for both species, whereas the incrystal effective optical polarizability is larger than the gas-phase static polarizability for both crystals. Hence, effects in addition to the molecular geometry change in the crystal must be considered in order to interpret the effective polarizability completely. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Acetanilide; RDX; Dipole moment; Polarizability; Crystal
1. Introduction Molecular crystal properties arise from the molecular properties, the molecular arrangement, and the molecular interactions. Hence, a proper understanding of molecular crystal properties relies in particular on knowing the molecular properties, which must be evaluated as ‘‘effective’’ properties appropriate to the crystal environment. One can then recognize a number of environmental effects that modify the properties of the ‘‘in-crystal’’ molecule from those of the free gas-phase molecule [1]. Perhaps most obvious of these is the different molecular geometry in the crystal. Nevertheless, this effect seems to have received comparatively little recognition or systematic study, so that molecular properties used for crystals have often been calculated for the gas-phase molecule geometry. There *
Corresponding author. Tel.: +44 161 200 4534; fax: +44 161 200 4584. E-mail address: [email protected] (R.W. Munn). 0301-0104/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.07.013
are exceptions, including work on phosphorobenzopyrene derivatives where the molecular geometry changes qualitatively between the gas phase and the crystal [2] and on 5-nitrouracil in two polymorphic forms [3]. There have also been attempts to calculate molecular structures in the crystal fields of surrounding molecules. However, the available studies [4,5] have tended to concentrate on the dipole moment, characteristic of the equilibrium electron density, rather than on the polarizability, characteristic of the response of the electron density to an external perturbation. We undertake here the simpler task of exploring what the properties of molecules are, given their structure in the crystal phase, with particular reference to the polarizability. Our interest in these general issues arises from work [6] on the energetics of charged states in the crystals of acetanilide (C6H5NHCOCH3, N-phenylacetamide: Fig. 1) and RDX (1,3,5-trinitro-1,3,5-triazacyclohexane or cyclotrimethylene trinitramine: Fig. 2). A link between the crystals is that acetanilide is one of the few molecular crystals for which the mechanism of optical damage has
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Fig. 1. Molecular structure of acetanilide. (a) In-crystal structure [16] and atomic numbering scheme; hydrogens not labelled. (Graphical display generated with the Materials VisualizerÔ from Accelrys Inc.) (b) Molecular skeleton in the energy-minimized gas-phase structure (black) and in the observed in-crystal structure (grey).
been reported in any detail [7], while RDX is well known as a detonator [8], and it has been remarked that the extreme conditions of optical damage in chemical materials simulate the initiation of detonation in solid explosives [9]. The processes of optical damage and the initiation of detonation in the two crystals therefore have some conceptual similarities, and we are exploring mechanisms for both based on the trapping of charged states near vacancies [6,10]. Our calculations require effective dipole moments and polarizabilities in the crystals. The polarizabilities can be obtained by analysing measured crystal refractive indices or the dielectric tensor [11], but we have to derive the dipole moments of the individual molecules from theoretical calculations. Analysis of high-precision electron densities derived from diffraction measurements can give in-crystal dipole moments [3,12], but these are total moments including contributions induced by the electric field of the surrounding dipoles through the molecular effective polarizability. Elsewhere, we calculate these induced contributions from the interactions between molecules that have the permanent dipole moment of an isolated molecule with the in-crystal geometry [10,13]. Similarly, cluster calculations [14] also give the total in-crystal dipole moment. Here, we present calculations of the dipole moments and polarizabilities of acetanilide and RDX in both the gas-phase and the in-crystal geometries, in order to explore the effect of the geometry changes while generating
Fig. 2. Molecular structure of RDX. (a) In-crystal structure [29] and atomic numbering scheme; hydrogens not labelled. (Graphical display generated with the Materials VisualizerÔ from Accelrys Inc.) (b) Molecular skeleton in the gas-phase structure obtained from electron diffraction [30] (black) and in the in-crystal structure (grey).
the necessary inputs for our work on the energetics of charged states. We find that for both systems the static polarizability for the in-crystal geometry aC is smaller than the gas-phase polarizability aG, whereas the observed effective optical polarizability in the crystal environment aE is larger than aG. Hence, the enhancement required to give aE is larger than might have been suspected, because it has to overcome the reduction from aG to aC in addition to accounting for the increase from aG to aE. The mechanism for such an enhancement is explored elsewhere in work on the C60 crystal [15], where the geometry issue is not significant and there is direct experimental evidence for the enhancement.
