Erratum to: Valencies of the lanthanides

Erratum to: Found Chem DOI 10.1007/s10698-017-9291-6

The authors regret that there are errors in equation (6) and subsequent discussion. The correct version is as follows:

$$ i = L\left[ { - \bar{E}_{\text{f}} + \left( {\Delta_{\text{i}} p} \right)\bar{E}_{\text{p}} - \left( {\Delta_{\text{i}} q} \right)\bar{E}_{\text{q}} + \left( {\Delta_{\text{i}} c_{ 3} } \right)\bar{E}^{ 3} } \right] + \left( { 5/ 2} \right)RT $$

(6)

The values of Δ_i p, −Δ_i q, and Δ_i c ₃ are given in Table 4. The second of these determines the loss of exchange energy and peaks at f⁷.

As with the tetrad effect, the irregularities in Δ_i c ₃ centred on the quarter- and the three-quarter-full shell are associated with the ability of electrons to keep apart better if their m _l values have the same sign rather than opposite. This eases the general increase in interelectronic repulsion in the first quarter of the series, where electrons have m _l values of the same sign, relative to the second quarter, where they have both positive and negative values (Table 2). On ionization, this easement is lost in the first quarter and gained in the second (Table 4); similarly in the third quarter over the fourth quarter.

Table 4 Values of the coefficients in Eq. (6)