Joel F. Liebmanl University of Cambridge Cambridge, England
Why is the Oxygen in Water Negative?
It is well known that the oxygen in a water molecule is negative and the hydrogen positive. As such, water provides a means of defining the oxidation states of hydrogen and oxygen. Oxygen always has an oxidation state of -2, except in H202where it is - 1 and in OF2where it is +2.% Likewise, hydrogen always has an oxidation state of +1, except for metal hydrides such as LiH where it is - L a By considering such compounds as COz and HC1, one can infer the oxidation states of C and C1. In this way the common oxidation states of all theelements can be systematically derived. However, because water is neither a strong base nor a strong acid, it is quite reasonable to assume the true charge on the hydrogen is less than +1 and likewise the true charge on oxygen smaller in magnitude than - 2 . Unfortunately the meaning of "true charge" is ambiguous since different experimental and theoretical methods give quite varying numerical results. Fortunately, trends usually seem to he invariant when one considers related compounds. Although the success of a paradigm is usually independent of the reasons for its validity, it is reasonable to ask "Why is the oxygen in water negative?". Perhaps we should begin with definitions-what is meant by "oxidation state"? One convenient definition is "The oxidation state for atoms in covalent 1 Present Address, Inorganic Materials Division, National Bureau of Standards, Washington, D. C., 20234. As of September 1972: University of Maryland, Baltimore, Maryland 21228. There are some other oxygen species, admittedly quite exotic, such as 0%-(superoxide ion), Ox+ (dioxygenyl cation), 0sFz (dioxygen diflnoride) and Oa- (oaonide ion) where the oxidation states are -I/%, +'/z, +1, and -I/$, respectively. SOxidation states of +I/, and + I / $ can he assigned to the remarkably common gas phase ions, Ha+and Hs*.For n odd, the H,+ ions have been observed for n up to around 100. For n even, only H2+ and H4 have been seen to date. +
compounds is obtained by assigning the pair of electrons in the valence bonds to the more electronegative atom and then counting the charge on the quasi-ion (I)." Electronegativity qualitatively reflects the electron withdrawing or releasing power of an element; the more electron withdrawing, the more electronegative. For at least the common elements, the reader probably has an idea of the relative ordering. Certainly, oxygen is considerably more electronegative than hydrogen. This is true whether one used the Pauling (t)or Mulliken (3) definitions for electronegativity. Mulliken defined the electronegativity, X, as the average of the ionization potential, IP (also written I) and the electron affinity, EA (also written A). Pauling derived his electronegativity values from thermodynamic data on bond strengths of "normal compounds." The choice of a set of compounds as "normal" is, unfortunately, not easy. Indeed, what constitutes a normal compound is seemingly situation dependent. For those people who primarily think in terms of the octet mle and electron pair bonds, compounds such as NzOz+and NaO look most abnormal. However, both appear in the experimental literature and atmospheric chemists are surprised neither by their existence nor their properties. The author finds it somewhat surprising that both electronegativity scales give approximately the same predictions in almost all cases where they are used. It would appear that the oxygen in water is negative because it has a higher electronegativity than the hydrogens. However, since "atomic charges" is the conceptual and physical antecedent to electronegativity and not the descendant, this answer is not sufficient. For our problem it makes sense to return t o individual observable properties of the H and 0 atoms. Let us
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consider the ionization potential and electron affinity of hydrogen and oxygen. Running to the nearest data compendium (4), we find that IP(H) = I P ( 0 ) = 13.60 within 0.02 eV! An electron volt is admittedly large, but 0.02 eV still comes out to an insignificant 0.5 kcal/mole. I t seems quite obvious that the difference in ionization potentials between H and 0 cannot he the decisive factor in the charge distribution of the water molecule, since it appears altogether negligible. The electron affinities are more revealing: EA(H) = 0.75 eV hut EA(0) = 1.47 eV. We thus see that H + 0- H is to be preferred over H- O+ H and this would appear to be the answer. Before the reader decides to conclude the initial issue is solved, let us return to the discussion of ionization potentials. What ion is produced by the ionization of the 0 atom? 0+, obviously. Having gone from the molecular to the atomic level, we can delve further considcring the electronic attributes of this ion. What is the spin and angular momentum of O+? Looking up oxygen in Moore's tables ( 5 ) , we find that O+ is not listed. Instead 0 I, 0 11, etc. take the place of 0 , 0+, etc. (Atomic spectroscopists have thc seemingly irrational habit of designating a neutral atom by "I" after the symbol, thc singly charged cation by "11" and so on through increasingly high Roman numerals. Sufficiently few anions have stable excited states that no provision has been made for their existence in cither these tables or in the nomenclature.) Looking up 0 11, one finds that the ground state has a 4S configuration. That is, the angular momentum is 0 since it is an S state. If the angular momentum had been 1, P would he used, 2 = D, 3 = F, 4 = G, etc. Thc spin 1s represented by its multiplicity or degeneracy, 2S 1. Since it is a quartet state, i.e., superscript 4, the spin is 3/2. The 4S state is read quartet "S." We also find the ground state of the oxygen atom is SPcorrcsponding to angular momentum equal 1 and spin equalling 1 as well. I n these tables information on an almost unbelievable number of excited states of the varying neutrals and ions are given but the energies are given in still another set of units. Moore, like many spectroscopists, gives energy in cm-' (or K for I'iayser) where 8066 cm-I equals 1eV.
