Dynamics and disorder: on the stability of pyrazinamide polymorphs

We would like to dedicate this paper to Professor Hans-Beat Bürgi on the occasion of his 80th birthday.

This article focuses on the structure and relative stability of four pyrazinamide polymorphs. New single crystal X-ray diffraction data collected for all forms at 10 K and 122 K are presented. By combining periodic ab initio DFT calculations with normal-mode refinement against X-ray diffraction data, both enthalpic and entropic contributions to the free energy of all polymorphs are calculated. On the basis of the estimated free energies, the stability order of the polymorphs as a function of temperature and the corresponding solid state phase transition temperatures are anticipated. It can be concluded that the α and γ forms have higher vibrational entropy than that of the β and δ forms and therefore they are significantly more stabilized at higher temperatures. Due to the entropy which arises from the disorder in γ form, it overcomes form α and is the most stable form at temperatures above ∼500 K. Our findings are in qualitative agreement with the experimental calorimetry results.

1. Introduction

The understanding of crystalline phase thermal stability is of paramount importance for drug systems, because it influences both the shelf-life and the bioavailability of solid state dosage forms. The stability of the crystalline phase is a matter of thermodynamic and kinetic factors. Thermodynamically, the crystal must be energetically more stable than any other phase – be that the liquid, gas or other solid-state forms. Meanwhile, the lack of thermodynamic stability may not lead to a transformation, if there is no feasible pathway from one form to another – in other words, kinetics has the final word in determining the fate of our crystalline phase.

Even without considering such complicating kinetic factors, the matter can become rather complex. In a polymorphic system, only one structure is the thermodynamically stable form at any given temperature and pressure. Enantiotropic polymorphism – where the thermodynamic stability of polymorphs changes order as a function of temperature – can be explained by differences in entropy as well as enthalpy. Entropic differences can arise due to both disorder and thermal motion. In this work, we will investigate such an enantiotropic system – pyrazinamide – and will try to elucidate the different contributions that lead to its enantiotropic behavior by means of a combination of computations (periodic density functional theory (DFT) calculations) and X-ray diffraction measurements.

From a pharmaceutical perspective, pyrazinamide is a very well known anti-tuberculosis drug listed by the World Health Organization on the Model List of Essential Medicines. It also exhibits strong antipyretic, fibrinolytic and antibacterial properties.

Despite its very simple molecular structure (Fig. 1), pyrazinamide has a complex solid form landscape; to this day four polymorphs have been found, and their structures (crystallographic data in Table 1) are well known (Takaki et al., 1960; Tiwari et al., 1982; Rø & Sørum, 1972; Cherukuvada et al., 2010; Castro et al., 2010; Wahlberg et al., 2014). The forms can be obtained by standard crystallization techniques such as slow evaporation of solvents or sublimation. In many cases, the polymorphs crystallize concomitantly. Based on a plethora of experimental evidence, including calorimetric measurements, hot-stage microscopy observations, spectroscopic measurements, grinding experiments, and long-term storage and powder X-ray diffraction (PXRD) diagrams, the relative stability of the polymorphs as a function of temperature has been proposed (Castro et al., 2010; Cherukuvada et al., 2010). Furthermore, tentative diagrams of the free energy versus temperature for the four forms and the liquid state is available (see Fig. 2).

Table 1
Crystallographic data of the structure refinements

Phase	α		β		γ		δ
T (K)	10	122	10	122	10	122	10	122
Formula	C5H5N3O
Formula weight (g mol^−1)	123.11
Crystal system	Monoclinic	Monoclinic	Monoclinic	Monoclinic	Monoclinic	Monoclinic	Triclinic	Triclinic
Space group	P21/n	P21/n	P21/c	P21/c	Pc	Pc
a (Å)	3.5885 (9)	3.6330 (10)	14.3433 (9)	14.3280 (3)	7.1818 (7)	7.1730 (17)	5.1026 (6)	5.1280 (14)
b (Å)	6.7605 (17)	6.753 (2)	3.6086 (2)	3.6330 (13)	3.6295 (4)	3.6500 (13)	5.7083 (7)	5.7080 (12)
c (Å)	22.434 (6)	22.546 (5)	10.6023 (7)	10.6280 (17)	10.6533 (11)	10.686 (2)	9.8487 (12)	9.857 (4)
α (°)	90	90	90	90	90	90	97.526 (4)	97.45 (3)
β (°)	92.748 (8)	92.39 (2)	100.9820 (10)	101.169 (7)	106.3770 (10)	106.487 (17)	98.499 (3)	98.04 (3)
γ (°)	90	90	90	90	90	90	106.564 (4)	106.55 (2)
V (Å^3)	543.6 (2)	552.7 (3)	538.72 (6)	542.7 (2)	266.43 (5)	268.27 (13)	267.37 (6)	269.45 (15)
Z, Z′	4, 1	4, 1	4, 1	4, 1	2, 1	2, 1	2, 1	2, 1
F(000)	256	256	256	256	128	128	128	128
Dx (g cm^−3)	1.5042	1.4797	1.518	1.5067	1.5347	1.5241	1.5293	1.5175
μ (mm^−1)	0.112	0.11	0.113	0.112	0.114	0.113	0.114	0.113
No. of measured reflections	9779	49596	4273	47668	4051	17605	3482	15213
[sin(θ)/λ]max (Å^−1)	0.831	1.078	0.763	1.078	0.777	1.145	0.835	1.128
No. of unique reflections	2486	5797	1853	5683	1941	5658	2278	4988
No. of observed reflections	1669	3372	1620	3664	1797	3415	1557	4005
Observed condition	I > 3σ(I)
Rint	0.048	0.0582	0.0111	0.0392	0.0183	0.0418	0.0258	0.0743
Refinement method	Full-matrix least-squares on F
No. of parameters	82	82	82	82	87	87	37	37
R1 (obs.)	0.0432	0.0368	0.0333	0.0370	0.0370	0.0474	0.0517	0.0397
wR (all)	0.0502	0.0477	0.0467	0.0567	0.0423	0.0545	0.0603	0.0647
GoF (all)	1.72	1.97	2.69	2.73	1.98	1.81	1.89	2.60
H-atom treatment	H-atom parameters constrained
Weighting scheme	w = 1/[σ^2(F)+0.0001F^2]
Δmax, Δmin (Å^−3)	0.70, −0.37	0.67, −0.28	0.53, −0.24	0.61, −0.28	0.36, −0.25	0.54, −0.30	0.75, −0.45	0.50, −0.27

Figure 1 Molecular structure of pyrazinamide.

Figure 2 Sketch of a G–T diagram which is in accordance with the observed phase transformations. The implied phase transformations, the transformation temperatures and the enthalpies of transformation derived from DSC measurements are given below the ordinate. The diagram is based on information and similar diagrams in previous work (Castro et al., 2010; Cherukuvada et al., 2010). The (*) implies that the transition enthalpy of the β to γ transition is not well determined, because the β sample was contaminated by γ-form crystals.

1.1. Description of stabilities

The solid-state phase transformations can be observed using differential scanning calorimetry (DSC). DSC provides phase transition temperatures and enthalpies, although these data have to be taken cum grano salis, since they are influenced by kinetics and by the phase purity of the sample. In particular, a recent study points to the difficulties in assessing the exact temperature of the α to γ transition (Li et al., 2020) because the transition temperature depends on the DSC heating rate. Based on the phase transformations observed during storage of crystals at a range of temperatures, Li et al. propose a transformation temperature of 392 (1) K. The difference in solid state enthalpies between α and γ seems to be temperature independent and amounts to 13.2 (6) J g⁻¹ corresponding to 1.6 (1) kJ mol⁻¹, with the α form being enthalpically the most stable.

Based on the observed phase transformations from DSC, hot-stage microscopy, Raman and PXRD measurements, it appears that at low temperatures, the γ form is the least stable – yet at higher temperatures all other forms – α, β and δ – transform to γ before reaching the melting point (Castro et al., 2010, Cherukuvada et al., 2010). Additionally, already at room temperature the δ form can transform into the α form. The free energy versus temperature diagram in Fig. 2 agrees with these observations. However, several other G–T diagrams could be sketched: in particular, it is difficult to draw any conclusions of the relative stabilities at 0 K for the β form in relation to the α and δ forms. Although the transformation to γ appears to occur at a lower temperature than for α and δ, the β form could be the most stable at 0 K if the G–T line for β is less curved than for the other forms. This would imply that the G–T curve of β would cross the curves of α and δ, implying possible phase transformations – which, however, could be kinetically hindered.

To get an understanding of the different contributions giving rise to a temperature dependence of the relative thermodynamic stabilities of the four polymorphs, it is necessary to obtain an insight into the enthalpic as well as entropic contributions to the free energy, i.e. to calculate G = H − TS, where H is the enthalpy, T is the temperature and S is the entropy. In this work, we use a combination of periodic DFT calculations and X-ray diffraction measurements to obtain an estimate of the free energy G at different temperatures, as outlined below.

1.2. Entropic contribution to thermodynamic stabilities

At absolute zero, a perfect crystal has zero entropy. However, disorder in the crystalline phase may give a contribution to the entropy even at T = 0 K.

It is well known that the γ form of pyrazinamide is disordered (Cherukuvada et al., 2010). The crystal structure shows that 15% of the molecules are rotated (vide infra). On one hand, this disorder gives rise to a small decrease in the enthalpic stability of the crystal, while on the other hand stabilizes the crystal entropically.

Whereas the disorder of the γ form is readily visible in the electron density derived from single-crystal diffraction experiments, we have found it interesting to investigate whether the other polymorphs are disordered in any way. Therefore, we have conducted measurements at 10 K. At this temperature, disorder that is not visible at higher temperatures – i.e. hiding as a contribution to the displacement ellipsoids – can be revealed. At 10 K the intermolecular vibrations are significantly reduced. The disorder will manifest itself as splitting of atomic positions, or as significantly larger ellipsoids than what can be expected to arise from intramolecular motion.

Apart from the disorder, the most substantial contribution to the entropy in the solid state is from the thermal vibrations in the crystal. Vibrational contributions to free energy are demanding to obtain from theoretical calculations for molecular crystals due to high computational costs, and because the accuracy of the calculated low-frequency phonons may be low. Thus, for the pyrazinamide polymorphs we apply a recently developed quantum crystallography method (Genoni et al., 2018), coined Dynamic Quantum Crystallography, of estimating vibrational entropy and enthalpy from frequencies refined against single crystal X-ray diffraction data (Hoser & Madsen, 2016; 2017). We term this refinement a normal-mode refinement (NoMoRe), and in recent years we have explained, validated, and applied this approach to various systems to estimate thermodynamic properties (Hoser et al., 2021; Sovago et al., 2020; Kofoed et al., 2019).

1.3. Enthalpic contribution to thermodynamic stability

While the NoMoRe procedure ensures an estimate of the vibrational entropy and enthalpy, the enthalpic differences due to inter- and intramolecular conformations of the molecules are not considered. In recent years, periodic DFT calculations including an empirical estimate of dispersion interactions have been shown to be able to give reasonable estimates of differences in crystal polymorph enthalpies and has been an important reason for the success of crystal structure prediction (Reilly et al., 2016). However, in our previous work (Wahlberg et al., 2014) we have explored how differences in the crystal geometries of pyrazinamide can lead to rather different DFT-estimated stabilities of the pyrazinamide polymorphs.

In the present contribution, we update that work using new methodology, in particular with respect to the empirical estimates of the dispersion forces. Next, we estimate contributions to the Gibbs free energies that arise from vibrations and disorder and we predict the ordering of stability of polymorphic forms at different temperatures.

2. Materials and methods

2.1. Single-crystal X-ray diffraction

Crystalline pyrazinamide, purchased from Sigma, was used without further purification. The α, β and δ polymorphs were crystallized from the saturated solution by slow evaporation at room temperature. The respective solvents were water, chloro­form and di­chloro­methane, in accordance with the work of Castro et al. (2010). Crystals of the α form were slowly heated in an oven to 160 °C and in what appears to be a single-crystal to single-crystal transformation turned to the γ form.

The diffraction measurements were performed using Bruker/Nonius in-house X-ray diffractometers, and the temperature was controlled by use of nitro­gen and helium open gas-flow systems (from Cryo Industries of America). All data were collected using molybdenum radiation and with area detectors. For each polymorph, data at 10 K and 122 K were collected. The 10 K data were limited to a resolution of maximum sin(θ)/λ = 0.8 Å⁻¹, whereas the 122 K data were obtained to at least sin(θ)/λ = 1.0 Å⁻¹. The data were integrated and reduced using the SAINT program.

For the deposited structures, the software JANA2006 (Petříček et al., 2014) was used for structure solution and refinement. Anisotropic displacement parameters were refined for non-hydrogen atoms. The hydrogen atoms were fixed at calculated positions and refined using the riding model. For the γ polymorph, a rigid-body approach was used for the minor disorder component.

The SHELXL program (Sheldrick, 2015) was used for block-refinement as part of the NoMoRe refinement.

An overview of the crystallographic information can be found in Table 1.

2.2. Theoretical calculations

Periodic ab-initio density functional theory (DFT) calculations were performed for the selected systems using the CRYSTAL17 program (Dovesi et al., 2017).

Electronic energy calculations. Electronic energies were calculated with two different functionals B3LYP (Lee et al., 1988) and PBE0 (Adamo & Barone, 1999) in combination with an D3 empirical dispersion (Grimme et al., 2010) energy correction and with a large pVTZP (Schäfer et al., 1994) basis set with polarization functions. The truncation parameters, TOLINTEG, were set to 7 7 7 7 25 and the shrinking factors in the reciprocal space, SHRINK, were set to 8 and 8.

