Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807025214/dn2180sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536807025214/dn2180Isup2.hkl |
CCDC reference: 651524
Key indicators
- Single-crystal X-ray study
- T = 298 K
- Mean (C-C) = 0.004 Å
- R factor = 0.071
- wR factor = 0.156
- Data-to-parameter ratio = 13.1
checkCIF/PLATON results
No syntax errors found
Alert level C PLAT066_ALERT_1_C Predicted and Reported Transmissions Identical . ?
Alert level G PLAT793_ALERT_1_G Check the Absolute Configuration of C11 = ... R
0 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 1 ALERT level C = Check and explain 1 ALERT level G = General alerts; check 2 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 0 ALERT type 2 Indicator that the structure model may be wrong or deficient 0 ALERT type 3 Indicator that the structure quality may be low 0 ALERT type 4 Improvement, methodology, query or suggestion 0 ALERT type 5 Informative message, check
To a solution of 2-naphthol (1, 14.42 g, 0.1 mol) in absolute EtOH (50 ml) was added the benzaldehyde and 25% ethanolic ammonia solution (20 ml). The mixture was left to stand at ambient temperature for 12 h, during which a crystalline product (1) separated out (Szatmari et al., 2003). The crystals were filtered off and washed with cool ethanol, and then recrystallized from ethanol.
All H atoms attached to C and O atom were fixed geometrically and treated as riding on their parent atoms with C—H = 0.93 (aromatic), 0.96 (methyl) and 0.98 Å (methine) and O—H = 0.82 Å, with Uiso(H) = 1.2Ueq(aromatic C, methine C, O) and Uiso(H) = 1.5Ueq(methyl C).
The title compound, (1), is a key intermediate used in the sythesis of amino naphthol,which was found to be potent chiral catalyst in the addition reactions of dialkylzincs to aldehydes.
In the title compound, C26H23NO3, the π-conjugated system formed by the methoxy-benzylidene-imine tautomer is essentially planar with the largest deviation being -0.104 (2)Å at N1. This plane makes dihedral angles of 67.46 (4)° and 72.51 (7)° with the methoxy-phenyl and the naphtalene planes respectively (Fig. 1). An intramolecular O—HN hydrogen bond is formed between the hydroxyl OH attached to the naphtalene group and the Schiff base N atom (Table 1). The crystal packing is stabilized by van der Waals forces.
For related literature, see: Szatmari et al. (2003).
