Systematic Study of Structure, Stability, and Electronic Absorption of

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Systematic Study of Structure, Stability, and Electronic Absorption of Tetrahedral CdSe Clusters with Carboxylate and Amine Ligands Kiet Anh Nguyen, Ruth Pachter, Jie Jiang, and Paul N Day J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02813 • Publication Date (Web): 24 Jul 2018 Downloaded from http://pubs.acs.org on July 29, 2018

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The Journal of Physical Chemistry

Systematic Study of Structure, Stability, and Electronic Absorption of Tetrahedral CdSe Clusters with Carboxylate and Amine Ligands Kiet A. Nguyen,a,b* Ruth Pachter,a,* Jie Jiang a,b and Paul N. Daya,b a

Air Force Research Laboratory, Wright-Patterson Air Force Base OH 45433 b

UES, Inc. Dayton OH 45432

*Corresponding author

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ABSTRACT

In this work, we carried out a systematic investigation to assess the effects of ligands on the structure, stability, and absorption spectra of ultrasmall CdSe tetrahedral quantum dots, where the cores of small tetrahedral quantum dots have been postulated to be stabilized by amine and carboxylate ligands. We found that amine and carboxylate ligands form extensive hydrogen bonding networks, which provide thermodynamic stability to the clusters. Based on the optimized structures, good agreement between observed and computed spectra was obtained. The ligands were also found to have a large influence on the color and intensity of the electronic absorption spectra, particularly for the small clusters, which were previously monitored with in situ UV-visible absorbance spectroscopy. Our work provides an understanding of the effect of ligands that influence thermodynamic stability and electronic absorption of ultrasmall quantum dots, thus potentially motivating further experimental exploration.


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1. Introduction Atomically precise group II-VI semiconductor quantum dots (QDs) with 1-2 nm in diameter are of interest, for example, due to narrow size distribution for improved control of spectral tuning,1 understanding QD formation and growth, e.g. to direct the ultimate shape, or in formation of CdSe superstructures that result in solid state emission at room temperature.2 In addition, although the two-photon absorption cross-section could be smaller in such clusters, the response is still much larger than for molecular systems (values larger than 103 GM were measured3). Stoichiometric clusters also template growth of anisotropic nanostructures, while stable (CdSe)19(benzoic acid/oleylamine) was shown to exhibit white light emission.4 Stoichiometric non-ligated (CdSe)n (n=13, 19, 34,…) clusters were demonstrated more than a decade ago,5 and amine-stabilized (CdSe)34 was recently found to be stable.6,7 (CdSe)34 passivated by oleylamine was also characterized.8 The optical properties of QDs are known to vary with their inorganic cores and passivating ligands. Indeed, in addition to the effects of quantum confinement resulting in size-dependent optical properties, the stoichiometry and structural motif of the cluster’s core are important variables for a detailed understanding of the origins of their stability and optical properties. Experimentally, atomic-resolution structures of stoichiometric semiconductor clusters is lacking, thus not allowing a detailed understanding of structure-property relationships for this class of materials. In our previous computational investigation of stoichiometric (CdSe)n, we found the (CdSe)13(n-alkylamine)13 tubular structure to be competitive with the cage-core structure when including amine ligands and the toluene solvent,9 obtaining an absorption spectrum in qualitative agreement with experiment.10

Recently,

Weeks and Tvrdy studied bare stoichiometric CdSe QDs using charge equilibration methods.11 This alternative approach with low computational cost extends the modeling of CdSe QDs to larger sizes.11 For nonstoichiometric II-VI chalcogenide semiconductor clusters, a wide range of sizes12,13 has been successfully synthesized.14-17 However, although experimental18-20 and theoretical studies14,21-27 were carried out in the past to understand the role of size variance, solvent, and surface ligands on linear14,2125

and nonlinear28,29 optical properties of such clusters that serve as fundamental building blocks for new ACS Paragon Plus Environment

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materials, a detailed understanding of ligand and structure on the optical properties of experimentally well-characterized nonstoichiometric metal rich clusters is still missing. Group II-VI chalcogenide clusters belong to different topological classes.30 The simplest tetrahedral framework, so-called supertetrahedral (Tn) has regular tetrahedrally shaped fragments of the cubic ZnS type, where n is the number of metallic layers in each cluster. Recently, relatively large clusters with interconverted cationic (Cd) and anionic (Se) sites (Ti, where i is the number of chalcogenide layers, see Figure 1) have been synthesized with a number of carboxylate and amine ligands.31 The crystal structures of three metallic cores (Cd35Se20, Cd56Se35, and Cd84Se56) and their absorption spectra have also have reported for clusters with benzoate and n-butylamine ligands.31 In these metal rich Ti clusters, the number of cations in a given i cluster is equal to the number of anions in the larger i + 1 cluster. Note that the growth of tetrahedral clusters is formed by the following series: 1, 3, 6, …, i(i + 1)/2 for each layer of anions or cations. The stoichiometry of a given Ti cluster following formulas: i(i + 1)(i + 2)/6 for anions and i(i + 1)(i + 2)(i + 3)/6 for cations.30 Although complete characterization of the molecular formula has not been done in this case, the reported number of benzoate ligands (designated as X-type) is equal to the number of n-butylamine ligands (designated as L-type), based on NMR data.31 Since these zinc-blende fragment tetrahedrons must be charge-balanced, the chemical formulas were deduced as Cd35Se20X30L30, Cd56Se35X42L42, and Cd84Se56X56L56.31