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4 The reader will note there is no special symbol for designating the angular momenta of the atoms or ions in the "'all-atom' Valence Bond resonance structures." The number of states formed by combination of the constituent angular momenta is sufficiently great that it is the exception, rather than the rule, when a given molecular state of interest cannot he formed. See ref. (6)in the section on the Wigner-Witmer rules. 5 More properly, since the two hydrogens in H20(or fluorines in OF2) are equivalent, the total wavefunction must reflect this symmetry. When expanding this wavefunction in terms of either the molecular orbital (MO) or valenee hond (VB) formulation, equal contributions from both the (0, 7, 1 ) [O, '/n, '/XI and (1, 7, 0) ['I., '/., O] structures in HzO (and likewise the (8, 7, 7) [O, '11, and (7, 7, 8) I>/%, I/*, 01 in OF.) must be comidered. The coefficients will be either equal or opposite in sign and equal in magnitude. This can be determined from the requirements that nuclear and electronic symmetry must be preserved. Since 1H (and 'OF) is afermion, the twonuclei must be antisymmetrized as: are the electrons. These effects of symmetry requirements were initially suggested by Deborah Van Vechten. 6 There is also the extremely high lying zP Ot state that would form s. (2, 6, 1) [0,'/2,'/J molecular state. Mulliken [ref. (3)l used a linear combination of the ZD and *P O+ to arrive at the ionization potential of oxygen when computing X ( 0 ) .
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Let us now write the water molecule in an unusual way using "all-atom" valence bond resonance structures. We write the covalent form as (H 0 H) and the two ionic forms we had earlier compared as (H+ 0- H) and (H- O+ H). We may write (H 0 H) as (1, 6, 1) ['/a, 1, l/a]. Thc (1, 6, 1) tells us that the H, 0, and H atoms have, respectively, 1, 6, and 1 electrons and the [I/%, 1, reflects the fact that the spin of the H, 0, and H atoms are 1, and We know the water molecule has all the electron spins paired, i.e., total spin 0. This means the (1, 6, 1) ['/a, 1, I/%] is acceptable since one can arithmetically combine 1, and to make 0 - 1 = 0). For (H+ 0- H) we write (0, 7, 1) [0, Sincc both hydrogens are equivalent, we should also include (H 0- H+) but this can be said to be built into the ~ y m b o l . ~Here too, the total spin may equal 0 = 0. Consider (H- O+ H) or since 0 (2, 5, 1) 10, a// 2,'/2]. This structure is unacceptable since neither 0 3/2 equals nor 0 a/2 0, as it must since the total spin is 0. We cannot conclude from this that no (H- O+ H) structure is possible but rather that one should consider state. The 0' ion does have an a (2, 5, 1) 10, '/a, excited state, the 2D, that may be irnplicat~d.~This state lies 3.25 eV above the ground state. To the extent that attraction between 0+ and H-, and 0strucand H + are the same, the (0, 7, 1) 10, ture is energetically preferred over the (2, 5, 1) 10, by approximately 4 eV (3.25 1.47 - 0.75 = 3.97). Whereas quantitative reasoning is admittedly inappropriate since it assumes ions are point charges (7), it appears certain to the author this 3.9 eV difference is significant, whereas the 0.72 eV difference derived by incorrect use of the 4S for 0+probably is not. We should not, therefore, be surprised that the 0 in H 2 0is negative. Earlier in the article, it was cited that the 0 in OF2 is ~ositive. Again we construct the "all-atom" valence bond resonance structures. We have (F 0 F) or (7, 6, 7) 1, 1/2], (F- Of F) which must be (8, 5,7) 10, '/a, '/a1 and (F+ 0- F) or (6, 7, 7) 11, '/a, '/?I. From data in the Handbook, we find EA(F) iA3.5 eV, IP(F) is 17.4 eV and from before, the relev;& 3.25 = 16.8 eV. ionization potential for 0 is 13.6 We thus conclude the (8, 5, 7) [O, structure is 1/2] by 17.4 preferred over the (6, 7, 7) 11, , 16.8 3.5 - 1.5 = 2.6 eV. This is substantial though less than that of H,O and hence OFr is polarized OZ6+ (F6-)2. Furthermore, the OF bond in OF2 is longer than the OH hond in H,O which lessens coulomhic attraction in the ionic structure of the former molecule. It thus comes as no surprise that the absolute value of the dipole moment of OF%,0.4D (8) is less than that of H20, 1.65D (9). Estimation of the dipole moment of the lone pairs on 0 to augment the H-0 dipole in H20 or decrement the 0-F dipole in OFz cannot be done quantitatively. However, one may conclude that the role of the lone pairs is less than would have been surmised by merely considering the differences for ionic and covalent structures in OF,, 2.6 eV, and HzO, 4 eV. It appears most unlikely that the direction of the molecular dipole is solely determined by the lone pairs, i.e., the 0-H bond dipole is polarized O+H- (10).
