Ryan A. Beck,Yue Huang,Alessio Petrone,Joseph W. Abbott,Peter J. Pauzauskie,Xiaosong Li
Electronic Structures and Spectroscopic Signatures of Noble-Gas-Doped Nanodiamonds
noble gas,defect,nanodiamond,Raman,UV/vis,absorption
Fluorescent nanodiamonds, that is, those containing optically active defects, have attracted interest for their ability to be used as qubits; for in vivo imaging; and as sensors for spin, stress, and temperature. One of the most commonly studied nanodiamond color centers is the nitrogen vacancy. However, there is strong interest in discovering other impurity centers that provide localized midband gap transitions. Noble gas atoms have garnered attention since they have been discovered within nanodiamonds produced through high-pressure–high-temperature laser-heated diamond anvil cell synthesis methods, where they are commonly used as hydrostatic pressure media. Noble gas atoms that exist in macrosized natural or synthetic diamonds have been shown to be able to form color centers. This research uses ab initio density functional theory and cluster models to systematically study the localized electronic structure for group VIII impurities of nanodiamond, including helium, neon, argon, krypton, and xenon. An in-depth examination of the interaction between the noble gas atom and diamond lattice has been carried out. The changes to the vibrational and UV/vis absorption spectra have been analyzed. It was determined that the energetically preferred geometry is dependent on the atom size. Most noble gas defects are stabilized within the nanodiamond lattice and exist in tetrahedral interstitial positions, except for the largest noble gas studied in this work, Xe, which was determined to prefer a substitutional configuration. Both Kr and Xe are expected to be able to manifest visible/near-IR optical responses when included in the diamond lattice.
Electronic Structures and Spectroscopic Signatures of Noble-Gas-Doped Nanodiamonds

Fluorescent nanodiamonds, that is, those containing optically active defects, have attracted interest for their ability to be used as qubits; for in vivo imaging; and as sensors for spin, stress, and temperature. One of the most commonly studied nanodiamond color centers is the nitrogen vacancy. However, there is strong interest in discovering other impurity centers that provide localized midband gap transitions. Noble gas atoms have garnered attention since they have been discovered within nanodiamonds produced through high-pressure–high-temperature laser-heated diamond anvil cell synthesis methods, where they are commonly used as hydrostatic pressure media. Noble gas atoms that exist in macrosized natural or synthetic diamonds have been shown to be able to form color centers. This research uses ab initio density functional theory and cluster models to systematically study the localized electronic structure for group VIII impurities of nanodiamond, including helium, neon, argon, krypton, and xenon. An in-depth examination of the interaction between the noble gas atom and diamond lattice has been carried out. The changes to the vibrational and UV/vis absorption spectra have been analyzed. It was determined that the energetically preferred geometry is dependent on the atom size. Most noble gas defects are stabilized within the nanodiamond lattice and exist in tetrahedral interstitial positions, except for the largest noble gas studied in this work, Xe, which was determined to prefer a substitutional configuration. Both Kr and Xe are expected to be able to manifest visible/near-IR optical responses when included in the diamond lattice.

