Calculated Effective Nuclear Charge (P)Values
letters
Element
Electron Configuration
T(3d)
274s)
7av
-
Slater's Rules and Electron Configurations To the Editor: The article "The Use of Effective Nuclear Charge (2') Calculations to Illustrate the Relative Energies of ns and (n- l)d Orbitals" by Christina Poth Brink (1)describes the use of Slater's rules to account for the fact that while the 4s orbital fills before the 3d orbitals for the 4th row elements, the 4s electrons are the first to be removed on ionization. Slater's rules had been used previously to justify that the v u n d state electron configuration for potassium is [Arl4s rather than [Ar13d1 (2,3). Also, I have used a similar approach to that described by Brink (1)to illustrate that the 3d orbitals become progressively more stable than the 4s orbital on going . - through the first transition wries. At this point, students often ask whv, for example, the h~oundstate electron configvation for Ti is [Arl:ld'4s2 rather than -IArl3d:. ~-~ - However. t h s oroblem can be solved again with the use of Slater's Ales, 'which lead to an effective nuclear charge of 3.15 for 4s electrons and 3.65 for 3d electrons if the electron configuration of Ti is [Ar13d24s2 (I).On the other hand, if the electron configuration of Ti had been [Ar13d4,the effective nuclear charge that the 3d electrons would have experienced is: ~
~~
~
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Consequently, despite the fact that the 3d orbitals are lower in energy than the 4s orbital, both 3d and 4s electrons of Ti [Ar13d24s2feel a higher effective nuclear charge and are therefore more stable than the 3d electrons of Ti IAr13d4.Accordingly, the ground state elertron confiwrntlon of Ti will be Ar13d'4s1 rather than [Ar13d4.Similarly, calculations can be performed for the effective nurlear rharge experienced hy the Bd and 4s electrons for the possihlc r l ~ -d "~ 4~s 'IAr13d".'4s1 ., . and . IAr13d-24s0 electron ~ - I ~~ configurations of the first transition metal row elements. The results are summarized in the table, where Z ,is the average of the effective nuclear charge calculated for the 3d and 4s electrons. It can be seen from the table that while the difference between the effective nuclear charge exoerienced bv the 3d and 4s electrons increases alona the first transition series, the average effective nuclear charge for the different possible electron configurations becomes more similar from Sc to Cu, so that exceptions to the electron configuration [Ar13d"4s2are not surprising. It is important to note that the calculations reported above and in reference ( 1 , are useful ta discern trends ilnn(: the 4th row elements, hut the actual numerical values must he intrroreted wlth a~niiderablecaution. More swcificallv. Slatrrk h e s are based on simpli@ing assumptiok that le;d to p o r agreement between the calculated and true effectivenuclear charges (31, and, therefore, the electronic energies estimated by Slater's rules are oRen not very accurate (4). In particular, Slater's rules underestimate the effective nuclear charge values for 3d electrons (5).Furthermore, the very wncept of effective nuclear charge is a crude and incomplete way of taking electron-eledmn repulsions into acwunt (6).Consequently, the use of Slater's rules leads to the result that for potassium the 4s orbital is lower in energy than the 3d orbital (11, while it is known that the 4s orbital energy is always above the 3d orbital energy (6). As pointed by Pilar (6) and Scem (71, the emoneous notion that the 4s orbital ever has a lower energy than that of 3d is extended by textbooks containing a diagram that represents the energy of atomic orbitals versus atomic ~~
956
>~
Journal of Chemical Education
number for plyelectronic atoms. This misleading diagram showing that the orbital energy for the 4s orbital bewmes lower than for 3d orbitals for certain values of atomic numher is still contained in some inorganic chemistry texb books published during the last decade (8-12). In conclusion, despite the apparent usefulness of Slater's rules to account for the ground state electron coniiiration of the 4th row elements, they lead to the erroneous idea that for potassium the 4s orbital is lower in energy than the 3d orbital. Rather, the energy due to the [ArI4s1configuration is lower than that due to the [Ar13d1configuration because of the electron re~ulsionterm.. in s-~ i t of e the fact that the 4s orbital energyis higher than the 3d orbital ene r m (6). Nevertheless, the sim~licitvof the Slater's rules makes them useful, for teaching purposes, to discern trends along the 4th row elements. Literature- Cited ~ ~ ~~
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1. Brink, C. P J Chem. Educ 1991,68,376371. 2. S h - , A . G . l n o w i c C h i s f r y ,2nd ed.: longman:London,1986;Chapter 3, p 67. 3. Butler, I. S.;Hmd,J.F.InorgonieChrmislry; Benjamin-Cwnming~:Redrwod City, CA, 1989:Chapter 2, p 55. The possible eleetmn eonEwrationa for potlssium are misprinted as IAr13$3p63d'snd IAr13s23$&'. 4. Huheey,J. E. InorgonicChomLstry. 3rd ed.; H a w a n d R o w : NewYork. 1983: C h a p ter 2, p37. 5. Poder+leld, W W .Inorganic Chomisfry;Addison-Wesley: Reading, MA, 1984; Chapter 2. o 8R.
Chapter 3. pp 57.58.
9. Cotton,FA.;WOkinaon,G.;Gaus,PL.BosicIn~~ganicChemisf~;Wiley:NewYork, 1981: Chapter 2, p 46. lo. Cotton, F A ; Wilkinson, G. Aduonced Inogonlc Chomishy, 5th ed.; W h y : New York, 1988. Chapter 17, p 628. 11. Reference 131, p 34. 12. S h r i u e ~ DF:At*ms.P. . W.;Langford,C.H. I~oq'~nicChomistry; OxfmdUniiiity Ress: Oxford. 1990; Chapter 1,p 23.
David Tudela Universidad Autbnorna de Madrid 28049-Madrid (SPAIN)
