INTERNUCLEAR DISTANCES IN HYDRIDES
Oct., 1960
1407
Ca++ when it comes in close contact with the-oxygens of the polyphosphate chain. For the association reaction producing aq. CaP3010-3 and the other polyphosphates, all the entropy change can be attributed to the freeing of the water molecules, whereas for aq. CaPz01-2 only half of the entropy (25) change is attributed to changes in hydration. The 30 =. SO’ ( a + b - C ) S % , O (26) deviation of CaP207-2 from this picture must be wheref is a structural factor, 2 and r1the charge and the result of the unexpected endothermicity of its crystal radius of the anion, respectively, and M is association reaction. its molecular weight. r2 is the crystal radius of the Naturally, if the value of (a b - c ) is known metal cation. Equation 25 was used in combina- with high certainty, then the free energy and ention with the Sovalues for aq. P207-4and P3010-~ thalpy of complex formation_ should be corrected to calculate f, msuming (a b - c) to equal by subtracting (a b - c ) A F H ~and o (a b - c ) . zero; f was found to be 1.48 and 2.28, respectively, A&I~o, respectively. not far ojT from Cobble’s estimated values for Bjerrum Radii.-Bjerrum radii44146have been tetrahedral ions. rl for P207-4 and P3010-‘ used as a mathematical criterion for covalent were taken as 2.3 and 3.2 A., r e ~ p e c t i v e l y . ~ ~ bonding. For the CaP207-2, CaHP2O7-l, Cap3Equation 25 then was used to compute So’ OlO+, CaHP3010-2and CaH2P3010-1complexes the for aq. CaP207-2and CaP3010-3,using the same calc$ated Bjerrum radii are 3.5, 3.8, 3.9, 5.2 and structural factors as those found above for the free 6.5 A., respectively. In agreement with previous anions and a value of 0.99 A. for r2 of Ca++. calculations4these computed values of the distances SO’ for aq. CaPz07-2 and CaP3OI0-3was found to of closest approach of calcium to the respective be - 128 and - 221 e.u., respectively. From p u r phosphate anions are significantly larger than those computed values of So and So’, (a b - C)SH?O encountered in covalent b~nding.~G for aq. CaPz07-2and CaP3010-3is found to be 24 Acknowledgments.-The authors wish to thank and 23 e.u., respectively, indicating a release of Mr. W. W. Morganthaler for making many of the about two water molecules. These water mole- measurements and Dr. John R. Tan mazer for cules probably are lost from the highly hydrated43 many stimulating discussions.
results when interpreted with the structural semi-empirical approach of -Cobble.‘ For oxyions Cobble42proposes that So is represented by
+
+
+
+
+
+
(42) J. W. Cobble, J . Chem. Phys., Pi, 1443 (1953). (43) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Academic Precis, Inc., New York. N. Y., 1955, p. 247, 319, 320.
(14) J Bjerrum, Chem. Reis 46, 381 (1950). (45) R M. Fuoss, Trans. F a r a d a y Soc., SO, 967 (1934). (16) R M. Funss, private communication.
INTERNUCLEAR DISTAXCES I N HYDEIDES* BY THOMAS R. P.GIBB,JR.,AND DAVIDP. SCHUMACHER Corltrzhution N o . 259, Department o j Chemistry, TuftsUniversity, Medford 55, Mmsuchuselts Receaued January P8, 1960
Metal-hydrogen internuclear distances in substantially all the known binary metallic and saline hydrides may be rationalized equally well on the basis of an ionic model or on the basis of a model utilizing delocalized covalent bonding. In the former the anionic imadius ( C N = 4) of hydrogen is 1.29 A., the cation radius is for the ion of maximum normal oxidation number. The internuclear distances in the Group I saline hydrides are shown to be increased by the anion-repulsion factor of Pading. The covalent model is that suggested by Pauling for application to metals, and employs a single-bond radius of 0.37 A. for hydrogen. Both models are applicable to saline as well as to metallic binary hydrides.