For smaller clusters, their

formations were31 monitored by in situ UV−visible spectroscopy in a diethyl ether solution of nbutylamine (n-BuNH2), cadmium benzoate (Cd(O2CPh)2), and bis(trimethylsilyl)selenide ((TMS)2Se) at low temperature. Although the core structures of the three clusters were reported to be tetrahedral, the nature of metal-ligand bonding formed by carboxylate ligands with metal atoms was not characterized. With the exception of in situ electronic spectra, basic chemical data for small Ti clusters is not known. For T4, based on the reported core structure and the Cd35Se20X30L30 formula, electronic structure calculations were carried out to study electronic and optical properties.32 Molecular dynamics simulations were also carried out to simulate spectral broadening using a cluster with ammonia and acetate ligands. The ACS Paragon Plus Environment

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splitting of the first absorption peak was attributed to the effects of spin−orbit coupling (SOC) using a structure passivated with pseudo hydrogen (with charge 1.5 e-) atoms.32 We were able to confirm the reported splitting of the first absorption peak (2.61 and 2.81 eV) in the spectral calculations carried out with pseudo hydrogens as ligands by RPA (random phase approximation), including SOC. However, the computed spectra with or without SOC for clusters passivated with carboxylate and amine ligands, which mimic the experimental conditions, are not significantly different, thus indicating that the origin of the dip in the absorption is to be attributed to the effect of ligands (see Supporting Information). In this work, a systematic study for a series of cadmium selenide Ti (i = 1-4) clusters (Figure 1) with carboxylate and amine ligands using ab initio electronic structure theory, density functional theory (DFT), and linear response time-dependent DFT (TDDFT), is carried out. In order to investigate the nature of ligand-metal bonding and its effect on the ground and excited states, we probe the binding energetics for various modes/facets of ligand attachment using DFT and Møller-Plesset second order perturbation theory (MP2).33,34 Spectral assignments using TDDFT are presented and compared with previous experiments.31 The effects of different carboxylate ligands on ground state energetics and electronic spectra are considered for the gas-phase and in solvent. 2. Computational Methods Kohn-Sham (KS)35 DFT and TDDFT electronic structure calculations were performed using the Stuttgart/Dresden (SD) valence basis set and ECP were used for Cd, (7s7p5d)/[5s5p2d],36,37 and Se, (4s5p2d)/[2s2p2d],38 including two additional sets of d-functions for Se (ζ = 0.475412, 0.207776)39 atoms. The additional polarization functions for atoms with high coordination are crucial for obtaining accurate structures and energetics of the clusters.40,41 Other atoms were treated with the 6-31G(d) basis set.42,43 For selected cases, MP2 and DFT calculations were carried out using the larger Def2-TZVP basis set.44 In our previous studies, the PBE045 functional was found to provide a good description for both the ground and excited states of stoichiometric9 and nonstoichiometric semiconductor clusters.26 The computed bond distances were about 0.03 Å longer for both CdS and CdSe clusters compared to the XACS Paragon Plus Environment

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ray structures.26 Excitation energies computed with PBE0,45 having a mean absolute error of 0.11 eV, were therefore employed to study structures and spectra in the present work. In addition, the effects of dispersion were also included here, using the empirical parameters of Grimme et al. (PBE0-D3),46 as the predicted PBE0-D3 structures (see Figure 1S-2S) and energetics (see Tables 1S-2S) were found to be in better agreement with the MP2 results. Thus, the PBE0-D3/SD-6-31G(d) results are discussed throughout, unless mentioned otherwise. TDDFT singlet excitation energies and oscillator strengths using the dipole length representation were calculated using the Gaussian 0947 and GAMESS48 programs. For some clusters, there are a number of conformational isomers.

Thus, Boltzmann averaging of excited state properties was done with

low-energy isomers (Qi) of these clusters. The linear extinction coefficients are computed with the normalized Gaussian lineshape function as49

ε (ν~) =

2 ln 2 4.32 × 10 −9

 − 4 ln 2 ~ ~  f 0 f (Qi ) 2 ( ) g ( Q ) exp ν ν ( Q ) −  , ∑ i i ∑f ν~ FWHM 0f i ~ FWHM ) 2 π i  (ν f  f

(1)

where g(Qi), f0f(Qi), and ν~0 f (Qi ) are the Boltzmann factor, oscillator strength, and transition frequency for a given Qi isomer, respectively. 3. Results and Discussion We begin with a general discussion on the bonding of L-type amine and carboxylate X-type ligands with metallic sites in CdSe clusters, and then discuss the results of structure, relative stability, and electronic absorption of each Ti cluster in the following sections. The bonding of carboxylate ligands to metallic sites can be classified as monodentate (M), symmetrical bidentate (SB), asymmetrical bidentate (AB), and bridging (Br), as shown in Figure 2. A carboxylate ligand forms a single Cd-O bond in the monodentate coordination. In the bidentate coordination, a carboxylate ligand forms two equivalent (non-equivalent) Cd-O bonds with a single Cd atom for symmetrical (asymmetrical) bonding.