Nanodiamonds have been the subject of intense study since the late 1990s for their potential in several applications. Their biocompatibility and ability to carry therapeutics make them excellent candidates for drug delivery, while their superior mechanical, thermal, and surface properties make them ideal materials for nanocomposite. Among the different types of nanodiamond, those which contain impurities in the diamond lattice are the most intriguing. They have the potential to form midband gap transition states arising from the presence of dopants within the diamond lattice. These so-called fluorescent nanodiamonds have potential applications for in vivo imaging and quantum computing because of their optical and spin properties. There is also demand for sensing and cryptography applications because of the high sensitivity of the intraband transitions to small changes in stress and temperature. There are more than 500 known defects that are optically active in diamond, most are due to the presence of impurity atoms within the diamond. Among them, the most common and studied nanodiamond color center is the nitrogen vacancy (NV) center. However, negatively charged silicon vacancy (SiV–) centers have started to attract more attention because of their short fluorescence lifetime and narrow zero-phonon line (ZPL) emission in the infrared range (1.68 eV). Noble gas defects are another impurity in diamond and have been reported in geological studies to be found in natural diamond, in interstellar diamonds located in meteorites (sometimes referred as presolar diamonds), and in diamonds doped through ion implantation, wherein a noble gas is commonly used as an inert environment/pressure medium. Even though commonly believed to be inert impurities in a diamond lattice, the noble gas atoms have been shown to form covalently bound defects with surrounding carbon atoms to form color centers. Group VIII atoms, helium (He), neon (Ne), argon (Ar), and xenon (Xe), have also been intentionally introduced into diamond, which results in color center formation. For example, He forms thermodynamically stable color centers, in spite of its small atomic size, with visible light range emissions around 580 nm. Among the noble gas impurities, Xe has attracted more attention as an impurity in diamond because it can couple with the vacancy in diamond and form stable defects that generate a near-infrared (IR) response at ∼1.53 eV (810 nm). The Xe color center is believed to have local D3d symmetry, where the Xe atom occupies the center of a split divacancy in diamond. The success of embedding noble gas using ion implantation is limited by the energy of the ion beam and size of the nanodiamond. Between 2001 and 2008, ionized noble gases, including He, Ar, Kr, and Xe, were successfully implanted into synthetic nanodiamonds to compare synthesized nanodiamond to presolar nanodiamond. The significance of understanding noble gas defects in nanodiamond increases as more nanodiamond synthetic methods are developed. For example, since noble gases are conventionally treated as chemically inert elements, they also are commonly used as near-hydrostatic pressure media in the high-pressure–high-temperature (HPHT) synthesis of nanodiamond. Such conditions provide the potential for these dopants to be incorporated into the synthesized nanodiamond lattice as interstitial or substitutional defects. Recently, nanodiamonds synthesized through HPHT were confirmed to have incorporated Ar. However, it is unknown if this incorporated Ar is able to introduce color centers to the nanodiamond system. Thus, a systematic study of noble gas defects in nanodiamonds is needed to help identify these centers and provide insight into their spectroscopic signatures. Despite the significance of noble gas impurities in diamond and the evidence of noble gas defects in presolar nanodiamond, there are limited theoretical studies focusing on the electronic structure and the UV/vis absorption spectra of noble-gas-doped nanodiamonds. These are needed to identify the various geometric configurations and explain why a near-infrared ZPL can be found in Xe-defected diamond but not in other noble gas diamonds. In this work, different geometric configurations of the group VIII atom nanodiamond impurities, including He, Ne, Ar, Kr, and Xe, are studied. The stability between the configurations is determined, and the vibrational Raman and UV/vis absorption spectroscopic signatures of each geometry are calculated.

In this study, nearly spherical diamond quantum dots (C182H142) were constructed using the 0.357 nm lattice parameter of bulk face-centered cubic diamond, thereby forming nanodiamond clusters with a diameter of ∼1.4 nm. This is smaller than, though approaching, experimental size. The dangling bonds on the surface of the diamond were passivated by hydrogen atoms according to the procedure described in ref (16). To construct the defect-containing nanodiamond, a noble gas atom (He, Ne, Ar, Kr, or Xe) is embedded into the nanodiamond lattice, which results in a nonsurface defect. These models have been previously shown to be effective in studying both the electronic and vibrational responses of pure and doped nanodiamond systems containing nitrogen and silicon vacancies, as well as surface defects. Since the diamond Bohr exciton radius is ∼1.6 nm, the systems in this work are expected to exhibit quantum confinement effects. All calculations were carried out using the Gaussian 16 electronic structure software package. The Kohn–Sham equation is solved using the hybrid Becke, 3-parameter, Lee–Yang–Parr (B3LYP) density functional to obtain the ground-state electronic structures, with a 6-31G(d) basis set for the carbon and hydrogen atoms. To account for scalar relativistic effects in the heavier atoms, the Stuttgart relativistic pseudopotential and associated basis sets were used for all noble gases except He and Ne, which used a 6-31G(d) basis. Geometries were considered optimized when the maximum and root-mean-square (RMS) forces were less than 0.000450 and 0.000300 hartree/Bohr, respectively, and maximum and RMS displacements were less than 0.0018 and 0.0012 Bohr, respectively. Time-dependent density functional theory (TDDFT) within the linear response framework was used to calculate the electronic structure of the excited states.

