Pathways of Growth of CdSe Nanocrystals from Nucleant (CdSe)34

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Pathways of Growth of CdSe Nanocrystals from Nucleant (CdSe) Clusters Lavrenty Gennady Gutsev, Bala Ramu Ramachandran, and Gennady Lavrenty Gutsev J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12716 • Publication Date (Web): 15 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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The Journal of Physical Chemistry

Pathways of Growth of CdSe Nanocrystals from Nucleant (CdSe)34 Clusters Lavrenty G. Gutsev,*a Bala R. Ramachandran,b Gennady L. Gutsevc a

Department Physics, Virginia Commonwealth University, Richmond, VA 23284, USA

b

College of Engineering & Science, Louisiana Tech University, Ruston, LA 71272, USA

c

Department of Physics, Florida A&M University, Tallahassee, Florida 32307, USA

ABSTRACT The initial steps in the growth of quantum platelets from the wurtzite-type (CdSe)34 clusters are simulated using density functional theory with the generalized gradient approximation. The nucleant (CdSe)34 cluster has been chosen for simulations because it has experimentally been found to be a magic-size nucleant for the low-temperature growth of CdSe quantum platelets. According to the results of our calculations, the growth is anisotropic and favors the (0001) direction, which is consistent with experimental findings. We found that growth in other directions lowers the symmetry of the resulting clusters and that the asymmetrical positioning of rhombic defects causes the growing platelet to bend due to the surface strain which appears to be the limiting factor of growth. An alternative pathway to quantum platelet growth could proceed via the decomposition of (CdSe)34 to (CdSe)13 in electron donating media, which was found to be thermodynamically favorable. The side-product (CdSe)21 generated in this process is capable of growing via hexagonal stacking as well as propagating as a nanotube.

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1. INTRODUCTION Semiconductor quantum dots (QD) present an area of growing interest due to the wide variety of their applications such as photovoltaics 1,2,3,4, opto-electronic design5, medical imaging 6

, micro-supercomputers7,8 and as bioactive fluorescent probes9.

It is well known that the

molecular properties of QDs such as the band gap width may be tuned by controlling the size and shape of a QD,10 which in turn depends on the initial growth conditions11. It is also possible to control QD properties by making compound core-shell materials with different II-VI materials composing the cores and shells 12. The stability of (CdSe)n, (CdTe)n, (ZnS)n and (ZnSe)n stoichiometric positively charged clusters was demonstrated in a study that employed mass spectrometry and density-functionaltheory (DFT)13, It was also established that there is an abundance of “magic-sized” clusters corresponding to n = 13, 33 and 34; the latter two may be isolated in toluene both with and without ligation. CdSe is a well-studied cluster and has been used as a model for theoretical surface ligation studies14,15. Recently, it was experimentally found that a CdSe cluster passivated by n-octylamine/di-n-pentylamine is an important intermediate in the low-temperature nucleation of wurtzite nanocrystal platelets. The authors managed 16 to isolate a ligated CdSe cluster and demonstrated that the growth process occurs via first-order kinetics without the accumulation of intermediates. This surprising result is achieved by means of the size control of the bundled lamellar flat templates. These experimental findings provide insight on how anisotropic nanocrystal growth via cluster assembly17 can be studied theoretically. A nucleating cluster acts as a template for the growth of a nanocrystal which possesses a wurtzite-like morphology. These templates should be flat and stackable according to the experimental data

18

. In addition, they are expected to be


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stoichiometric since nonstoichiometric clusters would not be edge compatible with one another. This is in agreement with the results of the previous experiments where it was shown that QBs passivated with amines, which are Lewis bases and thus called L-type ligands, retain a 1:1 Cd:Se stoichiometry 19. Several isomers of CdSe with a stackable morphology are shown in Figure 1, where structure I presents a bilayer wurtzite stack which was found to be preferred via a basin-hopping global search method

