Estimation of sp3d ValenceState Electronegativities for Elements of Groups V-0 Terry L. Meek University of the West Indies, Cave Hill, Barbados
Recently published tables of atomic electronegativities have been derived by different approaches. Bratsch ( I ) used an extension of the Mulliken (2)method to obtain valence-state electronegativities for all of the main group elements, calculating them from spectroscopicpromotion energies of atoms, cations, and anions. Allen (3) defmed electronegativity as the average oneelectron energy of the valence electrons of an atom in its ground state. Allen also used spectroscopic data to obtain values for the main group elements of the first five periods. Both scales agree quite closely with the Pauling ( 4 ) and Allred-Rochow (5)scales, and with each other, though they differ in some details. This work shows how each of the two methods can be extended to allow the estimation of electronegativities for atoms with one valence electron promoted to a d orbital. The question of d orbital participation in chemical bonding is a controversial one (6-Sa), and promotion energies to valence states involving them are high for isolated atoms. The arguments for and against d-orbital participation will not be presented here; I merely demonstrate the effect of including them.
Table 1. Configurations Used for Evaluation of Mulliken Electronegativities
Group
Valence
Orbital
Cation
Atom
Anion
-
Methods of Calculation Valence-State Electronegativity
In the Bratsch method, valence-state electronegativitya is defined by
where ZP and EA represent the ionization potential and electron aflinity; the subscripts V and G refer to valence state and ground state atoms; and P and P are the promotion energies of the cation and anion derived from the atom in its valence state. For an atom in a given valence state, values of a are calculated for each type of orbital, and these orbital electronegativities are combined in appropriate proportions (e.g., 25% s and 75% p for sp3)to yield the electronegativity of the atom in the desired valence state. Bratsch converts these Mullliken values from electron volts to Pauling units by the following relationship.
In this study, electronegativities were calculated for the elements of Groups V-O in periods 3-5, in the sp3d1valence states. No spectroscopic data are available for species with more than one d electron, and very little data for the elements in period 6. Valence-state configurations used for the atoms and ions are listed in Table 1, and promotion energies for these configurations in Table 2. For the ueutral atoms the slpmdl configurations were used whenever possible, to provide consistency. (The s2pm-'dl configuratious yield electronegativities for p and d orbitals that are similar, but slightly (0.8 to 1.7 eV) lower.) Atomic electronegativities were calculated from
Promotion Energies
The s + p and p + d promotion energies were mostly obtained directly from spectroscopic tables (9,10)or by one of the extrapolation methods outlined by Bratsch (1).Ideally these energies would include contributions from all relevant spectroscopic terms, suitably weighted in proportion to the number of microstates in each. However, the energies of many terms (especially for species with d electrons) are not available, so the promotion energies are often very approximate. Thus, they are only given to one decimal place. Furthermore, data are not available for S + d promotion energies, so the approximation wasmade that these are equal to the sum of the energies required for s + p plus p + d promotions. In the case of Group 0 atoms (and Group VII anions), s + p promotion is not possible. The energy differencesbetween s and p levels were estimated by extrapolation ofthe values for the Groups V-VII atoms (or Groups N-VI anions) in the same period. For other anions, promotion energies were generally estimated by extrapolation of the values for isoelectronic atoms and ions. The ground states of Group 0 anions were assumed to be ns2np6(n+ 1)s'. The Allen Method
In the Allen method, spectroscopic electronegativity is defmed by mEP+ nE. X"=
m+n
(4)
where m and n are the numbers of p and s electrons in an atom; and E, and E, are the energies required to remove a p or s electron from the atom. Volume 70 Number 10 October 1993
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Table 2. ValenceState Promotion Energies Used for Calculation of Mulliken Electronegativitiesa Configuration P+
"Calculated fmm data in refs 9 and I0 unless otherwise noted. b ~ ~ t i m a tfrom e d wmbination of other values. %timated by extrapolation of data for other species (see ten).