For

symmetrical bidentate coordination, the Cd atom is located in the carboxylate plane. This is usually not the case for asymmetrical bidentate (AB) and the bridging of one carboxylate ligand with two metal ACS Paragon Plus Environment

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atoms. The nitrogen atoms in L-type amine ligands can readily bind to cadmium atoms in CdSe clusters. L-type binding in Ti, CdSe clusters involves Cd-N interactions similar to those observed in stoichiometric CdSe clusters.9

In clusters with both L- and X-type ligands, hydrogen bonding between

the carboxylate oxygen and amino hydrogen atoms provides additional stability for the Ti clusters. Both carboxylate oxygen and amino hydrogen atoms can form bifurcated bonds (three-centered bonds) with two hydrogen and two oxygen atoms, respectively. In this work, an amino H-O distance of less than 2.6 Å is taken as a hydrogen bond (HB). For small pyramidal clusters, stable low-energy isomers are obtained with a distribution of ligands such that all facets contain an even mixture of carboxylates and amines that maximizes hydrogen bonding. For larger clusters, the effective surface curvature decreases ligand coordination space. Thus, steric effects become important, especially for bulky ligands. The Cd and Se atoms in Ti cores prefer tetra-coordination to avoid dangling bonds. Thus, the apex (A) Cd atoms are typically coordinated with three ligands. The following notations are used distinguish different ligand attachment configurations to the core Ti clusters. For the T1 pyramidal isomers with Cd4Se cores, four apex (4A) atoms are located at the four corners of the pyramids (see Figure 1 and Figure 3S). For T2 complexes, ligands are distributed among the six edges (6E), where each has one Cd atom, in addition to the 4A atoms. Each of the 6E edges has two and three Cd atoms for the T3 and T4 clusters, respectively. In addition, T3 and T4 clusters have one and three Cd atoms on each of the four faces (4F) of the pyramids. The A-, E-, and F-atoms are coordinated to one, two, and three other Se atoms, respectively, leading to respective vacant coordination numbers of three, two, and one. Thus, 4AX,2L2E2L4EX,L denotes a T2 cluster with one X-type and two L-type ligands at each A-atom (4AX,2L), two L-type ligands at two E-atoms (2E2L), while the other 4E-atoms having one X-type and one L-type ligands (4EX,L). Structure and Relative Energy of Isomers. The smallest supertetrahedral (T1) isomers have Cd4Se cores that must be coordinated with six carboxylate ligands to be a neutral complex. Five T1 Cd4SeX6L6 (X = benzoates, L = methylamine) isomers are shown in Figure 3S with different arrangements of ligands at 4A-atoms. The low energy T1 structures (a and b, Figure 3S and Table 1S) are found to have ACS Paragon Plus Environment

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2A2X,2L2AX,2L (two X and one L ligands at two A-atoms and one X and two L ligands at the other two) arrangements with different networks of HBs. Note that all Cd atoms are tetra-coordinated with AB coordination for benzoate ligands in these low-energy structures. The lowest (a) energy T1 isomer was found to form 10 HBs with an average (AHB) distance of 1.912 Å. The next nearby isomer (b) on the potential energy surface (PES), having the same number of HBs but a slightly larger distance (AHB = 1.940 Å), is located at about 4 (5) kcal/mol higher in energy in the gas-phase (solvent), indicating that the tighter HB network stabilizes the cluster. Structures distorted from the tetrahedral framework (d, and e, Figure 3S and Table 1S) with fewer HBs and/or bridging carboxylate ligands were found to be higher in energy. Interestingly, breaking the Cd-Se tetra-coordination (c, Figure 3S and Table 1S) appears to have little (no) energy penalty, about 2 kcal/mol (3 kcal/mol) higher (lower) compared to the lowest energy isomer (a) with C2 symmetry in the gas-phase at the PBE0-D3 (MP2) level of theory. It appears that two additional Cd-O bonds in structure c were formed to partially compensate the loss of a Cd-Se bond and a hydrogen bond. The T2 isomers have Cd10Se4 cores that are coordinated with 12 X-type carboxylate and 12 L-type amine ligands that are distributed among 4A and 6E atoms. The low-energy structures and relative energies for T2 clusters are given in Figure 4S and Table 2S, respectively. For the two types of carboxylate (X = formate and benzoate) and amine (L = methylamine) ligand pairs, the lowest-energy isomer (g) has the 4A2X,L2E2X4E2L conformation. This symmetric (D2) structure gives rise to 24 HBs (AHB = 2.078 Å) for the formate-methylamine (X = formate and L = methylamine) complex, but allows 28 HBs (AHB = 2.159 Å with four bifurcated HBs) for the benzoate-methylamine (X = benzoate and L = methylamine) cluster. The HBs are similar in distance (1.9-2.1 Å) for the two complexes, except for the four bifurcated HBs in the benzoate-methylamine cluster. Exchanging one A-L ligand with an E-X ligand gives rise to a much higher-energy 3AX,2LA2X,LE2X5EX,L (b) isomers. Placing two L-type ligands at E-Cd centers (4A2X,L2E2X4E2L, c) was found also to be unfavorable. For the benzoate-methylamine cluster, the next nearby isomer (f) on the PES is located at about 4 kcal/mol higher in energy. The effects of solvent on the energetics of these ligands are found to be small. In addition to less favorable ACS Paragon Plus Environment

