General low-temperature reaction pathway from precursors to monomers before nucleation of compound semiconductor nanocrystals

Little is known about the molecular pathway to monomers of semiconductor nanocrystals. Here we report a general reaction pathway, which is based on hydrogen-mediated ligand loss for the precursor conversion to ‘monomers' at low temperature before nucleation. We apply 31P nuclear magnetic resonance spectroscopy to monitor the key phosphorous-containing products that evolve from MXn+E=PPh2H+HY mixtures, where MXn, E=PPh2H, and HY are metal precursors, chalcogenide precursors, and additives, respectively. Surprisingly, the phosphorous-containing products detected can be categorized into two groups, Ph2P–Y and Ph2P(E)–Y. On the basis of our experimental and theoretical results, we propose two competing pathways to the formation of M2En monomers, each of which is accompanied by one of the two products. Our study unravels the pathway of precursor evolution into M2En monomers, the stoichiometry of which directly correlates with the atomic composition of the final compound nanocrystals.

A major advance in the NC synthesis occurred with the recognition that commercial tertiary phosphine TOP contains dioctylphosphine (HP(C 8 H 17 ) 2 , a secondary phosphine) that acts as an active impurity facilitating NC nucleation/growth but leading to low synthetic reproducibility (because of its varying amount from batch to batch) [13][14][15]23 . It was first suggested 15 and then experimentally demonstrated 23 that the use of commercial diphenylphosphine (HP(C 6 H 5 ) 2 or HPPh 2 , a secondary phosphine) resulted in an equilibrium of SeTOP þ HPPh 2 " TOP þ Se¼PPh 2 H. Meanwhile, high metal-to-Se and low Se-to-TOP feed ratios were found to shift the equilibrium to the right 23 , which remarkably improved the NC synthesis with high particle yield and synthetic reproducibility at low reaction temperatures [17][18][19]21,22,38 . E¼PPh 2 H is much more reactive than ETOP 15,23 . The use of ETOP þ HPPh 2 leading to the E precursor of E¼PPh 2 H instead of ETOP has been shown to be beneficial for the synthesis of NCs such as PbSe (refs 17,18) and CdSeS (ref. 38), while the direct use of E¼PPh 2 H (made from E þ HPPh 2 ) is preferable to the synthesis of NCs such as ZnSe (ref. 19), ZnSeS (ref. 21) and CuInS 2 (ref. 22). With the large number of recipes developed, recent studies have demonstrated clearly that the control of precursor reactivity has a strong impact on the reproducibility, particle yield, and size and size distribution of the resulting NCs [17][18][19]21,22,[36][37][38] . For example, the reactivity of thiourea precursors was shown to control the size, yield and batch-to-batch consistency of PbS NCs 37 .
Generally, the current state-of-the-art in NC synthesis is principally empirical, with little insight into the stepwise pathway by which monomers are generated. There exists 'an induction period' before nucleation occurs, which was briefly addressed for CdSe from CdX 2 þ SePR 3 (X ¼ carboxylate and R ¼ alkane groups ref. 33). During the induction period, the consumption of SePR 3 was visible, but NC absorbance did not appear. The consumption of SePR 3 was claimed to accumulate 'solutes' that may be composed of multiple monomer units; afterwards, nucleation took place. Accordingly, the formation of 'monomers' from precursors takes place at the beginning of the 'induction period'.
With the monomer in the form of Cd 1 Se 1 instead of Cd 2 Se 2 , the pathway from precursors to Cd 1 Se 1 monomers was recently documented for CdSe NCs in the presence of C 18 H 35 NH 2 as one additive from the reaction of Cd(OA) 2 þ SeTOP þ HPPh 2 . The P-containing products Ph 2 P-OOCC 17 H 33 (1a), Ph 2 PÀPPh 2 (1b), Ph 2 P-NHC 18 H 35 (1c) and Ph 2 P(Se)-NHC 18 H 35 (2c) were detected, and the equilibrium of 1c þ Se¼PPh 2 H"2c þ HPPh 2 was demonstrated 25 . Different NC systems are supposed to follow different reaction pathways to their monomers; for this seemingly obvious reason, we decided to investigate individual pathways from precursor evolution to monomers at low reaction temperatures in each of the reactions of MX n þ nE¼PPh 2 H þ HY, where M ¼ Cu (I), Cd (II), Zn (II), Ge (II), Pb (II) and In (III), E ¼ S, Se and Te, and HY ¼ RCOOH, HPPh 2 , RNH 2 , RSH and ROH. The anion X for the starting metal cations was chosen such that MX n is soluble under the reaction conditions and can often be a long-chain alkyl carboxylate or thiolate. This reaction system has proven to be practical for the synthesis of various NCs with high quality, enhanced reproducibility and yield [17][18][19]21,22,38 . However, the pathway from precursors to monomers of the reaction MX n þ nE¼PPh 2 H þ HY is perplexing to study because of the inevitable presence of HX and HPPh 2 (as explained by the below equations 1-6).
