The title molecule, [Ni(C6H17N3O)2](ClO4)2, possesses a crystallographic centre of symmetry at the NiII position. The coordination geometry around the NiII atom is distorted octahedral, consisting of six N atoms from two tripodal polyamine ligands, while the ethanol O atoms of the ligands remain uncoordinated. The crystal packing shows two-dimensional layers and an infinite three-dimensional framework which is stabilized by a hydrogen-bonded network.
Supporting information
CCDC reference: 158237
The title compound was synthesized by mixing the ligand
2-[bis(2-aminoethyl)amino]ethanol (0.147 g, 1 mmol) and NiII(ClO4)2.
6H2O (0.366 g, 1 mmol) in water. Purple crystals were obtained upon
evaporation.
Data were corrected for Lorentz and polarization effects. The H atoms were
geometrically fixed.
Data collection: XSCANS (Siemens, 1994); cell refinement: XSCANS; data reduction: SHELXTL (Sheldrick, 1990); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.
Bis{2-[bis(2-aminoethyl)amino]ethanol}-nickel(II) perchlorate
top
Crystal data top
[Ni(C6H17N3O)2](ClO4)2 | F(000) = 580 |
Mr = 552.06 | Dx = 1.648 Mg m−3 |
Monoclinic, P21/n | Mo Kα radiation, λ = 0.71073 Å |
a = 9.026 (1) Å | Cell parameters from 25 reflections |
b = 12.623 (2) Å | θ = 3.0–16.2° |
c = 10.683 (1) Å | µ = 1.17 mm−1 |
β = 113.90 (1)° | T = 298 K |
V = 1112.8 (2) Å3 | Prism, purple |
Z = 2 | 0.50 × 0.44 × 0.32 mm |
Data collection top
Siemens P4 diffractometer | 1700 reflections with I > 2σ(I) |
Radiation source: normal-focus sealed tube | Rint = 0.016 |
Graphite monochromator | θmax = 25.5°, θmin = 2.5° |
ω scans | h = 0→10 |
Absorption correction: empirical (using intensity measurements) (North et al., 1968) | k = 0→15 |
Tmin = 0.598, Tmax = 0.687 | l = −12→11 |
2397 measured reflections | 3 standard reflections every 97 reflections |
2061 independent reflections | intensity decay: 2.3% |
Refinement top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
R[F2 > 2σ(F2)] = 0.037 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.105 | w = 1/[σ2(Fo2) + (0.0669P)2 + 0.1837P] where P = (Fo2 + 2Fc2)/3 |
S = 1.06 | (Δ/σ)max = 0.001 |
2061 reflections | Δρmax = 0.59 e Å−3 |
192 parameters | Δρmin = −0.39 e Å−3 |
10 restraints | Extinction correction: SHELXL97 (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.0079 (18) |
Crystal data top
[Ni(C6H17N3O)2](ClO4)2 | V = 1112.8 (2) Å3 |
Mr = 552.06 | Z = 2 |
Monoclinic, P21/n | Mo Kα radiation |
a = 9.026 (1) Å | µ = 1.17 mm−1 |
b = 12.623 (2) Å | T = 298 K |
c = 10.683 (1) Å | 0.50 × 0.44 × 0.32 mm |
β = 113.90 (1)° | |
Data collection top
Siemens P4 diffractometer | 1700 reflections with I > 2σ(I) |
Absorption correction: empirical (using intensity measurements) (North et al., 1968) | Rint = 0.016 |
Tmin = 0.598, Tmax = 0.687 | 3 standard reflections every 97 reflections |
2397 measured reflections | intensity decay: 2.3% |
2061 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.037 | 10 restraints |
wR(F2) = 0.105 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.06 | Δρmax = 0.59 e Å−3 |
2061 reflections | Δρmin = −0.39 e Å−3 |
192 parameters | |
Special details top
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes)
are estimated using the full covariance matrix. The cell e.s.d.'s are taken
into account individually in the estimation of e.s.d.'s in distances, angles
and torsion angles; correlations between e.s.d.'s in cell parameters are only
used when they are defined by crystal symmetry. An approximate (isotropic)
treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s.
planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor
wR and goodness of fit S are based on F2, conventional
R-factors R are based on F, with F set to zero for
negative F2. The threshold expression of F2 >
σ(F2) is used only for calculating R-factors(gt) etc.
and is not relevant to the choice of reflections for refinement.
