2 de 3

8/12/2019 2 de 3

1/5

Research: Science and Education

1076 Journal of Chemical Education Vol. 77 No. 8 August 2000 JChemEd.chem.wisc.edu

In a thought-provoking article in the July 1998 issue ofthis Journal, R. J. Gillespie discussed the nature of the chemical

bonds in binary fluorides of main group elements in thesecond and third periods (1). His discussion was based on netatomic charges calculated by the so-called Atoms In Molecules(AIM) approach: the total electron densities are calculatedby ab initio methods, boundary surfaces between the atomsare drawn by invoking the zero flux criterion of Bader (2),and atomic charges are computed by integration of chargeover the space allotted to each atom. The atomic charges thusobtained are listed in Table 1 (3). On the basis of the largeatomic charges calculated for BF3and SiF4, Gillespie suggestedthat these molecules are much more ionic than has hithertobeen supposed, that the fully ionic model is a much betterdescription of the bonding than the fully covalent model,

and that it provides a simple explanation of the bond lengthsand bond energies.Questions concerning the mean bond energies, the bond

distances, or the most stable modification of the binaryfluorides of the second and third period elements at standardtemperature and pressure are scientific questions to whichthere are definite answers, though these will always be ac-companied by some experimental uncertainty. The questionof whether gaseous BF3or SiF4should be described as ionicor polar covalent compounds concerns our choice of wordsand the answer will depend on what we want to communicateto students or colleagues. We believe most chemists woulduse the term ionic to describe a molecule that (i) consists

of more or less spherical ions carrying net charges approachingan integer number of elementary charges and (ii) for whichthe major contribution to the bonding energy is due toCoulomb attraction between these net charges.

In the following we (i) use a spherical ion model toestimate the bond energies in these compounds for comparisonwith their experimental counterparts, (ii) estimate the bonddipole moments from the polarizabilities of the constituentions for comparison with those calculated for spherical ions,(iii) calculate an alternative set of net atomic charges fromthe atomic polar tensors, (iv) compare the experimental bonddistances with those obtained from a modified SchomakerStevensen rule, and (v) suggest that BF3or SiF4would, if theywere ionic substances, aggregate to dimeric or polymericspecies.

The Spherical Ion M odel and M ean Bond Energies

In the following we use the simple spherical ion model,which is commonly and successfully used to calculate theenergy of formation of an ionic solid from the gaseous neutralatoms (6, 7)

A(g) + kX(g) (A+k)(X1)k(s)

to calculate the energies of formation, Ee, of the gaseousion clusters

A(g) + kF(g) (A+k)(F1)k(g)

Mean bond energies may then be calculated fromMBEe= Ee/k (1)

The formation of a gaseous ionic molecule (or ion cluster),AFkor (A+k)(F)k, from the gaseous neutral atoms may bedivided into two steps: formation of the gaseous ions andformation of the ion cluster from the separated ions. Forma-tion of the gaseous ions requires the energy

IEi(A) kEA(F)where IEiis the ith ionization energy of the atom A and thesum extends from i= 1 to k, and EA(F) is the electron affinityof fluorine. Formation of the ion cluster from the separated

Should GaseousBF3and SiF4BeDescribed as Ionic Compounds?

Arne Haaland,* Trygve U. Helgaker, Kenneth Ruud, and D. J . Shorokhov

Department of Chemistry, University of Oslo, PB 1033 Blindern, N -0315 Oslo, Norway; *[email protected]

rofsecnatsiDdnoBdnasegrahCcimotAteN.1elbaTFAsediroulFraluceloM

k

esahPsaGehtni

A kMIA a TPA b mp/ecnatsiDdnoB

q ua/)F( q ua/)A( q ua/)F( q ua/)A( Rltpxe

c Rdclac

iL 1 49.0 49.0 68.0 68.0 651 561

eB 2 09.0 18.1 66.0 23.1 731 141

B 3 68.0 85.2 75.0 07.1 131 231

C 4 47.0 69.2 25.0 60.2 231 731

N 3 63.0 90.1 93.0 71.1 631 831

O 2 21.0 32.0 22.0 44.0 141 241

F 1 00.0 00.0 00.0 00.0 241 841

aN 1 49.0 49.0 88.0 88.0 391 991

gM 2 19.0 38.1 57.0 05.1 771 381

lA 3 88.0 56.2 46.0 09.1 361 761

iS 4

68.0 24.3

06.0 93.2 551 161P 3 48.0 15.2 95.0 87.1 651 061

S 2 17.0 34.1 74.0 59.0 951 061

lC 1 05.0 05.0 82.0 82.0 361 361

aReference 1.bRuud, K.; Haaland, A.; Shorokhov, D.J.; Helgaker, T.U.; unpublished.cBond distances for LiF(g), NaF(g) and ClF(g) from ref 4, other bond

distances from ref 5.

