Further evaluation of the shape of atomic Hirshfeld surfaces: M⋯H contacts and homoatomic bonds

This article is part of the collection Crystallography in Latin America: a vibrant community.

It is well known that Hirshfeld surfaces provide an easy and straightforward way of analysing inter­molecular inter­actions in the crystal environment. The use of atomic Hirshfeld surfaces has also demonstrated that such surfaces carry information related to chemical bonds which allow a deeper evaluation of the structures. Here we briefly summarize the approach of atomic Hirshfeld surfaces while further evaluating the kind of information that can be retrieved from them. We show that the analysis of the metal-centre Hirshfeld surfaces from structures refined via Hirshfeld Atom Refinement (HAR) allow accurate evaluation of contacts of type M⋯H, and that such contacts can be related to the overall shape of the surfaces. The com­pounds analysed were tetra­aqua­bis­(3-carb­oxy­propionato)metal(II), [M(C₄H₃O₄)₂(H₂O)₄], for metal(II)/M = manganese/Mn, cobalt/Co, nickel/Ni and zinc/Zn. We also evaluate the sensitivity of the surfaces by an investigation of seemingly flat surfaces through analysis of the curvature functions in the direction of C—C bonds. The obtained values not only demonstrate variations in curvature but also show a correlation with the hybridization of the C atoms involved in the bond.

1. Introduction

The importance of Hirshfeld surface analysis for the understanding of mol­ecules in the solid state is well known nowadays. More specifically, how mol­ecules pack together in the crystal and what types of inter­actions are responsible for the stabilization of mol­ecules in the crystalline phase. In this sense, Hirshfeld surface analyses have grown as a fast and visual manner of identifying and qu­anti­fying inter­molecular inter­actions, giving insights into the crystal environment. Furthermore, the analysis of inter­molecular inter­actions has aided the prediction of inter­actions in different com­pounds and, hence, allowed the development of new areas of research, such as crystal engineering and drug design.

The Hirshfeld surfaces are based on the Hirshfeld stockholder partitioning, in which the contribution of an atom to the mol­ecular electron density is defined by means of a weight function, which assumes values between 0 and 1, and depends on the share that the atom partakes in the whole mol­ecule (Hirshfeld, 1977). This partitioning method though generates con­tinuous atomic densities which lack boundaries. The insertion of a surface to the partitioning method and generalization for crystals [Equation (1)] yields the Hirshfeld surface, defined when w_i(r) = 0.5, thus indicating a region in space where the electron density of the mol­ecule accounts for half of that of the crystal (Spackman & Byrom, 1997; McKinnon et al., 1998).

The program CrystalExplorer generates Hirshfeld surfaces and different types of information can be retrieved from them (Jayatilaka et al., 2006; Spackman et al., 2021). The first type of information that could be retrieved from these surfaces was related to their overall shape. In this manner, the shape of the surfaces can be qu­anti­tatively described by the volume, surface area, globularity and asphericity of the surfaces. The globularity informs on how much the surface deviates from a spherical shape of the same area as the surface, in a way that a sphere would have globularity equal to unity. The asphericity parameter will inform if the surface is closer to an oblate, prolate or isotopic shape, thus being an indicator of the anisotropy of the surface (McKinnon et al., 1998).

The properties which can be mapped over the surfaces are related to either the distance of the atoms from the surface or the surface principal curvatures, allowing different information to be retrieved from these surfaces. The properties con­cerning distance parameters are d_e, d_i and d_norm, which represent, respectively, the closest distance from an atom outside the surface to the surface, the closest distance from an atom inside the surface to the surface and the distance of both atoms inside and outside the surface normalized by their van der Waals radii. The properties of the principal curvatures are Shape Index and Curvedness, which represent, respectively, the shape of the surfaces (i.e. if they are concave or convex) and how much shape the surfaces present (i.e. if they are flat or curved) (McKinnon et al., 2004).

One of the most important uses of the distance properties is the possibility of plotting fingerprint plots, which will map all contacts, inside and outside the surface, and their frequency, to generate a two-dimensional (2D) plot characteristic of each mol­ecule and polymorph, allowing a fast identification of the principal inter­actions taking place in the crystal and their qu­anti­fication (Spackman & McKinnon, 2002). These plots can also be broken into element contributions, allowing the evaluation of each contact in relation to its type and strength, so it is possible to qu­anti­tatively know what are the major contacts that stabilize the crystal packing.

The curvature properties inform on the shape of the surfaces and allow, for instance, the colour-coded visualization of regions of π–π inter­actions and hy­dro­gen bonds. The Shape Index property assumes values from −1.0 (concave surface, represented in red) to +1.0 (convex surface, represented in blue). One important feature of this property is its com­plementarity. In this way, the presence of a concave surface usually indicates that a convex region com­plementary to the concave region will be present, and if the surfaces are indeed com­plementary, we expect the values of S from both surfaces to be equal in modulus. Concerning the Curvedness property, its values range from −4.0 to +0.4, and one important feature is the presence of blue edges which delimit inter­action regions and give information on the coordination number of the mol­ecule (McKinnon et al., 2004).

1.1. Atomic Hirshfeld surfaces

In addition to the more typical mol­ecular Hirshfeld surfaces (HSs), it is also possible to obtain atomic or functional group HSs. This approach is especially useful for coordination polymers, in which it is not possible to isolate a com­plete fragment of the mol­ecule, so the mapping of properties is influenced by the strong chemical bond between an atom inside and an atom outside the surface. However, this method can be useful for other applications as well, which we will discuss briefly in the next section.

In the past, we have evaluated the different types of information that can be retrieved from atomic Hirshfeld surfaces, and it is summarized below:

1.1.1. Properties of distance

The properties based on distance parameters indicate the distance (and hence interaction strength) between the atom inside the surface and the atom outside the surface. For atomic HS of metal centres, d_e and d_norm can be useful to com­pare the strength of the coordination and evaluate possible distortions on the geometry. Additionally, the evaluation of distance parameters allows the generation of fingerprint plots, that are 2D plots unique for each mol­ecule and polymorph (Spackman & McKinnon, 2002). In the case of atomic Hirshfeld surfaces, the plot will be asymmetric due to the difference in atoms inside and outside the surface, but the principle remains the same: it is feasible to com­pare atoms in similar environments and easily visualize in two dimensions the similarities and differences between otherwise identical atoms, for example, in binuclear com­plexes presenting the same type of metal centre but in different environments (Gacki et al., 2020).

1.1.2. Local properties of curvature

Concerning the properties which take into account the surface principal curvatures, we have evaluated both Shape Index (S) and Curvedness (C), and, in both cases, unique information can be retrieved from these functions, allowing a deeper evaluation of the environment of the atom (Pinto et al., 2020a,b). For the systems we have studied, we noticed that when it comes to atomic HSs, the Shape Index property can indicate the coordination or not of an atom to a metal centre, apart from giving information on the curvature of the surface in the region in which the inter­atomic vector passes through the surface. Even though the surfaces are calculated based on Independent Atom Model (IAM) density, the information on whether the surfaces are concave or convex can give insights into the electronegativity of atomic fragments, where a concave surface usually indicates that the atom on the outside is more electronegative, and a convex surface can indicate that the atom inside instead is more electronegative. The Curvedness property, on the other hand, informs on the coordination number of an atom through the typical blue edges associated with regions of positive curvature (usually assuming values from −0.5 to +0.4), which delimit regions on the surface (McKinnon et al., 2004). The coordination number allows the environment of an atom to be easily summarized. In addition, regions in orange, usually corresponding to curvedness values smaller than −2.0, are indicative of very strong inter­actions.

We have also demonstrated that the values of the properties taken at the point where the inter­atomic vector passes through the surface appears to be dependent on the nature of the atoms involved, being possible to determine an inter­val at which certain type of bond will fall on. At the moment, we have found a characteristic inter­val for the following bond types (the C values taken at the surface of the first atom): Fe—O (−1.61 to −1.87), Cr—O (−2.02 to −2.25), Mn—O (−1.53 to −1.85), Co—O (−1.80 to −2.11), Cu—O (−1.69 to −2.71), Cu—N (−2.21 to −2.80), C—N (−1.59 to −2.24), C—O (−1.11 to −1.44), C=O (−0.99 to −1.20) and C≡O (−0.98 to −1.07). The smallest C values are obtained for the Cu atom, indicating the flattest surfaces for some Cu—O directions around this atom. The highest variation in C is found for the Cu atom, and this is expected to be due to the tendency of copper to exhibit Jahn–Teller distortion. Although there is superposition of values, it is clear that the type of atoms involved in the bond influences the curvature of the surface (Pinto et al., 2020a,b).