There are two categories of point defects that involve implanting a dopant into a nanodiamond, interstitial point defects (Xi) and substitutional point defects (Xs). For each category there are several different possible ways to construct the geometry of the system. Three possible geometries are used in this work, which are exhibited in Figure 1 alongside a perfect spherical nanodiamond (Figure 1a). For the interstitial point defect, the most probable location is at the highest symmetry interstitial space inside the diamond lattice at the center of one of the tetrahedrons. Since only one interstitial system is studied in this research, this system is labeled Xi, (Figure 2b). For the substitutional (Xs) defect, shown in Figure 1c, one of the carbon atoms is removed and replaced with a noble gas dopant. This leads to a local Td symmetry within the C3v symmetry of the entire cluster. The split vacancy (XiV, Figure 1d) geometry is formed when a dopant takes the center position between two adjacent carbon vacancies along the ⟨111⟩ crystallographic axis, thereby resulting in a local D3d symmetry. This is the same geometry that has been seen for other diamond defects, such as SiV. All configurations shown in Figure 1 are constructed and have their geometries optimized for each noble-gas-doped nanodiamond system. The results of the geometry relaxations are given in Figures 2–4. Figure 2 presents the geometric reorganization of the He, Ne, Ar, Kr, and Xe-doped nanodiamonds in the interstitial doping structure, Xi, compared to the pure diamond crystal lattice. Before geometry reorganization, the noble gas atom is located at the center of a symmetrical tetrahedron of the fcc structure. The distance from the noble gas to the nearest carbon RXC = 1.544 Å, and the angle ∠CXC = 109.5°. Figure 2 shows that the 3-fold symmetry along the ⟨111⟩ direction and local Td symmetry is mostly kept after relaxations both for He and Ne interstitial doping structures. Even though the expansion of the tetrahedron formed by the surrounding four carbons increases with the size of the doped atom, the doped atom is still located at the center of structure and has a similar distance to all surrounding carbons. However, for Ar, Kr, and Xe, not only is the 3-fold symmetry not kept in the ⟨111⟩ direction, but the doped noble gas moves along the ⟨111⟩ axis from the center of the tetrahedron. This results in a heavily distorted local geometry. The initial local geometry for the substitutional Xs systems is tetrahedral. Figure 3 shows that because of a larger repulsion, the lattice expansion around the noble gas dopant in the substitutional doping position is much greater than in the interstitial structure. The tetrahedral structure is already distorted for the smallest dopant, He, and the distortion increases as the dopant size increases. The strong repulsion between dopant and neighboring carbon atoms eventually leads to a relaxation toward local D2d symmetry. Figure 4 shows the optimized split-vacancy defect structures. Initial XiV systems have an RXC bond length of 1.943 Å. Unlike in the tetrahedral systems, there are three unique angles. The first ∠CXC = 80.95° is between two carbons at the same vacancy position, the second ∠CXC = 99.08° is between two carbons of two different vacancy positions, and the final ∠CXC = 180.0° is for two carbons on opposite sides of the dopant in two vacancy positions. Geometry optimization results in bond elongation because of the missing covalent bonds. The D3d symmetry is mostly maintained except for the smallest dopant, He. The He atom forms a geometry similar to the nitrogen vacancy where the He occupies a carbon vacancy position. Thus, the geometric distortion is largest for the He dopant and lowers the local symmetry to C3v from the split-vacancy structure.

To calculate the formation enthalpy for each noble gas system, we consider the following reaction:where X represents the noble gas atom in the system, n is an integer number for the quantity of carbon atoms that are removed from the system, and C182H142 and XC182–nH142 are the pure and defect-containing nanodiamond, respectively, with a H-passivated surface. The formation enthalpy ΔfH of this reaction is calculated asHere, H is the enthalpy of the system. μC and μX are the chemical potentials for the carbon and noble gas, respectively. Chemical potentials were obtained through DFT calculations, as detailed in the Supporting Information. As shown in Table 1, in general, the formation enthalpy of noble gas defects increases with the radius of the atom for all structures considered here. The same trend also has been reported in noble-gas-defected bulk diamond in earlier studies. For all noble gas defects, except Xe, the trend is ΔH(Xi) < ΔH(Xs) < ΔH(XiV). For Xe, the Xs structure is determined to have the lowest formation enthalpy. While the magnitude of the formation enthalpy increases, the difference between the various defect configurations becomes smaller (see Figure 5) as the size of the noble gas atom increases. This is mainly due to destabilization of the Xi structure as the repulsion between the noble gas atom and nearby carbon atoms increases. The change in formation enthalpy for the vacancy-containing structures (XiV) is smaller than the interstitial structure for all systems. This results in Xe having the lowest energetic differences between the possible defect structures.