raluceloMrofataDytiraloPdnaygrenEdnoB.2elbaTFAsediroulF

k esahPsaGehtni

A k EBM 892 /

lomJk 1 M

k

EBMe

/lomk 1

/ D

/*

iL 1 775 1 806 15.7 61.0

eB 2 636 57.1 495 95.6 24.0

B 3 246 24.2 153 82.6 86.0

C 4 984 80.3 013 13.6 58.0

aN 1 474 1 284 52.9 90.0

gM 2 315 57.1 074 05.8 02.0

lA 3 985 24.2 474 38.7 53.0

iS 4 395 80.3 023 74.7 15.0

NOTE: Experimental mean bond energies at 298 K (MBE298) were

calculated from standard energies of formation listed in ref 8. MolecularMadelung constants(Mk), mean bond energies (MBEe), and bond

polarities () were calculated from a spherical ion model. In the ratio

*/ ,

* is the induced dipole moment on the Fanion (eq 7).
http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/Journal/

8/12/2019 2 de 3

2/5


JChemEd.chem.wisc.edu Vol. 77 No. 8 August 2000 Journal of Chemical Education 1077

ions is accompanied by an energy change

k(+ke)(e)/(4oR)+[k(k1)/2] (e)2/(4oRFF)+kB/(R)n(2)

The first term in eq 2 represents the energy of Coulomb at-traction between A+kand Fions, the second the Coulombrepulsion between Fions, and the third the Born repulsionbetween A+kand Fions. Ris the AF distance, RFFis thedistance between the fluoride ions, ois the permittivity of

vacuum, andBis the Born constant. For calculations on solidalkali metal halides the exponent nis usually given a valuebetween 6 and 11 (7); we shall use 10.

In the case of a linear difluoride (BeF2or MgF2) the firsttwo terms in eq 2 may be combined to

1.75 (ke2/4oR)If we define a molecular Madelung constant, Mk=

M2 = 1.75, the total energy of the ion cluster relative to thegaseous atoms may be written as

E(R) =IEi(A) kEA(F) Mk(ke2/4oR) + kB/Rn

The equilibrium bond distance satisfies the condition

(dE/dR) = 0orMk(ke2/4oRe2) nkB/Ren+1= 0

This yieldskB/Ren=Mk(ke2/4oRe)(1/n)

and the energy of the ion cluster is given by

Ee=IEi(A) kEA(F) Mk(ke2/4oRe)(1 1/n) (3)

Similar relationships are easily derived for trigonal planarAF3, M3= 2.423, for tetrahedral AF4clusters, M4= 3.083,or for the gaseous ion pair AF, M1= 1.

The mean bond energies calculated from eq 1 are listedin Table 2. Comparison with experimental bond energies

shows that these calculations based on a simple ionic modelreproduce the bond energies of LiF(g) and NaF(g) to within5%. Both bond energies are actually overestimated and thefit could be improved by including the vibrational energies ofthe AF molecules in the calculations. The bond energies ofBeF2(g) and MgF2(g) are underestimated by 7 to 8%; the bondenergy of AlF3(g), by 20%. The bond energies of BF3(g) andSiF4(g), however, are underestimated by about 45%. Inclusionof the vibrational energies of the molecules would increasethe disparity between calculations and experiment. Finally,even though the computed AIM charges for the C and F atomsin CF4are +2.96 and 0.74, respectively, the calculated MBEeturns out to be negative; the ion cluster is calculated to bethermodynamically less stablethan the separated atoms.

The Polariza ble Ion M odel and Bond Polarities

The spherical ion model is unphysical because it assumesthat the cations and anions remain spherical when they arebrought close together. In reality each ion will be deformedby the other. In this section we shall use the polarizable ionmodel (9) to estimate the polarity of the AF bonds.