Data collection: SMART (Bruker, 2001); cell refinement: SMART; data reduction: SAINT (Bruker, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPIII (Burnett & Johnson, 1996) and ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97.
C26H23NO3 | F(000) = 840 |
Mr = 397.45 | Dx = 1.284 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2ybc | Cell parameters from 3850 reflections |
a = 20.790 (5) Å | θ = 2.6–27.8° |
b = 10.717 (3) Å | µ = 0.08 mm−1 |
c = 9.470 (2) Å | T = 298 K |
β = 102.952 (4)° | Block, colourless |
V = 2056.4 (9) Å3 | 0.46 × 0.45 × 0.16 mm |
Z = 4 |
Bruker APEX area-detector diffractometer | 3595 independent reflections |
Radiation source: fine-focus sealed tube | 3150 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.022 |
φ and ω scans | θmax = 25.0°, θmin = 1.0° |
Absorption correction: multi-scan (SADABS; Bruker, 2001) | h = −24→24 |
Tmin = 0.963, Tmax = 0.987 | k = −8→12 |
10108 measured reflections | l = −11→11 |
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)] = 0.071 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.156 | H-atom parameters constrained |
S = 1.22 | w = 1/[σ2(Fo2) + (0.048P)2 + 0.9676P] where P = (Fo2 + 2Fc2)/3 |
3594 reflections | (Δ/σ)max = 0.001 |
274 parameters | Δρmax = 0.19 e Å−3 |
0 restraints | Δρmin = −0.22 e Å−3 |
C26H23NO3 | V = 2056.4 (9) Å3 |
Mr = 397.45 | Z = 4 |
Monoclinic, P21/c | Mo Kα radiation |
a = 20.790 (5) Å | µ = 0.08 mm−1 |
b = 10.717 (3) Å | T = 298 K |
c = 9.470 (2) Å | 0.46 × 0.45 × 0.16 mm |
β = 102.952 (4)° |
Bruker APEX area-detector diffractometer | 3595 independent reflections |
Absorption correction: multi-scan (SADABS; Bruker, 2001) | 3150 reflections with I > 2σ(I) |
Tmin = 0.963, Tmax = 0.987 | Rint = 0.022 |
10108 measured reflections |
R[F2 > 2σ(F2)] = 0.071 | 0 restraints |
wR(F2) = 0.156 | H-atom parameters constrained |
S = 1.22 | Δρmax = 0.19 e Å−3 |
3594 reflections | Δρmin = −0.22 e Å−3 |
274 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 | ||
C11 | 0.27872 (11) | 0.4519 (2) | 0.0544 (3) | 0.0431 (6) | |
H11 | 0.2940 | 0.3665 | 0.0444 | 0.052* | |
C1 | 0.25378 (11) | 0.5060 (2) | −0.0956 (3) | 0.0422 (6) | |
N1 | 0.22533 (9) | 0.44746 (19) | 0.1312 (2) | 0.0473 (5) | |
C9 | 0.28741 (12) | 0.4774 (2) | −0.2060 (3) | 0.0450 (6) | |
C15 | 0.33480 (11) | 0.5258 (2) | 0.1447 (2) | 0.0416 (6) | |
O3 | 0.16486 (9) | 0.6186 (2) | −0.0324 (2) | 0.0700 (6) | |
H3 | 0.1771 | 0.5794 | 0.0433 | 0.105* | |
C19 | 0.20777 (12) | 0.3448 (3) | 0.1721 (3) | 0.0496 (6) | |
H19 | 0.2293 | 0.2730 | 0.1526 | 0.060* | |
C14 | 0.39236 (12) | 0.4702 (2) | 0.2144 (3) | 0.0485 (6) | |