20

; structure II corresponds to a four-layer wurtzite stack with four

hexagons on each layer and a single rhombic column defect which is formed by a complementary (Cd if a Se corner or Se if a Cd corner) atom connecting two hexagonal edges on each layer. Structure I also has an isomer I’ which may be constructed by moving one birhombic defect in such a way that it is arranged diagonally with respect to the first bi-rhombic defect. The state with the cluster I’ geometry is higher in total energy than the state with geometrical structure I by only 2-3 kcal/mol. We found that there is another isomer III which can be considered as a (6,0) nanotube precursor 21, whose state is close in total energy to the state with geometrical structure I. Thus, CdSe has at least three isomers of suitable stacking type which can be considered as seed clusters for a wurtzite-type nanocrystal growth and at least four isomers whose states are nearly degenerate in total energy when calculated as free-standing species. The goal of this paper is to gain insight into the growth of quantum platelets (QP) using the results of our density functional theory computations and the experimental data 16 as a guide. Since the experimental growth proceeds in an anisotropic fashion, it is important to find if there are energetically favorable directions of growth and explain the underlying mechanisms behind


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them. In addition, we also explored the proposed decomposition of CdSe to CdSe and (CdSe)21 which was experimentally used to grow nanobelts.

2. DETAILS OF COMPUTATIONS Our calculations were performed using density functional theory with the generalized gradient approximation (DFT-GGA) as implemented in the GAUSSIAN 09 suite of programs

22

.

We have chosen the BPW91 exchange-correlation functional, which is composed of the Becke exchange

23

and Perdew-Wang correlation24, along with the cc-pVDZ-pp (4s4p3d1f) basis for

Cd [24], the aug-cc-pVDZ-pp (5s4p3d) basis for Se

25

and the 18-electron effective core

potentials (ECP)26. The convergence thresholds for total energy and the forces were set to 10-8 eV and 10-3 eV/Å respectively. Although this exchange-correlation combination is among the oldest of the GGA variety, multiple test studies have shown that the BPW91 method provides a mean unsigned error in atomization energies which is similar to the errors obtained when using more recently developed exchange-correlation functionals 27. We also chose this method because it has shown good performance for the CdS

28

and CdSe 29 clusters. Errors related with the

basis set chosen have been found to decrease with increasing cluster size 30. Previously, we performed optimizations of the ground singlet state of a CdSe dimer using the BPW91/cc-pVDZ-pp approach and also using the coupled-cluster method with singles and doubles and non-iterative inclusion of triples [CCSD(T)] with larger cc-pVTZ-pp basis sets

31

.

The equilibrium bond distances and harmonic vibrational frequencies obtained at the BPW91/ccPZDZ-pp level of theory were 2.368 Å and 261.0 cm , which compare quite well with the values obtained at the CCSD(T)/cc-PVTZ-pp level: 2.361 Å and 260.6 cm , respectively. The values obtained using a multireference MRCI+Q method are similar: 2.373 Å and 257.3 cm 32.


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In this work, we perform a more involved benchmark where we tested both the effect of the method used as well as the basis set chosen. For DFT, we tested B3LYP 33,34 CAM-B3LYP 35

, B3PW91, PBE0 36, wB97XD 37 and PBE38; for post-HF, we tested CCSD(T) using three basis

sets of increasing quality: cc-pVDZ-PP, cc-pVTZ-PP, and cc-pVQZ-PP [24],39.We computed the dissociation energy , equilibrium bond length , harmonic vibrational frequency and the energy of the first singlet-triplet transition T = E Σ − E Π (see Table 1 and Table S1 in the ESI). Taking the MRCI+Q results 32 and our CCSD(T)/cc-pVQZ-PP results as benchmarks for evaluating the performance of the DFT methods and the cc-pVDZ-PP basis set, it is seen that all DFT functionals except BPW91 predict the wrong sign for T0 (see Table 1). With the largest basis set studied, all functionals except CAM-B3LYP yield the correct sign for T0 but the predicted magnitude is much smaller than the BPW91 one. This comparison suggests the BPW91/ cc-pVDZ-PP method to be considered as reliable for the present study.

