The structure and absolute configuration of the title compound, Λ-(+)589-[Co(C2H8N2)3]I3·H2O, has been determined. The configuration of the complex cation [Co(en)3]3+ is Λ(δδλ).
Supporting information
CCDC reference: 175331
Key indicators
- Single-crystal X-ray study
- T = 123 K
- Mean (C-C) = 0.005 Å
- R factor = 0.023
- wR factor = 0.066
- Data-to-parameter ratio = 32.1
checkCIF results
No syntax errors found
ADDSYM reports no extra symmetry
Alert Level C:
PLAT_420 Alert C D-H Without Acceptor N3 - H3N ?
PLAT_420 Alert C D-H Without Acceptor N3 - H3N' ?
PLAT_420 Alert C D-H Without Acceptor N4 - H4N ?
General Notes
REFLT_03
From the CIF: _diffrn_reflns_theta_max 30.10
From the CIF: _reflns_number_total 5190
Count of symmetry unique reflns 2943
Completeness (_total/calc) 176.35%
TEST3: Check Friedels for noncentro structure
Estimate of Friedel pairs measured 2247
Fraction of Friedel pairs measured 0.764
Are heavy atom types Z>Si present yes
Please check that the estimate of the number of Friedel pairs is
correct. If it is not, please give the correct count in the
_publ_section_exptl_refinement section of the submitted CIF.
0 Alert Level A = Potentially serious problem
0 Alert Level B = Potential problem
3 Alert Level C = Please check
[Co(en)3]Cl.d-tart·5H2O was prepared as described by Werner (1912) and
was divided into its optical isomers by using solubility differences of
diastereoisomer with d-tartrate. The optical isomer
Λ-(+)589-[Co(en)3]Cl.d-tart·5H2O was converted into (I) by shaking
with sodium iodide. The specific rotation of (I) in an aqueous solution at Na
D line (589 nm) is +88.8° g-1 cm3 dm-1. Crystals of (I) were grown from
15% NaI aqueous solution by slow evaporation at 277 K. Because they
effloresence in air, the specimen was protected by liquid paraffin and kept at
123 K during X-ray experiments.
All H atoms of the en ligands were placed in idealized positions and refined as
riding atoms with relative isotropic displacement parameters. Those of the
water molecule were located from difference Fourier maps and refined for their
positional parameters.
Data collection: PROCESS-AUTO (Rigaku, 1998); cell refinement: PROCESS-AUTO; data reduction: TEXSAN (Molecular Structure Corporation and Rigaku, 1999); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: TEXSAN; molecular graphics: ORTEPII (Johnson, 1976); software used to prepare material for publication: TEXSAN.
Crystal data top
[Co(C2H8N2)3]I3·H2O | F(000) = 1192 |
Mr = 637.96 | Dx = 2.397 Mg m−3 |
Orthorhombic, P212121 | Mo Kα radiation, λ = 0.7107 Å |
Hall symbol: P 2ac 2ab | Cell parameters from 10070 reflections |
a = 8.4086 (4) Å | θ = 2.2–20.8° |
