Classification of Zintl Ion Clusters using 4n Series Approach

Enos Masheija Rwantale Kiremire

Department of Chemistry and Biochemistry, University of Namibia Private Bag 13301, Windhoek, Namibia.

*Corresponding Author E-mail: kiremire15@yahoo.com

DOI : http://dx.doi.org/10.13005/ojc/320401

Zintlion clusters have the industrial potential for possible applications. A good understanding of such clusters in terms of their bonding, structures and chemical reactivity is extremely important. This paper attempts to categorize and predict the shapes of Zintl clusters of simple to medium nuclearity using the 4n series method.

Zintl ion; clusters; series; capping; encapsulated; fragment

Introduction

Results and Discussion

1[C] →1[4] →1[4+0] = 1[4n+0](n=1)→ S =  4n+0(n=1).

If we have 2 carbon fragments, 2[C], then the result is doubled as follows:

2[C] →2[4]= 2[4+0] = 2[4n+0] → S = 4n+0(n=2).

If we have x[C] fragments, then ; x[C] = x[4+0] → S=4n+0(n=x).

If a fragment has more than 4 valence electrons, then the extra electrons are expressed as a digit after 4n. Let us take the example of a 1[CH] fragment.

1[CH]→1[4+1] =1[4n+1]→S =4n+1(n=1); the valence electron content of the fragment V = 4(1)+1 = 5.

2[CH]→2[4+1] =2[4n+1]→S = 4n+2(n=2); V = 4(2)+2 = 10, the valence electron content of 2[CH] fragments.

What matters most in the 4n series method is the skeletal element and the valence electron density around it. For instance, a phosphorus fragment, 1[P] with 5 valence electrons is treated in the same way as a 1[CH] fragment which is isolobal to it.

Hence, 1[P] = 1[5]→1[4+1] = 1[4n+1]→4n+1(n=1); for 2[P] =2[4+1] →2[4n+1]→S = 4n+2(n=2). We can use the series formula S = 4n+2(n=2) to derive a corresponding hydrocarbon as in

Scheme 1: Converting a series formula into a hydrocarbon Click here to View Scheme

The skeletal bonds linking up the two carbon atoms is given by k = 2n-1 and since n =2, k =2(2)-1 = 3.  Since P₂  belongs to the same series S = 4n+2(n=2), k =2n-1 = 2(2)-1 = 3. Hence P₂ is linked by a triple bond P≡P.

Consider a [CH₂] fragment. The fragment has 6 valence electron content. These are converted into series as follows:

1[CH₂]→1[4+2] →S = 4n+2(n=1). Let us see how two such fragments can be transmuted into series formula.

2[CH2]→2[4+2]→2[4n+2] →S = 4n+4(n=2). The corresponding hydrocarbon F_CH = C₂H₄. We know that C₂H₄  has a double bond(C=C). Again the double bond can be derived from the series S = 4n+4; k = 2n-2 = 2(2)-2 = 2. In general, for series of the formula S = 4n+q, k = 2n-(q/2).

A sulphurflagment,1[S] alone also has 6 valence electrons like 1[CH₂]. The 4n series method treats 1[S] as [CH₂]. Thus, 1[S]⥈1[CH₂]; the two fragments are isolobal. Hence,

1[S] →1[6] =1[4+2]→4n+2(n=1).

2[S]→2[4+2] →2[4n+2] = 4n+4(n=2). The electron valence content of 2[S] is given by V = 4n+4 = 4(2)+4 = 12. Also the k value of S₂→k = 2n-2 = 2(2)-2 = 2. Hence, according to the series, the S₂ molecule is doubly bonded (S=S) as in C₂H₄. In general, for a series formula S = 4n+q, the corresponding k value is given by k = 2n-(q/2).

The categorization of clusters is easily done using 4n rather than 14n series. Although this has already been discussed in earlier work,it is being summarized here as many readers are not familiar with the 4n series method of categorizing clusters. The categorization follows the sequence (lower series): S = 4n+2(closo), 4n+4(nido), 4n+6(arachno), 4n+8(hypho) and 4n+10(klapo) and so on. The (higher series) are the capping series namely, S = 4n+0(mono-capped), 4n-2(bi-capped), 4n-4(tri-capped), 4n-6(tetra-capped), 4n-8(penta-capped), 4n-10(hexa-capped) and so on. Since the work on 4n series method is beginning to expand, the terms ‘lower series’ and ‘higher series’ are being proposed to refer to non-capping and capping series respectively. It is proposed that the digit after ‘4n’ be referred to as a ‘determinant’ of the series since it gives an indication of the type of cluster or fragment.

Derivation of Series Formula of Zintl ion Clusters

Sn₅^2―

5[Sn]→5[4+0]→4n+0(n=5)

q→0+2(n=0)

S = 4n+2(n=5), Closo cluster; k =2n-1=2(5)-1 =9.

The equivalent borane cluster, F_B = 4n+2 = [BH](5)+2(-) = B₅H₅^2― for closo system. The cluster will be expected to have a similar shape as B₅H₅^2―. The sketch of ideal predicted shape trigonalbipyramid is shown in F-1.