If we assume that gaseous LiF or NaF consists of twospherical ions with net charges e and that the metal atom issituated at the origin and the Fion on the negative z-axis,the electric dipole moment of the ion pair is given by

= ez++ (e)z= (e)z= eR (4)

whereRis the bond distance. See Figure 1.When an atom or monatomic ion is placed in an electric

field, the nucleus and the electrons are pulled in oppositedirections and the atom or ion is deformed. The center ofgravity of the electron cloud no longer coincides with thenucleus, and the atom acquires an electronic dipole moment.If the strength of the electric field Eis constant over theentire atom, the induced atomic dipole moment is given by

* =E+ E2

+ (5)whereis the polarizability and is the hyperpolarizabilityof the atom or ion (10). The polarizability is thus a measureof how easily the electron cloud is deformed by the electricfield. Atomic polarizabilities decrease from left to right acrossthe periodic table and increase with atomic number down agroup. The polarizability of an atomic anion is significantlylarger than that of the neutral atom, which in turn is signifi-cantly larger than that of the atomic cation.

In Figure 1 we indicate how the cations and anions of agaseous alkali metal halide polarize each other. The M+cationgenerates an electric field at the nucleus of the anion:

E= e/4

o

R2 (6)

If we assume this field to be constant over the anion and ifwe omit higher-order terms in eq 5, the induced dipolemoment on the anion is given by

* =

E

= e/4oR2= e/R2 (7)

whereis the polarizability and

=

/4ois the so-called

polarizability volume of the anion (10). Similarly, the fieldgenerated by the anion will induce an atomic dipole momenton the cation:

+* = +e/R2and the total dipole moment of the ion pair is given by

=+* ++*

Note that while (eq 4) is positive, the induced atomic orionic dipoles are both negative. Their net effect is thus toreduce the magnitude of the overall dipole moment (see Fig.1). Note also that polarization of the anion moves electrondensity into the overlap region; when polarization becomessufficiently large, the polarizable ion model merges with apolar covalent bonding model.

The experimental dipole moment of LiF is exptl= 6.28 Das compared to = eR= 7.41 D. Since the polarizability ofthe Fion is known to be much larger that the polarizabil ityof the Li+cation (9) we may write

* =exptl eR (8)

Figure 1. Above: The electric dipole moment of the ion pair A+F.

Below: Polarization of the anion (left) and of the cation (right). The

directions of the dipole moments are indicated by vectors pointing

from the negative to the positive pole.

e +e

= eR

e +e

e +e

* +*

z

z+= 0z= R
http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/

8/12/2019 2 de 3

3/5



The polarizability volume of the Fion depends on the en-vironment; its value in a crystal or in a molecule will differfrom that of the isolated ion (11). It may, however, be esti-mated by combining eqs 7 and 8;

(F) = 0.627 1030m3 (9)

Because of their high symmetry, linear AF2, trigonalplanar AF3, or tetrahedral AF4molecules have molecular

electric dipole moments equal to zero. We may, however,use the polarizable ion model to estimate bond dipoles.

If we assume both cations and anions to be spherical,the central atom (A) to be placed at the origin of the coordi-nate system, and the Fion to be on the negative z-axis, thebond dipole moment may be defined as

(AF) = kez++ (e)z= (e)z= eR (10)

The electric fields generated by the F ligands will cancel atthe nucleus of the central atom. The induced dipole momentof the cation will therefore be zero, while the induced dipolemoment on the Fion is given by

* =

Mke/R2 (11)

and the bond dipole is given by

(AF) = (AF) + * (12)

where Mkis the molecular Madelung constant defined inthe preceding section.

In Table 2, we list the bond dipole moments, (AF),calculated from eq 10 as well as the ratio

*/, where

* is

calculated from eq 11. It is seen that while the induced atomicdipoles in LiF or NaF reduce the overall bond dipole by 16and 9%, respectively, the bond dipole moments of BF3, CF4,and SiF4are reduced by 68, 85, and 51%, respectively. Toput it simply: the induced dipole moments suggest that the

electron transferred from A to F is moved halfway back toAthat is, into the overlap region.In this connection it may be useful to make comparisons

with gaseous HF. In this molecule, which most chemistswould describe as polar covalent rather than ionic, the ex-perimental dipole moment is 58% smaller than calculatedfrom eq 10. The calculations based on the spherical ion modelthus indicate that the purported Fanions in BF3or SiF4would be significantly distorted in the direction of polarcovalency.1

Atomic Charges Calculated by the Atomic PolarTensor Approach

In Figure 2 we reproduce the constant electron densitycontours in the molecular plane of the BF3molecule, andthe lines separating the atoms indicated by the zero fluxcriterion (1, 3). It is noteworthy that the space allotted to the Batom is very small. The figure suggests that the allotted spaceincludes only the K shell of the atom; electrons in the 2s or2p atomic orbitals on B would presumably be found in thoseregions of space assigned to the F atoms. Such a division ofspace may have led to overestimation of the negative chargesassigned to the F atoms and of the positive charge assignedto B. Perrin has offered convincing arguments that the zero-flux criterion generally will lead to exaggerated negativecharges on the smaller and more electronegative of the bondedatoms (12).

