Introduction

The emergence of quantum dots has inaugurated the nanotechnology era, igniting scientific exploration and technological advancement1,2,3. Among these, CdSe nanocrystals have emerged as exemplary materials, showing excellent optical and electronic properties poised to influence a multitude of fields including photonics, electronics, energy conversion/storage, nanomedicine, and biosensing4,5,6,7,8,9,10,11,12,13,14,15. The pivotal quantum confinement effect, stemming from their nanoscopic dimensions, underscores the unique properties of quantum dots (QD)s but also makes precise control of nanocrystal size and distribution imperative for effective applications16. Engineering nanocrystals with defined properties thus requires a detailed understanding of the nanocrystal formation process.

Conventional methods for monitoring nanocrystal formation rely on ensemble properties to glean kinetic insights. Techniques such as absorption spectroscopy, manifesting shifted absorption peaks with increasing sizes, and dynamic light scattering, commonly used to monitor bulk properties such as size and homogeneity, provide limited compositional growth information regarding how the electronic structure and coordination environments of core and surface atoms evolve during nanocrystal formation17,18,19. A detailed, atomic-level understanding of this compositional growth would provide microscopic insights into the structural, dynamic, and electronic environment changes in nanocrystals during synthesis, potentially guiding the rational design of experimental strategies to manipulate QD growth.

While techniques like scanning electron microscopy, tunneling electron microscopy, and atomic force microscopy offer exceptional spatial resolution for inspecting inner structures in quantum dots, they often fall short in providing quantitative measurements of environmental changes in Cd and Se atoms, e.g., electronic structure or local structure18,20,21,22,23. X-ray diffraction is powerful in providing atomic coordinates, but requires superior sample quality and careful statistical analysis, especially for small clusters that lack long-range periodicity due to their small size. Moreover, the periodicity requirements of diffraction techniques often blind them to heterogeneous surface interactions with ligands crucial for growth control and nanocrystal stabilization.

Nuclear magnetic resonance (NMR), widely employed for deriving atomic-resolution information across diverse systems24,25,26, has emerged as a powerful tool for studying quantum dots, and especially their surface ligands27,28,29,30,31. Information derived from NMR, such as chemical shift and chemical shift anisotropy (CSA), encapsulates rich details about chemical bonding, electronic/molecular structure, and lattice dynamics. Despite its high tolerance for sample inhomogeneity, the low sensitivity of conventional NMR has generally limited its utility in semiconductor nanocrystal studies, particularly for nuclei with low gyromagnetic ratios and at natural isotopic abundance, and long T1 relaxation times, which limit the experimental repetition rate23,24,25,32,33,34. Dynamic Nuclear Polarization (DNP) Solid-State NMR (SSNMR) circumvents this sensitivity issue by transferring electron polarization to nuclei, leveraging the larger Boltzmann population of electron spin. This signal enhancement, reaching up to 660-fold for 1H35, compresses months-long NMR experiments into days, vastly expanding its applicability across various systems28,36,37,38,39,40. The high sensitivity enables the optimization of NMR experimental conditions on the studied samples and opens up possibilities for conducting multidimensional NMR on naturally abundant samples. Additionally, the reduced T1 relaxation times due to the presence of radicals allow for much faster acquisition rates. Recent advancements in DNP sample preparation and pulse sequence design have significantly enhanced NMR performance for materials samples. These improvements enable multidimensional experiments that probe nuclear connectivity and separate isotropic chemical shifts from chemical shift anisotropy (CSA), providing valuable site-specific structural insights in various materials, including CdS, CdSe, and CdTe nanocrystals and nanoplatelets.

Materials in the CdX (X = O, S, Se, Te) family have been studied by SSNMR using 113Cd chemical shifts to elucidate their ligation environments27,28,32,33,36,41,42,43,44,45. We compile recent 113Cd chemical shift data in Fig. 1. The selection of chalcogen ligands (X) significantly affects the chemical shift in CdX4 compounds, with increasing shielding from S to Se, Te, and O. This counterintuitive trend has been theoretically explained by the paramagnetic deshielding effect counterbalancing the shielding from spin-orbital coupling36. Cd isotropic chemical shifts have been widely used to differentiate Cd environments in various contexts, including distinguishing core and surface Cd in CdSe quantum dots and nanoplatelets32,38,40, and even tracking the growth of different Cd sites during deposition procedures36. Recent studies have revealed heterogenous ligand binding modes on QD and nanoplatelet surfaces, observable via 13C NMR and infrared spectroscopy41. Similarly, 113Cd chemical shifts reveal different Cd binding modes, for example, contrasting carboxylate ligands in chelating (CdSe2O2), bridging (CdSe3O), and tilting (CdSeO3) configurations28. (Fig. 1) Non-chalcogenide ligands, like amines, have also been used in CdSe synthesis. 113Cd chemical shifts have been reported for (CdSe)13 clusters passivated with amine in a recent study42. Given the emerging diversity in the ligation and structures of quantum dots and related materials, many moieties remain unexplored by NMR. Here, we investigate new moieties and demonstrate the utility of 113Cd chemical shifts in probing the local environment.