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Journal of Chemical Education
Table 3. Configurations Used for Evaluation of Spectroscopic Electronegativity Group
v
VI
VII
0
II IIi IV
-
Orbital
Cation
Atom
s
s1p2d'
s2p2d1
P d
s2p1d' s2p2
s2p2d1 s2p2d'
s
s1p3d'
s2p3d'
P d
s2p2d' s2 p3
s2p3d' s2p3d'
s
siP4d'
s2p4d'
P d
s2p3d' sZp4
s2p4d' s2p4d1
s
siP5d'
s2p5d1
P d
s2p4d' sZP5
s2p5d1 s2p5d1
S
P'
slpl
P S
s1 p2
sip1 sip2
P
slp'
sip2
S
p3
s1p3
P
sip2
s1p3
These energies are calculated from spectroswpic data using, in the terminology of t h e Bratsch method,
E,=IP,+P'-PO
(5)
where P+and PO m a y be evaluated in a manner similar to t h a t described above.
Table 4. Promotion Energies Used for Calculation of Spectroscopic Electronegativities, Groups V-Oa
PO
P+ eV
Configuration
S'
Se'
eV
As
P
Te'
(s2p3)
1.83
1.72
1.57
1.40
1.36
(s1p4)
H.7
12.1
10.3
8.55
8.9
(s2pZd')
14.2
13.6'
11.2
9.22
8.31
(~'p~d')~
24.2
23.7
20.3
16.5
15.2
CI*
Br+
I+
S
Se
0.74
0.81
1.07
0.58
0.65
(s1p5)
12.30
12.3
10.69
9.25
9.29'
(s2p3d1)
16.9
15.8
13.0
9.22
8.64
( ~ ' p ~ d ' ) ~ 28.7
27.5
23.2
18.2
17.4
Ar+
Kr+
Xe+
Ci
BrC
(s2p5)
0.06
0.22
0.43
0.04
0.15
(sip6) (s2p4d1)
13.5
13.5
13.0
10.6
10.9
18.9
16.9
13.4
11.6
10.7
( ~ l p ~ d ' ) ~ 32.0
30.1
26.1
22.0
21.4
(s2p4)
(sZP5d')
Figure 1. Mulliken orbital electronegativnies for atoms of Groups V0, periods 3-5, in sp3d1states. Dotted lines represents and p eiectronegativities of period 4 atoms in 'Typical" valence states (ref 1).
Ar
Kr
14.1
12.4
aCaloulatedfrom data in refs Sand I0 unless otherwise noted. 4~~timated from combination of other values. %stimated by extrapolation of data for other species (see ten).
Figure 2. One-electron orbital energies for atoms of Groups V-O, periods 3-5, in s2pmd' configurations. Doned lines represents and p energies of period 4 atoms in ground stales (ref 3). Volume 70
Number 10 October 1993
801
Table 5. Promotion Energies Used for Calculation of Spectroscopic Electronegativities, Gmups lCIVa
Configuration
s1p3 Values calculated from data in refs Sand 10 unless otherwise noted. '~stimatedfrom data for other wecies
Table 6. Mulllken Electronegativitiesof Atoms in sp3d1(tbp) State
Atom Valence
State
~lectronegativity~ eV o
-
-
d
$3 Atom
-. - 'Tnelap valdes far orbgals were calalated dsmg eq I : for amms s m g eq 3 on ~ aan t polent a s from ref 2a electron anhnes fmm refs 21 and 22 Lower valsncy values fmm Table 5, ref 1. %quation 2. ~
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Journal of Chemical Education
However, Allen includes the energies of all s~ectrosco~ic terms. reeardless of sinele or double o ~ c ; ~ a n of q &b%als.Allen c&ulates these elecroneeativjties in Rvdberm. which he converts to-pading units-by mil: tiplyingby 2.30016. Thus, the multiplier for converting electron volts directly to Pauling units is 2.30016113.595 or 0.16919. This method can be extended to atoms in various valence states, including those with electrons occupying d orbitals. In this work the atoms of Groups V-0 in periods 3-5, with configurationss2pmd',were examined. The configurations of these atoms, and the cations derived from them, are listed in Table 3. Appropriate spectroscopic term energies were used to calculate the energies of these atoms and cations, which are given in Table 4. The average one-electron energies are given by
(Similar calculations were also carried out for the configurations s'pm+'d', and yielded very similar electronegativities. The energies of the ~ ~ ~ " ' configurations d' are more accurately known because they involve only p + d transitions in the neutral atom and only one s + d transition in each cation.) The method was also applied to the Groups 11,111, and IV elements in the slp', s'p2, and s'p3 states, respectively The relevant configurations and energies appear in Tables 3 and 5. The electronegativities of these atoms were calculated using eq 4.