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π-stacking, higher energy isomers appear to have fewer HBs and/or bridging carboxylate ligands, similar to the structure-energy relationship observed in the T1 clusters. The Cd20Se10 framework has four faces (4F, each with one Cd atom coordinated with three Se atoms), in addition to 4A-atoms and six edges (each has two Cd atoms) in the T3 isomers. Twenty X-type ligands are required for an overall neutral system. With the same number (20) of L-type ligands, the 2A2X,L2AX,2L5E2X,2LE4X4FL distribution of ligands gives the lowest-energy isomer with 40 HBs for the methylamine-benzoate cluster (see Figure 5S and Table 3S). However, the PES is quite flat. The next nearby isomers, 2A2X,L2AX,2L6E2X,2L2E2X,2L2FX2FL (b, C2 symmetry) and 2A2X,L2AX,2L5E2X,2LE4X4FL (e, C2 symmetry) are slightly higher in energy in the gas-phase, by 1.1 kcal/mol and 1.5 kcal/mol, respectively. However, the two isomers with C2 symmetry are essentially isoenergetic in ethyl ether. Similar energy separations are predicted for the methylamine-formate complexes. Considering the larger T4, the Cd35Se20 framework with one tetra-coordinated metal center was the smallest among the Ti clusters experimentally isolated and characterized.31 The complex was reported to comprise of thirty benzoate and butylamine ligands,31 with one ligand for each vacant Cd atom, assuming the metal atoms are tetra-coordinated.

However, the atomic positions of the X- and L-type

ligands are not known. Thus, there is a significant computational challenge using first principles methods to examine all possible ligand arrangements for its 4F, 6E, and 4A Cd atoms. It is also not obviously clear that the T4 and larger cores can accommodate the proposed ligand density. Recently, molecular dynamics simulations and geometry optimization for the formate-ammonia complex using the PBE functional was found to retain the T4 core with the 4AX,2L6E4X,2L4F2X,L ligand distribution.32 By substituting different numbers X and L ligands at the A, E, and F coordination sites, we found a number of isomers with much lower energies (Figure 6S and Table 4S). Some isomers are predicted to have distorted T4 cores with bridging X-type ligands. The carboxylate and amine ligands considered here were found to overcome steric crowding to retain the T4 framework for low-energy conformers. These structures exhibit extensive networks of HBs, consisting mainly of AB-X ligands.

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factor for thermodynamic stability of the clusters. Among different formate-ammonia configurations explored in this study, the lowest-energy complex was found to have a 4A2X,L6E4X,2L4F3L (a) ligand distribution with C2 symmetry. This structure with 72 HBs (1.877-2.322 Å, AHB = 1.998 Å) is about 44 kcal/mol (42 kcal/mol lower in diethyl ether) lower in energy than the previously reported32 4AX,2L6E4X,2L4F2X,L structure (70 HBs 1.852-2.574 Å, AHB = 2.041 Å). To explore the surface packing with larger ligands, we substitute ammonia with methylamine and investigate the effects of the alkyl group. In addition to steric effects, each alkyl substitution removes one potential hydrogen bond from ammonia, and subsequently changes the PES for the formate-coordinated T4 clusters. The two most favorable isomers (4AX,2L4E3X,3L4E2X,4L3F2X,LF3L (i) and 4A2X,L2E4X,2L 2E3X,3L2F2X,L 2F3L (l)) among the methylamine-formate complexes, are different from the most favorable formate-ammonia structures. These nearly isoenergetic isomers are about 20 kcal/mol and 19 kcal/mol lower in energy than the 4A2XL6E4X,2L4F3L (a) structure. The corresponding energy gap is reduced to about 12 kcal/mol in diethyl ether. Replacing formate with benzoate ligands slightly changes the relative energies, but isomers i and l remain the two most favorable structures for benzoate-methylamine clusters. Before moving to the next topic, we summarize our findings on the ligation of the symmetric Ti tetrahedral cores. The tetrahedral symmetry of the cores is broken to facilitate tetra-coordination of the metallic cores and to maximize X-L hydrogen bonding in order to produce stable structures. In some cases, it results in symmetric structures. For the T1 and T2 clusters, the lowest energy structures were found to have C2 and D2 symmetries, respectively. In these cases, the preservation of symmetry appears to be promoted by hydrogen bonding since the corresponding Ti clusters (Cd4SeX6 and Cd10Se4X12) without L-type ligands were found to have C1 symmetry. Similarly, the T3 and T4 clusters without Ltype ligands also possess C1 symmetry. However, the T4 cluster was found to have C2 symmetry for lowest energy structure after ligating with X = formate and L = ammonia while ligating with other X and L ligands distorted stable clusters to C1 symmetry. The PES of the T3 clusters with X and L


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ligations are flat for the symmetric and non-symmetric structures. For these larger clusters with the Xtype benzoate ligands, π-stacking of the phenyl rings is another factor that can affect their stabilities. Binding Energy. The stability of the Ti clusters, as provided by L-type ligands, was studied by analyzing binding energies. These were computed by removing all L-type ligands from isomers having a combination of X-L ligands. The lowest energy optimized structures of carboxylate-Ti clusters were used as references. For the T1 clusters, the tetrahedral motif, however, is not retained with carboxylate ligands (namely, without L ligands). Structures of larger carboxylate-Ti clusters are also distorted with bridging Cd-O bonds instead of the bidentate coordination obtained with the X-L ligand mixture. However, bridging Ti complexes with T symmetry are located at significantly higher energy on the PES. The L-type ligand binding energies are listed in Table 1. For a given X-L ligand pair, the average binding energy increases slightly with cluster sizes, about 2 kcal/mol (1 kcal/mol) upon going from clusters T2 to T4 with formate-ammonia (formate-methylamine) ligands. For benzoate-methylamine ligands, the binding energy increases from about 27 kcal/mol to 28 kcal/mol upon going from T1 to T4. The binding strengths are predicted to reduce by 4-6 kcal/mol in diethyl ether (dielectric constant ε = 4.24) compared to the gas-phase.

