Understanding Cu(I) local environments in MOFs via^63/65Cu NMR spectroscopy

Abstract

The field of metal–organic frameworks (MOFs) includes a vast number of hybrid organic and inorganic porous materials with wide-ranging applications. In particular, the Cu(I) ion exhibits rich coordination chemistry in MOFs and can exist in two-, three-, and four-coordinate environments, which gives rise to many structural motifs and potential applications. Direct characterization of the structurally and chemically important Cu(I) local environments is essential for understanding the sources of specific MOF properties. For the first time, ^63/65Cu solid-state NMR has been used to investigate a variety of Cu(I) sites and local coordination geometries in Cu MOFs. This approach is a sensitive probe of the local Cu environment, particularly when combined with density functional theory calculations. A wide range of structurally-dependent ^63/65Cu NMR parameters have been observed, including ⁶⁵Cu quadrupolar coupling constants ranging from 18.8 to 74.8 MHz. Using the data from this and prior studies, a correlation between Cu quadrupolar coupling constants, Cu coordination number, and local Cu coordination geometry has been established. Links between DFT-calculated and experimental Cu NMR parameters are also presented. Several case studies illustrate the feasibility of ^63/65Cu NMR for investigating and resolving inequivalent Cu sites, monitoring MOF phase changes, interrogating the Cu oxidation number, and characterizing the product of a MOF chemical reaction involving Cu(II) reduction to Cu(I). A convenient avenue to acquire accurate ⁶⁵Cu NMR spectra and NMR parameters from Cu(I) MOFs at a widely accessible magnetic field of 9.4 T is described, with a demonstrated practical application for tracking Cu(I) coordination evolution during MOF anion exchange. This work showcases the power of ^63/65Cu solid-state NMR spectroscopy and DFT calculations for molecular-level characterization of Cu(I) centers in MOFs, along with the potential of this protocol for investigating a wide variety of MOF structural changes and processes important for practical applications. This approach has broad applications for examining Cu(I) centers in other weight-dilute systems.

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Introduction

Metal–organic frameworks (MOFs) are porous crystalline materials composed of organic and inorganic components, arranged in a motif that features metal cations or metal–inorganic clusters connected by organic linkers.^1,2 Due to their porosity, structural diversity, and functionality, these materials have shown promise for diverse applications in fields such as gas storage, gas separation, catalysis, sensing and drug delivery.^3–6 The metal-centered entities are typically referred to as secondary building units (SBUs); the SBU composition and coordination can be tailored to achieve desired MOF topologies and properties.^7,8

Copper(I) is a versatile metal that can adopt a multitude of coordination states; Cu(I) applications range from serving as active sites in catalysts to playing an integral role in proteins and biology. From a materials perspective, Cu(I) has the ability to form a wide variety of cluster-based compounds and MOFs.⁹ The copper(I) halide clusters Cu_xX_y (X = Cl, Br, I) exhibit unique luminescent behaviors.⁹ Cu(I)-based MOFs have demonstrated catalytic activity in addition to luminescent properties.^10–12 Cu(I) centers in MOFs can adopt three distinct local coordination geometries: two-coordinate linear, three-coordinate trigonal planar, and four-coordinate tetrahedral. Cu(I) can bind to a variety of different donor atoms on MOF linkers, including nitrogen, sulfur, phosphorus, and oxygen, and can form diverse one-, two-, and three-dimensional frameworks.^10,12–18

Structural characterization is critical to understanding the molecular-level origins of unique MOF properties. The coordination state, geometry, local environment, and position of Cu(I) sites in the SBU and MOF influence the properties and applications of the resulting material. Cu(I) is generally regarded as a “spectroscopically silent” target that cannot be probed through traditional routes such as EPR and UV-vis spectroscopies, which makes characterization very challenging. Solid-state NMR spectroscopy can provide detailed information regarding local atomic environments in MOFs,^19–26 including in cases of low sample crystallinity,^27,28 short-range disorder,^29,30 and framework defects.^31–33 Many of the metal centers incorporated into MOFs are potential targets for NMR experiments.^20,3463/65Cu solid-state NMR is one of the few spectroscopic techniques that can directly probe Cu(I) metal centers, and has previously been used to extract rich short-range data from simpler Cu(I) compounds.^35–5063/65Cu NMR is subject to the anisotropic quadrupolar and chemical shift (CS) NMR interactions, and is thus a useful tool for understanding the three-dimensional local geometry and bonding around Cu(I) sites.^{35,36,51–5663/65}Cu solid-state NMR is a promising untapped avenue for probing the local metal structure and unravelling structure–property relationships in Cu(I) MOFs.

Copper has two NMR active isotopes, ⁶³Cu and ⁶⁵Cu, which are both quadrupolar nuclei with a spin number (I) of 3/2. The electric quadrupolar moments (Q) of both nuclei are relatively high, where Q(⁶³Cu) = −0.220 and Q(⁶⁵Cu) = −0.204 barn.^57,58 The natural abundance of ⁶³Cu is 69.2% and ⁶⁵Cu is 30.8%,⁵⁹ yet ⁶⁵Cu is generally the preferred option for solid-state NMR in systems where sensitivity is not an issue due to the smaller Q and higher gyromagnetic ratio (γ, where γ(⁶⁵Cu) = 7.6104 × 10⁷ rad T⁻¹ s⁻¹ and γ(⁶³Cu) = 7.1088 × 10⁷ rad T⁻¹ s⁻¹).⁶⁰ In situations when the Cu(I) density within a material is low (e.g., catalytic applications), the significantly more abundant ⁶³Cu isotope may be a more prudent choice for NMR experiments. The sizeable Q of both isotopes renders ^63/65Cu NMR spectra very broad when Cu does not reside in a local environment of high symmetry, making spectral acquisition challenging. The same anisotropic quadrupolar and chemical shift interactions that give rise to broadened and complicated ^63/65Cu NMR spectra also encode a wealth of information regarding the local Cu environment.

The ^63/65Cu NMR signals of many materials are broadened into the “ultra-wideline” frequency regime⁶¹ and are difficult to acquire, which has limited the use of ^63/65Cu NMR for practical applications. Non-spinning (i.e., static) experiments are well-suited for acquiring ultra-wideline ^63/65Cu NMR spectra.^35,51 Challenges associated with ^63/65Cu NMR have been partially mitigated through the use of increasingly accessible high magnetic fields (i.e., >18.8 T).^19,35,53,54 The second order quadrupolar interaction (QI) that broadens central transition (+1/2 ↔ −1/2) ^63/65Cu NMR spectra is inversely proportional to the magnetic field strength, which results in narrower signals at higher fields. Higher magnetic fields also enhance the population difference between the +1/2 and −1/2 spin states, increasing NMR sensitivity. While ¹H–⁶³Cu RESPDOR NMR experiments have been used to examine a Cu(I) MOF,⁶² there have been no reports regarding direct Cu(I) NMR of MOFs.

In this work, we report a ^63/65Cu NMR study of Cu(I) MOFs featuring copper sites in various two-, three- and four-coordinate environments. The ^63/65Cu NMR parameters quantified from 21.1 T data reveal key information regarding local symmetry and coordination about Cu. We use data from this work and prior studies to illustrate how the Cu quadrupolar coupling constant (C_Q) values are highly dependent on the coordination number and geometric configuration of Cu(I) in MOFs, and present a general scale to guide researchers in determining the Cu(I) coordination number from C_Q(Cu) values in MOFs and many other compounds. This experimental approach can be employed to monitor the structural evolution of MOFs, such as phase transitions, via effects on Cu(I) local environments. In favorable situations, the resolution of ultra-wideline ^63/65Cu solid-state NMR spectra is sufficient to resolve signals from multiple Cu(I) sites.³⁵ Practical applications of ^63/65Cu NMR are explored with experiments on a Cu(I)/Cu(II) mixed valence MOF featuring paramagnetic metal centers that lacks single crystal X-ray diffraction (XRD) data. A comprehensive examination of density functional theory (DFT) calculations and associated geometry optimizations have been performed to better understand the structural origins of experimental electric field gradient (EFG) tensors, along with any discrepancies between calculated and experimental NMR parameters. To finish, we show that ⁶⁵Cu solid-state NMR spectra of Cu(I) MOFs can be successfully acquired at a more accessible lower magnetic field of 9.4 T with sufficient resolution to accurately extract Cu NMR parameters. The practical applications of this concept are illustrated by using ⁶⁵Cu NMR at 9.4 T to elucidate local structural transformations associated with anion exchange in Cu MOFs. The ^63/65Cu solid-state NMR approach in this work demonstrates a promising investigative route for the characterization of Cu(I)-based MOFs and their derivative materials, whether the crystal structure is known or unknown. The MOFs involved in this work are [CuCl(bpy)], [CuI(bpy)], [Cu₂I₂(bpy)], [Cu₂Cl₂(bpy)], [Cu₂I₂(pyz)], [Cu₄I₄(DABCO)₂], {[CuI][Cu(pdc)(H₂O)]·1.5MeCN·H₂O}_n, Cu₂BDC, Cu(bpy)_1.5NO₃·1.25H₂O, Cu₃(4hypymca)₃, SLUG-22, [Cu₆I₆(DABCO)₂], and Cu₂(pyz)₂(SO₄)(H₂O)₂, with additional details provided in Table S1.†