H14 | 0.3982 | 0.3852 | 0.2015 | 0.058* | |
O2 | 0.48452 (9) | 0.71911 (19) | 0.4146 (2) | 0.0688 (6) | |
C23 | 0.15520 (12) | 0.3332 (3) | 0.2488 (3) | 0.0509 (6) | |
C13 | 0.44148 (12) | 0.5365 (3) | 0.3026 (3) | 0.0520 (6) | |
H13 | 0.4804 | 0.4967 | 0.3481 | 0.062* | |
C2 | 0.20013 (12) | 0.5824 (2) | −0.1284 (3) | 0.0518 (6) | |
C12 | 0.43377 (12) | 0.6605 (3) | 0.3241 (3) | 0.0488 (6) | |
C8 | 0.34508 (12) | 0.4043 (2) | −0.1819 (3) | 0.0516 (6) | |
H8 | 0.3618 | 0.3716 | −0.0901 | 0.062* | |
O1 | 0.00340 (10) | 0.3040 (2) | 0.4600 (3) | 0.0894 (8) | |
C24 | 0.12699 (14) | 0.4356 (3) | 0.3000 (3) | 0.0617 (7) | |
H24 | 0.1426 | 0.5150 | 0.2865 | 0.074* | |
C16 | 0.32864 (12) | 0.6507 (3) | 0.1655 (3) | 0.0584 (7) | |
H16 | 0.2904 | 0.6913 | 0.1176 | 0.070* | |
C17 | 0.37703 (13) | 0.7179 (3) | 0.2549 (3) | 0.0621 (8) | |
H17 | 0.3712 | 0.8028 | 0.2684 | 0.074* | |
C10 | 0.26409 (14) | 0.5238 (3) | −0.3472 (3) | 0.0565 (7) | |
C4 | 0.20852 (16) | 0.6009 (3) | −0.3738 (3) | 0.0700 (9) | |
H4 | 0.1926 | 0.6328 | −0.4663 | 0.084* | |
C3 | 0.17802 (15) | 0.6293 (3) | −0.2683 (4) | 0.0664 (8) | |
H3A | 0.1413 | 0.6813 | −0.2884 | 0.080* | |
C22 | 0.13130 (13) | 0.2173 (3) | 0.2716 (3) | 0.0622 (8) | |
H22 | 0.1495 | 0.1470 | 0.2383 | 0.075* | |
C7 | 0.37670 (15) | 0.3805 (3) | −0.2887 (4) | 0.0665 (8) | |
H7 | 0.4152 | 0.3332 | −0.2687 | 0.080* | |
C21 | 0.08089 (14) | 0.2029 (3) | 0.3429 (3) | 0.0704 (9) | |
H21 | 0.0655 | 0.1237 | 0.3582 | 0.085* | |
C5 | 0.2979 (2) | 0.4947 (3) | −0.4552 (3) | 0.0783 (10) | |
H5 | 0.2820 | 0.5243 | −0.5488 | 0.094* | |
C25 | 0.07700 (14) | 0.4224 (3) | 0.3697 (3) | 0.0698 (8) | |
H25 | 0.0585 | 0.4924 | 0.4031 | 0.084* | |
C6 | 0.3529 (2) | 0.4250 (4) | −0.4264 (4) | 0.0841 (11) | |
H6 | 0.3748 | 0.4069 | −0.4995 | 0.101* | |
C20 | 0.05380 (13) | 0.3057 (3) | 0.3907 (3) | 0.0639 (8) | |
C18 | 0.47447 (15) | 0.8432 (3) | 0.4520 (4) | 0.0748 (9) | |
H18A | 0.4674 | 0.8945 | 0.3668 | 0.112* | |
H18B | 0.5126 | 0.8724 | 0.5210 | 0.112* | |
H18C | 0.4365 | 0.8476 | 0.4939 | 0.112* | |
C26 | −0.01964 (17) | 0.1877 (4) | 0.4935 (4) | 0.1035 (14) | |
H26A | −0.0367 | 0.1424 | 0.4057 | 0.155* | |
H26B | −0.0540 | 0.1991 | 0.5451 | 0.155* | |
H26C | 0.0160 | 0.1415 | 0.5528 | 0.155* |
U11 | U22 | U33 | U12 | U13 | U23 | |
C11 | 0.0411 (13) | 0.0409 (13) | 0.0499 (14) | 0.0025 (11) | 0.0156 (11) | −0.0014 (11) |
C1 | 0.0360 (12) | 0.0380 (13) | 0.0503 (14) | −0.0050 (10) | 0.0048 (10) | −0.0027 (11) |