We decided therefore to calculate the net atomic chargesin these molecules by an alternative procedure, namely fromthe Atomic Polar Tensor (APT) (13). In the APT approachthe net charge on each atom is determined by calculating thechange of the electric dipole moment of the molecule whenthe atom is displaced from its equilibrium position. Thephysical basis for the calculations is easily understood byconsidering a diatomic molecule AB with net atomic chargesequal to Q. The electric dipole moment is given by

AB=QR+A* +B* (13)

Figure 2. Constant electron density contour map in the molecular

plane of the BF3molecule. Lines perpendicular to the contours are

lines along which the interatomic (zero flux) surfaces that separate

one atom from another cut the molecular plane. Reproduced with

permission from ref 1.

Figure 3. Comparison of net atomic charges on F atoms/ ions in

the gaseous fluorides of second- and third-period elements calcu-

lated by the AIM and ATP approaches.

1.00

0.75

0.50

0.25

0.00

Q(F)

/e

APT

AIM

Li Be B C N O F

1.0

0.8

0.6

0.4

0.2

Q(F)/e

APT

AIM

Na Mg Al Si P S Cl
http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/Journal/

8/12/2019 2 de 3

4/5


JChemEd.chem.wisc.edu Vol. 77 No. 8 August 2000 Journal of Chemical Education 1079

The derivative of ABwith respect to the bond distance isdetermined numerically by increasing the bond distance bydRand calculating the change of the dipole moment dAB.From eq 13 it follows that

dAB/dR=Q+R(dQ/dR) + (dA*/dR) + (dB*/dR)

If the variation ofQand the atomic dipoles with bond distancemay be neglected, the net atomic charge is given simply by

Q= dAB/dR (14)

High-level quantum chemical calculations on the binaryfluorides of the second- and third-period elements yield theAPT atomic charges listed in Table 1 (4). In Figure 3 wecompare the net charges on the F atoms obtained by the twomethods. It is seen that with the exception of NF3and OF2,the APT approach yields smaller negative charges on the Fatoms than the AIM; in most of the molecules studied (BeF2,BF3, CF4, and all the third-period compounds from AlF3toClF) the difference exceeds 0.2 au. The difference betweenthe positive charges on the central atoms (A) depends on thenumber of F substituents; for BF3the positive charge on the

central atom is calculated to be 0.88 au smaller by APT; forCF4, 0.90 au smaller; and for SiF4, 1.03 au smaller.Most chemists would probably describe a molecule as

consisting of approximately spherical, overlapping atoms or ions.If the choice is made to describe a molecule as consisting ofsharply delineated, non-interpenetrating atoms, the zero-fluxcriterion provides a quantum-mechanically sound procedurefor drawing the boundary surfaces (14). The shapes of thecentral atoms in BF3or SiF4thus obtained, are, however, farfrom spherical, and the net atomic charges are much higherthan obtained by the APT approach. At the present time thereis, in our view, no compelling reason for preferring one setof atomic charges over the other. Calculations by either

approach may yield reliable information about the relativemagnitude of atomic charges in related molecules, say CF4and SiF4, but the absolute magnitudes of the atomic chargesthus obtained should probably be regarded as less meaningful.

AF Bond D istances

We now turn our attention to the AF bond distances(see Table 1 and Fig. 4). Gillespie and coworkers noted thatthe bond distances in each of the two periods decrease fromgroup 1 to group 13 or 14, and then increase slowly to group17. They found that the bond distances up to BF3 in thesecond period and to SiF4in the third are in better agree-ment with the sum of the ionic radii of the bonded atomsthan with the sum of the covalent radii, and concluded thatthe bond distances in these compounds are more consistentwith an ionic than with a covalent model (3).