Table 7. Spectrosco#c Electronegativities of Atoms in sZPdt Configuration Atom ValenceConfigu ration
One-Electron Energya eV s
p
d
22.8
13.7
1.6
Xspg PU
Table 8. Spectroscopic Electronegativities of Atoms in sipm Configurations Atom Configuration
One-Electron Energya eV
s
Atom 14.9
2.52
. -.- .
-.
--
'Values for atoms in ground states calculated from data in Table 3, ref2. For sZpmd', orbiial energies fmm eq 5: atom energies from eq 6. Ionization potentials taken fmm ref 20. 'Convened fmm eV by multiplying by 0.16919 (see ten). Results The calculated orbital electronegativities and resultant atomic electronegativities of Gmups V-0 atoms in periods 3-5 are listed in Table 6. Their average one-electron energies are given in Table 7. In both tables, corresponding values for atoms restricted to the use of s and p orbitals are included for camparison. As expected, the orbital electronegativities and oneelectron energies of s and p orbitals show general increases with increasing atomic number across a period and decreases down a group, with the values for s orbitals being substantially (60-70%) higher than those for p orbitals. For d orbitals, the values of orbital electronegativities vary irregularly across the period, decrease down the group, and are very low. One-electron energies are even lower and show no systematic variation. Sample data are plotted in Figures 1and 2. Increased Nectronegativities The most strikine feature of both sets of data is the lame of the s and p orbitais increase in e~ectro~e~ativitylenergy that results from ~romotionof either an s or D electron to a d orbital. This can be rationalized by the 10w:~enetrating (hence poor-shielding) ability of electrons in d orbitals, which leads to an increase in the effective nuclear charge experienced by the remaining s and p electrons.
P
XSP~ PU
Atom
9.92 5.96 7.94 1.34 sip' s2 B s'p2 s2p' C sip3 szp2 Mg sip' s2 Ai sip2 s2p' Si sip3 sZp2 Ca s'p' s2 *Zn sip' s2 sip2 Ga s2p' sip3 Ge s2p2 Sr sip' s2 'Cd sip' s2 In sip2 s2p' Sn sip3 s2p3 'Ba s'p' s2 'Hg sip' s2 'TI s'p2 sZp' 'Pb sip3 s2p2 'Values for atoms in ground states calculated fmm data in Table 3, ref 2, except where indicated (');for these, and valence-stateatoms,orbital energies from eq 5 and atom energies from eq 4. Ionization potentials from ref 20. b~onvenad from eV by multiplying by 0.16919 (see text). Be
These high electronegativitieslenergiesfor s and p electrons apparently outweigh the low values for the d electrons when the orbital electronegativities are combined (Figs. 3 and 4).Atomic electronegativity actually increases significantly when an electron is promoted to a d orbital, contrary to the expectations of many authors (11-18). Rough calculations suggest that electronegativities would increase even further if two or three electrons were promoted to d orbitals. These increased electronegativities Volume 70 Number 10 October 1993
803
Table 9. Mulliken Electronegativities of Group II Elements: Ground States and Valence States
Element Valence
State
~lectrone~ativity~ Atom
-
4.65 4.4 4.11 3.6 3.29 2.9 3.07 2.7 2.79 2.5 4.99 4.4 4.62
Figure 3. Mulliken valence-state electronegativities of atoms of Groups V-O, periods 3 5 (Pauiing units). Closed circles represent sp3d states, and open circles represent 'vpical" states (ref 1).