Here, we present our study on the reaction pathway from precursors to M 2 E n monomers for the reaction of MX n þ nE¼PPh 2 H þ HY. Conclusively, various P-containing compounds are detected for the metal M ¼ Cu (I), Cd (II), Zn (II), Ge (II), Pb (II) and In (III) in combination with the chalcogen E ¼ S, Se and Te. Most importantly and surprisingly, we are able to categorize these P-containing compounds into two groups of Ph 2 P-Y (1) and Ph 2 P(E)-Y (2), which are summarized in Supplementary Table 1 and Supplementary Note 1 (with Y ¼ -OOCC 17 H 33 (a), -PPh 2 (b), -NHC 18 H 35 (c), -SC 12 H 25 (d) and -OC 12 H 25 (e)), together with the detailed information on their assignment that includes our calculation of 31 P NMR chemical shifts and a summary of the experimental information available in the literature. Accordingly, we propose two competing pathways leading to M 2 E n monomers as illustrated by equations 1 and 2 (with further explanation in equations 3-6).
where M ¼ cation Cu (I), Cd(II), Zn (II), Ge (II), Pb (II) and In (III), n ¼ 1, 2 and 3 of the oxidation state of monovalent, divalent and trivalent M, respectively, X ¼ anion (such as carboxylate C 17 H 33 COO À ), E ¼ S, Se and Te, and additive HY ¼ RCOOH (a), HPPh 2 (b), RNH 2 (c), RSH (d) and ROH (e). A monomer in the form of M 2 E n is proposed, which leads to NC nucleation followed by growth. The H atoms involved in the first and second H-mediated ligand loss steps are denoted as H 0 and H 00 , respectively. It is noteworthy that other secondary phosphines such as dicyclohexylphosphine (HPCy 2 ) leads to precursor E¼PCy 2 H to start with; the correlation between the reactivity of E¼PR 2 H (such as with R ¼ Ph or Cy) and the size of the resulting NCs will be the subject of another study. Our general stepwise pathway from precursor evolution to M 2 E n monomers at low reaction temperatures should result in a much more in-depth fundamental understanding, which may advance the design and synthesis of colloidal semiconductor NCs and advance the realization of their potential.

Results
NMR study of various reaction systems. The reactions studied are presented in Fig. 1 Fig. 25 and which is supported by Supplementary Fig. 24 with the reaction of [Cd(Se 2 PPh 2 )] 2 (3) þ Cd(OA) 2 þ HY þ HPPh 2 . On the basis of our in situ 31 P NMR monitoring of a large number of reactions dealing with six metal cations (M) and three chalcogens (E) in the presence of the five types of HY additives, we propose a conceptual pathway ( Fig. 6) that demonstrates the probable reactions from precursors to monomers. This distinct pathway starts with the coordination of n E¼PPh 2 H molecules per MX n , followed by the H-mediated ligand loss of n HX molecules to result in one M(EPPh 2 ) n (A). Afterwards, A undergoes dimerization to D that reacts with HY to E and/or F, or reacts with HY leading to B and/or C that undergoes dimerization to E and/or F, respectively. M 2 E n and 1 are then produced from E (equation 1), while M 2 E n and 2 from F (equation 2). Metathesis equilibria are involved, in which there are reversible exchanges of small ligand molecules, HPPh 2 , E¼HPPh 2 and HY (around metal chalcogenide centres, such as D þ HY"E þ E¼PPh 2 H and D þ HY"F þ HPPh 2 ), and chalcogenide exchange reactions such as 1 þ Se¼PPh 2 H"2 þ HPPh 2 , which affect the detection of 1, 2 and HPPh 2 . The chalcogenide exchange equilibria were examined by density functional theory (DFT) shown in Supplementary Table 2 and Supplementary Note 2. Furthermore, we performed extensive DFT calculations for the probable isomers of the intermediates A-F shown in Fig. 6; therefore, we are able to elucidate further the pathway we proposed in Fig. 7, in which the probable isomers with detailed bonding skeletons of each intermediate A-F are illustrated, providing a much deeper understanding. Figure 1 presents our 31 P NMR spectra collected from four representative mixtures of Cd(OA) 2 þ SeTOP þ HPPh 2 (a) and with the additional