b = 11.2321 (6) Å | µ = 6.21 mm−1 |
c = 18.7217 (7) Å | T = 123 K |
V = 1768.2 (1) Å3 | Block, red |
Z = 4 | 0.40 × 0.35 × 0.30 mm |
Data collection top
Rigaku RAXIS-RAPID Imaging Plate diffractometer | 5024 reflections with F2 > 2σ(F2) |
Detector resolution: 10.00 pixels mm-1 | Rint = 0.028 |
ω scans | θmax = 30.1° |
Absorption correction: integration (NUMABS; Higashi, 1999) | h = −11→11 |
Tmin = 0.098, Tmax = 0.155 | k = −15→15 |
20028 measured reflections | l = −26→26 |
5190 independent reflections | |
Refinement top
Refinement on F2 | w = 1/[σ2(Fo2) + {0.05[Max(Fo2,0) + 2Fc2]/3}2] |
R[F2 > 2σ(F2)] = 0.023 | (Δ/σ)max = 0.001 |
wR(F2) = 0.066 | Δρmax = 0.41 e Å−3 |
S = 1.04 | Δρmin = −0.83 e Å−3 |
5163 reflections | Absolute structure: (Flack, 1983), 2247 Friedel pairs |
161 parameters | Absolute structure parameter: 0.01 (3) |
H atoms treated by a mixture of independent and constrained refinement | |
Crystal data top
[Co(C2H8N2)3]I3·H2O | V = 1768.2 (1) Å3 |
Mr = 637.96 | Z = 4 |
Orthorhombic, P212121 | Mo Kα radiation |
a = 8.4086 (4) Å | µ = 6.21 mm−1 |
b = 11.2321 (6) Å | T = 123 K |
c = 18.7217 (7) Å | 0.40 × 0.35 × 0.30 mm |
Data collection top
Rigaku RAXIS-RAPID Imaging Plate diffractometer | 5190 independent reflections |
Absorption correction: integration (NUMABS; Higashi, 1999) | 5024 reflections with F2 > 2σ(F2) |
Tmin = 0.098, Tmax = 0.155 | Rint = 0.028 |
20028 measured reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.023 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.066 | Δρmax = 0.41 e Å−3 |
S = 1.04 | Δρmin = −0.83 e Å−3 |
5163 reflections | Absolute structure: (Flack, 1983), 2247 Friedel pairs |
161 parameters | Absolute structure parameter: 0.01 (3) |
Special details top
Refinement. Refinement using reflections with F2 > -3.0 σ(F2). The
weighted R-factor (wR) and goodness of fit (S) are based
on F2. R-factor (gt) are based on F. The threshold
expression of F2 > 2.0 σ(F2) is used only for calculating
R-factor (gt). |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
I1 | −0.27354 (3) | 0.29713 (2) | 0.43098 (1) | 0.01783 (5) | |
I2 | 0.27602 (3) | 0.20650 (2) | 0.15342 (1) | 0.01797 (5) | |
I3 | −0.23108 (3) | 0.39484 (2) | 0.19287 (1) | 0.01579 (5) | |
Co1 | 0.21642 (5) | 0.47850 (4) | 0.35446 (2) | 0.00957 (8) | |
O1 | 0.5136 (5) | 0.5259 (3) | 0.5261 (2) | 0.0356 (9) | |
N1 | 0.3277 (4) | 0.3618 (3) | 0.4132 (2) | 0.0141 (6) | |
N2 | 0.1070 (3) | 0.3399 (3) | 0.3121 (2) | 0.0137 (6) | |
N3 | 0.3900 (3) | 0.4734 (3) | 0.2839 (2) | 0.0149 (6) | |
N4 | 0.1087 (3) | 0.5838 (3) | 0.2858 (2) | 0.0146 (6) | |
N5 | 0.3167 (4) | 0.6136 (3) | 0.4054 (2) | 0.0164 (6) | |