It is, however, well known that polar bonds tend to beshorter than the sum of the covalent radii (15), and someyears ago we suggested a Modified SchomakerStevensen(MSS) rule for the prediction of polar covalent bond distancesbetween atoms in groups 13 through 17:

R(A B) = rA+ rB c|A B|n (15)

where rand denote the bonding radii and electronegativitycoefficients of the two bonded atoms, the constant c=8.5pm,and n= 1.4 (16). In combination with the associated bondingradii, this simple expression reproduces bond distances in

Figure 4. Comparison of experimental and calculated (modified

SchomakerStevensen rule, eq 15) bond distances in the gaseous

fluorides of second- and third-period elements.

170

160

150

140

130

R/pm

Calc

Exp

Li Be B C N O F

200

190

180

170

160

150

R/pm

Calc

Exp

Na Mg Al Si P S Cl

simple, gaseous compounds of elements in groups 13 through17 with an average deviation of 2 pm (16).

Use of the MSS rule yields the calculated AF bond dis-tances listed in Table 1 and displayed in Figure 4.2The purelyempirical relationship, eq 15, derived for polar bonds betweenelements in groups 13 through 17 is seen to reproduce the trendsacross the second and third period noted by Gillespie andcoworkers. It reproduces the bond distance in BF3to thenearest pm, while the SiF bond distance in SiF4is overesti-mated by 6 pm. We note, however, that the calculated bonddistance reproduces the experimental SiF bond distance in

Figure 5. (A) A schematic representation of a possible polymeric

chain form of BF3. (B) The structure of a dimer similar to that ob-

served for AlCl3in the gas phase (5) and for AlF3in argon matrices

(18, 19). (C) A possible layered structure of SiF4similar to that of

crystalline SnF4

(21). (D) A possible polymeric chain form of SiF4.

F

F

F

F

F

Sn

Sn

Sn

FSn

F

F

F

F

F

F

Sn

Sn

B

F

B

FF

B

F F FF F F

B

F

B

FF F

F F

Sn

C D

B

Sn

A
http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/

8/12/2019 2 de 3

5/5



H3SiF, 159 pm (5), to within 2 pm. The shortening of thebond in SiF4relative to H 3SiF is commonly attributed to anincrease of atomic charge on Si, hence increasing polarity ofthe SiF bonds with increasing number of electronegativesubstituents (17).

The MSS rule reproduces bond distances across the entirepolarity range from nonpolar covalent to ionic bonds. Thereis no breakdown for the elements in groups 14, 13, or 2 sig-

naling a transition to ionic bonding. We conclude that theobserved bond distances in BF3or SiF4are equally consistentwith descriptions in terms of ionic or polar covalent bonding.

Physical States a t Standard Temperature a nd Pressure

Ionic compounds tend to form solids at room tempera-ture. Thus the melting points of LiF, NaF and MgF2are 845,993, and 1261 C, respectively, while solid BeF2and AlF3sublime at 800 and 1291 C. Both BF3and SiF4, however,are gaseousat room temperature.

Crystalline AlF3forms a three-dimensional network inwhich each Al atom/ion is surrounded by six F atoms/ions.In his article Gillespie suggests that formation of solid BF3of similar structure is precluded because the B3+ion is toosmall to be surrounded by six F(1). We find this suggestionreasonable, but since the B3+ion is large enough to accom-modate four Fto form [BF4], we see no obvious reason whyBF3, if it were ionic, should not form halogen-bridgedpolymers as indicated in Figure 5Aor at least dimers likethose found in gaseous AlCl3or in matrix isolated AlF3(5,18, 19) (see Fig. 5B).

Gaseous BF3under a pressure of 1 atm condenses to aliquid at 100 C and freezes to a solid at 127 C. The crys-talline material contains molecular BF3units with a BF bonddistance that is indistinguishable from that determined for thegaseous molecule, while the shortest distance between B and F

atoms in different molecules is more than twice as long (20).Similarly we would expect SiF4, if it were ionic, to forma layered structure similar to that of solid SnF4(21) (see Fig.5C), or a polymeric chain structure as shown in Figure 5D.

Conclusions

Both AIM and APT calculations indicate that the BFbonds in BF3and the SiF bonds in SiF4are very polar,though the net atomic charges on the central atoms obtainedby the APT approach are nearly a full elementary chargesmaller than those obtained by the AIM method. The meanbond energies of BF3and SiF4calculated from the sphericalion model are less than 60% of the experimental value, andcalculations on the polarizable ion model indicate that theF anions are strongly polarized in a manner indicatingsignificant covalent bonding contributions. Finally, thesecompounds form monomeric gases at room temperature,whereas ionic compounds generally form oligomeric orpolymeric aggregates that are stabilized through Coulombattractions between oppositely charged ions.