Fig. 1: A survey of 113Cd chemical shift data in various nanomaterials.
figure 1

We analyzed several Cd-binding moieties, including those involving chalcogen and nitrogen-based ligands. The new moieties introduced in this study are highlighted with red squares. For example, the CdSe2NO moiety represents a coordination of Cd with two Se atoms, one N atom, and one O atom. Notably, 113Cd chemical shifts are highly indicative of binding environments. Detailed experimental values, including chemical shifts, chemical shift anisotropy, and corresponding literature references, are provided in Supplementary Table 1.

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CdSe atomically precise clusters (containing well-defined atoms)46, also known as “magic size” clusters47, are hypothesized to be kinetically trapped intermediates in nanocrystal formation (Fig. 2); they can further grow into nanocrystals or nanoplates under specific conditions46,48,49. Meanwhile, etching with butylamine can convert nanocrystalline CdSe samples into smaller clusters50. Specific changes in electronic and molecular structure over the transition between magic size clusters and mature nanocrystals are of great interest. Such insights will enable the discovery of new strategies to control size distribution and nanocrystal chemistry generally. Structural studies of atomically precise clusters are few in the literature40,45,51, despite their immense potential. Motivated by the available detailed structures of these systems, and by their chemical reactivity, we attack the central question of identification of the NMR peaks for specific atoms in the cluster. Here, we demonstrate that Cd atoms with different ligands exhibit distinctive chemical shifts, enabling us to uncover the ligand distribution on the cluster surface. Our findings highlight the critical role of molecular forces, such as hydrogen bonding and steric clashes, in determining ligand distribution.

Fig. 2: Energy profile of CdSe QD growth.
figure 2

An energy of formation profile is presented along number of atoms per crystal, with structural models of CdSe350nm, CdSe408nm nanoclusters as metastable intermediates, and the 2.8 nm mature QD as the final product.

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Results and discussion

Structural models of the atomically precise CdSe clusters are depicted in Fig. 2 as we determined from single crystal X-ray diffraction and pair distribution function analysis as described earlier47. With edge lengths from 1.7 to 2.6 nm, each cluster features a tetrahedral, Zinc Blende (ZB, a common crystal structure in QD with a cubic lattice) cadmium selenide core enriched in cadmium, surrounded by a layer of benzoate and N-butylamine ligands. The precise formulas derived from solution NMR and Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) and well-defined structures of these clusters significantly facilitate the analysis of NMR spectra47. The clusters are denoted as CdSe350nm and CdSe408nm, respectively, based on their maximum absorption wavenumbers (i.e., 350 nm and 408 nm). Their formula, number of ligands, and coordination sites are summarized in Supplementary Table 2. Additionally, we present the structural model of a spherical nanocrystal with a diameter of 2.8 nm, representing the oleic acid-capped CdSe QD studied in this work (Supplementary Fig. 1).

An improved sample preparation method for successful material DNP studies

In DNP experiments, a radical, often a nitroxide biradical, is combined with the sample to provide an exogenous source of unpaired electrons. Continuous microwave radiation facilitates the transfer of electron polarization to nearby nuclei through the cross effect52. To achieve successful NMR signal enhancement, meticulous sample preparation is crucial. Direct polarization transfer from polarizing radicals to nearby nuclei is limited to a short range, typically within a few nanometers, due to dipolar coupling; polarization then propagates via spin diffusion, usually through the solvent, which can extend over much greater distances53. Nevertheless, the diffusion length is constrained by the proton T1 (a few seconds in many samples) and the solvent’s deuteration level. Homogeneous mixing of the sample with the radical ensures uniform polarization transfer to the sample, thereby improving the overall enhancement.

A common radical impregnation procedure for preparing DNP samples involves soaking solid samples with a radical solution to impregnate the samples with radicals. However, this impregnation procedure often results in heterogeneity due to insufficient mixing, and separation may occur during cooling, as DNP experiments are typically conducted at around 100 K. This challenge is frequently tackled by utilizing host materials such as silicon dioxide or hexagonal boron nitride for the radical-sample mixture, preventing separation during cooling and improving microwave efficiency to achieve significant enhancements37,38. However, the presence of host materials reduces the effective sample volume within the NMR rotor38. After optimizing the ratio of sample to host material and refining preparation procedures, a balance has been achieved between DNP enhancement and sample loading, improving overall sensitivity37.

Initially, we used the radical impregnation procedure by preparing an AMUPol solution in a 1:9 protonated/deuterated toluene mixture and adding it to powder samples without host materials. However, we observed a low enhancement factor, which we attribute to insufficient and inhomogeneous mixing of the added radicals. The bulky structure of radicals may cause limited diffusion of radicals through the samples. To overcome this, we implemented an alternative preparation method (Fig. 3a). Using the same protonated/deuterated toluene (ratio 1:9) as a solvent for AMUPol, we dissolved the radical and then added samples in small increment into the radical solution to attain a well-mixed, homogenous solution-like consistency. This approach was particularly effective for CdSe materials, as toluene is a commonly used solvent for these samples. The 90% deuterated toluene provided an optimal balance between facilitating spin diffusion and minimizing proton relaxation effects from protonated methyl groups, which could otherwise reduce DNP enhancement. Additionally, using toluene as a “native” solvent, instead of alternatives like tetrachloroethane, allowed us to study CdSe materials in a more representative environment.