R-factors based on F2 are statistically about twice as large
as those based on F, and R- factors based on ALL data will be
even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Ni | 0.0000 | 0.0000 | 0.0000 | 0.03322 (19) | |
O1 | 0.3478 (3) | 0.3406 (2) | 0.0922 (3) | 0.0696 (7) | |
N1 | 0.1795 (3) | 0.11752 (18) | 0.0019 (2) | 0.0399 (5) | |
N2 | 0.0635 (3) | −0.07110 (19) | −0.1514 (3) | 0.0475 (6) | |
H2A | 0.0853 | −0.1402 | −0.1320 | 0.057* | |
H2B | −0.0203 | −0.0661 | −0.2338 | 0.057* | |
N3 | 0.2068 (3) | −0.06743 (19) | 0.1594 (2) | 0.0450 (6) | |
H3A | 0.1894 | −0.0718 | 0.2364 | 0.054* | |
H3B | 0.2231 | −0.1334 | 0.1355 | 0.054* | |
C1 | 0.2132 (5) | 0.0962 (3) | −0.1195 (4) | 0.0661 (10) | |
H1A | 0.3202 | 0.1229 | −0.1030 | 0.079* | |
H1B | 0.1355 | 0.1347 | −0.1968 | 0.079* | |
C2 | 0.2054 (6) | −0.0183 (3) | −0.1560 (5) | 0.0717 (11) | |
H2C | 0.2026 | −0.0251 | −0.2474 | 0.086* | |
H2D | 0.3027 | −0.0534 | −0.0930 | 0.086* | |
C3 | 0.3212 (4) | 0.1045 (3) | 0.1340 (4) | 0.0633 (9) | |
H3C | 0.4166 | 0.1305 | 0.1234 | 0.076* | |
H3D | 0.3052 | 0.1486 | 0.2019 | 0.076* | |
C4 | 0.3522 (5) | −0.0024 (3) | 0.1854 (5) | 0.0775 (13) | |
H4A | 0.4158 | 0.0004 | 0.2835 | 0.093* | |
H4B | 0.4174 | −0.0376 | 0.1446 | 0.093* | |
C5 | 0.1144 (4) | 0.2271 (3) | −0.0080 (4) | 0.0623 (9) | |
H5A | 0.0976 | 0.2407 | 0.0747 | 0.075* | |
H5B | 0.0086 | 0.2285 | −0.0837 | 0.075* | |
C6 | 0.2115 (5) | 0.3185 (3) | −0.0272 (4) | 0.0701 (10) | |
H6A | 0.2455 | 0.3015 | −0.1001 | 0.084* | |
H6B | 0.1433 | 0.3810 | −0.0545 | 0.084* | |
Cl | −0.2791 (7) | 0.3491 (5) | 0.0071 (5) | 0.0512 (11) | 0.50 |
O2 | −0.3952 (13) | 0.4190 (7) | 0.0207 (17) | 0.068 (3) | 0.50 |
O3 | −0.1755 (11) | 0.3094 (7) | 0.1357 (6) | 0.079 (3) | 0.50 |
O4 | −0.3545 (12) | 0.2592 (6) | −0.0712 (11) | 0.117 (4) | 0.50 |
O5 | −0.1852 (10) | 0.4025 (6) | −0.0511 (10) | 0.111 (3) | 0.50 |
Cl' | −0.2914 (8) | 0.3279 (5) | 0.0128 (6) | 0.0567 (14) | 0.50 |
O2' | −0.4037 (18) | 0.4124 (10) | −0.0151 (19) | 0.111 (6) | 0.50 |
O3' | −0.3515 (17) | 0.2410 (8) | 0.0609 (19) | 0.205 (6) | 0.50 |
O4' | −0.2909 (14) | 0.2925 (11) | −0.1112 (8) | 0.122 (4) | 0.50 |
O5' | −0.1399 (12) | 0.3495 (13) | 0.1173 (15) | 0.201 (9) | 0.50 |
H1 | 0.417 (3) | 0.372 (4) | 0.075 (2) | 0.110 (18)* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Ni | 0.0295 (3) | 0.0379 (3) | 0.0331 (3) | 0.00180 (19) | 0.01355 (19) | −0.00067 (19) |