N6 | 0.0457 (4) | 0.4964 (3) | 0.4252 (2) | 0.0165 (6) | |
C1 | 0.3161 (4) | 0.2424 (3) | 0.3780 (2) | 0.0164 (7) | |
C2 | 0.1474 (4) | 0.2302 (3) | 0.3539 (2) | 0.0147 (7) | |
C3 | 0.3620 (4) | 0.5643 (3) | 0.2267 (2) | 0.0177 (7) | |
C4 | 0.1846 (4) | 0.5692 (3) | 0.2146 (2) | 0.0169 (7) | |
C5 | 0.2028 (5) | 0.6670 (3) | 0.4564 (2) | 0.0230 (9) | |
C6 | 0.1054 (5) | 0.5660 (4) | 0.4877 (2) | 0.0228 (9) | |
H1N | 0.4362 | 0.3839 | 0.4177 | 0.0170* | |
H1N' | 0.2802 | 0.3585 | 0.4592 | 0.0170* | |
H1O | 0.579 (9) | 0.459 (6) | 0.523 (4) | 0.0431* | |
H1O' | 0.542 (8) | 0.575 (6) | 0.568 (4) | 0.0431* | |
H1a | 0.3862 | 0.2383 | 0.3383 | 0.0196* | |
H1b | 0.3419 | 0.1812 | 0.4111 | 0.0196* | |
H2N | −0.0047 | 0.3524 | 0.3134 | 0.0164* | |
H2N' | 0.1404 | 0.3302 | 0.2640 | 0.0164* | |
H2a | 0.0791 | 0.2233 | 0.3941 | 0.0176* | |
H2b | 0.1364 | 0.1616 | 0.3246 | 0.0176* | |
H3N | 0.4880 | 0.4898 | 0.3071 | 0.0180* | |
H3N' | 0.3942 | 0.3964 | 0.2630 | 0.0180* | |
H3a | 0.4001 | 0.6399 | 0.2416 | 0.0212* | |
H3b | 0.4147 | 0.5414 | 0.1839 | 0.0212* | |
H4N | −0.0006 | 0.5630 | 0.2828 | 0.0175* | |
H4N' | 0.1183 | 0.6641 | 0.3009 | 0.0175* | |
H4a | 0.1492 | 0.4975 | 0.1929 | 0.0202* | |
H4b | 0.1587 | 0.6348 | 0.1848 | 0.0202* | |
H5N | 0.4072 | 0.5859 | 0.4308 | 0.0197* | |
H5N' | 0.3485 | 0.6722 | 0.3717 | 0.0197* | |
H5a | 0.2585 | 0.7074 | 0.4932 | 0.0276* | |
H5b | 0.1351 | 0.7215 | 0.4322 | 0.0276* | |
H6N | −0.0414 | 0.5372 | 0.4041 | 0.0197* | |
H6N' | 0.0119 | 0.4200 | 0.4408 | 0.0197* | |
H6a | 0.0189 | 0.5966 | 0.5147 | 0.0274* | |
H6b | 0.1699 | 0.5173 | 0.5174 | 0.0274* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
I1 | 0.01328 (9) | 0.0218 (1) | 0.0184 (1) | 0.00009 (9) | −0.00024 (7) | −0.00200 (8) |
I2 | 0.0170 (1) | 0.0202 (1) | 0.01671 (9) | −0.00206 (9) | 0.00326 (8) | −0.00106 (8) |
I3 | 0.01590 (9) | 0.01023 (9) | 0.0212 (1) | 0.00086 (7) | 0.00111 (8) | 0.00006 (7) |
Co1 | 0.0094 (2) | 0.0080 (2) | 0.0114 (2) | 0.0001 (2) | −0.0005 (2) | −0.0004 (1) |
O1 | 0.045 (2) | 0.035 (2) | 0.027 (2) | 0.002 (2) | −0.012 (2) | −0.009 (1) |
N1 | 0.015 (1) | 0.014 (1) | 0.013 (1) | 0.0017 (10) | −0.004 (1) | −0.0009 (9) |
N2 | 0.014 (1) | 0.013 (1) | 0.015 (1) | −0.0012 (9) | −0.005 (1) | 0.0010 (10) |
N3 | 0.014 (1) | 0.018 (1) | 0.013 (1) | 0.001 (1) | 0.0019 (9) | 0.0015 (10) |
N4 | 0.015 (1) | 0.011 (1) | 0.017 (1) | 0.0014 (10) | 0.0008 (10) | 0.0043 (10) |
N5 | 0.021 (1) | 0.012 (1) | 0.016 (1) | −0.005 (1) | −0.001 (1) | −0.0022 (10) |
N6 | 0.017 (1) | 0.012 (1) | 0.020 (1) | −0.001 (1) | 0.0065 (9) | 0.001 (1) |
C1 | 0.018 (1) | 0.011 (1) | 0.021 (2) | 0.005 (1) | 0.000 (1) | −0.002 (1) |
