Roman
Gajda
,
Anna
Piekara
,
Daniel
Tchoń
,
Krzysztof
Woźniak
and
Wojciech A.
Sławiński
*
Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland. E-mail: wslawinski@chem.uw.edu.pl
First published on 14th September 2022
A H4B4O92− ion which makes up the (NH4)2B4O5(OH)4·2H2O crystal structure has two types of boron–oxygen bonds, i.e. single B–O bonds and an intermediate between single and double BO bonds. Differences between these two bond types are visible not only because they differ by their lengths but also a topology of electron density distribution differs. This also gives a hint as to how to distinguish between these two bond types. Experimental results based on multipole model refinement gave excellent agreement with theoretical calculations and literature data. Calculations at bond critical points for B–O and B
O (electron density, the Laplacian of electron density and the localized-orbital locator function) suggest us how boron–oxygen bonds should be categorised with respect to compounds previously reported in the literature. Additionally, a novel synthesis method for the investigated compound has been developed, which involves crystallization from an aqueous solution of BH3NH3 dissolved in a mixture of tetrahydrofuran and water.
In this paper, along with examining the H4B4O92− ion, we will look deeper into the phenomena of B–O and BO bonds. The results presented here originate from high-resolution, single crystal X-ray diffraction experiments. Collection of high quality data allowed us to obtain experimental charge density distributions. Multipole model refinement according to the Hansen–Coppens theory was adopted. Experimental data were analyzed and compared with theoretical DFT based calculations.
NH3BH3 + 4H2O → NH4+ + B(OH)4− + 3H2 |
THF was chosen for the high solubility of ammonia borane in it and its volatility.6 The mixture was sealed and allowed to stand at room temperature for 7 days. After this time, crystals of (NH4)2B4O5(OH)4·2H2O began to form at the bottom of the vessel.
Spherical refinement | |
---|---|
Crystal system, space group | Monoclinic, P21 |
a, b, c (Å) | 7.16499(7), 10.59066(11), 7.24742(6) |
β(°) | 98.6290(9) |
V (Å3) | 543.72(1) |
Z | 2 |
F(000) | 276.244 |
D x (Mg m−3) | 1.609 |
Radiation type | MoKα |
No. of reflections for cell measurement | 51![]() |
θ range (°) for cell measurement | 3.5–65.9 |
μ (mm−1) | 0.16 |
Data collection | |
Diffractometer | SuperNova, Dual, HyPix 6000HE HPC |
Scan method | ω scans |
Absorption correction | Multi-scan |
T min, Tmax | 0.738, 1.000 |
Measur., independ., observ. [I ≥ 2σ(I)] refl. | 94![]() ![]() ![]() |
R int | 0.056 |
θ values (°) | θ max = 62.7, θmin = 3.4 |
(sin![]() |
1.250 |
Range of h, k, l | h = −17→17, k = −26→26, l = −18→18 |
Refinement on | F 2 |
R[F2 > 2σ(F2)], wR(F2), S | 0.045, 0.114, 1.08 |
No. of reflections | 17![]() |
No. of parameters | 218 |
No. of restraints | 10 |
Absolute structure | Hooft et al.35 |
Absolute structure parameter | −0.03 (14) |
Multipole refinement | |
---|---|
Refinement on, parameters, reflections |
F, 460, 13![]() |
R[F2 > 2σ(F2)], R(all) | 0.039, 0.038 |
wR[F2 > 2σ(F2)], S | 0.071, 1.156 |
Weighting scheme | w = 1/[σ2(Fo2)] |
(Δ/σ)max | 0.015 |
Δ>max, Δ>min (e Å−3) | 0.571, −0.308 |
Atom | Fract x | Fract y | Fract z |
---|---|---|---|
O(1) | 0.06319(6) | 0.44385(4) | 0.68750(7) |