3. RESULTS AND DISCUSSION When simulating growth of wurtzite nanocrystals, we combined CdSe isomers with themselves. One may gauge the energetic anisotropy of growth in a certain direction by comparing the calculated total energies of the CdSe clusters to one another. It is important to note that our methodology is only valid for materials that grow via a nucleant intermediate also known as cluster assembly. Of course, there are other growth mechanisms; for example, the zinc blende phase of CdSe grows without such an intermediate

40

the phase which is obtained is

strongly dependent on reaction conditions41. Guided by the recent experiment on quantum platelet growth from CdSe nucleant clusters

16

and our previous experience with CdSe clusters, we will explore the possible growth

pathways and the optical properties of a quantum platelet. Next, we will analyze the proposed


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thermodynamically favorable decomposition of CdSe → CdSe + (CdSe)21 assisted by electron capture.

3.1. Growth of Quantum Crystals from "#$%&' There are at least three possible pathways of growth of the I+I type clusters which are illustrated in Figure 2. In terms of energetic favorability from most favorable to least, they can be arranged (see Table 2) as follows: 1. Hexagon-hexagon stacking which corresponds to growth in the (0001) direction. 2. Rhombic-ring opening which results in two new hexagons. 3. Hexagon-hexagon side-locking where no rhombi are opened in the process but two new hexagons are formed. Combined with pathway 2, this should roughly correspond to 112*0 growth. The first pathway of growth was found to be highly favored which is consistent with experimental data where the (0002) fringes are clearly visible on the TEM edge-view images. Also, the (0001) pattern corresponds to the highest peak on the XRD spectrum of the CdSe QPs 16

. The second pathway is more favorable than the third one due to the release of rhombic strain;

however, the third pathway should become more favorable when the second pathway is performed first since it becomes possible to form more rings by this two-step mechanism than by pathway 3 alone. This two-step mechanism of growth by this method is shown in Figure 3. Judging from this mechanism, one may conclude that pathway 2 would give the QP width and pathway 3 would give it thickness. The energy of this step can be gauged by comparison to pathway 3: about 0.53 eV are gained with the formation of each ring; therefore, approximately 3.18 eV would be gained after the cluster is at least twice as wide as it is thick. In experiments, these QP’s are much longer than they are wide and are 2-5 times wider than they are thick. That


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is, the predicted energetic order of our pathways is in agreement with experiment. The diagonaldefect isomer I’ can easily be added on this way as well; however, such a connection could make rhombic defects difficult for new clusters to access by pathway 2, which in turn will also inhibit pathway 3. Experimentally it was found that the lattice parameter c contracts during growth. We note that there is a significant bond-length contraction between the two faces fusing together via pathway 1 which supports this observation. Next, we simulated growth using cluster II. The first thing to note about this cluster is that its local topology matches the shape of the cluster formed by pathway 1 for cluster I if one cuts a corner of the resultant CdSe cluster off. The most energetically favorable pathway for II+II coalescence is similar to pathway 1 for I+I, i.e., hexagonal stacking in the (0001) direction; however, the resulting cluster bends quite significantly because the hexagonal face opposite to the rhombic face contracts while the rhombic face expands causing the whole cluster to bend towards the hexagonal side. A gap would form on the rhombic side of the resultant cluster, should this growth pattern continue, and the cluster will become fragile and easy to shear. The bending phenomenon happens due to next nearest-neighbor interactions on the surface which causes the surface to bend. Therefore, a solvent that shields surface sites from one another will prevent this kind of bending for longer periods of growth via pathway 1. Since pathways 2 and 3 for the growth of I will cause the rhombic sites to be asymmetrical, it should be expected that the same bending phenomenon can inhibit further growth in the (0001) direction. This cluster combination seems to be realistic for simulating long-term growth and can be observed in the experimental HRTEM imaging where the cross-section is to be asymmetric and possess an apparent sharp edge. The binding energies per CdSe formula unit are also presented in Table 2.