Fig. 3: An optimized DNP-NMR sample preparation method for studying CdSe materials.
figure 3

a The general sample preparation procedure used in this study to prepare DNP-NMR samples. b–d Examples of significant signal enhancements on 1H (both 16 scans), 13C (both 16 scans, CP Experiments) and 113Cd (both 4096 scans, CP Experiments) using DNP-NMR, comparing spectra with the microwave source on and off. Source data are provided as a Source Data file.

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The DNP enhancements achieved using this protocol are shown in Fig. 3b–d; they are comparable to or slightly lower than those reported for host-based methods. However, the lower enhancement can be compensated for by high sample loading in the rotor; the high loading of studied materials is evidenced by the observation of 113Cd signals with the gyrotron off (Fig. 3d); the overall high sensitivity enables us to easily optimize experimental parameters (using 8-128 scans) and acquire high signal-to-noise (S/N) spectra. (For example, in Fig. 3d, with 2.8 h acquisition with 2.5 s pulse delay, the 113Cd peak at −20 ppm has S/N~300.) The high S/N facilitated confident spectrum fitting to extract NMR information. It is also worth noting that the advantage of not using host materials is even more prominent in Fast MAS studies, where even smaller rotor diameters are used.

NMR reveals symmetric and asymmetric bonding in the core and on the surface, respectively, in the mature QD

We initiated our measurements by examining 113Cd nuclei on the mature oleate-capped QDs. Opting for ZB-quantum dots with a mean diameter of approximately 2.8 nm ensured comparability in size to the largest cluster, CdSe408nm, with an estimated tetrahedral edge length of 2.567 nm. Similar CdX QD with different sizes or shapes or chalcogen element X have been studied through 113Cd NMR, identifying Cd atoms in the core or on the surface through 113Cd-13C, 113Cd-77Se and 113Cd spin diffusion experiments28,37,38,40. Similarly, we identified two major Cd environments in the mature QD sample, corresponding to core and surface Cd atoms (Fig. 4).

Fig. 4: Spectral assignments for core and surface Cd atoms in QD.
figure 4

a Comparison of Direct Excitation (DE, red) and 1H-113Cd cross-polarization (CP, blue) spectra for the 2.8 nm QD. Peaks corresponding to core Cd, surface Cd, and starting material Cd oleate are labeled as #1, #2, and #3, respectively. Spinning sidebands are indicated with asterisks. b Illustration showing how Cd atoms near ligands exhibit higher CP efficiency in the 1H-113Cd CP experiment. c The spectrum was fitted to extract the chemical shift and chemical shift anisotropy (CSA). Full fitting parameters and results can be found in Supplementary Fig. 2. Source data are provided as a Source Data file.

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To further confirm the assignments of these two environments, we applied a common solid-state NMR technique by comparing the 113Cd spectra obtained using direct excitation (DE) on 113Cd nuclei (in red) and through cross-polarization (CP) transfer from nearby 1H to 113Cd (in blue). The surface Cd, located near ligands containing 1H, exhibited high 1H −113Cd cross-polarization efficacy, resulting in amplified surface signal as compared to the core signal in 1H-113Cd CP spectra (Fig. 4a, blue), making use of the large gyromagnetic ratio and polarization of 1H. Similar strategies have proven effective in many non-DNP SSNMR studies32,33,34. Direct enhancement of 113Cd, on the other hand, results in spectra with a dominant signal from the core, due simply to the larger proportion of core sites in the sample. The effective depth for direct polarization transfer from the solvent has been shown by previous DNP studies to approach 40 Å (4 nm)54, which, for the sizes of QD used in the current study, allows effective polarization of the entire core. In the CP spectrum, we observed surface Cd, characterized by the isotropic peak and spinning sidebands, as well as the core Cd, assumed to be layers underneath the surface due to short-ranged 1H −113Cd polarization transfer. In the DE spectrum (Fig. 4a, red), we observed an intense peak for core Cd and very weak signals for surface Cd. We noted a slightly shifted center and broader linewidth for the core Cd peak compared to the CP spectrum.(Fig. 4a, peak #1 expansion) We attribute this to the fact that CP probes core atoms with only a limited penetration depth, while DE can probe the full ensemble of core Cd atoms. Despite being highly similar in structure, i.e., both representing a CdSe4 moiety, the interior core Cd do show a slight chemical shift perturbation compared to core Cd close to the surface.