Figure 1 Click here to View Figure

Bi₃Cr₂(CO)₆^3―

3[Bi] →3[4+1] →4n+3(n=3)

2[Cr(CO)₄]→2[14+0]→2[14+0-10]=2[4+0]→4n+0(n=2)

[6-8](CO) = – 2(CO)→0-4(n=0)

q→0-3(n=0)

S = 4n-4(n=5), Cp = C³C[M-2]; tri-capped cluster.

Si₄(CuR)₂^4―

4[Si]→4[4+0] →4n+0(n=4)

2[CuRH₂]→4n+0(n=2)

[0-4](H) = -4H→0-4(n=0)

q→0+4(n=0)

S =4n+0(n=6), mono-capped series, Cp = C¹C[M-5]. This is a mono-capped trigonal bipyramid.

Figure 2 Click here to View Figure

Pb₅G₂^4―; G = Mo(CO)₃

5[Pb] →5[4+0] →4n+0(n=5)

2[Mo(CO)₄]→4n+0(n=2)

[6-8](CO) = – 2(CO)→0-4(n=0)

q→0+4(n=0)

S = 4n+0(n=7); Cp = C^IC[M-6]. Thus, the series predicts a mono-capped octahedral cluster.

As₇^3―

7[As]→7[4+1] →4n+7(n=7)

q→0+3(n=0)

S=4n+10(n=7) ; k =2n-5 = 2(7)-5 =9. A skeletal sketch is shown in F-3A.

Figure 3a  Click here to View Figure

Bi₃Ni₄(CO)₆^3―

3[Bi] →3[4+1] →4n+3(n=3)

4[Ni(CO)₂]→4n+0(n=4)

[6-8](CO) = – 2(CO)→0-4(n=0)

q→0+3(n=0)

S = 4n-4(n=7), Cp = C³C[M-4]; tri-capped tetrahedral cluster.

Bi₃Ni₆(CO)₉^3―

3[Bi] →3[4+1] →4n+3(n=3)

6[Ni(CO)₂]→4n+0(n=6)

[9-12](CO) = – 3(CO)→0-6(n=0)]

q→0+3(n=0)

S = 4n-6(n=9)(n=9); Cp = C⁴C[M-5]; tetra-capped cluster.

In₄Bi₅^3―

4[In] →4[4n-1]= 4n-4(n=4)

5[Bi]→5[4+1]=4n+5(n=5)

q→0+3(n=0)

S = 4n+4(n=9); Nido cluster, F_B = 4n+4 = [BH](9)+4(H) = B₉H₁₃. The nido cluster is derived from B₁₀H₁₀^2― following Rudolph correlation system¹⁰. This is graphically represented in F-3B  below.

Figure 3b Click here to View Figure

Si₉(ZnPh)^3―

9[Si] →9[4+0]→ 4n+0(n=9)

1[ZnPh(H)]→1[14+0]→1[14+0-10] = 1[4+0]→ 4n+0(n=1)

[0-1](H)→    0-1(n=0)

q→  0+3(n=0)

S = 4n+2(n=10), closo cluster; k =2n-1 =2(10)-1 = 19.

F_B = 4n+2 = [BH](10)+2(-1) = B₁₀H₁₀^2―  for closo system. The cluster is predicted to have a shape similar to that of B₁₀H₁₀^2―cluster. This is graphically represented by the skeletal sketch F-4. The shape  resembles a beautiful doubly closed basket. One end of the closed tip resides the Zn skeletal element.

Figure 4 Click here to View Figure

Sn₉Cr(CO)₃^4―

9[Sn]→9[4+0]→4n+0(n=9)

1[Cr(CO)₄]→4n+0(n=1)

[3-4](CO) = – 1(CO)→0-2(n=0)

q→0+4(n=0)

S = 4n+2(n=10), Closo cluster; F_B = B₁₀H₁₀^2―. Cluster expected to have a similar shape as B₁₀H₁₀^2―.

Figure 5 Click here to View Figure

Sn₉IrL₂^3―

9[Sn]→4n+0(n=9)

1[IrHL₂]→4n+0(n=1)

[0-1](H) = – 1(H)→0-1(n=0)

q→0+3(n=0)

S = 4n+2(n=10), Closo

Shape predicted to be similar to that of B₁₀H₁₀^2―.

Sn₉W(CO)₃^4―

9[Sn]→9[4+0]→4n+0(n=9)

1[W(CO)₄]→4n+0(n=1)

[3-4](CO) = – 1(CO)→0-2(n=0)

q→0+4(n=0)

S = 4n+2(n=10), Closo cluster; F_B = B₁₀H₁₀^2―. Cluster expected to have a similar shape as B₁₀H₁₀^2―. Isomerism occurs in this case as W now occupies the equatorial position.