Moreover, we tried two approaches – full geometry optimization and optimization of atom coordinates only, with cell parameters fixed at those from the 10 K measurements.

Phonon calculations were performed in CRYSTAL17 to provide an ansatz for the Normal Mode Refinements (NoMoRe). The standard 6-31G(d,p) basis set was applied. It has been used extensively and gives reasonable relative stabilities of related systems; it has also been used for the estimation of vibrational frequencies. We optimized the geometry (only the coordinates, starting from the experimental geometry). Subsequently, we calculated the normal modes and their frequencies at the Γ point of the Brillouin zone. The convergence criteria for geometry optimization were set to the default for frequency calculations using the PREOPTGEOM keyword. As we optimized only the coordinates, the frequencies were calculated using the cell parameters from the 122 K XRD measurements. Input for CRYSTAL17 frequency calculations can be easily created using our cif2crystal routine (https://shade.ki.ku.dk/docs/cif2crystal.html).

2.3. The normal-mode refinements (NoMoRe)

We used the nomore.chem.uw.edu.pl web server (a version of the NoMoRe Python program) to conduct refinements against pyrazinamide polymorph X-ray data from 122 K. For α, β and δ we submitted normal-mode vectors and their frequencies obtained from theoretical calculations, structure factor files and input files for SHELXL with a model of the given structure. For each polymorphic form we refined six frequencies, corresponding to the low-energy acoustic and optical phonons, which lead us to reasonable models (with quite low agreement indices (wR²) and anisotropic displacement parameters (ADPs) similar to those from routine SHELXL refinement, see supporting information). The NoMoRe python program was adapted to refine the disordered γ polymorph. During these refinements, the parameters describing the minor disorder component were kept constant. The electron density related to the minor disorder component does not overlap with the density of the major component, and thereby the displacement parameters of the major component appear unaffected by the disorder.

2.4. Evaluation of thermodynamic functions

In the case of all polymorphic forms we used known thermodynamic equations, which we already applied for polymorphs of di­methyl-3,6-di­chloro-2,5-di­hydroxy­terephthalate (Kofoed et al., 2019). For each polymorph the free energy (G) is calculated as it is shown in the following equations:

where H is enthalpy, T is temperature in K and S is entropy. The enthalpic part can be divided into U, crystal packing energy, and a , pressure × volume, term which take into account the expansion of the unit cell with temperature

(where the pΔV term is calculated at a pressure of 1 atm), whereas

E_total is an electronic energy which is accessible from DFT calculations and the contribution from vibrational energy, F_vib is

Where the summation in equation (1) runs over frequencies ν, h is Planck's constant and k is the Boltzmann constant. The first part of the equation is the zero-point energy (ZPE), while the second part is the contribution to enthalpy (Hvib) coming from normal-mode vibrations. In a similar fashion, the vibrational entropy can be obtained by summation over all normal-mode vibrations:

In the case of NoMoRe all the frequencies obtained from the calculations in CRYSTAL17 (and for which a subset was subsequently refined against the diffraction data) were used in order to obtain full vibrational contributions to free energy.

For the γ form, we additionally took into account the entropy arising from disorder, as outlined below.

2.5. Entropy of mixing for γ polymorphic form

Disorder can stabilize the γ pyrazinamide structure by increasing the entropy. We estimate these entropy contributions by calculating the entropy of mixing.

where x₁ and x₂ are the experimentally observed occupancies (0.15 and 0.85).

3. Results and discussion

3.1. Structures and intermolecular interaction description

The structures of the pyrazinamide polymorphs have already been described and are well known. The data for all pyrazinamide polymorphs obtained in this study at 122 K are of a high-resolution [sin(θ)/λ > 1.0 Å⁻¹], giving more confidence in the atomic positions and the description of disorder than previous studies. Previously, a comparable resolution data of sin(θ)/λ > 1.0 Å⁻¹ have only been reported for α and β polymorphs (Rajalakshmi et al., 2014; Jarzembska et al., 2014). The data obtained at 10 K are of a slightly lower resolution [sin(θ)/λ ≃ 0.8 Å⁻¹], simply due to experimental limitations where the cost of helium sets a limit to the experiment time. However, the displacement parameters of the α, β and δ polymorphs derived from the 10 K data indicates that there is no disorder in these systems. The γ form is thereby the only form where a more advanced model is needed for the calculation of the enthalpic contribution to the free energy via periodic DFT calculations.

Comparing energy frameworks (Turner et al., 2015, Spackman et al., 2021) generated for pyrazinamide polymorphs (Fig. 3) we immediately see that in the α, β and δ polymorphs dimers are formed by pyrazinamide molecules via the hydrogen bonding between amide groups. For those structures, this is the strongest interaction. Such dimers are stabilized by other weaker - mostly dispersive - interactions. The γ form is a remarkable exception – here, neighboring pyrazinamide molecules form chains via hydrogen bonding interactions of amide groups with nitro­gen from the aromatic ring. Furthermore, such chains are stabilized by dispersive interactions (see supporting materials). Therefore, proper dispersion corrections are crucial for theoretical calculations for this system.

Figure 3 Energy frameworks generated for pyrazinamide polymorphs [CrystalExplorer (Spackman et al., 2021), B3LYP level of theory].

Comparison of anisotropic displacement parameters (ADPs) reveals that ADPs for the α and γ forms are significantly larger than those for the other polymorphic forms (Fig. 4). In the case of the α form this observation can be rationalized by comparison of unit-cell volumes and densities for different polymorphic forms – the α form has significantly higher cell volume and lower density than the other polymorphic forms – thus, the atoms have more space to vibrate and in consequence the ADPs are larger.

Figure 4 Visual comparison of non-hydrogen ADPs from 122 K. Ellipsoids are depicted at the 90% probability level.

Large ADPs for the α and γ forms are a hint that the vibrational entropy can give important contributions to the relative stability of polymorphic systems. However, the system with the largest ADPs does not always have the largest entropy, because the intramolecular vibrations can play a significant role, as we have demonstrated previously (Kofoed et al., 2019).

3.2. On the disorder of γ polymorph

The γ polymorph is statically disordered. This has been observed also in previous studies (Wahlberg et al., 2014). Evident electron density maxima showing presence of a second disorder component are present in the Fourier difference maps. In Fig. 5 the asymmetric unit is depicted showing the major disorder component along with the backbone of the pyrazinamide molecule related to the minor disorder component. Two orientations of the minor site are possible.

Figure 5 Asymmetric unit of the pyrazinamide γ polymorph showing the backbone of the minor disorder component and two possible orientations of the molecule that may occupy the disordered site.

Determining which of the orientations occupy the minor disordered site is not straightforward. Furthermore, both presented orientations might be present resulting in three disordered components in total. We did refinements with either the A or B disorder components present, and found that the R₁ value was more than 1% lower when component A was present. In both cases, the disorder component ratio was refined to approximately 85:15. It is consistent with a structure model reported earlier, where the disorder ratio is 87:13 (Cherukuvada et al., 2010). There, the minor disorder component is also considered in orientation A.

Analysis of hydrogen bonding also hints that a pyrazinamide molecule with orientation A would result in an energetically more favorable state. In Fig. 6(a), a structural motif as formed by the major component is depicted also indicating the hydrogen bonding. There are four (two unique) hydrogen bonds associated with each molecule. Expansion of the hydrogen bond network results in a layer. If one molecule is replaced with the minor disorder component in the A orientation, then four other hydrogen bonds are possible [see Fig. 6(b)]. However, if a local structure with a minor disorder component in its B orientation is considered, then only one rather long and thus inefficient hydrogen bond is formed with the molecules of the major disorder component [see Fig. 6(c)].

Figure 6 Local structures of (a) solely the major disorder component; (b) the major disorder component and one molecule of the minor component – orientation A; (c) the major disorder component and one molecule of the minor component – orientation B. D⋯A distances of possible hydrogen bonds are shown as solid lines, while dashed lines indicate D⋯H.

3.3. Lattice and total electronic energies

The lattice energies for pyrazinamide polymorphs were already calculated using various different methods (Wahlberg et al., 2014). It was found that differences in lattice energies are extremely small and the stability order of the pyrazinamide polymorphs can be reverted by applying a slightly different calculation scheme (e.g. by changing a basis set or by small changes of a unit cell).

Herein we conducted once again total and lattice energy calculations at different levels of theory and this time with the D3 dispersion correction. The lowest electronic energy we obtained for the β form, whereas the highest for the α form (see Table 2). As the high total electronic energy for the α form is in a good agreement with experimental results, such low energy calculated for the β form is surprising – according to the experimental results the most stable form at low temperature should be the δ form. Wahlberg et al. (2014) managed to calculate energies which reproduce experimental stability order by means of theoretical computations with fixed unit-cell parameters at 122 K, with large modified VZP basis set and Grimme dispersion correction. In our case, although we applied a TZVP basis set and D3 dispersion correction, the β form exhibits lower total energy than the δ form.

Table 2
Differences in total electronic energies (kJ mol⁻¹) relative to the δ form

A negative sign implies that the structure is more stable than δ. Here, the calculations for the γ polymorphic form were conducted for the main disorder component. Level of theory: TZVP (Schäfer et al., 1994), D3 dispersion correction. Cell (10 K) implies that the cell constants are constrained to the experimentally determined cell at 10 K.

DFT method	Geometry	α	β	γ	δ
B3LYPD3	Cell and coordinates optimised	2.4	−1.9	−1.0	0
PBE0D3	Cell and coordinates optimised	1.8	−1.8	−0.4	0
B3LYPD3	Cell (10 K), coordinates optimised	2.1	−1.8	−0.9	0
PBE0D3	Cell (10 K), coordinates optimised	2.0	−1.4	0.0	0
B3LYPD3	Cell (123 K), coordinates optimised	2.6	−1.7	−0.7	0

Regarding the γ form of pyrazinamide, in Table 2 we present results of calculations which we obtained for the main component, i.e. without disorder. In such a case, the γ polymorph have almost equal energy to the δ form. In the real crystal structure, we do observe disorder and thereby the lattice/total electronic energy for the disordered structure is slightly higher than for the hypothetical non-disordered crystal. This destabilization is recompensed at higher temperatures by contributions from the configurational entropy.

In the work of Wahlberg et al. (2014), a 2 × 1 × 1 supercell with P1 symmetry was constructed, and one out of eight molecules were flipped to reflect the disorder observed experimentally. In the present case, we have constructed a somewhat larger supercell (2 × 3 × 2) to ensure that the flipped molecules are isolated from each other, in this supercell one out of 24 molecules was flipped. The electronic energy calculated in that manner (B3LYPD3, cell fixed and coordinates optimized) is 0.35 kJ mol⁻¹ higher than the energy calculated for pure γ main disorder component (as in Table 2). Occupancy ratio is 85:15, this would correspond to flipping four molecules out of 24. Considering this occupancy ratio, and with the assumption that the flipped molecules do not interact, we may estimate the electronic energy for the disordered structure to be 4 × 0.35 kJ mol⁻¹ higher than for major γ component. It means that the disordered structure is energetically less stable by 1.4 kJ mol⁻¹ than the non-disordered γ structure (major component only). When a 1.4 kJ mol⁻¹ value is added to the energy obtained for the non-disordered γ structure (from Table 2, using B3LYPD3 and fixed cell at 10 K, the γ form is −0.9 kJ mol⁻¹ more stable than δ) we see that the γ form is becoming less stable than δ by 0.5 kJ mol⁻¹ at 0 K.

3.4. Entropy, zero-point energy and contribution to enthalpy from lattice vibrations

The entropy and the contribution to enthalpy from lattice vibrations were calculated from frequencies obtained after NoMoRe refinement. Those contributions are temperature dependent and together with ZPE are presented in Fig. 7. As the vibrational contributions to the free energy are positive, a lower value indicates that the structure is more stabilized by the lattice vibrations. From Fig. 7 we can immediately observe that with the increase in temperature two forms, α and γ, are starting to have significantly lower energies, stabilized by entropy. At room temperature the energy difference between polymorphic forms is almost 4 kJ mol⁻¹ (between δ and α or between γ and β). Such energy differences can easily overcome differences in electronic/lattice energies between polymorphic forms.

Figure 7 Contributions to the free energy from vibrations (Hvib +ZPE-TS) for four polymorphic forms as a function of temperature.

In principle, these vibrational contributions can be calculated directly from frequencies obtained from periodic DFT calculations at the Γ point (this is our starting point for NoMoRe). Even with such simple model it appears that the α form is stabilized by entropy, but within this model γ does not exhibit higher vibrational entropy than β (see supporting information). There might be a few explanations for that, and the most obvious one is that with this model we do not consider the change of frequencies due to phonon dispersion. Consequently, we do not consider acoustic modes and some low-frequency modes, which are heavily affected by phonon dispersion and thus might be inaccurately modeled.

Apart from the entropic contributions from vibrations, the configurational entropy, which arises from static disorder, contributes to the γ form free energy. This contribution equals 3.5 J mol⁻¹ K⁻¹, which at room temperature will lower the free energy by 1.1 kJ mol⁻¹, and at 392 K – the temperature of the experimentally estimated phase transition from the α to γ form – around 1.6 kJ mol⁻¹.