Figures 6–8 show the computed Raman absorption spectra of noble-gas-doped nanodiamonds. Heavy hydrogens (100 amu) are used to remove surface-capping C–H bond vibrations from the C–C vibrational region so we can analyze the vibrational signatures of the defects. In each plot, the diamond Raman band at ∼1320 cm–1 can be observed, which indicates that the diamond lattice is maintained. A more in-depth examination of the responses belonging to pure nanodiamond can be found in ref (40). Upon examination of the Xi vibrational spectra (Figure 6), it is observed that as the size of the noble gas dopant increases, the number of active Raman modes increases. This corresponds to a lowering of the symmetry, as marked in Figure 2, which corresponds to the noble gas moving from the high-symmetry interstitial point in the diamond. Examination of the diamond Raman peak indicates that as the size of the doped noble gas increases, additional peaks separate at higher energies (>∼ 1330 cm–1). These peaks correspond to sp- and sp2-like C–C bond vibrations caused by the noble gas expanding the doping site. This expansion causes compression to the rest of the diamond lattice. Similar absorption features have been seen in response to graphitic-like structures manifesting on the nanodiamond surface. The vibrational spectra for the Xs and XiV geometries (Figures 7 and 8, respectively) show that the defects do not strongly affect the diamond vibrational band in the >1330 cm–1 range. The Xs and XiV geometries show an increase in activity in the ∼800 to ∼1200 cm–1 energy region. These responses arise because of diamond lattice modes coupling to the vibrational modes of the defect center. The Xi defects (Ar–Xe) can be seen to also contain these modes because of the distorted diamond lattice around the noble gas defect. The complex nature of the Raman spectra makes it challenging to differentiate between the different noble gases and their geometries. However, examination of these spectra is able to give interesting insights into the lattice deformations resulting from the presence of noble gas dopants.

In order to differentiate between the noble gas species, as well as the different geometries, the electronic structure is examined. Partial density of states (DOS) and predicted UV/vis absorption spectra are plotted in Figures 9–14. DOS plots have total density for both spin-up (positive values) and spin-down (negative values), as well as contributions by both the noble gas atom and surrounding nearest-neighbor carbon atoms, for intraband states plotted. The absorption spectra for each species contain the natural transition orbital (NTO) for the first, bright transition with the leaving, “hole,” orbital on the left and the arriving, “electron,” orbital on the right. In each figure, the first plot is the pure diamond for comparison. Because of quantum confinement effects, the band gap for the pure 1.4 nm diameter diamond is larger than the 5.5 eV bulk at ∼6.4 eV. For hydrogen-terminated carbon clusters, quantum confinement is mostly mediated by the valence band. Although additional virtual orbitals arising from surface hydrogens exist, they do not mix with localized defect states. Figure 9 contains the DOS for the Xi systems, which are the most stable configuration for all noble gas species except Xe. Although He and Ne color centers have been observed experimentally in bulk diamond, we did not observe any midgap states for the Hei or Nei configuration of the diamonds, which agrees with previous reports. With similar atomic sizes, He and Ne Xi defects bring similar distortion to the nanodiamond lattice. This distortion, however, does not greatly affect the band gap of the doped systems, as can be seen in Figure 9. In addition, no He or Ne contributions are observed within the diamond band since neither He or Ne are able to bond to the surrounding carbons. Therefore, the lowest energy excited states of He and Ne Xi are interband transitions, which are similar to pure diamond transitions, at ∼6 eV. This is confirmed by the TDDFT results in Figure 10a–c, where both the absorption spectra and the leaving and arriving orbitals for the pure diamond and nanodiamonds with He and Ne dopants are of the same character. The energetic values for each transition are given in Table 2 and are shown to be similar. For larger noble gas atoms in the interstitial position, lattice deformations and hybridization between the noble gas and carbon atoms give rise to midgap states. These midgap states allow for transitions lower in energy than the pure diamond band-to-band transitions at 6.43 eV. As shown in Table 2, the Kr Xi optical response is ∼0.6 eV lower in excitation energy than the Ari response (2.78 and 3.48 eV, respectively) and should be more detectable when probed by visible light. The NTOs inset into Figure 10 show these