Multipole refinement and electron density analysis in natural borosilicate datolite using X-ray diffraction data

The electron density distribution in the layer silicate datolite, Ca[BOH(SiO₄)], was analyzed using high-precision single-crystal X-ray diffraction data (Mo Kα, T = 293 K). The Hansen–Coppens multipole model and Bader's topological analysis of the electron density provides a basis for the quantitative characterization of the bonded interaction of datolite. The results are presented both in the form of maps of the electron density distribution and its Laplacian, and in a compact way in terms of the critical points of the electron density. The relative electronegativities are also discussed. It was shown that closed-shell type interactions exist between Ca and O atoms, whereas Si—O and B—O bonds exhibit an intermediate nature with a strong covalent component. An analysis of the topology of the electrostatic potential demonstrates the relevance of considering this physical property to obtain a complete picture of structure-forming factors.

Computing details

Data reduction: PROMETHEUS (Zucker et al., 1983); program(s) used to refine structure: MOLDOS96 (J. Protas, 1996).

Figures

(datolite)

Crystal data

BCaHO5Si	F(000) = 320
Mr = 159.99	Dx = 2.988 Mg m^−3
Monoclinic, P21/a	Mo Kα radiation, λ = 0.71069 Å
Hall symbol: -P 2yab	Cell parameters from 15 reflections
a = 9.646 (6) Å	θ = 6.0–12.8°
b = 7.620 (4) Å	µ = 1.99 mm^−1
c = 4.839 (3) Å	T = 293 K
β = 90.14 (5)°	Sphere, pale green
V = 355.7 (4) Å^3	0.25 × 0.25 × 0.25 × 0.13 (radius) mm
Z = 4

Data collection

Four-circle diffractometer	2584 reflections with I > 1.96u(I)
Radiation source: Normal focus Mo-X-ray 40kV-20 mA	Rint = 0.026
Graphite monochromator	θmax = 50.1°, θmin = 7.0°
integrated intensities data fom θ/2θ scans	h = −20→20
Absorption correction: for a sphere Zucker et al. (1983)	k = −15→15
Tmin = ?, Tmax = ?	l = −10→10
6018 measured reflections	1 standard reflections every 100 reflections
2584 independent reflections	intensity decay: no decay, variation 2%

Refinement

Refinement on F	w = 1/(s**2 + 0.000225F**2)
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.014	Δρmax = 0.63 e Å^−3
wR(F^2) = 0.019	Δρmin = −0.36 e Å^−3
S = 1.04	Extinction correction: Becker-Coppens type 1 isotropic
2583 reflections	Extinction coefficient: 0.56 (2)
267 parameters

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

	x	y	z	Uiso*/Ueq
H	0.584	0.552	0.829	0.036 (7)*
B	0.34077 (5)	0.41057 (6)	0.56786 (10)	0.0054 (3)
Ca	0.33610 (1)	0.10613 (1)	0.99161 (2)	0.00639 (5)
O1	0.03739 (5)	0.40109 (6)	0.24048 (9)	0.0074 (2)
O2	0.45730 (4)	0.30115 (5)	0.67017 (8)	0.0063 (2)
O3	0.21047 (4)	0.33474 (6)	0.67514 (8)	0.0063 (2)
O4	0.14598 (5)	0.08787 (5)	0.31499 (9)	0.0070 (2)
O5	0.33680 (5)	0.41344 (6)	0.25851 (9)	0.0073 (2)
Si	0.08438 (1)	0.26617 (2)	0.46891 (3)	0.00425 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
B	0.00482 (14)	0.00566 (15)	0.00583 (14)	−0.00014 (12)	0.00031 (12)	−0.00006 (11)
Ca	0.00589 (3)	0.00680 (3)	0.00647 (3)	−0.00007 (2)	0.00041 (2)	−0.00047 (2)
O1	0.00735 (13)	0.00702 (12)	0.00792 (12)	−0.00029 (11)	−0.00136 (11)	0.00287 (10)
O2	0.00488 (12)	0.00751 (13)	0.00637 (12)	0.00201 (10)	0.00101 (9)	0.00095 (10)
O3	0.00451 (11)	0.00832 (13)	0.00601 (12)	−0.00182 (10)	−0.00005 (9)	0.00027 (10)
O4	0.00888 (14)	0.00427 (12)	0.00798 (12)	0.00083 (10)	0.00233 (11)	0.00022 (9)
O5	0.00700 (13)	0.00978 (14)	0.00509 (11)	−0.00055 (11)	0.00020 (10)	0.00063 (10)
Si	0.00371 (5)	0.00411 (5)	0.00492 (5)	−0.00028 (3)	0.00006 (3)	0.00032 (3)

Geometric parameters (Å, º)

Si—O1	1.5754 (11)	Ca—O1^iv	2.2830 (15)
Si—O2^i	1.6493 (11)	Ca—O2	2.4502 (16)
Si—O3	1.6560 (11)	Ca—O3^v	2.6613 (17)
Si—O4	1.6601 (11)	Ca—O3	2.6152 (17)
B—O2	1.4836 (11)	Ca—O4^vi	2.4177 (16)
B—O3	1.4786 (11)	Ca—O5^iii	2.5283 (16)
B—O4^ii	1.4706 (11)	Ca—O5^vi	2.6743 (17)
B—O5	1.4975 (11)	O5—H^vii	0.9100
Ca—O1^iii	2.2800 (15)
O1—Si—O2^i	113.85 (5)	O1^iv—Ca—O3^v	78.83 (5)
O1—Si—O3	115.25 (6)	O1^iv—Ca—O3	135.83 (5)
O1—Si—O4	108.78 (6)	O1^iv—Ca—O4^vi	107.62 (5)
O2^i—Si—O3	106.75 (5)	O1^iv—Ca—O5^iii	142.91 (5)
O2^i—Si—O4	106.13 (5)	O1^iv—Ca—O5^vi	76.42 (5)
O3—Si—O4	105.39 (5)	O2—Ca—O3^v	159.63 (5)
O2—B—O3	107.89 (6)	O2—Ca—O3	56.32 (5)
O2—B—O4^ii	108.82 (6)	O2—Ca—O4^vi	144.06 (5)
O2—B—O5	111.06 (6)	O2—Ca—O5^iii	111.32 (5)
O3—B—O4^ii	107.27 (6)	O2—Ca—O5^vi	76.99 (5)
O3—B—O5	109.69 (6)	O3^v—Ca—O3	142.54 (5)
O4^ii—B—O5	111.96 (6)	O3^v—Ca—O4^vi	55.50 (5)
O1^iii—Ca—O1^iv	77.75 (5)	O3^v—Ca—O5^iii	74.14 (5)
O1^iii—Ca—O2	81.15 (5)	O3^v—Ca—O5^vi	112.83 (5)
O1^iii—Ca—O3^v	81.80 (5)	O3—Ca—O4^vi	93.80 (5)
O1^iii—Ca—O3	114.57 (5)	O3—Ca—O5^iii	78.60 (5)
O1^iii—Ca—O4^vi	133.40 (5)	O3—Ca—O5^vi	72.55 (5)
O1^iii—Ca—O5^iii	73.71 (5)	O4^vi—Ca—O5^iii	77.05 (5)
O1^iii—Ca—O5^vi	146.85 (5)	O4^vi—Ca—O5^vi	74.86 (5)
O1^iv—Ca—O2	86.73 (5)	O5^iii—Ca—O5^vi	137.78 (5)

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