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The astute reader might have noticed that to have OF, a singlet, when (F+ 0- F) was written (6, 7, 7) the 0- and F electron spins had to he [I, This means the parallel, i.e., 0 = 1 -OF unit cannot be bound. Quantum mechanical calculations (11) have shown OF- is bound relative to 3P 0 IS F- by 0.2 eV. We have assumed for the whole of this article that spin is conserved. Therefore, OF-, in the calculated '2 state (8 = 0) cannot separate lS F- as S = 1 0 # 0. (2,11, A, and m to 3P 0 for linear molecules correspond to S, P, D, and F for atoms.) The lowest lying allowed separation products = 0) and 'D 0 2PF (S = are 2P 0F- (S = 0 0 = 0). Separation to either of these sets of products require more than 2 eV. We thus find (6, 7, 7) [I, '/2, '/21 and (6, 7, 7) [O, '/z, '/?I approximately thermoneutral. This type of analysis can be extended to Li20 and CszO. In these highly ionic molecules, the (0, 8, 0) [O, 0,0] structure gains considerable importance. However, one should realize that free 02-is unstable rel* tive to 0- and a free electron by 8 eV (12). This value is initially surprising given the large number of ionic metal oxide salts. However, it gains credability by extrapolating from the energies of related 7 and 8 electron systems. From Moore's tables or the Handbook, we find the second ionization potential for Na is 47.1 eV, the first ionization potential for Neis 21.5 eV, and the relevant number for F- is 3.5 eV.' Extrapolating (constant second differences) we find the ionization potential of 0%-is around -7 eV in reasonable agreement with experiment. The (0, 8, 0) [O, 0, 01 structure of LizO and CsnO has both the terminal atoms positive. Therefore, by coulombic repulsion, it is not unexpected that the Li-0-Li or Cs-0-Cs angle is larger than the H-0-H angle in H20 (13,14). The Li20 molecule is known to be linear and therefore has no dipole moment for comparison with those of Cs20 is bent (I6' 16) even Or OF'' In though one might have expected the Cs-0 bond to be 1t has been that more polar than the Li-0, bond polarity is largely irrelevant and that Cs-Cs bonding is important. Alternatively, this bending may be reconciled by noting that the Cs-0 bond is longer than Li-0 and thus Cs+-Cs+ repulsion and Cs+-02attraction are both less than the 'Orresnondine Li interactions. ' Two point charges gl and 9%a t a distance R have an electrostatic attraction (or repulsion) of 14.4 g,q,/R eV. For a linear M+ 02-M+ configuration, the coulomb attraction is 3 X 14.4/Rx-0. The experimental Li-0 bond distance in Li20 is 1.59 A (14). It should be noted that LiF and LipO have almost identical Li-X bond lengths, R(Li-F) = 1.56389 A (17). Whereas 02- is expected to be larger than F-, the increased Li-0 coulomb attraction helps to shrink the LiO bond. The corresponding bond length in Cs2O is unknown. However. we mav assume that the Cs-0 bond in Cs20 is about the same size as the Cs-? bond in CsF. This latter bond length is 2.3453 A and hence the Cs-0 bond length is probably around 2.4 A
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I P (F-)is quite obviously the same as EA (F).
