Understanding metal–ligand inter­actions in coordination polymers using Hirshfeld surface analysis

Properties related to the size and shape of Hirshfeld surfaces provide insight into the nature and strength of inter­actions among the building blocks of mol­ecular crystals. In this work, we demonstrate that functions derived from the curvatures of the surface at a point, namely, shape index (S) and curvedness (C), as well as the distances from the surface to the nearest external (d_e) and inter­nal (d_i) nuclei, can be used to help understand metal–ligand inter­actions in coordination polymers. The crystal structure of catena-poly[[[(1,10-phenanthroline-κ²N,N′)copper(II)]-μ-4-nitro­phthalato-κ²O¹:O²] trihydrate], {[Cu(C₈H₃NO₆)(C₁₂H₈N₂)]·3H₂O}_n, described here for the first time, was used as a prototypical system for our analysis. Decomposition of the coordination polymer into its metal centre and ligand mol­ecules followed by joint analysis of the Hirshfeld surfaces generated for each part unveil qualitative and semi-qu­anti­tative information that cannot be easily obtained either from conventional crystal packing analysis or from Hirshfeld surface analysis of the entire polymeric units. The shape index function S is particularly sensitive to the coordination details and its mapping on the surface of the metallic centre is highly dependent on the nature of the ligand and the coordination bond distance. Correlations are established between the shape of the Hirshfeld surface of the metal and the geometry of the metal–ligand contacts in the crystals. This could be applied not only to estimate limiting coordination distances in metal–organic compounds, but also to help establish structure–property relationships potentially useful for the crystal engineering of such materials.

Computing details

Data collection: CrysAlis PRO (Rigaku OD, 2015); cell refinement: CrysAlis PRO (Rigaku OD, 2015); data reduction: CrysAlis PRO (Rigaku OD, 2015); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2016 (Sheldrick, 2015b); molecular graphics: PROGRAM FOR GRAPHICS?; software used to prepare material for publication: SHELXL2016 (Sheldrick, 2015b) and PLATON (Spek, 2009).

catena-Poly[[[(1,10-phenanthroline-κ²N,N')copper(II)]-µ-4-nitrophthalato-κ²O¹:O²] trihydrate]

Crystal data

[Cu(C8H3NO6)(C12H8N2)]·3H2O	F(000) = 1036
Mr = 506.91	Dx = 1.68 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 3666 reflections
a = 16.6652 (12) Å	θ = 3.8–28.7°
b = 6.6975 (3) Å	µ = 1.15 mm^−1
c = 18.6763 (12) Å	T = 298 K
β = 105.963 (7)°	Needle, blue
V = 2004.2 (2) Å^3	0.67 × 0.09 × 0.05 mm
Z = 4

Data collection

Rigaku Xcalibur Atlas Gemini ultra diffractometer	3508 reflections with I > 2σ(I)
Detector resolution: 10.4186 pixels mm^-1	Rint = 0.082
ω scans	θmax = 29.5°, θmin = 2.5°
Absorption correction: multi-scan (CrysAlis PRO; Rigaku OD, 2015)	h = −19→21
Tmin = 0.821, Tmax = 1.000	k = −8→6
14972 measured reflections	l = −23→23
4952 independent reflections

Refinement

Refinement on F^2	11 restraints
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.051	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.125	w = 1/[σ^2(Fo^2) + (0.0498P)^2 + 0.3946P] where P = (Fo^2 + 2Fc^2)/3
S = 1.03	(Δ/σ)max = 0.001
4952 reflections	Δρmax = 0.55 e Å^−3
316 parameters	Δρmin = −0.60 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Single-crystal X-ray diffraction data were collected on an Xcalibur Atlas Gemini Ultra diffractometer and reduced using the CrysAlisPro software (Rigaku, 2018). The structure was solved by direct methods in SHELXS and refined with a full-matrix least-squares procedure using SHELXL-2016/6 (Sheldrick, 2015). All non-hydrogen atoms were refined with anisotropic atomic displacement parameters.

