organic compounds
4-Diphenylphosphanyl-8-methyl-1,5-naphthyridine
aDepartment of Applied Chemistry, College of Science, Nanjing University of Technology, Nanjing 210009, People's Republic of China
*Correspondence e-mail: zhuhjnjut@hotmail.com
In the title compound, C21H17N2P, the dihedral angles between the 1,5-naphthyridine ring system (r.m.s. deviation = 0.005 Å) and the phenyl rings are 89.18 (8) and 77.39 (8)°. The phenyl rings are almost perpendicular, making a dihedral angle of 88.12 (8)°. The only possible intermolecular interaction is a very weak aromatic π–π stacking interaction [centroid–centroid separation = 3.898 (2) Å].
Related literature
For further synthetic details and background to the role of the title compound as an intermediate in the synthesis of OLED materials, see: Chen et al. (2012).
Experimental
Crystal data
|
Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL.
Supporting information
10.1107/S1600536813013196/hb7082sup1.cif
contains datablocks I, global. DOI:Structure factors: contains datablock I. DOI: 10.1107/S1600536813013196/hb7082Isup2.hkl
Supporting information file. DOI: 10.1107/S1600536813013196/hb7082Isup3.cml
The title compund was synthesized according to the published procedure (Chen et al., 2012). Yellow blocks were obtained by dissolving it (0.5 g) in tetrahydrofuran (20 ml) and evaporating the solvent slowly at room temperature for about 5 d.
H atoms were positioned geometrically and refined as riding groups, with C—H = 0.93 Å for aromatic H, and constrained to ride on their parent atoms, with Uiso(H) = xUeq(C), where x = 1.2 for aromatic H, and x = 1.5 for other H.
Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell
CAD-4 EXPRESS (Enraf–Nonius, 1994); data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).Fig. 1. The molecular structure of (I), with displacement ellipsoids drawn at the 50% probability level. | |
Fig. 2. A packing diagram of (I). |
C21H17N2P | Z = 2 |
Mr = 328.34 | F(000) = 344 |
Triclinic, P1 | Dx = 1.243 Mg m−3 |
Hall symbol: -P 1 | Mo Kα radiation, λ = 0.71073 Å |
a = 7.2320 (14) Å | Cell parameters from 25 reflections |
b = 7.4470 (15) Å | θ = 10–14° |
c = 16.780 (3) Å | µ = 0.16 mm−1 |
α = 99.78 (3)° | T = 293 K |
β = 93.35 (3)° | Block, yellow |
γ = 98.58 (3)° | 0.30 × 0.20 × 0.10 mm |
V = 877.4 (3) Å3 |
Enraf–Nonius CAD-4 diffractometer | 2285 reflections with I > 2σ(I) |
Radiation source: fine-focus sealed tube | Rint = 0.023 |
Graphite monochromator | θmax = 25.4°, θmin = 1.2° |
ω/2θ scans | h = 0→8 |
Absorption correction: ψ scan (North et al., 1968) | k = −8→8 |
Tmin = 0.954, Tmax = 0.984 | l = −20→20 |
3500 measured reflections | 3 standard reflections every 200 reflections |
3224 independent reflections | intensity decay: 1% |
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.050 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.155 | H-atom parameters constrained |