C2 | 0.020 (1) | 0.008 (1) | 0.016 (1) | 0.001 (1) | −0.002 (1) | −0.001 (1) |
C3 | 0.016 (1) | 0.019 (2) | 0.018 (2) | 0.002 (1) | 0.005 (1) | 0.006 (1) |
C4 | 0.019 (1) | 0.016 (2) | 0.016 (1) | 0.000 (1) | −0.002 (1) | 0.004 (1) |
C5 | 0.030 (2) | 0.018 (2) | 0.021 (2) | 0.000 (1) | 0.007 (1) | −0.005 (1) |
C6 | 0.031 (2) | 0.019 (2) | 0.018 (2) | −0.001 (1) | 0.008 (1) | −0.003 (1) |
Geometric parameters (Å, º) top
CO1—N1 | 1.949 (3) | N5—H5N | 0.950 |
CO1—N2 | 1.975 (3) | N5—H5N' | 0.950 |
CO1—N3 | 1.969 (3) | N6—C6 | 1.494 (5) |
CO1—N4 | 1.968 (3) | N6—H6N | 0.950 |
CO1—N5 | 1.981 (3) | N6—H6N' | 0.950 |
CO1—N6 | 1.963 (3) | C1—C2 | 1.495 (5) |
O1—H1O | 0.93 (7) | C1—H1a | 0.950 |
O1—H1O' | 0.99 (7) | C1—H1b | 0.950 |
N1—C1 | 1.497 (4) | C2—H2a | 0.950 |
N1—H1N | 0.950 | C2—H2b | 0.950 |
N1—H1N' | 0.950 | C3—C4 | 1.510 (5) |
N2—C2 | 1.499 (4) | C3—H3a | 0.950 |
N2—H2N | 0.950 | C3—H3b | 0.950 |
N2—H2N' | 0.950 | C4—H4a | 0.950 |
N3—C3 | 1.499 (5) | C4—H4b | 0.950 |
N3—H3N | 0.950 | C5—C6 | 1.517 (6) |
N3—H3N' | 0.950 | C5—H5a | 0.950 |
N4—C4 | 1.486 (5) | C5—H5b | 0.950 |
N4—H4N | 0.950 | C6—H6a | 0.950 |
N4—H4N' | 0.950 | C6—H6b | 0.950 |
N5—C5 | 1.479 (5) | | |
| | | |
I1···N1i | 3.447 (3) | O1···N1 | 3.211 (5) |
I1···N6 | 3.497 (3) | O1···C5 | 3.324 (6) |
I1···N1ii | 3.525 (3) | O1···C6 | 3.536 (6) |
O1···N5 | 2.970 (5) | C2···C4iii | 3.565 (5) |
| | | |
N1—CO1—N2 | 85.4 (1) | C5—N5—H5N' | 109.3 |
N1—CO1—N3 | 90.2 (1) | H5N—N5—H5N' | 109.5 |
N1—CO1—N4 | 173.3 (1) | CO1—N6—C6 | 109.7 (2) |
N1—CO1—N5 | 92.3 (1) | CO1—N6—H6N | 109.4 |
N1—CO1—N6 | 92.3 (1) | CO1—N6—H6N' | 109.4 |
N2—CO1—N3 | 93.0 (1) | C6—N6—H6N | 109.4 |
N2—CO1—N4 | 89.8 (1) | C6—N6—H6N' | 109.4 |
N2—CO1—N5 | 174.7 (1) | H6N—N6—H6N' | 109.5 |
N2—CO1—N6 | 90.6 (1) | N1—C1—C2 | 106.1 (3) |
N3—CO1—N4 | 85.4 (1) | N1—C1—H1a | 110.3 |
N3—CO1—N5 | 91.7 (1) | N1—C1—H1b | 110.3 |
N3—CO1—N6 | 175.8 (1) | C2—C1—H1a | 110.3 |
N4—CO1—N5 | 92.9 (1) | C2—C1—H1b | 110.3 |
N4—CO1—N6 | 92.4 (1) | H1a—C1—H1b | 109.5 |
N5—CO1—N6 | 84.7 (1) | N2—C2—C1 | 107.3 (3) |
H1O—O1—H1O' | 110 (7) | N2—C2—H2a | 110.0 |
CO1—N1—C1 | 108.9 (2) | N2—C2—H2b | 110.0 |
CO1—N1—H1N | 109.6 | C1—C2—H2a | 110.0 |
CO1—N1—H1N' | 109.6 | C1—C2—H2b | 110.0 |
C1—N1—H1N | 109.6 | H2a—C2—H2b | 109.5 |
C1—N1—H1N' | 109.6 | N3—C3—C4 | 106.7 (3) |
H1N—N1—H1N' | 109.5 | N3—C3—H3a | 110.2 |
CO1—N2—C2 | 109.4 (2) | N3—C3—H3b | 110.2 |
CO1—N2—H2N | 109.5 | C4—C3—H3a | 110.2 |
CO1—N2—H2N' | 109.5 | C4—C3—H3b | 110.2 |
C2—N2—H2N | 109.5 | H3a—C3—H3b | 109.4 |
C2—N2—H2N' | 109.5 | N4—C4—C3 | 107.1 (3) |
H2N—N2—H2N' | 109.5 | N4—C4—H4a | 110.1 |
CO1—N3—C3 | 110.1 (2) | N4—C4—H4b | 110.1 |
CO1—N3—H3N | 109.3 | C3—C4—H4a | 110.0 |