additives of oleylamine (C 18 H 35 NH 2 , b), dodecylthiol (C 12 H 25 SH, c) and dodecylalcohol (C 12 H 25 OH, d). It is Se¼PPh 2 H rather than SeTOP that reacts with Cd(OA) 2 because of SeTOP þ HPPh 2 "Se¼PPh 2 H þ TOP (refs 15,23). The products 1a (Ph 2 P-OOCC 17 H 35 ) and 1b (Ph 2 P-PPh 2 ) equilibrate via Ph 2 P-COOR (1a) þ HPPh 2 "RCOOH þ Ph 2 P-PPh 2 (1b), which is weighted to the right at room temperature (RT) 21,24 . The additional products of 2a (Ph 2 P(Se)-OOCC 17 H 35 ) and 2b (Ph 2 P(Se)-PPh 2 ) from the mixtures of Cd(OA) 2 , Zn(OA) 2 or Ge(OA) 2 þ Se¼PPh 2 H are shown in Supplementary Figs 3-5. The addition of a primary amine C 18 H 35 NH 2 to the mixture of Fig. 1a, as shown in Fig. 1b, resulted in additional 1c (Ph 2 P-NHC 18 H 35 ) and 2c (Ph 2 P(Se)-NHC 18 H 35 ). The use of the thiol C 12 H 25 SH generated 1d (Ph 2 P-SC 12 H 25 ) without the detection of 1a and 1b (Fig. 1c). Similarly, the use of the alcohol C 12 H 25 OH produced 1e (Ph 2 P-OC 12 H 25 ) and 2e (Ph 2 P(Se)-OC 12 H 25 ; Fig. 1d). The same P-containing compounds were observed from the mixtures with Pb(OA) 2 replacing Cd(OA) 2 ( Supplementary Fig. 5), which strongly suggests that Compounds 1a-e (Ph 2 P-Y) have their own similar pathways (for different Y), and Compounds 2a-e (Ph 2 P(Se)-Y) have their own similar pathways (for different Y). Thus, we propose that Compounds 1 and 2 follow two different paths for their formation from their own immediate precursors (Figs 1 and 2).
The temporal evolution of the absorption of growing CdSe NCs (shown in Supplementary Figs 6-7) suggests that the amount of additives, thiol C 12 H 25 SH or alcohol C 12 H 25 OH affects nucleation/growth, in addition to other experimental parameters such as the temperature and amount of HPPh 2 used. Focusing on the identification of the reaction pathway before nucleation, the present study does not address the control of the size and size distribution, which could be affected by various experimental parameters including cation-to-anion feed molar ratios and the nature of Se¼PR 2 H as shown by Supplementary Figs 8 and 9. In addition, the size and size distribution of the CdSe NCs synthesized with SeTOP þ HPR 2 (dicyclohexylphosphine (or HPCy 2 ) and HPPh 2 ) are different from those with Se¼PCy 2 H and Se¼PPh 2 H. Previously, the reaction of Cd(OA) 2 þ Se¼PCy 2 H was reported to lead to Compound Cy 2 P-OOCC 17 H 33 (1a analogue) and Cy 2 P(Se)-OOCC 17 H 33 (2a analogue) 24 . Therefore, the present study on the general reaction pathway 2Cd(OA) 2 (2) (1) from precursors to M 2 E n monomers before nucleation at low reaction temperatures should benefit the field by leading to a better understanding of the 'induction periods' to tailor, optimize and manipulate nucleation/growth, which offers finer control of the size and size distribution of NCs produced. Figure 2 shows our 31 P NMR spectra collected from four representative mixtures of Cd(OA) 2 þ S¼PPh 2 H (a) and with the additional additives of oleylamine (C 18 H 35 NH 2 , b), dodecylthiol (C 12 H 25 SH, c) and dodecylalcohol (C 12 H 25 OH, d). The chalcogenide S is generally less reactive than Se and Te under QD formation conditions [10][11][12] 21,22 . The P-containing products detected from the S¼PPh 2 H-related reactions with Cd(OA) 2 (without additional HPPh 2 but with free HPPh 2 present) are similar to other chalcogenide-related reactions (Figs 1 and 3). Again, the products from the four reactions ( Fig. 2) are grouped into Compounds 1 and 2. For example, the products formed are elucidated as follows: 1a without an additive (Fig. 2a), 1a and 1c with an amine additive (Fig. 2b), 1d with a thiol additive (Fig. 2c) and 1e and 1a with an alcohol additive (Fig. 2d). The major difference between the Cd þ S reactions (Fig. 2) and the Cd þ Se reactions ( Fig. 1) is the formation of 2b 0 (Ph 2 P(S)-PPh 2 ) under all conditions. Compound 2b 0 was also detected from a mixture of Zn(OA) 2 þ S¼PPh 2 H shown in Supplementary Figs 10-12.