The core Cd peak exhibited no spinning sidebands at 8 kHz magic angle spinning (MAS), indicating minimal chemical shift anisotropy (CSA). CSA, intrinsic to chemical bonding, suggests that the chemical bond environment of the Cd atoms is highly symmetric for the core Cd atoms, consistent with the tetrahedral bonding geometry with Se atoms. Conversely, the surface Cd displayed a large CSA, evidenced by the presence of many spinning sidebands. Experiments were conducted at MAS rates of 8, 11.111, and 13.333 kHz in order to distinguish the isotropic peak from the spinning sidebands. Since the isotropic peak position is invariant with respect to the MAS rate, but spinning sidebands are spaced at integer multiples of the MAS rate, the latter can be easily identified by their apparent motion in the spectrum as the MAS rate is altered. (Supplementary Fig. 2). Quantitative spectral fitting revealed the following parameters: for core Cd, δ(iso) = −52.2 ppm, | Δ | <10 ppm, η < 0.05; for surface Cd, δ(iso) = −312.2 ppm, Δ = −255.6 ppm, η = 0.79. (Fig. 4c, Supplementary Table 3, all 113Cd shifts referenced to Me2Cd). Values for both sites are very consistent with previous studies, including those where different sizes or shapes of CdSe materials were examined (Fig. 1)19,32,38,41. Such a result suggests that 113Cd chemical shifts are highly sensitive to their local environment, i.e. distinguishing core and surface, but less sensitive to global structure. The large values of CSA parameters, Δ and η of surface Cd indicate that their local electronic environment is notably asymmetric. These surface Cd atoms are hypothesized to be located at the dominant {100} facet, bonding with two Se atoms and two oxygen atoms from the carboxylate group in the ligand28,41.

Additionally, we measured 77Se spectra by DE and 1H-77Se CP. Similarly, we discerned the surface and core Se atoms, with chemical shifts of −524 ppm and −614 ppm, respectively (Supplementary Fig. 3; all 77Se shifts are referenced to Me2Se). Such assignments agree with previous reports made based on 77Se spin diffusion experiments to distinguish core and surface Se28. The observed Se chemical shifts are indicative of the ZB structure rather than the Wurtzite structure38 as expected for the QDs used in this study. In addition to the two major peaks, we observed another broad up-field peak, which can be decomposed into two peaks centered at −656 and −701 ppm (Supplementary Table 4). We cannot confidently assign these minor peaks; we tentatively attribute them to heterogenous surface Se at other types of facets. Se atoms in Site 4 show a considerably large CSA value, indicating that they might be uncoordinated.

Spectral assignments in Cluster408nm reveals ligand distribution

Next, we investigated the larger CdSe cluster, CdSe408nm, which has an edge length of 2.6 Å and a slightly smaller volume than the spherical 2.8 nm QD. The formula for CdSe408nm is Cd84Se56X56L56, where X represents benzoate and L represents N-butylamine. We recorded both DE and 1H-113Cd CP spectra for 113Cd nuclei. (Fig. 5a–d) We again collected spectra at different MAS frequencies to exclude spinning sidebands and determine three major isotropic shifts, at −22, −164, and −236 ppm (Fig. 5a–c). Assigning these peaks was possible by analyzing the structural model of CdSe408nm (Fig. 2), which has 84 cadmium atoms in four types of Cd environments: vertex (4), edge (30), face (40), and interior (10). The diversity of atom types is further complicated by the presence of two ligand types, benzoate and N-butylamine, that coordinate surface Cd atoms using oxygen and nitrogen atoms, respectively.

Fig. 5: Spectral assignments for distinctive sites in CdSe408nm.
figure 5

a–c1H-113Cd CP spectra recorded at various magic angle spinning (MAS) speeds, along with fitted spectra for four distinct Cd environments. Root-Mean-Square (RMS) values were calculated to quantify the differences between the experimental and fitted spectra. The solid red line represents the experimental spectrum, while the dashed black line corresponds to the synthesized spectrum, combining the fits for various sites. The difference spectrum between the experimental and synthesized spectra is shown as a red solid curve in the lower panel with a dashed blue line as the baseline at 0. d113Cd DE spectra recorded at 13.333 kHz, along with the corresponding fitted spectra. Experimental, synthesized, and difference spectra are displayed in the same format. Details on the fitting procedure are provided in the experimental section, and the fitting results are summarized in Supplementary Table 5. Source data are provided as a Source Data file.

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Despite this complexity, we assigned the first isotropic peak at −22 ppm to the interior and face Cd atoms bound to N-butylamine. We base this assignment on the following observations:

  1. 1.

    The interior atoms have a highly similar chemical bonding environment to the core Cd atoms in mature QD. We observed significant signals from interior Cd in the QD sample in both DE and CP experiments (Fig. 4a). Similarly, we expect interior Cd atoms in the clusters to be polarized and contribute to the observed signal. As the majority of interior Cd atoms in the clusters are located one layer beneath the surface, they fall within the expected range for direct polarization transfer from radicals in DE experiments and 1H −113Cd cross-polarization in the CP experiment54. The isotropic chemical shift for the core Cd in the 2.8 nm QD is −52.2 ppm, which is closest to −22 ppm. Therefore, we assign this peak to the core Cd atoms.

  2. 2.

    The interior Cd atoms alone cannot account for the intensity of this peak since they constitute only 11.9% of the total Cd atoms. Peak intensities on the DE spectrum should semi-quantitatively represent Cd atom stoichiometry. Considering the depth from the surface and distance from the ligands and polarizing radicals, the relative signal intensity of interior Cd atoms should be lower than the stoichiometric ratio of interior and surface atom types. However, the peak in question comprises approximately 56.4% of the total signal, as calculated by peak integration on the DE spectrum, suggesting that it must contain intensity from surface atoms. The face Cd atoms have the closest chemical environment to the core Cd, with three sites bonded with Se and one site coordinated with a ligand. The combined percentage of face and center Cd atoms (59.5%) closely matches the peak intensity (56.5%). We later discovered that only face Cd ligated with N-butylamine exhibit matching chemical shifts, and these are the dominant type of face Cd atoms (see below).