Most recently, we have found a relationship between the Curvedness value at the point where the inter­atomic vector passes across the surface and the electron density at the bond critical point (BCP) for bonds presenting C atoms. This relationship allows estimation of the electron density at the BCP for bonds containing C atoms making use of a simple exponential equation (Pinto et al., 2021). Although more data are needed to enhance the precision of the calculated values, the results demonstrate that these surfaces carry useful information, beyond a general semi-qualitative description of the inter­molecular inter­actions, which is usually the main application of the method in the literature.

1.1.3. General properties of shape

Apart from the functions which one can map over the Hirshfeld surface, there are certain qu­anti­tative parameters related to the shape of the surface which can be com­plementary to this mapping. These parameters are the volume and area of the surface, and the globularity (G) and asphericity (Ω). The globularity parameter evaluates by how much the surface area deviates from a sphere which is isovolumetric with the surface, assuming a maximum value of 1.0 for a sphere. The asphericity parameter measures the deviation of the surface from an isotropic object, thus differentiating an isotropic (Ω = 0.0) from an oblate (Ω = 0.25) or a prolate (Ω = 1.0) object (McKinnon et al., 2004). Even though these parameters appear to provide the same information, they are actually com­plementary, as G is a function of geometric descriptors (area and volume), while Ω is a function of the principal moments of inertia of the molecule. These parameters can be a qu­anti­tative way to demonstrate geometry distortions or deviations from a regular shape (McKinnon et al., 2004; Pinto et al., 2020a,b).

1.2. Examples of applications

Although the method was initially investigated for de­scrib­ing transition-metal centres in coordination polymers, the applications of the method have so far demonstrated its use­fulness in retrieving unique information even from mol­ecular com­plexes, and a few examples are briefly discussed here. Haezam et al. (2019) used the atomic HS to evaluate the strength of inter­actions involving an Sn centre. With the use of properties d_e, d_norm, S and C, the authors were able to visually differentiate the stronger coordination bonds from the weaker inter­actions, also evaluating the distortion in the geometry through the fingerprint plot. Chettri et al. (2019) evaluated the distorted geometry of the tetra­coordinated Cu^II atom from bis­[2-(4,5-diphenyl-1H-imidazol-2-yl)-4-nitro­phenolato]cop­per(II) dihydrate. In this case, the curvature functions S and C were used, along with fingerprint plots. Another inter­esting example of atomic HS being used to evaluate the environment of an atom is the case of the two analogues of bis­(2-{[(2,6-di­chloro­benzyl­idene)hydrazinyl­idene]meth­yl}phenolato)me­tal(II), with metal(II) being either Co^II or Cu^II. In this study, even though the coordination distances were very similar, the atomic HSs were able to distinguish between the chemical environments, yielding very distinguishable fingerprint plots (Manawar et al., 2020). The authors also verified the presence of Co⋯H contacts, which cause asymmetries in both the atomic surface and the fingerprint plot. Gacki et al. (2020) were also able to evaluate different coordination spheres for three Mn metal centres from a coordination polymer. With the d_norm property, they were able to verify the difference in coordination strength when changing ligands but maintaining the coordinated atom, in this case, O, while fingerprint plots highlighted the differences among the three Mn centres. Khosa et al. (2020) evaluated an Mn centre in a coordination polymer using the d_norm property and fingerprint plot. They were able to verify inter­actions of the Mn⋯H type occurring in the corners of the cubic-like Mn surface and retrieve information on the coordination geometry. Lastly, Abendrot et al. (2020) have evaluated the Zn^II Hirshfeld surfaces for five metal centres divided into four com­pounds. They were able to evaluate the strength of the inter­actions through the d_norm property and analyse the different contact contributions through fingerprint plots, enabling the com­parison of coordination spheres.

Throughout our study on the Hirshfeld surface for metal centres, we have perceived the importance of M⋯H contacts for shaping the surfaces, in a way that surfaces with more defined shapes, such as cubic, present fewer M⋯H contacts than surfaces with irregular shapes, usually presenting elongated edges and vertices (Pinto et al., 2020a). However, every structure we evaluated so far was determined considering the IAM, hence the D—H distances were somehow fixed during the refinement steps. Here we evaluate the atomic Hirshfeld surfaces for a series of isostructural transition-metal com­plexes, namely, tetra­aqua­bis­(hy­dro­gen maleato)metal(II) (abbreviated as MHmA), refined via the Hirshfeld Atom Refinement (HAR) procedure, which allows free refinement of H-atom parameters. In addition, since the curvature of the atomic surfaces in the direction of the inter­atomic vector appears to be influenced by the difference in electronegativity of the atoms involved in the bond, we also evaluate the atomic Hirshfeld surface for C atoms bonded to other C atoms in high-quality determined structures from the literature. Since this type of bond is expected to be flat, it will serve as a parameter indicating the sensitivity of the surfaces to small variations in the environment of the atom, thus providing some insight into the nature of the covalent bonds.

2. Methodology

2.1. Synthesis and crystallization

All single crystals used in this work were obtained from the slow evaporation of an aqueous solution of maleic acid and the respective metal nitrate, except for Mn, for which car­bon­ate was used. All syntheses were performed at approximately 50 °C and stirring for 2 h, except for CoHmA, which did not need heating and was synthesized at room temperature.

2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Data was collected at room temperature on an Agilent Xcalibur four-circle dif­frac­tometer with an Atlas (Gemini Ultra) detector, using Mo Kα radiation (λ = 0.71073 Å). Data reduction was performed by the CrysAlis PRO software (Rigaku OD, 2019). The structures were solved by the intrinsic phasing method using SHELXT (Sheldrick, 2015) in OLEX2 (Dolomanov et al., 2009), and refined initially by the full-matrix least-squares method on F², using SHELXL (Sheldrick, 2015). In the last cycle, the OLEX2 engine was used for the refinement, also making use of the modulus NoSpherA2 (Kleemiss et al., 2021) in order to perform the Hirshfeld Atom Refinement. In this step, the positional parameters of H atoms, which were initially fixed, were freely refined, and the displacement parameters, which were being considered isotropic, were anisotropically refined. The mol­ecular wavefunction was calculated using ORCA (Version 5.0; Neese, 2022) at the PBE0/x2c-TZVPP level of theory, taking into account relativistic effects through the Douglas–Kroll–Hess Hamiltonian (DKH2). The calculations also considered solvation by water in order to take into account inter­molecular hy­dro­gen bonds. PLATON (Spek, 2020) was used to calculate geometric parameters for hy­dro­gen bonds.

Table 1
Experimental details

For all structures: triclinic, P, Z = 1. Experiments were carried out at 298 K with Mo Kα radiation using a Rigaku Xcalibur Gemini ultra diffractometer with an Atlas detector. The absorption correction was Gaussian (CrysAlis PRO; Rigaku OD, 2019). All H-atom parameters were refined.

	MnHmA	CoHmA	ZnHmA	NiHmA
Crystal data
Chemical formula	[Mn(C4H3O4)2(H2O)4]	[Co(C4H3O4)2(H2O)4]	[Zn(C4H3O4)2(H2O)4]	[Ni(C4H3O4)2(H2O)4]
Mr	357.13	361.13	367.59	360.89
a, b, c (Å)	5.3263 (2), 7.3743 (4), 9.3688 (4)	5.2222 (2), 7.3322 (2), 9.2293 (3)	5.2307 (2), 7.3259 (3), 9.2246 (3)	5.1780 (2), 7.3254 (2), 9.1449 (4)
α, β, γ (°)	109.863 (4), 104.606 (4), 93.344 (4)	109.125 (3), 104.376 (3), 93.224 (3)	108.753 (3), 104.626 (3), 93.202 (3)	108.423 (3), 104.583 (3), 92.929 (3)
V (Å^3)	330.69 (3)	319.76 (2)	320.23 (2)	315.25 (2)
μ (mm^−1)	1.06	1.41	1.98	1.61
Crystal size (mm)	0.63 × 0.30 × 0.17	0.60 × 0.48 × 0.38	0.8 × 0.36 × 0.29	0.59 × 0.35 × 0.13
Data collection
Tmin, Tmax	0.628, 0.846	0.657, 0.739	0.394, 0.706	0.650, 0.903
No. of measured, independent and observed [I ≥ 2u(I)] reflections	19553, 3387, 3080	15610, 3273, 3147	17325, 3302, 3187	12425, 3240, 3136
Rint	0.035	0.030	0.034	0.027
(sin θ/λ)max (Å^−1)	0.857	0.862	0.860	0.858
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.022, 0.044, 1.17	0.018, 0.039, 1.13	0.019, 0.045, 1.22	0.019, 0.044, 1.16
No. of reflections	3387	3273	3302	3240
No. of parameters	161	161	161	160
No. of restraints	2	2	0	2
Δρmax, Δρmin (e Å^−3)	0.32, −0.37	0.38, −0.36	0.45, −0.37	0.34, −0.43
Computer programs: CrysAlis PRO (Rigaku OD, 2019), SHELXT2018 (Sheldrick, 2015), olex2.refine (Bourhis et al., 2015) and OLEX2 (Dolomanov et al., 2009).