Results and discussion

MOFs with four-coordinate Cu(I) sites

Representative ^63/65Cu NMR of tetrahedral Cu(I) sites in MOFs: [CuCl(bpy)] and [CuI(bpy)]. The most common bonding configuration for Cu(I) in MOFs is in a four-coordinate tetrahedral or distorted tetrahedral fashion. The Cu-X-bpy series of MOFs (X = Cl, Br, I, bpy = 4,4′-bipyridine) have exhibited potential applications in photocatalytic hydrogen production.¹⁰ [CuCl(bpy)] is a neutral three-dimensional framework with open pores measuring ca. 2 × 4 Å. This compound crystallizes in the I4₁/acd space group (Fig. 1(a)).¹⁶ Cu(I) resides in a slightly distorted tetrahedral environment in which adjacent Cu(I) centers are bound to two 4,4′-bpy ligands and bridged by two μ₂-Cl atoms (Fig. 1(a)). The ^63/65Cu static NMR spectra of [CuCl(bpy)] at 21.1 T are shown in Fig. 1(e and i). Both the ⁶³Cu and ⁶⁵Cu NMR spectra exhibit typical QI-dominated powder patterns that can be simulated using a single signal arising from one unique Cu site, which is consistent with the XRD structure.¹⁶ The metallic Cu(0) signal denoted by an asterisk (*) originates from the NMR probe, rather than the sample (Fig. S3†). There is also an additional check on the C_Q obtained from simulating the spectra at 21.1 T; the condition C_Q(⁶³Cu)/C_Q(⁶⁵Cu) = 1.078 must be satisfied, owing to the ratio between the respective nuclear Q values. Despite the dominance of the QI, there are fine features in the ^63/65Cu NMR spectra that cannot be simulated using only quadrupolar parameters, which unambiguously confirms that Cu chemical shift anisotropy (CSA) must be present. The ^63/65Cu NMR parameters (Table 1) were determined to be C_Q(⁶⁵Cu) = 30.0(4) MHz, η_Q = 0.45(3), δ_iso = 500(50) ppm, Ω = 600(200) ppm, κ = 0.4(1), α = 10(3)°, β = 28(3)°, and γ = 35(3)°; see the ESI† for descriptions of the NMR parameters.

Fig. 1 (a–d) A schematic illustration of the local and long-range structure in [CuCl(bpy)], [CuI(bpy)], [Cu₂I₂(bpy)], and [Cu₂I₂(pyz)]. The MOF pore size is listed below each structure. In (e–h), the experimental (“Exp.,” blue) and simulated (“Sim.,” red) ⁶⁵Cu static NMR spectra of [CuCl(bpy)], [CuI(bpy)], [Cu₂I₂(bpy)] and [Cu₂I₂(pyz)] at 21.1 T are shown, with the corresponding ⁶³Cu NMR spectra and simulations in (i–l). The asterisk (*) denotes a signal from metallic copper (Cu⁰) and the pound (#) marks a signal from probe background. The plus symbol (+) marks a resonance arising from residual CuI at 0 ppm after thermal treatment. A background ²³Na signal is also noted in (j). The definitions of *, #, and + also apply to all other figures in this work.

Table 1 Experimental and calculated^a63/65Cu NMR parameters

Site	Method^b^,^c	C Q(^65Cu)^d (MHz)	C Q(^63Cu)^d (MHz)	η Q	δ iso (ppm)	Ω (ppm)	κ	α (°)	β (°)	γ (°)
a Differences between the experimental and calculated values for both the CS tensor parameters and Euler angles are considerable due to the computational difficulties involved with calculating Cu CS tensor parameters. b The “Exp.” label denotes experimental Cu NMR parameters obtained from best-fit simulations of ^65/63Cu NMR spectra acquired at 21.1 T. c The “Calc.” label denotes the NMR parameters obtained from plane-wave DFT calculations using the CASTEP software package. A geometry optimization of all atoms in the reported crystal structure was performed before calculation of NMR parameters; see the Materials and Methods section for additional details. Please see Table S5 for additional calculations performed using defined cluster models. d The ^65/63Cu NMR spectra were simulated independently. The experimental CQ(^63Cu)/CQ(^65Cu) ratio of 1.080 was found to be very close to the accepted quadrupole moment ratio Q(^63Cu)/Q(^65Cu) of 1.078,^57 which gives additional confidence to the simulated fits.
[CuCl(bpy)]
Cu1	Exp.	30.0(4)	33.5(4)	0.45(3)	500(50)	600(200)	0.4(1)	10(3)	28(3)	35(3)
Cu1	Calc.	34.1	36.8	0.41	2188.7	2402.7	−0.24	27.3	60.4	−134.0
[CuI(bpy)]
Cu1	Exp.	28.7(3)	30.2(4)	0.50(4)	400(50)	300(200)	1.0(1)	90(2)	35(2)	10(2)
Cu1	Calc.	28.6	30.8	0.45	1215.0	806.2	−0.24	34.3	45.0	−172.4
[Cu 2 I 2 (bpy)]
Cu1	Exp.	24.0(4)	26.0(5)	0.18(3)	280(50)	400(200)	−1.0(3)	0(3)	25(2)	65(5)
Cu1	Calc.	25.5	27.5	0.47	867.3	741.4	0.15	23.4	20.0	−57.2
[Cu 2 Cl 2 (bpy)]
Cu1	Exp.	30.0(3)	32.0(5)	0.25(2)	230(30)	500(100)	0.1(2)	0(2)	25(3)	58(2)
Cu1	Calc.	27.6	29.4	0.80	1070.0	906.5	−0.67	103.1	89.5	92.8
[Cu 2 I 2 (pyz)]
Cu1	Exp.	18.8(4)	19.6(5)	0.35(2)	300(50)	480(50)	−0.8(2)	10(3)	25(2)	60(4)
Cu1	Calc.	18.2	19.6	0.53	3701.7	2585.8	−0.53	−53.5	4.6	43.5
[Cu 4 I 4 (DABCO) 2 ]
Cu1	Exp.	22.1(5)	23.8(3)	0.09(3)	320(40)	250(75)	1.0(4)	0	0	0
Cu1	Calc.	16.4	17.7	0.22	−58.33	335.57	−0.56	−90	12.5	−180
Cu2	Exp.	20.6(3)	22.0(4)	0.14(4)	280(20)	280(50)	1.0(3)	0	0	0
Cu2	Calc.	15.3	16.5	0.37	−90.4	589.8	0.17	7.4	85.8	−160.5
Cu3	Exp.	26.7(6)	29.1(5)	0.03(3)	320(40)	200(50)	1.0(3)	0	0	0
Cu3	Calc.	23.0	24.8	0.02	−58.8	265.7	−0.87	90.0	5.4	−90.0
{[CuI][Cu(pdc)(H 2 O)]·1.5MeCN·H 2 O} n
Cu1	Exp.	22.0(3)	24.0(2)	0.02(2)	400(15)	150(200)	1.0(4)	0	0	0
Cu1	Calc.	23.2	25.0	0.02	970.0	441.2	−0.87	0	15.9	90
Cu 2 BDC
Cu1	Exp.	53.0(3)	57.0(4)	0.22(3)	200(150)	1800(300)	1.0(4)	0	0	0
Cu1	Calc.	57.5	62.0	0.17	3713.6	6569.0	0.24	158.7	2.2	25.4
Cu(bpy) 1.5 NO 3 ·1.25H 2 O
Cu1	Exp.	74.0(4)	79.0(6)	0.18(2)	300(100)	0	0	0	0	0
Cu1	Calc.	74.5	80.3	0.17	1337.3	2229.1	0.16	−40.8	1.3	39.0
Cu2	Exp.	55.2(8)	58.5(4)	0.00(0)	1300(200)	0	0	0	0	0
Cu3	Exp.	0	0	0	700(100)	0	0	0	0	0
Cu 3 (4hypymca) 3
Cu1	Exp.	74.8(6)	80.6(4)	0.55(2)	150(200)	0	0	0	0	0
Cu1	Calc.	95.6	103.1	0.11	786.4	744.3	0.16	98.5	180.0	−136.0
SLUG-22
Cu1,2	Exp.	63.0(1.0)	67.0(8)	0.34(2)	100(150)	1500(200)	1.0(1)	0	0	0
Cu1	Calc.	40.0	44.2	0.74	786.5	3181.5	−0.24	174.4	172.4	53.0
Cu2	Calc.	42.2	45.5	0.86	859.8	3055.1	−0.24	−17.3	3.17	−22.3
[Cu 6 I 6 (DABCO) 2 ]
Cu1,2,3	Exp.	19.1(3)	21.4(3)	0.70(2)	670(20)	0	0	0	0	0
Cu1	Calc.	19.2	20.7	0.54	81.27	709.4	0.45	−28.6	125.2	175.7
Cu2	Calc.	19.3	20.8	0.25	124.5	724.9	−0.18	96.3	21.1	−143.4
Cu3	Calc.	7.2	7.8	0.34	324.5	704.7	0.53	0	104.3	0
Cu4	Exp.	24.1(2)	27.0(2)	0.20(3)	280(50)	0	0	0	0	0
Cu4	Calc.	24.1	26.0	0.24	257.0	868.6	−0.90	−90	0.22	90
Cu 2 (pyz) 2 (SO 4 )(H 2 O) 2
Cu1	Exp.	25.2(2)	27.2(4)	0.54(2)	500(100)	900(100)	0.0	70(2)	−4(2)	−11(3)
Cu1	Calc.	23.7	25.5	0.55	2079.4	2995	−0.39	43.5	58.0	−73.0