O1 | 0.0707 (16) | 0.0752 (17) | 0.0666 (16) | −0.0282 (14) | 0.0316 (14) | −0.0081 (13) |
N1 | 0.0337 (12) | 0.0455 (13) | 0.0412 (13) | −0.0011 (10) | 0.0160 (10) | 0.0023 (10) |
N2 | 0.0505 (15) | 0.0484 (14) | 0.0488 (14) | 0.0003 (11) | 0.0254 (12) | −0.0096 (11) |
N3 | 0.0412 (13) | 0.0450 (14) | 0.0458 (13) | 0.0047 (11) | 0.0146 (11) | 0.0041 (11) |
C1 | 0.078 (2) | 0.077 (2) | 0.062 (2) | −0.019 (2) | 0.0470 (19) | −0.0085 (18) |
C2 | 0.091 (3) | 0.068 (2) | 0.087 (3) | −0.009 (2) | 0.068 (3) | −0.0165 (19) |
C3 | 0.0449 (17) | 0.074 (2) | 0.056 (2) | −0.0156 (17) | 0.0050 (15) | 0.0099 (17) |
C4 | 0.050 (2) | 0.068 (2) | 0.082 (3) | −0.0069 (18) | −0.0062 (19) | 0.020 (2) |
C5 | 0.0443 (17) | 0.0475 (18) | 0.092 (3) | −0.0049 (14) | 0.0243 (17) | −0.0018 (17) |
C6 | 0.065 (2) | 0.053 (2) | 0.084 (3) | −0.0085 (18) | 0.021 (2) | 0.0076 (19) |
Cl | 0.063 (2) | 0.0437 (17) | 0.0414 (17) | 0.0168 (12) | 0.0157 (13) | −0.0030 (12) |
O2 | 0.078 (5) | 0.041 (4) | 0.115 (8) | 0.010 (3) | 0.071 (5) | 0.002 (4) |
O3 | 0.100 (7) | 0.084 (5) | 0.037 (3) | 0.031 (4) | 0.011 (3) | 0.008 (3) |
O4 | 0.113 (7) | 0.064 (5) | 0.129 (8) | 0.007 (4) | 0.002 (5) | −0.066 (6) |
O5 | 0.127 (6) | 0.118 (6) | 0.142 (6) | 0.040 (5) | 0.112 (6) | 0.043 (5) |
Cl' | 0.062 (2) | 0.055 (3) | 0.063 (2) | 0.0285 (16) | 0.0362 (17) | 0.0077 (15) |
O2' | 0.144 (9) | 0.093 (7) | 0.111 (9) | 0.081 (7) | 0.068 (6) | 0.016 (5) |
O3' | 0.251 (15) | 0.126 (8) | 0.324 (15) | 0.055 (9) | 0.205 (14) | 0.116 (10) |
O4' | 0.130 (8) | 0.178 (11) | 0.066 (4) | 0.080 (7) | 0.048 (5) | 0.005 (5) |
O5' | 0.057 (5) | 0.239 (17) | 0.260 (18) | −0.032 (8) | 0.016 (8) | −0.146 (13) |
Geometric parameters (Å, º) top
Ni—N2 | 2.122 (2) | C1—C2 | 1.492 (5) |
Ni—N2i | 2.122 (2) | C3—C4 | 1.441 (5) |
Ni—N3 | 2.129 (2) | C5—C6 | 1.512 (5) |
Ni—N3i | 2.129 (2) | Cl—O3 | 1.404 (4) |
Ni—N1i | 2.191 (2) | Cl—O5 | 1.409 (5) |
Ni—N1 | 2.191 (2) | Cl—O4 | 1.410 (4) |
O1—C6 | 1.395 (5) | Cl—O2 | 1.422 (5) |
N1—C1 | 1.472 (4) | Cl'—O5' | 1.398 (5) |
N1—C3 | 1.480 (4) | Cl'—O4' | 1.400 (5) |
N1—C5 | 1.490 (4) | Cl'—O3' | 1.410 (5) |
N2—C2 | 1.462 (4) | Cl'—O2' | 1.417 (5) |
N3—C4 | 1.475 (4) | | |
| | | |
N2—Ni—N2i | 180.00 (16) | C2—N2—Ni | 110.11 (19) |
N2—Ni—N3 | 91.17 (10) | C4—N3—Ni | 110.69 (18) |