Since the static dielectric constant (expressed as a ratio relative

to that of vacuum) of a solvent is a relative measure of its chemical polarity. Thus, binding energies in nonpolar solvent such as n-hexane with lower dielectric constant (ε =1.88), would be closer to the corresponding gas-phase values. The computed results for Tn (T1 = 25.2, T2 = 27.2, T3 = 26.8 ,T4 = 26.6, for X = benzoate and L = methylamine) clusters in n-hexane are indeed closer to the corresponding gas-phase values. The additive effects of ligands in large cluster sizes might provide an important contributing factor for their observed stability.31 It was speculated that T4 clusters with two carboxylates at the apex positions might be prone to desorption of CdLX2 molecules (Z-type ligands).31,32 While previous calculations32 for the T4 cluster reported almost zero binding energy for CdLX2 (X = formate, L = ammonia), experimental observations strongly supported the tetrahedral framework for the isolated T4-T6 clusters with all four corner Cd atoms.31 Thus, the binding in these Z-type ligands is reexamined in the gas-phase and in solvent. The ACS Paragon Plus Environment

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dissociation energies of CdLX2 (X = formate, L = ammonia and methylamine) are listed in Table 2 for the T4 clusters. Desorption of CdLX2 for T4 clusters was found to be endoergic (Table 2). For a given X-L ligand pair, the dissociation energy is reduced in solvent. For the T4 cluster with formate and methylamine ligands, the respective dissociation energies of a Z-type ligand in the gas-phase and in diethyl ether are about 38 kcal/mol and 28 kcal/mol. The corresponding dissociation energies for formate and ammonia ligands are predicted to be comparable, 39 kcal/mol (gas-phase) and 29 kcal/mol (diethyl ether).

However, additional amine coordination in CdLX2, leading to stable CdL2X2

complexes, can lower their dissociation energies.

Neglecting the additional L-ligand stabilization

energy for Cd35Se20X30L30 (X = formate and L = methylamine), the dissociation energy reduces to about 15 kcal/mol (9 kcal/mol) in the gas-phase (solvent) but remains endoergic (Table 2). Thus, in high amine concentration the stability of the T4 structure with all four corner Cd atoms might be reduced. Electronic Spectra. The growth of Ti complexes in diethyl ether was previously monitored with in situ UV-visible absorbance spectroscopy from -78 °C to 22 °C.31 Isobestic points in the spectra were used to identify the conversion of small clusters to larger ones. From the experimental spectra, a broad (FWHM ~ 0.5 eV) absorption peak at 4.71 eV (λmax = 263 nm) for the smallest cluster was observed at 42 °C after 42 minutes. At higher temperature (0 °C), this cluster was found to subsequently convert into a larger one, with the first and second absorption maxima at 3.94 eV (λmax = 315 nm and FWHM ~ 0.3 eV) and 4.13 eV (λmax = 300 nm, FWHM = 0.3 eV), respectively. The product formed at room temperature with the first absorption peak at

(3.54 eV, λmax = 350 nm, FWHM = 0.2 eV) was

determined to have the T4 core using a combination of single-crystal X-ray diffraction and atomic pair distribution function analysis. Controlled reactions at higher temperature were also used to extend the synthesis, isolation, and characterization of structures and spectra of larger single-sized QDs (T5-T6). However, for small clusters, the basic chemical data remains elusive, except for in situ spectral data. Experimental absorption maxima of the T4 and smaller clusters are listed in Table 3 along with the computed values. The 4.71 eV absorption peak from the in situ UV-visible absorbance spectroscopy, attributed to first observed cluster, appears to correlate with the computed maximum (4.84 eV in diethyl ACS Paragon Plus Environment

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ether) for the T1 cluster (Table 3). The first absorption maximum is predicted to red-shift to 4.3 eV for the larger T2 cluster.

However, the next larger cluster (observed at 0 °C) was reported to have a

lowest-energy absorption peak at 3.94 eV and a more intense one at 4.13 eV.31 These maxima are better correlated with the computed spectral maxima (3.78 eV and 4.15 eV) for the T3 cluster in diethyl ether (Figure 3). The higher-energy band is predicted to be less intense for T3, in contrast to a stronger absorbance observed for the second (4.13 eV) band, which may have increased from higher transitions and/or other absorbing species (possibly T2).