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

	x	y	z	Uiso*/Ueq
Cu1	0.29521 (2)	0.04033 (5)	0.83969 (2)	0.02400 (13)
O1	0.24972 (14)	−0.3215 (3)	0.74930 (12)	0.0354 (5)
O2	0.36098 (14)	−0.1280 (3)	0.79494 (12)	0.0300 (5)
O3	0.32293 (14)	−0.7274 (3)	0.79076 (12)	0.0313 (5)
O4	0.25333 (15)	−0.8232 (3)	0.67656 (13)	0.0425 (6)
O5	0.51248 (16)	−0.0458 (3)	0.60593 (16)	0.0475 (7)
O6	0.55854 (15)	−0.3089 (4)	0.56354 (13)	0.0439 (6)
O7	0.08459 (17)	−0.2360 (4)	0.72494 (19)	0.0598 (8)
H7A	0.1351 (4)	−0.228 (3)	0.7518 (7)	0.072*
H7B	0.068 (2)	−0.355 (2)	0.712 (2)	0.072*
O8	0.08378 (18)	0.0981 (4)	0.63726 (19)	0.0637 (8)
H8A	0.1324 (12)	0.151 (5)	0.653 (2)	0.076*
H8B	0.084 (2)	−0.008 (4)	0.663 (2)	0.076*
O9	0.0044 (2)	−0.0833 (4)	0.8264 (2)	0.0693 (9)
H9A	0.036 (2)	−0.116 (6)	0.799 (2)	0.083*
H9B	−0.028 (2)	−0.181 (4)	0.829 (3)	0.083*
N1	0.28942 (16)	−0.1565 (3)	0.91839 (13)	0.0257 (6)
N2	0.20930 (16)	0.1796 (3)	0.87686 (14)	0.0261 (6)
N3	0.51521 (16)	−0.2269 (4)	0.59854 (15)	0.0312 (6)
C1	0.3302 (2)	−0.3265 (4)	0.93652 (17)	0.0318 (7)
H1	0.367258	−0.366515	0.91006	0.038*
C2	0.3197 (2)	−0.4479 (4)	0.99395 (19)	0.0366 (8)
H2	0.349506	−0.566538	1.005359	0.044*
C3	0.2656 (2)	−0.3921 (5)	1.03325 (18)	0.0365 (8)
H3	0.258346	−0.472086	1.071708	0.044*
C4	0.2206 (2)	−0.2122 (4)	1.01518 (16)	0.0301 (7)
C5	0.23488 (19)	−0.1003 (4)	0.95724 (16)	0.0247 (6)
C6	0.1605 (2)	−0.1402 (5)	1.05078 (19)	0.0415 (9)
H6	0.15003	−0.212909	1.089671	0.05*
C7	0.1188 (2)	0.0316 (5)	1.0288 (2)	0.0423 (9)
H7	0.079968	0.074532	1.052929	0.051*
C8	0.19115 (19)	0.0820 (4)	0.93460 (16)	0.0258 (6)
C9	0.1325 (2)	0.1500 (5)	0.96934 (18)	0.0315 (7)
C10	0.0912 (2)	0.3274 (5)	0.9422 (2)	0.0402 (8)
H10	0.051121	0.378509	0.963356	0.048*
C11	0.1095 (2)	0.4258 (5)	0.8848 (2)	0.0394 (8)
H11	0.082147	0.54422	0.866926	0.047*
C12	0.1692 (2)	0.3486 (5)	0.85311 (18)	0.0346 (7)
H12	0.181482	0.417361	0.814142	0.041*
C13	0.3220 (2)	−0.2712 (4)	0.75496 (16)	0.0243 (6)
C14	0.37110 (18)	−0.3767 (4)	0.70923 (15)	0.0212 (6)
C15	0.35810 (18)	−0.5781 (4)	0.68943 (15)	0.0222 (6)
C16	0.3997 (2)	−0.6611 (4)	0.64177 (17)	0.0298 (7)
H16	0.391902	−0.795494	0.629252	0.036*
C17	0.4525 (2)	−0.5487 (4)	0.61252 (17)	0.0295 (7)
H17	0.47985	−0.605043	0.580268	0.035*
C18	0.46332 (19)	−0.3519 (4)	0.63230 (16)	0.0252 (6)
C19	0.42458 (19)	−0.2633 (4)	0.68105 (16)	0.0243 (6)
H19	0.434416	−0.129922	0.694513	0.029*
C20	0.3049 (2)	−0.7186 (4)	0.72018 (17)	0.0254 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu1	0.0309 (2)	0.0197 (2)	0.0269 (2)	0.00178 (14)	0.01712 (17)	0.00112 (13)