N2i—Ni—N3 | 88.83 (10) | N1—C1—C2 | 113.8 (3) |
N2—Ni—N3i | 88.83 (10) | N2—C2—C1 | 112.4 (3) |
N2i—Ni—N3i | 91.17 (10) | C4—C3—N1 | 115.3 (3) |
N3—Ni—N3i | 180.00 (16) | C3—C4—N3 | 115.4 (3) |
N2—Ni—N1i | 97.68 (9) | N1—C5—C6 | 119.0 (3) |
N2i—Ni—N1i | 82.32 (9) | O1—C6—C5 | 111.9 (3) |
N3—Ni—N1i | 98.18 (9) | O3—Cl—O5 | 108.7 (6) |
N3i—Ni—N1i | 81.82 (9) | O3—Cl—O4 | 105.3 (7) |
N2—Ni—N1 | 82.32 (9) | O5—Cl—O4 | 110.8 (7) |
N2i—Ni—N1 | 97.68 (9) | O3—Cl—O2 | 110.3 (8) |
N3—Ni—N1 | 81.82 (9) | O5—Cl—O2 | 110.4 (6) |
N3i—Ni—N1 | 98.18 (9) | O4—Cl—O2 | 111.2 (8) |
N1i—Ni—N1 | 180.00 (12) | O5'—Cl'—O4' | 116.1 (10) |
C1—N1—C3 | 114.3 (3) | O5'—Cl'—O3' | 104.9 (9) |
C1—N1—C5 | 108.9 (3) | O4'—Cl'—O3' | 104.2 (8) |
C3—N1—C5 | 109.5 (3) | O5'—Cl'—O2' | 114.0 (11) |
C1—N1—Ni | 106.50 (19) | O4'—Cl'—O2' | 108.5 (9) |
C3—N1—Ni | 106.47 (18) | O3'—Cl'—O2' | 108.3 (9) |
C5—N1—Ni | 111.06 (17) | | |
| | | |
N2—Ni—N1—C1 | 12.6 (2) | N2—Ni—N3—C4 | 82.5 (3) |
N2i—Ni—N1—C1 | −167.4 (2) | N2i—Ni—N3—C4 | −97.5 (3) |
N3—Ni—N1—C1 | 104.9 (2) | N3i—Ni—N3—C4 | 85 (96) |
N3i—Ni—N1—C1 | −75.1 (2) | N1i—Ni—N3—C4 | −179.6 (3) |
N1i—Ni—N1—C1 | −104 (22) | N1—Ni—N3—C4 | 0.4 (3) |
N2—Ni—N1—C3 | −109.8 (2) | C3—N1—C1—C2 | 83.5 (4) |
N2i—Ni—N1—C3 | 70.2 (2) | C5—N1—C1—C2 | −153.6 (3) |
N3—Ni—N1—C3 | −17.5 (2) | Ni—N1—C1—C2 | −33.8 (4) |
N3i—Ni—N1—C3 | 162.5 (2) | Ni—N2—C2—C1 | −31.3 (4) |
N1i—Ni—N1—C3 | 134 (21) | N1—C1—C2—N2 | 45.1 (5) |
N2—Ni—N1—C5 | 131.0 (2) | C1—N1—C3—C4 | −83.8 (4) |
N2i—Ni—N1—C5 | −49.0 (2) | C5—N1—C3—C4 | 153.7 (4) |
N3—Ni—N1—C5 | −136.6 (2) | Ni—N1—C3—C4 | 33.5 (4) |
N3i—Ni—N1—C5 | 43.4 (2) | N1—C3—C4—N3 | −36.1 (5) |
N1i—Ni—N1—C5 | 15 (21) | Ni—N3—C4—C3 | 18.3 (5) |
N2i—Ni—N2—C2 | 104 (98) | C1—N1—C5—C6 | −55.0 (4) |
N3—Ni—N2—C2 | −71.7 (3) | C3—N1—C5—C6 | 70.7 (4) |
N3i—Ni—N2—C2 | 108.3 (3) | Ni—N1—C5—C6 | −172.0 (3) |
N1i—Ni—N2—C2 | −170.1 (2) | N1—C5—C6—O1 | −73.1 (5) |
N1—Ni—N2—C2 | 9.9 (2) | | |
Symmetry code: (i) −x, −y, −z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···O2ii | 0.82 (3) | 2.09 (3) | 2.895 (14) | 168 (5) |
O1—H1···O2′ii | 0.82 (3) | 2.25 (3) | 3.041 (18) | 162 (4) |
N2—H2A···O3i | 0.90 | 2.29 | 3.156 (9) | 161 |
N3—H3A···O1iii | 0.90 | 2.28 | 3.113 (4) | 155 |
N3—H3B···O4i | 0.90 | 2.25 | 3.089 (10) | 155 |
N3—H3B···O4′i | 0.90 | 2.15 | 3.038 (14) | 171 |