TeTOP is much more reactive than SeTOP and STOP in QD engineering [10][11][12] . Under the reaction conditions, this fact is readily discernible, as TeTOP ( Supplementary Fig. 14) reacts completely when the first spectrum (1) of the each reaction shown in Fig. 3 was collected. Again, the products 1a (Fig. 3a), 1c (together with 1a, in the presence of amine Fig. 3b), 1d (in the presence of thiol Fig. 3c) and 1e (in the presence of alcohol Fig. 3d) were detected in addition to 1b. The same P-containing products were detected from the Ge(OA) 2 þ TeTOP þ HPPh 2 þ HY reactions ( Supplementary Fig. 19). As shown in Supplementary Figs 15-17, the amount of HPPh 2 used affects the ratio of 1a and 1b detected in the mixture of Cd(OA) 2 þ TeTOP þ HPPh 2 : the more HPPh 2 is used, the more diphosphine compound 1b is detected, the trend of which is similar to what was reported for CdSe because of the equilibrium of Ph 2 PÀCOOR (1a) þ HPPh 2 "RCOOH þ Ph 2 PÀPPh 2 (1b) being weighted towards the right at RT 21,24 . Notably under these conditions, no Compound 2 (Ph 2 P(Te)-Y) was observed. The Te-P bond strength is lower than that of Se-P or S-P and, thus, Ph 2 P(Te)-Y might be too reactive to be detected.
For the S, Se and Te chalcogenide series with Cd (II) under all examined conditions (Figs 1-3), Ph 2 P-Y (1a-e) and/or Ph 2 P(E)-Y (2a-e) are identified as major P-containing products. For the other divalent metal salts of Zn, Ge and Pb studied, the same trends were discovered ( Supplementary Figs 1-21). For E ¼ Se ( Supplementary Figs 1-2) in the absence of additional additives, 1a and 1b were predominantly found. With amine addition, 1c and 2c are also formed. With thiol addition, 1d is formed as a main product, and with alcohol addition, both 1e and 2e are formed. For E ¼ S, 1a-e were detected along with 2b 0 ( Supplementary Figs 10-13). For E ¼ Te, none of Ph 2 P(Te)-Y but 1a-e were observed ( Supplementary Figs 14-21). Thus, for all the combinations investigated, the reaction of MX 2 þ E¼PPh 2 H þ HY appeared to follow equation 1 to produce 1 and/or equation 2 to produce 2 along with the formation of M 2 E 2 monomers.
More interestingly, the detection of P-containing compounds for Cu (I) and In (III) is similar to that for M (II). C 12 H 25 SH has been used as a solvent and a ligand to improve the synthesis of CuInSe 2 and CuInS 2 QDs 22,29-31 . Representative 31 P NMR data for the synthesis of Cu 2 Se, In 2 Se 3 and CuInSe 2 using Se¼PPh 2 H and S¼PPh 2 H as the Se and S precursors are shown in Fig. 4, and for the synthesis of Cu 2 S, In 2 S 3 and CuInS 2 in Supplementary   Fig. 4a 22 . Intriguingly, at RT per 15 min (Fig. 4e with expansion), the additional peaks near free Se¼PPh 2 H (B7.3 p.p.m.) are readily interpreted as coordinated Se¼PPh 2 H to In (Fig. 4e and Supplementary Fig. 22). The products 1d and 2d are observed with the absence of Se¼PPh 2 H (Fig. 4d, the In-only experiment), whereas only 2d is formed in the reaction with the presence of Se¼PPh 2 H (Fig. 4f with both the presence of Cu and In). Thus, the observation of Compounds 1 and 2 could be affected by several factors, including the equilibrium of 1 þ Se¼PPh 2 H"2 þ HPPh 2 , which could be weighted towards the right (Supplementary Table 2 and Supplementary Note 2), similar to TOP þ Se¼PPh 2 H" SeTOP þ HPPh 2 (refs 15,23), except for 1b þ Se¼PPh 2 H"2b þ HPPh 2 (refs 21,23-25).