2. Acetanilide 2.1. Structure The acetanilide crystal has attracted attention because the molecule contains the peptide linkage
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–CONH– and takes part in an extended hydrogenbonded network in the crystal. As such, the crystal has features that make it a plausible model for biological systems. The crystal lacks a centre of symmetry, although there appear to have been no proposals to exploit the resulting quadratic non-linear optical behaviour. However, acetanilide differs from most organic crystals with non-linear optical potential because it has been the subject of rather detailed investigation of the mechanism of optical damage [7], which is an important limitation for practical applications in nonlinear optics. We take the in-crystal molecular structure from single-crystal neutron diffraction measurements [16]. The molecule is found to adopt the amide form rather than its imidol tautomer; the phenyl ring deviates significantly from C2v symmetry, with the carbon atoms adopting the boat conformation B14 . There appears to be no suitable molecular structure available for the gas phase, but the conformations and relative stabilities of acetanilide in the vapour phase have been determined from vibrationally resolved electronic spectra obtained by resonant two-photon ionization in a supersonic jet expansion [17]. These experiments show that the molecule exists as the trans geometrical isomer, having the phenyl ring oriented anti to the methyl group, the same as found in the crystal. We have therefore used the crystal-phase structure as the starting point for full geometry optimization to obtain the gas-phase structure, within the same theoretical approach that we use to calculate the molecular properties, namely using density functional theory with the B3LYP hybrid functional [18–20] at the 6-311++G** level within the Gaussian 98 software package [21]. This approach should take sufficient account of correlation to yield a realistic geometry and properties. The molecular skeletons in the gas-phase and in-crystal structures are shown superimposed in Fig. 1, which shows relatively modest changes. The most noticeable change in the crystal is a twisting seen most clearly in the methyl group but actually involving a rather pronounced twist about the bond connecting the acetamido substituent to the phenyl ring. This presumably serves to relieve some of the steric repulsion between the acetamido group and the hydrogen atom nearest it on the benzene ring [22]. Acetanilide lacks molecular symmetry in either phase, but in order to compare detailed results in the two phases we need to define molecular axes that should be comparable in both. For this purpose we adopt the atomic numbering scheme used in reporting the crystal structure [16] (see Fig. 1). We define the long L-axis to coincide with the vector from the carbon atom C4 to the carbon atom C1 that carries the acetamido substituent in the para position to it; the normal N-axis to be perpendicular to the L-axis and the vector from the car-
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bon atom C3 to carbon atom C5 (both meta to C1), so that the axis is roughly normal to the mean plane of the ring; and the medium M-axis to be perpendicular to L and N. 2.2. Dipole moment Our results are given in Table 1. The change in structure in the crystal induces a significant component of the dipole moment out of the LM plane, but the M component falls slightly and as a result the magnitude changes rather little. Our values lie among those reported from numerous measurements, mostly in benzene solution, as shown in the Table. Values measured in dioxane solution are mostly significantly higher, presumably because of the effect of the polar solvent, and are not shown. 2.3. Polarizability Our results are given in Table 2. The pattern of changes from the gas phase to the crystal structure differs from those in the dipole moment. The changes are fairly small, but in each case the polarizability is reduced in the crystal structure, by 412% for the LL component and over 3% in the MM component, but essentially zero in the NN component, so that the mean polarizability decreases by something over 3%. The value calculated for the crystal structure can be compared with the effective polarizability in the crystal environment calculated [10] from the crystal refractive indices, which is thus the optical rather than the static polarizability. There is considerable enhancement over the static polarizability for the in-crystal structure, to the extent that aE exceeds aG by 412% even though aG exceeds aC by 3%. This is attributable mainly to the 30% enhancement in the NN component, since the LL components are much the same and the MM component is actually the smallest of those reported here, at some 5% smaller than in the gas-phase molecule. For comparison, calculations using bond and group polarizabilities [23] gave a mean polarizability that corre˚ 3. sponds to 15.3 A