3.5. G-T diagrams

Based on the crystal energies and the vibrational contributions to entropy and enthalpy derived from the normal-mode refinements, and by considering the consequences of disorder in the γ form for both enthalpy and entropy, it is possible to calculate the free energies as a function of temperature for all four polymorphs (see Fig. 8). As evident from our calculated energies, it is not straightforward to assess the order of stability at 0 K for the pyrazinamide polymorphs. We therefore make three different curves with different offsets on the abscissa, corresponding to different estimates of the 0 K enthalpies. In terms of the vibrational contribution to the entropy, these models are identical. The three models are presented in the three columns of Fig. 8. Model 1: periodic DFT (B3LYP, fixed cell, TZP, D3) calculations including destabilization of the γ form due to disorder. Model 2: periodic DFT results from Wahlberg et al. (2014) (Approach III, model B3LYP-D/VTZ-mod in that work). Model 3: average values of experimentally observed enthalpy differences, as observed from DSC measurements (Cherukuvada et al., 2010). In this model, we assume that the observed enthalpy differences are temperature independent. For this reason, the vibrational enthalpy calculated from the lattice dynamical model was not included.

Figure 8 The variation of free energies as a function of temperature. The three models are described in the text. The upper part of the figure shows the total G–T curves, whereas the lower part shows the differences in free energies with respect to the δ form. The δ form therefore becomes a horizontal line at G = 0. For the γdis model we are including the entropy arising from disorder in the free energy calculation for γ.

Comparison of Gibbs free energies obtained from the different models reveals the importance of accurate total electronic and lattice energy calculations (Fig. 8). Due to those differences, we do observe that free energies obtained from the two theoretical models differ, especially at low temperatures.

3.6. Discussion

The vibrational contributions to the free energy, as derived from the NoMoRe procedure, shows that the γ and α forms behave similarly, and are stabilized at higher temperatures as compared to the β and δ forms (see Fig. 7).

Whereas the vibrational stabilization of α and γ are similar in size, the disorder in the γ form contributes in two ways to form an enantiotropic relationship between these two polymorphs: first, the disorder decreases the packing energy, i.e. the γ form is enthalpically destabilized by the disorder. At the same time, the disorder adds a residual entropy component to the γ crystal. At higher temperatures, this entropic stabilization effects that the γ form becomes the stable form. Experimentally, this change in stability is observed at 392 K.

Our 10 K structures confirm the disorder found in the γ form at higher temperatures and at the same time rule out any major disorder in any other forms. These accurate structures, being close to the `0 K' ansatz used in most ab initio calculations, provide a good benchmark for further optimization of theoretical calculations of polymorphism in organic crystal systems.

Our difficulties in assessing the order of stability of the polymorphs at 0 K imply that many different G–T diagrams can be constructed, giving very different phase transition temperatures, none of which are in full agreement with the experimentally observed. Since the experimental phase transition temperatures may at the same time be influenced by kinetic factors they may be overestimated. The observed phase transition from δ to α is at 298 K, whereas all our models predict a phase transition well below room temperature. Similarly, our models predict the phase transitions of β to γ to be below room temperature. In contrast, the α to γ transition is predicted to be well beyond room temperature, as observed experimentally.

The effect of thermal expansion and anharmonicity is not part of the NoMoRe approach used in this study. One approach to include anharmonicity would be to impose a quasi-harmonic approach, where a range of NoMoRe models are refined against X-ray diffraction data obtained at differing temperatures. For each temperature, an ansatz could be obtained from periodic DFT calculations performed using the unit-cell dimensions obtained experimentally at that temperature.

Although this approach is not unfolded in the present work, we have performed periodic DFT calculations based on the room-temperature structures obtained from the literature. The calculations of frequencies were performed at the γ point of the Brillouin zone – thus, no contribution from acoustic phonons were included. The thermodynamic properties obtained from these purely in-silico models are compared to similar calculations using the 122 K unit cells in Table S2 of the supporting information. As expected, due to thermal expansion, we observe on average a decrease in the vibrational frequencies at room temperature. This leads to an increased stabilization of all polymorphs. Furthermore, we observe that the delta form is slightly more stabilized compared to the other forms. Thus, including anharmonicity into the models might allow the delta form to be the most stable polymorph in a larger temperature window than we obtain in the G–T diagrams in Fig. 8.

4. Conclusions

In this contribution, we demonstrate that it is possible to obtain a stability order at temperatures above room temperature which agrees with experimental results. This is obtained by combining vibrational contributions to the free energy estimated from frequencies from NoMoRe with electronic energies from periodic DFT calculations. All our models predict that at high temperatures α and γ are stabilized by entropy and are the most stable polymorphic forms. These observations agree with previous investigations. Moreover, we observe that, due to configurational entropy arising from disorder, the γ form becomes more stable than α at elevated temperatures. Although our models can grasp these gross trends of the polymorph stabilities, we are still quite far away from the observed stabilities at room temperature. The work by Cherukuvada et al. (2010) strongly suggests that the δ form is the most stable below room temperature, whereas the α form is the most stable at room temperature, until eventually the γ form is the most stable until the melting point. We believe that a large part of these discrepancies between our models and the experimentally observed events are due to inaccurate assessment of the electronic energies. Even with a large basis set and D3 dispersion correction we are unable to predict the experimentally most plausible β/δ energy rank at 0 K. Of course, as we have discussed above, there is no direct evidence that the β polymorph is less stable than the δ polymorph at 0 K. Accurate electronic energies/lattice energies are crucial for predicting relative stability of polymorphic systems. It is remarkable that although advanced methods of computational chemistry have been developed there are still problems with calculations of electronic energies for such small rigid system as pyrazinamide, and different approaches lead to different stability ordering. For example: For model 2 (see Fig. 8) the stabilization of the delta form by 2 kJ mol⁻¹ at 0 K would have resulted in a stability ordering at room temperature in close agreement with the observations of Cherukuvada et al.

Aree and coworkers (Aree et al., 2013, 2014; Aree & Bürgi, 2012) conducted complete and beautiful analysis of stability ordering for glycine polymorphs. They carefully analyzed lattice energies, vibrational zero-point energies, vibrational enthalpies, and entropies and they found out that the most important contributions to the differences in the free energies of the polymorphs of glycine are the lattice energies, on one hand, and the zero-point energies, on the other. The pyrazinamide polymorphs are different – beside lattice energies, the entropy contributions to free energy differences are crucial for estimating stabilities and phase transition temperatures. Furthermore, it is important to consider not only the vibrational entropies, but also contributions from configurational entropy, which are arising from disorder. Here, we estimated those contributions from occupancies; in future work we will present some more advanced models for configurational entropy estimation for the γ pyrazinamide polymorph.

Supporting information

Computing details

(alpha10K)

Crystal data

C5H5N3O	Z = 4
Mr = 123.1	F(000) = 256
Monoclinic, P21/n	Dx = 1.504 Mg m^−3
Hall symbol: -P 2yabc	Mo Kα radiation, λ = 0.71073 Å
a = 3.5885 (9) Å	Cell parameters from 9779 reflections
b = 6.7605 (17) Å	θ = 3.2–36.2°
c = 22.434 (6) Å	µ = 0.11 mm^−1
β = 92.748 (8)°	T = 10 K
V = 543.6 (2) Å^3	Prism, colorless

Data collection

Bruker CCD diffractometer	1669 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.048
Graphite monochromator	θmax = 36.2°, θmin = 3.2°
Bruker CCD scans	h = −5→4
9779 measured reflections	k = −10→10
2486 independent reflections	l = −35→36

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.043	H-atom parameters constrained
wR(F^2) = 0.050	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.72	(Δ/σ)max = 0.009
2486 reflections	Δρmax = 0.70 e Å^−3
82 parameters	Δρmin = −0.37 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.04626 (17)	0.96722 (10)	0.08394 (3)	0.00907 (18)
N1	0.4338 (2)	0.56610 (12)	0.21265 (4)	0.0080 (2)
N2	0.4628 (2)	0.48882 (12)	0.08984 (3)	0.0071 (2)
N3	0.2338 (2)	0.77105 (11)	0.00877 (3)	0.0094 (2)
C1	0.3353 (2)	0.66144 (13)	0.11036 (4)	0.0059 (2)
C2	0.5534 (2)	0.39283 (13)	0.19177 (4)	0.0080 (2)
C3	0.1950 (2)	0.81339 (12)	0.06601 (3)	0.0066 (2)
C4	0.5700 (2)	0.35444 (14)	0.13091 (4)	0.0076 (2)
C5	0.3239 (2)	0.70026 (14)	0.17137 (4)	0.0072 (2)
H1n3	0.342764	0.661784	−0.001192	0.0113*
H2n3	0.150182	0.852614	−0.01873	0.0113*
H1c2	0.630481	0.291554	0.219712	0.0096*
H1c4	0.660583	0.228466	0.118164	0.0091*
H1c5	0.235047	0.826543	0.184153	0.0086*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0118 (3)	0.0069 (3)	0.0086 (3)	0.0031 (3)	0.0010 (2)	−0.0001 (3)
N1	0.0090 (4)	0.0077 (3)	0.0074 (4)	0.0000 (3)	0.0006 (3)	0.0004 (3)
N2	0.0074 (4)	0.0063 (3)	0.0078 (3)	0.0003 (3)	0.0008 (3)	0.0003 (3)
N3	0.0144 (4)	0.0081 (4)	0.0058 (4)	0.0046 (3)	0.0005 (3)	0.0010 (3)
C1	0.0055 (4)	0.0056 (4)	0.0065 (4)	−0.0004 (3)	0.0007 (3)	0.0005 (3)
C2	0.0082 (4)	0.0080 (4)	0.0077 (4)	0.0001 (3)	−0.0001 (3)	0.0019 (3)
C3	0.0060 (4)	0.0066 (4)	0.0072 (4)	−0.0001 (3)	0.0006 (3)	0.0005 (3)
C4	0.0079 (4)	0.0060 (4)	0.0090 (4)	0.0008 (3)	0.0013 (3)	0.0002 (3)
C5	0.0071 (4)	0.0070 (4)	0.0074 (4)	0.0001 (3)	0.0011 (3)	−0.0005 (3)

Geometric parameters (Å, º)

O1—C3	1.2446 (11)	N3—H2n3	0.87
N1—C2	1.3399 (13)	C1—C3	1.5002 (13)
N1—C5	1.3419 (13)	C1—C5	1.3961 (14)
N2—C1	1.3429 (13)	C2—C4	1.3940 (14)
N2—C4	1.3372 (13)	C2—H1c2	0.96
N3—C3	1.3295 (12)	C4—H1c4	0.96
N3—H1n3	0.87	C5—H1c5	0.96
C2—N1—C5	115.97 (8)	C4—C2—H1c2	118.84
C1—N2—C4	116.47 (8)	O1—C3—N3	123.95 (8)
C3—N3—H1n3	120	O1—C3—C1	119.55 (7)
C3—N3—H2n3	120	N3—C3—C1	116.49 (7)
H1n3—N3—H2n3	120	N2—C4—C2	121.60 (8)
N2—C1—C3	118.47 (8)	N2—C4—H1c4	119.2
N2—C1—C5	121.72 (8)	C2—C4—H1c4	119.2
C3—C1—C5	119.80 (8)	N1—C5—C1	121.88 (9)
N1—C2—C4	122.33 (8)	N1—C5—H1c5	119.06
N1—C2—H1c2	118.84	C1—C5—H1c5	119.06

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H1n3···N2^i	0.87	2.37	3.0655 (14)	137.28
N3—H2n3···O1^ii	0.87	2.01	2.8752 (14)	178.06
C4—H1c4···O1^iii	0.96	2.39	3.3252 (16)	163.66

Symmetry codes: (i) −x+1, −y+1, −z; (ii) −x, −y+2, −z; (iii) x+1, y−1, z.