CO1—N3—H3N' | 109.3 | C3—C4—H4b | 110.0 |
C3—N3—H3N | 109.3 | H4a—C4—H4b | 109.5 |
C3—N3—H3N' | 109.3 | N5—C5—C6 | 107.2 (3) |
H3N—N3—H3N' | 109.5 | N5—C5—H5a | 110.0 |
CO1—N4—C4 | 108.8 (2) | N5—C5—H5b | 110.0 |
CO1—N4—H4N | 109.6 | C6—C5—H5a | 110.0 |
CO1—N4—H4N' | 109.6 | C6—C5—H5b | 110.0 |
C4—N4—H4N | 109.7 | H5a—C5—H5b | 109.5 |
C4—N4—H4N' | 109.7 | N6—C6—C5 | 105.6 (3) |
H4N—N4—H4N' | 109.4 | N6—C6—H6a | 110.4 |
CO1—N5—C5 | 110.2 (2) | N6—C6—H6b | 110.4 |
CO1—N5—H5N | 109.3 | C5—C6—H6a | 110.4 |
CO1—N5—H5N' | 109.3 | C5—C6—H6b | 110.4 |
C5—N5—H5N | 109.3 | H6a—C6—H6b | 109.5 |
Symmetry codes: (i) x−1, y, z; (ii) x−1/2, −y+1/2, −z+1; (iii) −x, y−1/2, −z+1/2. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1N′···N6 | 0.95 | 2.59 | 2.821 (4) | 94 |
N2—H2N′···N3 | 0.95 | 2.67 | 2.862 (4) | 92 |
N3—H3N′···N2 | 0.95 | 2.66 | 2.862 (4) | 92 |
N4—H4N′···N5 | 0.95 | 2.63 | 2.862 (4) | 94 |
N5—H5N···N1 | 0.95 | 2.63 | 2.834 (4) | 93 |
N6—H6N···N4 | 0.95 | 2.60 | 2.838 (4) | 94 |
N1—H1N···O1 | 0.95 | 2.66 | 3.211 (4) | 117 |
N5—H5N···O1 | 0.95 | 2.11 | 2.970 (4) | 150 |
Experimental details
Crystal data |
Chemical formula | [Co(C2H8N2)3]I3·H2O |
Mr | 637.96 |
Crystal system, space group | Orthorhombic, P212121 |
Temperature (K) | 123 |
a, b, c (Å) | 8.4086 (4), 11.2321 (6), 18.7217 (7) |
V (Å3) | 1768.2 (1) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 6.21 |
Crystal size (mm) | 0.40 × 0.35 × 0.30 |
|
Data collection |
Diffractometer | Rigaku RAXIS-RAPID Imaging Plate diffractometer |
Absorption correction | Integration (NUMABS; Higashi, 1999) |
Tmin, Tmax | 0.098, 0.155 |
No. of measured, independent and observed [F2 > 2σ(F2)] reflections | 20028, 5190, 5024 |
Rint | 0.028 |
(sin θ/λ)max (Å−1) | 0.706 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.023, 0.066, 1.04 |
No. of reflections | 5163 |
No. of parameters | 161 |
No. of restraints | ? |
H-atom treatment | H atoms treated by a mixture of independent and constrained refinement |
Δρmax, Δρmin (e Å−3) | 0.41, −0.83 |
Absolute structure | (Flack, 1983), 2247 Friedel pairs |
Absolute structure parameter | 0.01 (3) |
Selected geometric parameters (Å, º) topCO1—N1 | 1.949 (3) | CO1—N4 | 1.968 (3) |
CO1—N2 | 1.975 (3) | CO1—N5 | 1.981 (3) |
CO1—N3 | 1.969 (3) | CO1—N6 | 1.963 (3) |
| | | |
N1—CO1—N2 | 85.4 (1) | N2—CO1—N6 | 90.6 (1) |
N1—CO1—N3 | 90.2 (1) | N3—CO1—N4 | 85.4 (1) |
N1—CO1—N4 | 173.3 (1) | N3—CO1—N5 | 91.7 (1) |
N1—CO1—N5 | 92.3 (1) | N3—CO1—N6 | 175.8 (1) |
N1—CO1—N6 | 92.3 (1) | N4—CO1—N5 | 92.9 (1) |
N2—CO1—N3 | 93.0 (1) | N4—CO1—N6 | 92.4 (1) |
N2—CO1—N4 | 89.8 (1) | N5—CO1—N6 | 84.7 (1) |