Table 1 Dipole moments for acetanilide; all values in D Source
Phase
lL
lM
Present calculations Present calculations Experiment
Gas
0.717
3.455
0.018
3.529
Crystal
0.784
3.397
0.974
3.620
Experiment
Benzene solution CCl4 solution
lN
l
3.41–4.01 3.5 [22]
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Table 2 ˚3 Polarizability components aAB and mean polarizabilities for acetanilide in different phases; all values in A Type of polarizability aG: gas aC: crystal aE: effective
Mean ð13Tr aÞ
AB LL
LM
LN
MM
MN
NN
22.09 21.14 22.23
1.31 1.05 2.24
0.01 0.74 0.55
16.33 15.80 15.55
0.01 0.62 0.58
9.21 9.17 12.04
3. RDX 3.1. Structure RDX is an energetic material used as a secondary explosive or detonator. It owes its sensitivity to the N– NO2 bonds [24], which are strongly polar and appear to be highly sensitive to the molecular environment [25,26]. There are suggestions that the physical state of an explosive affects its pyrotechnic sensitivity [25,27], so that studies of the properties of the molecule in different phases are of direct practical importance. RDX crystallizes in a, b, and c polymorphic forms [28], the first being stable at room temperature [29]. In the a-form crystal, the molecule adopts a chair conformation, with two of the NO2 groups occupying axial (A) positions and one occupying a pseudo-equatorial (E) position (the AAE conformer, site symmetry C1); there is an approximate mirror plane passing through the latter group, which makes the other two nearly equivalent (pseudo-Cs symmetry, see Fig. 2). On the other hand, electron diffraction indicates that the gasphase RDX molecule adopts the AAA conformer of the chair structure with C3 symmetry [30,31]. Questions remain as to whether this is the equilibrium structure or a time average over different conformers [32–36], but we adopt it here for studying the effect of the change of structure from the gas phase to the crystal. In the a polymorph the crystal forces cause a significant qualitative change from this molecular structure [37]. The molecular skeletons in the gas-phase and in-crystal structures are shown superimposed in Fig. 2. It can be seen that the change in conformation in the crystal is accompanied by a bending of the ring into a more upright chair, consistent with the picture that in the crystal a somewhat strained structure is stabilized by the crystal forces. The deviation of the ring from planarity can be described by a single angle h = 33.9° in the gas phase but in the crystal by angles h1 = 53.3° and h2 = 43.7° at the opposite ends of the chair [35]. The more flattened chair in gaseous RDX agrees with the hypothesis that the strain on the molecule is relieved upon vaporization [33]. The inequivalence of the nitro groups in the crystal also allows them to twist by different amounts about the N–N axes, whereas in the gas phase they all rotate to the same extent (u = 19.1°), giving rise to the C3 symmetry
15.88 15.37 16.61
deduced from the electron diffraction measurements [30]. As for acetanilide, to compare detailed results in the gas and (a-form) crystal phases we need to define a set of molecular axes that should be comparable in either phase. This is obviously complicated by the different conformers. In the gas-phase molecule, the threefold axis is one natural choice, and then we can choose the other pair of axes perpendicular to it. In the crystal, we make use of the approximate mirror plane running through the pseudo-equatorial NO2 group. We adopt the atomic numbering scheme used in reporting the crystal structure [29] (see Fig. 2), where this group contains nitrogen N1, and choose an auxiliary point Y midway between the other two nitro group nitrogens (N2 and N3). Then we define the long L-axis parallel to the vector Y–N1; the normal N-axis perpendicular to the L-axis and the vector N3–N2 (and hence roughly normal to some mean plane of the ring); and the medium M-axis perpendicular to L and N. Thus, in the gas-phase molecule the N-axis is the threefold symmetry axis, which we use explicitly in defining the molecular structure for our calculations (see [38]). 3.2. Dipole moment Our results are given in Table 3. The change in structure in the crystal increases the magnitude of the dipole moment in the normal direction while also inducing components perpendicular to this direction, as expected by the lowering of symmetry. As a result, the magnitude of the dipole moment increases by over 15%. Measurements of the dipole moment of RDX are scarce, but the values measured in a range of solvents [39] bracket our calculated values. Values measured in dioxane solution are significantly smaller.