O1	0.0270 (13)	0.0369 (12)	0.0473 (14)	0.0007 (10)	0.0185 (11)	−0.0021 (10)
O2	0.0357 (13)	0.0257 (11)	0.0358 (12)	−0.0010 (9)	0.0218 (11)	−0.0066 (9)
O3	0.0469 (15)	0.0258 (11)	0.0267 (12)	−0.0045 (9)	0.0194 (11)	0.0013 (8)
O4	0.0430 (16)	0.0440 (14)	0.0400 (14)	−0.0182 (12)	0.0104 (12)	−0.0080 (11)
O5	0.0465 (16)	0.0332 (14)	0.0728 (19)	−0.0042 (11)	0.0332 (15)	0.0100 (12)
O6	0.0465 (16)	0.0572 (15)	0.0394 (14)	−0.0095 (12)	0.0312 (13)	−0.0087 (11)
O7	0.0378 (16)	0.0531 (16)	0.093 (2)	0.0064 (13)	0.0248 (16)	0.0153 (16)
O8	0.0407 (18)	0.0568 (18)	0.095 (2)	−0.0091 (14)	0.0207 (17)	0.0148 (16)
O9	0.073 (2)	0.0598 (19)	0.081 (2)	−0.0078 (16)	0.0312 (19)	−0.0077 (16)
N1	0.0292 (15)	0.0226 (12)	0.0285 (14)	0.0025 (10)	0.0134 (12)	0.0020 (10)
N2	0.0289 (15)	0.0211 (12)	0.0308 (14)	0.0029 (10)	0.0127 (12)	0.0012 (10)
N3	0.0255 (15)	0.0403 (16)	0.0303 (15)	−0.0053 (12)	0.0120 (12)	0.0015 (11)
C1	0.035 (2)	0.0287 (16)	0.0330 (18)	0.0066 (14)	0.0125 (15)	0.0030 (13)
C2	0.044 (2)	0.0263 (16)	0.0361 (19)	0.0073 (15)	0.0056 (17)	0.0080 (13)
C3	0.045 (2)	0.0360 (18)	0.0269 (17)	−0.0057 (15)	0.0066 (16)	0.0081 (13)
C4	0.0333 (19)	0.0343 (17)	0.0231 (16)	−0.0054 (14)	0.0087 (14)	0.0020 (12)
C5	0.0258 (17)	0.0270 (15)	0.0233 (15)	−0.0015 (12)	0.0098 (13)	−0.0033 (11)
C6	0.053 (2)	0.051 (2)	0.0301 (19)	−0.0058 (18)	0.0262 (18)	0.0000 (15)
C7	0.044 (2)	0.057 (2)	0.036 (2)	0.0004 (18)	0.0272 (18)	−0.0068 (16)
C8	0.0271 (17)	0.0293 (15)	0.0233 (15)	−0.0030 (12)	0.0105 (14)	−0.0041 (11)
C9	0.0286 (18)	0.0367 (17)	0.0328 (18)	−0.0029 (14)	0.0143 (15)	−0.0112 (13)
C10	0.032 (2)	0.044 (2)	0.049 (2)	0.0078 (15)	0.0175 (17)	−0.0106 (16)
C11	0.035 (2)	0.0313 (18)	0.051 (2)	0.0118 (14)	0.0092 (18)	−0.0020 (15)
C12	0.037 (2)	0.0309 (17)	0.0357 (19)	0.0048 (14)	0.0102 (16)	0.0036 (13)
C13	0.0311 (18)	0.0200 (14)	0.0252 (16)	0.0058 (12)	0.0135 (14)	0.0036 (11)
C14	0.0230 (16)	0.0209 (14)	0.0218 (15)	0.0014 (11)	0.0098 (13)	−0.0003 (11)
C15	0.0236 (16)	0.0236 (14)	0.0204 (14)	−0.0010 (11)	0.0080 (13)	0.0003 (11)
C16	0.040 (2)	0.0248 (15)	0.0296 (17)	−0.0032 (13)	0.0180 (15)	−0.0071 (12)
C17	0.0327 (19)	0.0328 (16)	0.0278 (17)	0.0009 (14)	0.0164 (15)	−0.0065 (13)
C18	0.0266 (17)	0.0300 (16)	0.0224 (15)	0.0001 (12)	0.0123 (13)	0.0030 (12)
C19	0.0285 (17)	0.0204 (14)	0.0266 (16)	0.0020 (12)	0.0121 (14)	0.0002 (11)
C20	0.0282 (18)	0.0197 (14)	0.0310 (17)	0.0023 (12)	0.0128 (14)	−0.0013 (11)