Symmetry codes: (i) −x, −y, −z; (ii) x+1, y, z; (iii) −x+1/2, y−1/2, −z+1/2. |
Experimental details
Crystal data |
Chemical formula | [Ni(C6H17N3O)2](ClO4)2 |
Mr | 552.06 |
Crystal system, space group | Monoclinic, P21/n |
Temperature (K) | 298 |
a, b, c (Å) | 9.026 (1), 12.623 (2), 10.683 (1) |
β (°) | 113.90 (1) |
V (Å3) | 1112.8 (2) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm−1) | 1.17 |
Crystal size (mm) | 0.50 × 0.44 × 0.32 |
|
Data collection |
Diffractometer | Siemens P4 diffractometer |
Absorption correction | Empirical (using intensity measurements) (North et al., 1968) |
Tmin, Tmax | 0.598, 0.687 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 2397, 2061, 1700 |
Rint | 0.016 |
(sin θ/λ)max (Å−1) | 0.606 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.037, 0.105, 1.06 |
No. of reflections | 2061 |
No. of parameters | 192 |
No. of restraints | 10 |
H-atom treatment | H atoms treated by a mixture of independent and constrained refinement |
Δρmax, Δρmin (e Å−3) | 0.59, −0.39 |
Selected geometric parameters (Å, º) topNi—N2 | 2.122 (2) | Ni—N3i | 2.129 (2) |
Ni—N2i | 2.122 (2) | Ni—N1i | 2.191 (2) |
Ni—N3 | 2.129 (2) | Ni—N1 | 2.191 (2) |
| | | |
N2—Ni—N2i | 180.00 (16) | N2i—Ni—N1i | 82.32 (9) |
N2—Ni—N3 | 91.17 (10) | N3—Ni—N1i | 98.18 (9) |
N2i—Ni—N3 | 88.83 (10) | N3i—Ni—N1i | 81.82 (9) |
N3—Ni—N3i | 180.00 (16) | N1i—Ni—N1 | 180.00 (12) |
N2—Ni—N1i | 97.68 (9) | | |
Symmetry code: (i) −x, −y, −z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···O2ii | 0.82 (3) | 2.09 (3) | 2.895 (14) | 168 (5) |
O1—H1···O2'ii | 0.82 (3) | 2.25 (3) | 3.041 (18) | 162 (4) |
N2—H2A···O3i | 0.8997 | 2.2918 | 3.156 (9) | 161.02 |
N3—H3A···O1iii | 0.8995 | 2.2774 | 3.113 (4) | 154.47 |
N3—H3B···O4i | 0.9004 | 2.2495 | 3.089 (10) | 155.01 |
N3—H3B···O4'i | 0.9004 | 2.1457 | 3.038 (14) | 170.87 |
Symmetry codes: (i) −x, −y, −z; (ii) x+1, y, z; (iii) −x+1/2, y−1/2, −z+1/2. |
Nonredox-active metals such as NiII and ZnII are potentially of interest as hydrolytic cleaving agents of DNA, and their reactivity in model systems may lead to functional DNA cleaving molecules. Metal-polyamine complexes of NiII or ZnII are frequently used as models for hydrolases. Among the polyamine ligands designed, tripodal polyamines are especially of interest owing to their implication in a wide variety of biochemical and supramolecular