2.3. Hirshfeld surfaces and com­putational details

The Hirshfeld surfaces for atomic entities were calculated using the CrystalExplorer software (Version 21.5; Turner et al., 2017). The normalization for X—H bonds was disabled in order to maintain the bond distance values calculated using the HAR method. The properties d_norm, Shape Index and Curvedness were mapped onto the surfaces, and fingerprint plots were also calculated. The program VESTA (Momma & Izumi, 2011) was used to calculate the distortion index, quadratic elongation and effective coordination number for the com­plexes.

Concerning the evaluation of the C atoms, high-quality structures undergoing charge–density analysis were retrieved from the Cambridge Structural Database (CSD; Groom et al., 2016), and the atomic Hirshfeld surfaces were also calculated using the CrystalExplorer software. The values for Shape Index and Curvedness were taken for the surfaces of both C atoms, at the point where the inter­atomic vector passes through the surface. A list of the structures used, and their respective references, can be found in supporting information (Table S2).

3. Results and discussion

3.1. Isostructural series

We have remeasured an isostructural series com­prised of four com­plexes, presenting either Mn, Co, Ni or Zn as the metal centre coordinated with two hy­dro­gen maleate ions and four water mol­ecules, already described in the literature (Lis, 1983; Gupta et al., 1984; Sequeira et al., 1992; Mahalakshmi et al., 2013; Ruggiero & Korter, 2016) (Fig. 1). All the com­plexes crystallize in the space group P, with the metal centre lying on the centre of inversion, and hence, half of the mol­ecule is generated by the symmetry operation (−x, −y, −z). The inter­esting feature of this series is the fact that a change in metal nature changes the orientation of the axial water mol­ecules, which, in turn, results in the H atoms from the water mol­ecule inter­acting with the O atom from the hygrogen maleate ligand with different strengths throughout the series (Ruggiero & Korter, 2016). The strength of this hy­dro­gen bond (here labelled O5—H5A⋯O2) stabilizes the O1—C1—O2 group to a lesser or greater degree, which indirectly influences the positioning of the H atom participating in the short intra­molecular hy­dro­gen bond present in the hy­dro­gen maleate ligand, here labelled as O3—H3A⋯O2 (Ruggiero & Korter, 2016; Malaspina et al., 2017). Fig. 2 presents a schematic description of the inter­play between water mol­ecule tilting and H3A atom positioning.

Figure 1 The crystal structure and labelling scheme for MHmA, with M = Mn, Co, Ni and Zn.

Figure 2 Schematic representation of the influence of the water tilt angle on the intra­molecular short hy­dro­gen bond.

The geometric parameters for the com­plexes are described in Table S3, while those con­cerning hy­dro­gen bonds are presented in Table 2. As already mentioned, the HAR was performed in order to locate H atoms with higher accuracy in com­parison to the usual method of fixing positional parameters and using a riding model to describe the isotropic displacement parameters. This caused the D—H distances to be longer than those usually found in the literature, especially for the short intra­molecular hy­dro­gen bond O3—H3A⋯O2. However, a com­parison with neutron data available in the literature for the Zn com­pound (Sequeira et al., 1992) reveals that the HAR method retrieves very accurate bond lengths for those bonds containing H atoms, including the seemly long O3—H3A bond (Fig. S1).

Table 2
Geometric parameters (Å, °) for hy­dro­gen bonds

First line: MnHmA; second line: CoHmA; third line: NiHmA; fourth line: ZnHmA.

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O3—H3A⋯O2	1.141 (14)	1.276 (14)	2.4134 (7)	174.6 (16)
	1.103 (15)	1.321 (15)	2.4225 (7)	175.8 (11)
	1.084 (17)	1.350 (17)	2.4321 (8)	174.8 (16)
	1.103 (17)	1.327 (17)	2.4273 (8)	174.9 (16)
O5—H5A⋯O2	0.918 (12)	2.488 (14)	2.9492 (8)	111.3 (11)
	0.921 (12)	2.289 (13)	2.8625 (7)	120.0 (12)
	0.920 (13)	2.184 (14)	2.8149 (8)	125.0 (12)
	0.920 (12)	2.256 (14)	2.8600 (7)	122.8 (12)
O5—H5B⋯O4	0.964 (13)	1.817 (13)	2.7691 (8)	168.9 (11)
	0.953 (12)	1.843 (12)	2.7818 (7)	167.9 (11)
	0.966 (14)	1.857 (14)	2.8019 (8)	165.3 (13)
	0.961 (14)	1.844 (14)	2.7901 (8)	167.6 (13)
O5—H5A⋯O3	0.918 (12)	2.005 (14)	2.8489 (8)	152.1 (13)
	0.921 (12)	2.073 (14)	2.8723 (8)	144.4 (13)
	0.920 (13)	2.148 (15)	2.8991 (8)	138.2 (13)
	0.920 (12)	2.118 (14)	2.8854 (8)	140.1 (13)
O6—H6A⋯O4	0.952 (12)	1.933 (12)	2.8530 (8)	161.9 (10)
	0.960 (12)	1.923 (12)	2.8632 (7)	165.7 (10)
	0.973 (14)	1.925 (14)	2.8711 (8)	163.3 (14)
	0.987 (14)	1.908 (14)	2.8656 (8)	162.6 (14)
O6—H6B⋯O1	0.981 (12)	1.858 (12)	2.8390 (8)	178.3 (10)
	0.961 (11)	1.908 (11)	2.8667 (7)	174.9 (11)
	0.959 (12)	1.920 (12)	2.8757 (8)	174.1 (13)
	0.985 (12)	1.878 (12)	2.8586 (6)	173.8 (13)
C3—H3⋯O6	1.080 (11)	2.571 (11)	3.5474 (9)	150.1 (8)
	1.070 (11)	2.515 (11)	3.4766 (8)	149.2 (8)
	1.078 (15)	2.471 (14)	3.4477 (9)	150.0 (11)
	1.099 (15)	2.492 (14)	3.4706 (9)	147.7 (11)

According to the geometry of the coordination sphere, in all cases, the distance M—O5 [and the symmetry related M—O5ⁱ; symmetry code: (i) −x, −y, −z] is shorter than the other M—O bonds, thus indicating a distorted octa­hedral geometry for the com­plexes under study. The distortion indexes (D), quadratic elongations (<λ>) and effective coordination numbers (ECoN) calculated for the metal centre polyhedra are displayed in Table 3.

Table 3
Qu­anti­tative parameters for the metal coordination sphere and Hirshfeld surfaces; average distances in Å

	(M—O)av (Å)	D	<λ>	ECoN	M⋯O (%)	M⋯H (%)	VH (Å^3)	AH (Å^2)	G	Ω
Mn	2.1871	0.01611	1.0071	5.9311	81.0	19.0	16.74	43.89	0.721	0.003
Co	2.1003	0.01685	1.0053	5.9231	84.3	15.7	13.36	36.10	0.754	0.003
Ni	2.0650	0.01191	1.0054	5.9634	86.3	13.7	12.11	33.13	0.770	0.004
Zn	2.1043	0.01860	1.0060	5.9057	86.6	13.4	12.59	33.44	0.783	0.003

3.2. Hirshfeld surfaces for the metal centres

The Hirshfeld surfaces for the metal centres are depicted in Fig. 3, along with their two-dimensional (2D) fingerprint plots. The properties mapped onto the surfaces are the Shape Index and Curvedness. Qu­anti­tative parameters are com­piled in Tables 3 and 4.

Table 4
Values of S and C taken at the bonding region

Mn—O1	−0.92	−1.38
Mn—O5	−0.94	−1.44
Mn—O6	−0.94	−1.36
Co—O1	−0.93	−1.47
Co—O5	−0.91	−1.51
Co—O6	−0.96	−1.42
Ni—O1	−0.91	−1.50
Ni—O5	−0.91	−1.51
Ni—O6	−0.94	−1.47
Zn—O1	−0.94	−1.48
Zn—O5	−0.94	−1.52
Zn—O6	−0.94	−1.46

Figure 3 Hirshfeld surfaces for the metal centres with the mapping of Curvedness (first line, C) and Shape index (second line, S), along with their respective fingerprint plots.