Geometric parameters (Å, º)

Cu1—O2	1.9168 (19)	C3—H3	0.93
Cu1—O3^i	1.9237 (19)	C4—C5	1.389 (4)
Cu1—N2	1.987 (2)	C4—C6	1.430 (4)
Cu1—N1	1.997 (2)	C5—C8	1.425 (4)
O1—C13	1.226 (4)	C6—C7	1.349 (5)
O2—C13	1.278 (4)	C6—H6	0.93
O3—C20	1.270 (4)	C7—C9	1.432 (5)
O4—C20	1.228 (4)	C7—H7	0.93
O5—N3	1.223 (3)	C8—C9	1.391 (4)
O6—N3	1.229 (3)	C9—C10	1.396 (5)
O7—H7A	0.855 (5)	C10—C11	1.362 (5)
O7—H7B	0.857 (5)	C10—H10	0.93
O8—H8A	0.860 (5)	C11—C12	1.391 (4)
O8—H8B	0.861 (5)	C11—H11	0.93
O9—H9A	0.861 (5)	C12—H12	0.93
O9—H9B	0.859 (5)	C13—C14	1.511 (4)
N1—C1	1.321 (4)	C14—C19	1.381 (4)
N1—C5	1.363 (4)	C14—C15	1.400 (4)
N2—C12	1.327 (4)	C15—C16	1.386 (4)
N2—C8	1.364 (4)	C15—C20	1.510 (4)
N3—C18	1.465 (4)	C16—C17	1.379 (4)
C1—C2	1.395 (4)	C16—H16	0.93
C1—H1	0.93	C17—C18	1.367 (4)
C2—C3	1.362 (5)	C17—H17	0.93
C2—H2	0.93	C18—C19	1.386 (4)
C3—C4	1.410 (5)	C19—H19	0.93
O2—Cu1—O3^i	91.58 (9)	C9—C7—H7	119
O2—Cu1—N2	169.02 (10)	N2—C8—C9	123.3 (3)
O3^i—Cu1—N2	94.40 (9)	N2—C8—C5	116.0 (2)
O2—Cu1—N1	94.69 (9)	C9—C8—C5	120.6 (3)
O3^i—Cu1—N1	161.86 (10)	C8—C9—C10	116.6 (3)
N2—Cu1—N1	82.38 (9)	C8—C9—C7	117.6 (3)
C13—O2—Cu1	115.85 (19)	C10—C9—C7	125.8 (3)
C20—O3—Cu1^ii	120.74 (18)	C11—C10—C9	120.2 (3)
H7A—O7—H7B	114 (2)	C11—C10—H10	119.9
H8A—O8—H8B	107 (2)	C9—C10—H10	119.9
H9A—O9—H9B	109 (2)	C10—C11—C12	119.8 (3)
C1—N1—C5	118.2 (2)	C10—C11—H11	120.1
C1—N1—Cu1	129.2 (2)	C12—C11—H11	120.1
C5—N1—Cu1	112.57 (19)	N2—C12—C11	121.9 (3)
C12—N2—C8	118.2 (3)	N2—C12—H12	119.1
C12—N2—Cu1	128.9 (2)	C11—C12—H12	119.1
C8—N2—Cu1	112.91 (18)	O1—C13—O2	125.9 (3)