It is critical to perform additional experimental investigation regarding the formation of Compound 2 from a direct path. Figure 5 shows the corroborative evidence for equation 2 (Figs 6 and 7 and Supplementary Figs 1-9). These experiments relied on the independent preparation of cadmium bis(diselenophosphinate) (Cd(Se 2 PPh 2 ) 2 , 3) 24 , which reacted with Cd(OA) 2 in the presence of HY of C 18 H 35 NH 2 (a), C 12 H 25 SH (b) and C 12 H 25 OH (c). The reaction of 3 þ Cd(OA) 2 þ HY leads to 2c, 2d and 2e, respectively. It is noteworthy that 1 was not detected. The addition of oleic acid did not lead to 2a (not shown). These results suggest that equation 2 is active at the appropriate temperatures tested (with the amine, thiol and alcohol, but not with the acid). According to the previous study on 3 þ Cd(OA) 2 (ref. 24), it is reasonable that the presence of HPPh 2 could speed up equation 2. As shown by Supplementary Fig. 24, the catalytic amount of HPPh 2 (0.05 eq. based on 3) accelerated significantly each of the three reactions, with 2 still being the main product. With more HPPh 2 (1.00 eq. based on 3), additional 1c (with 1b), 1d (with 1a and 2a) and 1e were detected, respectively. Thus, HPPh 2 could also initiate another equation 1 to 1 þ Cd 2 Se 2 (via A (Cd(SePPh 2 ) 2 ) as shown in Supplementary Fig. 25). The results shown by Fig. 5 and Supplementary Fig. 24 clearly support that the equilibrium of 1e þ Se¼PPh 2 H"2e þ HPPh 2 is weighted towards the right, which is in agreement with our DFT examination shown in Supplementary Table 2 and Supplementary Note 2. Figure 6 presents a schematic interpretation of our experimental results (shown in Figs 1-5 and Supplementary Figs 1-24). When a mixture of metal carboxylate and chalcogenide TOP compound (ETOP) was mixed with dialkylphosphine such as HPPh 2 with or without the presence of additives such as amines, thiols and/or alcohols, the formation of NCs begins with chalcogen E exchange, namely ETOP þ HPPh 2 "TOP þ E¼PPh 2 H (refs 15,23-25), the exchange of which activates the chalcogenide. Subsequently, the activated E¼PPh 2 H reacts by (2) (1) (1) (1) (1) (1) (1)  Figure 6 is formulated for the case of M (II), but also applies to M (I) and M (III) where their monomers are accordingly proposed to be M 2 E and M 2 E 3 , respectively. Obviously, A and B are connected by equilibrium A þ HY"B þ E¼PPh 2 H, while A and C by A þ HY"C þ HPPh 2 . Consequently, B and C are correlated by B þ E¼PPh 2 H"C þ HPPh 2 , similarly to DFT study. To further understand the fundamental chemistry involved in the putative pathway proposed in Fig. 6, let us turn our attention to the possible isomers with their bonding skeletons of each of the intermediate species A to F proposed in Fig. 6. In addition to metal ions (M), chalcogenides (E) and diphenylphosphinio species (Ph 2 P), intermediates B to F contain the various Y groups. Consequently, each intermediate has multiple possible constitutional isomers, while most possible combinations of bonds, such as P-E, E-E, P-P, P-Y and E-Y bonds, exist in well-known compounds, and all such bonds can in principle coordinate to metal ions leading to multiple possibilities. For example, for Y ¼ NHR in Fig. 6, the N could bond to Cd, P or Se; if N is bound to P, two bonding arrangements (M-P-N and M-N-P) could in principle be expected. These uncertainties are amenable to DFT calculations, which provide useful information to minimize positional isomers, with the cancellation of errors in the DFT approximation [39][40][41][42] . In this way, the calculated bonding trends should be reliable. The possibilities in Fig. 7 are distinguished by DFT calculations at the M06//B3LYP/ 6-31þþG (d, p), Stuttgart/Dresden (SDD) level in ODE media. Our DFT-calculated structures and energies of many more possible isomers are shown in Supplementary Tables 3-25 including structural, geometric and rotational isomers. An additional description and discussion of the isomers of each intermediate A to F can be found immediately before Supplementary Tables 3-17.   