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The [CuI(bpy)] MOF (Fig. 1(b)) has a topology and local coordination of Cu(I) ions similar to that in [CuCl(bpy)]. The main difference between these compounds is that the Cu–I bond length in [CuI(bpy)] is ca. 0.2 Å longer than the Cu–Cl distance in [CuCl(bpy)]. The Cu NMR powder pattern (Fig. 1(f and j)) could be simulated using one unique Cu site (Table 1). [CuI(bpy)] has a lower C_Q and slightly higher η_Q (C_Q(⁶⁵Cu) = 28.7(3) MHz, η_Q = 0.50(4)) than [CuCl(bpy)], partially due to the more ionic nature of the Cu–I bond, illustrating the sensitivity of Cu NMR to local structure.

^63/65Cu solid-state NMR for detecting phase transitions in MOFs: [CuI(bpy)] and [Cu₂I₂(bpy)]. MOFs may undergo a phase transition upon external stimuli, such as exposure to different temperatures and pressures. A typical approach for monitoring long-range structural effects of MOF phase changes is powder XRD (PXRD); however, PXRD cannot intimately probe short-range structural variations, whereas solid-state NMR offers much more information regarding the local metal structure in MOFs.^63,64 With this in mind, the ability of ^63/65Cu NMR to investigate phase transitions in MOFs was explored using [CuI(bpy)].

The three-dimensional porous [CuI(bpy)] MOF is transformed to two-dimensional [Cu₂I₂(bpy)] with heat (Fig. 1(b, c) and S4†).⁶⁵ [CuI(bpy)] crystallizes in the I4₁/acd space group. The single unique Cu(I) center resides in a CuN₂I₂ slightly distorted tetrahedral local environment, which involves bonding to two N atoms from separate 4,4′-bpy ligands along with two bridging μ₂-I ligands. In contrast, [Cu₂I₂(bpy)] is a two-dimensional layered material that crystallizes in the P1̄ space group with layer stacking along the crystallographic b axis. In [Cu₂I₂(bpy)], there is one Cu(I) site in a CuNI₃ distorted tetrahedral environment, which is bound to three μ₃-I species and one nitrogen atom from the 4,4′-bpy ligands. ^63/65Cu solid-state NMR experiments were performed to investigate the local structure at Cu in both [CuI(bpy)] and the [Cu₂I₂(bpy)] product from thermal treatment (Fig. 1(b and c)). These MOFs give rise to well-defined ^63/65Cu NMR powder patterns, which are dominated by the QI but also influenced by CSA, and are both indicative of one unique Cu site. The NMR spectra of [CuI(bpy)] and [Cu₂I₂(bpy)] are visually distinct and yield different ^63/65Cu NMR parameters (Table 1). The C_Q(⁶⁵Cu) value of 28.7(3) MHz in [CuI(bpy)] is reduced to 24.0(4) MHz in [Cu₂I₂(bpy)], with the increased symmetry at Cu attributed to the change from a CuN₂I₂ to a CuNI₃ local environment. The η_Q parameter is also sensitive to the phase change, falling from 0.50(4) in [CuI(bpy)] to 0.18(3) in [Cu₂I₂(bpy)], which is indicative of increased axial symmetry about the Cu center in [Cu₂I₂(bpy)].

In a manner similar to [CuI(bpy)], the three-dimensional [CuCl(bpy)] MOF can also undergo a transformation to the two-dimensional [Cu₂Cl₂(bpy)] MOF upon thermal treatment. The ^63/65Cu NMR spectra of these two MOFs (Fig. S5†) are distinct and diagnostic of the phase change. While the C_Q(Cu) values are very similar in both forms, η_Q changes from 0.45(3) in [CuCl(bpy)] to 0.25(2) in [Cu₂Cl₂(bpy)] (Table 1), producing a clear spectral difference indicative of a significant increase in local axial symmetry. The results indicate that ^63/65Cu NMR is a viable spectroscopic route for tracking phase changes in Cu MOFs.

^63/65Cu solid-state NMR in reticular MOFs: [Cu₂I₂(bpy)] and [Cu₂I₂(pyz)]. The reticular synthesis of MOFs from specifically selected metal centers and organic linkers is an active field of research, since the pore size and eventual material properties can be controlled to a significant degree. Adjustment of the linker length while retaining key binding functional groups has proven an effective avenue to modify the pore size and specific surface area without changing the MOF topology.⁶⁶ In the previous case, ^63/65Cu NMR was used to investigate [Cu₂I₂(bpy)]. If the bpy linker is substituted with pyrazine (pyz) during synthesis, the [Cu₂I₂(pyz)] MOF is obtained. The shorter pyz linker means that [Cu₂I₂(pyz)] has a pore size of ca. 4 × 3 Å, while the longer bpy ligand translates to a larger ca. 4 × 7 Å aperture in [Cu₂I₂(bpy)]. The [Cu₂I₂(pyz)] MOF crystallizes in triclinic symmetry (space group P1̄) and has one unique Cu(I) site residing in a distorted tetrahedral CuNI₃ environment. While the Cu(I) local bonding geometries are similar between [Cu₂I₂(bpy)] and [Cu₂I₂(pyz)],^65,67 the ^63/65Cu NMR powder patterns are relatively narrower in [Cu₂I₂(pyz)] (Fig. 1), and C_Q(⁶⁵Cu) falls from 24.0(4) MHz in [Cu₂I₂(bpy)] to 18.8(4) MHz in [Cu₂I₂(pyz)]. One reason for the decrease in C_Q is the smaller bond angle and bond length distributions involving Cu, while another possibility lies in long-range influences on the EFG that originate beyond the first coordination sphere of Cu (i.e., the effect of different N-bound linker groups). A more detailed discussion can be found in the ESI.†

^63/65Cu solid-state NMR for resolving inequivalent Cu(I) sites in MOFs: [Cu₄I₄(DABCO)₂]. In many MOFs there are multiple unique metal sites, which can often be challenging to characterize and distinguish using NMR techniques. Higher-resolution solid-state NMR techniques (e.g., MAS, MQMAS) are not applicable due to the large quadrupolar interactions and broad lineshapes in ^63/65Cu solid-state NMR; however, wideline NMR experiments on nuclei such as ³⁵Cl have demonstrated that it is possible to distinguish multiple inequivalent sites.^68,69 In this section, we show that ^63/65Cu NMR can resolve separate resonances arising from several crystallographically inequivalent Cu sites in MOFs.

Many MOFs containing Cu_xI_y clusters feature multiple unique Cu(I) sites and have luminescent properties. The luminescent [Cu₄I₄(DABCO)₂] MOF is composed of Cu₄I₄ clusters along with 1,4-diazabicyclo[2.2.2]octane (DABCO) linkers (Fig. 2(a)).¹² This material crystallizes in the P₄/mcc space group and has three inequivalent Cu(I) sites in the Cu₄I₄ unit, where the Cu sites are populated in the ratio Cu1 : Cu2 : Cu3 = 1 : 2 : 1. Each inequivalent Cu(I) site resides in a CuNI₃ distorted tetrahedral environment, with the three coordinated iodine atoms originating from the Cu₄I₄ cluster and the nitrogen atom from a DABCO linker. The ^63/65Cu NMR spectra (Fig. 2(b and c)) are both >400 kHz broad at 21.1 T, with fine features that hint at overlapping Cu resonances. Simulations of experimental data confirm that there are two narrower and overlapping Cu signals of higher intensity nested within a less intense, broader underlying signal; the NMR parameters obtained from simulations are summarized in Table 1.

Fig. 2 A schematic illustration of the long-range structure of [Cu₄I₄(DABCO)₂] along with the local structure about Cu is shown in (a). The experimental (b) ⁶³Cu and (c) ⁶⁵Cu static NMR spectra (blue), cumulative simulations (red), and individual Cu site simulations (black, purple, green) of [Cu₄I₄(DABCO)₂] at 21.1 T are also included.