O5—N3—O6	123.3 (3)	O1—C13—C14	119.6 (3)
O5—N3—C18	118.3 (2)	O2—C13—C14	114.4 (3)
O6—N3—C18	118.4 (3)	C19—C14—C15	119.9 (2)
N1—C1—C2	122.3 (3)	C19—C14—C13	117.7 (2)
N1—C1—H1	118.8	C15—C14—C13	122.1 (2)
C2—C1—H1	118.8	C16—C15—C14	119.2 (3)
C3—C2—C1	119.7 (3)	C16—C15—C20	116.4 (2)
C3—C2—H2	120.1	C14—C15—C20	124.4 (2)
C1—C2—H2	120.1	C17—C16—C15	121.4 (3)
C2—C3—C4	119.5 (3)	C17—C16—H16	119.3
C2—C3—H3	120.2	C15—C16—H16	119.3
C4—C3—H3	120.2	C18—C17—C16	118.1 (3)
C5—C4—C3	117.0 (3)	C18—C17—H17	121
C5—C4—C6	118.2 (3)	C16—C17—H17	121
C3—C4—C6	124.8 (3)	C17—C18—C19	122.7 (3)
N1—C5—C4	123.2 (3)	C17—C18—N3	119.0 (2)
N1—C5—C8	116.1 (2)	C19—C18—N3	118.3 (3)
C4—C5—C8	120.7 (3)	C14—C19—C18	118.7 (3)
C7—C6—C4	121.0 (3)	C14—C19—H19	120.6
C7—C6—H6	119.5	C18—C19—H19	120.6
C4—C6—H6	119.5	O4—C20—O3	125.8 (3)
C6—C7—C9	122.0 (3)	O4—C20—C15	118.7 (3)
C6—C7—H7	119	O3—C20—C15	115.3 (3)

Symmetry codes: (i) x, y+1, z; (ii) x, y−1, z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O7—H7A···O1	0.855 (10)	2.023 (10)	2.7239 (2)	138.7 (14)
O7—H7B···O9^iii	0.856 (18)	1.96 (2)	2.7838 (2)	161 (1)
O8—H8A···O4^i	0.86 (3)	1.95 (2)	2.7676 (2)	159 (1)
O8—H8B···O7	0.86 (3)	1.91 (3)	2.7706 (2)	177 (3)
O9—H9A···O7	0.86 (4)	1.96 (4)	2.7960 (2)	165 (4)
O9—H9B···O8^iii	0.86 (3)	1.94 (3)	2.7788 (2)	165 (4)
C1—H1···O5^iv	0.93	2.42	3.2867 (2)	154
C3—H3···O4^v	0.93	2.41	3.3380 (2)	175
C12—H12···O1^i	0.93	2.56	3.4453 (2)	158

Symmetry codes: (i) x, y+1, z; (iii) −x, y−1/2, −z+3/2; (iv) −x+1, y−1/2, −z+3/2; (v) x, −y−3/2, z+1/2.