Introduction As shown by Libowitz and Gibb’ the metalhydrogen internuclear distance in t>hirteenmetallic hydrides of the Choup IVA, lanthanide and actinide families is equal approximately to the sum of a constant H- radius of 1.29 8. (for coordination of less than six) and the radius of the cation of maximum normal oxidation number. In the present paper additional metallic hydrides and saline hydrides, Le., sub:jtantially all hydrides for which data are available, are also shown to obey this simple relationship provided suitable correct,ions for coordination are made. While “radii” of any sort must be viewed merely as useful aids without much fund.amenta1 significance, the predictioii of * This reseamh was supported by t h e United States Atutiiic E n ergy Commissi,m. ( 1 ) C;. Liboivitz and (lYj6).
T. R. 1’. CibL. Jr. Tiiia J ~ u I ~ . Y60, . ~ L310 ,
internuclear distance is extremely useful in many ways. The only other rationalization of metdhydrogen distances which appears accurate enough to be useful is that of Pauling2 which has been applied to only three hydrides. An improved calculation based on Pauling’s method is presented below. Coordination Number Correction for the Hydride Anion.--Because of the dependence of coordination number corrections of ionic radii on t.he exponent l/(n - 1)2a,3 where n is the Born repulsion exponent, it follows that for the hydride ion, where n is
1660 (1948);
(2a) L. P a d i n g , “Nature ot t h e Chemical Bond,“ (3rd Ed.), Cornell U n i o . Press, Ithaca, N. T., 1959. ( 3 ) W. H. Zachariasen, Z. K r i s t . . 80, 187 (1931); cf., C. Kittel.
“Introduction t o Solid State Physics.” John Wiley and Sons, Inc., New I - o r k , h-.Y., 1957. p. 81.
Vol. 64 TABLE I INTERNUCLEAR DISTANCE ( d M H ) AND CORRECTED SUM O F IONIC RADII.hfETALLIC HYDRIDES Cation radius AH a n d charge (1.40 A. Total CN dhlH dMH (CN 6) CM~a~ion Ac.t CNHfor CN = 6 ) corr. calcd. obsd.
-
-
Ref.
(1.98) .. (2.18) .. ...... (4) .88 I11 6 0 2.20 2.20 .go' I1 17 1.90 4 -0.10 1.92? 7 0.08 .60a IV 17 0 2.32 2.39 .92a I1 0 6 0 2.07 2.07 .77" IV -4 -0.18 -0.10 0.08 2.08 -4 - .18 - .10 2.05 .78'IV .08 (5, 7 -4 - .18 - .29 . 5gg v .ll 1.70 1.68 15 N4 - .18 .29 1.78 1.72 .6iWv 4 - .ll 7,8 -4 - .18 - .29 1.79 1.74 .68O V 4 .ll 7,8, n 4 - .I8 - .29 1.63 1.67 . 5 Y VI 4 .ll 7, 10 (1.72) 1.73 4 - .18 - .29 11,12 ( .6l 1 I ) C 4 - .ll 2.05 2.03 6 0 0 7, 13, 16 . (iY IV 6 0 2.38 2.41 -0.10 4 -0.18 1 .or 111 8 0.08 ~ 3 . 2 ~ .2G 0.9Yb IV -12 - .07 -2.32 2.29 7 .19 4 - .18 .01 2.34 2.32 7 0.938 IV* 12 .I9 The CN's for the group V metals are taken as 4 for an intera For lws symmetrical structures the CN is approximate. penetrating pair of bcc lattices. There is some uncertainty about the structure of these hydrides. * The choice of oxidation number IV is an exception to the general rule. It seems mnre likely that the central ion is U+6 and that ion-repulsion accounts for the large U-H distance. The tabular radius for U* is 0.86A. e The cupric ion radius is not tabulated. The 12(4/15). * Zschariasen, cf. ref. 3. f Goldschmidt, ref. 4. radius shown is an average for cupric halides and oxide. Ahrens, cf. ref. 4. 0.68' I11
(8) (8) 6 8 6 -8" -8 -4
(0.08) ( .08) 0
(4)
(-0.18) (- .IS) 0 -0.18
(-0.10) ( .lo)
I
.
.
.
.
.