N1 | 0.0422 (11) | 0.0527 (13) | 0.0500 (12) | −0.0042 (10) | 0.0166 (9) | −0.0037 (10) |
C9 | 0.0477 (14) | 0.0381 (13) | 0.0493 (14) | −0.0145 (11) | 0.0110 (11) | −0.0054 (11) |
C15 | 0.0400 (13) | 0.0460 (14) | 0.0416 (13) | 0.0027 (11) | 0.0150 (10) | 0.0013 (11) |
O3 | 0.0528 (11) | 0.0709 (14) | 0.0869 (15) | 0.0181 (10) | 0.0167 (11) | −0.0049 (11) |
C19 | 0.0415 (14) | 0.0586 (16) | 0.0471 (15) | 0.0015 (12) | 0.0067 (11) | 0.0033 (12) |
C14 | 0.0515 (15) | 0.0448 (14) | 0.0490 (15) | 0.0082 (12) | 0.0106 (12) | 0.0054 (11) |
O2 | 0.0471 (11) | 0.0767 (14) | 0.0738 (13) | 0.0016 (10) | −0.0048 (10) | −0.0210 (11) |
C23 | 0.0415 (14) | 0.0624 (17) | 0.0471 (15) | −0.0023 (12) | 0.0061 (11) | 0.0079 (13) |
C13 | 0.0418 (14) | 0.0623 (17) | 0.0485 (15) | 0.0108 (13) | 0.0032 (11) | 0.0062 (13) |
C2 | 0.0451 (14) | 0.0436 (14) | 0.0628 (17) | −0.0031 (12) | 0.0041 (13) | −0.0050 (12) |
C12 | 0.0416 (14) | 0.0594 (16) | 0.0450 (14) | 0.0027 (12) | 0.0089 (11) | −0.0055 (12) |
C8 | 0.0509 (15) | 0.0515 (15) | 0.0562 (16) | −0.0106 (12) | 0.0203 (12) | −0.0082 (12) |
O1 | 0.0590 (13) | 0.131 (2) | 0.0864 (16) | −0.0128 (13) | 0.0337 (12) | 0.0164 (15) |
C24 | 0.0603 (17) | 0.0684 (19) | 0.0603 (18) | −0.0131 (15) | 0.0221 (14) | −0.0063 (14) |
C16 | 0.0404 (14) | 0.0519 (16) | 0.0747 (19) | 0.0104 (12) | −0.0043 (13) | −0.0091 (14) |
C17 | 0.0522 (16) | 0.0472 (16) | 0.081 (2) | 0.0068 (13) | 0.0027 (15) | −0.0147 (14) |
C10 | 0.0691 (18) | 0.0505 (16) | 0.0467 (15) | −0.0215 (14) | 0.0061 (13) | −0.0002 (12) |
C4 | 0.087 (2) | 0.0587 (18) | 0.0534 (18) | −0.0173 (17) | −0.0086 (17) | 0.0079 (14) |
C3 | 0.0602 (18) | 0.0526 (17) | 0.075 (2) | 0.0024 (14) | −0.0099 (16) | 0.0052 (15) |
C22 | 0.0514 (16) | 0.0642 (18) | 0.0703 (19) | 0.0080 (14) | 0.0120 (14) | 0.0200 (15) |
C7 | 0.0680 (19) | 0.0654 (19) | 0.077 (2) | −0.0162 (15) | 0.0395 (17) | −0.0199 (16) |
C21 | 0.0553 (17) | 0.076 (2) | 0.080 (2) | −0.0058 (16) | 0.0140 (16) | 0.0311 (17) |
C5 | 0.110 (3) | 0.082 (2) | 0.0457 (17) | −0.032 (2) | 0.0229 (18) | −0.0029 (16) |
C25 | 0.0616 (18) | 0.086 (2) | 0.069 (2) | −0.0114 (16) | 0.0295 (16) | −0.0113 (16) |
C6 | 0.105 (3) | 0.091 (3) | 0.070 (2) | −0.032 (2) | 0.050 (2) | −0.0225 (19) |
C20 | 0.0419 (15) | 0.097 (2) | 0.0540 (17) | −0.0034 (16) | 0.0123 (13) | 0.0135 (16) |
C18 | 0.0595 (18) | 0.081 (2) | 0.082 (2) | −0.0133 (16) | 0.0116 (16) | −0.0308 (18) |
C26 | 0.063 (2) | 0.157 (4) | 0.094 (3) | −0.034 (2) | 0.0249 (19) | 0.029 (3) |