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One can see that they are somewhat smaller than those obtained previously using a double zeta basis set and the B3LYP method for smaller clusters 42. In the case of cluster II as a nucleant, we have also studied the ways in which growth may be inhibited. The most obvious way is when two rhombic sides meet one another. One rhombus may open and be transformed into a hexagon whereas it will be difficult for the other rhombus to be accessed by other nucleating clusters for ring-opening growth via pathway 2. It is also possible to create new rhombi in the process when two hexagonal edges meet each other which leads to the rhombi trapped inside the lattice (see Figure 4). Surprisingly, this type of irregular growth is favorable and is energetically comparable to growth via pathway 2. However, such a cluster formation seems to only be possible if cluster II meets its alternative stacking order isomer (Se on the rhombic corner facing the viewer instead of Cd). The cluster (CdSe)68 formed in this way is 0.8 eV higher in total energy; therefore, such clusters are unlikely to be present in large amounts. It appears that structure I is a good starting point for the initial growth steps and for gauging the anisotropy of growth; however, since we do not expect the template to retain mirror plane symmetry we consider structure II as a better choice for the later steps where C, symmetry is not expected. The asymmetry of cluster II helps understanding the reason why the length of a QP can be limited and also in explaining the formation of crystalline defects during growth.

3.2. Optical Spectra of "#$%-. It has been experimentally observed

16

that thicker quantum platelets are red shifted. In

attempting to reproduce the experimental findings, we have used the time-dependent DFT (TDDFT) method

43

and calculated the first six singlet-singlet transitions for the product cluster

(CdSe)68 resulted from pathway 1 as well as the one resulting from pathway 3. The first singlet-


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singlet transition with oscillation strength f ≠ 0 for pathway 3 was found at 1.65 eV and the one following it was at 1.77 eV. These values are quite close to the band gap of 1.73 eV of the bulk CdSe. It should be noted that the largest distance between opposite atoms in this cluster is approximately 2.8 nm while the Bohr exciton radius of CdSe is 5.6 nm 44. When we consider the product cluster corresponding to pathway 1, we find that the first transition with f ≠ 0 has a much lower energy than that for pathway 3; namely, it corresponds to an excitation of only 1.14 eV with the next followed by a transition at 1.29 eV. These values can be compared to the corresponding values of 1.86 eV and 1.99 eV obtained for CdSe with geometrical structure I and 1.47 eV and 1.70 eV with geometrical structure II. On the basis of the results of our TDDFT computations, one can conclude that thickness does indeed cause a red shift. It is interesting to note that (0001) stacking can also lead to a red shift. To gain insight as to why this can occur, we have displayed the molecular orbitals involved into the first optical transitions of both pathways in Figure 5. We note that the highest occupied MO (HOMO) is represented by a band of antibonding p-orbitals on the Se sites extending from one rhombic defect to the other one in the case of the cluster generated by (0001) stacking (i.e., via pathway 1). This band originates from the atomic orbitals of the second hexagonal layer. The lowest occupied MO (LUMO) is localized on the atoms of the surface hexagonal layer. Therefore, the HOMO-LUMO transition can be thought as an electron transfer along the wurtzite c axis. For the cluster formed via pathway 3, we displayed the HOMO and LUMO + 1 composition because this transition is a magnitude stronger than the HOMO-LUMO transition. The HOMO is similar to that of the cluster formed via pathway 1 and is composed mostly of Se p orbitals. It is localized on the top layer with respect to the viewer. The LUMO + 1 is localized on the Se atoms of the bottom layer.


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For both pathways, we compared the first singlet-triplet transition computed by TDDFT to the HOMO-LUMO gap and found that they are in close agreement. For the cluster stemming from pathway 1, we found 1.11 eV (TDDFT) vs 1.12 eV (HLG), for the cluster corresponding to pathway 3, we found an exact match: 1.64 eV (TDDFT) and 1.64 eV (HLG). This is in agreement with the results obtained for the smaller (CdS)n 45 and (CdSe)n

29

clusters. The state

compositions are summarized in Table S2 of the ESI.