S = 1.00 | w = 1/[σ2(Fo2) + (0.096P)2] where P = (Fo2 + 2Fc2)/3 |
3224 reflections | (Δ/σ)max = 0.001 |
217 parameters | Δρmax = 0.17 e Å−3 |
0 restraints | Δρmin = −0.23 e Å−3 |
C21H17N2P | γ = 98.58 (3)° |
Mr = 328.34 | V = 877.4 (3) Å3 |
Triclinic, P1 | Z = 2 |
a = 7.2320 (14) Å | Mo Kα radiation |
b = 7.4470 (15) Å | µ = 0.16 mm−1 |
c = 16.780 (3) Å | T = 293 K |
α = 99.78 (3)° | 0.30 × 0.20 × 0.10 mm |
β = 93.35 (3)° |
Enraf–Nonius CAD-4 diffractometer | 2285 reflections with I > 2σ(I) |
Absorption correction: ψ scan (North et al., 1968) | Rint = 0.023 |
Tmin = 0.954, Tmax = 0.984 | 3 standard reflections every 200 reflections |
3500 measured reflections | intensity decay: 1% |
3224 independent reflections |
R[F2 > 2σ(F2)] = 0.050 | 0 restraints |
wR(F2) = 0.155 | H-atom parameters constrained |
S = 1.00 | Δρmax = 0.17 e Å−3 |
3224 reflections | Δρmin = −0.23 e Å−3 |
217 parameters |
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. |
x | y | z | Uiso*/Ueq | ||
P | 0.18105 (10) | 0.17196 (9) | 0.71974 (4) | 0.0529 (2) | |
N1 | 0.2284 (3) | 0.3164 (3) | 0.89550 (13) | 0.0603 (6) | |
C1 | −0.0068 (5) | −0.0965 (4) | 0.59708 (17) | 0.0711 (8) | |
H1B | −0.1116 | −0.0650 | 0.6223 | 0.085* | |
N2 | 0.2453 (3) | −0.1579 (3) | 0.92992 (13) | 0.0569 (6) | |
C2 | −0.0308 (6) | −0.2312 (5) | 0.5287 (2) | 0.0906 (11) | |
H2B | −0.1507 | −0.2917 | 0.5087 | 0.109* | |
C3 | 0.1213 (7) | −0.2762 (5) | 0.4901 (2) | 0.0976 (13) | |
H3A | 0.1048 | −0.3655 | 0.4432 | 0.117* | |
C4 | 0.2974 (6) | −0.1907 (5) | 0.5202 (2) | 0.0914 (11) | |
H4A | 0.4009 | −0.2230 | 0.4942 | 0.110* | |
C5 | 0.3227 (5) | −0.0553 (4) | 0.58980 (18) | 0.0734 (8) | |
H5A | 0.4433 | 0.0028 | 0.6098 | 0.088* | |
C6 | 0.1710 (4) | −0.0060 (3) | 0.62951 (15) | 0.0579 (7) | |
C7 | 0.4103 (3) | 0.3111 (3) | 0.71826 (14) | 0.0501 (6) | |
C8 | 0.5758 (4) | 0.2855 (4) | 0.75679 (17) | 0.0644 (7) | |
H8A | 0.5754 | 0.1889 | 0.7854 | 0.077* | |
C9 | 0.7416 (4) | 0.4013 (4) | 0.75339 (19) | 0.0757 (8) | |
H9A | 0.8516 | 0.3842 | 0.7806 | 0.091* | |
C10 | 0.7445 (5) | 0.5412 (4) | 0.7101 (2) | 0.0822 (10) | |
H10A | 0.8568 | 0.6181 | 0.7071 | 0.099* | |
C11 | 0.5835 (5) | 0.5682 (4) | 0.6713 (2) | 0.0844 (10) | |
H11A | 0.5859 | 0.6635 | 0.6419 | 0.101* | |
C12 | 0.4175 (4) | 0.4557 (3) | 0.67539 (17) | 0.0652 (7) | |
H12A | 0.3080 | 0.4764 | 0.6491 | 0.078* | |
C13 | 0.2210 (3) | 0.0390 (3) | 0.79998 (14) | 0.0476 (6) | |
C14 | 0.2313 (3) | 0.1306 (3) | 0.88168 (14) | 0.0468 (6) | |
C15 | 0.2393 (5) | 0.3962 (4) | 0.97172 (18) | 0.0744 (9) | |
H15A | 0.2379 | 0.5226 | 0.9827 | 0.089* | |
C16 | 0.2527 (4) | 0.3065 (4) | 1.03778 (18) | 0.0736 (8) | |
H16A | 0.2609 | 0.3736 | 1.0903 | 0.088* | |
C17 | 0.2539 (3) | 0.1222 (4) | 1.02590 (15) | 0.0557 (6) | |
C18 | 0.2437 (3) | 0.0284 (3) | 0.94493 (15) | 0.0478 (6) | |