C11—N1 | 1.458 (3) | O1—C26 | 1.398 (4) |
C11—C15 | 1.507 (3) | C24—C25 | 1.357 (4) |
C11—C1 | 1.514 (3) | C24—H24 | 0.9300 |
C11—H11 | 0.9800 | C16—C17 | 1.366 (4) |
C1—C2 | 1.363 (3) | C16—H16 | 0.9300 |
C1—C9 | 1.416 (3) | C17—H17 | 0.9300 |
N1—C19 | 1.247 (3) | C10—C4 | 1.396 (4) |
C9—C10 | 1.407 (4) | C10—C5 | 1.400 (4) |
C9—C8 | 1.407 (4) | C4—C3 | 1.332 (4) |
C15—C16 | 1.364 (3) | C4—H4 | 0.9300 |
C15—C14 | 1.367 (3) | C3—H3A | 0.9300 |
O3—C2 | 1.347 (3) | C22—C21 | 1.376 (4) |
O3—H3 | 0.8200 | C22—H22 | 0.9300 |
C19—C23 | 1.447 (3) | C7—C6 | 1.373 (5) |
C19—H19 | 0.9300 | C7—H7 | 0.9300 |
C14—C13 | 1.365 (4) | C21—C20 | 1.360 (4) |
C14—H14 | 0.9300 | C21—H21 | 0.9300 |
O2—C12 | 1.355 (3) | C5—C6 | 1.340 (5) |
O2—C18 | 1.404 (4) | C5—H5 | 0.9300 |
C23—C22 | 1.373 (4) | C25—C20 | 1.371 (4) |
C23—C24 | 1.382 (4) | C25—H25 | 0.9300 |
C13—C12 | 1.360 (4) | C6—H6 | 0.9300 |
C13—H13 | 0.9300 | C18—H18A | 0.9600 |
C2—C3 | 1.395 (4) | C18—H18B | 0.9600 |
C12—C17 | 1.362 (4) | C18—H18C | 0.9600 |
C8—C7 | 1.348 (4) | C26—H26A | 0.9600 |
C8—H8 | 0.9300 | C26—H26B | 0.9600 |
O1—C20 | 1.356 (3) | C26—H26C | 0.9600 |
N1—C11—C15 | 108.21 (19) | C12—C17—C16 | 119.9 (3) |
N1—C11—C1 | 109.98 (19) | C12—C17—H17 | 120.1 |
C15—C11—C1 | 112.93 (19) | C16—C17—H17 | 120.1 |
N1—C11—H11 | 108.5 | C4—C10—C5 | 122.1 (3) |
C15—C11—H11 | 108.5 | C4—C10—C9 | 118.4 (3) |
C1—C11—H11 | 108.5 | C5—C10—C9 | 119.5 (3) |
C2—C1—C9 | 118.4 (2) | C3—C4—C10 | 120.9 (3) |
C2—C1—C11 | 122.4 (2) | C3—C4—H4 | 119.5 |
C9—C1—C11 | 119.2 (2) | C10—C4—H4 | 119.5 |
C19—N1—C11 | 119.5 (2) | C4—C3—C2 | 121.2 (3) |
C10—C9—C8 | 116.8 (2) | C4—C3—H3A | 119.4 |
C10—C9—C1 | 120.2 (2) | C2—C3—H3A | 119.4 |
C8—C9—C1 | 123.0 (2) | C23—C22—C21 | 121.4 (3) |
C16—C15—C14 | 117.3 (2) | C23—C22—H22 | 119.3 |
C16—C15—C11 | 120.8 (2) | C21—C22—H22 | 119.3 |
C14—C15—C11 | 121.8 (2) | C8—C7—C6 | 120.9 (3) |
C2—O3—H3 | 109.5 | C8—C7—H7 | 119.5 |
N1—C19—C23 | 122.6 (2) | C6—C7—H7 | 119.5 |
N1—C19—H19 | 118.7 | C20—C21—C22 | 119.4 (3) |
C23—C19—H19 | 118.7 | C20—C21—H21 | 120.3 |
C13—C14—C15 | 121.5 (2) | C22—C21—H21 | 120.3 |
C13—C14—H14 | 119.2 | C6—C5—C10 | 121.4 (3) |
C15—C14—H14 | 119.2 | C6—C5—H5 | 119.3 |
C12—O2—C18 | 117.4 (2) | C10—C5—H5 | 119.3 |
C22—C23—C24 | 117.8 (2) | C24—C25—C20 | 119.8 (3) |
C22—C23—C19 | 119.9 (3) | C24—C25—H25 | 120.1 |
C24—C23—C19 | 122.4 (3) | C20—C25—H25 | 120.1 |
C12—C13—C14 | 120.2 (2) | C5—C6—C7 | 119.8 (3) |
C12—C13—H13 | 119.9 | C5—C6—H6 | 120.1 |
C14—C13—H13 | 119.9 | C7—C6—H6 | 120.1 |