To support our hypothesis, we conducted density functional theory (DFT) calculations on the NMR parameters of smaller pyramidal cluster that is missing corner cadmium atoms and only contains face and edge Cd atoms (Fig. 6a). Previous studies have shown that calculated 113Cd chemical shifts are in excellent agreement with experimental values for various Cd compounds, including CdSeO3, CdSe2O2, and CdSe3O moieties on the CdSe QD surface (Fig. 1)55,56. In this model cluster, the face Cd atoms were ligated with N-butylamine, while the edge ones were ligated with one N-butylamine and one benzoate. Chemical shifts are calculated for individual Cd sites as shown by the solid bars (Fig. 6b); Gaussian distributions were fitted to core and surface sites to extract averages and standard deviations. The average of the face Cd (−38 ppm) closely matches the experimentally observed resonance (−22 ppm), supporting our assignment of this peak to both face and interior Cd atoms. Previous studies of a similar CdSe3N moiety, present in (CdSe)13 clusters, reported chemical shift between −60 and −70 ppm; considering the nearly 1000 ppm-wide chemical shift range of 113Cd and the variation in coordination geometry, the similarity is consistent with our observed values42.

Fig. 6: DFT calculations-assisted Cd chemical shift assignments.
figure 6

a The cluster model used for DFT calculations of NMR parameters, where face Cd atoms are shown in purple and are ligated with N-butylamine, while edge Cd atoms are shown in yellow and are ligated with both N-butylamine and benzoate. Se atoms are omitted for clarity. b DFT calculation results for ¹¹³Cd chemical shifts of the face (purple) and edge Cd (yellow) atoms, fitted to Gaussian distributions with corresponding mean and standard deviation. Source data are provided as a Source Data file.

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We conducted further quantitative analysis of the CP and DE spectra by fitting them with four Cd sites, two of which are the interior Cd and face Cd with N-butylamine, as discussed above. Utilizing spectra acquired at multiple spinning speeds, we restrained the fittings by employing the same NMR parameters to fit all spectra in order to prevent overfitting (Fig. 5a–d). The fitted peak for the interior Cd is highlighted in gray, and the fitting results are as follows: δ(iso) = −22 ± 2 ppm, | Δ|<10 ppm, |η|<0.05. The upbound of | Δ | and |η| values here are chosen arbitrarily to reflect a minimal chemical shift anisotropy due to the symmetric bonding environment in interior atoms.

The fitted peak for the face Cd is highlighted in blue, and according fitting parameters are as follows: δ(iso) = −22 ± 2 ppm, Δ = 156 ± 5 ppm, η = 0.4 + 0.1/−0.2. The calculated Δ is 189 ± 27 ppm, and η is 0.4 ± 0.1, both of which are consistent with experimental values. Despite similarity in isotropic shift for face and interior Cd, the face Cd shows considerably larger CSA as it has an asymmetric bonding environment due to coordination with the nitrogen atom in N-butylamine.

The third fitted peak, highlighted in red, has an accurately determined isotropic chemical shift; however, due to weak intensity and overlap with nearby peaks, its CSA parameters cannot be confidently fitted: δ(iso) = −164 ± 5 ppm, | Δ|<150 ppm, |η|<1. The fourth fitted peak, highlighted in green, has the following fitting parameters: δ(iso) = −236 ± 5 ppm, Δ = −158 ± 15 ppm, |η|<0.6.

We assigned the peak at −164 ppm to the face Cd atoms coordinated with benzoate. The CdSe3O moiety is similar to previously reported surface Cd atoms with a bridging carboxylate group (Fig. 1), whose reported chemical shift (~−150 ppm) closely matches the observed −164 ppm. We also used DFT to calculate the chemical shifts of this environment based on the simplified model but with benzoate on the face; however, the calculated chemical shifts for the four face sites show a large deviation, indicating that our model is either trapped in a local minimum during geometry minimization or intrinsically unstable. However, a recent DFT calculation based on a more simplified model of the CdSe₃O moiety, employing spin-orbital levels and the ZORA Hamiltonian (consistent with our theoretical approach), yielded a value of −129 ppm, close to the observed −164 ppm55.

We assigned the peak at −236 ppm to edge Cd atoms coordinated with one benzoate and one N-butylamine. The chemical shifts of such Cd atoms were calculated to be −222 ± 35 ppm (Fig. 6b), consistent with the observed fourth peak at −236 ppm. We ruled out other models, such as edge atoms with two N-butylamine or two benzoate ligands.(Supplementary Discussion) There is no published experimental data for the Cd2N2 moiety, but, for the Cd2O2 moiety, Cd atoms with a similar configuration shown in Fig. 1 have a chemical shift between −310 and −322 ppm.

We also measured 77Se spectra and fitted them for the cluster (Supplementary Fig. 4, Supplementary Table 6). Overall, the spectra are quite congested; site-specific assignments of these peaks have not been performed due to extensive peak overlap and limited experimental data available for referencing.