C19 | 0.2366 (4) | −0.2382 (3) | 0.85361 (17) | 0.0638 (7) | |
H19A | 0.2389 | −0.3645 | 0.8426 | 0.077* | |
C20 | 0.2241 (4) | −0.1471 (3) | 0.78760 (16) | 0.0576 (6) | |
H20A | 0.2179 | −0.2133 | 0.7350 | 0.069* | |
C21 | 0.2657 (4) | 0.0179 (4) | 1.09549 (16) | 0.0724 (8) | |
H21A | 0.2718 | 0.1022 | 1.1460 | 0.109* | |
H21B | 0.3761 | −0.0394 | 1.0935 | 0.109* | |
H21C | 0.1565 | −0.0752 | 1.0911 | 0.109* |
U11 | U22 | U33 | U12 | U13 | U23 | |
P | 0.0594 (4) | 0.0457 (4) | 0.0574 (4) | 0.0135 (3) | 0.0070 (3) | 0.0149 (3) |
N1 | 0.0850 (16) | 0.0364 (11) | 0.0630 (14) | 0.0140 (10) | 0.0175 (12) | 0.0113 (10) |
C1 | 0.086 (2) | 0.0568 (16) | 0.0678 (18) | −0.0071 (15) | −0.0020 (16) | 0.0218 (14) |
N2 | 0.0624 (14) | 0.0436 (11) | 0.0676 (14) | 0.0070 (10) | 0.0070 (11) | 0.0191 (10) |
C2 | 0.124 (3) | 0.066 (2) | 0.070 (2) | −0.022 (2) | −0.013 (2) | 0.0194 (17) |
C3 | 0.166 (4) | 0.0558 (19) | 0.061 (2) | −0.009 (2) | 0.003 (2) | 0.0081 (15) |
C4 | 0.136 (3) | 0.065 (2) | 0.077 (2) | 0.024 (2) | 0.029 (2) | 0.0121 (17) |
C5 | 0.091 (2) | 0.0604 (17) | 0.0681 (18) | 0.0135 (15) | 0.0148 (16) | 0.0055 (14) |
C6 | 0.0759 (18) | 0.0475 (14) | 0.0505 (14) | 0.0035 (13) | 0.0023 (13) | 0.0162 (11) |
C7 | 0.0615 (15) | 0.0364 (12) | 0.0539 (14) | 0.0121 (11) | 0.0124 (12) | 0.0061 (10) |
C8 | 0.0623 (17) | 0.0624 (17) | 0.0735 (18) | 0.0144 (14) | 0.0100 (14) | 0.0214 (14) |
C9 | 0.0608 (18) | 0.087 (2) | 0.076 (2) | 0.0133 (16) | 0.0077 (15) | 0.0024 (17) |
C10 | 0.082 (2) | 0.069 (2) | 0.088 (2) | −0.0125 (17) | 0.0211 (19) | 0.0113 (17) |
C11 | 0.100 (3) | 0.0589 (18) | 0.096 (2) | −0.0019 (17) | 0.017 (2) | 0.0296 (17) |
C12 | 0.0796 (19) | 0.0476 (14) | 0.0709 (18) | 0.0105 (14) | 0.0071 (14) | 0.0175 (13) |
C13 | 0.0499 (14) | 0.0399 (12) | 0.0547 (14) | 0.0068 (10) | 0.0084 (11) | 0.0121 (10) |
C14 | 0.0460 (13) | 0.0402 (12) | 0.0560 (14) | 0.0065 (10) | 0.0102 (11) | 0.0121 (10) |
C15 | 0.113 (3) | 0.0438 (15) | 0.0681 (18) | 0.0187 (15) | 0.0194 (17) | 0.0057 (13) |
C16 | 0.098 (2) | 0.0628 (18) | 0.0591 (17) | 0.0169 (16) | 0.0137 (16) | 0.0018 (14) |
C17 | 0.0519 (15) | 0.0614 (16) | 0.0563 (15) | 0.0096 (12) | 0.0090 (12) | 0.0152 (12) |
C18 | 0.0437 (13) | 0.0456 (13) | 0.0576 (14) | 0.0082 (10) | 0.0116 (11) | 0.0158 (11) |
C19 | 0.082 (2) | 0.0361 (13) | 0.0733 (18) | 0.0077 (12) | 0.0043 (15) | 0.0130 (12) |
C20 | 0.0713 (17) | 0.0409 (13) | 0.0591 (15) | 0.0070 (12) | 0.0045 (13) | 0.0072 (11) |
C21 | 0.0725 (19) | 0.090 (2) | 0.0609 (17) | 0.0143 (16) | 0.0112 (14) | 0.0279 (15) |
P—C7 | 1.823 (3) | C9—C10 | 1.367 (4) |
P—C6 | 1.825 (3) | C9—H9A | 0.9300 |
P—C13 | 1.836 (2) | C10—C11 | 1.358 (5) |
N1—C15 | 1.308 (3) | C10—H10A | 0.9300 |
N1—C14 | 1.367 (3) | C11—C12 | 1.369 (4) |
C1—C2 | 1.374 (4) | C11—H11A | 0.9300 |
C1—C6 | 1.392 (4) | C12—H12A | 0.9300 |
C1—H1B | 0.9300 | C13—C20 | 1.370 (3) |
N2—C19 | 1.312 (3) | C13—C14 | 1.416 (3) |