With the NMR parameters successfully extracted, plane-wave DFT calculations were performed to assign ^63/65Cu resonances to crystallographic sites. The calculated ^63/65Cu NMR parameters (Table 1) indicate that Cu sites 1 and 2 should exhibit similar NMR parameters, including relatively smaller C_Q(^63/65Cu) values, while site 3 should correspond to unique NMR parameters and a larger C_Q(^63/65Cu). Accordingly, the two narrower components of the spectrum were assigned to Cu sites 1 and 2, with the broader signal corresponding to site 3. Given the similarities in C_Q values between Cu sites 1 and 2, an alternate NMR parameter, such as η_Q, must be used to distinguish between them. A careful examination of the left quadrupolar “horn” of the two narrower signals located between +150 and +250 kHz in the ⁶³Cu NMR spectra reveals significant detail, which differentiates the Cu1 and Cu2 powder patterns based on η_Q values. A comparison of local structural parameters between Cu2 and Cu1 shows that Cu2 has both the larger Cu–I bond length distribution and ∠N–Cu–I distribution of all Cu sites;¹² this combination reflects a relatively lower axial symmetry in the Cu2 local environment and should result in a relatively higher η_Q value. Cu2 is thus assigned to the signal with η_Q = 0.14(4) and Cu1 is assigned to the signal with a smaller η_Q of 0.09(3). This assignment is also consistent with DFT calculations (Table 1, where η_Q(Cu2) > η_Q(Cu1) > η_Q(Cu3)). For a more detailed discussion, please see the ESI.†

^63/65Cu NMR of mixed valence Cu(I/II) MOFs: {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n and Cu₂BDC. There is a distinct family of mixed-valence MOFs that incorporate both Cu(I) and Cu(II) metal centers, which have a variety of diverse structures, unique electronic properties, and catalytic applications.^70,71 The mixed valence {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n (where pdc = pyridine-3,5-dicarboxylic acid) MOF was selected as a test compound to investigate if ^63/65Cu NMR could be used to probe materials containing both Cu(I) and Cu(II).⁷² The pdc linker contains both nitrogen and carboxylate groups, which can form MOFs with two separate types of metal nodes upon reaction with CuI. The {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n MOF features a paddlewheel-type local structure incorporating Cu(II) centers, along with a Cu₄I₄ cluster containing Cu(I) (Fig. 3(a)). Cu 2p_3/2 XPS spectra (Fig. S7(a)†) confirmed that both Cu(I) and Cu(II) centers were present in the sample. The single crystal XRD structure of {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n⁷² features Cu(I) sites in CuNI₃ distorted tetrahedral environments. The ^63/65Cu NMR spectra (Fig. 3(b and c)) were simulated using one Cu signal with a small amount of CSA (Fig. S8†). Nevertheless, the prominent CuI signal in the middle of the spectrum introduces uncertainty in CSA quantification and may obscure additional Cu signals, although the likelihood of their presence is low.

Fig. 3 (a) A schematic illustration of the long-range and local structure in the {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n MOF, including the Cu(I) and Cu(II) clusters. The blue experimental and red simulated (b) ⁶⁵Cu and (c) ⁶³Cu static NMR spectra at 21.1 T are also shown.

A C_Q(⁶⁵Cu) value of 22.0(3) MHz and η_Q of 0.02(2) were obtained from {[Cu(I)][Cu(II)(pdc)(H₂O)]·1.5MeCN·H₂O}_n; the near-zero η_Q value is in good agreement with the high local rotational symmetry at Cu(I) indicated from the single crystal XRD structure.⁷² The very slight departure from perfect C₃ rotational symmetry indicated by the η_Q value of 0.02 can be traced to one of the Cu-bonded iodine atoms, which lies slightly out of a truly C₃ symmetrical ligand arrangement. The dominance of the QI on ^63/65Cu NMR spectral appearance, paired with the high signal-to-noise ratio, indicates that there is very little paramagnetic influence on the Cu(I) NMR parameters. The lack of paramagnetic effects can be attributed to two reasons. First, the paddlewheel Cu₂ dimer in its ground state is an antiferromagnetically coupled spin singlet due to the short Cu–Cu bond length;⁷³ the EPR spectrum of this MOF yielded a g-value of 2.161 (Fig. S7(b)†), which falls in the range of reported g-values for MOFs containing a Cu₂ dimer in paddle-wheel units.^74–78 Second, the distance between the Cu(I) and Cu(II) dimers is 7.05 Å, which is long enough that the Cu(I) spin energy levels are only perturbed to a minor degree by any paramagnetic interaction.

In addition to the direct synthesis of Cu (I/II) MOFs, a post-synthetic approach to Cu(I/II) MOFs affords alternate avenues for tuning MOF properties; however, it is difficult or impossible to obtain diffraction-caliber single crystals of product using this approach. Potential applications for ^63/65Cu solid-state NMR in the characterization of post-reduction Cu(I)-containing MOFs were explored by examining the case of Cu₂BDC synthesis from the reduction of CuBDC. Cu(II) sites in the two-dimensional CuBDC (BDC, 1,4-benzendicarboxylic acid) MOF can be partially reduced with L-ascorbic acid (LA acid) via post-synthetic modification to introduce Cu(I) sites, forming a three-dimensional Cu₂BDC MOF (Fig. 4(a)).¹⁴ Powder XRD (Fig. S9†) clearly indicates that Cu₂BDC resides in a different phase than the parent CuBDC MOF, but further analysis of the Cu local environment is hampered by the difficulties in obtaining Cu₂BDC single crystals. The parent CuBDC MOF contains a paddlewheel local structure about Cu, where each Cu(II) center is linked to four carboxylic groups from BDC linkers along with one water molecule, forming a stacked layered structure held together through intermolecular interactions. After LA-acid post-synthetic modification to produce the Cu₂BDC MOF, half of the Cu(II) sites in the MOF were reduced to Cu(I) (Fig. 4(a)). The four-coordinate Cu(I) center in Cu₂BDC resides in a local CuO₄ environment of seesaw geometry, with Cu(I) connected to two carboxylic oxygen atoms (O1, O2) from two BDC ligands, one oxygen atom (O3) of a water molecule, and one oxygen atom (O4) of a bridging OH group. The successful reduction of Cu(II) centers to Cu(I) was confirmed by Cu 2p_3/2 X-ray photoelectron spectroscopy (XPS, Fig. S9†) and X-band EPR (Fig. S10†). The ^63/65Cu NMR spectra of Cu₂BDC (Fig. 4(b and c)) features a QI-dominated NMR powder pattern that yields C_Q(⁶⁵Cu) = 53.0(3) MHz and η_Q = 0.22(3); the well-defined spectrum with relatively sharp features is also indicative of a highly ordered local structure. Although Cu(I) is four-coordinate in this system, the C_Q value is much larger than those of other four-coordinate Cu(I) centers previously discussed. This discrepancy arises from the seesaw local geometry about Cu(I) in Cu₂BDC, which is a much more significant deviation from tetrahedral symmetry versus previous examples of distorted tetrahedral geometry.

Fig. 4 (a) The reduction of CuBDC to Cu₂BDC and the local environment of Cu(I) in CuBDC and Cu₂BDC is pictured. (b) Blue experimental (b) ⁶⁵Cu and (c) ⁶³Cu static NMR spectra of Cu₂BDC at 21.1 T are shown, along with simulations incorporating CSA effects (red trace) and neglecting CSA effects (black trace). Note the effects of CSA on the central spectral discontinuity. The signal from ²³Na background is also indicated in the ⁶³Cu NMR spectrum but truncated for clarity.

A CSA span value of 1800 ppm was necessary to achieve good agreement between the simulated and experimental ^63/65Cu NMR spectra of Cu₂BDC (Fig. 4(b and c)), owing to the hyperfine interaction. The presence of paramagnetic centers, with their associated unpaired electrons, influences the NMR spectral appearance and CSA parameters of nearby diamagnetic nuclei.^79–83 The corresponding hyperfine interactions between Cu(II) unpaired electrons and Cu(I) nuclei leads to very large ^63/65Cu NMR span values. We have performed localized molecular orbital calculations on Cu₂BDC, which revealed that the unpaired electrons of Cu(II) are indeed able to sample regions proximate to Cu(I) (Fig. S11†); this finding, together with the unremarkable Cu chemical shift of 200 ppm, indicates that an electron delocalization effect is present rather than a spin-polarization effect.^79,82,83 This shows how ^63/65Cu NMR can be a robust local characterization technique in the presence of proximate paramagnetic Cu(II) centers, extending the applications of this technique to a wider variety of Cu MOFs.

MOFs with three-coordinate Cu(I) sites

Cu(bpy)_1.5NO₃·1.25H₂O. One of the first reported MOFs containing three-coordinate Cu(I) was Cu(bpy)_1.5NO₃·1.25H₂O in the 1990s.¹⁵ This MOF has applications in anion exchange due to weak bonding between the nitrate ions and the framework. In addition, Cu(bpy)_1.5NO₃·1.25H₂O and its analogue {[M₂(4,4′-bpy)₃(NO₃)₄]·xH₂O}_n (M = Co, Ni, Zn) MOFs have demonstrated reversible adsorption of small molecules such as CH₄, N₂, and O₂.⁸⁴ Cu(bpy)_1.5NO₃·1.25H₂O crystallizes in the orthorhombic space group Fddd and is cationic, featuring large rectangular channels propagating along the [100], [010], and [001] axes which measure 26 × 20, 10 × 12, and 43 × 18 Å, respectively (Fig. 5(a)). The pores are occupied by anionic charge-balancing nitrate anions along with water molecules. The unit cell of the as-made MOF contains one unique Cu(I) site bound to three nitrogen atoms originating from three separate 4,4′-bpy linkers in a distorted trigonal planar CuN₃ geometric arrangement (Fig. 5(b)), along with water molecules.