O(2) | 0.24306(6) | 0.29958(5) | 0.53000(7) |
O(3) | 0.31420(7) | 0.44619(4) | 0.95184(6) |
O(4) | 0.49498(7) | 0.30342(5) | 0.79399(6) |
O(5) | 0.37996(6) | 0.49770(4) | 0.64351(5) |
O(6) | 0.19981(7) | 0.63914(4) | 0.81436(6) |
O(7) | 0.56577(7) | 0.35028(6) | 0.49451(6) |
O(8) | 0.9144(7) | 0.27897(5) | 0.49693(7) |
O(9) | 0.49778(7) | 0.29138(5) | 0.12259(6) |
O(10) | 0.06317(19) | 0.87621(9) | 0.94202(19) |
O(11) | 0.14951(11) | 0.11372(8) | 0.85189(11) |
B(1) | 0.24174(8) | 0.50941(5) | 0.77181(8) |
B(2) | 0.42137(8) | 0.36466(6) | 0.61207(8) |
B(3) | 0.07436(8) | 0.34303(6) | 0.57214(8) |
B(4) | 0.43707(9) | 0.34731(6) | 0.95314(8) |
N(1) | 0.25347(7) | 0.10041(5) | 0.27331(8) |
N(2) | 0.27296(9) | 0.59516(5) | 0.12259(7) |
H(1A) | 0.160(4) | 0.043(3) | 0.297(4) |
H(1B) | 0.215(3) | 0.124(2) | 0.155(3) |
H(1C) | 0.255(5) | 0.163(3) | 0.345(5) |
H(1D) | 0.375(4) | 0.062(3) | 0.295(4) |
H(2A) | 0.296(3) | 0.537(3) | 0.188(3) |
H(2B) | 0.337(5) | 0.650(3) | 0.254(5) |
H(2C) | 0.157(4) | 0.611(3) | 0.252(4) |
H(2D) | 0.311(5) | 0.573(3) | 0.376(3) |
H(6) | 0.151(4) | 0.684(3) | 0.710(3) |
H(7) | 0.511(2) | 0.3516(16) | 0.4376(19) |
H(8) | 0.818(3) | 0.304(3) | 0.524(4) |
H(9) | 0.570(8) | 0.221(4) | 0.113(9) |
H(10A) | 0.086(3) | 0.7876(19) | 0.936(3) |
H(10B) | 0.107(7) | 0.923(5) | 0.848(5) |
H(11A) | 0.159(2) | 0.0330(13) | 0.848(2) |
H(11B) | 0.094(6) | 0.173(4) | 0.950(5) |
In this equation, ρc(r) and ρv(r) are spherical core and valence densities. The third term contains the sum of the angular functions dlm±(θ,φ) to take into account the aspherical deformations. The angular functions dlm±(θ,φ) are real spherical harmonic functions. The coefficients Pval and Plm± are multipole populations for the valence and deformation density multipoles. κ and κ′ are scaling parameters which describe whether valence and deformation densities are expanding or contracting. In the Hansen–Coppens formalism, Pval, Plm±, κ and κ′ are refineable parameters together with the atomic coordinates and thermal displacement coefficients. The XD2016 program package was used to conduct multipole model refinement.13 For both experimental and theoretical data the same approach has been applied. Multipoles of non-hydrogen atoms were refined up to hexadecapoles, whereas hydrogen atoms were refined up to dipoles only. Because all atoms are placed at general positions, no special positions are involved and no constraints for any multipoles were used. Parameters κ were refined for all types of atoms and κ′ was set to 1. The length of the O–H bonds was constrained as 0.96 Å. The anisotropic thermal parameters of hydrogen atoms were calculated using so called SHADE3 (Simple Hydrogen Anisotropic Displacement Estimator).14
![]() | ||
Fig. 2 H4B4O92− ion. Single B–O and transient B![]() |
Donor contact D–H | d(D–H) [Å] | d(H⋯A) [Å] | <DHA angle [°] | d(D⋯A) [Å] | Acceptor A | Symmetry code |
---|---|---|---|---|---|---|
O(6)–H(6) | 0.920 | 1.805 | 172.85 | 2.720 | O(8) | −x, y + 1/2, −z + 1 |
O(7)–H(7) | 0.523 | 2.358 | 132.36 | 2.738 | O(9) | x, y, z − 1 |
O(8)–H(8) | 0.790 | 1.854 | 158.97 | 2.607 | O(7) | x − 1, y, z |
O(9)–H(9) | 0.912 | 1.871 | 147.31 | 2.684 | O(6) | −x + 1, y − 1/2, −z + 2 |
N(1)–H(1A) | 0.939 | 1.930 | 169.66 | 2.858 | O(1) | −x, y − 1/2, −z + 1 |
N(1)–H(1B) | 0.896 | 2.178 | 160.27 | 3.036 | O(11) | x, y, z − 1 |
