Coulombic Models in Chemical Bonding II. Dipole Moments of Binary Hydrides Lawrence J. Sacks1 Christopher Newport College, Newport News, VA 23606 In the previous paper of this series ( I ) , a coulombic model for chemical substances was described and several illustrative applications were presented. Briefly, the model shows that all substances may be considered; a t least as a first approximation, to be assemblages of cations and anions, with unshared electron pairs frequently acting as anions. Different structure types are attributed to packing consequences rather than bond tvoe. ". Molecules are neutral assknhlages consisting of one or more highly charged cations, each comvletelv surrounded bv anions and.. freauentlv. . ..lone pairs of eiectrons, giving a negatively charged surface. An anion of unique structure and narticular interest is hydride ion, H-; this configuration is assigned to hydrogen in all its compounds. For example, methane is formulated as a C4+ core surrounded by four hydride ions to form the tetrahedral, nonpolar methane molecule. Ammonia is taken as three hydride ions and an electron pair around the N5+ core; water is described as containing two hydride ions and two lone oairs on the 06+core: and HCI or H F is constructed from onehydride ion and three electron pairs on the halogen core. A useful simplification for purposes of calculations is the reduction of the particles to point charges. Several applications of the model have been described in the first paper of this series. An application of theoretical interest concerns the rotational barrier in ethane. resented in the followine paper; another is dipole moments, particularly for binary hydrides. The coulombic model describes dipole moments of hinary hydrides as the resultant of the dipolar contributions of the hydride ions and the electron pairs around the positively charged central atom. Known distances and angles to the hydride ions are used to determine a range of interdependent values for distances and angles for the lone pairs, as described below. Such explanations, however, are in direct conflict with those based on Valence Bond (VB) theory, which attribute molecular polarity to the resultant of the polarities of the bonds within the molecule (2-5); therefore, the coulombic model is also in conflict with the related concept of electronegativity and with those representations of wave equations purporting to reflect these concepts (6). The coulomhic model and VB model will now he evaluated as they apply to HC1, the molecule frequently used to demonstrate the VB concepts of polar bonds and the calculation of "partial ionic character" of bonds. First, the dipole moment of HC1 will be described by the point charge approximation of the coulombic model; then, consideration will be eiven - to ~ossihlestructures that could corresoond with two reference states for polar l~onds(2, 3, 7)and with the final "hybrid" molecule The . ouroose - of these considerations is to determine whether such reference states-a nonpolar ("covalent") structure for the zero dinole moment canonical form and an "ionic"structure for the 100%reference polarity form-can he physically realistic. Whether the bond is "17%
ionic" ( 2 , 8 )is not the main point; the issue is whether any such description has possible correspondence with reasonable electron distributions. Calculation of Dipole Moment Coulombic Point Charge Model Hydrogen chloride, according to the point-charge model, has C3., symmetry of the three lone pairs with respect to the CI-H molecular axis. The centroids of charge of these electron pairs, a t a distance 1from the chlorine nucleus, make an angle, @, with the molecular axis and an angle, 8, with one another (see figure). For any Cav structure the two angles are related by 4 = arccos
(T)+
1 2 cod
'"
or:
I t is postulated that the molecular dipole is the resultant of the contributions of the charge distribution asymmetries of H--C17+ and of C17+ with each of the three lone pairs of electrons. The contribution of the H--C17+ is and the contribution (in the opposite direction) from the three lone pairs is l'he experimental dipole moment is alternately reported as 1.03 D ( 9 )or 1.08 1) (10) corresponding, respectively, to3.43 X 10-."'C.m and 3.60 X IO-"'Cm.'rhe dioole moment ot'the molecule is, therefore for the lower reference value or 3.60 X C.m for the higher value. The higher value is used in the following discussion, but no significant difference occurs if the lower value is used. Solving for the two variables, we have lcos 4
= 2.49 X
lo-"
m
No satisfactory way has been found to fixuniauelveither the distance of the electron pairs from the nucleus o i t h e angles, 4 or 8; however, only the same rather narrow range of values satisfies either the premises of the coulomhic model or the chemistry of the molecule. This range is determined as follows: the point-charge model requires that the hydride ion occupy a smaller volume than lone pairs on the same core, and that the distance of the hydride ion from the center of the core be greater than that for the center of charge for the lone pairs. This is recognition of the attraction of the nroton for its pair of ~ ~ l r c t r o and n s the repulsion of the proton for thecore. l'he coulombic forceialso require a wearer an& of separation of the centers of charge of &y twoelectron pairs, 8, than of an electron pair with an hvdrideion. This ~ l a c e sas . a lower limit on 8, the tetrahedral angle, arccos (-i/3), and, ~
Taken, in part, from papers presented at the 184th ACS National Meeting. Kansas City, MO. 1982. and the Eighth Biennial Chemical Education Conference. Storrs. CT. 1984. 'On leave. 1985-86, Laboratory of Chemical Evolution. Department of Chemistry. University of Maryland. College Park, MD 20742.