Validating chemical shift assignments with Cluster350nm

We then investigated the smaller cluster, Cluster350nm, with an estimated edge length of 1.7 nm. The formula for this system is Cd35Se20X30L30, where X represents benzoate and L represents N-butylamine. The structure model shows that it has a vertex (4), an edge (18), a face (12), and an interior (1). The 1H-113Cd CPMAS spectrum shows two major peaks at −20 ppm and −260 ppm. (Fig. 7) The first peak is very close to the −22 ppm peak for the interior and face Cd in the cluster408nm. Therefore, we assign this peak also to the interior and face Cd with N-butylamine. Since there is only one interior Cd in Cluster350nm, this validates our previous assignment of this peak to both interior and face Cd to account for this most intense peak.

Fig. 7: Spectral assignments for distinctive sites in CdSe350nm.
figure 7

1H-113Cd CP spectra of CdSe350nm at 8.4 kHz (red solid line) and 11 kHz (blue solid line). The 8.4 kHz spectrum is fitted with four distinct Cd environments, represented as blue (face Cd), gray (interior Cd), green (edge Cd), and red (potential vertex Cd). The overall fit is shown by the black dashed line. The line at −164 ppm emphasizes the absence or minimal presence of a peak at this position in the 11 kHz spectrum, in contrast to CdSe408nm. Detailed fitting results are provided in Supplementary Table 7. Source data are provided as a Source Data file.

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The other peak is at −260 ppm, close to the peak (−236 ppm) assigned to edge Cd coordinated with one benzoate and one amine in Cluster408nm. Though it is somewhat shifted, we still assign this peak to the edge Cd coordinated with benzoate and amine. We attribute the slight chemical shift perturbation to different ligand packing as cluster size decreases, leading to variation in bond length or angle between Cd and N/O atoms, especially considering the bulky side chain in both types of ligands.

In Cluster350nm, we observe minimal or no peak at/around −164 ppm, which would correspond to face Cd coordinated with benzoate. This is especially evident in the 11 kHz MAS spectrum; at 8 kHz, an overlap of spinning sidebands falls in this region (Fig. 7). This suggests that there is little or no Cd in such an environment in Cluster350nm. Notably, Cluster350nm has only 3 face Cd compared to 10 in Cluster408nm, and the space available on each face is much smaller. The rigid, bulky phenyl side chain of benzoate may cause steric clashes due to the limited space, making such ligation less likely. This ligand arrangement on the facets is consistent with a model displaying the lowest energy in a quantum mechanics (QM) calculation51. (To be discussed later)

Quantitative fitting of the spectrum shows that the CSA parameters of the face and edge Cd are quite similar to those seen in CdSe408nm (Supplementary Table 7), indicating that these two types of Cd share a similar electronic environment with their counterpart in Cluster408nm (Supplementary Table 5).

To further validate our proposed model, we performed a 1H-15N CP experiment using room-temperature NMR to probe the 15N chemical shift of the N-butylamine ligand bound at various sites (face vs. edge).(Supplementary Fig. 5) The spectrum reveals a single broad peak (Full-Width at Half Height: 8.65 ppm) at 30.5 ppm. This result indicates that the 15N chemical shift is insufficient to differentiate slight variations in the Cd environments to which the nitrogen is bound. This observation is consistent with the behavior of the Cd(benzoate)2(N-butylamine)2 compound, where the Cd atom has six coordination sites instead of four, yet the 15N chemical shift changes by only ~2 ppm. We anticipate that multinuclear multidimensional NMR experiments, capable of correlating signals from different ligands or their bound Cd atoms, could provide valuable validation of our model. However, such experiments require isotopically labeled ligands, which we will attempt to produce for future investigations.

Ligand distribution models and HB network

Based on our experimental findings, we propose ligand distributions for both clusters. For the CdSe350nm cluster, all face sites are coordinated with flexible N-butylamine ligands to prevent steric clashes. The edge sites are coordinated with one N-butylamine and one benzoate each, while the vertex sites are coordinated with three benzoate ligands (Fig. 8a). We also show that such a distribution is the only model consistent with our experimental and computational results.(Supplementary Discussion: Ligand distribution model validation) The ligand distribution in the CdSe408nm cluster is similar except for face Cd. NMR analysis suggests that some face Cd atoms coordinate with benzoate ligands. We distributed the benzoate ligands across the face sites to maximize the number of hydrogen bonds formed between benzoate and N-butylamine (Fig. 8b, details discussed below). Although we have limited experimental data on ligand coordination at the vertex sites, modeling of the vertex Cd atoms results in sufficient space for them to be able to coordinate with three benzoate ligands without inducing steric clashes.

Fig. 8: Ligand distribution models.
figure 8

Proposed ligand distribution models for CdSe350nm (a) and CdSe408nm (b) based on NMR-derived restraints, are shown. A close-up view highlights the potential hydrogen bond (HB), with the corresponding distance between H and O atoms labeled, between X (benzoate) and L (N-butylamine) on the surface of the CdSe408nm cluster.