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(18, 19). The (0,8, 0) [0, 0, 01 structure for Li20 is stabilized by 9 eV relative to the Cs analog. However, the (0, 7, 1) [O, / structure for Li20 is stabilized by only 3 eV relative to CszO. We thus conclude that the (0, 8, 0) [O, 0, 0] structure is less important for Cs than for Li. The difference is not 9 - 6 = 3 eV. We must also include the relative ionization potentials of Li and Cs since the (0, 7, 1) [O, '/%I structure contains one less ionized metal atom. Experimentally (4, 6) the energy difference is around 1.5 eV. The (0, 8, 0) 10, 0, 01 structure is thus favored by 4.5 eV for LizO over Cs20. Since CsrO resembles H20 more than does Li,O, it is not surprising that Cs20 would bend to what is normally considered the more water-like geometry. In conclusion, we find the oxygen in water is negative because a negative charge, unlike a positive, can be stabilized using ground state ionic resonance structures. An analogous effect reduces the positive charge of the oxygen in OF,, experimentally observable as a low molecular dipole moment. The highly polar Li20 and Cs20 have negative oxygens, but here the negative charge is reduced by the intrinsic instability of Ox-. This instability and the long Cs-0 bond decrease the polarity of the Cs,O molecule so that it may bend from the Li,O linear geometry a more water-like structure. The author wishes to acknowledge the editorial assistance of Deborah Van Vechten and fruitful discussions with Drs. RI. Harmony and P. A. Kollman. He also wishes to thank the N.R.C. for his NATO Postdoctoral Fellowship and the Ramsay Memorial Trustees for their honorary award. Literature Cited (1) D o u o ~ ~ B. s . F..A N D MODANIEL. D. H.. "Concepts and Models of Inorganic Chemistry." Blhisdell Publishing Co.. New York. 1965, p. 48.
(2) PAOLIND, L., J . Amer. Cham. soc., 5 4 , 3 3 6 0 (1932). (3) MuLLmelr, R. S.,J. Chsm. Phvs., 2 , 7 8 2 (1934): 3 , 5 7 3 (1935). (4) WEABT. R. C.. (Editor-in-chien, "Handbook of Chemistry and physios:' (61.t ~ d . )chemical . ~ ~ CO. 1970-1. b b ~ ~ (5) MOORE, C. E., "Atomic Energy Levels." U S . Natl. Bureau of Standards, Circular No. 467, 7'01. 1. (1947); Vol. 2, (1953): and Vol. 3 , (1958). A less complete. h u t more current compendium ia Moons. C. E.. "Ionization Potentials and Ionization Limits Derived from the Analyaes of Optical Spectra" Nat. Stand. Ref. Data Ser., Nst. Bur. stand.( u . 8 . ) . NSRDS-NBS 34 (1970). (6) H ~ x z e ~ s a 0.. , "Moleoular Speotroscopy snd Molecular Structure," Yol. 1, pp. 315-22 and 446-7 and Vol. 3 , ~ p 281-96. . D. Van Nostrand Co.. Ino., Princeton. 1950 and 1966 respectively. (7) Thovgh he does not use this formalism, DIBENT, W. E.. "NO"-Existent . D. 22. oites this comoounds.''~ a r o e lDekker. Nerv ~ m k 1965. rnet&d. Hovever, he doesn't feel it is reliablef$ quantitatively computing bond enerpies. Dooo. R. E., A N D LITTLE,R., N L I ~ I188, I T ~737 . (1960). N e ~ s o r Jn.. . R. D.. Lme. Jn., D. R . . nao M * n r o ~ ~A.. A., "Selected Values of Electric Dipole Moments for Molecules in the Gas Phase" Nht. Stand. Ref. Data Ser.. Nat. Bur. Stand. (US.). NSRDSNBS lO(1967). However, see C O U G ~ OC. NA,, , PIOC.Roll. SOC.,A, 207.63 (1951). O'HABE.P. A. G . , A N D WAHL,A. C.,J . Chem. Phvs., 53. 2469 (1870). S~ucrer, W. K . . A N D KIBER.R. W.. N a t w e . 211,963 (1966). BsmLEn, A,, ST*"FFER.J. L., K L E X P E ~ ~W., R .A N D ~ V ~ A E T O NL.. . J. Chcm. Phya., 39, 2299 (1063). These authors also present tables giving "typical oxygen angles,'' a comparison of diatomic oxides and fluorides, and a comparison of solid and gaseous L i compounds. WalTE. D.. SESHARDI. K. S., D E R E ~D. , F.. MINN. D. E., A N D L ~ ~ e v a xM r ,. J.. J . Chem. Phus. 2463 (1963). Bircnmn. A,. S T A ~ F EJ.E L., ~ , A N D KLEMPERER, W.. J . Chem. Phss.. 46, 605 (1967). W ~ I ~ ~ O C. N D., , E ~ U in . them., 7 , 234 (1970). (16) COX, w.. (17) WHARTON, L..et BI., J . them. PAWS.,38,1203 (1963). M. L.. AND MANDFL..M., P h w Rev.. 9 2 . 9 0 1 (1953). (18) Howrc, A,, STITCH, antiquated, set 01 bond lengths see - T ~ ~ (19) FOP. .,,IuI, I,U~ of inters to mi^ Distanoes and Configurations in Molecules and Ions," The Chemical Society Special Publication X11. London, 1958 and its supplement. Special publication XIS, 1965.
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