Fig. 5 (a) The 3D framework structure and (b) local structure of the Cu(bpy)_1.5NO₃·1.25H₂O MOF. The charge-balancing NO₃⁻ anion and guest water molecules are omitted for clarity. (c) ⁶⁵Cu and (d) ⁶³Cu static NMR spectra of Cu(bpy)_1.5NO₃·1.25H₂O at 21.1 T; the blue traces are experimental, black are simulated, and red are simulated using NMR parameters from DFT calculations.

The ^63/65Cu static solid-state NMR spectra of the as-made hydrated Cu(bpy)_1.5NO₃·1.25H₂O MOF at 21.1 T are shown in Fig. 5(c and d). The local Cu environment is significantly distorted from trigonal planar symmetry (∠N₁–Cu–N₂ = 125.39°, ∠N₁–Cu–N₃ = 125.71°, ∠N₂–Cu–N₃ = 108.54°), which leads to an increased C_Q(^63/65Cu) value and spreads the ^63/65Cu NMR spectral powder patterns across breadths of ca. 3 MHz and 4 MHz, respectively. The ^63/65Cu NMR spectra feature a broad signal with some additional details, along with metallic copper (*) and background signals (#).

A successful simulation of all spectral features is challenging due to the multiple Cu powder patterns, despite the single Cu(I) site present in this MOF. Several spectral simulation strategies were explored, but only one produced a satisfactory fit (Fig. S12†), which is discussed below. The extremely broad underlying powder pattern with corresponding quadrupolar horns marked “Cu1” in Fig. 5, which has the highest integrated ratio of ca. 80%, originates from the Cu(bpy)_1.5NO₃·1.25H₂O MOF. The extracted parameters are C_Q(⁶⁵Cu) = 74.0(4) MHz, C_Q(⁶³Cu) = 79.0(6) MHz, η_Q = 0.18(2), and δ_iso = 300(100) ppm, where both C_Q values are remarkably high among reported values.^35,51 This assignment is also supported by DFT calculations, which yielded C_Q,calc (⁶⁵Cu) = 74.5 MHz and η_Q,calc = 0.17 (Table 1, Fig. 5(c and d)). Another narrower resonance labelled Cu2, with an integrated area ratio of ca. 18%, is assigned to a side product; the NMR parameters are reported in Table 1 for reference. The experimental PXRD pattern of Cu(bpy)_1.5NO₃·1.25H₂O in Fig. S2† agrees well with the pattern simulated from the reported crystal structure, yet the experimental diffractogram also exhibits some additional reflections at low angles that are attributed to the Cu(I) impurity. There is also a trace amount of an unidentified impurity accounting for ca. 2% of total spectral intensity that is labelled with the “&” character and assigned to a Cu3 species.

^63/65Cu NMR of [Cu₃(4hypymca)₃]. The electrically conductive two-dimensional [Cu₃(4hypymca)₃] MOF¹³ is composed of Cu(I) centers connected by 4-hydroxypyrimidine-5-carbonitrile (4hypymca) linkers. [Cu₃(4hypymca)₃] crystallizes in the orthorhombic system (Pbcm space group), with a long-range structure consisting of equidistant flat layered sheets (Fig. 6(a)). The single unique three-coordinate Cu(I) center is bound to N atoms from three separate 4hypymca linkers, forming a distorted trigonal planar local environment of relatively low symmetry about Cu. Accordingly, the ^63/65Cu NMR spectra (Fig. 6(b and c)) are quite broad. The ⁶³Cu NMR spectrum extends across a frequency range of ca. 5.3 MHz at 21.1 T, which corresponds to exceptionally large C_Q(⁶³Cu) = 80.6(4) MHz and C_Q(⁶⁵Cu) = 74.8(6) MHz values.

Fig. 6 (a) The long-range and local structure of Cu₃(4hypymca)₃. The experimental (blue) and simulated (red) ⁶⁵Cu static NMR spectra and ⁶³Cu static NMR spectra at 21.1 T are shown in (b and c), respectively. ²⁷Al marks a signal from probe background. The signal from ²³Na background is also marked in the ⁶³Cu NMR spectrum, but is truncated for clarity.

While both [Cu₃(4hypymca)₃] and Cu(bpy)_1.5NO₃·1.25H₂O feature Cu(I) bound to three nitrogen atoms, the η_Q value is significantly higher in [Cu₃(4hypymca)₃] (Table 1). Cu(bpy)_1.5NO₃·1.25H₂O features Cu coordinated to three N atoms of pyridine groups, but the Cu center in [Cu₃(4hypymca)₃] is connected to two pyridine-based N atoms and one nitrile N atom, which corresponds to decreased axial symmetry about Cu and a higher η_Q value. The average trigonal distortion (, where θ_i, i = 1, 2, 3 are the three ∠N–Cu–N bond angles around Cu) is also larger in [Cu₃(4hypymca)₃] than in Cu(bpy)_1.5NO₃·1.25H₂O by 8.0°, which further explains the increase in η_Q.

MOFs with two-coordinate Cu(I) sites

Some MOFs feature Cu(I) in two-coordinate linear arrangements. The SLUG-22 MOF is composed of Cu₂(4,4′-bpy)₂ units, where the two-coordinate Cu(I) center is connected to two nitrogen atoms from separate 4,4′-bpy linkers in a distorted N–Cu–N linear geometry, with a long-range structure consisting of one-dimensional chains of infinite length (Fig. 7(a)). ^63/65Cu static solid-state NMR spectra of SLUG-22 at 21.1 T (Fig. 7(b and c)) are extremely broad, owing to the low local symmetry of the linear two-coordinate environment at Cu and the correspondingly large C_Q value. Simulations (Table 1) necessitated the use of CS parameters, but indicated only a single Cu(I) site with C_Q(⁶⁵Cu) = 63.0(1.0) MHz and η_Q = 0.34(2) was present; this contrasts with the reported crystal structure¹⁸ that indicated there are two inequivalent Cu(I) sites. A careful examination of the ^63/65Cu NMR spectra reveals slightly broader features in the experimental spectra, which could be indicative of two nearly identical overlapping Cu powder patterns that cannot be resolved. Indeed, the crystal structure shows that the Cu centers reside in very similar local environments.¹⁸ Furthermore, Fig. 7 illustrates how the frequency of the central spectral discontinuity is affected by CSA, and in particular, the exceptionally large span value of 1500 ppm.

Fig. 7 (a) The 3D framework structure and local structure of the SLUG-22 MOF. The (b) ⁶⁵Cu and (c) ⁶³Cu static NMR spectra at 21.1 T are shown in blue, along with the red simulation which includes CSA effects, and the black trace which does not include CSA effects. Note the difference in the central “divot” spectral feature between the red (CSA) and black (no CSA) simulations; CSA is necessary to properly fit this feature. The asterisks (*) denote the signal from metallic copper (Cu⁰) and the pound (#) marks the signal from probe background, which are truncated for clarity. The signal from ²³Na background is also marked in the ⁶³Cu NMR spectrum.

In order to investigate the origins of the abnormally large Cu CSA in SLUG-22, EPR and XPS experiments were performed (Fig. S13†), which indicated this material was largely free of Cu(II) or other paramagnetic impurities. The lack of any plausible hyperfine interactions indicates the sizeable CSA in SLUG-22 likely arises from the linear two-coordinate local geometry at Cu. Large CSA spans have been recorded from other transition metal compounds in linear configurations (e.g., linear HgX₂).⁸⁵ We found that cluster DFT calculations using the RHF method and 6-31++G**/6-311++G** basis sets were the most reliable avenue for calculating Cu span values (vide infra, Table S5†); these particular calculations also predicted a substantial Cu CSA span value in SLUG-22 arising from the local linear coordination geometry at Cu.

There are more complicated MOFs featuring mixed coordinate Cu(I) local environments that can be examined using ^63/65Cu NMR. We investigated the [Cu₆I₆(DABCO)₂] framework, which contains four distinct Cu sites and produced a complicated Cu NMR spectrum that lacked clear singularities. The results and discussion regarding these experiments can be found in the ESI.†

DFT calculations of EFG tensors

To obtain further insight into experimental NMR results and the local Cu(I) environments, plane-wave DFT calculations using GIPAW methods were performed. The EFG tensor parameters are sensitive to the local environment, which provides a metric to predict and optimize crystal structures.^86–92 In this section, we examine Cu(I) structural insights obtained from plane-wave DFT calculations of ^63/65Cu EFG tensors in MOFs. It should be noted that the XRD crystal structures were obtained at low temperatures while our Cu NMR experiments were performed at room temperature, which could lead to discrepancies between calculated and experimental Cu NMR parameters due to issues such as temperature-dependent unit cell dimensions and dynamics. To verify that temperature changes did not introduce significant changes to Cu NMR parameters, low-temperature NMR experiments were performed on selected MOFs, which yielded Cu NMR spectra nearly identical to room temperature spectra (Fig. S15†). This finding signified that, in this case, the experimental temperature did not play a significant role in the accuracy of calculated NMR parameters. This result is not particularly surprising, as all the MOFs investigated in this work have rather rigid frameworks.