transitions to be localized around the noble gas dopant. Examination of Figures 11 and 12 for the substitutional (Xs) systems demonstrate that all of the noble gas systems are able to introduce midgap states. In the case of the small dopants (He and Ne), this is surprising because neither were able to form color centers in the Xi systems. Examination of the DOS plot, however, shows that there are no contributions to the midgap states by the noble gas. This implies that instead of the noble gas being responsible for the midgap states, it is the carbon vacancy that is responsible, and the noble gas is inactive within the defect. While the leaving orbital for Ars looks similar to both the He and Ne Xs systems, and there is little contribution to the HOMO by Ar, the arriving orbitals can be seen to have Ar character. Since both Kr and Xe Xs systems have noble gas contributions to the midgap states, Ar is the smallest noble gas that is able to participate in the electronic transition, similar to what was observed for the Xi systems. This is seen again in Figures 13 and 14 for the divacancy systems. Molecular orbital diagrams for the most stable configuration for each noble gas dopant can be found in the Supporting Information (Figures S17–S23). As shown in Table 2, the diamond systems containing Kr and Xe have absorption features within the visible energy range. Of particular interest is the XeiV system, which has two degenerate transitions at 2.20 eV originating from the highest occupied molecular orbital to the two degenerate molecular orbitals (Figure 14f). These transitions echo previous literature that has examined the Xe color center in diamond. However, in our case, these responses have been blue-shifted from their value of 1.53 eV because of quantum confinement effects, similar to what has been seen before for nanodiamond systems. While not predicted to be the ground state, the small difference in formation energy for the Xe center between different configurations in relation to the energy required to form the defect means that multiple geometries are expected to be able to form. Since the ZPL energy of Xe is comparable to the other widely studied nanodiamond defects, such as Si, Xe defects have high potential for spintronic applications where the heavier center can lead to longer coherence times. The TDDFT results, in combination with the formation energy results, explain why an Ar color center in diamond is challenging to observe experimentally. As shown in Figures 11 and 13, Ars, and AriV are able to introduce midgap states that fall within the visible energy range (shown in Table 2). However, the large formation energy difference between the Ari system and both the Ars and AriV systems make Ars and AriV less common in diamond than Ar Xi defects, which do not have unfilled midgap states, as shown in Figure 9. When comparing the TDDFT-generated absorption spectrum for the most stable configuration for Ar and Xe in Figures 10 and 14, we can clearly see that the Xe system has responses in the visible range that the Ar system lacks. These results indicate that noble gas centers in diamond are able to give rise to intraband states, which manifest as UV/vis features. However, the required lattice deformations to introduce these states mean that, for noble gas systems smaller than Xe or Kr, it is highly unlikely to be experimentally realized.

In this work, noble gas (He, Ne, Ar, Kr, and Xe) defects in nanodiamond have been systematically studied using DFT. Several possible geometric configurations of each noble gas atom have been studied. The optical and Raman vibrational absorption spectra for each noble gas species have been constructed and examined. For the noble gas atoms, except Xe, the interstitial (Xi) geometry is the most stable configuration. It was determined that the formation energy difference between the Xi configuration and other configurations decreases with increasing atomic size. As such, for larger noble gas defects, it may be possible to form multiple geometric configurations. DOS results and absorption spectra unveil that Xe near-infrared range transitions are associated with a split-divacancy. Even though the Ar XiV geometry introduces similar midgap states and allows bright midgap transitions, which should enable Ar as a potential color center, the formation energy of the defect is much higher than other Ar-containing geometric configurations. This explains why experimental UV–vis results have not found Ar color centers in diamond or nanodiamond, even though Ar has been experimentally incorporated within nanodiamond. However, given that Kr shows absorption features within the visible energetic range (2.78 eV) for the most stable structure, it is possible that using Kr as a high-pressure–high-temperature pressure medium may lead to the formation of color centers.