For the next larger T4 cluster with ammonia and

methylamine ligands, the computed maxima of 3.62 eV (2.68 eV) and 3.77 eV (~ 2.8 eV) were obtained by Boltzmann averaging results for the two lowest-energy isomers in the gas-phase (in solvent). While the gas-phase computed spectral features show good agreement with experiment,31

the second

maximum appears as a shoulder due to the shifts in excitation energies underlying the absorption bands (Figure 4a). Replacing formate ligands with benzoate ligands red-shifts absorption peaks to 3.55 eV (3.48 eV in the gas-phase) and 3.65 eV (3.59 eV in the gas-phase), in better agreement with the corresponding experimental maxima of 3.54 eV and 3.72 eV,31

respectively (Figure 4b). These two

bands arise from four strong transitions with excitation energies from 3.47 eV to 3.68 eV (3.54 eV to 3.73 eV) in the gas-phase (in diethyl ether). The molecular orbitals (MO) involved in the transitions are shown in Figure 4 using the Avogadro program.50 The first band comprises of two nearly degenerate transitions, originating mainly from the highest occupied MO (HOMO), HOMO ̵ 1 to the lowest occupied MO (LUMO) while the second band involves two transitions from lower occupied MOs to the LUMO. These occupied and virtual MOs have major contributions from π-orbitals of the core metal atoms. A similar MO picture was obtained for the T3 cluster with slight blue-shifts in the energies of occupied MOs but with a much larger increase from the LUMO, which is also increased upon going to the smaller T2 cluster. However, the LUMO has significant contributions from the π-orbitals of the L-ligands of the T2 cluster. Thus, transitions from their occupied MOs to the LUMO have some degree of charge-transfer character. Therefore, removing methylamine ligands from was found to significantly shift the first excitation energy for the T2 cluster (~ 0.2 eV) but not for other clusters (see Table 5S). ACS Paragon Plus Environment

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Experimentally, the isolated tetrahedral clusters (with reported core edges in the range of 1.7 (T4) to 2.6 nm (T6) in length)51 were found to exhibit size-dependent absorption features, having lowest absorption maxima at 3.54 eV (T4), 3.26 eV (T5), and 3.04 eV (T6) for X = benzoate and L = butylamine in diethyl ether.31 Taking these absorption maxima as the lowest-energy excitations (LEEs), a red-shift 0.5 eV can be attributed to ~ 1 nm of the increase of the core edges. The experimental quantum-confined shift is about the same as the computed (for X = benzoate and L = methylamine in the same solvent) red-shift of 0.52 eV for the LEEs (Table 5S) upon going from T2 (0.8 nm) to T4 (1.7 nm). A slightly larger red-shift (0.74 eV, see Table 3) is obtained with the computed absorption maxima, as they are not necessarily the LEEs. 4. Conclusions Ab initio and density functional theory electronic structure calculations were carried out to explore the structure and stability of cadmium selenide supertetrahedral Ti clusters with carboxylate and amine ligands. The clusters are found to be stabilized by a network of hydrogen bonds facilitated by X-L ligand pair interactions, in addition to the ligand-to-metal bonding. The carboxylate and amine clusters appear to retain their Ti motifs with all four Cd corner atoms. Removing a CdLX2 molecule from the T4 cluster is endoergic. However, the pyramidal shapes are distorted, forming bridging complexes upon the removal of amines. Good agreement between the observed and computed structure and spectrum is obtained for the T4 cluster. Computed spectra for smaller clusters correlate with experimental spectra obtained with in situ UV-visible absorbance spectroscopy. Red-shifts are observed for the lowest excitation energies with increased cluster size from T1 to T4. Acknowledgements We gratefully acknowledge support from the Air Force Office of Scientific Research and computational resources and helpful assistance provided by the AFRL DSRC. Supporting Information RPA results for the T4 clusters, computed structures, excitation energies, and relative energies for T1T4 clusters. This material is available free of charge via the Internet at http://pubs.acs.org ACS Paragon Plus Environment

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Table 1. Summary of computed average binding energy (in kcal/mol) per L-type ligand in the gas-phase and diethyl ether. Cluster Gas-phase Diethyl ether Cd4SeX6L6 X = O2C-C6H5, L = H2N-CH3 26.6a 22.7a Cd10Se4X12L12 X = O2CH, L = NH3 25.4b 21.2b c X = O2CH, L = H2N-CH3 27.1 22.7c X = O2C-C6H5, L = H2N-CH3 28.6d 24.7d Cd20Se10X20L20 X = O2CH, L = H2N-CH3 28.3 23.3 X = O2C-C6H5, L = H2N-CH3 28.3 24.2 Cd35Se20X30L30 X = O2CH, L = NH3 27.3 22.7 X = O2CH, L = H2N-CH3 28.0 23.2 X = O2C-C6H5, L = H2N-CH3 28.2 23.9 a binding energy includes zero-point energy corrections: 24.2 (gas), 20.4 (diethyl ether) b binding energy includes zero-point energy corrections: 22.6 (gas), 18.4 (diethyl ether) c binding energy includes zero-point energy corrections: 24.9 (gas), 20.5 (diethyl ether) d binding energy includes zero-point energy corrections: 26.2 (gas), 22.4 (diethyl ether)


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Table 2. Summary of computed dissociation energies (in kcal/mol) for the Cd35Se20X30L30 → CdLX2 + Cd34Se20X28L29 reaction. Values in parentheses are dissociation energies for the Cd35Se20X30L30 + L → CdL2X2 + Cd34Se20X28L29 reaction. Cluster Gas-phase Diethyl ether X = O2CH, L = H3N 39.0 29.3 X = O2CH, L = H2N-CH3 37.9 (15.1) 27.8 (9.4)


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Table 3. Summary of computeda and experimental (Expt.)31 absorption maxima (in eV) and extinction coefficients (in parentheses, in M-1cm-1) in the gas-phase and diethyl ether. Cluster T1 Cd4SeX6L6 X = O2C-C6H5, L = H2N-CH3 T2 Cd10Se4X12L12 X = O2C-C6H5, L = H2N-CH3 T3 Cd20Se10X20L20 X = O2C-C6H5, L = H2N-CH3

Gas-phase

Diethyl ether

Expt.