GIPAW DFT calculations on the Cu MOF systems were evaluated by first examining the correlations between the calculated and experimental EFG tensor parameters in discrete Cu(I) coordination complexes with relevant Cu(I) local environments. The experimental Cu NMR data was taken from previous reports by Tang³⁵ and Yu,⁵⁶ using crystal structures obtained from the Cambridge Crystallographic Data Centre (CCDC). As shown in Fig. S16 and Appendix A of the ESI,† the calculated principal components of the Cu EFG tensor in this dataset exhibit a decreased Γ_RMSE (the EFG distance metric expressing the deviation between experimental and computed EFG parameters;⁹³ see ESI†) after geometry optimization, from 0.071 a.u. before to 0.053 a.u. after. After geometry optimization, the slope of the respective plot is closer to 1, the y-intercept is reduced, and R² is higher, which all indicate a better agreement with experimental values.

The correlation between DFT-calculated and experimental Cu EFG tensor components |V_kk| (k = 1, 2, 3) based on our current MOF dataset are shown in Fig. 8(a and b). After geometry optimization, the Γ_RMSE of the MOF Cu dataset was calculated to be 0.119 a.u., which is significantly larger than the 0.053 a.u. of the dataset constructed from prior reports. Bar plots of calculated versus experimental C_Q and η_Q values are shown in Fig. S25;†C_Q depends on a single EFG tensor component (V₃₃) and is generally calculated quite accurately, while η_Q calculations are dependent on all three EFG tensor components and are therefore less accurate. The SLUG-22 and Cu₃(4hypymca)₃ MOFs are responsible for the increased Γ value in the MOF dataset (Fig. 8(c)). When excluding SLUG-22 and Cu₃(4hypymca)₃, the Γ_RMSE value is a much more reasonable 0.047 a.u. These results indicate that further investigation of the local structure and geometry optimization in SLUG-22 and Cu₃(4hypymca)₃ is warranted.

Fig. 8 Relationships between the principal components (|V_kk|, k = 1,2,3) of calculated and experimental ^63/65Cu EFG tensors in MOFs (a) before and (b) after geometry optimization. (c) The Γ values for all MOFs after geometry optimization. The Γ_RMSE including the results from all MOFs is shown as a green dashed line, while the Γ_RMSE excluding SLUG-22 and Cu₃(4hypymca)₃ is shown as a red dashed line. (d) The EFG distance in the optimized SLUG-22 structure is shown, as obtained after plane-wave DFT calculations using different geometry optimization approaches. The x-axis labels in (d) are as follows; XRD structure: no optimization; DFT: geometry optimization without optimization of unit cell dimensions; DFT-shape: optimization with unit cell using a fixed-shape constraint; DFT-volume: optimization with unit cell dimensions using a fixed-volume constraint; DFT-D2 and DFT-D3: optimization using the D2 and D3 dispersion corrections with an optimized damping parameter (Fig. S17†).^86,93 Note that there are two inequivalent but similar Cu sites in the reported XRD structure of SLUG-22.

Discussion regarding the local structure of SLUG-22. There are three potential explanations for the significant differences observed between the experimental and calculated Cu EFG parameters of SLUG-22. The first possibility involves the presence of paramagnetic Cu(II) that could impact spectral appearance and influence the accuracy of extracted Cu EFG parameters; however, XPS and EPR experiments (Fig. S13†) indicated no detectable amounts of Cu(II) species. The second source is a potential temperature dependence of the SLUG-22 phase or unit cell dimensions, since the original XRD structure was obtained at low temperature and our NMR experiments were performed at room temperature. Hardware limitations prohibited low-temperature ^63/65Cu NMR experiments at 21.1 T, and ^63/65Cu WURST-CPMG NMR experiments at 9.4 T on these systems were not successful due to low T₂ values. As a surrogate, the ¹H–¹³C CP/MAS NMR spectra of SLUG-22 at 208 and 298 K were acquired and found to be quite similar (Fig. S18†), suggesting that no significant structural deviations or phase changes occur at lower temperatures. The third source is fundamental structural issues arising from the DFT geometry optimizations performed prior to EFG calculations, which was found to merit further investigation.

Four DFT optimization schemes of the SLUG-22 crystal structure were explored (Fig. 8(d)). All the geometry-optimized structures yielded lower SCF energies versus the XRD structure, yet the agreement between calculated and experimental Cu EFG tensor parameters using any of the calculation strategies did not show significant improvement, which is puzzling. A more detailed examination of the experimental PXRD patterns in the original work describing SLUG-22 ¹⁸ (Fig. S19(a)†) revealed that several intense reflections expected at low angles from the reported single crystal structure are not apparent in the original experimental data, particularly the prominent reflection at ca. 9°, while additional unexpected reflections are present. Our geometry-optimized structures generated using a myriad of DFT-based approaches failed to improve the agreement between experimental and calculated XRD patterns (Fig. S19(b)†). Based on the considerable deviation between the experimental and calculated PXRD patterns, along with the inaccuracy of calculated EFG tensor parameters, it appears that the reported single crystal structure of SLUG-22 is incorrect in some manner, which illustrates another practical application of Cu NMR.

Discussion regarding the local structure of Cu₃(4hypymca)₃. As with SLUG-22, we observed no improvement in the agreement between calculated and experimental EFG tensor components of the Cu₃(4hypymca)₃ MOF despite employing a variety of different geometry optimization strategies prior to NMR calculations (Fig. 9(a)). The most striking change in the local optimized geometry about Cu is a reduction of > 0.1 Å in the Cu–N bond length to the linker cyanide group. Variations in bond lengths and bond angles have a known influence on EFG parameters.^94,95 To investigate further, we systematically altered the Cu–N bond length and then calculated the EFG tensor parameters and relative energy of the system, as shown in Fig. 9(b). While the minimum energy is associated with a Cu–N bond distance of 1.95 Å, this distance leads to a considerable gap between calculated and experimental Cu EFG tensor parameters. In comparison, a Cu–N bond length of 2.20 Å maximizes the accuracy of the calculated EFG tensor parameters, but results in an unacceptably high system energy. In this case, the most likely situation is a Cu–N bond length that results in a mutual minimization of system energy and Γ, where the trends intersect in Fig. 9(b). This data suggests that the Cu–N bond length in the Cu₃(4hypymca)₃ MOF crystal structure is slightly longer than the reported value of 2.00 Å. In addition, it is possible that plane-wave DFT calculations do not properly account for intermolecular interactions between the 2D sheets in this MOF, or there could be “slipping” of relative positions between the 2D MOF sheets that cannot be clearly identified via XRD studies.

Fig. 9 (a) The EFG distance of optimized Cu₃(4hypymca)₃ structure with different approaches, along with (b) the dependence of Γ on Cu–N bond length.

Calculations of Cu EFG tensor orientations and CS tensor parameters. DFT calculations are known to reliably yield the orientation of the Cu EFG tensor, and the EFG tensor orientations for these Cu MOF systems along with a brief discussion are provided in Appendix B of ESI.† The calculated CS parameters are listed in Table 1 for reference, but we highlight that agreement between calculated and experimental CS values is rather poor (Fig. S26 in Appendix C†), and plane-wave DFT calculations evidently are not a reliable predictor of Cu CS parameters in MOFs at this time. While calculating EFG parameters only involves the electronic ground state of a system, CS calculations involve both the ground and excited states, which increases the computational complexity. For instance, Tang et al. performed CS calculations using different DFT basis sets and methods on discrete cluster models of Cu(I) compounds,³⁵ but only obtained partial agreement with experimental results depending on the particular approach. Calculating CS parameters for heavier atoms such as Cu is also challenging due to factors such as spin–orbit effects,⁹⁶ relativistic considerations,^97,98 and the many possible hybrid functionals that can be applicable.⁹⁹ The relatively high uncertainty of experimental CS values (Table S6†) as a result of multi-variable fitting may also influence the agreement with calculated CS values; larger uncertainties in the experimental CS parameters will generally result in poorer agreement with accurately calculated values.

We also performed calculations on geometry-optimized cluster models. The results using several different methods and basis sets are listed in Table S5.† The CS span values calculated using RHF/6-31++G** and RHF/6-311++G** (Fig. S21†) demonstrated better agreement with experimental span values when compared to plane-wave DFT calculations. In contrast, the calculated EFG tensors with all cluster models (Fig. S20†) yielded poorer agreement with experimental values when compared to plane-wave DFT calculations (Fig. 8(b)).