Table 3 Dipole moments for RDX; all values in D Source
Phase
Present calculations Present calculations Experiment
Gas Crystal Various solutions
lL
lM
0
0
1.930
0.163
lN
l
6.404
6.404
7.147
7.405 6.0–7.5 [39]
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At first sight our results appear counter-intuitive. The dipole moments of the axial nitro groups in the gasphase molecule all contribute equally to the total moment by symmetry, and therefore it might seem that changing one group to equatorial would reduce the total rather than increasing it. We have therefore explored how far this effect can be reproduced in a pure bond-dipole model, as follows. From the calculated total dipole moment in the gas-phase molecule and the angle between the N–NO2 bond and the threefold axis, we deduce a bond dipole of 3.11 D parallel to the N–NO2 bond. We then take this value and apply it unchanged to calculate the total dipole moment for the in-crystal molecular structure, which we find to be 6.69 D, some 412% larger than the value calculated directly. In fact, the ‘‘intuitive’’ argument is misleading in this case, because the outcome depends critically on the angle between the N–NO2 bond and the threefold axis. For example, if the three N–NO2 bonds in the gas-phase molecule were coplanar, their bond dipoles would cancel by symmetry, and then any deviation from planarity in the crystal would necessarily change the total moment to a larger value. However, comparison of the structures in Fig. 2 suggests that the geometry changes in the crystal increase the contributions of the axial N–NO2 groups by more than they decrease that of the equatorial one. 3.3. Polarizability Our results are given in Table 4. For the gas-phase molecule, the polarizability anisotropy aNN < aMM = aLL is consistent with the negative Kerr coefficient measured for RDX in dioxane solution [40]. In the crystal, the LL component increases slightly, consistent with the greater spatial extension along this direction towards the pseudo-equatorial nitro group. At the same time, the MM component decreases by over 10%, with the NN component little changed, with the result that the mean value decreases by a little over 3%. In the effective polarizability there is a 10% average enhancement over the polarizability for the in-crystal structure: a 5% increase in the LL component, a 1212% increase in the MM component, and a 13% increase in the NN component. As a result, aE exceeds aG by 6%. For comparison, an additiv˚ 3 for the ity scheme gave a mean polarizability of 15 A gas-phase molecule [41]; ab initio calculations gave ˚ 3 for a geometry-optimized AAE structure [42]; 12.3 A
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˚ 3 deduced from the and a group polarizability of 5.5 A Clausius–Mossotti equation for the crystal assuming that only the N–NO2 group is responsible for the polar˚3 izability gave a mean molecular polarizability of 16.5 A [24]. The values of the polarizability anisotropy c deduced ˚3 from the present calculations are 4.55, 3.88 and 3.30 A for the gas-phase, crystal-phase and effective polarizabilities, respectively, so that the crystal environment decreases the anisotropy. The anisotropy deduced from the depolarization of Rayleigh scattering in different solvents has been quoted [39] as c2 35, whence c is some ˚ 3; this is larger than our calculated anisotropies, 6.0 A but refers to RDX in solution, where polarographic studies indicate that all nitro groups are inequivalent [43].