Despite the fact that the bond distance variations are very small going from one com­plex mol­ecule to another (about 5%), the HS for the metal centres are sensitive enough to account for the small structural deviations throughout the series, as can be seen by the differences in the fingerprint plots (especially at higher d_e and d_i values, which account for noncoordinative inter­actions), by the shapes of the surfaces in Fig. 3, and by the different colouring of the Curvedness property, which presents some yellow and red features with different intensities for different surfaces. Also, the characteristic blue edges delimiting regions of inter­action allow the visualization of the difference in the shape of the surfaces, with the surface for Mn presenting a twisted-like appearance, which diminishes when going to the end of the series. Both Fig. 3 and Table 3 enable the visualization of the difference in the vol­ume of the surfaces. As expected, the metal with the greatest coordination distances (Mn) presents the biggest volume, while the metal with the smallest coordination dis­tances (Ni) presents the smallest volume.

The values for S and C taken at the point where the inter­atomic vector passes through the surface (Table 4), although not being extremely precise, indicate the same pattern seen in other com­pounds of the same kind. In this sense, the S function presents values close to −1.0, indicating a highly concave surface, and the C values appear to depend on the nature of the elements present in the bond, being close to −1.4 for Mn—O and around −1.5 for the other types of bonds.

Concerning the mapping of the Shape Index property, the greatest variation among the surfaces is related to the extension of the red areas of the concave surface. These areas appear in all sides of the surface, in a direction perpendicular to the coordination vector, and indicate the coordination of the metal centre to the O atoms. The different extensions of the red areas are in agreement with the variations in volume for the surface, hence the biggest red area is related to the biggest surface (Mn), while the smallest red area is related to the smallest surface (Ni).

The Curvedness property is more efficient in differentiating the surfaces for different metals, with different colouring for the different metal surfaces. In mol­ecular Hirshfeld surfaces, red areas on the Curvedness property indicate highly flat regions, often associated with hy­dro­gen bonds (usually C < −2.0). It is inter­esting to see small red regions on the metal surfaces. However, in this case, these regions coincide largely with M⋯O contacts.

Another inter­esting feature of the metal surfaces is the influence of the noncoordinated O2 atom (Fig. 4). The surfaces are distorted in the region close to this atom, indicating its influence on the surface shape. The fact that there is no particular region delimited in blue for this contact along with the convex shape of the surface perpendicular to the vector between the metal and O2 (demonstrated by the blue colour of the Shape Index property), corroborate that there is no coordination to this atom. However, despite its long distance from the metal (approximately 3.3 Å), it still has an influence on the surface shape.

Figure 4 Influence of atom O2 in the surface for the metal centre viewed with the mapping of both (a) Curvedness and (b) Shape Index. Here, the MnHmA mol­ecule is used as the example.

The decom­position of the 2D fingerprint plots into the individual contact contributions demonstrates that only M⋯O and M⋯H contacts are present, as expected. However, the percentage of M⋯H contacts appears to relate to the surface globularity, in a way that the higher the M⋯H contact frequency, the further away from a sphere is the surface (smaller globularity). This pattern is seen in other series as well. For instance, in the series of metal acetyl­acetonates and, also, when evaluating the iron metal centre coordinated to acetyl­acetonate derivatives in com­parison to unaltered acetyl­acetonate (Pinto et al., 2020a,b).

3.3. Hirshfeld surfaces for C atoms

Given the sensitivity of atomic HS for M⋯H noncovalent inter­actions, now we evaluate the response of these surfaces for covalent bonds between atoms of the same nature, i.e. with no difference in electronegativity, which is expected to generate flat surfaces.

It has already been discussed in the literature that the curvature of the atomic Hirshfeld surfaces appears to be related to the charge transfer between atoms (Pendás et al., 2002). In this way, for ionic com­pounds, usually the cation will be associated with a convex surfaces, while the anion will present a concave surface, and a contact between two anions will present flat inter­atomic surfaces (Pendás et al., 2002). On the other hand, we have noticed that for non-ionic com­pounds, there is a relationship regarding the surface curvature and the atom electronegativity. In this way, the most electronegative atom will present a convex surface, while the least electronegative atom in the bond will present a concave surface (Fig. 5), but planar surfaces are still seen between atoms of the same nature, i.e. when there is no difference in electronegativity. However, when closely evaluating the curvature property values, one can see that not only the chemical nature of the atoms appears to influence these values, but also the nature of the electron-density distribution, in this case, indicated by the hybridization. We take as an example C atoms.

Figure 5 Example of the atomic Hirshfeld surface curvatures for atoms with different electronegativities (C—O) and atoms of the same nature (C—C). The property mapped over the surfaces is Shape Index.

Through a search of the CSD we found 17 high-quality structures undergoing a charge–density analysis and, initially, we evaluated the behaviour of the curvature properties on C—C bonds. In this manner, we evaluated the values for both curvature properties (S and C) when taken at the point where the inter­atomic vector passes through the surface between two covalently bonded C atoms. The attempt to correlate either S or C with topological parameters was not as successful in categorizing different C—C bonds or in finding trends as was the evaluation of both S and C in relation to the geometry of the bond. A plot of S versus C demonstrates that different geometries group together in specific regions of the plot (Fig. 6), according to the hybridization of both C atoms involved in the bond. Apart from this categorization, it is also possible to see that even though surfaces between atoms of the same nature roughly appear as flat, the curvature properties span a wide range of values, with S varying from 0.57 to 0.97 and C from −1.5 to −2.4, allowing the discernment of four regions: (1) high C and low S, (2) low C and low S, (3) low C and inter­mediate S, and (4) inter­mediate C and high S. Each of these regions are associated with a particular geometry, as demonstrated in Fig. 6. The first group is solely com­posed of C—C bonds from the quadratic acid, which com­prise a very distinct geometry, also presenting curved bonds (Lee et al., 1999; Şerb et al., 2011). The second group com­prises single, double and resonant bonds between two sp² C atoms. The third group involves single bonds between one sp² and one sp³ C atom, and the fourth group com­prises single bonds between two sp³ C atoms. It is inter­esting to note that the points associated with group (iii) are located in between groups (ii) and (iv), while its geometry is also a combination of the geometries related to groups (ii) and (iv). It is also inter­esting to note that bonds from group (i) (quadratic acid) are the most curved; this distinction is evidenced from the curvedness values. These results indicate once again the sensitivity of the Hirshfeld surfaces to small structural variations and also demonstrate that the curvature functions carry information on the chemical bonds.

Figure 6 Plot of S versus C showing the different geometries grouped together according to their S and C values. Atom X refers to any chemical element. Dashed bonds mean any bond type. See main text for complete description.

4. Conclusion

Throughout recent years, we have analysed different series of crystal structures in order to evaluate the sensitivity of atomic Hirshfeld surfaces to small variations in the environment of an atom. We have obtained various results that indicate that the surfaces carry information on the nature of the chemical bonds, related to both the strength and the geometry of the contacts. In this article, more specifically, we were able to combine the accuracy of H-atom parameters derived from the HAR procedure and the atomic HS for metal centres to obtain information related to M⋯H contacts, and we also demonstrate that geometry information can be retrieved from the curvature functions even for atomic surfaces that otherwise appear flat. In addition, we indicate the possibility of associating the HS properties Curvedness and Shape Index to distinguish between distinct types of C—C bonds. Given that HSs are easily and rapidly calculated using CrystalExplorer, we call attention to the amount and variety of information that can be extracted when mapping the curvature properties onto the surfaces.

5. Related literature

References in the supporting information: César et al. (2013); Hathwar & Guru Row (2011); Chua et al. (2017); Domagała et al. (2009); Parrish et al. (2006); Yearley et al. (2008); Yearley et al. (2007); Farrugia et al. (2008); Hathwar & Guru Row (2010); Pavan et al., (2013); Şerb et al. (2011); Zhurov & Pinkerton (2014); Sarkar et al. (2015); Krawczuk et al. (2015).