3.3. Decomposition of "#$%&' to "#$%01 + "#$%1& It has been experimentally found that the decomposition of CdSe to CdSe is thermodynamically favorable

16

. To simulate the decomposition process, we chose cluster I,

where we can strip off 26 atoms by cutting between the two birhombic sites. The resulting CdSe3 cluster relaxes to a C4 BN-fullerene cluster, which corresponds to the global minimum in total energy, with relatively small changes to the initial geometry. In the case of CdSe ; however, the resulting belt-like C, cluster geometry clearly is quite far away from the core-shell topology of the energetically preferred geometrical structure of C symmetry. However, it seems to be reasonable to perform the decomposition in this fashion because birhombic sites are easily capable of opening and would thus assist in the resulting CdSe cluster geometrical relaxation. According to the results of our computations, the decompositions of both neutral and singly negatively charged CdSe clusters to the lowest total energy states of the , CdSe,

clusters are energetically unfavorable. However, the decomposition 3 and CdSe of a doubly charged CdSe3 cluster to the singly charged CdSe3 and CdSe clusters is

energetically favored (see Figure 6 and Table 2). The change in thermodynamic favorability is likely related to the increased ionicity of the parent cluster.


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Some of II-VI group clusters have been previously investigated by DFT and were found to be able to attach multiple extra electrons when the cluster size grows 46. We calculated the first and second electron affinities of the CdSe cluster with geometrical structure I and found that their values are 3.0 eV and 1.25 eV, respectively. Considering that the decomposition of the cluster occurs in an electron donating solvent n-octylamine (L-type), it is reasonable to assume that doubly charged species can be formed in solution. When we optimize the belt-like CdSe resultant cluster of C, symmetry obtained from the cleavage of cluster I, we find that it is able to relax to the BN-fullerene cluster, whose state possesses the lowest total energy among other isomers. Such a final relaxation makes the overall reaction favorable. We note that the C, belt structure has an appreciably larger electron affinity than the C core-shell cluster: 2.71 eV versus 2.38 eV. When modeling nanocrystal growth from the (CdSe)21 and (CdSe)13 clusters, one can notice that the topology of the CdSe3 cluster is similar to that of the parent CdSe cluster; thus, the former cluster could be grown in a similar way to its parent cluster. However, the hexagons of the (CdSe)21 BN-fullerene cage are less flat and it appears to be more like a prolate spheroid or nanotube precursor than a fragment of bulk. Correspondingly, the CdSe3 stacking is energetically less favorable than that of the CdSe nucleant. We demonstrated growth in three directions for CdSe3 in Figure 7 in the same manner as we did for CdSe. Growth by opening rhombi results in nanotube propagation and is slightly less energetically favorable than the stacking of two hexagons. Finally, the least favorable mechanism is the stacking of three hexagons, because in this case only one pair of hexagons actually is connected. In summary, one of the most favorable pathway of growth is similar to pathway 3 for CdSe, and nanotube growth, which resembles pathway 2, is the second most favored. The neutral product of


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decomposition, CdSe , does not bind to another CdSe strongly, since the energy of association is only −0.3 eV. If one assumes that it is possible for a CdSe association product to relax to the cluster which corresponds to the global minimum; namely, the oblate CdSe3 cluster of C, symmetry, the association energy only changes marginally to −0.5 eV. This pattern could be related to high stability of the CdSe cluster with C symmetry. We conclude this section by noting that the CdSe decomposition reaction is energetically favored in an electron-donating environment where the CdSe cluster is capable of binding two extra electrons. It is also apparent that the barrier of the reaction is likely quite high both due to the fact that two electrons need to be attached to CdSe and the large amount of relaxation is required to reach the optimal geometry of the lowest total energy state of the (CdSe)13 cluster.