Fig. 1. The relevant pathway to the formation of monomers and 2 is shown in Supplementary Fig. 25.   Table 2 and Supplementary Note 2). Note that another secondary phosphine, dicyclohexylphosphine (HPCy 2 ), was also tested (as shown in Supplementary Figs 1 and 3); precursor E¼PCy 2 H instead of E¼PPh 2 H also leads to Compound Cy 2 P-Y (1) and Cy 2 P(E)-Y (2). The correlation between the reactivity of E¼PR 2 H (with R ¼ Ph or Cy) and the size of resulting NCs is the subject of another study. The dotted box is for a system to start from single-source precursors (such as 3 shown in Supplementary Fig. 25 with E ¼ Se and M ¼ Cd (II)). See Supplementary Fig. 26  The most stable A is with the P-Se-Cd-Se-P skeleton among the seven isomers computed (Supplementary Table 3). For the two predominant species B1 and B2 found, they have the Se-Cd-P-Y and P-Se-Cd-Y skeletons, respectively. B1 versus B2 includes P-Y versus M-Y bonds, without E-Y bonds. With Y ¼ NHR for CdSe (Supplementary Table 4), the B1 isomer was calculated to be 10.1 kJ mol À1 (free energy DG) more stable than B2. This energy trend of B1oB2 was not found for the other Y. For Y ¼ SR (Supplementary Table 4), the distinction is quite clear that the direct metal-bound B2 isomer P-Se-Cd-SR was calculated to be 82.5 kJ mol À1 more stable than the B1 isomer with Se-Cd-P-SR. For Y ¼ OR (Supplementary Table 5), the B2 isomer with the P-Se-Cd-OR skeleton was found to be at the lowest energy, but the B1 isomer with the Se-Cd-P-OR skeleton was only 6.9 kJ mol À1 higher-an energy difference that is close to the accuracy of the DFT method and could be affected by the exact nature of various R groups, the solvent used and the temperature employed. For Y ¼ OOCR (Supplementary Table 6), the directly metal-bound B2 isomer is 111.3 kJ mol À1 more stable than the B1 isomer with Se-Cd-P-OOCR. For Y ¼ PPh 2 (Supplementary Table 6), B2 is 58.7 kJ mol À1 more stable than B1.
Intermediate C with an extra chalcogen E atom compared with intermediate B evidently has more constitutional possibilities. Intriguingly, the connectivity follows similar patterns to that of intermediate B. For Y ¼ NHR (Supplementary Table 7), C1 with the Se-Cd-Se-P-N connectivity has the lowest energy. Note that there is an extra Se inserted between the Cd and P atoms. The most stable Cd-N-bound species C2 was found to contain the four-membered N-Cd*-Se-P-Se-(Cd*) ring, which was 18.7 kJ mol À1 calculated. For Y ¼ SR (Supplementary Table 8), C2 with a direct Cd-SR bond is favoured much more than the other isomers considered. Complexes with this C2-type connectivity but with Y ¼ SSPPh 2 have been characterized experimentally 35 . For Y ¼ OR (Supplementary Table 9), C1 and C2 differ by only 2.3 kJ mol À1 and can therefore be considered iso-energetic. For Y ¼ OOCR (Supplementary Table 10), C2 with the direct Cd-OOCR bonding is much more stable, similar to the case of Y ¼ SR.
Consequently, for Y ¼ NHR, B1 and C1 are preferred. For Y ¼ OR, the selectivity is not obvious. For Y ¼ SR and OOCR, B2 and C2 are favoured. Thus, the preference on the bonding skeleton calculated for intermediates B and C is similar. The nature of the chalcogenide also affects the relative stability of B1 versus B2 (Supplementary Table 18) as well as that of C1 versus C2 (Supplementary Table 19). For Y ¼ NHR specifically, B2 and C2 are stabilized for E ¼ S, whereas B1 and C1 are more stable for E ¼ Te than for E ¼ Se. For CdSe, our preliminary efforts on the kinetics associated with the putative pathway A þ HÀY-B þ Se¼PPh 2 H are presented in Supplementary Figs 28-31 and Supplementary Note 5 with A1b for A and B2a for B. The trend of the kinetics computed seems to be in agreement with our experimental data showing the slowest disappearance of SeTOP (Fig. 1) and of 3 (Fig. 5) is from the batch with HY ¼ RNH 2 .