Volume 63
Number 5
May 1986
.~~ ~
~~
373
Table 1. Dipole Moment Calculations: HCIa I. prn
cos 4
4. Des
cos a
50 60 70
0.498 0.415 0.356 0.333 0.311 0.277 0.249 0.226 0.208 0.192 0.176 0.166 0.124 0.083 0.000
60.1 65.5 69.2
-0.128 -0.242 -0.310 -0.333 -0.355 -0.385 -0.407 -0.423 -0.425 -0.445 -0.453 -0.459 -0.477 -0.490 -0.5
R = Arccos
a. Deg
- I)
(w (3
6 = ~rccos
100 120 130 140 150 200 300 llirnl
. ".. ..
75.6 76.9 79 60 80.4 82.8 65.2 90.0
.
37 104 108
x 2 x 1.60 x
114 115 116 116.4 116.9 117.3 116.5 119.3
120
OeOrnetric Relationshipsfor HCI Molecule. eZ2-representsthe centroidof charge of a pair 01elecbam. The lone pain are at a distance, I,from the CI nucleus and d horn another lone pair. Fw the c o ~ l o r n bmodel. i~ H re~resentsme 1- ~ o l ncharae t of the H- ion: for covalent models, H represents the proton and a Pair of electrons Is separately located with its centroid of charge along the imernuclear axis at a distance, s,from lhe Center of the CI.
-
.
10-fPc x
~ C O = S 9.60 ~
x
IO-~=C.ICOS~
hence, !COS+ = 2.49 X lo-% (24.9 pm). Anowable values are in box (a- ten).
as an upper limit on 1, a distance less than the H-C1 separation. With these boundary conditions pre-established, 1and 0 are selected from values shown in Table 1. I t is seen that the allowed range for 1is about 80 t o 120 pm, corresponding to angles of 9 between 111 and 116'. This range of values distributes the hydride ion andlone pairs over the surface of the C1 core to provide the negatively charged surface postulated as necessary for molecules. Valence Bond Model for HCI The valence hond model considers HC1 as a structure intermediate between "covalent" H:C1 of zero dipole moment and "ionic" H+Cl- with a dipole moment given by point electronic charges a t the internuclear distance of 127 C.m (6.07 D). as shown above for the Dm. 2.03 X ~oulomhicmodel, but this t i m e i n the opposite direction. The molecule is represented by a wave equation having primary resemblanceto the waveequation for a nonpola;"covalent" molecule, ah^, along with two "ionic" contributions, C+A+B- and d+*-~+(11). For HC1, the d (H-Clf) contribution is dismissed as insignificant compared to the c (H+Cl-) term on the basis of the relative electronegativities of the two atoms. Since the experimental dipole moment, 1.03 D. renresents onlv 17% of the 6.07 D calculated for two electronicunits separated by thr equilibrium bond length of 127 Dm (12). the bond is said to harr 1 7 9 "ioniccharacter". ~ e r 6 a ~ s b e c a u the s e calculation is so simple, it appears in the majority of general chemistry textbooks dealing with dipole moments, as well as some advanced texts. It is suhmitted, however, that this calculation has no physical basis, because a suitable "cuvalent" structure with zero dipolr moment has nor been described, herause the "ionir" srructure centers the honding pair farther from the chlorine than does a reasonable "covalent" structure, and because a 17%shift of electron density from a possible nonpolar structure toward a reasonable "ionic" structure produces a dipole moment far in excess of the experimental value. Each of these structures-the "nonpolar", the "ionic", and the "17% ionic" will now be considered in detail.