Quadrupolar coupling constant and the Cu(I) coordination number

The observed quadrupolar coupling constant (C_Q) largely depends on the coordination number of Cu(I). A summary of the C_Q(⁶⁵Cu) values in MOFs is illustrated in Fig. 10, along with relevant values in small metal–organic coordination compounds from previous reports.^35,51,56 The C_Q(⁶⁵Cu) values of four-coordinate tetrahedral Cu(I) centers are generally <40 MHz. The C_Q(⁶⁵Cu) values of three-coordinate Cu(I) range from 40 MHz to 80 MHz. Four-coordinate Cu(I) in a pseudo-three coordinate environment is correlated to C_Q(⁶⁵Cu) values between 40 and 50 MHz,⁵¹ which lies just between the bulk of four- and three-coordinate Cu environments. ^63/65Cu NMR reports on two-coordinate Cu(I) ions are not common; both the SLUG-22 MOF in this work and the previously reported small molecule ClCuP(2,4,6)₃³⁵ yielded C_Q(⁶⁵Cu) values between 60 and 65 MHz. There were no prior ^63/65Cu solid-state NMR reports of Cu(I) centers in a four-coordinate seesaw local geometry before this work; this environment appears to produce C_Q values comparable to three- and two-coordinate Cu(I) arrangements. The compiled empirical results from this and prior studies in Fig. 10 provides a convenient and general NMR-based tool to estimate the coordinate state of Cu(I) in unknown environments across a variety of materials and compounds.

Fig. 10 Copper C_Q(⁶⁵Cu) values of Cu(I) MOFs, along with those previously reported for other Cu(I) compounds.

⁶⁵Cu solid-state NMR at 9.4 T

The Cu MOFs in this study were examined by ^63/65Cu NMR using a high magnetic field of 21.1 T. Unfortunately, high fields are not always readily accessible, but there are several previous studies regarding ⁶⁵Cu ultra-wideline NMR at 9.4 T.^35,51 In MOFs, the Cu concentration is diluted, which poses an additional obstacle.

We set out to find if ⁶⁵Cu solid-state NMR of Cu(I) MOFs was feasible at a more accessible field of 9.4 T (i.e., ν₀(¹H) = 400 MHz), which would open up this technique to researchers across a broad swath of institutions. In addition, performing the Cu NMR experiments at different magnetic fields allows one to extract unambiguous CS and QI parameters along with the second-order quadrupolar isotropic shift. A major challenge at 9.4 T is spectral width; broadening from the second-order quadrupolar interaction is inversely proportional to B₀, thus ^63/65Cu NMR spectra are spread across a significantly larger frequency range at lower magnetic fields. To increase the signal-to-noise ratio and reduce experimental times, the WURST-CPMG pulse sequence can be employed.¹⁰⁰ The WURST-CPMG sequence yields NMR spectra composed of a series of spikelets that trace out the overall spectral manifold, rather than the smooth continuous lineshape obtained from solid echo experiments. A spikelet spectrum can be acquired significantly faster than a solid echo spectrum. Using seven Cu(I) MOFs from this study as examples, we obtained ⁶⁵Cu NMR spectra at 9.4 T ranging from ca. 500 to 3000 kHz in breadth (Fig. 11). The 9.4 T data was then simulated independently in order to assess the reliability of these results against those obtained at 21.1 T. The ⁶⁵Cu NMR parameters obtained at 9.4 T (Table S6†) were consistent with those obtained from ^63/65Cu experiments at 21.1 T, validating the accuracy of the extracted NMR parameters in Table 1. These findings prove that ^63/65Cu NMR of Cu(I) MOFs and other Cu-dilute systems is experimentally viable at 9.4 T. The experimental times are listed in Table S4.†

Fig. 11 The experimental (blue) and simulated (red) ⁶⁵Cu static WURST-CPMG NMR spectra of [CuCl(bpy)], [Cu₂Cl₂(bpy)] [CuI(bpy)], [Cu₂I₂(bpy)], [Cu₂I₂(pyz)] and [Cu₄I₄(DABCO)₂] at 9.4 T are shown at right, along the 15 sub-spectra required to assemble the overall spectrum of Cu₂BDC at left.

Applications of ^63/65Cu solid-state NMR for anion exchange reactions

Anions are present in many MOFs to maintain charge balance with the cationic framework, which opens the door for versatile anion-exchange applications in fields such as the capture of undesirable pollutants (e.g., ClO₄⁻, HCrO₄⁻).^101,102 Understanding the chemistry taking place during anion exchange in MOFs is critical for the design of tailored MOFs to address specific applications. We used the Cu₂(SO₄)(pyz)₂(H₂O)₂ MOF to demonstrate how ^63/65Cu solid-state NMR at 9.4 T can be used to investigate Cu local structural evolution during chemical reactions such as anion exchange.

The (Cu₂(SO₄)(pyz)₂(H₂O)₂) MOF, termed 1, was synthesized using CuSO₄·5H₂O and pyrazine in hydrothermal conditions.^103,104 The Cu(I) center in 1 is in a distorted tetrahedral CuN₂O₂ local environment. Cu is connected to two pyrazine linkers, which form zig-zag one-dimensional chains that are bridged by sulfate ions, and Cu is also coordinated to water molecules that are oriented perpendicular to the 1D chains. The ⁶⁵Cu solid-state NMR spectrum at 9.4 T (Fig. 12) features a well-defined powder pattern exhibiting a C_Q(⁶⁵Cu) of 25.2(2) MHz and a η_Q of 0.54(2), with the C_Q value lying in the established range of four-coordinate Cu (Fig. 10).

Fig. 12 The ⁶⁵Cu solid-state NMR spectra of 1 (Cu₂(SO₄)(pyz)₂(H₂O)₂) and associated products after exposure to different aqueous solutions, as measured at 9.4 T. The asterisk (*) denotes a signal from metallic copper (Cu⁰) and the pound (#) indicates a resonance from a by-product containing Cu₂O.

While 1 is stable in air and water, this material quickly turns from dark red to orange when exposed to aqueous NaNO₃ solution, yielding 1@NO₃⁻. A white insoluble precipitate is evident when BaCl₂/HCl is added, indicating that a migration of SO₄²⁻ from 1 into solution has occurred. As a soft acid, the Cu(I) ion prefers to coordinate with the soft base of nitrogen rather than the hard base of oxygen, which explains the formation of a precipitate. The ⁶⁵Cu NMR spectrum of 1@NO₃⁻ is a much broader ca. 3 MHz, which corresponds to a C_Q(⁶⁵Cu) of 46.5(8) MHz and a η_Q of 0.28(5) (Fig. 12). Using Fig. 10 as a guide, the significant increase in C_Q(⁶⁵Cu) from 1 to 1@NO₃⁻ indicates that the local coordination at Cu has changed from four-coordinate to two- or three-coordinate. When 1 was immersed in a NaClO₄ solution, the powder changed to an orange-yellow color, and the resulting product was termed 1@ClO₄⁻. The ⁶⁵Cu NMR spectrum of 1@ClO₄⁻ at 9.4 T has an impressive breadth of ca. 7 MHz, with a C_Q(⁶⁵Cu) of 67.0(6) MHz and η_Q of 0.23(7); the increase in C_Q again indicates that Cu now resides in a two- or three-coordinate local environment. When 1 is exposed to aqueous NaCl, the original dark red color is retained, however, the ⁶⁵Cu NMR spectral breadth is considerably narrowed and the lineshape is altered in a distinct fashion. The 1@Cl⁻ compound corresponds to a decreased C_Q(⁶⁵Cu) of 15.5(4) MHz, which indicates that the four-coordinate tetrahedral geometry is preserved at Cu, along with a significantly increased η_Q of 0.98(2). The well-defined ⁶⁵Cu NMR powder patterns of 1 after exposure to NO₃⁻, ClO₄⁻ and Cl⁻ indicates that the local structure about Cu is relatively ordered in all instances. Using the estimated Cu coordination states obtained from the various ⁶⁵Cu NMR spectra of 1 and its derivatives in mind, a search of the CCDC database was performed for any structures potentially matching or similar to the anion-exchanged products obtained in this study. Three compounds were identified: {Cu(pyz)(NO₃)}_n which contains a two-coordinate CuN₂ moiety,¹⁰⁵ {Cu(pyz)_1.5(ClO₄)}_n with a three-coordinate CuN₃ local structure,¹⁰⁵ and {CuCl(pyz)}_n with a four-coordinate CuCl₂N₂ environment.¹⁰⁶ The reported structures had been synthesized independently through solvothermal routes, and not via the anion-exchange approach we employed.