Intermediates E and F are proposed as the very immediate precursors leading to monomers M 2 E n with Compounds 1 and 2, respectively. E1 could have resulted from dimerization of B1 and E2 from B2. F1 could have resulted from dimerization of C1 and F2 from C2. Again, DFT calculations were performed to address the question of whether the various Y species are bound to Cd or to Se or to P. Clearly, E and F are computationally demanding. Generally, E isomers follow the trend of B isomers, and F follows C: low-energy B isomers lead to low-energy E, and C to F. In all cases, the four-membered ring Cd*-Se-Cd-Se-(Cd*) was found by minimization. For Y ¼ NHR (Supplementary Table 11), E1 with the P-N bond is much more stable than E2 with the Cd-N bond by B150 kJ mol À1 . For Y ¼ SR (Supplementary Table 11), E2 with the Cd-S bond is more stable than E1, but the difference is smaller (32.7 kJ mol À1 ) than that (82. 5  B1. For Y ¼ OR (Supplementary Table 12), E1 is much more stable than E2, whereas B1 is similar to B2. For Y ¼ OOCR (Supplementary Table 13), isomers such as E2 (with the Cd-Y bond) are the most stable ones found. Intermediate F consists of two more E atoms than E. For Y ¼ NHR (Supplementary Table 14), F1, with Se inserted between the Cd and P, namely Cd-Se-P-N, is 196.6 kJ mol À1 more stable than F2 with the direct Cd-N bond. For Y ¼ SR (Supplementary  Table 15), F2 is 78.0 kJ mol À1 more stable than F1. For Y ¼ OR (Supplementary Table 15), F1 is 126.1 kJ mol À1 more stable than F2. For Y ¼ OOCR (Supplementary Table 16), F2 is 78.8 kJ mol À1 more stable than F1. For Y ¼ PPh 2 , D2 (a dimer of A) is more stable than D1 (equivalent to F1) by 86.6 kJ mol À1 .
Although speculative, our current proposal is that E and F (or possibly higher oligomers such as from the dimerization of E and F) 43 facilitate the release of 1 and 2, respectively. The release of Compound 1 is more apparent from E1 (via the M-P bond cleavage) than from E2; the Cd-P bond expected to break for E1 to lose 1 has a length of 2.66 Å (longer than 2.58 Å in B1). In addition, the release of Compound 2 is more apparent from F1 (via the M-E bond cleavage) than from F2; the Cd-Se bond expected to break for F1 to lose 2 has a length of 2.74 Å (longer than 2.69 Å in C1). For the release of 1 and 2 from E2 and F2, respectively, it seems reasonable that the formation of a Y-P bond (via the interaction of Y with Ph 2 P and with Ph 2 P(E)) could be accompanied by the cleavage of M-Y and P-E bonds 44 . It has been suggested that the oligomerization to [Cd 2 Se 2 ] m is accompanied by a decrease in free energy for at least m ¼ 6 (ref. 24); this thermodynamic stability of [M 2 E n ] m may be the driving force of the overall reaction 45 .

Discussion
The molecular pathway of precursor evolution to monomers responsible for nucleation at low reaction temperature to semiconductor NCs has been recognized as a major challenge in advancing the design and synthesis of high-quality NCs with high synthetic reproducibility and particle yield. We have successfully rationalized a general reaction pathway for precursor evolution to monomers at low reaction temperatures from the mixture of MX n þ ETOP þ HPPh 2 þ HY or MX n þ E¼PPh 2 H þ HY. On the basis of the experimental and computational investigations, we propose the monomer of M 2 E n and its formation accompanied by the loss of ligand Ph 2 P-Y (1) and Ph 2 P(E)-Y (2) via two competing paths. Experimentally, the combination of six metal ions of monovalent, divalent or trivalent, three chalcogenides and five types of additive HY (of carboxylic acid, dialkylphosphine, amine, thiol or alcohol) results in the P-containing products of Ph 2 P-Y (1) and Ph 2 P(E)-Y (2). The in-depth interpretation of the mechanism is supported by our DFT calculations. Our proposed pathway features a series of H-mediated ligand loss/exchange reactions triggered by dialkylphospine chalcogenides (such as E¼PPh 2 H) to form intermediate A (M-(EPPh 2 ) n ), which leads to intermediate E (YPh 2 P-ME n M-PPh 2 Y, equation 1) and intermediate F (YPh 2 PE-ME n M-EPPh 2 Y, equation 2), the formation of which consists of dimerization and reaction with HY. The disassociation of ligand 1 from E and ligand 2 from F results in M 2 E n monomers. Clearly, HY participates in the formation of monomers and thus could accelerate nucleation; meanwhile, a large amount of HY plays the role of a solvent and, thus, could retard nucleation. Importantly, the general pathway applies to metal chalcogenide NCs made