374
C17+
H
rm = 127 pm contribution of CltH-: 2.03 X 10-lsC.m %Wbution M 3 lme paws: 2.39 X lo-%m For 3 lone pairs.
prn, = 3
d = 1 [2(1 - cas
Journal of Chemical Education
Nonpolar Canonical Form No direct guidance is provided for the electron distribution for this structure in any of the sources espousing its validity; however, only two possibilities exist-a nonpolar H-Cl bond or a nonpolar HCI molecule-and each can occur without the other. As is shown below, the position of the lone pairs will determine whether a molecule with a nonpolar hond would he nonpolar. Nonpolar Bond. An "obvious" choice for nonpolar HCl is to position the bonding pair halfway between the two nuclei, so that the bond is truly non~olar.For the molecule also to he nonpolar, it is necessary that the contribution of the three lone pairs also he zero; this occurs only if they are coplanar with the C17+ core ("so2"). . . . Two problems arise from this model. One is the expected chemistrv of a chlorine atom structured with nearlv. Dlr ".. symmetry of the lone pairs and a honding pair localized on one side of t h e ~ l a n of e the lone airs. Such anatom would he expected to hla good accepto;(~ewis acid). Ammonia, for example, might be expected to form a nitrogen-chlorine bond through the lone pair. T h e second problem is with the meaning of "equal sharing" for a "covalent" hond between different atoms. With radii as different as those for H and C1, placement of an electron pair a t the midpoint of the hond represents equal sharing only if one atom is considerably more equal than the other. The problem is accentuated when one considers HI-here, the honding pair would be buried deep within the iodine core. NonpolarMolecule. If the constraint of anonpolar bond is removed in favor of such electron distribution as is needed to obtain a nonpolar molecule, different problems arise. As in the coulomhic model, the three nonbonding electron pairs are taken as symmetrically arranged around the molecular axis at a distance 1 from the C1 nucleus and a t an angle, @, from the axis (see figure); 1 and 4 are interdependent, as shown ~reviouslv:here. however. the location of the bondine pair of'electrok a ~ s bto he dktermined. Three contribc tions to the molecular d i ~ o l moment e are added: that of the 'proton with one electron of the honding pair located a t a distance, s, from the CI nucleus; in the same direction is the contrihution of the resultant of the three lone pairs, each paired with two units of positive charge from the C1 core; in the opposite direction is the contrihution of the other bonding electron with one unit of charge of the C17+core:
w,~, = e(r - s) + Geleos 4 - e.s
= e(r
+ Glcos 4 - 2s)
Table 2. Electron Pair Positlon for "Nonpolar" HCld
pm and most of the range places electron density primarily beyond the proton! Percent Ionic Character Two changes must be considered in attempting to assign physical significance to any "% ionic character" for HC1-the shift in the bonding pair and the change in the angles between lone pairs. Since the effects are additive they can be considered separately. Bonding Pair. I t is generally implied, if not explicitly stated, that the polarity of the HC1 molecule is due to a greater attraction of C1 than of H for the bonding pair of electrons. This is said to he due to the greater electronegativity of C1 than H, and the HC1 bond is usually said to have "17% ionic character" (2, 8). If only the bonding pair were involved. there would be a shift from 62.5 Dm from C1 to about 52pm from CI. As shown above, howe;er, reasonable distanws from CI to the elertron pair for the ionic structure are greater than those for the nonpolar HC1 representation, i.e.. there is a shift of the electron pair of the "nonpolar" cadonical form away from C1 as theconfiguration changes toward the "ionic" model. Lone Pairs. A shift of 17%from the c o ~ l a n aarrangement r uf lone pnirsaround theCI toward the tetrahedral roniiguratiun of the"ionic" model yields angles among the lone pairs 01 86.7". The dipolr moment for such a molecule (with the bondine. air still at the midpoint ut the bond, would depend on the &auce to the centers of charge of the lone pairs,
where r is the H-CI bond length, 127 pm, and e is the electronic charge. Some values calculated for positions of the electron pairs are shown in Table 2. Some values of particular interest are: 1) For s < 63.5 pm (bonding pair closer to C1 than to H) the lone
pairs must also be hetween H and CI. The lone pain remain almost coplanar with C1 until s approaches r , i.e., until the model approaches the hydridic structure of the coulomhic model. 3) Far I = s = 74.7 pm, the lane pairs are less than 3" behind the CI (74.7 pm is the minimum distance to the lone pairs according to the eoulambic model, occurring when all angles are tetrahedral). 41 F m s = 127 pm, the bond length, the angle between lone pairs rangesirom obout 7R0for1 = 10Upm (thcCIradiusinCI1 ,1311 to just over 83' for the "ionic radius" of CI-, 181 pm.