4. Discussion and conclusions We have calculated the changes in molecular dipole moment and polarizability between gas-phase and incrystal structures of acetanilide and RDX. In each case, what we have taken as the gas-phase structure cannot be considered as definitive, for acetanilide because we have obtained it theoretically and for RDX because there is continuing discussion over the role of conformers in the gas phase other than the one we have taken, though it was derived to fit experimental measurements. On the other hand, in each case the in-crystal structure, which is our primary concern, can be regarded as established experimentally. We have used the same method of calculation for each pair of structures, and hence our results should provide at least a good semi-quantitative representation of how the geometry change affects the dipole moment and polarizability. The calculated changes are noticeable but quite small in acetanilide (212% or 0.1 D increase in the dipole moment and 3% decrease in the polarizability), and even in the case of RDX where there is a gross change in geometry between the two structures, the changes are not as large as might have been expected (15% or 1 D increase in the dipole moment and 3% decrease in the polarizability). In both cases the dipole moment increases and the polarizability decreases. Hence, as the molecule becomes more polar it becomes less polarizable. Comparable conclusions emerge from other
Table 4 ˚3 Polarizability components aAB and mean polarizabilities for RDX in different phases; all values in A Type of polarizability G
a : gas aC: crystal aE: effective
Mean ð13Tr aÞ
AB LL
LM
LN
MM
MN
NN
17.70 17.83 18.77
0 0.04 0.01
0 0.71 0.90
17.70 15.71 17.68
0 0.01 0.42
13.15 13.35 15.08
16.18 15.63 17.18
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work – for the constituent molecules in the water dimer [44], for molecules in an environment of discrete solvent molecules studied by direct reaction-field calculations [45], and for three squaric acid conformers [46]. A decrease in polarizability is also compatible with the principle that systems tend to change naturally towards a state of minimum polarizability [47]. As noted in Section 1, there are various factors that change the crystal polarizability from the gas-phase static polarizability aG, of which the change in structure is only one [1]. For each molecule we have therefore compared the static polarizability aC calculated for the crystal structure not only with aG but also with the total effective optical polarizability aE in the crystal environment obtained [10,13] by analysis of the crystal refractive indices. In each case, we find aE > aG > aC. Crystal effective polarizabilities are commonly found to be greater than gas-phase polarizabilities, but we have shown directly that in the two cases studied here the change of geometry in going from the gas-phase molecule to the crystal actually works in the opposite direction, to reduce the polarizability. Some of the net increase in the effective polarizability can be attributed to the fact that, being derived from the refractive indices, it refers to the relevant optical frequency, where it should be larger than the zero-frequency static polarizability calculated here, but away from absorption bands the increase with frequency is not expected to be large. We therefore conclude that using the in-crystal structure for calculations of molecular properties in the crystal phase is necessary as a correct approach. However, it is not sufficient for the polarizability because additional environmental effects can have larger effects than the geometry change, and in the opposite direction. Thus, our results show the value of theoretical calculations in allowing one to disentangle different contributions to the effective polarizability. The increase in the effective polarizability over that calculated for the in-crystal structure indicates a particularly important role for other environmental effects. The environmental origin of enhanced effective polarizability is taken up in work on the C60 crystal [15], for which the enhancement over the gas-phase polarizability is deduced directly from experimental data rather than from theoretical computations. For C60 the geometry issue is not significant, and the effective polarizability is reduced or affected negligibly by other environmental effects considered hitherto (orbital confinement; the effect of the large permanent electric fields in the crystal caused by the dipole moments of the molecules; and the marked non-uniformity of these fields over molecular dimensions [1]). In that case, the observed enhancement is ascribed to the effect of crystal charge-transfer configurations in which an electron is not confined to a single molecule (in the sense of the tight-binding approximation). Such configurations are analogous to
the unbound states in the gas-phase molecule, but their energy is lowered in the dielectric medium provided by the other molecules and so their contribution to the polarizability is raised. This mechanism is sufficiently general to apply to all molecular crystals, and estimates for C60 indicate that the enhancement via this mechanism is sufficient to outweigh the reduction from the other environmental effects. For the more complicated molecules of acetanilide and RDX, the enhancement found in the effective polarizability is then presumably the resultant of the increase caused by this mechanism and the decrease caused by the changes of molecular structure in the crystal and other environmental factors; it has been suggested that hydrogen bonding and polarizability are intimately connected [48], and so in acetanilide hydrogen bonding may also play a role. Evidence for other molecular crystals indicates that the effective polarizability is generally enhanced over the gas-phase polarizability. If acetanilide and RDX are reasonably representative molecular crystals, in the sense that in-crystal geometry changes typically reduce the effective polarizability, then the enhancement to be explained by environmental effects such as charge-transfer is larger than hitherto suspected.
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