systems (Mao et al., 1993; Anderegg & Gramlich, 1994; Murthy & Karlin, 1993; Lu et al., 1998). Some reported NiII-tripodal polyamine complexes exhibit very high hydrolytic activity towards phosphate esters and are potential artificial DNA-cut agents (De Rosch & Trogler, 1990; Tafesse et al., 1993). In the course of our work on synthesis of metal-asymmetric tripodal heteropolyamine complexes, we obtained a new 1:2 NiII—L complex, the title complex, with a structure of firstly infinite two-dimensional layers, then infinite three-dimensional framework stabilized by the hydrogen-bond network. \sch
As depicted in Fig. 1, NiII is located at the symmetric center and exhibits a slightly distorted octahedral geometry with six nitrogen atoms from two of the tripodal polyamine ligands. Four primary amine N atoms form the equatorial plane in which the NiII atom lies almost in the middle with equal NiII—N distances [NiII—N2 = NiII—N2(-x, -y, -z) = 2.122 Å, NiII—N3 = NiII—N3(-x, -y, -z) = 2.129 Å], while the apical N atom (tertiary amine N atom) is a little bit further from the central NiII atom [NiII—N1= NiII—N1(-x, -y, -z) = 2.191 Å]. All the N—NiII—N bond angles range from 82.32° to 91.17°. The perchlorate anions ClO2O3O4O5 and Cl'O2'O3'O4'O5' are disorder, with occupancy factors of 0.50. Six kinds of hydrogen disordered bonds occur in the structure. The hydrogen bond between O1 of the ethoxyl-pod and N3 of ethenyl amine pod of the adjacent ligand [N3—H3a—O1(0.5 - x, -0.5 + y, 0.5 - z), N3—O1 = 3.114 Å and N3—H3a—O1 154.5°] is responsible for the formation of the two-dimensional sheet-like NiII—L2 cation polymers which spread along the (1, 0, -1) plane to form an infinite network (see Fig. 2). Three kinds of additional hydrogen bonds exist inside the layer between the nitrogen atoms of the ethenyl amine pods and perchlorate anions: N2—H2a—O3(-x, -y, -z), N2—O3 = 3.156 Å and N2—H2a—O3 161.02°; N3—H3b—O4(-x, -y, -z), N3—O4 = 3.089 Å and N3—H3b—O4 155.01°; N3—H3b—O4'(-x, -y, -z), N3—O4' = 3.038 Å and N3—H3b—O4' 170.87°. The other two kinds of hydrogen bond [O1—H1— O2(1 + x, y, z), O1—O2 = 2.895 Å and O1—H1—O2 168°; O1—H1—O2'(1 + x, y, z), O1—O2' = 3.041 Å and O1—H1—O2' 162°] between oxygen of the ethoxyl-pod and perchlorate anions cross-link the layers into one three-dimensional framework, as is depicted in Fig 2.