The experimental PXRD patterns of 1@NO₃⁻, 1@ClO₄⁻, 1@Cl⁻, along with the calculated PXRD patterns of {Cu(pyz)(NO₃)}_n, {Cu(pyz)_1.5(ClO₄)}_n, and {CuCl(pyz)}_n from the reported solvothermal approaches are shown in Fig. S22.† The experimental PXRD pattern of 1@Cl⁻ matches perfectly with the calculated pattern of {CuCl(pyz)}_n, indicating the anion-exchanged product 1@Cl⁻ is identical to solvothermally synthesized {CuCl(pyz)}_n. This also confirms that a four-coordinate Cu(I) tetrahedral environment exists in 1@Cl⁻, as predicted from C_Q(⁶⁵Cu) NMR values. In contrast, the PXRD patterns of anion-exchanged 1@NO₃⁻ and 1@ClO₄⁻ look similar to those of solvothermally synthesized {Cu(pyz)(NO₃)}_n and {Cu(pyz)_1.5(ClO₄)}_n, but are not identical. It appears that the pairs of 1@NO₃⁻ and {Cu(pyz)(NO₃)}_n MOFs, and the 1@ClO₄⁻, and {Cu(pyz)_1.5(ClO₄)}_n MOFs, are of similar connectivities but reside in different crystal structures (i.e., space groups). The Cu(I) coordination numbers are two and three in {Cu(pyz)(NO₃)}_n and {Cu(pyz)_1.5(ClO₄)}_n, respectively, which is consistent with expectations based on the experimental 1@NO₃⁻ and 1@ClO₄⁻C_Q(⁶⁵Cu) values. The Cu(I) center is generally considered to be a soft acid, and preferentially binds with soft base ligands such as N donors and halogen ions, rather than with hard bases such as O donors. In good agreement, we observed that the formation of 1@Cl⁻ from 200 mg of 1 in a saturated aqueous solution concluded within ca. 30 min. In the context of hard and soft acids and bases, the cleavage of Cu(I)–O bonds to H₂O and SO₄²⁻ and the formation of Cu(I)–Cl bonds to yield a CuCl₂N₂ tetrahedral coordination environment in 1@Cl⁻ is favorable and should proceed quickly. In a similar finding, the reaction of 1 with NO₃⁻ was also noted to conclude within 30 min; the zig-zag one-dimensional chains are sufficiently stable enough to exist without sulfate ions or coordinated water molecules, which then yields a two-coordinated Cu(I)N₂ configuration with NO₃⁻ solely as a charge balancing anion. In stark contrast, the formation of 1@ClO₄⁻ requires ca. 12 hours of reaction time. After the cleavage of Cu–O bonds to H₂O and SO₄²⁻, the formation of Cu–N bonds to pyrazine linkers in a new trigonal geometry requires a much longer duration because perchlorate is a very weakly coordinating anion and is not directly bound to Cu(I).

Conclusions

A series of Cu(I)-containing MOFs featuring Cu sites in different coordination environments have been examined using ^63/65Cu ultra-wideline NMR and DFT calculations. The diversity of local environments of Cu(I) centers in MOFs leads to C_Q(⁶⁵Cu) values ranging from 18.8 to 74.8 MHz, which are diagnostic of the local Cu coordination environment and geometry. Multiple broad and overlapping ^63/65Cu NMR signals arising from several unique Cu sites in MOFs can be resolved under favorable situations, and then simulated to extract information on the Cu local environment.

^63/65Cu NMR spectroscopy provides direct evidence regarding the evolution of local Cu environments during MOF structural transformation processes. The sensitivity of this technique can also be exploited to monitor and characterize MOF phase transitions. Even in the challenging case of Cu(I/II) mixed valence MOFs, ^63/65Cu NMR spectra can be obtained, and are influenced by paramagnetic interactions when Cu(I) is especially proximate to Cu(II). We have proven ^63/65Cu NMR can be performed within reasonable experimental times at a lower magnetic field of 9.4 T despite the weight dilution of Cu(I) centers in MOFs. DFT-calculated ^63/65Cu EFG tensor parameters have been presented and rigorously compared with experimental values; calculations using geometry-optimized structures generally lead to better agreement with experimental results except for two instances, and the origins of these disagreements were explored. We have established a list of C_Q(Cu) values from this and previous studies that permits estimation of local Cu coordination using only the C_Q value, which is broadly applicable to many other Cu systems. This study highlights the versatility of ^63/65Cu solid-state NMR, extending its relevance beyond MOFs and towards any chemical systems containing either abundant or dilute Cu(I) centers, with applications in fields such as catalysis, surface chemistry, solar cells, and biochemistry.

Materials and Methods

Sample preparation

The reported procedures were followed for MOF synthesis when possible.^{12–16,18,65,107} All details regarding synthesis and non-NMR characterization of the Cu compounds can be found in the ESI.†

Solid-state NMR experiments

In general, ^63/65Cu NMR spectra were acquired under static conditions using the solid echo or WURST-CPMG (Wideband Uniform Rate Smooth Truncation-Carr Purcell Meiboom Gill)^100,108 pulse sequences. Solid echo experiments give rise to a smooth continuous lineshape, while WURST-CPMG experiments concentrate the signal into discrete spikelets that trace out the overall manifold of the powder pattern. Most of the ultra-wideline ^63/65Cu NMR spectra in this work were too broad to be acquired in a single experiment, which necessitated the use of the VOCS (variable-offset cumulative spectra) method.¹⁰⁹ The VOCS approach involves acquiring several sub-spectra at evenly spaced transmitter offsets using otherwise identical experimental parameters, and then co-adding the subspectra together to obtain the total ^63/65Cu NMR spectrum. All ⁶³Cu and ⁶⁵Cu NMR spectra were referenced to solid CuCl at 0 ppm.

Solid-state NMR experiments at 21.1 T. Experiments at 21.1 T were conducted at the National Ultrahigh-field NMR Facility for Solids in Ottawa, Canada using a Bruker Avance II spectrometer. ⁶³Cu and ⁶⁵Cu NMR spectra were acquired using a home-built solenoid single-channel probe with a silver NMR coil (ν₀(⁶³Cu) = 238.73 MHz, ν₀(⁶⁵Cu) = 255.74 MHz). All ^63/65Cu NMR spectra were acquired using a solid-echo pulse sequence (90°–90°). The interpulse delay was set to 30 μs. Additional experimental parameters are listed in Tables S2 and S3.† Background signals of the probe and various sample containers are discussed in footnote b of Table S3 and shown in Fig. S3.†

Solid-state NMR experiments at 9.4 T. All experimental parameters can be found in ESI and Table S4.†

NMR simulations

Extraction of NMR parameters was performed using the WSolids software package.¹¹⁰ The experimental error bounds for each measured parameter were determined by visual comparison of simulated spectra; the parameter in question was varied bidirectionally from the best-fit value, keeping other parameters constant, until differences were observed. The reader is directed towards the “NMR interactions and NMR parameters” section in the ESI† for a discussion of NMR interactions.

Quantum chemical calculations

The CASTEP Academic Release version code 19.11 ¹¹¹ was used to calculate ⁶⁵Cu magnetic shielding and electric field gradient (EFG) tensor parameters via ab initio plane-wave density functional theory (DFT) methods. Calculations were performed on the SHARCNET computational network (https://www.sharcnet.ca/). Perdew, Burke, and Ernzerhof (PBE) functionals were employed with the generalized gradient approximation (GGA)¹¹² for the exchange correlation energy in all instances, with a plane-wave basis set cutoff energy of 800 eV. NMR parameters were calculated using “on-the-fly” ultrasoft pseudopotentials and the gauge-including projector-augmented wave (GIPAW) formalism.^113,114 The DFT C_Q (MHz) values were obtained from calculated EFG tensor parameters using the most recently reported ^63/65Cu quadrupole moment.⁵⁷ The calculated ⁶³Cu and ⁶⁵Cu magnetic (chemical) shielding values (σ) in each MOF were converted to the corresponding chemical shift (δ) values using the formula δ_iso = σ_ref − σ_iso. Note that σ_ref is the ^63/65Cu shielding for the reference sample CuCl(s), where σ_ref (CuCl(s)) was calculated to be 702.68 ppm. Further details regarding geometry optimization schemes, along with the software and methodology used for cluster DFT calculations, can be found in the ESI.†

EFG tensor analysis

The EFG tensor has three principal components denoted V₁₁, V₂₂, and V₃₃, defined such that |V₃₃| ≥ |V₂₂| ≥ |V₁₁|. The agreement between experimental V^exp_kk, k = 1, 2, 3 and V^cal_kk, k = 1, 2, 3 can be evaluated using the EFG distance metric Γ^86,93 (in atomic units, a.u.). Please see the ESI† for a detailed explanation of EFG tensor parameters and Γ.

Author contributions

W. Z.: conceptualization, investigation, formal analysis, methodology, computation, writing, review, editing; B. E. G. L.: writing, review, editing; V. V. T.: investigation, review, editing; S. C.: investigation; Y. H.: conceptualization, resources, funding, formal analysis, writing, review, editing.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

Y. H. thanks the Natural Science and Engineering Research Council (NSERC) of Canada for a Discovery Grant. Access to the 21.1 T NMR spectrometer was provided by the Government of Canada Ultrahigh-Field NMR Collaboration Platform, operated by the National Research Council of Canada with support from Laboratories Canada, and a consortium of other Canadian Government Departments and Universities. We thank Dr Mathew Willans at the J. B. Stothers NMR Facility (University of Western Ontario) for his assistance with ⁶⁵Cu WURST-CPMG NMR experiments at 9.4 T. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: http://www.sharcnet.ca), Compute/Calcul Canada, and the Digital Research Alliance of Canada.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4sc00782d

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