Supporting information

Computing details

Tetraaquabis(3-carboxypropionato)manganese(II) (MMn)

Crystal data

[Mn(C4H3O4)2(H2O)4]	Z = 1
Mr = 357.13	F(000) = 183.525
Triclinic, P1	Dx = 1.793 Mg m^−3
a = 5.3263 (2) Å	Mo Kα radiation, λ = 0.71073 Å
b = 7.3743 (4) Å	Cell parameters from 7273 reflections
c = 9.3688 (4) Å	θ = 3.0–36.9°
α = 109.863 (4)°	µ = 1.06 mm^−1
β = 104.606 (4)°	T = 298 K
γ = 93.344 (4)°	Prism, colourless
V = 330.69 (3) Å^3	0.63 × 0.30 × 0.17 mm

Data collection

Rigaku Xcalibur Gemini ultra diffractometer with an Atlas detector	3387 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	3080 reflections with I ≥ 2u(I)
Graphite monochromator	Rint = 0.035
Detector resolution: 10.4186 pixels mm^-1	θmax = 37.6°, θmin = 2.4°
ω scans	h = −9→9
Absorption correction: gaussian (CrysAlis PRO; Rigaku OD, 2019)	k = −12→12
Tmin = 0.628, Tmax = 0.846	l = −16→15
19553 measured reflections

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	Primary atom site location: dual
R[F^2 > 2σ(F^2)] = 0.022	All H-atom parameters refined
wR(F^2) = 0.044	w = 1/[σ^2(Fo^2) + (0.0112P)^2 + 0.0202P] where P = (Fo^2 + 2Fc^2)/3
S = 1.17	(Δ/σ)max = 0.001
3387 reflections	Δρmax = 0.32 e Å^−3
161 parameters	Δρmin = −0.37 e Å^−3
2 restraints

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

	x	y	z	Uiso*/Ueq
Mn1	0.5	0.5	0.0	0.02354 (4)
O6	0.17539 (10)	0.63644 (8)	−0.09901 (6)	0.02884 (9)
H6A	0.176 (2)	0.7625 (17)	−0.0248 (13)	0.052 (3)
H6B	−0.006 (2)	0.5686 (17)	−0.1351 (14)	0.044 (3)
O5	0.25361 (11)	0.22490 (8)	−0.08093 (6)	0.03389 (11)
H5B	0.273 (2)	0.1430 (17)	−0.0188 (14)	0.052 (3)
H5A	0.152 (3)	0.1497 (18)	−0.1817 (14)	0.068 (4)
O1	0.35076 (9)	0.55933 (7)	0.20922 (5)	0.03005 (10)
O2	0.69527 (10)	0.76593 (9)	0.38470 (6)	0.04108 (13)
O4	0.70832 (12)	0.97260 (8)	0.87417 (5)	0.04048 (13)
O3	0.83930 (11)	0.95375 (9)	0.66590 (6)	0.04406 (14)
C4	0.67058 (13)	0.90784 (9)	0.73002 (7)	0.02680 (11)
C1	0.46970 (11)	0.66972 (9)	0.34814 (6)	0.02366 (10)
C2	0.33347 (12)	0.68135 (10)	0.47090 (7)	0.02894 (12)
H2	0.1404 (18)	0.5951 (17)	0.4220 (12)	0.061 (3)
C3	0.41848 (13)	0.77718 (10)	0.62846 (7)	0.02911 (12)
H3	0.286 (2)	0.7594 (16)	0.6947 (11)	0.057 (3)
H3A	0.777 (3)	0.871 (2)	0.5321 (17)	0.057 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mn1	0.02150 (6)	0.02687 (7)	0.02184 (6)	0.00024 (4)	0.00755 (4)	0.00811 (5)
O6	0.0252 (2)	0.0314 (2)	0.0272 (2)	0.00409 (18)	0.00701 (17)	0.00791 (18)
H6A	0.054 (8)	0.052 (8)	0.040 (7)	0.014 (6)	0.015 (6)	0.003 (6)
H6B	0.021 (5)	0.049 (7)	0.061 (8)	−0.003 (5)	0.011 (5)	0.019 (6)
O5	0.0360 (3)	0.0329 (3)	0.0245 (2)	−0.0100 (2)	0.00188 (19)	0.0080 (2)
H5B	0.063 (9)	0.044 (7)	0.047 (8)	0.002 (6)	0.011 (7)	0.018 (6)
H5A	0.083 (10)	0.061 (9)	0.032 (7)	0.005 (7)	0.004 (7)	−0.005 (6)
O1	0.0278 (2)	0.0372 (2)	0.01795 (17)	−0.00238 (18)	0.00689 (15)	0.00242 (16)
O2	0.0306 (2)	0.0596 (3)	0.0221 (2)	−0.0135 (2)	0.01017 (18)	0.0031 (2)
O4	0.0584 (3)	0.0364 (3)	0.01792 (19)	−0.0067 (2)	0.0065 (2)	0.00479 (18)
O3	0.0353 (3)	0.0587 (4)	0.0223 (2)	−0.0181 (2)	0.00400 (19)	0.0025 (2)
C4	0.0325 (3)	0.0264 (3)	0.0172 (2)	0.0005 (2)	0.0047 (2)	0.00519 (19)
C1	0.0221 (2)	0.0287 (3)	0.0170 (2)	0.0008 (2)	0.00621 (17)	0.00464 (19)
C2	0.0236 (2)	0.0374 (3)	0.0201 (2)	−0.0033 (2)	0.0083 (2)	0.0034 (2)
H2	0.029 (5)	0.092 (9)	0.048 (7)	−0.018 (6)	0.016 (5)	0.010 (6)
C3	0.0292 (3)	0.0350 (3)	0.0198 (2)	−0.0010 (2)	0.0106 (2)	0.0044 (2)
H3	0.056 (7)	0.075 (8)	0.034 (6)	−0.009 (6)	0.025 (5)	0.004 (5)
H3A	0.051 (9)	0.078 (11)	0.025 (11)	−0.020 (8)	0.009 (8)	0.002 (9)

Geometric parameters (Å, º)

Mn1—O6^i	2.2114 (5)	O2—C1	1.2618 (8)
Mn1—O6	2.2114 (5)	O2—H3A	1.276 (14)
Mn1—O5	2.1343 (5)	O4—C4	1.2272 (7)
Mn1—O5^i	2.1343 (5)	O3—C4	1.2877 (8)
Mn1—O1	2.2156 (4)	O3—H3A	1.140 (14)
Mn1—O1^i	2.2156 (4)	C4—C3	1.4894 (9)
O6—H6A	0.952 (11)	C1—C2	1.4892 (8)
O6—H6B	0.981 (10)	C2—H2	1.077 (9)
O5—H5B	0.964 (12)	C2—C3	1.3417 (8)
O5—H5A	0.919 (11)	C3—H3	1.081 (9)
O1—C1	1.2498 (7)
O6^i—Mn1—O6	180.0	H5A—O5—Mn1	129.1 (9)
O5^i—Mn1—O6	87.40 (2)	H5A—O5—H5B	107.5 (10)
O5—Mn1—O6	92.60 (2)	C1—O1—Mn1	126.25 (4)
O5—Mn1—O6^i	87.40 (2)	H3A—O2—C1	111.6 (5)
O5^i—Mn1—O6^i	92.60 (2)	H3A—O3—C4	111.5 (6)
O5^i—Mn1—O5	180.0	O3—C4—O4	121.75 (6)
O1^i—Mn1—O6^i	87.384 (18)	C3—C4—O4	118.22 (6)
O1—Mn1—O6	87.384 (18)	C3—C4—O3	120.01 (5)
O1^i—Mn1—O6	92.616 (18)	O2—C1—O1	122.34 (5)
O1—Mn1—O6^i	92.616 (18)	C2—C1—O1	116.72 (5)
O1—Mn1—O5^i	96.915 (19)	C2—C1—O2	120.94 (5)
O1^i—Mn1—O5	96.915 (19)	H2—C2—C1	112.7 (5)
O1^i—Mn1—O5^i	83.085 (19)	C3—C2—C1	129.73 (6)
O1—Mn1—O5	83.085 (19)	C3—C2—H2	117.6 (5)
O1^i—Mn1—O1	180.0	C2—C3—C4	130.30 (6)
H6A—O6—Mn1	110.5 (7)	H3—C3—C4	113.3 (5)
H6B—O6—Mn1	119.6 (7)	H3—C3—C2	116.4 (5)
H6B—O6—H6A	105.9 (10)	O3—H3A—O2	174.6 (13)
H5B—O5—Mn1	121.3 (7)
Mn1—O1—C1—O2	1.42 (6)	O2—C1—C2—C3	−3.60 (8)
Mn1^i—O1—C1—O2	1.42 (6)	O4—C4—C3—C2	−176.81 (7)
Mn1^i—O1—C1—C2	−177.87 (5)	O3—C4—C3—C2	4.83 (9)
Mn1—O1—C1—C2	−177.87 (5)	C4—C3—C2—C1	2.59 (10)
O1—C1—C2—C3	175.70 (6)

Symmetry code: (i) −x+1, −y+1, −z.