4.87 (2.31 × 104)

4.84 (2.77 × 104)

4.71

4.29 (3.31 × 104)

4.29 (4.25 × 104)

3.76 (9.95 × 104)b 3.78 (1.42 × 105)b 3.94 4.13 (1.61 × 104)b 4.15 (2.12 × 104)b 4.13

T4 Cd35Se20X30L30 X = O2CH, L = H2N-CH3

3.62 (1.57 × 105)c 3.68 (1.88 × 105)c 3.77 (1.06 × 105)c 3.8d X = O2C-C6H5, L = H2N-CH3 3.48 (1.25 × 105) 3.55 (2.04 × 105) 3.54 3.59 (1.06 × 105) 3.65 (1.68 × 105) 3.72 a Computed spectra were obtained using Gaussian line shape with FWHM of 0.2. bSpectral maxima were obtained by Boltzmann averaging using Gaussian line shape with FWHM of 0.2 eV. cSpectral maxima were obtained by Boltzmann averaging using Gaussian line shape with FWHM of 0.1 eV. dShoulder.


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References

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Cluster and of a Polymeric Chain of Thiolate-Bridged Cd17 Sulfide Clusters.Eur. J. Inorg. Chem. 2010, 3299−3306. (18) Soloviev, V. N.; Eichhöfer, A.; Fenske, D.; Banin, U. Molecular Limit of a Bulk Semiconductor: Size Dependence of the “Band Gap” in CdSe Cluster Molecules.J. Am. Chem. Soc. 2000, 122, 2673−2674. (19) Soloviev, V. N.; Eichhöfer, A.; Fenske, D.; Banin, U. Molecular Limit of a Bulk Semiconductor: Size Dependent Optical Spectroscopy Study of CdSe Cluster Molecules.Phys. Stat. Sol. B 2001, 224, 285−289. (20) Soloviev, V. N.; Eichhöfer, A.; Fenske, D.; Banin, U. Size Dependent Optical Spectroscopy Study of a Homologous Series of CdSe Cluster Molecules.J. Am. Chem. Soc. 2001, 123, 2354−2364. (21) Kuz'mitskii, V. A.; Gael, V. I.; Filatov, I. V. Quantum-chemical Calculation of the Electronic Structure and Excited States of ZnS and CdS Clusters.J. Appl. Spectrosc. 1996, 63, 594−602. (22) Eichkorn, K.; Ahlrichs, R. Cadmium Selenide Semiconductor Nanocrystals: A Theoretical Study.Chem. Phys. Lett. 1998, 288, 235−242. (23) Lopez del Puerto, M.; Tiago, M. L.; Chelikowsky, J. R. Excitonic Effects and Optical Properties of Passivated CdSe Clusters.Phys. Rev. Lett. 2006, 97, 096401/1−096401/4. (24) Lopez del Puerto, M.; Tiago, M. L.; Chelikowsky, J. R. Ab Initio Methods for the Optical Properties of Cdse Clusters.Phys. Rev. B 2008, 77, 045404/1−045404/10. (25) Frenzel, J.; Joswig, J.-O.; Seifert, G. Optical Excitations in Cadmium Sulfide Nanoparticles.J. Phys. Chem. C 2007, 111, 10761−10770. (26) Nguyen, K. A.; Pachter, R.; Day, P. N.; Su, H. Theoretical Analysis of Structures and Electronic Spectra in Molecular Cadmium Chalcogenide Clusters.J. Chem. Phys. 2015, 142, 234305/1−234305/11 (27) Zhu, X.; Chass, G. A.; Kwek, L.-C.; Rogach, A. L.; Su, H. Excitonic Character in Optical Properties of Tetrahedral CdX (X = S, Se, Te) Clusters.J. Phys. Chem. C 2015, 119, 29171−29177. (28) Zhang, X.; Tian, Y.; Jin, F.; Wu, J.; Xie, Y.; Tao, X.; Jiang, M. Self-Assembly of an Organic Chromophore with Cd−S Nanoclusters: Supramolecular Structures and Enhanced Emissions.Cryst. Growth Des. 2005, 5, 565−570. (29) Nguyen, K. A.; Pachter, R.; Day, P. N. Calculations of One- and Two-Photon Absorption Spectra for Molecular Metal Chalcogenide Clusters with Electron-Acceptor Ligands.J. Phys. Chem. A 2017, 121, 1748. (30) Feng, P.; Bu, X.; Zheng, N. The Interface Chemistry between Chalcogenide Clusters and Open Framework Chalcogenides.Acc. Chem. Res. 2005, 38, 293−303. (31) Beecher, A. N.; Yang, X.; Palmer, J. H.; LaGrassa, A. L.; Juhas, P.; Billinge, S. J. L.; Owen, J. S. Atomic Structures and Gram Scale Synthesis of Three Tetrahedral Quantum Dots.J. Am. Chem. Soc. 2014, 136, 10645−10653. (32) Voznyy, O.; Mokkath, J. H.; Jain, A.; Sargent, E. H.; Schwingenschlögl, U. Computational Study of Magic-Size CdSe Clusters with Complementary Passivation by Carboxylic and Amine Ligands.J. Phys. Chem. C 2016, 120, 10015. (33) Pople, J. A.; Binkley, J. S.; Seeger, R. Theoretical Models Incorporating Electron Correlation.Int. J. Quantum Chem. Symp. 1976, 10, 1. (34) Pople, J. A.; Krishnan, R.; Schlegel, B.; Binkley, J. S. Derivative Studies in Hartree-Fock and Møller-Plesset Theories Int. J. Quantum Chem. Symp. 1979, 13, 325. (35) Kohn, W.; Sham, L. J. Self-consistent field equations including exchange and correlation effects.Phys. Rev. 1965, 140, A1133−A1138. (36) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. Energy Adjusted pseudopotentials for the first row transition-elements.J. Chem. Phys. 1987, 86, 866−872. (37) Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-adjusted ab initio pseudopotentials for the 2nd and 3rd row transition-elements.Theor. Chem. Acc. 1990, 77, 123−141. ACS Paragon Plus Environment