N(1)–H(1C) | 0.843 | 1.981 | 173.95 | 2.821 | O(2) | |
N(1)–H(1D) | 0.948 | 1.878 | 174.90 | 2.823 | O(5) | −x + 1, y − 1/2, −z + 1 |
N(2)–H(2A) | 0.882 | 1.984 | 162.39 | 2.837 | O(3) | |
N(2)–H(2B) | 0.757 | 2.083 | 177.49 | 2.839 | O(4) | −x + 1, y + 1/2, −z + 2 |
N(2)–H(2C) | 0.837 | 2.213 | 164.90 | 3.028 | O(11) | −x, y + 1/2, −z + 2 |
N(2)–H(2D) | 0.822 | 2.084 | 172.45 | 2.900 | O(5) | x, y, z + 1 |
O(10)–H(10A) | 0.955 | 2.033 | 149.63 | 2.897 | O(6) | |
O(10)–H(10B) | 0.937 | 2.039 | 125.52 | 2.694 | O(11) | x, y + 1, z |
O(11)–H(11A) | 0.858 | 1.958 | 143.08 | 2.694 | O(10) | x, y − 1, z |
O(11)–H(11B) | 1.066 | 2.606 | 155.03 | 3.601 | O(10) | −x, y − 1/2, −z + 2 |
Boron/oxygen interactions were investigated to some extent by Straub (1995).1 On the basis of bond lengths we can distinguish single B–O, double BO, triple B
O and transient B
O bonds. The length of a single B–O bond is reported to be ca. 1.470 Å, whereas the length of transient bonds B
O should vary between 1.360 Å and 1.386 Å. In the case of the H4B4O92− ion, there are fourteen boron–oxygen bonds. Their lengths are presented in Table 4. It can be clearly observed that there are two different groups of bonds. Atoms B(1) and B(2) create a B–O bond, whereas B(3) and B(4) form a B
O bond. In Fig. 2, localisation of these bonds in the H4B4O92− ion is depicted by solid and dotted bonds, respectively.
Bond | Length [Å] | Bond | Length [Å] |
---|---|---|---|
B(1)–O(1) | 1.5025(7) | B(3)–O(1) | 1.3659(7) |
B(1)–O(3) | 1.4889(7) | B(3)–O(2) | 1.3700(7) |
B(1)–O(5) | 1.4619(7) | B(3)–O(8) | 1.3724(7) |
B(1)–O(6) | 1.4494(7) | B(4)–O(3) | 1.3673(7) |
B(2)–O(2) | 1.4944(8) | B(4)–O(4) | 1.3647(7) |
B(2)–O(4) | 1.4928(7) | B(4)–O(9) | 1.3740(7) |
B(2)–O(5) | 1.4647(8) | ||
B(2)–O(7) | 1.4436(7) |
The differences between B–O and BO should also be observable when we take into consideration properties such as electron density and the Laplacian of electron density at bond critical points (BCPs). Issues of BCPs are well defined by the quantum theory of atoms in molecules (QTAIM).24,25
There is very little known about the distribution of charge density in B–O and BO bonds. The most recent paper by Michalski et al. presents topological parameters for the B–O bonds obtained on the basis of DFT calculations in Gaussian.3 In the molecule investigated in that paper (ABEMID trimethylammonio-dicyano(methylmercapto)borate), properties at the bond critical points corresponding to B–O bonds have values as follows: electron density ρ(3,−1)(r) = 1.236 (e Å−3) and Laplacian ∇2ρ(3,−1)(r) = 16.519 (e Å−5). A positive value of the Laplacian in conjunction with a relatively large value of ρ(3,−1)(r) suggest that the bond has dative character. The same paper also investigated 27 molecules with a B–S bond which has been selected from the CSD database and the calculations were performed for their derivatives whereas the S atom has been replaced by an O atom. In that set of molecules the average values of properties at bond critical points were as follows: ρ(3,−1)(r) varied between 0.896 and 1.383 (e Å−3) and the Laplacian ∇2ρ(3,−1)(r) varied between 12.417 and 22.406 (e Å−5). It must be emphasised that these results are only based on DFT calculations, whereas the results presented in our paper have their origins in experimental data.