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Previous QM computation studies have shown that HB networks significantly enhance the thermodynamic stability of clusters51. However, performing QM geometry optimizations to accurately evaluate HB networks in large clusters is challenging due to the high flexibility of ligands and the complexity of the energy landscape. As a result, using QM-calculated HB numbers as an energy function to explore ligand distribution space and identify configurations that maximize HB formation is computationally prohibitive. To efficiently estimate the number of HBs, we developed an algorithm that counts: (1) intra-HBs (where X and L ligands are bound to the same Cd atom) and (2) inter-HBs (between X and L ligands on adjacent Cd atoms). For inter-HBs, we restricted the count to one HB per adjacent Cd pair. Using this algorithm to compute the number of HBs as an energy function, we performed a Monte Carlo simulation to assign ligands on the CdSe cluster surface, maximizing HB formation without experimental restraints. The maximum HB configurations yielded 114 and 226 HBs for CdSe350nm and CdSe408nm, respectively. Applying the same algorithm to calculate HBs in our proposed models (Fig. 8a, b), we found 102 HBs for the CdSe350nm model and 220 HBs for the CdSe408nm model. These results suggest that while our proposed models do not achieve the maximum possible HB formation, they nonetheless support extensive HB networks, particularly in the case of CdSe408nm, where space constraints are reduced.

Our model for the CdSe350nm cluster aligns closely with a previously proposed model based on energy minimization (EM) among a few candidates51. In the EM study, the most stable isoform of Cd35Se20X30L30 (X = formate, L = ammonia) shows a configuration with three L ligands on the face, seven X ligands and five L ligands on the edge, and two X ligands and one L ligand on the vertex. Our model differs by swapping one X ligand from the edge with one L ligand on the vertex. This difference could be attributed to the smaller ligands used in the EM calculations. Our assignment is supported by the absence of a characteristic peak around −310 ppm for the CdSe2O2 moiety, which would be expected in the EM model but not in our NMR-derived model.

In conclusion, in this study, we demonstrated that the 113Cd chemical shift serves as a unique probe for distinguishing different sites in CdSe nanomaterials. We successfully addressed a key challenge in assigning experimental 113Cd chemical shifts to well-defined Cd environments in atomically precise CdSe clusters with the help of quantum mechanical calculations, supplemented by previous experimental results in similar environments. The newly obtained chemical shift data for these novel moieties will aid in the structural assignment of related systems in future research. Furthermore, we used 113Cd chemical shifts to tackle the complex problem of determining ligand distribution on the surface of CdSe clusters. Our findings indicate that hydrogen bonding and steric clashes are key drivers of ligand arrangement, with flexible amine ligands being favored in the facets when spatial constraints are present in small clusters. Our work paves the way for exploring structural transitions from clusters to mature QDs, as we provide chemical shift information for both states. We anticipate that future studies will leverage 113Cd chemical shifts to dynamically monitor structural changes and investigate how growth conditions influence growth.

Methods

Cluster and QD synthesis

Atomically precise CdSe350nm, CdSe408nm tetrahedral clusters were synthesized from cadmium benzoate and bis(trimethylsilyl)selenide according to Beecher et al. 47 Following Hamachi et al. 57, 2.8 nm CdSe nanocrystals were synthesized from 1,3-diphenyl-2-imidazolidineselone (0.150 mmol, 1.0 equiv), cadmium oleate (0.180 mmol, 1.2 equiv,) and oleic acid (0.360 mmol, 2.4 equiv.). The morphology of QDs is shown in TEM image in Supplementary Fig. 1. The absence of precursors, such as cadmium benzoate or Cd(benzoate)₂(N-butylamine)₂, in the cluster samples can be confirmed by the lack of peaks at the corresponding chemical shifts in the 113Cd NMR spectra. Chemical shifts for cadmium benzoate and Cd(benzoate)₂(N-butylamine)₂ can be inferred from Fig. 4a and Supplementary Fig. 6, respectively.

DNP sample preparation

All samples were packed into 3.2 mm sapphire rotors (Bruker Corp.), sealed using silicone rubber disks specifically adapted for the rotor size, and finally capped with zirconia drive caps optimized for cryogenic operation. Samples were packed and sealed in a glove box under a nitrogen atmosphere to prevent sample oxidation. AMUpol dissolved in 90% deuterated toluene served as the DNP polarization reagent. 30 μL of 20 mM AMUPol radical solution was added to a mortar, and 20–30 mg of powder-form CdSe samples were gradually introduced in small increments to ensure full dissolution. The resulting mixture was highly homogeneous and solution-like. Subsequently, the mixed solutions were carefully pipetted into 3.2 mm sapphire Bruker rotors. The total sample weight ranges from 20 mg to 30 mg, with radical concentrations ranging from 8.8 mM to 17.8 mM across various samples, determined using an EMX Nano Benchtop EPR spectrometer(Bruker). These prepared samples were stored at 4 °C prior to DNP-NMR measurements.