N2—C18 | 1.369 (3) | C14—C18 | 1.413 (3) |
C2—C3 | 1.364 (5) | C15—C16 | 1.394 (4) |
C2—H2B | 0.9300 | C15—H15A | 0.9300 |
C3—C4 | 1.362 (5) | C16—C17 | 1.355 (4) |
C3—H3A | 0.9300 | C16—H16A | 0.9300 |
C4—C5 | 1.391 (4) | C17—C18 | 1.411 (3) |
C4—H4A | 0.9300 | C17—C21 | 1.513 (3) |
C5—C6 | 1.380 (4) | C19—C20 | 1.399 (3) |
C5—H5A | 0.9300 | C19—H19A | 0.9300 |
C7—C8 | 1.381 (4) | C20—H20A | 0.9300 |
C7—C12 | 1.390 (3) | C21—H21A | 0.9600 |
C8—C9 | 1.379 (4) | C21—H21B | 0.9600 |
C8—H8A | 0.9300 | C21—H21C | 0.9600 |
C7—P—C6 | 102.31 (12) | C10—C11—H11A | 119.8 |
C7—P—C13 | 102.97 (11) | C12—C11—H11A | 119.8 |
C6—P—C13 | 100.69 (11) | C11—C12—C7 | 121.0 (3) |
C15—N1—C14 | 115.8 (2) | C11—C12—H12A | 119.5 |
C2—C1—C6 | 121.5 (3) | C7—C12—H12A | 119.5 |
C2—C1—H1B | 119.3 | C20—C13—C14 | 116.6 (2) |
C6—C1—H1B | 119.3 | C20—C13—P | 125.1 (2) |
C19—N2—C18 | 116.9 (2) | C14—C13—P | 117.97 (16) |
C3—C2—C1 | 119.9 (3) | N1—C14—C18 | 122.9 (2) |
C3—C2—H2B | 120.0 | N1—C14—C13 | 117.7 (2) |
C1—C2—H2B | 120.0 | C18—C14—C13 | 119.5 (2) |
C4—C3—C2 | 120.2 (3) | N1—C15—C16 | 125.1 (2) |
C4—C3—H3A | 119.9 | N1—C15—H15A | 117.4 |
C2—C3—H3A | 119.9 | C16—C15—H15A | 117.4 |
C3—C4—C5 | 120.1 (4) | C17—C16—C15 | 120.3 (3) |
C3—C4—H4A | 119.9 | C17—C16—H16A | 119.8 |
C5—C4—H4A | 119.9 | C15—C16—H16A | 119.8 |
C6—C5—C4 | 120.8 (3) | C16—C17—C18 | 117.2 (2) |
C6—C5—H5A | 119.6 | C16—C17—C21 | 122.4 (3) |
C4—C5—H5A | 119.6 | C18—C17—C21 | 120.4 (2) |
C5—C6—C1 | 117.5 (3) | N2—C18—C17 | 119.3 (2) |
C5—C6—P | 125.9 (2) | N2—C18—C14 | 122.1 (2) |
C1—C6—P | 116.6 (2) | C17—C18—C14 | 118.6 (2) |
C8—C7—C12 | 117.7 (2) | N2—C19—C20 | 124.6 (2) |
C8—C7—P | 125.38 (19) | N2—C19—H19A | 117.7 |
C12—C7—P | 116.9 (2) | C20—C19—H19A | 117.7 |
C9—C8—C7 | 120.8 (3) | C13—C20—C19 | 120.4 (2) |
C9—C8—H8A | 119.6 | C13—C20—H20A | 119.8 |
C7—C8—H8A | 119.6 | C19—C20—H20A | 119.8 |
C10—C9—C8 | 120.1 (3) | C17—C21—H21A | 109.5 |
C10—C9—H9A | 120.0 | C17—C21—H21B | 109.5 |
C8—C9—H9A | 120.0 | H21A—C21—H21B | 109.5 |
C11—C10—C9 | 120.0 (3) | C17—C21—H21C | 109.5 |
C11—C10—H10A | 120.0 | H21A—C21—H21C | 109.5 |
C9—C10—H10A | 120.0 | H21B—C21—H21C | 109.5 |
C10—C11—C12 | 120.4 (3) | ||
C6—C1—C2—C3 | −1.3 (5) | C7—P—C13—C14 | 76.6 (2) |
C1—C2—C3—C4 | 1.4 (5) | C6—P—C13—C14 | −178.00 (19) |
C2—C3—C4—C5 | −0.9 (5) | C15—N1—C14—C18 | 0.5 (4) |
C3—C4—C5—C6 | 0.3 (5) | C15—N1—C14—C13 | −179.6 (2) |
C4—C5—C6—C1 | −0.2 (4) | C20—C13—C14—N1 | −180.0 (2) |
C4—C5—C6—P | −178.5 (2) | P—C13—C14—N1 | −6.0 (3) |
C2—C1—C6—C5 | 0.7 (4) | C20—C13—C14—C18 | −0.1 (3) |
C2—C1—C6—P | 179.2 (2) | P—C13—C14—C18 | 173.91 (17) |
C7—P—C6—C5 | 19.7 (3) | C14—N1—C15—C16 | −0.2 (5) |
C13—P—C6—C5 | −86.2 (2) | N1—C15—C16—C17 | −0.5 (5) |
C7—P—C6—C1 | −158.59 (19) | C15—C16—C17—C18 | 0.9 (4) |
C13—P—C6—C1 | 95.5 (2) | C15—C16—C17—C21 | −179.2 (3) |
C6—P—C7—C8 | −91.8 (2) | C19—N2—C18—C17 | −179.6 (2) |