4.1
5.55 4.9
"valencs-statevalues from Table 5, ref 1 Gmund state values calculated from ionization potentials in ref 20 and electron aflinities in ref 22. 'Equation 3
would lead to decreases in bond polarities, for example, in fluorides and chlorides of atoms with "expanded octets". Lower bond polarities are consistent with the decreases observed in the average bond energies in such compounds (86,191. Mulliken Electronegativities
It is interesting to note a similar phenomenon for the Mulliken electronegativities of the Group I1 elements. The values calculated by Bratsch (1)for the sp' state are slightly higher than those of the same elements in the ground (s2)states (Table 9). Although the energies (hence electronegativities) of p electrons are substantially less than those of s electrons, promotion of one s electron brings about a sizable increase in the electronegativity of the remaining one. Conversely, promotion of an electron from an s to a p orbital causes a decrease in the average one-electron energy of the atom. Comparison of these energies for the Groups II-IV elements in their ground and valence states (Table8) shows a slight increase in both s and p energies, but a decrease in average energy due to the greater p-eledmn contribution. The usual group and period trends still occur. Although the extent (ifany) of d-orbital participation in bonding is uncertain, the calculations discussed above show that i t would result in a substantial increase in atomic electronegativityfor elements in Groups V-O. Such an increase could account for the weaker bonds formed by these elements when they are in high valence states. Literature Cited 1. Bratseh, S. G. J Chem.Edue. 1988,65,34. 2. Mu1liken.R. S. J. Chom Phys. 1954.2.782. 3. lien, L.C.J Am. Chom Soe. lsB9,111,9115.
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Journal of Chemical Education
F gure 4 Spectroscopic electronegatlvltles of atoms of Gro~PsV-0, penoas 2-5 (Padng unlts) Closea clrcles represent s2pmaconffg"rat ons, and open circles represent ground slates (ref3)
4. Pauhg,L. J Am. Chom. Soe. 1932,54,3570. 5. Allred, A. L.; Raehow, E. G. J . Inwg. Nucl Chem. 1858.5, 2%. 6. Corn", F . A : W ~ n s o n , G . ~ u a m d l n o r g o n i c C h o m l s l r y5thed.; , Wiie%NewYork, 1968; pp 2628. 7. M d a y , K.M.; M a c k R. A. Intmducfion to Modem 1norg.nie Chemislry. 4th ed; Blaekie, Glasgow, and London, 1969: pp 350-351. 8. Huheey,J. E.lnownCChomisfry, 3rd ed.; Harper and Raw: New York, 1983; (a1 pp 826837; (bl Table E l . pp A32-A40. Na9. Mwre, C. E. AumY Energv Leu& Nnhond Slandoni Refirem Data Se-; tional Bvreau ofsfandads; 35, Waahvytan, DC, 1971:Vals. 1-111. 10. Bashkin, S.; Stoner, J. O.AtomC Enegy Leuel and G m f k n Dhmm;North Holland: New York, 1978: Vols. l. 2. 11. Skinner, H.A.:PnWlard, H.O.%M. FamdoySac 1953.49.1254. 12. Pritchad, H. 0.:Skinner, H. A.Chom. Re". 1955.55. 745. 13. Hinze, J:J&e, H. H. J . A m Chem. Soc. 1862.84.540. 11. Hinre, J.; Whitehead, M.A.; JaUee, H. H. JAm. Cham Sac. 1963.85.148. 15. Hime, J.:Jaffe,H.H. J.Phya Chom. 1963,67.1501. 16. Huheey, J. E. J Phya Chom. 1866,69,3284. 17. Huhsey, J. E. J. Phys Chom. 1866.70,2086. 18. sanderson, R. T. l n w g o n r chemistry; %inhold: N ~ W y a k , 1961: pp 20,402. 19. Greenwood, N. N.: E m s h s w , A ChomiaW of the E k m e d s ; Pergaman: New York, 1964; p 915. 20. Moore, C. E. Notional S t a n d u d Reference Dafo Series; National Bweav of Band a d s 31; Weshington, OC, 1970. 21. Hafop, M.; Iuoeberger, W. C. J. Phys Chom. Ref Doto 1995, 14. 736. 22. Bratsch. S. G.; Lagoswki, J. J. Polyhedron 1986,5,1761.