from both toxic metals such as Cd (II) and Pb (II) and more benign metals such as Cu (I), Zn (II) and In (III). The insights into the chemical nature of the M 2 E n monomer the building block, could provide the basis for the field to enable the manipulation of the chemical processes for rational design and synthesis of a variety of NCs with complex stoichiometry. The use of secondary phosphines together with beneficial additive HY should be a general and practical avenue to engineer metal chalcogenide NCs at low reaction temperatures with high quality, enhanced synthetic reproducibility and particle yield. We anticipate that the insight gained on the molecular pathway for precursor evolution into various types of M 2 E n monomers may enable the field to synthesize sophisticated NCs, including phase-change materials, with better-controlled chemical processes via cation exchange as well as doping and co-doping with monovalent and trivalent metal ions [46][47][48][49][50][51][52] . We are actively exploring the correlation between the pathway of monomer formation with the formation of magic-size and regular QDs, aiming at the control of product properties including the size and size distribution. In addition, we believe that, similar to the endeavour of the development of organic syntheses, the basic chemistry reported embraces the advance of the NC synthesis from an empirical art to science with pathway-enabled design leading towards the full realization of the NC potential [53][54][55][56][57] . Methods 31 P NMR measurements. 31 P NMR was performed on a Bruker AV-III 400 spectrometer operating at 161.98 MHz, referenced with an external standard, 85% H 3 PO 4 . Usually, we used D1 ¼ 2 s (64 scans total taking B3 min; unless mentioned otherwise). NMR samples were usually prepared and loaded in NMR tubes in a glovebox and properly sealed. All chemicals used are commercially available from Sigma-Aldrich and were used as received (or otherwise specified). The used ligands and additives are oleic acid (OA, tech. 90%), diphenylphosphine (HPPh 2 , 99%, Strem Chemicals), oleic amine (OLA, C 18 H 35 NH 2 , tech. 70%), 1-dodecanethiol (C 12 H 25 SH, 98%) and lauryl alcohol (C 12 H 25 OH, 98%). The elemental chalcogens used are sulfur (S, precipitated, Anachemia), selenium (Se, 200 mesh, 99.999%, Alfa Aeser) and tellurium (Te, 200 mesh, 99.8%). For the assignment of Compounds 1 and 2, sodium hydride (NaH, 95%, dry), chlorodiphenylphosphine (Ph 2 P-Cl, 97%, Alfa Aeser) were used. Compounds 1 (Ph 2 P-Y) and 2 (Ph 2 P(E)ÀY) detected with NMR are related to the formation of monomers/solutes/NCs, and have been use to explore the formation of monomers since 2006 (refs 13,15,23-25). The P-containing products detected with 31 P NMR are listed as follows: 1a (Ph 2 P-OOCC 17 H 33 ), 1b (Ph 2 P-PPh 2 ), 1c (Ph 2 P-NHC 18 H 35 ), 1d (Ph 2 P-SC 12 H 25 ), 1e (Ph 2 P-OC 12 H 25 ), 2a (Ph 2 P(Se)-OOCC 17 H 33 ), 2b (Ph 2 P(Se)-PPh 2 ), 2b 0 (Ph 2 P(S)-PPh 2 ), 2c (Ph 2 P(Se)-NHC 18 H 35 ), 2d Ph 2 P(Se)-SC 12 H 25 ) and 2e Ph 2 P(Se)-OC 12 H 25 ).
Computational. Our DFT calculations were performed using Gaussian 09, with ethyl groups (-C 2 H 5 ) applied to represent the alkyl group of C 17 H 33 COO-, C 18 H 35 NH-, C 12 H 25 S-and C 12 H 25 O-; no simplicity was applied for the phenyl group of -PPh 2 . Full geometry optimizations were carried out to locate all of the stationary points via a hybrid B3LYP functional method with the SDD basis set and the corresponding effective core potential for the Cd, Se and Te atoms, and the allelectron 6-31þþG(d, p) basis set for the other atoms of C, H, O, N, P and S, namely B3LYP/6-31þþG(d, p), SDD. The use of effective core potential and allelectron basis was the same as before 25 . Systematic harmonic frequency calculations were performed to ensure that all the structures obtained are true minima on the potential energy surfaces. A polarized continuum model (PCM-SMD) with dielectric constant e ¼ 2.0 was utilized to simulate the solvent effect of ODE via a hybrid M06 functional method with the same basis sets as mentioned above by performing single-point calculation on the optimized structures at the B3LYP/6-31þþ G(d, p), SDD level, namely M06//B3LYP/6-31þþG(d, p), SDD. The charges and dominant occupancies of natural bond orbitals have been analysed with the help of the natural bond orbital analysis.
Data availability. The authors declare that all relevant data supporting the findings of this study are available from the authors on request.