In Table 5 we compare values of electron density and the Laplacian obtained for B–O and BO bonds which exist in the H4B4O92− ion. The results from multipole model refinement based on experimental data (XD exp. data) are compared with the multipole model refinement based on theoretical dynamic structure factors (XD theor. data) and with the topology of electron density obtained directly from DFT calculations in CRYSTAL17 (Topond14). As wee see from Table 5, just by comparing the values of ρ(3,−1)(r) and ∇2ρ(3,−1)(r) we can clearly distinguish whether a particular boron oxygen interaction is a B–O or B
O bond. For B–O, the electron density (XD theor. data) at BCPs is lower and varied from 0.97 to 1.08 e Å−3 (with an average of 1.04 e Å−3), whereas for B
O it varied from 1.30 to 1.46 e Å−3 (with the average of 1.40 e Å−3). As a consequence, the second derivative of electron density – Laplacian – showed significant differences. Generally speaking, the Laplacian for B–O was lower than 10 (e Å−5), whereas for B
O it was higher than 10 (e Å−5). The results of ρ(3,−1)(r) and ∇2ρ(3,−1)(r) obtained on the basis of the theoretical dynamic structure factors were in good agreement with those obtained directly from DFT calculations. However, taking the multipole refinement of experimental data into consideration we see that although the values of ρ(3,−1)(r) still correspond very well to the experimental data, the Laplacian was a little bit biased. The results presented in this paper do not contradict recent theoretical calculations but rather are complementary. It must be underlined that the origin of all the datasets investigated in this study was a single crystal X-ray diffraction measurement. Calculations of multipole model refinement in XD take into account the whole crystal structure, including the surrounding solvent molecules. Also Crystal17, which is a source of dynamic theoretical structure factors and a starting point for further Topond14 calculations is devoted to periodic system calculations. That is why it is obvious that some differences with the literature data obtained from the DFT calculations of the gas phase molecule must appear. However, we believe that the results presented in this paper (based on diffraction experiments), in particular values of ρ(3,−1)(r) and ∇2ρ(3,−1)(r), will work much better to classify some future structures containing boron/oxygen interactions. It will enable the assignment of B–O or B
O bond type.
Topond14 | XD exp. data | XD theor. data | ||||
---|---|---|---|---|---|---|
B–O | ρ (3,−1)(r) [e Å−3] | ∇2ρ(3,−1)(r) [e Å−5] | ρ (3,−1)(r) [e Å−3] | ∇2ρ(3,−1)(r) [e Å−5] | ρ (3,−1)(r) [e Å−3] | ∇2ρ(3,−1)(r) [e Å−5] |
B(1)–O(1) | 1.026 | 8.435 | 1.21(5) | −1.7(2) | 0.97(1) | 9.37(5) |
B(1)–O(3) | 1.073 | 9.326 | 1.24(5) | −0.6(2) | 1.04(1) | 8.32(5) |
B(1)–O(5) | 1.127 | 8.868 | 1.24(5) | 0.8(2) | 1.08(1) | 8.18(4) |
B(1)–O(6) | 1.080 | 9.326 | 1.25(5) | 2.0(2) | 1.01(1) | 11.56(5) |
B(2)–O(2) | 1.019 | 8.314 | 1.08(5) | 2.6(2) | 1.05(1) | 4.43(5) |
B(2)–O(4) | 1.019 | 8.266 | 1.02(5) | 9.2(2) | 1.00(1) | 8.23(5) |
B(2)–O(5) | 1.120 | 8.796 | 1.14(5) | 7.0(2) | 1.10(1) | 5.56(5) |
B(2)–O(7) | 1.134 | 10.218 | 1.53(5) | −9.8(2) | 1.05(1) | 12.67(5) |
Average | 1.075 | 8.939 | 1.21(2) | 1.19(1) | 1.04(1) | 8.54(2) |
B![]() |
||||||
B(3)–O(1) | 1.437 | 17.761 | 1.46(5) | 12.5(3) | 1.40(1) | 18.56(6) |
B(3)–O(2) | 1.410 | 16.773 | 1.35(5) | 20.9(3) | 1.39(1) | 12.84(6) |
B(3)–O(8) | 1.323 | 15.809 | 1.70(5) | −2.4(3) | 1.30(1) | 10.53(6) |
B(4)–O(3) | 1.431 | 17.472 | 1.44(5) | 14.8(3) | 1.46(1) | 11.72(6) |
B(4)–O(4) | 1.417 | 17.158 | 1.57(5) | 6.8(3) | 1.44(1) | 12.49(6) |
B(4)–O(9) | 1.336 | 15.881 | 1.35(5) | 9.1(3) | 1.38(1) | 10.17(6) |
Average | 1.392 | 16.809 | 1.48(2) | 10.28(1) | 1.40(1) | 12.72(2) |