DNP-NMR experiments

DNP experiments were conducted on a Bruker 9.4 T (equivalent to 400 MHz for 1H) spectrometer equipped with a Neo console. A 3.2 mm HXY triple-channel probe was configured in HX mode and tuned accordingly to facilitate 1H, 13C, 113Cd, and 77Se experiments. The sample temperature was maintained at approximately 100 K, with samples spun at various spinning speeds (i.e., 8 kHz, 11.111 kHz, 13.333 kHz). The typical pulse powers were 100 kHz (50 W) for 1H, 62.5 kHz (37 W) for 13C, 62.5 kHz (55 W) for 113Cd, and 62.5 kHz (65 W) for 77Se. Direct excitation experiments were performed using a 90° excitation pulse followed by echo detection with a rotor-synchronized echo delay (two rotor periods). All cross-polarization (CP) spectra were acquired through polarization transfer from 1H to the observed nuclei, with the CP conditions optimized at various magic-angle spinning speeds. Proton decoupling was applied using the SPINAL-64 scheme with a 100 kHz 1H RF field during all spectra acquisitions, except for 1H spectra. For more detailed information on the NMR experimental parameters for each spectrum presented, please refer to the Supporting Information (Supplementary Table 8). 113Cd T1 is measured to be approximately 1 s for cluster samples (Supplementary Fig. 7); in the direct excitation experiment, 10 s pulse delay was used to ensure magnetization fully recovered to equilibrium to improve the accuracy of stoichiometry measurements. To demonstrate sample integrity following DNP-NMR experiments, we measured UV-Vis spectra of a CdSe350nm sample before and after the NMR experiments, which showed minimal changes. (Supplementary Fig. 8)

Chemical shifts for 13C nuclei were referenced externally to the downfield adamantane line at 40.48 ppm, while chemical shifts for other nuclei were referenced accordingly by calculation to correspond to 0 ppm for DSS in D2O (1H), Me2Cd (113Cd), and Me2Se (77Se). Spectra were processed using Topspin 3.6.0 and plotted using the nmrglue software58. The orientation-dependent chemical shift anisotropy (CSA) was determined by the inequality |δzz−δ(iso)|≥ |δxx−δ(iso)|≥ |δyy−δ(iso) |. Based on this expression, δ(iso), Δ, and η were calculated as follows: δ(iso) = (δxx + δyy + δzz)/3, Δ = δzz−δ(iso), and η = (δyy - δxx)/Δ.

Spectrum fitting

The fitting of the 113Cd spectra was conducted in Topspin utilizing the sola module and verified with SIMPSON spectrum simulation59. To determine the number of sites to be included in the fitting, we compared 113Cd spectra taken at various spinning speeds to identify the isotropic chemical shift, as spinning sidebands move with changes in spinning speed. For the peak centered at −22 ppm, two isotropic chemical shifts corresponding to the core and face Cd atoms, as detailed in the main text, were used to fit. Once the isotropic chemical shifts were fixed, spectra taken at 8 kHz were utilized to fit the chemical shift anisotropy (CSA) information, as they contained more spinning sidebands than spectra acquired at higher MAS rates and thus better preserved the CSA information. The initial values of the CSA parameters, peak intensity, and line broadening parameters were manually adjusted to roughly match the experimental spectra. Subsequently, the Simplex algorithm was applied to optimize the fitting. Both Lorentzian and Gaussian broadening were applied to fit lineshapes. The derived CSA parameters were then employed to fit spectra taken at 11.111 and 13.333 kHz, with variables only in peak intensities and line broadening parameters. All fittings were evaluated by calculating the root-mean-square (rms) value of the normalized fitting and experimental spectra. The successful fitting of spectra taken at various spinning speeds with the same set of isotropic and CSA parameters significantly bolstered confidence in the extracted NMR parameters. Fitting errors were estimated to have a 2% influence on the overall fitting by varying each parameter individually.

DFT calculation

DFT calculations of 113Cd NMR parameters were conducted using ORCA (5.0.3)60. Given the computational challenges associated with heavy atoms like Cd and Se, direct calculations on the clusters, even the smaller ones, are computationally expensive. As an alternative, we constructed smaller CdSe structure models comprising only the face and edge Cd atoms.(Fig. 6a) These models were employed to investigate the effects of different ligands on Cd chemical shifts by generating models with varying ligand distributions. Subsequently, all structure models underwent QM geometry optimization. DFT calculations were then performed using the PBE0 functional with ZORA relativistic correction55 and SARC/J method for NMR calculations. The basis sets employed for different elements were as follows: hydrogen, carbon, nitrogen, oxygen: “def2-SVP, cadmium: “SARC-ZORA-TZVP”, selenium: “def2-TZVP”. The calculated nuclei shielding shift was then referenced against the calculated shielding values for model compounds Me2Cd and Me2Se before being compared to experimental chemical shifts.

Hydrogen Bond calculation and Monte Carlo Simulation

The code for hydrogen bond (HB) calculations and Monte Carlo simulations used in ligand assignment is available on GitHub (https://github.com/Xyunyao/CdSe_nmr_DFT). Both intra- and intermolecular HBs between butylamine and benzoate are counted. For intermolecular HBs between adjacent Cd atoms, only one HB is considered per butylamine-benzoate pair, since correct molecular orientation is required. We applied this HB counting function as a scoring metric, using Monte Carlo simulations and Metropolis criteria to maximize HB formation. Given the simplified HB counting algorithm, this method estimates the effectiveness of HB formation rather than identifying conformers with the maximum number of HBs.