Tetraaquabis(3-carboxypropionato)cobalt(II) (MCo)

Crystal data

[Co(C4H3O4)2(H2O)4]	Z = 1
Mr = 361.13	F(000) = 185.540
Triclinic, P1	Dx = 1.875 Mg m^−3
a = 5.2222 (2) Å	Mo Kα radiation, λ = 0.71073 Å
b = 7.3322 (2) Å	Cell parameters from 10326 reflections
c = 9.2293 (3) Å	θ = 2.4–37.4°
α = 109.125 (3)°	µ = 1.41 mm^−1
β = 104.376 (3)°	T = 298 K
γ = 93.224 (3)°	Prism, light pink
V = 319.76 (2) Å^3	0.60 × 0.48 × 0.38 mm

Data collection

Rigaku Xcalibur Gemini ultra diffractometer with an Atlas detector	3273 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	3147 reflections with I ≥ 2u(I)
Graphite monochromator	Rint = 0.030
Detector resolution: 10.4186 pixels mm^-1	θmax = 37.8°, θmin = 2.4°
ω scans	h = −8→8
Absorption correction: gaussian (CrysAlis PRO; Rigaku OD, 2019)	k = −12→12
Tmin = 0.657, Tmax = 0.739	l = −15→15
15610 measured reflections

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	Primary atom site location: dual
R[F^2 > 2σ(F^2)] = 0.018	All H-atom parameters refined
wR(F^2) = 0.039	w = 1/[σ^2(Fo^2) + (0.0146P)^2 + 0.0113P] where P = (Fo^2 + 2Fc^2)/3
S = 1.13	(Δ/σ)max = −0.001
3273 reflections	Δρmax = 0.38 e Å^−3
161 parameters	Δρmin = −0.36 e Å^−3
2 restraints

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

	x	y	z	Uiso*/Ueq
Co1	0.5	0.5	1.0	0.01872 (3)
O6	0.18182 (9)	0.63246 (7)	0.90095 (5)	0.02493 (8)
H6A	0.191 (2)	0.7614 (16)	0.9754 (14)	0.047 (3)
H6B	0.002 (2)	0.5669 (16)	0.8714 (15)	0.046 (3)
O5	0.25295 (9)	0.23973 (7)	0.92312 (6)	0.02752 (8)
H5B	0.279 (2)	0.1533 (16)	0.9816 (14)	0.045 (3)
H5A	0.167 (3)	0.1661 (18)	0.8180 (14)	0.062 (4)
O1	0.64060 (8)	0.43943 (6)	0.79483 (5)	0.02507 (8)
O4	0.30140 (12)	0.02489 (7)	0.12471 (5)	0.03590 (11)
O2	0.29639 (10)	0.22836 (8)	0.61724 (6)	0.03702 (12)
O3	0.15743 (11)	0.04311 (9)	0.33283 (6)	0.04002 (13)
C1	0.52292 (10)	0.32848 (8)	0.65485 (6)	0.02075 (9)
C4	0.33272 (12)	0.09124 (8)	0.26956 (6)	0.02401 (9)
C2	0.66435 (12)	0.32158 (9)	0.53166 (7)	0.02567 (10)
H2	0.859 (2)	0.4124 (17)	0.5832 (12)	0.056 (3)
C3	0.58347 (12)	0.22601 (9)	0.37300 (7)	0.02619 (10)
H3	0.718 (2)	0.2460 (17)	0.3071 (11)	0.053 (3)
H3A	0.214 (2)	0.124 (2)	0.4628 (18)	0.054 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Co1	0.01777 (5)	0.02146 (5)	0.01611 (5)	0.00010 (3)	0.00582 (3)	0.00526 (3)
O6	0.02181 (18)	0.02780 (19)	0.02438 (18)	0.00363 (15)	0.00697 (15)	0.00787 (16)
H6A	0.057 (8)	0.040 (7)	0.049 (8)	0.021 (6)	0.026 (6)	0.010 (6)
H6B	0.032 (6)	0.038 (6)	0.065 (9)	−0.004 (5)	0.013 (6)	0.015 (6)
O5	0.0302 (2)	0.02609 (19)	0.02065 (18)	−0.00658 (16)	0.00394 (15)	0.00521 (16)
H5B	0.050 (8)	0.034 (6)	0.051 (8)	0.003 (5)	0.008 (6)	0.021 (6)
H5A	0.068 (9)	0.061 (8)	0.032 (7)	−0.010 (7)	0.004 (6)	−0.005 (6)
O1	0.02367 (18)	0.03064 (19)	0.01652 (16)	−0.00165 (15)	0.00717 (13)	0.00248 (14)
O4	0.0532 (3)	0.0319 (2)	0.01658 (17)	−0.0049 (2)	0.00861 (18)	0.00357 (16)
O2	0.0286 (2)	0.0533 (3)	0.01973 (19)	−0.0137 (2)	0.00983 (16)	0.00168 (19)
O3	0.0332 (2)	0.0536 (3)	0.0198 (2)	−0.0163 (2)	0.00553 (17)	0.0007 (2)
C1	0.0199 (2)	0.0250 (2)	0.01552 (18)	0.00071 (17)	0.00634 (16)	0.00415 (16)
C4	0.0297 (3)	0.0236 (2)	0.0161 (2)	0.00116 (18)	0.00568 (18)	0.00460 (17)
C2	0.0220 (2)	0.0327 (3)	0.0185 (2)	−0.00298 (19)	0.00843 (18)	0.00319 (19)
H2	0.035 (6)	0.080 (9)	0.041 (6)	−0.017 (6)	0.010 (5)	0.010 (6)
C3	0.0271 (3)	0.0311 (3)	0.0186 (2)	−0.0008 (2)	0.01076 (19)	0.00422 (19)
H3	0.048 (6)	0.077 (8)	0.032 (6)	−0.005 (6)	0.025 (5)	0.009 (5)
H3A	0.035 (8)	0.064 (10)	0.040 (11)	−0.026 (7)	0.017 (7)	−0.008 (8)

Geometric parameters (Å, º)

Co1—O6^i	2.1328 (4)	O4—C4	1.2276 (7)
Co1—O6	2.1328 (4)	O2—C1	1.2610 (7)
Co1—O5	2.0472 (4)	O2—H3A	1.322 (15)
Co1—O5^i	2.0472 (4)	O3—C4	1.2913 (7)
Co1—O1	2.1208 (4)	O3—H3A	1.102 (15)
Co1—O1^i	2.1208 (4)	C1—C2	1.4914 (7)
O6—H6A	0.959 (11)	C4—C3	1.4893 (8)
O6—H6B	0.962 (10)	C2—H2	1.085 (10)
O5—H5B	0.953 (11)	C2—C3	1.3420 (8)
O5—H5A	0.921 (11)	C3—H3	1.069 (9)
O1—C1	1.2528 (6)
O6^i—Co1—O6	180.0	H5A—O5—Co1	125.3 (8)
O5^i—Co1—O6	88.684 (19)	H5A—O5—H5B	107.8 (11)
O5—Co1—O6	91.316 (19)	C1—O1—Co1^i	127.80 (4)
O5—Co1—O6^i	88.684 (19)	H3A—O2—C1	111.5 (5)
O5^i—Co1—O6^i	91.316 (19)	H3A—O3—C4	111.0 (6)
O5^i—Co1—O5	180.0	O2—C1—O1	122.88 (5)
O1—Co1—O6^i	88.139 (17)	C2—C1—O1	116.28 (5)
O1^i—Co1—O6	88.139 (17)	C2—C1—O2	120.84 (5)
O1—Co1—O6	91.861 (17)	O3—C4—O4	121.54 (6)
O1^i—Co1—O6^i	91.861 (17)	C3—C4—O4	118.34 (5)
O1^i—Co1—O5^i	96.267 (17)	C3—C4—O3	120.10 (5)
O1—Co1—O5	96.267 (17)	H2—C2—C1	112.0 (5)
O1—Co1—O5^i	83.733 (17)	C3—C2—C1	129.77 (5)
O1^i—Co1—O5	83.733 (17)	C3—C2—H2	118.2 (5)
O1—Co1—O1^i	180.0	C2—C3—C4	130.53 (5)
H6A—O6—Co1	108.6 (8)	H3—C3—C4	112.8 (5)
H6B—O6—Co1	118.2 (7)	H3—C3—C2	116.7 (5)
H6B—O6—H6A	107.7 (10)	O3—H3A—O2	175.9 (11)
H5B—O5—Co1	121.1 (7)
Co1^i—O1—C1—O2	−2.45 (6)	O4—C4—C3—C2	178.12 (6)
Co1—O1—C1—O2	−2.45 (6)	O2—C1—C2—C3	3.25 (8)
Co1—O1—C1—C2	176.88 (5)	O3—C4—C3—C2	−3.49 (8)
Co1^i—O1—C1—C2	176.88 (5)	C1—C2—C3—C4	−2.45 (9)
O1—C1—C2—C3	−176.09 (6)

Symmetry code: (i) −x+1, −y+1, −z+2.