4. CONCLUSION A DFT-based interpretation simulation of the experimental findings on the growth of quantum platelets from CdSe nucleants at low temperatures is presented in this work. We found the preferred pathway of growth, which can be described by hexagonal stacking in the (0001) direction, to be in good agreement with experimental data. When considering growth in the other crystal wurtzite lattice directions we noted the rhombic-ring openings to be an important mechanism for initially driving the growth process, before side-locking operations become more energetically favored. Besides the fact that such pathways are less energetically favorable, they may be inhibited because rhombic defects have an affinity for one another and will prevent growth if they meet. When analyzing the simulated TDDFT optical spectra we noted that the spectra of thicker clusters were red shifted in agreement with experiment. We also found


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that the first singlet-triplet transition energy obtained form our TDDFT computations is nearly identical to the HOMO-LUMO gap. To further investigate (0001) growth, we used an asymmetrical cluster and demonstrated that asymmetry of rhombic defects can cause the cluster to bend and become fragile, which will then limit growth by hexagonal stacking. We also investigated the second pathway of growth proposed in experimental work, where the CdSe nucleant cluster decomposes. We found that the decomposition of CdSe → CdSe + CdSe3 is indeed favorable in an electrondonating environment which the amines used in experiment constitute. We also noted that the CdSe3 cluster has geometrical similarity to its parent cluster and is capable of initiating growth in a similar fashion to its parent cluster as well as extending itself as a nanotube.

Author information Corresponding Author *E-mail: [email protected] ORCID L. G. Gutsev: 0000-0002-9679-9093 Notes The authors declare no competing financial interest

Acknowledgement Portions of this research were conducted with high-performance computational resources provided by the Louisiana Optical Network Infrastructure (http://www.loni.org). This research has also used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. BRR acknowledges the support from the National Science Foundation under Grant Number OIA-1541079.


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Supporting information Total energies of the CdSe dimer for a variety of methods and basis sets, first six singlet-singlet as well as the first three singlet-triplet transitions of (CdSe)68 (Pathway 1 and 3) and (CdSe)34 structures I and II.

Table 1. Comparison of the Results of Computations on the Separation of 1Σ+ and 3Π States of the CdSe Monomer Performed with Basis sets of Increasing Size. Method

B3LYP

CAMB3LYP

B3PW91

Basis T0(kcal/mol) a

ωB97XD

BPW91 CCSD(T)

cc-pvDZ-PP +0.02

+0.15

+0.03

Basis T0(kcal/mol)

PBE0

+0.05

+0.04

–0.08

+0.01

–0.15

–0.13

cc-pvTZ-PP –0.05

+0.06

–0.04

Basis

–0.02

–0.04

cc-pvQZ-PP

T0(kcal/mol)

–0.07

+0.04

–0.06

–0.04

–0.06

–0.17

–0.19

Re(Å)

2.379

2.355b

2.355

2.349

2.356

2.364

2.353c

ωe(cm-1)

248.6

258.3

260.9

264.8

254.2

256.2

263.5

D0 (kcal/mol)d

16.72

15.04

19.40

20.51

17.42

21.55

20.04

T0= Etot(1Σ+) – Etot(3Π) in eV. The negative sign means that the singlet state is lower than the triplet state. b Parameters of the singlet 1Σ+ state. a


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c

The results of the CCSD(T)/aug-cc-pVnT-PP computations: Re = 2.373 A, ωe = 256.5 cm-1. See Ref. 32. d Do = Etot(Cd) + Etot(Se) – [Etot(CdSe) + ZPVE(CdSe)]. The Se atom is computed in its ground triplet state (Hund’s rule).


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Table 2. Total Change in Internal Energies (∆H) and Binding Energies per CdSe unit (BE) of Products for the Association of "#$%&' Clusters, the Decomposition of "#$%&' I Cluster to "#$%01 + "#$%1& , the Association of "#$%01 Clusters, the Association of "#$%1& Clusters and the Binding Energies per CdSe of "#$%1& , "#$%01 and "#$%&' I.

