Factors Influencing the Dispersion of Lengths of Interatomic Vectors

Abstract

Table 2.1 presents empirical estimates of the first two central moments of interatomic vector lengths with the described properties. In this case terminal monatomic entities belong to a certain type. The dispersion of lengths of these vectors expressed by the second central moment m ₂ shows the value of 7.383 Ų for the sample of vector lengths of Zn²⁺ → 0, this value being much higher than 5.192 Ų for the sample of vector lengths for Zn²⁺ → S. In the case of such great sample sizes the variance equality of these data sets can be tested using sample characteristics of $F = S_1^2/S_2^2:$

$${H_0}:\sigma _1^2 = \sigma _2^2against{H_1}:\sigma _1^2 \ne \sigma _2^2$$

We will use the estimate of the above characteristics F ₁ = m₂(Zn^{2 +} → 0)/m ₂(Zn^{2 +} → S) = 1.422. The critical Fvalue on the significance level of α = 0.05 for v₁ = n(Zn^{2 +} → 0) — 1 and v₂ = n(Zn^{2 +} →S) — 1 is 1.011 [1]. Since F > F_crit the hypothesis H ₀ of the equality of dispersions can be rejected. The vector lengths of Co³⁺ → Cl and Co³⁺ → N also show a significant difference between their dispersions. In both cases of central monatomic entities one could explain the differences between the dispersions of interatomic vector lengths with different qualities of their terminal entities. The values of m ₂ of the samples of vectors of Zn²⁺ → S and Zn²⁺ → N exhibit, however, only a small difference (0.139 Ų). Similarly, the estimates of the second central moments of samples Cu²⁺ →Cl and Cu²⁺ → N are comparatively near.