We believe that if the term ionic compound is taken tomean that it consists of nearly spherical ions carrying net chargesapproaching an integer number of elementary charges, andthat the major contribution to the bonding energy is due toCoulomb attraction between these charges, then i t would bemisleading to refer to BF3and SiF4as ionic compounds.

Acknowledgments

We are grateful to R. J. Gillespie and R. DeKock forstimulating discussions and helpful comments.

Notes

1. The electron densit ies at the bond crit ical points (0) inBF3and SiF4also indicate significant covalent bonding contribu-

tions. In the second period 0increases from 0.075 au in LiF to0.217 au in BF3to 0.288 in F2; in the third period from 0.051in NaF to 0.154 in SiF4to 0.187 au in ClF (3). We are grateful toR. J. Gillespie for bringing this point to our attention.

2. The bonding radii of the elements in groups 13 to 17 arelisted in ref 16. The bonding radii of Li, Na, Be, and Mg atomswere calculated using the MSS rule, the bonding radius of C, andthe experimental bond distances in gaseous LiCH 3and NaCH3(Grotjahn, D. B.; Pesch, T. C.; Xin, J.; Ziurys, L. M. J. Am. Chem.Soc. 1997,119, 12368). In Be(CH 3)2and Mg[CH2C(CH3)3]2(6)rLi= 165.1, rNa= 165.8, rBe= 99.9 and rMg= 145.8 pm.

Literature Cited

1. Gillespie, R. J. J. Chem. Educ. 1998,75, 923.2. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clar-

endon: Oxford, 1990.3. Gillespie, R. J.; Johnson, S. A.; Tang, T.-H .; Robinson, E. A.

Inorg. Chem.1997,36, 3022.4. Huber, K. P.; Herzberg G. Molecular Spectra and Molecular

Str ucture, IV, Constants of D iatomic Molecules; van Nostrand:New York, 1979.

5. LandoltBrnstein, Numeri cal Data and Functional Relation-ships in Science and Technology, New Series, Group II ; Atomic

and Molecular Physics; Springer: Berlin; Vol. 7, 1976; Vol. 15,1987; Vol. 21, 1992; Vol. 23, 1995.

6. Such calculations are described in many introductory or in-termediate level textbooks in inorganic chemistry. See, for ex-ample, Cotton, F. A.; Wilkinson, G.; Gaus, P. L. Basic Inor-ganic Chemistr y; Wiley: New York, 1996.

7. For a thorough discussion wi th extensive references seeSherman, J.Chem. Rev.1932,11, 93.

8. Thermochemical mean bond energies at 298 K were calculatedfrom standard energies of formation listed in Barin, I. Thermo-chemical Data of Pure Substances; VCH: Weinheim, 1993.

9. Rittner, E. S. J. Chem. Phys. 1951,19, 1030.10. Atkins, P. W. Physical Chemistr y, 6th ed.; Oxford University

Press: Oxford, 1998; p 653.11. Hati, S.; Datta, B.; Datta, D. J. Phys. Chem.1996,100, 19808.12. Perrin, C. L. J. Am. Chem. Soc.1991,113, 2865.

13. Cioslowski, J. J. Am. Chem. Soc.1989,111, 8333.14. Bader, R. F. W.Can. J. Chem. 1999,77, 86.15. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell

University Press: Ithaca, NY, 1960; pp 228 ff.16. Blom, R.; Haaland, A. J. Mol. Struct. 1985,128, 21.17. Rempfer, B.; Oberhammer, H.; Auner, N. J. Am. Chem. Soc.

1986,108, 3893.18. Snelson, A. J. Phys. Chem.1967,71, 3202.19. Curtiss, L. A. Int. J. Quant. Chem.1978,14, 709.20. Antipin, M. Yu.; llern, A. M.; Sukhoverkhov, V. F.; Struchkov,

Yu. T.; Buslaev, Yu. A.Dokl. Akad. Nauk. SSSR1984,279, 892(in Russian);Bull. Acad. Sci. USSR1984,33, 435 (in English).

21. Bork, M.; Hoppe, R. Z. anorg. all g. Chem. 1996,622, 1557.
http://jchemed.chem.wisc.edu/Journal/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/Journal/Issues/1998/Jul/abs923.htmlhttp://jchemed.chem.wisc.edu/http://jchemed.chem.wisc.edu/Journal/Issues/2000/Aug/http://jchemed.chem.wisc.edu/Journal/

2 de 3

Documents