I
-
-
-
I
+
@
small, the dependence of apparent radius on coordination number will be unusually large. Accordingly, we have chosen to apply a correction to the H- radius of the same form used by Zachariasen3 for cation radii but with an appropriate increase in the multiplier. The cation correction may be additive, when it has the form A = 0.6 log ( C N / 6 ) where the G in the denominator adjusts the correction to zero for CN = 6, or the cation correction may be multiplicative as tabulated in reference 4, in which case it is arbitrarily adjusted to unity for CN = 6. The resulting equation for internuclear distance is then given by either d ~ == u r h i + 3- 0.6 log(CNx/G) + ru- + log(CXu/G) == crx+
+ c'rw-
where d l is~the~ internuclear distance in the ionic substance, T M + is the tabular cation radius for (4) Landolt-Bornstein "Tahellen." Vol. I, "Kristalle" Pt. 4, A. Eucken. Ed., Springer-Verlag. Berlin, 6th Ed., 1950, p. 523. ( 5 ) (a) F . 11. Ellinger, C. E. Holley, Jr., R. N. R. Mulford, W. C. Koehler a n d W. €€. Zachariasen, T H r s JOURNAL, 69, 1226 (1955); (hr F. H. Ellinper, C . E. Holley. Jr., B. B. McInteer, D. Pavone, R. M. Potter, E. Staritzky a n d W. H. Zachariasen, J. A m . Chem.. Soc., 7 7 , 2647 (1955:. (6) S. S. Gidhu. L. Ileaton a n d D. D. Zauheris, Acto Cryst., 9, 607 (19.56,. (7) W. B. Pearson, "A Ilandbook of Lattice Spacings and Structures of Metals a n d Alloys," Prrgamon Press. New York, ti.Y., 1958. (8) D. Knowles, IGR-R/C 190, hlarch, 1957. (9) B. Stalinski, Bull. Acad. Polon. Sri.. CI. iii, 2 : 245 (1964). (IO) C. A. Snavfly and D. A. Vaughn, J . A m . Chem. So 2.. 71, 313 (1949). (11) J. C. Warf a n d W. Feitknecht, Helb. Chim. A d o , 33, 613 (1950). (12) J. A. GoedkDop a n d A. F. Andresen, Acto Cryst., 8 , 118 (1955). (13) J. Worsbam, W. K. Wilkinson a n d C . G. Shull, -1.Phys. Chem. Solids, 3, 303 (1957). (14) ,I. C. Warf a n d W. 1,. Korst. dclo Cryst.. 9, 452 (1958); cf., also Ph.D. Theris, W. L. Korst. U n i r . Southern California (1936). (1.5) 11. J . Trzeeiak, D. F. Dilthey a n d M. W. hlallett. BXI-1112 (1958). ( I O ) A. :\Iaeland (iinpuh.) reports ~ M H A. f o r liiiiitirrg nonstoichionietrir, coinpusition a t room temperature.
2.03
CN = 6, T I I - is a constant radius of H - for CN = 6, c and cr are multiplicative corrections depending both on the Born exponent and on C N . The hydrogen anion radius r H - is taken as 1.40 A. for CN = 6 and the value 1.29 A. used previously is considered merely a rough average (for lower CN's). The only novelty in these equations is the inclusion of a separate corrective term for H-; for anions of n = 7-12 this correction is unnecessary. The two equations are substantially the same within the approximations customary in dealing with ionic radii. The use of a single CN correction factor bascd on a mean Born exponent has better prcccdent, but the double correction cited above is convenient in that the well-known Zachariasen data may be used without change. Results are shown for metallic hydrides in Table I. Several dihydrides of more electronegative metals are included for comparison with Table 111. The sensitivity of the apparerit H- radius to CN is in line with what one might expcct of a tenuous ion of low electron-density. This tenuosity and bulkiness (compared to covalent H) are strongly supported by the large internuclear distance and high refractive index in LiH, for example. Ion-repulsion Correction of Internuclear Distance for Saline Monohydrides.-The Pauling expression for also includes the Born repulsion exponent and while very tedious to calculate it gives a rough relation of d i m to the Born exponent and radius ratio. As the latter increases in the alkali metal group, the Born exponent also increases. Thus, F ( p ) increases from 0.981 for LiH to 1.027 for CsH. The repulsive coefficient B2a is 0.0367 as evaluated from F ( p ) for LiH. Datta for the alkali metal hydrides are shown in Table 11. As noted by Pauling2" in the case of true salts of uiisyinmetrical valence type, c q . , alknline-earth nietal fluoridcs, thc observed metal-anion distances
INTERNUCLEAR DISTANCES IN HYDRIDES
Oct., 1960
are closely approximated by the sum of the uncorrected radii. This same behavior is shown by alkali-earth metal hydrides as evidenced by Table 111. The poor agreement for MgH2 is not more than one would expect to arise from the lack of similarity of the bonding in hydrides and fluorides. Magnesium hydride is crystallographically almost identical to MgF2 where the anion (radius 1.33 A.) is less easily deformed. The principal H-H distance in MgHz is 2.76 A. which is close to twice the E[- radius (1.40 k.) suggested herein. Excellent agreement is shown for most of the known di- and trihydrides with the exception of EuH2, YbHz and T.hrHlawhose H - positions are not known with certainty and in which the internuclear distances are therefore not final. The quadrivalent Ac ionic radius is not available. TABLE I1 SALINE MONOHYDRIDES Hydride
Catim radius
LiH NaH KH RbH CsH
0.68 0.98 1.33 1.48 1.67
Radius sum
(rH =
1.40
A.)