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250000

0.4

200000

150000

AU

M-1cm-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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T4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Figure 1. CdSe (Cd = black) skeletal structures for T1-T4 and structures with an equal number formate and 42 amonia ligands. Tn structures have four apex-Cd atoms, (n-1) Cd-atoms on each of the six edges. T3 and 43 44 T4 have 1 and 3 Cd atoms, respectively, at each of the four faces. Varying number of anion ligands (T1 = 45 6, T2 = 12, T3 = 20, T4 = 30) are added for neutral clusters. 46 47 48 49 50 51 52 53 ACS Paragon Plus Environment 54 55 56

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1 2 3 4 R 5 R R R 6 7 C C C C 8 O O 9 O O O O O O 10 11 Cd Cd Cd Cd Cd 12 13 Monodentate Symmetrical Bidentate Asymmetrical Bidentate Bridging 14 15 16 17 18 19 Symmetrical Bidentate 20 21 Bridging 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Asymmetrical 48 Monodentate 49 Bidentate 50 51 52 53 ACS Paragon Plus Environment 54 Figure 2. Schematic carboxylate binding modes (a) and 3D examples the T1 cluster with benzoates (R = 55 phenyl) and methylamine ligands. 56

a)

b)


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AU

M-1cm-1

1 2 3 4 5 6 7 8 9 10 11 12 13 0.6 14 150000 15 16 17 18 19 20 0.4 100000 21 22 23 24 25 26 27 0.2 50000 28 29 30 31 32 33 34 0 0.0 35 3.0 3.5 4.0 4.5 36 37 eV 38 39 40 41 Figure 3. Computed (using Gaussian line shape with fwhm of 0.2 eV) Boltzman averaged linear absorption 42 spectra in the gas-phase (dash) and in diethyl ether (solid) for Cd20Se10X20L20 (X = O2CH, L = H2N-CH3) 43 44 compared with the experimental spectrum (square, X = O2C-C6H5, L = H2N-(CH2)3CH3) in diethyl ether.31 45 46 47 48 49 50 51 52 53 ACS Paragon Plus Environment 54 55 56

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1 250000 2 3 4 5 6 0.4 200000 7 8 9 10 150000 11 12 13 14 0.2 100000 15 16 17 18 19 50000 20 21 22 23 0 0.0 24 3.0 3.5 4.0 4.5 25 26 eV 27 250000 28 29 30 31 0.4 200000 32 33 34 35 150000 36 37 38 39 40 0.2 100000 41 42 43 44 50000 45 46 47 48 49 0.0 0 50 3.0 3.5 4.0 4.5 51 52 eV Figure 4. Computed (using Gaussian line shape with fwhm of 0.1 eV) Boltzman averaged linear absorption 53 ACS Paragon Environment spectra in the gas-phase (dash) and in diethyl ether Plus (solid) for Cd35Se20X30L30 with X = O2CH, L = H2N-CH3 54 55 (a), and with X = O2C-C6H5, L = H2N-CH3 (b) compared with the experimental spectrum (square, X = O2C56 C H , L = H N-(CH ) CH ) in diethyl ether.

AU

M-1cm-1

a

AU

M-1cm-1

b

Cd10Se4X12L12

CdThe 20Se 10X20Lof 20 Physical Chemistry Journal

Cd35Se20X30L30

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1 2 3 4 5 6 7 a (-0.97) a (-1.13) a (-1.51) 8 L 9 10 11 12 13 14 15 16 17 H b1 (-5.76) a (-5.46) a (-5.51) 18 19 20 21 22 23 24 25 26 27 28 29 H-1 b2 (-5.78) a (-5.51) a (-5.55) 30 31 32 33 34 35 36 37 38 39 40 H-2 b3 (-5.96) a (-5.56) a (-5.65) 41 42 43 44 45 46 47 48 49 50 51 52 H-3 b2 (-5.96) a (-5.62) a (-5.76) 53 ACS Paragon Plus Environment 54 Figure 5. Lowest (L) virtual, higher virtual, highest (H) occupied , and lower occupied orbitals with 55 symmetry labels at cutoff value of 0.01 au for CdSe clusters. Orbital energies (in eV) are in parentheses. 56

Systematic Study of Structure, Stability, and Electronic Absorption of

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