2)
"Ionic" Canonical Form The "ionic" reference state for VB description of HC1 is generally considered to consist of some high-symmetry arrangement of eight electrons around the chlorine core plus a (separate) proton which does not affect the CI-. Pauling's approach, reflected implicitely in most current textbooks, is to describe the chloride ion as "spherically symmetrical, so that the center of charge for the 18 electrons coincides with the chlorine nucleus" (14): . ., an obvious choice is tetrahedral. although certain electron arrangements between sp2+ p and sp3 would suffice, as would Linnett's double quartet (15). Because it most closely resembles the Czv symmetry of the "final" structure. the tetrahedral (su3) distribution of four electron pairs around the C17+ core is taken as the electron configuration of the chloride ion. The dipole moment of H+-C1- would be the same regardless of the distance of the centers of charge of the electron pairs from the Cl nucleus (0, having the samevalue calculatC.m (6.8 D), but ed for the point-charge model, 2.03 X in the opposite direction. The only variable t o be considered is 1, and its only significance for this calculation is in the meaning of "% ionic character", discussed below. A range of values might he taken as between the "covalent" radius, 99 pm and the "ionic" radius of C1-, 180 pm (16). The entire range is well beyond the "nonpolar bond" distance of 63.5 ~~~~~
~
~
ploneWim = 6elcos 4
= 5.53 X
C.m.1
The contribution for the three lone pairs a t the "covalent" C.m, ahout 1.5 times radius of 100 pm would be 5.5 X the ex~erimentalvalue, and would increase in direct proportion t o about three times the experimental value a t the "ionic" radius of 180 pm. The molecular dipole moment would thus be a t least 2% times the experimental value if both contributions were considered. Dlscusslon of ResuIIs
I t does not anoear nossible to find either of the charge to the "nonpolar" or distributions f k ' ~ ~ 1 correspond ~ t o "ionic" canonical form nostulated bv VB theow as reference states for assigning significance to percent ionic character of bonds or to the equivalent concept of bond polarity. Even the "least worst" case for VB models gives a dipole moment substantially in excess of the experimental value for the frequently cited "17% ionic" resonance hybrid. Distributions more in keeping with the change from a "covalent" toward "ionic" bond either make the hydrogen hydridic (i.e., they conform to the distribution of the point-charge model) or give dipole moments several times the experimental value. In the vernacular of the wave equation cited above, the disregarded d term, d k - c ~ +which , corresponds to the coulombic model, is the most significant term, with negligible contribution from the c term (for H+C1-) and little or no contribution from the "covalent" (a) term-just the opposite conclusion from that offered bv electronegativitv a r m ments. Only the lack of specified reference states for the two commonlv postulated reference states has permitted this concept to become so pervasive. If they are required to have ~hvsicalmeaning, the association of dipole moment with a shift in electron density of the bonding pair of electrons loses credibility. Changing from 17% to some other percentage of "ionic character" would bring no significant relief for the basic problem: the proposition that dipole moments are the result of bond moments (2,171 is a misconception. While the semiquantitative results of the point-charge model adeauatelv describe dinole moments (and test alternate modeis), a qualitative juigment concerning polarity of molecules can be made without anv calculations. The criterion for polarity is the existence in:the molecule of a unique Volume 63
Number 5
May 1986
375
Table 3. Lone Palr Angles and Distances In Blnary Hydrldes Hydrlde
p. D
re.", pm
H-E-H, deg
NH3 PHs NFS3 OH2 FH CIH
1.47 0.58 0.23 1.85 1.91 1.07
101 142 137 95.8 92 127
107.3 93.1 102.1 104.45 (0.a.)
(".a,)
Accepted range 8 I, pm
(n.a.1 (n.a.) (n.4 112-130 111-114 111-1 16
71. 122. 93 70-95 70-90 80-120
.Uniqwly
fixed faone laxt pair. BFor comparison. NFJ 1s indded; me calculatlonr are only approximate because of !he wersirnpllflcatlon of Vesling F- ap a pint Charge.