(alpha122K)

Crystal data

C5H5N3O	Z = 4
Mr = 123.1	F(000) = 256
Monoclinic, P21/n	Dx = 1.480 Mg m^−3
Hall symbol: -P 2yabc	Mo Kα radiation, λ = 0.71073 Å
a = 3.633 (1) Å	Cell parameters from 49596 reflections
b = 6.753 (2) Å	θ = 1.8–50.0°
c = 22.546 (5) Å	µ = 0.11 mm^−1
β = 92.39 (2)°	T = 122 K
V = 552.7 (3) Å^3	Prism, colorless

Data collection

Nonius Kappa CCD diffractometer	Rint = 0.058
Radiation source: X-ray tube	θmax = 50.0°, θmin = 1.8°
49596 measured reflections	h = −7→7
5797 independent reflections	k = −14→14
3372 reflections with I > 3σ(I)	l = −48→48

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.037	H-atom parameters constrained
wR(F^2) = 0.048	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.97	(Δ/σ)max = 0.003
5797 reflections	Δρmax = 0.67 e Å^−3
82 parameters	Δρmin = −0.28 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.04766 (11)	0.96838 (6)	0.083573 (16)	0.02164 (9)
N1	0.43760 (13)	0.57110 (7)	0.212104 (18)	0.01981 (9)
N2	0.46057 (10)	0.49020 (6)	0.089971 (16)	0.01564 (7)
N3	0.22848 (14)	0.76950 (6)	0.008882 (16)	0.02294 (10)
C1	0.33459 (11)	0.66336 (6)	0.110297 (17)	0.01327 (8)
C2	0.55614 (13)	0.39750 (7)	0.19160 (2)	0.01839 (10)
C3	0.19371 (12)	0.81413 (6)	0.065870 (16)	0.01521 (8)
C4	0.56968 (13)	0.35721 (7)	0.13100 (2)	0.01710 (9)
C5	0.32592 (13)	0.70424 (7)	0.170880 (19)	0.01656 (9)
H1n3	0.342869	0.661931	−0.000923	0.0275*
H2n3	0.136825	0.84789	−0.018565	0.0275*
H1c2	0.634595	0.297187	0.219531	0.0221*
H1c4	0.65955	0.23091	0.118467	0.0205*
H1c5	0.237816	0.83087	0.183448	0.0199*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.03063 (17)	0.01680 (14)	0.01750 (13)	0.01203 (12)	0.00138 (12)	−0.00050 (11)
N1	0.02582 (17)	0.01937 (16)	0.01410 (13)	0.00367 (13)	−0.00087 (12)	0.00056 (12)
N2	0.01942 (14)	0.01291 (13)	0.01458 (12)	0.00452 (11)	0.00055 (10)	−0.00004 (10)
N3	0.0361 (2)	0.01927 (17)	0.01347 (13)	0.01463 (15)	0.00061 (13)	0.00027 (12)
C1	0.01441 (13)	0.01194 (14)	0.01343 (13)	0.00259 (10)	0.00023 (10)	−0.00002 (10)
C2	0.02129 (17)	0.01746 (17)	0.01632 (15)	0.00333 (13)	−0.00055 (12)	0.00338 (13)
C3	0.01813 (15)	0.01349 (14)	0.01399 (13)	0.00487 (11)	0.00038 (10)	0.00007 (11)
C4	0.02065 (16)	0.01338 (15)	0.01725 (15)	0.00463 (12)	0.00076 (12)	0.00153 (12)
C5	0.02044 (16)	0.01510 (15)	0.01409 (13)	0.00315 (12)	0.00015 (11)	−0.00120 (12)

Geometric parameters (Å, º)

O1—C3	1.2424 (8)	N3—H2n3	0.87
N1—C2	1.3379 (9)	C1—C3	1.5030 (8)
N1—C5	1.3436 (8)	C1—C5	1.3952 (8)
N2—C1	1.3433 (8)	C2—C4	1.3961 (9)
N2—C4	1.3375 (8)	C2—H1c2	0.96
N3—C3	1.3309 (8)	C4—H1c4	0.96
N3—H1n3	0.87	C5—H1c5	0.96
C2—N1—C5	116.08 (4)	C4—C2—H1c2	118.87
C1—N2—C4	116.36 (4)	O1—C3—N3	123.99 (4)
C3—N3—H1n3	120	O1—C3—C1	119.47 (4)
C3—N3—H2n3	120	N3—C3—C1	116.53 (4)
H1n3—N3—H2n3	120	N2—C4—C2	121.64 (4)
N2—C1—C3	118.28 (4)	N2—C4—H1c4	119.18
N2—C1—C5	121.88 (4)	C2—C4—H1c4	119.18
C3—C1—C5	119.83 (4)	N1—C5—C1	121.76 (4)
N1—C2—C4	122.27 (4)	N1—C5—H1c5	119.12
N1—C2—H1c2	118.86	C1—C5—H1c5	119.12

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H1n3···N2^i	0.87	2.39	3.0870 (12)	137.29
N3—H2n3···O1^ii	0.87	2.01	2.8828 (12)	176.92
C4—H1c4···O1^iii	0.96	2.42	3.3479 (15)	163.26

Symmetry codes: (i) −x+1, −y+1, −z; (ii) −x, −y+2, −z; (iii) x+1, y−1, z.

(beta10K)

Crystal data

C5H5N3O	Z = 4
Mr = 123.1	F(000) = 256
Monoclinic, P21/c	Dx = 1.518 Mg m^−3
Hall symbol: -P 2ycb	Mo Kα radiation, λ = 0.71073 Å
a = 14.3433 (9) Å	Cell parameters from 4273 reflections
b = 3.6086 (2) Å	θ = 2.9–32.8°
c = 10.6023 (7) Å	µ = 0.11 mm^−1
β = 100.982 (1)°	T = 10 K
V = 538.72 (6) Å^3	Prism, colorless

Data collection

Bruker APEX II CCD diffractometer	Rint = 0.011
Radiation source: X-ray tube	θmax = 32.8°, θmin = 2.9°
4273 measured reflections	h = −20→20
1853 independent reflections	k = −5→5
1620 reflections with I > 3σ(I)	l = −14→15

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.033	H-atom parameters constrained
wR(F^2) = 0.047	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.69	(Δ/σ)max = 0.006
1853 reflections	Δρmax = 0.53 e Å^−3
82 parameters	Δρmin = −0.24 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.10075 (4)	0.08701 (16)	0.13098 (6)	0.01041 (16)
N2	0.26708 (5)	0.52551 (18)	−0.03045 (6)	0.00861 (18)
N3	0.08402 (4)	0.26789 (19)	−0.07798 (6)	0.01029 (19)
N1	0.37683 (5)	0.47633 (19)	0.21811 (6)	0.00941 (18)
C4	0.35771 (5)	0.6392 (2)	−0.00375 (8)	0.0091 (2)
C2	0.41225 (5)	0.6123 (2)	0.11953 (8)	0.0092 (2)
C1	0.23193 (5)	0.3857 (2)	0.06768 (7)	0.0077 (2)
C5	0.28608 (5)	0.3646 (2)	0.19168 (8)	0.0089 (2)
C3	0.13194 (4)	0.2360 (2)	0.04208 (7)	0.0083 (2)
H1n3	0.111546	0.361273	−0.137119	0.0123*
H2n3	0.025176	0.195362	−0.097296	0.0123*
H1c4	0.385718	0.741879	−0.071325	0.0109*
H1c2	0.477145	0.693636	0.134257	0.011*
H1c5	0.257616	0.267626	0.259712	0.0107*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0098 (3)	0.0125 (3)	0.0091 (3)	−0.00132 (19)	0.00228 (19)	0.0012 (2)
N2	0.0088 (3)	0.0085 (3)	0.0087 (3)	0.0001 (2)	0.0018 (2)	−0.0003 (2)
N3	0.0079 (3)	0.0140 (3)	0.0086 (3)	−0.0019 (2)	0.0005 (2)	0.0010 (2)
N1	0.0089 (3)	0.0103 (3)	0.0088 (3)	0.0004 (2)	0.0011 (2)	−0.0009 (2)
C4	0.0094 (3)	0.0093 (3)	0.0089 (4)	−0.0003 (2)	0.0026 (2)	0.0000 (3)
C2	0.0082 (3)	0.0095 (3)	0.0098 (4)	−0.0001 (2)	0.0016 (2)	−0.0008 (3)
C1	0.0081 (3)	0.0072 (3)	0.0079 (3)	0.0006 (2)	0.0015 (2)	−0.0004 (3)
C5	0.0091 (3)	0.0095 (3)	0.0082 (3)	0.0002 (2)	0.0017 (2)	0.0002 (3)
C3	0.0082 (3)	0.0075 (3)	0.0091 (4)	0.0006 (2)	0.0014 (2)	−0.0007 (3)

Geometric parameters (Å, º)

O1—C3	1.2402 (10)	N1—C5	1.3404 (10)
N2—C4	1.3410 (10)	C4—C2	1.3928 (11)
N2—C1	1.3383 (11)	C4—H1c4	0.96
N3—C3	1.3315 (9)	C2—H1c2	0.96
N3—H1n3	0.87	C1—C5	1.3958 (10)
N3—H2n3	0.87	C1—C3	1.5081 (9)
N1—C2	1.3392 (11)	C5—H1c5	0.96
C4—N2—C1	116.41 (6)	C4—C2—H1c2	119.02
C3—N3—H1n3	120	N2—C1—C5	121.90 (7)
C3—N3—H2n3	120	N2—C1—C3	118.77 (6)
H1n3—N3—H2n3	120	C5—C1—C3	119.30 (7)
C2—N1—C5	116.40 (6)	N1—C5—C1	121.63 (8)
N2—C4—C2	121.69 (8)	N1—C5—H1c5	119.19
N2—C4—H1c4	119.15	C1—C5—H1c5	119.19
C2—C4—H1c4	119.15	O1—C3—N3	124.67 (6)
N1—C2—C4	121.95 (7)	O1—C3—C1	119.14 (6)
N1—C2—H1c2	119.02	N3—C3—C1	116.18 (7)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H1n3···O1^i	0.87	2.44	3.1836 (10)	143.62
N3—H2n3···O1^ii	0.87	2.05	2.9004 (9)	167.40
C4—H1c4···N1^iii	0.96	2.43	3.3173 (11)	152.80
C5—H1c5···N2^iv	0.96	2.44	3.3228 (11)	152.13

Symmetry codes: (i) x, −y+1/2, z−1/2; (ii) −x, −y, −z; (iii) x, −y+3/2, z−1/2; (iv) x, −y+1/2, z+1/2.

(beta122K)

Crystal data

C5H5N3O	Z = 4
Mr = 123.1	F(000) = 256
Monoclinic, P21/c	Dx = 1.507 Mg m^−3
Hall symbol: -P 2ycb	Mo Kα radiation, λ = 0.71073 Å
a = 14.3280 (3) Å	Cell parameters from 47668 reflections
b = 3.6330 (13) Å	θ = 1.5–50.0°
c = 10.6280 (17) Å	µ = 0.11 mm^−1
β = 101.169 (7)°	T = 122 K
V = 542.7 (2) Å^3	Prism, colorless

Data collection

Nonius Kappa CCD diffractometer	Rint = 0.039
Radiation source: X-ray tube	θmax = 50.0°, θmin = 1.5°
47668 measured reflections	h = −30→30
5683 independent reflections	k = −7→7
3664 reflections with I > 3σ(I)	l = −22→22

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.037	H-atom parameters constrained
wR(F^2) = 0.057	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.73	(Δ/σ)max = 0.007
5683 reflections	Δρmax = 0.61 e Å^−3
82 parameters	Δρmin = −0.28 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.10104 (2)	0.08967 (10)	0.13054 (3)	0.01714 (8)
N2	0.26707 (3)	0.52114 (11)	−0.03056 (3)	0.01258 (8)
N3	0.08433 (2)	0.26399 (12)	−0.07818 (3)	0.01675 (9)
N1	0.37652 (3)	0.48180 (12)	0.21780 (3)	0.01501 (9)
C4	0.35746 (3)	0.63614 (13)	−0.00370 (4)	0.01372 (9)
C2	0.41194 (3)	0.61422 (13)	0.11939 (4)	0.01401 (9)
C1	0.23198 (3)	0.38497 (11)	0.06739 (4)	0.01089 (8)
C5	0.28601 (3)	0.36893 (13)	0.19127 (4)	0.01363 (9)
C3	0.13210 (2)	0.23566 (12)	0.04176 (4)	0.01257 (9)
H1n3	0.111103	0.364314	−0.136541	0.0201*
H2n3	0.026283	0.182203	−0.098338	0.0201*
H1c4	0.385442	0.736548	−0.071296	0.0165*
H1c2	0.476822	0.696444	0.134195	0.0168*
H1c5	0.257526	0.274435	0.25931	0.0163*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.01318 (13)	0.02322 (17)	0.01516 (12)	−0.00382 (11)	0.00314 (10)	0.00270 (12)
N2	0.01145 (13)	0.01548 (15)	0.01071 (12)	−0.00073 (11)	0.00193 (10)	0.00007 (11)
N3	0.01118 (13)	0.02421 (19)	0.01374 (14)	−0.00358 (13)	−0.00037 (11)	0.00194 (13)
N1	0.01150 (13)	0.02144 (17)	0.01149 (13)	−0.00029 (13)	0.00068 (10)	−0.00097 (12)
C4	0.01220 (14)	0.01673 (17)	0.01258 (14)	−0.00136 (13)	0.00323 (11)	0.00041 (13)
C2	0.01049 (14)	0.01750 (18)	0.01385 (15)	−0.00168 (13)	0.00189 (11)	−0.00182 (13)
C1	0.00965 (13)	0.01226 (15)	0.01059 (13)	0.00048 (12)	0.00154 (10)	−0.00025 (12)
C5	0.01159 (14)	0.01849 (18)	0.01063 (14)	−0.00022 (13)	0.00177 (11)	0.00119 (13)
C3	0.01008 (14)	0.01405 (16)	0.01336 (14)	−0.00013 (12)	0.00176 (11)	−0.00024 (13)

Geometric parameters (Å, º)

O1—C3	1.2379 (6)	N1—C5	1.3370 (6)
N2—C4	1.3379 (6)	C4—C2	1.3898 (7)
N2—C1	1.3357 (6)	C4—H1c4	0.96
N3—C3	1.3289 (6)	C2—H1c2	0.96
N3—H1n3	0.87	C1—C5	1.3933 (7)
N3—H2n3	0.87	C1—C3	1.5050 (5)
N1—C2	1.3374 (7)	C5—H1c5	0.96
C4—N2—C1	116.38 (3)	C4—C2—H1c2	119.07
C3—N3—H1n3	120	N2—C1—C5	121.86 (4)
C3—N3—H2n3	120	N2—C1—C3	118.73 (3)
H1n3—N3—H2n3	120	C5—C1—C3	119.39 (4)
C2—N1—C5	116.42 (3)	N1—C5—C1	121.68 (4)
N2—C4—C2	121.80 (4)	N1—C5—H1c5	119.16
N2—C4—H1c4	119.1	C1—C5—H1c5	119.16
C2—C4—H1c4	119.1	O1—C3—N3	124.74 (4)
N1—C2—C4	121.85 (4)	O1—C3—C1	119.08 (3)
N1—C2—H1c2	119.07	N3—C3—C1	116.15 (4)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H1n3···O1^i	0.87	2.46	3.1955 (11)	143.02
N3—H2n3···O1^ii	0.87	2.04	2.9056 (6)	170.34
C4—H1c4···N1^iii	0.96	2.44	3.3279 (11)	152.87
C5—H1c5···N2^iv	0.96	2.46	3.3366 (11)	152.09

Symmetry codes: (i) x, −y+1/2, z−1/2; (ii) −x, −y, −z; (iii) x, −y+3/2, z−1/2; (iv) x, −y+1/2, z+1/2.