Tetraaquabis(3-carboxypropionato)nickel(II) (MNi)

Crystal data

[Ni(C4H3O4)2(H2O)4]	Z = 1
Mr = 360.89	F(000) = 186.545
Triclinic, P1	Dx = 1.901 Mg m^−3
a = 5.1780 (2) Å	Mo Kα radiation, λ = 0.71073 Å
b = 7.3254 (2) Å	Cell parameters from 6529 reflections
c = 9.1449 (4) Å	θ = 2.5–37.4°
α = 108.423 (3)°	µ = 1.61 mm^−1
β = 104.583 (3)°	T = 298 K
γ = 92.929 (3)°	Prism, light blue
V = 315.25 (2) Å^3	0.59 × 0.35 × 0.13 mm

Data collection

Rigaku Xcalibur Gemini ultra diffractometer with an Atlas detector	3240 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	3136 reflections with I ≥ 2u(I)
Graphite monochromator	Rint = 0.027
Detector resolution: 10.4186 pixels mm^-1	θmax = 37.6°, θmin = 2.5°
ω scans	h = −8→8
Absorption correction: gaussian (CrysAlis PRO; Rigaku OD, 2019)	k = −12→12
Tmin = 0.650, Tmax = 0.903	l = −15→15
12425 measured reflections

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	Primary atom site location: dual
R[F^2 > 2σ(F^2)] = 0.019	All H-atom parameters refined
wR(F^2) = 0.044	w = 1/[σ^2(Fo^2) + (0.0175P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.16	(Δ/σ)max = 0.0004
3240 reflections	Δρmax = 0.34 e Å^−3
160 parameters	Δρmin = −0.42 e Å^−3
2 restraints

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

	x	y	z	Uiso*/Ueq
Ni1	0.5	0.5	1.0	0.01662 (3)
O6	0.18605 (10)	0.63275 (7)	0.90276 (6)	0.02259 (8)
H6A	0.192 (3)	0.7620 (19)	0.9783 (16)	0.040 (3)
H6B	0.007 (2)	0.5657 (19)	0.8741 (18)	0.044 (3)
O5	0.24723 (10)	0.24694 (7)	0.92421 (6)	0.02416 (9)
H5B	0.279 (3)	0.1544 (17)	0.9798 (17)	0.044 (3)
H5A	0.180 (3)	0.172 (2)	0.8174 (16)	0.061 (4)
O1	0.64002 (10)	0.44066 (7)	0.79812 (5)	0.02274 (8)
O4	0.31124 (14)	0.02375 (8)	0.12619 (6)	0.03435 (12)
O2	0.29716 (11)	0.22763 (9)	0.62039 (7)	0.03484 (13)
O3	0.15856 (13)	0.04470 (10)	0.33378 (7)	0.03864 (14)
C1	0.52286 (12)	0.32946 (8)	0.65788 (7)	0.01913 (9)
C4	0.33791 (14)	0.09214 (9)	0.27101 (8)	0.02319 (11)
C2	0.66578 (13)	0.32398 (10)	0.53432 (8)	0.02408 (11)
H2	0.860 (2)	0.4182 (18)	0.5854 (16)	0.053 (3)
C3	0.58724 (14)	0.22845 (10)	0.37518 (8)	0.02506 (12)
H3	0.722 (3)	0.2522 (18)	0.3082 (15)	0.056 (4)
H3A	0.210 (3)	0.128 (2)	0.461 (2)	0.048 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ni1	0.01652 (5)	0.01858 (5)	0.01368 (5)	0.00004 (3)	0.00507 (3)	0.00376 (3)
O6	0.0210 (2)	0.0258 (2)	0.0208 (2)	0.00381 (16)	0.00636 (17)	0.00738 (17)
H6A	0.040 (8)	0.044 (8)	0.036 (8)	0.018 (6)	0.013 (6)	0.008 (6)
H6B	0.023 (6)	0.048 (8)	0.066 (11)	0.002 (6)	0.012 (7)	0.027 (7)
O5	0.0261 (2)	0.02238 (19)	0.0193 (2)	−0.00476 (17)	0.00487 (17)	0.00310 (16)
H5B	0.054 (9)	0.029 (7)	0.042 (8)	0.008 (6)	−0.003 (7)	0.013 (6)
H5A	0.078 (11)	0.053 (8)	0.026 (7)	0.010 (8)	0.003 (8)	−0.011 (6)
O1	0.0219 (2)	0.0277 (2)	0.01472 (18)	−0.00164 (16)	0.00640 (15)	0.00175 (15)
O4	0.0517 (3)	0.0306 (2)	0.0156 (2)	−0.0035 (2)	0.0091 (2)	0.00264 (17)
O2	0.0283 (2)	0.0494 (3)	0.0177 (2)	−0.0139 (2)	0.00911 (19)	0.0000 (2)
O3	0.0334 (3)	0.0510 (3)	0.0187 (2)	−0.0154 (2)	0.0059 (2)	−0.0010 (2)
C1	0.0193 (2)	0.0225 (2)	0.0140 (2)	0.00068 (18)	0.00593 (18)	0.00335 (18)
C4	0.0302 (3)	0.0223 (2)	0.0148 (2)	0.0022 (2)	0.0058 (2)	0.00380 (19)
C2	0.0220 (3)	0.0303 (3)	0.0168 (2)	−0.0025 (2)	0.0081 (2)	0.0027 (2)
H2	0.039 (7)	0.064 (9)	0.054 (9)	−0.011 (6)	0.022 (6)	0.013 (7)
C3	0.0276 (3)	0.0293 (3)	0.0171 (3)	−0.0007 (2)	0.0106 (2)	0.0036 (2)
H3	0.059 (8)	0.059 (8)	0.050 (8)	−0.005 (7)	0.036 (7)	0.002 (7)
H3A	0.049 (10)	0.053 (10)	0.035 (12)	−0.005 (8)	0.024 (9)	−0.003 (9)

Geometric parameters (Å, º)

Ni1—O6^i	2.0879 (5)	O4—C4	1.2270 (8)
Ni1—O6	2.0879 (5)	O2—C1	1.2599 (8)
Ni1—O5	2.0281 (5)	O2—H3A	1.351 (18)
Ni1—O5^i	2.0281 (5)	O3—C4	1.2939 (9)
Ni1—O1	2.0789 (5)	O3—H3A	1.083 (17)
Ni1—O1^i	2.0789 (5)	C1—C2	1.4905 (8)
O6—H6A	0.974 (12)	C4—C3	1.4897 (10)
O6—H6B	0.960 (12)	C2—H2	1.094 (11)
O5—H5B	0.965 (12)	C2—C3	1.3424 (9)
O5—H5A	0.921 (12)	C3—H3	1.079 (12)
O1—C1	1.2545 (7)
O6^i—Ni1—O6	180.0	H5A—O5—Ni1	122.7 (10)
O5^i—Ni1—O6	89.56 (2)	H5A—O5—H5B	104.5 (12)
O5—Ni1—O6	90.44 (2)	C1—O1—Ni1^i	127.83 (4)
O5—Ni1—O6^i	89.56 (2)	H3A—O2—C1	111.5 (6)
O5^i—Ni1—O6^i	90.44 (2)	H3A—O3—C4	110.7 (7)
O5^i—Ni1—O5	180.0	O2—C1—O1	123.15 (6)
O1—Ni1—O6^i	87.625 (19)	C2—C1—O1	116.07 (5)
O1^i—Ni1—O6	87.625 (19)	C2—C1—O2	120.78 (6)
O1—Ni1—O6	92.375 (19)	O3—C4—O4	121.45 (7)
O1^i—Ni1—O6^i	92.375 (19)	C3—C4—O4	118.34 (6)
O1^i—Ni1—O5^i	96.572 (19)	C3—C4—O3	120.19 (6)
O1—Ni1—O5	96.572 (19)	H2—C2—C1	112.3 (6)
O1—Ni1—O5^i	83.428 (19)	C3—C2—C1	129.93 (6)
O1^i—Ni1—O5	83.428 (19)	C3—C2—H2	117.8 (6)
O1—Ni1—O1^i	180.0	C2—C3—C4	130.65 (6)
H6A—O6—Ni1	109.5 (8)	H3—C3—C4	112.6 (7)
H6B—O6—Ni1	116.6 (7)	H3—C3—C2	116.7 (7)
H6B—O6—H6A	107.4 (11)	O3—H3A—O2	174.7 (14)
H5B—O5—Ni1	120.8 (8)
Ni1^i—O1—C1—O2	−3.12 (6)	O4—C4—C3—C2	179.35 (7)
Ni1—O1—C1—O2	−3.12 (6)	O2—C1—C2—C3	3.36 (8)
Ni1—O1—C1—C2	176.55 (5)	O3—C4—C3—C2	−2.26 (9)
Ni1^i—O1—C1—C2	176.55 (5)	C1—C2—C3—C4	−2.39 (10)
O1—C1—C2—C3	−176.32 (6)

Symmetry code: (i) −x+1, −y+1, −z+2.