In the literature, charge density has already been described in the case of several structures containing boron.26–29 Although some of them include B–O, those manuscripts were not directly focused on the bond charge and types. However, information about the properties at BCPs of such bonds (see Table 6) is presented in some of them. For example, Durka et al.26 compared the experimental and theoretical data for two boron–oxygen bonds. On the basis of what we have already observed the comparison of those data with our findings appears interesting. Experimental values (bond length, density, and Laplacian) suggest that both of them are just single B–O bonds. Whereas on the basis of the theoretical values of bond length and Laplacian we would rather categorise them as BO bond type. Anyway, experimental and theoretical results seem to be inconsistent in this case. In the second example, the paper written by Jarzembska et al.,27 there are four boron–oxygen bonds. Two of the bond lengths were longer than 1.46 Å, with the value of charge density being ca. 1 e Å−3 and its Laplacian being <10 e Å−5. It is clear that these bonds should be considered as a single B–O bond. On the other hand, the two other bonds are significantly shorter (d < 1.4 Å) and the Laplacian is >10 e Å−5 and the density varied between 1.3 and 1.4 e Å−3. These bonds should be categorised as B
O.
Experimental | Theoretical | ||||||
---|---|---|---|---|---|---|---|
Bond | length [Å] | ρ (3,−1)(r) [e Å−3] | ∇2ρ(3,−1)(r) [e Å−5] | length [Å] | ρ (3,−1)(r) [e Å−3] | ∇2ρ(3,−1)(r) [e Å−5] | |
1 | B–O26 | 1.4544(3) | 1.21(2) | 5.7(1) | 1.376 | 1.29 | 25.79 |
2 | B–O26 | 1.4428(3) | 1.26(2) | 6.6(1) | 1.375 | 1.30 | 25.93 |
3 | B–O27 | 1.4985(3) | 1.1 | 6.9 | |||
4 | B–O27 | 1.4678(4) | 1.1 | 9.6 | |||
5 | B–O27 | 1.3892(4) | 1.3 | 13.4 | |||
6 | B–O27 | 1.3509(4) | 1.4 | 18.9 |
Fig. 3 presents the comparison of properties at BCPs such as the electron density and its Laplacian obtained from both experimental and theoretical data. Selected literature data (corresponding to Table 6) are also included. As we see it is easily possible to distinguish zones which correspond to particular types of bonds, B–O (bluish region) and BO (reddish area) respectively. As was already mentioned above, in the case of B–O bonds values of charge densities vary between 1.0 and 1.3 e Å−3, whereas for B
O, the charge density is more likely between 1.3 and 1.5 e Å−3. Laplacian, except for some outliers, have positive values. For B–O bonds, the values of Laplacian are mostly between 5 and 10 e Å−5 and between 10 and 20 for B
O bonds.
![]() | ||
Fig. 3 Comparison of the electron density and its Laplacian at bond critical points corresponding to B–O (bluish region) and B![]() |
Fig. 4 presents the topology of the electron density distribution in the vicinity of the B(3) atom. The hydrogen atom H(8) is off plane. All three BO bonds: B(3)–O(1), B(3)–O(2) and B(3)–O(8) lay in the plane of the figure. Pictures compare the results obtained on the basis of multipole model refinement (XD2016) conducted on the basis of experimental (X-ray measurement) and theoretical (CRYSTAL17) data. In the first row of Fig. 4 gradient lines of the electron density are presented. Blue circles represent bond critical points whereas green circles show ring critical points. According to the atoms in molecules theory,24 each atom is considered with its atomic basin. It is simply a space where the paths of the gradient vectors of the electron density terminate in a given nucleus. The shape of a particular basin is defined by its neighboring atoms and is open at the exterior of the molecule. The gradient paths do not cross the boundaries of the basins. The atom zones are closed by a zero-flux surface surrounding each atom in the molecule. Partition of molecules into such zones is presented in the first row of Fig. 4. Contour values for the residual density and deformation density are 0.05 e Å−3. For the Laplacian maps, particular contours are ±2, 4, 8, 20, 40, 80, 200, 400 and 1000 e Å−5. Blue contours denote positive values and red contours correspond to negative values. On deformation density maps, solid blue lines show electron concentration, whereas dotted red lines denote the depletion of electrons. One can easily find a positive value of Laplacian in the middle of the trace of each B
O bond. On the map of the deformation density the free electron pairs of O(1), O(2) and O(8) are visible.