(gamma10K)

Crystal data

C5H5N3O	Z = 2
Mr = 123.1	F(000) = 128
Monoclinic, Pc	Dx = 1.535 Mg m^−3
Hall symbol: P -2yc	Mo Kα radiation, λ = 0.71073 Å
a = 7.1818 (7) Å	Cell parameters from 4051 reflections
b = 3.6295 (4) Å	θ = 5.6–33.5°
c = 10.6533 (11) Å	µ = 0.11 mm^−1
β = 106.377 (1)°	T = 10 K
V = 266.43 (5) Å^3	Prism, colorless

Data collection

Bruker APEX II CCD diffractometer	Rint = 0.018
Radiation source: X-ray tube	θmax = 33.5°, θmin = 5.6°
4051 measured reflections	h = −11→11
1941 independent reflections	k = −5→5
1797 reflections with I > 3σ(I)	l = −16→16

Refinement

Refinement on F	2 constraints
R[F^2 > 2σ(F^2)] = 0.037	H-atom parameters constrained
wR(F^2) = 0.042	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.98	(Δ/σ)max = 0.063
1941 reflections	Δρmax = 0.36 e Å^−3
87 parameters	Δρmin = −0.25 e Å^−3
0 restraints	Absolute structure: 901 of Friedel pairs used in the refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
O1a	0.619126	−0.1368 (3)	0.530832	0.0164 (3)	0.8455 (10)
N1a	0.04605 (18)	0.2202 (3)	0.40898 (15)	0.0128 (3)	0.8455 (10)
N2a	0.27593 (15)	0.2869 (3)	0.66896 (13)	0.0120 (3)	0.8455 (10)
N3a	0.64937 (14)	0.0493 (3)	0.73905 (13)	0.0163 (3)	0.8455 (10)
C4a	0.08998 (18)	0.3954 (4)	0.63175 (14)	0.0133 (3)	0.8455 (10)
C3a	0.55256 (14)	0.0063 (3)	0.61342 (14)	0.0126 (3)	0.8455 (10)
C2a	−0.02349 (18)	0.3608 (4)	0.50272 (15)	0.0129 (3)	0.8455 (10)
C1a	0.34579 (16)	0.1450 (4)	0.57524 (15)	0.0109 (3)	0.8455 (10)
C5a	0.23294 (19)	0.1129 (4)	0.44641 (15)	0.0121 (3)	0.8455 (10)
H1n3a	0.589844	0.132383	0.793958	0.0196*	0.8455 (10)
H2n3a	0.772124	−0.005689	0.766194	0.0196*	0.8455 (10)
H1c4a	0.033808	0.499441	0.69554	0.016*	0.8455 (10)
H1c2a	−0.156264	0.440495	0.480252	0.0155*	0.8455 (10)
H1c5a	0.289624	0.011602	0.382451	0.0145*	0.8455 (10)
O1b	−0.0083 (3)	0.3036 (13)	0.3879 (3)	0.0164 (3)	0.1545 (10)
N1b	0.5614 (4)	−0.0688 (15)	0.5182 (3)	0.0128 (3)	0.1545 (10)
N2b	0.3659 (2)	0.2342 (11)	0.68783 (17)	0.0120 (3)	0.1545 (10)
N3b	−0.0068 (4)	0.4664 (15)	0.5939 (4)	0.0163 (3)	0.1545 (10)
C4b	0.5511 (3)	0.1231 (12)	0.7308 (3)	0.0133 (4)	0.1545 (10)
C3b	0.0730 (2)	0.3262 (12)	0.5057 (3)	0.0126 (4)	0.1545 (10)
C2b	0.6475 (3)	−0.0260 (14)	0.6461 (4)	0.0129 (4)	0.1545 (10)
C1b	0.27952 (17)	0.1925 (10)	0.55958 (16)	0.0109 (4)	0.1545 (10)
C5b	0.3753 (4)	0.0414 (13)	0.4754 (2)	0.0121 (4)	0.1545 (10)
H1n3b	0.062862	0.494751	0.674589	0.0196*	0.1545 (10)
H2n3b	−0.128571	0.529664	0.570856	0.0196*	0.1545 (10)
H1c4b	0.618712	0.147043	0.822016	0.016*	0.1545 (10)
H1c2b	0.78033	−0.100715	0.680798	0.0155*	0.1545 (10)
H1c5b	0.307145	0.014819	0.384379	0.0145*	0.1545 (10)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1a	0.0114 (4)	0.0171 (5)	0.0209 (5)	0.0021 (3)	0.0052 (3)	−0.0011 (4)
N1a	0.0113 (4)	0.0145 (5)	0.0115 (5)	0.0003 (4)	0.0015 (3)	−0.0009 (4)
N2a	0.0115 (4)	0.0129 (5)	0.0116 (5)	−0.0001 (4)	0.0032 (3)	0.0012 (4)
N3a	0.0106 (4)	0.0197 (5)	0.0167 (5)	0.0033 (4)	0.0005 (4)	0.0003 (4)
C4a	0.0124 (5)	0.0145 (5)	0.0143 (5)	0.0000 (4)	0.0058 (4)	−0.0006 (5)
C3a	0.0088 (4)	0.0117 (5)	0.0154 (5)	−0.0005 (4)	0.0005 (4)	0.0020 (5)
C2a	0.0098 (4)	0.0147 (6)	0.0144 (5)	0.0007 (4)	0.0038 (4)	−0.0010 (5)
C1a	0.0090 (5)	0.0109 (5)	0.0128 (5)	−0.0015 (4)	0.0030 (4)	0.0006 (4)
C5a	0.0105 (4)	0.0141 (6)	0.0113 (5)	−0.0001 (4)	0.0025 (4)	−0.0009 (5)
O1b	0.0111 (4)	0.0196 (5)	0.0166 (6)	0.0013 (3)	0.0011 (4)	0.0026 (4)
N1b	0.0117 (4)	0.0147 (6)	0.0127 (6)	0.0013 (4)	0.0046 (4)	−0.0002 (4)
N2b	0.0116 (4)	0.0114 (5)	0.0131 (6)	−0.0002 (4)	0.0034 (4)	−0.0011 (4)
N3b	0.0112 (4)	0.0196 (6)	0.0183 (7)	0.0046 (4)	0.0042 (4)	0.0007 (4)
C4b	0.0119 (5)	0.0147 (6)	0.0121 (7)	−0.0012 (4)	0.0015 (5)	−0.0005 (5)
C3b	0.0093 (4)	0.0112 (6)	0.0181 (7)	0.0009 (4)	0.0053 (5)	0.0016 (4)
C2b	0.0097 (5)	0.0156 (7)	0.0125 (7)	0.0003 (4)	0.0018 (5)	0.0004 (5)
C1b	0.0090 (5)	0.0106 (6)	0.0133 (6)	−0.0014 (4)	0.0033 (5)	0.0001 (4)
C5b	0.0106 (4)	0.0143 (6)	0.0116 (7)	0.0003 (4)	0.0034 (5)	−0.0007 (4)

Geometric parameters (Å, º)

O1a—C3a	1.2285 (15)	C2a—C3b	0.696 (2)
O1a—N1b	0.468 (4)	C1a—C5a	1.3880 (19)
O1a—C2b	1.253 (4)	C1a—N2b	1.211 (3)
N1a—C2a	1.337 (2)	C1a—C1b	0.489 (2)
N1a—C5a	1.3455 (18)	C1a—C5b	1.202 (3)
N1a—O1b	0.495 (4)	C5a—H1c5a	0.96
N1a—C3b	1.065 (3)	C5a—C1b	1.192 (2)
N2a—C4a	1.3406 (17)	C5a—C5b	1.015 (3)
N2a—C1a	1.340 (2)	C5a—H1c5b	1.0228
N2a—N2b	0.649 (2)	H1n3a—C4b	0.6525
N2a—C1b	1.222 (2)	H1n3a—H1c4b	0.3166
N3a—C3a	1.3320 (18)	H1c4a—H1n3b	0.3463
N3a—H1n3a	0.87	H1c5a—C5b	1.0136
N3a—H2n3a	0.87	H1c5a—H1c5b	0.1222
N3a—C4b	0.737 (3)	O1b—C3b	1.229 (4)
N3a—C2b	1.023 (4)	N1b—C2b	1.337 (5)
C4a—C2a	1.3921 (19)	N1b—C5b	1.346 (4)
C4a—H1c4a	0.96	N2b—C4b	1.341 (3)
C4a—N3b	0.744 (3)	N2b—C1b	1.340 (2)
C4a—C3b	1.337 (3)	N3b—C3b	1.332 (5)
C4a—H1n3b	0.6529	N3b—H1n3b	0.87
C3a—C1a	1.5111 (16)	N3b—H2n3b	0.87
C3a—N1b	1.069 (4)	C4b—C2b	1.392 (5)
C3a—C4b	1.323 (3)	C4b—H1c4b	0.96
C3a—C2b	0.683 (2)	C3b—C1b	1.511 (3)
C2a—H1c2a	0.96	C2b—H1c2b	0.96
C2a—O1b	1.275 (4)	C1b—C5b	1.388 (4)
C2a—N3b	1.020 (4)	C5b—H1c5b	0.96
C3a—O1a—N1b	59.4 (5)	N1a—O1b—C2a	86.3 (5)
C3a—O1a—C2b	31.90 (12)	N1a—O1b—C3b	59.4 (4)
N1b—O1a—C2b	89.9 (5)	C2a—O1b—C3b	32.23 (14)
C2a—N1a—C5a	116.14 (13)	O1a—N1b—C3a	98.4 (5)
C2a—N1a—O1b	72.1 (5)	O1a—N1b—C2b	69.6 (4)
C2a—N1a—C3b	31.16 (11)	O1a—N1b—C5b	165.4 (8)
C5a—N1a—O1b	154.8 (5)	C3a—N1b—C2b	30.44 (16)
C5a—N1a—C3b	85.62 (15)	C3a—N1b—C5b	85.8 (3)
O1b—N1a—C3b	97.1 (5)	C2b—N1b—C5b	116.1 (3)
C4a—N2a—C1a	116.34 (12)	N2a—N2b—C1a	86.7 (2)
C4a—N2a—N2b	179.2 (3)	N2a—N2b—C4b	178.1 (3)
C4a—N2a—C1b	95.02 (12)	N2a—N2b—C1b	65.4 (2)
C1a—N2a—N2b	64.4 (2)	C1a—N2b—C4b	95.0 (2)
C1a—N2a—C1b	21.38 (9)	C1a—N2b—C1b	21.35 (11)
N2b—N2a—C1b	85.8 (2)	C4b—N2b—C1b	116.3 (2)
C3a—N3a—H1n3a	120	C4a—N3b—C2a	103.1 (5)
C3a—N3a—H2n3a	120	C4a—N3b—C3b	74.2 (3)
C3a—N3a—C4b	73.2 (2)	C4a—N3b—H1n3b	46.92
C3a—N3a—C2b	30.22 (14)	C4a—N3b—H2n3b	162.8
H1n3a—N3a—H2n3a	120	C2a—N3b—C3b	30.97 (16)
H1n3a—N3a—C4b	47.01	C2a—N3b—H1n3b	150.01
H1n3a—N3a—C2b	150.22	C2a—N3b—H2n3b	89.5
H2n3a—N3a—C4b	165.94	C3b—N3b—H1n3b	120
H2n3a—N3a—C2b	89.78	C3b—N3b—H2n3b	120
C4b—N3a—C2b	103.3 (3)	H1n3b—N3b—H2n3b	120
N2a—C4a—C2a	121.49 (14)	N3a—C4b—C3a	74.5 (3)
N2a—C4a—H1c4a	119.26	N3a—C4b—H1n3a	77.27
N2a—C4a—N3b	164.2 (4)	N3a—C4b—N2b	167.1 (4)
N2a—C4a—C3b	92.44 (14)	N3a—C4b—C2b	45.7 (2)
N2a—C4a—H1n3b	115.1	N3a—C4b—H1c4b	73.61
C2a—C4a—H1c4a	119.25	C3a—C4b—H1n3a	151.17
C2a—C4a—N3b	45.5 (4)	C3a—C4b—N2b	92.59 (18)
C2a—C4a—C3b	29.48 (10)	C3a—C4b—C2b	28.97 (13)
C2a—C4a—H1n3b	122.22	C3a—C4b—H1c4b	148.08
H1c4a—C4a—N3b	74.49	H1n3a—C4b—N2b	115.51
H1c4a—C4a—C3b	147.9	H1n3a—C4b—C2b	122.84
H1c4a—C4a—H1n3b	11.59	H1n3a—C4b—H1c4b	5.44
N3b—C4a—C3b	73.4 (4)	N2b—C4b—C2b	121.5 (2)
N3b—C4a—H1n3b	76.73	N2b—C4b—H1c4b	119.26
C3b—C4a—H1n3b	147.66	C2b—C4b—H1c4b	119.25
O1a—C3a—N3a	124.81 (9)	N1a—C3b—C4a	168.3 (4)
O1a—C3a—C1a	119.96 (11)	N1a—C3b—C2a	96.5 (3)
O1a—C3a—N1b	22.1 (2)	N1a—C3b—O1b	23.6 (2)
O1a—C3a—C4b	157.02 (13)	N1a—C3b—N3b	145.40 (19)
O1a—C3a—C2b	76.1 (4)	N1a—C3b—C1b	98.2 (2)
N3a—C3a—C1a	115.23 (12)	C4a—C3b—C2a	79.6 (3)
N3a—C3a—N1b	146.01 (19)	C4a—C3b—O1b	157.0 (2)
N3a—C3a—C4b	32.22 (11)	C4a—C3b—N3b	32.37 (16)
N3a—C3a—C2b	49.0 (3)	C4a—C3b—C1b	82.96 (15)
C1a—C3a—N1b	98.42 (19)	C2a—C3b—O1b	77.6 (3)
C1a—C3a—C4b	83.01 (13)	C2a—C3b—N3b	48.9 (3)
C1a—C3a—C2b	163.5 (4)	C2a—C3b—C1b	158.9 (4)
N1b—C3a—C4b	175.2 (3)	O1b—C3b—N3b	124.8 (2)
N1b—C3a—C2b	97.1 (4)	O1b—C3b—C1b	120.0 (3)
C4b—C3a—C2b	81.1 (4)	N3b—C3b—C1b	115.2 (2)
N1a—C2a—C4a	122.28 (12)	O1a—C2b—N3a	171.1 (3)
N1a—C2a—H1c2a	118.86	O1a—C2b—C3a	72.0 (3)
N1a—C2a—O1b	21.66 (16)	O1a—C2b—N1b	20.50 (19)
N1a—C2a—N3b	152.46 (19)	O1a—C2b—C4b	141.87 (19)
N1a—C2a—C3b	52.3 (3)	O1a—C2b—H1c2b	98.94
C4a—C2a—H1c2a	118.86	N3a—C2b—C3a	100.8 (4)
C4a—C2a—O1b	141.00 (15)	N3a—C2b—N1b	153.3 (3)
C4a—C2a—N3b	31.4 (2)	N3a—C2b—C4b	31.00 (15)
C4a—C2a—C3b	70.9 (3)	N3a—C2b—H1c2b	87.87
H1c2a—C2a—O1b	99.08	C3a—C2b—N1b	52.5 (3)
H1c2a—C2a—N3b	88.05	C3a—C2b—C4b	69.9 (3)
H1c2a—C2a—C3b	166.38	C3a—C2b—H1c2b	170.41
O1b—C2a—N3b	163.0 (3)	N1b—C2b—C4b	122.3 (3)
O1b—C2a—C3b	70.2 (3)	N1b—C2b—H1c2b	118.86
N3b—C2a—C3b	100.1 (3)	C4b—C2b—H1c2b	118.86
N2a—C1a—C3a	118.25 (11)	N2a—C1b—C1a	93.1 (3)
N2a—C1a—C5a	122.14 (12)	N2a—C1b—C5a	163.14 (15)
N2a—C1a—N2b	28.91 (11)	N2a—C1b—N2b	28.87 (11)
N2a—C1a—C1b	65.5 (3)	N2a—C1b—C3b	89.42 (18)
N2a—C1a—C5b	167.39 (17)	N2a—C1b—C5b	151.00 (16)
C3a—C1a—C5a	119.58 (14)	C1a—C1b—C5a	103.2 (4)
C3a—C1a—N2b	89.36 (13)	C1a—C1b—N2b	64.3 (3)
C3a—C1a—C1b	175.6 (3)	C1a—C1b—C3b	177.2 (5)
C3a—C1a—C5b	74.26 (15)	C1a—C1b—C5b	57.9 (3)
C5a—C1a—N2b	151.04 (16)	C5a—C1b—N2b	167.3 (3)
C5a—C1a—C1b	56.8 (3)	C5a—C1b—C3b	74.24 (15)
C5a—C1a—C5b	45.44 (14)	C5a—C1b—C5b	45.55 (14)
N2b—C1a—C1b	94.4 (3)	N2b—C1b—C3b	118.3 (2)
N2b—C1a—C5b	163.43 (18)	N2b—C1b—C5b	122.14 (18)
C1b—C1a—C5b	101.9 (3)	C3b—C1b—C5b	119.58 (18)
N1a—C5a—C1a	121.62 (15)	C1a—C5b—C5a	77.0 (2)
N1a—C5a—H1c5a	119.19	C1a—C5b—H1c5a	133.45
N1a—C5a—C1b	101.62 (16)	C1a—C5b—N1b	101.5 (2)
N1a—C5a—C5b	178.0 (3)	C1a—C5b—C1b	20.18 (10)
N1a—C5a—H1c5b	124.56	C1a—C5b—H1c5b	139.3
C1a—C5a—H1c5a	119.19	C5a—C5b—H1c5a	56.49
C1a—C5a—C1b	20.07 (11)	C5a—C5b—N1b	176.6 (4)
C1a—C5a—C5b	57.55 (18)	C5a—C5b—C1b	56.98 (19)
C1a—C5a—H1c5b	113.75	C5a—C5b—H1c5b	62.3
H1c5a—C5a—C1b	139.14	H1c5a—C5b—N1b	124.83
H1c5a—C5a—C5b	61.68	H1c5a—C5b—C1b	113.47
H1c5a—C5a—H1c5b	6.07	H1c5a—C5b—H1c5b	6.38
C1b—C5a—C5b	77.5 (2)	N1b—C5b—C1b	121.6 (2)
C1b—C5a—H1c5b	133.55	N1b—C5b—H1c5b	119.19
C5b—C5a—H1c5b	56.21	C1b—C5b—H1c5b	119.19
N3a—H1n3a—C4b	55.71	C4a—H1n3b—H1c4a	146.14
N3a—H1n3a—H1c4b	112.21	C4a—H1n3b—N3b	56.36
C4b—H1n3a—H1c4b	163.3	H1c4a—H1n3b—N3b	111.06
C4a—H1c4a—H1n3b	22.26	H1n3a—H1c4b—C4b	11.26
C5a—H1c5a—C5b	61.83	C5a—H1c5b—H1c5a	56.11
C5a—H1c5a—H1c5b	117.82	C5a—H1c5b—C5b	61.49
C5b—H1c5a—H1c5b	60.84	H1c5a—H1c5b—C5b	112.78