2.08 2.38 2.73 2.88 3.07
Born exponent (av.)
5 6 7 7.5 8.5
dMH
dMH
F(g)
calcd.
obad.17
0.981 0.992 1.006 1.014 1.027
2.04 2.36 2.75 2.92 3.15
2.04 2.44 2.85 3.02 3.17
TABLE I11 UNCORRECTEDSuki C ~ FTABULAE CATIONRADIIAND r M H = 1.40 A. FOR DIHYDRIDES AND TRIHYDRIDES O F ELEMENTS O F
Loa ELECTRONEGATIVITY Tabular cation radius (charge)
Plus 1.40
8.
dMH
obsd.
Ref. (dam obsd.)
1.95 2.05 5(a) 2.34 2.35( mean) 19 2.50 2,53(mean) 19 2.69 2.7l(mean) 19 5 2.46 2.45 7, 14 2.43 2.43 14 2.41 2.40 14 2.39 2.38 1 2.36 2.33 7, 14 2.35 2.49(mean) 17 2.34 2.31 7, 14 2.26 2,35(mean) (2.51) 3.46 1 7 2.48 2.41 7 2.39 2 20 1 2.30 2.32 .9oev 2.32 1 .93eIVb 2.33 2.32 1 .90 IV 2.30 .90 IV 2.30 (2.31) 17 Considered Uyl in ref. 1. TTempleton, c j . ref. 21. 0 . 65” 0.94e 1.10“ 1.290 l.OGTIIIa 1.03TIII I.OITIII 0.99TIII .9GTIII .95TIII .94TIII .SGTIII 1 llelII l.08“[11 0.DOe1V
Discussion of the Ionic Model for Hydrides.The data shown in Tables 1-111 indicate that the conventional treatment of internuclear distances in salts may be appl.ied successfully to hydrides of the less electronegative metals. The only novelty is the choice of a saline model for the metallic or semi-metallic hydrides. The advantage of the saline model lies in the ease with which it may be adapted to the estimation of lattice-energies and the (21) D. H. Templeton and C. 11. Dauben, J . Am. Chem. Soc., T 6 , 5238 (1954).