N2—CO1—N5 | 174.7 (1) | | |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1N'···N6 | 0.95 | 2.59 | 2.821 (4) | 94 |
N2—H2N'···N3 | 0.95 | 2.67 | 2.862 (4) | 92 |
N3—H3N'···N2 | 0.95 | 2.66 | 2.862 (4) | 92 |
N4—H4N'···N5 | 0.95 | 2.63 | 2.862 (4) | 94 |
N5—H5N···N1 | 0.95 | 2.63 | 2.834 (4) | 93 |
N6—H6N···N4 | 0.95 | 2.60 | 2.838 (4) | 94 |
N1—H1N···O1 | 0.95 | 2.66 | 3.211 (4) | 117 |
N5—H5N···O1 | 0.95 | 2.11 | 2.970 (4) | 150 |
The compound with the complex cation [Co(en)3]3+ (en = ethylenediamine) has played an important role in the development of crystallography for chiral crystals. [Co(en)3]3+ was the first transition metal complex not only to have its absolute configuration determined with anomalous scattering of X-rays (Saito et al., 1955) but also to have its circular dichroism (CD) spectrum measured in both the solid and solution state (Mathieu, 1953; McCaffery & Mason, 1963). Therefore, it has been regarded as a typical substance for investigating the relationship between a chiral crystal structure and the CD spectrum (Kuroda & Saito, 1976; Mason & Seal, 1976; Ernst & Royer, 1993).
In this study, we have examined the crystal structure and absolute configuration of the title compound, (I), for our study of the anisotropic character of optical activity (OA) and CD for [Co(en)3]3+ in the solid state. The ratio of the lattice constants is a:b:c = 0.449:0.600:1, explicitly different from that reported by Jaeger (1919) of a:b:c = 0.8276:1:0.7386. On the other hand, the ratio of the lattice constants of the racemic compound (Whuler et al., 1980) is similar to Jaeger's report (Jaeger, 1919).
The configuration of the [Co(en)3]3+ complex in (I) is Λ(δδλ), meaning the lel2ob form of the three ethylenediamine ligands. In the crystals of the racemate, the configuration is ob2lel (Whuler et al., 1980). Usually there occurs an inversion between conformations of ethylenediamine ligands δ and λ in solution. However, the difference of free energy of each ligand between δ and λ was reported to be about 2 kJ mol-1 (Beattie, 1971; Sudmeier et al., 1971). From a thermodynamic poit of view, the magnitude of enthalpies in various configurations of [Co(en)3]3+ was shown as follows; lel3 < lel2ob < ob2lel < ob3, where statistical and other entropy effects were not considered. The lel2ob configuration is more stable than ob2lel energetically. The complex cation in (I) may be energetically more stable than that in the racemate if the hydrogen bonding is not considered.
In (I), the Co—N bond distances are 1.949 (3)–1.981 (3) Å and the N—Co—N bond angles are 84.7 (1)–93.0 (1) and 173.3 (1)–175.8 (1)°. As shown in Fig. 2, the C3 axis of the complex cation is approximately parallel to a.