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3a—H1n3a···O1a^i	0.87	2.47	3.1924 (15)	140.53
N3a—H1n3a···N1b^i	0.87	2.47	3.211 (4)	144.07
C4b—H1n3a···O1a^i	0.65	2.47	3.095 (3)	160.31
C4b—H1n3a···N1b^i	0.65	2.47	3.048 (5)	150.07
N3a—H2n3a···N1a^ii	0.87	2.26	3.0728 (16)	155.70
N3a—H2n3a···O1b^ii	0.87	2.05	2.829 (3)	149.30
C2b—H2n3a···N1a^ii	1.34	2.26	3.466 (3)	147.57
C2b—H2n3a···O1b^ii	1.34	2.05	3.189 (4)	139.81
C4a—H1c4a···N1a^iii	0.96	2.47	3.361 (2)	154.24
C4a—H1c4a···O1b^iii	0.96	2.27	3.198 (4)	162.26
N3b—H1c4a···N1a^iii	1.05	2.47	3.462 (4)	158.05
N3b—H1c4a···O1b^iii	1.05	2.27	3.244 (6)	154.39
C2a—H1c2a···O1a^iv	0.96	2.40	3.2306 (16)	145.25
C5a—H1c5a···N2a^v	0.96	2.50	3.384 (2)	153.81
C5a—H1c5a···N2b^v	0.96	2.46	3.401 (3)	168.01
C5b—H1c5a···N2a^v	1.01	2.50	3.358 (3)	142.52
C5b—H1c5a···N2b^v	1.01	2.46	3.205 (4)	130.15
C2a—H2n3b···O1a^iv	1.33	2.12	3.2306 (16)	137.32
N3b—H2n3b···O1a^iv	0.87	2.12	2.954 (4)	160.33
N3a—H1c4b···O1a^i	1.03	2.22	3.1924 (15)	155.55
N3a—H1c4b···N1b^i	1.03	2.26	3.211 (4)	152.57
C4b—H1c4b···O1a^i	0.96	2.22	3.095 (3)	150.29
C4b—H1c4b···N1b^i	0.96	2.26	3.048 (5)	138.85
C2b—H1c2b···O1b^ii	0.96	2.41	3.189 (4)	137.60
C5a—H1c5b···N2a^v	1.02	2.50	3.384 (2)	144.98
C5a—H1c5b···N2b^v	1.02	2.42	3.401 (3)	159.57
C5b—H1c5b···N2a^v	0.96	2.50	3.358 (3)	149.44
C5b—H1c5b···N2b^v	0.96	2.42	3.205 (4)	138.28

Symmetry codes: (i) x, −y, z+1/2; (ii) x+1, −y, z+1/2; (iii) x, −y+1, z+1/2; (iv) x−1, y+1, z; (v) x, −y, z−1/2.

(gamma122K)

Crystal data

C5H5N3O	Z = 2
Mr = 123.1	F(000) = 128
Monoclinic, Pc	Dx = 1.524 Mg m^−3
Hall symbol: P -2yc	Mo Kα radiation, λ = 0.71073 Å
a = 7.1730 (17) Å	Cell parameters from 17605 reflections
b = 3.6500 (13) Å	θ = 5.6–54.5°
c = 10.686 (2) Å	µ = 0.11 mm^−1
β = 106.487 (17)°	T = 122 K
V = 268.27 (13) Å^3	Prism, colorless

Data collection

Nonius Kappa CCD diffractometer	Rint = 0.042
Radiation source: X-ray tube	θmax = 54.5°, θmin = 5.6°
17605 measured reflections	h = −16→16
5658 independent reflections	k = −7→8
3415 reflections with I > 3σ(I)	l = −24→24

Refinement

Refinement on F	2 constraints
R[F^2 > 2σ(F^2)] = 0.047	H-atom parameters constrained
wR(F^2) = 0.055	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.81	(Δ/σ)max = 0.048
5658 reflections	Δρmax = 0.54 e Å^−3
87 parameters	Δρmin = −0.30 e Å^−3
0 restraints	Absolute structure: 2369 of Friedel pairs used in the refinement

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
O1a	0.619126	−0.13465 (18)	0.530832	0.02294 (15)	0.8102 (6)
N1a	0.04711 (10)	0.22907 (18)	0.40821 (8)	0.01715 (14)	0.8102 (6)
N2a	0.27610 (8)	0.28411 (16)	0.66800 (8)	0.01484 (13)	0.8102 (6)
N3a	0.64923 (8)	0.0452 (2)	0.73854 (8)	0.02208 (15)	0.8102 (6)
C4a	0.09127 (10)	0.3950 (2)	0.63059 (8)	0.01717 (15)	0.8102 (6)
C3a	0.55222 (8)	0.00686 (17)	0.61309 (8)	0.01585 (14)	0.8102 (6)
C2a	−0.02217 (9)	0.36676 (19)	0.50179 (8)	0.01671 (16)	0.8102 (6)
C1a	0.34612 (8)	0.14585 (19)	0.57464 (8)	0.01220 (12)	0.8102 (6)
C5a	0.23349 (10)	0.11906 (19)	0.44580 (8)	0.01509 (14)	0.8102 (6)
H1n3a	0.587973	0.110127	0.794565	0.0265*	0.8102 (6)
H2n3a	0.773893	0.00544	0.764514	0.0265*	0.8102 (6)
H1c4a	0.035131	0.497168	0.694386	0.0206*	0.8102 (6)
H1c2a	−0.15468	0.448935	0.479393	0.0201*	0.8102 (6)
H1c5a	0.29022	0.019378	0.381921	0.0181*	0.8102 (6)
O1b	−0.00731 (13)	0.3129 (6)	0.38739 (15)	0.02294 (17)	0.1898 (6)
N1b	0.5618 (2)	−0.0630 (7)	0.51893 (16)	0.01715 (16)	0.1898 (6)
N2b	0.36472 (12)	0.2377 (5)	0.68678 (9)	0.01484 (15)	0.1898 (6)
N3b	−0.00783 (17)	0.4698 (7)	0.59240 (17)	0.02208 (18)	0.1898 (6)
C4b	0.54889 (13)	0.1252 (5)	0.73004 (14)	0.01717 (18)	0.1898 (6)
C3b	0.07339 (10)	0.3318 (5)	0.50512 (13)	0.01585 (16)	0.1898 (6)
C2b	0.64648 (15)	−0.0230 (6)	0.64661 (17)	0.01671 (18)	0.1898 (6)
C1b	0.27928 (8)	0.1984 (4)	0.55896 (8)	0.01220 (15)	0.1898 (6)
C5b	0.37603 (17)	0.0486 (5)	0.47553 (11)	0.01509 (16)	0.1898 (6)
H1n3b	0.063062	0.512883	0.671711	0.0265*	0.1898 (6)
H2n3b	−0.1318	0.516917	0.570153	0.0265*	0.1898 (6)
H1c4b	0.615801	0.147307	0.821263	0.0206*	0.1898 (6)
H1c2b	0.779155	−0.099138	0.681976	0.0201*	0.1898 (6)
H1c5b	0.308519	0.024207	0.384481	0.0181*	0.1898 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1a	0.01475 (18)	0.0279 (3)	0.0265 (3)	0.00582 (17)	0.00646 (17)	−0.0019 (2)
N1a	0.01330 (19)	0.0227 (3)	0.0138 (2)	0.00201 (17)	0.00109 (16)	−0.00080 (19)
N2a	0.01402 (18)	0.0187 (2)	0.01162 (19)	0.00105 (17)	0.00335 (14)	−0.00043 (18)
N3a	0.01380 (19)	0.0281 (3)	0.0201 (2)	0.00430 (18)	−0.00200 (17)	0.0000 (2)
C4a	0.0153 (2)	0.0208 (3)	0.0164 (2)	0.00226 (19)	0.00621 (19)	−0.0019 (2)
C3a	0.01100 (17)	0.0159 (2)	0.0189 (3)	0.00087 (16)	0.00150 (17)	0.00188 (19)
C2a	0.0120 (2)	0.0197 (3)	0.0182 (3)	0.00339 (19)	0.00399 (18)	0.0001 (2)
C1a	0.01017 (19)	0.0134 (2)	0.0126 (2)	−0.00061 (16)	0.00252 (14)	0.00024 (18)
C5a	0.01245 (19)	0.0206 (3)	0.0116 (2)	0.00148 (18)	0.00244 (16)	−0.0018 (2)
O1b	0.01432 (19)	0.0304 (3)	0.0210 (3)	0.00446 (18)	0.0000 (2)	0.0020 (2)
N1b	0.0138 (2)	0.0217 (3)	0.0166 (3)	0.00330 (18)	0.0053 (2)	−0.0018 (2)
N2b	0.01411 (19)	0.0174 (2)	0.0130 (3)	0.00115 (17)	0.00381 (18)	−0.00239 (17)
N3b	0.0150 (2)	0.0277 (3)	0.0250 (3)	0.00734 (19)	0.0078 (2)	0.0004 (2)
C4b	0.0149 (2)	0.0216 (3)	0.0134 (3)	0.0011 (2)	0.0014 (2)	−0.0008 (2)
C3b	0.01138 (18)	0.0156 (3)	0.0209 (3)	0.00191 (17)	0.00498 (19)	0.0016 (2)
C2b	0.0119 (2)	0.0199 (3)	0.0168 (3)	0.0029 (2)	0.0017 (2)	0.0005 (2)
C1b	0.0103 (2)	0.0129 (2)	0.0136 (3)	−0.00024 (16)	0.00377 (18)	−0.00041 (17)
C5b	0.0126 (2)	0.0203 (3)	0.0124 (3)	0.00195 (18)	0.0037 (2)	−0.0022 (2)