O3—C2—C1 | 124.1 (2) | O1—C20—C21 | 125.0 (3) |
O3—C2—C3 | 115.1 (3) | O1—C20—C25 | 114.7 (3) |
C1—C2—C3 | 120.8 (3) | C21—C20—C25 | 120.4 (3) |
O2—C12—C13 | 116.5 (2) | O2—C18—H18A | 109.5 |
O2—C12—C17 | 124.2 (2) | O2—C18—H18B | 109.5 |
C13—C12—C17 | 119.2 (2) | H18A—C18—H18B | 109.5 |
C7—C8—C9 | 121.7 (3) | O2—C18—H18C | 109.5 |
C7—C8—H8 | 119.2 | H18A—C18—H18C | 109.5 |
C9—C8—H8 | 119.2 | H18B—C18—H18C | 109.5 |
C20—O1—C26 | 117.6 (3) | O1—C26—H26A | 109.5 |
C25—C24—C23 | 121.3 (3) | O1—C26—H26B | 109.5 |
C25—C24—H24 | 119.4 | H26A—C26—H26B | 109.5 |
C23—C24—H24 | 119.4 | O1—C26—H26C | 109.5 |
C15—C16—C17 | 121.9 (2) | H26A—C26—H26C | 109.5 |
C15—C16—H16 | 119.1 | H26B—C26—H26C | 109.5 |
C17—C16—H16 | 119.1 |
Experimental details
Crystal data | |
Chemical formula | C26H23NO3 |
Mr | 397.45 |
Crystal system, space group | Monoclinic, P21/c |
Temperature (K) | 298 |
a, b, c (Å) | 20.790 (5), 10.717 (3), 9.470 (2) |
β (°) | 102.952 (4) |
V (Å3) | 2056.4 (9) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 0.08 |
Crystal size (mm) | 0.46 × 0.45 × 0.16 |
Data collection | |
Diffractometer | Bruker APEX area-detector |
Absorption correction | Multi-scan (SADABS; Bruker, 2001) |
Tmin, Tmax | 0.963, 0.987 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 10108, 3595, 3150 |
Rint | 0.022 |
(sin θ/λ)max (Å−1) | 0.595 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.071, 0.156, 1.22 |
No. of reflections | 3594 |
No. of parameters | 274 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.19, −0.22 |
Computer programs: SMART (Bruker, 2001), SMART, SAINT (Bruker, 2001), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), ORTEPIII (Burnett & Johnson, 1996) and ORTEP-3 for Windows (Farrugia, 1997), SHELXL97.
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The title compound, (1), is a key intermediate used in the sythesis of amino naphthol,which was found to be potent chiral catalyst in the addition reactions of dialkylzincs to aldehydes.
In the title compound, C26H23NO3, the π-conjugated system formed by the methoxy-benzylidene-imine tautomer is essentially planar with the largest deviation being -0.104 (2)Å at N1. This plane makes dihedral angles of 67.46 (4)° and 72.51 (7)° with the methoxy-phenyl and the naphtalene planes respectively (Fig. 1). An intramolecular O—HN hydrogen bond is formed between the hydroxyl OH attached to the naphtalene group and the Schiff base N atom (Table 1). The crystal packing is stabilized by van der Waals forces.