It is worthy underlining that in the case of theoretical data the residual density map is almost absolutely flat, whereas in the case of experimental data the situation is different. The charts presented in the ESI† show that in both cases, experimental and theoretical, the residual electron density has a normal distribution (see Fig. 1 in the ESI†). However, even if it is randomly spread across the map, it can still affect the contours, especially if it is relatively high as in the experimental data case. Charts of the fractal distribution of the residual electron density presented in the ESI (Fig. 3†) show that peaks and holes on the residual density maps are equal or less than 0.2 e Å−3, whereas in the case of experimental data they vary between 0.3 and −0.6 e Å−3. Maps obtained on the basis of theoretical calculations show us what we would obtain if the experimental data were measured without any errors.
The topology presented in Fig. 5 looks similar. Four B–O type bonds, lying in a plane, are presented: B(1)–O(6), B(1)–O(5), B(2)–O(7) and B(2)–O(5). Laplacian maxima are visible at ca. the mid-points of bond paths. The deformation density maps also show the electron which belongs to the free electron pairs of oxygen atoms.
For the H4B4O92− ion, B–O type bonds are formed by boron atoms B(1) and B(2). As shown in Fig. 2, each of these boron atoms formed four such bonds (tetragonal arrangement). B(3) and B(4) atoms create BO type bonds and each of them formed three such bonds (flat arrangement). It is expected that the boron atoms within the tetragonal arrangement would have different atomic charges than boron atoms connected to three oxygen atoms. Indeed, as we see from Table 7, the net atomic charges of integrated atomic basins corresponding to B(1) and B(2) were equal to +1.96 and +2.13 e, respectively. In the case of B(3) and B(4), the net charges of atomic basins were slightly but noticeably higher and vary between +2.21 and +2.27 e. Boron atoms surrounded by four oxygen atoms (forming B–O type bonds) had lower net atomic charge than boron atoms surrounded by only three oxygen atoms (forming B
O type bonds) as was expected.
Atom | Charge [e] | Atom | Charge [e] |
---|---|---|---|
B(1) | 1.96 | O(6) | −1.35 |
B(2) | 2.13 | O(7) | −1.4 |
B(3) | 2.27 | O(8) | −1.5 |
B(4) | 2.21 | O(9) | −1.65 |
O(1) | −2.00 | ||
O(2) | −1.75 | ||
O(3) | −1.86 | ||
O(4) | −1.61 | ||
O(5) | −1.60 |
One of the convenient tools for analyzing the experimental electron density is the localized-orbital locator (LOL). In a nutshell, it is a function introduced by Schmider and Becke which gives a measure of the relative velocity of electrons at a point r
ν(r) = t(r)/[1 + t(r)] |
ν(r) can obtain values within the range 0 ≤ ν ≤ 1. When the value is higher than 0.5, the space is associated with localized orbitals, whereas for values smaller than 0.5, the space is associated with the ionic and van der Waals bonds. The results of the LOL calculations presented in this paper are conducted according to the approach proposed by Tsirelson and Stash, where instead of the kinetic energy density calculated directly from Hartree–Fock wave functions, the kinetic energy density is obtained from the Hartree–Fock electron density.32–34 It is clearly seen in Fig. 6 that the values of ν between the B and O atoms are lower than 0.5, which is expected for the ionic bonds and consistent with the information about BCPs’ topological properties (positive value of Laplacian).
Footnote |
† Electronic supplementary information (ESI) available: Normal distribution of residual electron density plots, structure factors as a function of sin![]() |
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