Geometric parameters (Å, º)

O1a—C3a	1.2285 (9)	C2a—C3b	0.6881 (12)
O1a—N1b	0.4736 (18)	C1a—C5a	1.3880 (12)
O1a—C2b	1.2639 (19)	C1a—N2b	1.2145 (14)
N1a—C2a	1.3348 (13)	C1a—C1b	0.4991 (10)
N1a—C5a	1.3436 (11)	C1a—C5b	1.1928 (17)
N1a—O1b	0.4961 (16)	C5a—H1c5a	0.96
N1a—C3b	1.0667 (17)	C5a—C1b	1.1952 (13)
N2a—C4a	1.3344 (11)	C5a—C5b	1.0139 (15)
N2a—C1a	1.3366 (12)	C5a—H1c5b	1.0193
N2a—N2b	0.6330 (11)	H1n3a—C4b	0.6689
N2a—C1b	1.2129 (13)	H1n3a—H1c4b	0.3276
N3a—C3a	1.3309 (12)	H1c4a—H1n3b	0.3601
N3a—H1n3a	0.87	H1c5a—C5b	1.0205
N3a—H2n3a	0.87	H1c5a—H1c5b	0.1275
N3a—C4b	0.7578 (13)	O1b—C3b	1.229 (2)
N3a—C2b	1.008 (2)	N1b—C2b	1.335 (2)
C4a—C2a	1.3898 (13)	N1b—C5b	1.344 (2)
C4a—H1c4a	0.96	N2b—C4b	1.3344 (15)
C4a—N3b	0.7626 (16)	N2b—C1b	1.3366 (14)
C4a—C3b	1.3303 (18)	N3b—C3b	1.331 (2)
C4a—H1n3b	0.6852	N3b—H1n3b	0.87
C3a—C1a	1.5057 (11)	N3b—H2n3b	0.87
C3a—N1b	1.059 (2)	C4b—C2b	1.390 (2)
C3a—C4b	1.3288 (18)	C4b—H1c4b	0.96
C3a—C2b	0.6781 (12)	C3b—C1b	1.5057 (14)
C2a—H1c2a	0.96	C2b—H1c2b	0.96
C2a—O1b	1.2721 (19)	C1b—C5b	1.3880 (18)
C2a—N3b	1.016 (2)	C5b—H1c5b	0.96
C3a—O1a—N1b	58.2 (2)	N1a—O1b—C2a	86.2 (2)
C3a—O1a—C2b	31.53 (6)	N1a—O1b—C3b	59.57 (19)
N1b—O1a—C2b	88.1 (2)	C2a—O1b—C3b	31.88 (7)
C2a—N1a—C5a	116.04 (7)	O1a—N1b—C3a	99.4 (2)
C2a—N1a—O1b	72.0 (2)	O1a—N1b—C2b	71.15 (19)
C2a—N1a—C3b	30.80 (6)	O1a—N1b—C5b	164.0 (4)
C5a—N1a—O1b	155.2 (2)	C3a—N1b—C2b	30.20 (8)
C5a—N1a—C3b	85.88 (8)	C3a—N1b—C5b	85.98 (14)
O1b—N1a—C3b	96.8 (2)	C2b—N1b—C5b	116.04 (16)
C4a—N2a—C1a	116.28 (7)	N2a—N2b—C1a	86.67 (12)
C4a—N2a—N2b	177.72 (16)	N2a—N2b—C4b	176.9 (2)
C4a—N2a—C1b	94.50 (7)	N2a—N2b—C1b	64.97 (11)
C1a—N2a—N2b	65.11 (12)	C1a—N2b—C4b	94.46 (11)
C1a—N2a—C1b	21.89 (5)	C1a—N2b—C1b	21.90 (5)
N2b—N2a—C1b	86.81 (13)	C4b—N2b—C1b	116.28 (11)
C3a—N3a—H1n3a	120	C4a—N3b—C2a	101.8 (2)
C3a—N3a—H2n3a	120	C4a—N3b—C3b	73.31 (16)
C3a—N3a—C4b	73.29 (12)	C4a—N3b—H1n3b	49.09
C3a—N3a—C2b	29.83 (7)	C4a—N3b—H2n3b	160.42
H1n3a—N3a—H2n3a	120	C2a—N3b—C3b	30.51 (8)
H1n3a—N3a—C4b	47.91	C2a—N3b—H1n3b	150.23
H1n3a—N3a—C2b	149.74	C2a—N3b—H2n3b	89.63
H2n3a—N3a—C4b	163.28	C3b—N3b—H1n3b	120
H2n3a—N3a—C2b	90.21	C3b—N3b—H2n3b	120
C4b—N3a—C2b	102.89 (15)	H1n3b—N3b—H2n3b	120
N2a—C4a—C2a	121.79 (8)	N3a—C4b—C3a	73.60 (14)
N2a—C4a—H1c4a	119.1	N3a—C4b—H1n3a	74.86
N2a—C4a—N3b	164.75 (18)	N3a—C4b—N2b	166.68 (19)
N2a—C4a—C3b	93.02 (8)	N3a—C4b—C2b	45.00 (12)
N2a—C4a—H1n3b	116.58	N3a—C4b—H1c4b	74.13
C2a—C4a—H1c4a	119.1	C3a—C4b—H1n3a	145.96
C2a—C4a—N3b	45.72 (16)	C3a—C4b—N2b	93.12 (9)
C2a—C4a—C3b	29.20 (5)	C3a—C4b—C2b	28.78 (6)
C2a—C4a—H1n3b	119.03	C3a—C4b—H1c4b	147.68
H1c4a—C4a—N3b	74.09	H1n3a—C4b—N2b	117.81
H1c4a—C4a—C3b	147.47	H1n3a—C4b—C2b	119.29
H1c4a—C4a—H1n3b	16.5	H1n3a—C4b—H1c4b	10.76
N3b—C4a—C3b	73.39 (17)	N2b—C4b—C2b	121.79 (12)
N3b—C4a—H1n3b	73.65	N2b—C4b—H1c4b	119.1
C3b—C4a—H1n3b	142.53	C2b—C4b—H1c4b	119.1
O1a—C3a—N3a	124.49 (5)	N1a—C3b—C4a	168.35 (17)
O1a—C3a—C1a	119.94 (6)	N1a—C3b—C2a	96.66 (14)
O1a—C3a—N1b	22.35 (9)	N1a—C3b—O1b	23.64 (9)
O1a—C3a—C4b	157.60 (7)	N1a—C3b—N3b	145.24 (9)
O1a—C3a—C2b	77.11 (17)	N1a—C3b—C1b	98.11 (11)
N3a—C3a—C1a	115.57 (7)	C4a—C3b—C2a	80.20 (15)
N3a—C3a—N1b	145.71 (10)	C4a—C3b—O1b	157.59 (11)
N3a—C3a—C4b	33.11 (6)	C4a—C3b—N3b	33.31 (8)
N3a—C3a—C2b	47.70 (17)	C4a—C3b—C1b	82.38 (8)
C1a—C3a—N1b	98.34 (10)	C2a—C3b—O1b	77.56 (13)
C1a—C3a—C4b	82.46 (7)	C2a—C3b—N3b	48.58 (13)
C1a—C3a—C2b	162.3 (2)	C2a—C3b—C1b	159.1 (2)
N1b—C3a—C4b	174.37 (15)	O1b—C3b—N3b	124.49 (11)
N1b—C3a—C2b	98.03 (19)	O1b—C3b—C1b	119.94 (13)
C4b—C3a—C2b	80.61 (18)	N3b—C3b—C1b	115.57 (11)
N1a—C2a—C4a	122.15 (7)	O1a—C2b—N3a	171.16 (15)
N1a—C2a—H1c2a	118.92	O1a—C2b—C3a	71.35 (16)
N1a—C2a—O1b	21.77 (7)	O1a—C2b—N1b	20.77 (9)
N1a—C2a—N3b	153.45 (10)	O1a—C2b—C4b	141.89 (9)
N1a—C2a—C3b	52.54 (14)	O1a—C2b—H1c2b	98.81
C4a—C2a—H1c2a	118.92	N3a—C2b—C3a	102.5 (2)
C4a—C2a—O1b	141.08 (8)	N3a—C2b—N1b	154.20 (14)
C4a—C2a—N3b	32.49 (9)	N3a—C2b—C4b	32.11 (8)
C4a—C2a—C3b	70.60 (13)	N3a—C2b—H1c2b	86.84
H1c2a—C2a—O1b	98.96	C3a—C2b—N1b	51.77 (15)
H1c2a—C2a—N3b	86.98	C3a—C2b—C4b	70.61 (16)
H1c2a—C2a—C3b	166.42	C3a—C2b—H1c2b	169.38
O1b—C2a—N3b	163.58 (16)	N1b—C2b—C4b	122.15 (12)
O1b—C2a—C3b	70.56 (14)	N1b—C2b—H1c2b	118.92
N3b—C2a—C3b	100.91 (16)	C4b—C2b—H1c2b	118.92
N2a—C1a—C3a	118.12 (7)	N2a—C1b—C1a	93.13 (14)
N2a—C1a—C5a	122.06 (6)	N2a—C1b—C5a	163.69 (7)
N2a—C1a—N2b	28.21 (5)	N2a—C1b—N2b	28.22 (6)
N2a—C1a—C1b	64.97 (14)	N2a—C1b—C3b	89.99 (9)
N2a—C1a—C5b	167.28 (8)	N2a—C1b—C5b	150.20 (8)
C3a—C1a—C5a	119.80 (7)	C1a—C1b—C5a	102.04 (17)
C3a—C1a—N2b	89.96 (7)	C1a—C1b—N2b	65.16 (14)
C3a—C1a—C1b	175.07 (18)	C1a—C1b—C3b	175.7 (2)
C3a—C1a—C5b	74.45 (8)	C1a—C1b—C5b	57.09 (14)
C5a—C1a—N2b	150.24 (8)	C5a—C1b—N2b	167.03 (11)
C5a—C1a—C1b	57.37 (14)	C5a—C1b—C3b	74.56 (8)
C5a—C1a—C5b	45.49 (7)	C5a—C1b—C5b	45.46 (7)
N2b—C1a—C1b	92.95 (16)	N2b—C1b—C3b	118.12 (10)
N2b—C1a—C5b	163.95 (8)	N2b—C1b—C5b	122.06 (8)
C1b—C1a—C5b	102.35 (16)	C3b—C1b—C5b	119.80 (9)
N1a—C5a—C1a	121.68 (8)	C1a—C5b—C5a	77.48 (11)
N1a—C5a—H1c5a	119.16	C1a—C5b—H1c5a	133.72
N1a—C5a—C1b	101.22 (8)	C1a—C5b—N1b	101.20 (11)
N1a—C5a—C5b	177.23 (13)	C1a—C5b—C1b	20.57 (5)
N1a—C5a—H1c5b	124.85	C1a—C5b—H1c5b	139.59
C1a—C5a—H1c5a	119.16	C5a—C5b—H1c5a	56.31
C1a—C5a—C1b	20.59 (5)	C5a—C5b—N1b	176.3 (2)
C1a—C5a—C5b	57.03 (9)	C5a—C5b—C1b	57.17 (9)
C1a—C5a—H1c5b	113.38	C5a—C5b—H1c5b	62.11
H1c5a—C5a—C1b	139.56	H1c5a—C5b—N1b	124.73
H1c5a—C5a—C5b	62.19	H1c5a—C5b—C1b	113.48
H1c5a—C5a—H1c5b	6.54	H1c5a—C5b—H1c5b	6.5
C1b—C5a—C5b	77.37 (10)	N1b—C5b—C1b	121.68 (12)
C1b—C5a—H1c5b	133.56	N1b—C5b—H1c5b	119.16
C5b—C5a—H1c5b	56.35	C1b—C5b—H1c5b	119.16
N3a—H1n3a—C4b	57.23	C4a—H1n3b—H1c4a	130.8
N3a—H1n3a—H1c4b	114.21	C4a—H1n3b—N3b	57.26
C4b—H1n3a—H1c4b	146.84	H1c4a—H1n3b—N3b	110.1
C4a—H1c4a—H1n3b	32.7	H1n3a—H1c4b—C4b	22.4
C5a—H1c5a—C5b	61.5	C5a—H1c5b—H1c5a	59.04
C5a—H1c5a—H1c5b	114.42	C5a—H1c5b—C5b	61.54
C5b—H1c5a—H1c5b	58.49	H1c5a—H1c5b—C5b	115.01