1409
prediction of unknown hydride structures. Rationalization of known structures by Pauling’s radius-ratio rules and detailed examination by means of crystal-field effects of small changes in internuclear distance with H-content become of interest in connection with this model. In preparing the tables use was made of the compilations in references 7, 17 and 18. Most of the cited structures have been determined either by neutron diffraction or by analogy with closely similar substances so studied. Some question exists as to the structure of the Group V hydrides which is variously reported as NaC1-type, bodycentered cubic, tetragonal and orthorhombic. A tetragonal distortion of the bcc structure was used for the calculations reported here. There is a progressive increase in d-spacings with increasing H-content for all three of the Group V metalhydrogen systems, and the calculated values may therefore be in better agreement than appears from Table I. The very small M-H distances afford support for the marked effect of codrdination number on the effective H-radius. The three tables indicate that practically all hydrides may be treated as salts insofar as metalhydrogen distances are concerned. Di- and trihydrides of those elements whose electronegativity is above about 1.2 on Pauling’s scale, e.g., Mg, Ti, Zr, Hf, etc., require coordination number corrections whereas such corrections are not required for the more salt-like metallic di- and tri-hydrides, e.g., lanthanide and actinide hydrides, or the obviously saline hydrides such as CaH2. The H-positions in CaH2, SrH2 and 13aH2 are not known from neutron studies, but the original X-ray worklg appears unequivocal. Note that in the case of ThH2 and Th4H16 different oxidation numbers for T h suggest themselves. It is reasonable to suppose that the codrdination number corrections for MH2 and MHS stivctures are diminished by compeiisating errors, as mentioned above for CaH2, etc. Actually, the CN correction for H appears too large here and somewhat better results are obtained if it is neglected, as in reference 1. The Delocalized Covalent Bonding ModelsPauling2 has used the relation = r,,
+ 0.3 log(v/CrV)
to rationalize internuclear distances in metals. This relation was applied by Pauling to many metals, and to a few metallic hydrides using an r1 for hydrogen of 0.28 k. While giving good results in three cases (TiH2, ZrH2, PdH), it failed in the case of UH3. In obtaining the results shown in Table IT-,the relation used is dYI3
where
= I1
+ 0.37 + 0.3 log (Cb’rnclTh/l’m)
is the Pauling single-bond radius €or thc 0.37 is the single-bond radius of II (half the separation in I&) and the subscripts ni and h TI
( 1 7 ) “Some Physical Properties of the Hydiides ” CCRL 161’3. R. E. Elson, H. C . Hornig and W. 1., Jolly, d oE., Lirermore. CaIIf., 1935. (18) R. W. G. Wgckoff, “Cryetal Structures ” lnterscience Publishers. Inc., New York, N. Y., 1948. 119) E. Zintl and A. Harder, Z. Elektrorhem.. 41, 33 (10%).
1410
Vol. 64
11. E. UNGNADE, E. D. LOUGHRAN AND L. W. KISSINGER
refer i,o metal and hydrogen, respectively. The valence of I€ is assumed to be unity. The excellent agreement with observed ~ M is H shown in the table. It might be pointed out that both the delocalized bond and ionic models suffer from minor drawbacks. In the former, the appropriate valence of the metal is not always known in advance and this greatly diminishes the predictive value of the model.20 I n the ionic model one must accept the usual clrambscks of all spherical-ion models, namely, that the anions may sometimes interpenetrate, as in the classical instance of 0 2 -in rutile. Thus, in the ionic model of UH3,if the H- ions are not to penetrate one another, their radius must be approxiIpately 0.86 8. If the H- radius is actually 1.29 A. then they must interpenetrate by just l / 3 of this radiuis) which seems high although H- would be expected to be a "soft" and very tenuous ion. Y o such interpenetration occurs in the rutile analog, hlgH2, but it is observed in several metallic hydrides. Both models suffer from a difficulty common to all expressions which rely quantitatively on coordination number. This term is only explicit in simple or highly symmetrical structures, and becomes somewhat arbitrary in distorted structures. Conclusions.-The agreement of the ionic and delocalized covalent models with each other and with experimental metal-hydrogen distances, indicates lhat there is no sharp difference between saline and metallic hydrides. The ionic model provides a better rationalization of the metallic characier of some hydrides (Le.) when the normal cation oxidation number is in excess of the normal hydrogen-metal ratio) and interprets the consequent excess cationic charge in terms of generalized metallic bonding. Both models minimize the contribution of metal-metal interaction, in keeping with the observed properties of metallic hydrides, but the ionic model stresses the high electron density around €1. This is in keeping with the considerable electron-affinity of H and the fundamental stability of the helium configuration. (20) R. F Rundlc. J A m . Chrm. Soc., 73, 4172 11951).
TABLE IV INTERNUCLEAR DISTANCESBY THE PAULING EQCATIOX EXAMPLES FROM FOUR GROUPS) (REPRESENTATIVE C N Valence of of Hydride
KH CaHz TiHZ VH $1 CrH