C13—P—C7—C8 | 12.4 (2) | C19—N2—C18—C14 | 0.7 (3) |
C6—P—C7—C12 | 88.9 (2) | C16—C17—C18—N2 | 179.7 (2) |
C13—P—C7—C12 | −166.89 (19) | C21—C17—C18—N2 | −0.2 (3) |
C12—C7—C8—C9 | 0.7 (4) | C16—C17—C18—C14 | −0.6 (4) |
P—C7—C8—C9 | −178.5 (2) | C21—C17—C18—C14 | 179.5 (2) |
C7—C8—C9—C10 | −1.4 (4) | N1—C14—C18—N2 | 179.6 (2) |
C8—C9—C10—C11 | 1.0 (5) | C13—C14—C18—N2 | −0.3 (3) |
C9—C10—C11—C12 | 0.0 (5) | N1—C14—C18—C17 | −0.1 (4) |
C10—C11—C12—C7 | −0.7 (5) | C13—C14—C18—C17 | 180.0 (2) |
C8—C7—C12—C11 | 0.3 (4) | C18—N2—C19—C20 | −0.7 (4) |
P—C7—C12—C11 | 179.6 (2) | C14—C13—C20—C19 | 0.1 (4) |
C7—P—C13—C20 | −110.0 (2) | P—C13—C20—C19 | −173.4 (2) |
C6—P—C13—C20 | −4.6 (3) | N2—C19—C20—C13 | 0.3 (4) |
Experimental details
Crystal data | |
Chemical formula | C21H17N2P |
Mr | 328.34 |
Crystal system, space group | Triclinic, P1 |
Temperature (K) | 293 |
a, b, c (Å) | 7.2320 (14), 7.4470 (15), 16.780 (3) |
α, β, γ (°) | 99.78 (3), 93.35 (3), 98.58 (3) |
V (Å3) | 877.4 (3) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm−1) | 0.16 |
Crystal size (mm) | 0.30 × 0.20 × 0.10 |
Data collection | |
Diffractometer | Enraf–Nonius CAD-4 diffractometer |
Absorption correction | ψ scan (North et al., 1968) |
Tmin, Tmax | 0.954, 0.984 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 3500, 3224, 2285 |
Rint | 0.023 |
(sin θ/λ)max (Å−1) | 0.603 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.050, 0.155, 1.00 |
No. of reflections | 3224 |
No. of parameters | 217 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.17, −0.23 |
Computer programs: CAD-4 EXPRESS (Enraf–Nonius, 1994), XCAD4 (Harms & Wocadlo, 1995), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008).
Acknowledgements
The authors thank the Center of Testing and Analysis, Nanjing University, for support.
References
Chen, C., Wang, K., Jiang, P., Song, G. & Zhu, H. (2012). Inorg. Chem. Commun. 17, 116–119. Web of Science CSD CrossRef CAS Google Scholar
Enraf–Nonius (1994). CAD-4 EXPRESS. Enraf–Nonius, Delft, The Netherlands. Google Scholar
Harms, K. & Wocadlo, S. (1995). XCAD4. University of Marburg, Germany. Google Scholar
North, A. C. T., Phillips, D. C. & Mathews, F. S. (1968). Acta Cryst. A24, 351–359. CrossRef IUCr Journals Web of Science Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar
This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
The tittle compound, (I), is an intermediate for manufacturing OLED materials (Chen et al., 2012). We now report its crystal structure (Fig. 1).
The 1,5-naphthyridine ring system is nearly planar with an r.m.s. deviation of 0.005Å; its mean plane is oriented with respect to the two phenyl rings at 89.18 (8) and 77.39 (8)°. The two phenyl rings are twisted to each other with a dihedral angle of 88.12 (8)°. The crystal packing of the molecules in the crystal is influenced by van der Waals forces (Fig. 2).