Figure 6 Click here to View Figure

Sn₉IrL₂^3―

9[Sn]→4n+0(n=9)

1[IrHL₂]→4n+0(n=1)

[0-1](H) = – 1(H)→0-1(n=0)

q→0+3(n=0)

S = 4n+2(n=10), Closo

Shape predicted to be similar to that of B₁₀H₁₀^2―.

Pb₁₀^2―

10[Pb]→4n+0(n=10)

q→0+2(n=0)

S =4n+2(n=10), Closo clusterF_B = [BH](10)+2(-1) = B₁₀H₁₀^2―.The negative charge is added since the system is closo. The graphical representation is shown below.

Figure 7 Click here to View Figure

Ni@Pb₁₀^2―

1[Ni] →1[10] = 1[14-4]→1[4n-4] = 4n-4(n=1)

10[Pb]→10[4n+0]→4n+0(n=10)

q→0+2(n=0)

S = 4n-2(n=11), Cp = C²C[M-9]

Figure 8  Click here to View Figure

Ni@Pb₁₂^2―

1[Ni] →1[10] = 1[14-4]→1[4n-4] = 4n-4(n=1)

12[Pb]→12[4n+0]→4n+0(n=12)

q→0+2(n=0)

S = 4n-2(n=13), Cp = C²C[M-11]. This means 2 of the 13 skeletal elements are capped around the remaining 11 others. This could imply the inner set of [5:1:5] skeletal elements as shown in F-9.

Figure 9 Click here to View Figure

Ni₂Sn₁₇^4―

2[Ni]→2[10]=2[14-4] →2[14-4-10]= 2[4n-4]→4n-8(n=2)

17[Sn] →17[4+0]→17[4n+0] →4n+0(n=17)

q→0+4(n=0)

S = 4n-4(n=19)→Cp = C¹+C² →C³C[M-16]

According to the 4n series, the cluster is tri-capped. This implies, 3 skeletal atoms are capping versus 16 ones which are not capping.  A possible skeletal shape consistent with this prediction in sketched graphically below. Thus, the 2 nickel atoms are regarded as capping in addition to one of the 17 Sn skeletal elements that acts as a bridge of two Sn8 fragments. This is sketched in F-10.

Figure 10  Click here to View Figure

General considerations

A wide range of small to medium nulearity Zintl ion clusters taken from several sources11-14have been analyzed and categorized using 4n series method. The results are summarized in Table 1. The common Zintl ion clusters belong to the clusters series S = 4n+6, 4n+4 and 4n+2. They comprise of skeletal elements ranging from two (M-2) to thirteen (M-13). As can be seen from Table 1, capping series as defined by 4n series method are not common. But capping may be induced if a capping fragment is introduced into a cluster. The capping fragment is usually a transition metal atom with ligands or a metal atom or a main group element such as aluminum (Al). A good example of a capping fragment is M(CO)3, M = Cr, Mo, and W. The valence content V of the fragment = 12 = 14-2. Hence, it belongs to the series S = 14n-2 ⥈4n-2 series. If Sn94― belongs to S = 4n+4(nido) and M(CO)3 belongs to S =4n-2(capping series), then Sn94―+ M(CO)3→ Sn9[M(CO)3]4― and net S = (4n+4)+(4n-2) = 4n+2(closo). This means that the nido cluster has been transformed into a closo cluster by adding the capping fragment. The nido cluster S = 4n+4(n=9), corresponds to an equivalent borane FB =B9H13 while the closo corresponds to an equivalent closo borane S =4n+2(n=10), FB= B10H102―. The capping fragment, M(CO)3 corresponds to adding (+B, -H) or [BH]2+ fragment to B9H13 cluster. Other good capping fragments are Ni(CO), S = 4n-2, and PtL, L =PPh3, S = 4n-2. Other fragments, M(CO)2, M = Fe, Ru, Os which have a content of 12 valence electrons could be good candidates.

Addition of a metal atom to a closo cluster, may generate a capped cluster. For instance, a nickel atom, [Ni] has 10 valence electrons. According to series it belongs to 14-4 →S = 14n-4 ↭4n-4. Therefore it has a capping influence when it is encapsulated in a cluster. For instance, Pb102―(S = 4n+2)+Ni(S =4n-4)→Ni@ Pb102―(S=4n-2).Thus, the encapsulated cluster becomes a bi-capped cluster, Cp = C2C[M-9]. This implies the [M-9] closo nucleus comprises of 9 atoms arranged as 4:1:4 capped by 2 atoms one on one side of the nucleus and the remaining on the other. The whole structure resembles a doubly closed basket as indicated in the sketched graph for 2.2.15. The encapsulated Zintl cluster Ni@Pb122― can be analyzed in the same way and it is found to belong to the same bi-capped series, S = 4n-2 and Cp = C2C[M-11]. This means that 2 skeletal atoms are capping on 11 others. The [M-11] closo atoms are observed to be organized in an approximate order [5:1:5]. The entire doubly closed basket-like closed structure has a skeletal atom arrangement 1:[5:1:5]:1. This arrangement is shown in a graphical skeletal sketch in 2.2.16 above.

Table 1: Categorization of Zintl Ion Clusters

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