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3a—H1n3a···O1a^i	0.87	2.47	3.2081 (15)	142.72
N3a—H1n3a···N1b^i	0.87	2.46	3.231 (2)	147.53
C4b—H1n3a···O1a^i	0.67	2.47	3.109 (2)	160.02
C4b—H1n3a···N1b^i	0.67	2.46	3.071 (3)	152.09
N3a—H2n3a···N1a^ii	0.87	2.29	3.0819 (17)	152.21
N3a—H2n3a···O1b^ii	0.87	2.09	2.8432 (19)	144.48
C2b—H2n3a···N1a^ii	1.33	2.29	3.475 (2)	146.34
C2b—H2n3a···O1b^ii	1.33	2.09	3.206 (2)	137.83
C4a—H1c4a···N1a^iii	0.96	2.47	3.3640 (17)	154.34
C4a—H1c4a···O1b^iii	0.96	2.28	3.204 (2)	162.25
N3b—H1c4a···N1a^iii	1.05	2.47	3.464 (2)	157.02
N3b—H1c4a···O1b^iii	1.05	2.28	3.249 (3)	153.39
C2a—H1c2a···O1a^iv	0.96	2.40	3.2376 (15)	145.82
C5a—H1c5a···N2b^v	0.96	2.48	3.4237 (18)	167.83
C5b—H1c5a···N2b^v	1.02	2.48	3.237 (2)	130.54
C2a—H2n3b···O1a^iv	1.33	2.14	3.2376 (15)	136.67
N3b—H2n3b···O1a^iv	0.87	2.14	2.946 (2)	154.79
N3a—H1c4b···O1a^i	1.05	2.23	3.2081 (15)	153.99
N3a—H1c4b···N1b^i	1.05	2.27	3.231 (2)	151.12
C4b—H1c4b···O1a^i	0.96	2.23	3.109 (2)	151.23
C4b—H1c4b···N1b^i	0.96	2.27	3.071 (3)	139.81
C2b—H1c2b···O1b^ii	0.96	2.42	3.206 (2)	138.71
C5a—H1c5b···N2b^v	1.02	2.45	3.4237 (18)	158.65
C5b—H1c5b···N2b^v	0.96	2.45	3.237 (2)	138.57

Symmetry codes: (i) x, −y, z+1/2; (ii) x+1, −y, z+1/2; (iii) x, −y+1, z+1/2; (iv) x−1, y+1, z; (v) x, −y, z−1/2.

(delta10K)

Crystal data

C5H5N3O	V = 267.37 (6) Å^3
Mr = 123.1	Z = 2
Triclinic, P1	F(000) = 128
Hall symbol: -P 1	Dx = 1.529 Mg m^−3
a = 5.1026 (6) Å	Mo Kα radiation, λ = 0.71073 Å
b = 5.7083 (7) Å	Cell parameters from 3482 reflections
c = 9.8487 (12) Å	θ = 3.8–36.4°
α = 97.526 (4)°	µ = 0.11 mm^−1
β = 98.499 (3)°	T = 10 K
γ = 106.564 (4)°	Prism, colorless

Data collection

Bruker CCD diffractometer	1557 reflections with I > 3σ(I)
Radiation source: X-ray tube	Rint = 0.026
Graphite monochromator	θmax = 36.4°, θmin = 3.8°
Bruker CCD scans	h = −6→8
3482 measured reflections	k = −7→9
2278 independent reflections	l = −16→10

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.052	H-atom parameters constrained
wR(F^2) = 0.060	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 1.89	(Δ/σ)max = 0.009
2278 reflections	Δρmax = 0.75 e Å^−3
82 parameters	Δρmin = −0.45 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.80279 (16)	1.15416 (17)	0.10137 (8)	0.0099 (3)
N1	0.24192 (19)	1.0429 (2)	0.37110 (9)	0.0090 (3)
N3	0.78450 (19)	0.7462 (2)	0.07150 (9)	0.0100 (3)
N2	0.4225 (2)	0.6582 (2)	0.24913 (9)	0.0087 (3)
C1	0.5108 (2)	0.8887 (2)	0.22346 (11)	0.0074 (4)
C3	0.7141 (2)	0.9412 (2)	0.12567 (10)	0.0077 (4)
C2	0.1525 (2)	0.8119 (2)	0.39533 (11)	0.0086 (4)
C4	0.2413 (2)	0.6198 (2)	0.33518 (11)	0.0094 (4)
C5	0.4228 (2)	1.0807 (2)	0.28350 (11)	0.0088 (4)
H1n3	0.719439	0.602946	0.095843	0.0121*
H2n3	0.895435	0.76246	0.01184	0.0121*
H1c2	0.021983	0.776118	0.456511	0.0103*
H1c4	0.170531	0.456534	0.356113	0.0113*
H1c5	0.492648	1.243534	0.261932	0.0105*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0112 (4)	0.0098 (5)	0.0112 (4)	0.0033 (4)	0.0055 (3)	0.0065 (3)
N1	0.0099 (5)	0.0108 (6)	0.0093 (4)	0.0044 (4)	0.0050 (4)	0.0058 (4)
N3	0.0114 (5)	0.0111 (6)	0.0110 (4)	0.0042 (4)	0.0076 (4)	0.0062 (4)
N2	0.0099 (5)	0.0092 (6)	0.0099 (4)	0.0039 (4)	0.0050 (3)	0.0059 (4)
C1	0.0075 (5)	0.0088 (6)	0.0074 (4)	0.0025 (5)	0.0029 (4)	0.0046 (4)
C3	0.0065 (5)	0.0111 (6)	0.0066 (4)	0.0024 (5)	0.0024 (4)	0.0044 (4)
C2	0.0086 (5)	0.0106 (7)	0.0089 (4)	0.0032 (5)	0.0045 (4)	0.0060 (4)
C4	0.0111 (6)	0.0086 (6)	0.0107 (5)	0.0029 (5)	0.0053 (4)	0.0059 (4)
C5	0.0103 (5)	0.0083 (6)	0.0096 (5)	0.0028 (5)	0.0044 (4)	0.0057 (4)

Geometric parameters (Å, º)

O1—C3	1.2387 (16)	N2—C4	1.3364 (16)
N1—C2	1.3322 (18)	C1—C3	1.5124 (16)
N1—C5	1.3465 (16)	C1—C5	1.393 (2)
N3—C3	1.3345 (18)	C2—C4	1.397 (2)
N3—H1n3	0.87	C2—H1c2	0.96
N3—H2n3	0.87	C4—H1c4	0.96
N2—C1	1.3346 (18)	C5—H1c5	0.96
C2—N1—C5	115.88 (12)	N3—C3—C1	115.37 (11)
C3—N3—H1n3	120	N1—C2—C4	122.56 (11)
C3—N3—H2n3	120	N1—C2—H1c2	118.72
H1n3—N3—H2n3	120	C4—C2—H1c2	118.72
C1—N2—C4	116.24 (12)	N2—C4—C2	121.46 (12)
N2—C1—C3	118.28 (12)	N2—C4—H1c4	119.27
N2—C1—C5	122.38 (11)	C2—C4—H1c4	119.27
C3—C1—C5	119.33 (11)	N1—C5—C1	121.47 (12)
O1—C3—N3	124.87 (10)	N1—C5—H1c5	119.26
O1—C3—C1	119.75 (12)	C1—C5—H1c5	119.27

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H2n3···O1^i	0.87	2.02	2.8788 (14)	170.41

Symmetry code: (i) −x+2, −y+2, −z.

(delta122K)

Crystal data

C5H5N3O	V = 269.45 (15) Å^3
Mr = 123.1	Z = 2
Triclinic, P1	F(000) = 128
Hall symbol: -P 1	Dx = 1.518 Mg m^−3
a = 5.1280 (14) Å	Mo Kα radiation, λ = 0.71073 Å
b = 5.7080 (12) Å	Cell parameters from 15213 reflections
c = 9.857 (4) Å	θ = 2.1–53.3°
α = 97.45 (3)°	µ = 0.11 mm^−1
β = 98.04 (3)°	T = 122 K
γ = 106.55 (2)°	Prism, colorless

Data collection

Nonius Kappa CCD diffractometer	Rint = 0.074
Radiation source: X-ray tube	θmax = 53.3°, θmin = 2.1°
15213 measured reflections	h = −9→10
4988 independent reflections	k = −12→9
4005 reflections with I > 3σ(I)	l = −21→21

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.040	H-atom parameters constrained
wR(F^2) = 0.065	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.60	(Δ/σ)max = 0.002
4988 reflections	Δρmax = 0.50 e Å^−3
82 parameters	Δρmin = −0.27 e Å^−3
0 restraints

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.80224 (6)	1.15293 (5)	0.10104 (3)	0.01598 (8)
N1	0.24229 (7)	1.04167 (6)	0.37038 (3)	0.01502 (8)
N3	0.78478 (6)	0.74568 (6)	0.07172 (3)	0.01500 (8)
N2	0.42276 (7)	0.65832 (6)	0.24927 (4)	0.01519 (8)
C1	0.51158 (6)	0.88913 (6)	0.22318 (3)	0.01115 (8)
C3	0.71342 (6)	0.93999 (6)	0.12568 (3)	0.01188 (8)
C2	0.15238 (8)	0.81092 (7)	0.39541 (4)	0.01459 (9)
C4	0.24172 (8)	0.61977 (6)	0.33507 (4)	0.01692 (10)
C5	0.42242 (8)	1.07968 (6)	0.28310 (4)	0.01394 (9)
H1n3	0.717086	0.601443	0.094668	0.018*
H2n3	0.899009	0.76319	0.013578	0.018*
H1c2	0.022155	0.775221	0.456841	0.0175*
H1c4	0.171016	0.456326	0.355873	0.0203*
H1c5	0.491614	1.242633	0.261398	0.0167*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.01577 (11)	0.01287 (11)	0.02105 (13)	0.00347 (9)	0.00899 (9)	0.00537 (9)
N1	0.01815 (13)	0.01233 (12)	0.01903 (13)	0.00797 (10)	0.00962 (10)	0.00446 (9)
N3	0.01526 (12)	0.01350 (12)	0.01836 (13)	0.00530 (10)	0.00879 (10)	0.00231 (9)
N2	0.01856 (13)	0.01038 (11)	0.02058 (13)	0.00643 (10)	0.01079 (10)	0.00462 (9)
C1	0.01148 (11)	0.00976 (12)	0.01388 (12)	0.00430 (9)	0.00499 (9)	0.00287 (9)
C3	0.01061 (11)	0.01196 (12)	0.01364 (12)	0.00341 (9)	0.00417 (9)	0.00240 (9)
C2	0.01690 (13)	0.01356 (13)	0.01756 (13)	0.00727 (11)	0.00931 (11)	0.00535 (10)
C4	0.02141 (15)	0.01137 (13)	0.02314 (16)	0.00714 (11)	0.01331 (13)	0.00672 (11)
C5	0.01641 (13)	0.01033 (12)	0.01829 (13)	0.00601 (10)	0.00832 (11)	0.00414 (10)

Geometric parameters (Å, º)

O1—C3	1.2393 (7)	N2—C4	1.3330 (9)
N1—C2	1.3335 (8)	C1—C3	1.5028 (9)
N1—C5	1.3405 (9)	C1—C5	1.3903 (8)
N3—C3	1.3340 (7)	C2—C4	1.3953 (8)
N3—H1n3	0.87	C2—H1c2	0.96
N3—H2n3	0.87	C4—H1c4	0.96
N2—C1	1.3372 (8)	C5—H1c5	0.96
C2—N1—C5	116.23 (4)	N3—C3—C1	115.80 (4)
C3—N3—H1n3	120	N1—C2—C4	122.03 (4)
C3—N3—H2n3	120	N1—C2—H1c2	118.98
H1n3—N3—H2n3	120	C4—C2—H1c2	118.98
C1—N2—C4	116.39 (4)	N2—C4—C2	121.68 (4)
N2—C1—C3	118.12 (4)	N2—C4—H1c4	119.16
N2—C1—C5	121.98 (4)	C2—C4—H1c4	119.16
C3—C1—C5	119.90 (4)	N1—C5—C1	121.68 (4)
O1—C3—N3	124.64 (4)	N1—C5—H1c5	119.16
O1—C3—C1	119.55 (4)	C1—C5—H1c5	119.16

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N3—H2n3···O1^i	0.87	2.01	2.8784 (16)	171.76

Symmetry code: (i) −x+2, −y+2, −z.