end. In this context, "end" can also mean edge or face. Other Binary Hydrldes
Dipole moments can be described for other binary hydrides by the point-charge model in a manner similar to that for HC1. The ranee of acce~tablevalues for the an& subtending the lone pairs and for the distance betweenucenters of charge of lone pairs and the cation nucleus are shown for some molecules of interest in Table 3. Of special interest is ammonia because with known distances and aneles to the three hydride ions the centroid of charge of the L n e pair is uniquely fixed, a t 71 pm. Note that the angles and distances are consistent with postulates of the model: the lone pair is closer to the core than the hydride ions due to repulsion between proton and core, and the lower repulsion between two hydride ions than between a hydride ion and an electron pair results in H-N-H angles less than tetrahedral. Finally, the three hydride ions and the electron pair effectively surround the N5+ core, providing the negatively charged surface postulated as essential for a molecule. For phosphine, the larger core has an expectedly greater distance to the electron pair (122 pm versus 71 pm for ammonia). Mher Blnary Molecules
*Ithough
bonds appear be unnecessary and insufficient for describing the dipole moments of binary hydrides, their contribution to the dipole moments of other molecules has not been ruled out; however, the difficulty encountered for HC1 in establishing reference states for the "covalent" and "ionic" configurations is also encountered when molecules such as CIF or CO are considered. I t appears that "nonpolar" can have relevance only with bonds between identical atoms. Dipole moments for these other molecules can also be explained without recourse to polar bonds. In the case of ClF, for example, consider as reference states two isolated halide anions, C1- and F-, each with four pairs
376
Journal of Chemical Education
of valence electrons tetrahedrally arranged around the core. What will happen to one of the pairs if it should become bonded to a second core as well? In the case of chlorine, the pair will he constrained to a smaller region due to the additional positive field. This will allow the remaining three lone pairs dn chlorine to spread out over a larger poition of the surface of the chlorine atom, effectively shifting negative charge toward the fluorine. Note that delocalization of the pair over one or both atoms has no effect on this question of charge distribution-we do not care which electrons are where, only about changes in charge distribution from the isolated atoms to the bonded pair. The bonding pair on fluorine will undergo a much smaller decrease in effective size, since the fluorine valence electrons, in a lower energy level than chlorine's, initially occupy a smaller region. I t might even be amued that the bonding nair on fluorine mdves toa largerrigion, but that is not rential to the matter. The point is hat there is not as murhdecrease in thedipolar contribution of the lone pairs of fluorine as there is from those on chlorine, and a net shift of electron density of lone pairs toward fluorine occurs. What about the bonding pair? It probably contributes little if anything to the molecular dipole directly, but does influence the orientation of the lone pairs, hence indirectly affects the dipole moment. In general, the ereater the discrenancv in size of the two haloeen atoms. the more polar the mb1ecu"le will be. Note that, alihongh the rule a o ~ l i e sto hvdroeen. as well as the other halonens. that atom must be treateiuniquely, as described above. Acknowledgment T h e thoughtful criticisms of a reviewer were most helpful and are greatly appreciated. Literature Cited -~~ (I1 Ssck8.L. J. J,Cham.Edur. 1985,63,288. (2) Pauiing. L:'Tho Natureof fheChomicalBond",3rdd.;C~mellUniv.Prw.Ithaea, NY. 1960.Ch2.3. (31 Ebbing. D. D.: Wrighton. M . S. '"General Chemistry"; Houghton-Mifflin: Baaton.
-
.
1W.d l ...., n ?.d.-
(41 McQuarris,D. A.;Ro&,P.A:'GeneralChemiatry": Freeman:New York,1961:~387. (51 Mortimer.C.E."lntroductiontoChemiatry";VanNost2and:NewYork, 1977:pp 179, 7 9"
(6) Ref. 2, Ch 3.
(7)Douplss.H:McOaniel.D.H."ConeepkandModehinInowanieChemistry..,2nded.; wiley:N*W~ork, 1963:p 76. f N ~ W is) ~ a v i sE~. ;. G ~ ~K.ID.: wwhit , ten,^. W." ~ r i n e i p h o chemistry";saund~ra:
York. 19W p 230. Ref,,,78, (101 wea8t,R,c.,Ed."HandbwkofChemiatryandPh~sics",60thd.;C.RC.Pr~:Baea Raton, FL. 1970; E-63.
,,,, ns,,-, " , ~..,..".
(12) Huheey,J.E."lnorganicChemistri",3rdd.:Harper&Ra~:NewYork,1983:pA-32. (131 Ref 10. p F-21% (141 Psuling, L. "Colleee Chemistry". 3rd ad.;Freeman: San Raneiseo, 1964:p 27s. (151 Linnett, J. W. "The Electronic Structure of Moleeul~s,A New Approach Widey: New York. 1954. (161 Weast,R.C.,Ed."HandbwkofChemistrysndPhyales",62ndd.:C.R.C.P~ua:h~ Raton, FL, 1981;p F-177. (17) hf.4~389.