(CdSe)34+(CdSe)34 -> (CdSe)68 Growth Pathways (CdSe)68 (I+I) Pathway 1 Pathway 2 Pathway 3 (CdSe)68 (II+II) (0001) Stacking (CdSe)68 (II+II') Rhombic meeting

∆E (eV)

Binding energy per CdSe (eV/CdSe)

-2.88 -1.85 -1.06

3.11 3.10 3.08

-1.02

3.09

-2.09

3.09

(CdSe)34 decomposition to (CdSe)13 (C3) ∆E 0.52 0.77 1.14 -0.36

(CdSe)34(Cs)-> (CdSe)21(C3h)+(CdSe)13(C3) (CdSe)34-(Cs) ->(CdSe)21(C3h)-+(CdSe)13(C3) (CdSe)34-(Cs) ->(CdSe)21(C3h)+(CdSe)13-(C3) (CdSe)34-2 (Cs) -> (CdSe)21-(C3h) + (CdSe)13-(C3)

(CdSe)34 decomposition to (CdSe)13 (Cs) ∆E 10.64 10.05 8.55

(CdSe)34 (Cs) -> (CdSe)21(C3h) + (CdSe)13(Cs) (CdSe)34-(Cs) ->(CdSe)21(C3h)+(CdSe)13-(Cs) (CdSe)34-2(Cs) -> (CdSe)21-(C3h) + (CdSe)13-(Cs)

(CdSe)21(C3h)+(CdSe)21(C3h) -> (CdSe)42 Growth Pathways

(CdSe)21(C3h)+(CdSe)21(C3h) -> (CdSe)42 (2 hexagon) (CdSe)21(C3h)+(CdSe)21(C3h) -> (CdSe)42 (3 hexagon) (CdSe)21(C3h)+(CdSe)21(C3h) -> (CdSe)42 (1 hexagon)

∆E -1.17 -0.50 -0.37

Binding energy per CdSe (eV/CdSe) 3.08 3.06 3.06

∆E -0.30

Binding energy per CdSe (eV/CdSe) 3.04

(CdSe)13 Self-Association

(CdSe)13 (C3) + (CdSe)13 (C3) -> (CdSe)26 (association)


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(CdSe)13 (C3) + (CdSe)13 (C3) -> (CdSe)26 (Cs)

-0.53

3.05

Neutral Cluster Binding Energies

(CdSe)13(C3) (CdSe)21(C3h) (CdSe)34(Cs)


Binding energy per CdSe (eV/CdSe) 3.03 3.05 3.06

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Figure 1. The lowest energy free standing CdSe isomers. I and I’ are two-layered, II is four-layered and III is a (6,0) type nanotube precursor. For II we color the internal Cd’s red and the internal Se orange, there are three internal Cd and three internal Se. In the case of I and II, we also indicate the orientation of the wurzite crystal axis. The squares indicate locations of at least two rhombi.


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Figure 2. The three pathways of growth by a I+I reaction. Pathway 1: Growth in the (0001) direction. Pathway 2: Rhombic ring opening growth. Pathway 3: Side-locking growth. Red dotted lines represent bonds broken, blue dotted lines represent bonds formed. It is recommended that the reader compare these images to Figure 4 in Ref. [16].


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Figure 3. The next proposed step of growth corresponding to a combination of rhombic ring opening followed by a side-locking operation (Pathways 2+3). Blue dotted lines represent bonds formed. It is recommended that the reader compare this image to Figure 4 in Ref 16.


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Figure 4. The most energetically favorable mechanisms of II+II and II+II’ growth. II+II represents (0001) growth where surface-surface interactions cause the cluster to bend. II+II’ represents the combination of two rhombic defects. Red dotted lines represent bonds broken, blue dotted lines represent bonds formed.


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Figure 5. Molecular orbitals for the resulting clusters of Pathway 1 (A), and Pathway 3 (B). In the second case, we present also LUMO +1 because the oscillation strength of the HOMO →LUMO +1 transition is much larger than that of the HOMO → LUMO transition.


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Figure 6. The decomposition of CdSe3 to CdSe3 and CdSe . The reaction becomes energetically favorable after intermediate CdSe cluster relaxes to its C core-shell shape.


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Figure 7. Growth pathways of CdSe3 + CdSe3 . In clockwise order starting from the top left: CdSe3 of C4 symmetry, single hexagonal stacking, double hexagonal stacking, nanotube propagation.


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TOC Abstract:


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Pathways of Growth of CdSe Nanocrystals from Nucleant (CdSe)34

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