Tetraaquabis(3-carboxypropionato)zinc(II) (MZn)

Crystal data

[Zn(C4H3O4)2(H2O)4]	Z = 1
Mr = 367.59	F(000) = 188.514
Triclinic, P1	Dx = 1.906 Mg m^−3
a = 5.2307 (2) Å	Mo Kα radiation, λ = 0.71073 Å
b = 7.3259 (3) Å	Cell parameters from 9149 reflections
c = 9.2246 (3) Å	θ = 2.5–37.5°
α = 108.753 (3)°	µ = 1.98 mm^−1
β = 104.626 (3)°	T = 298 K
γ = 93.202 (3)°	Prism, colourless
V = 320.23 (2) Å^3	0.8 × 0.36 × 0.29 mm

Data collection

Rigaku Xcalibur Gemini ultra diffractometer with an Atlas detector	3302 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	3187 reflections with I ≥ 2u(I)
Graphite monochromator	Rint = 0.034
Detector resolution: 10.4186 pixels mm^-1	θmax = 37.7°, θmin = 2.4°
ω scans	h = −8→8
Absorption correction: gaussian (CrysAlis PRO; Rigaku OD, 2019)	k = −12→12
Tmin = 0.394, Tmax = 0.706	l = −15→15
17325 measured reflections

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	Primary atom site location: dual
R[F^2 > 2σ(F^2)] = 0.019	All H-atom parameters refined
wR(F^2) = 0.045	w = 1/[σ^2(Fo^2) + (0.0196P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.22	(Δ/σ)max = −0.0004
3302 reflections	Δρmax = 0.45 e Å^−3
161 parameters	Δρmin = −0.36 e Å^−3
0 restraints

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

	x	y	z	Uiso*/Ueq
Zn1	0.5	0.5	0.0	0.02193 (4)
O6	0.18251 (9)	0.63397 (7)	−0.09847 (6)	0.02547 (8)
H6A	0.191 (3)	0.7619 (18)	−0.0165 (17)	0.049 (4)
H6B	0.001 (2)	0.5620 (18)	−0.1302 (17)	0.044 (3)
O5	0.74923 (10)	0.75863 (7)	0.07715 (6)	0.02844 (9)
H5A	0.823 (3)	0.8336 (19)	0.1831 (14)	0.062 (4)
H5B	0.728 (3)	0.8482 (17)	0.0199 (17)	0.051 (4)
O1	0.35599 (10)	0.55970 (7)	0.20517 (5)	0.02616 (9)
O3	0.84172 (12)	0.95479 (10)	0.66665 (7)	0.04056 (14)
O2	0.70036 (11)	0.77103 (9)	0.38193 (6)	0.03762 (13)
O4	0.69638 (14)	0.97497 (8)	0.87429 (6)	0.03701 (12)
C1	0.47400 (11)	0.67068 (8)	0.34469 (7)	0.02121 (9)
C2	0.33349 (13)	0.67803 (10)	0.46803 (8)	0.02628 (11)
H2	0.134 (2)	0.5830 (19)	0.4135 (14)	0.053 (3)
C4	0.66585 (13)	0.90784 (9)	0.72976 (7)	0.02470 (11)
C3	0.41470 (13)	0.77346 (9)	0.62642 (8)	0.02670 (11)
H3	0.276 (3)	0.7561 (19)	0.6945 (14)	0.059 (4)
H3A	0.787 (3)	0.874 (2)	0.537 (2)	0.041 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Zn1	0.02028 (5)	0.02397 (6)	0.02151 (6)	0.00034 (3)	0.00717 (4)	0.00743 (4)
O6	0.02276 (19)	0.0283 (2)	0.0247 (2)	0.00369 (16)	0.00706 (17)	0.00817 (17)
H6A	0.055 (9)	0.034 (7)	0.052 (9)	0.017 (6)	0.012 (7)	0.005 (6)
H6B	0.032 (7)	0.038 (7)	0.060 (10)	0.001 (6)	0.023 (7)	0.008 (7)
O5	0.0306 (2)	0.0270 (2)	0.0216 (2)	−0.00643 (17)	0.00401 (18)	0.00475 (17)
H5A	0.103 (13)	0.038 (7)	0.023 (7)	0.002 (8)	0.010 (7)	−0.012 (5)
H5B	0.062 (9)	0.023 (6)	0.053 (9)	−0.001 (6)	−0.005 (7)	0.011 (6)
O1	0.02479 (19)	0.0316 (2)	0.01728 (19)	−0.00177 (16)	0.00703 (16)	0.00237 (15)
O3	0.0339 (3)	0.0537 (3)	0.0205 (2)	−0.0159 (2)	0.0053 (2)	0.0004 (2)
O2	0.0295 (2)	0.0535 (3)	0.0202 (2)	−0.0138 (2)	0.00978 (19)	0.0013 (2)
O4	0.0548 (3)	0.0331 (2)	0.0170 (2)	−0.0049 (2)	0.0089 (2)	0.00367 (17)
C1	0.0206 (2)	0.0251 (2)	0.0161 (2)	0.00071 (18)	0.00613 (18)	0.00444 (17)
C2	0.0226 (2)	0.0333 (3)	0.0192 (3)	−0.0025 (2)	0.0084 (2)	0.0034 (2)
H2	0.038 (7)	0.071 (9)	0.042 (7)	−0.012 (6)	0.022 (6)	0.003 (6)
C4	0.0314 (3)	0.0236 (2)	0.0163 (2)	0.0015 (2)	0.0057 (2)	0.00458 (18)
C3	0.0280 (3)	0.0311 (3)	0.0193 (3)	−0.0006 (2)	0.0107 (2)	0.0043 (2)
H3	0.069 (9)	0.073 (9)	0.033 (7)	−0.005 (7)	0.033 (7)	0.005 (6)
H3A	0.039 (8)	0.037 (8)	0.037 (11)	−0.011 (7)	0.010 (8)	0.001 (8)

Geometric parameters (Å, º)

Zn1—O6^i	2.1307 (5)	O3—C4	1.2913 (9)
Zn1—O6	2.1307 (5)	O3—H3A	1.103 (16)
Zn1—O5	2.0456 (5)	O2—C1	1.2630 (8)
Zn1—O5^i	2.0456 (5)	O2—H3A	1.327 (16)
Zn1—O1	2.1366 (5)	O4—C4	1.2277 (8)
Zn1—O1^i	2.1366 (5)	C1—C2	1.4916 (9)
O6—H6A	0.986 (12)	C2—H2	1.120 (11)
O6—H6B	0.983 (12)	C2—C3	1.3419 (9)
O5—H5A	0.920 (11)	C4—C3	1.4911 (9)
O5—H5B	0.961 (13)	C3—H3	1.098 (12)
O1—C1	1.2524 (7)
O6^i—Zn1—O6	180.0	H5B—O5—Zn1^i	122.4 (8)
O5^i—Zn1—O6	91.03 (2)	H5B—O5—H5A	106.0 (11)
O5—Zn1—O6	88.97 (2)	C1—O1—Zn1	127.25 (4)
O5—Zn1—O6^i	91.03 (2)	H3A—O3—C4	111.6 (7)
O5^i—Zn1—O6^i	88.97 (2)	H3A—O2—C1	112.0 (6)
O5^i—Zn1—O5	180.0	O2—C1—O1	122.90 (6)
O1^i—Zn1—O6^i	87.552 (19)	C2—C1—O1	116.30 (5)
O1—Zn1—O6	87.552 (19)	C2—C1—O2	120.79 (6)
O1^i—Zn1—O6	92.448 (19)	H2—C2—C1	111.1 (6)
O1—Zn1—O6^i	92.448 (19)	C3—C2—C1	129.88 (6)
O1—Zn1—O5^i	83.44 (2)	C3—C2—H2	119.0 (6)
O1^i—Zn1—O5	83.44 (2)	O4—C4—O3	121.58 (6)
O1^i—Zn1—O5^i	96.56 (2)	C3—C4—O3	120.14 (6)
O1—Zn1—O5	96.56 (2)	C3—C4—O4	118.26 (6)
O1^i—Zn1—O1	180.0	C4—C3—C2	130.55 (6)
H6A—O6—Zn1	106.7 (8)	H3—C3—C2	117.1 (7)
H6B—O6—Zn1	116.2 (8)	H3—C3—C4	112.4 (7)
H6B—O6—H6A	108.5 (11)	O2—H3A—O3	174.8 (12)
H5A—O5—Zn1^i	123.8 (10)
Zn1—O1—C1—O2	2.60 (6)	O3—C4—C3—C2	3.12 (9)
Zn1^i—O1—C1—O2	2.60 (6)	O2—C1—C2—C3	−3.48 (8)
Zn1^i—O1—C1—C2	−176.87 (5)	O4—C4—C3—C2	−178.57 (6)
Zn1—O1—C1—C2	−176.87 (5)	C1—C2—C3—C4	2.38 (10)
O1—C1—C2—C3	176.00 (6)

Symmetry code: (i) −x+1, −y+1, −z.