Comments on Purser's Article: "Lewis Structures are Models for

Chemical Education Today

Letters Comments on Purser’s Article: “Lewis Structures Are Models for Predicting Molecular Structure, Not Electronic Structure” Some time ago in this Journal (1), Purser expressed strong views on the proper teaching of Lewis structures, as summarized in the quoted title. Purser acknowledges the increasing impact of modern ab initio computational research on general chemistry textbooks, while lamenting the resulting “inconsistency” in the treatment of standard bonding topics such as expanded octets, d-orbital participation, and resonance structures of 2nd-row oxyanions. His strongest criticisms are directed at an article in this Journal (2) and associated Natural Bond Orbital (NBO)-based wave function analysis methods (3). Because Purser’s criticisms are based on substantial factual misrepresentations and errors, it seemed desirable to call attention to a few of the conspicuous misstatements in order that readers may judge the opinions and conclusions from a more informed perspective. The natural resonance theory (NRT) structures and bond orders of ref 2 are obtained by an algorithm (for further details, see ref 4 ) which is neither implemented nor licensed in the Spartan package,1 and could not have produced the values quoted by Purser (e.g., Table 3 of ref 1). The “natural bond order” values quoted in ref 1 are therefore spurious, unrelated to the authentic NRT values employed in ref 2; for example, the natural bond order entries in Purser’s Table 3 should be 1.75 (not 1.50) for NO2 and 1.41 (not 1.50) for O3. Purser’s “natural bond order” numbers (1), whatever their origin,2 do not contribute to useful discussion of ref 2. Even more surprisingly, Purser cites the original Natural Population Analysis (NPA) paper (5) to justify the statement (ref 1, p 1014): “[T]he Mulliken and Lowdin (sic) population analysis methods of calculating bond orders tend to overestimate the electron population in high-energy molecular orbitals relative to low-energy molecular orbitals.” No such statement is made, or remotely inferred, in ref 5. The idea expressed by the sentence is absurd, because the fixed molecular orbital occupancies (2.0 for low-energy MOs and 0.0 for high-energy MOs in a closed-shell system) are never altered by NPA or other charge analysis methods. Like the bond order numbers, Purser’s source for this statement is apparently non-existent. Purser is also misinformed about the relationship between NPA charges and NBO Lewis structure determination. He repeatedly criticizes NPA charges because they are supposedly derived from erroneous Lewis structure assignments.3 The truth is that NPA logically and numerically precedes determination of NBOs, natural Lewis structure, and NRT resonance structure corrections (as even cursory study of ref 5 or NBO program structure makes clear). Purser’s imagined reasons for rejecting NPA atomic charge distributions on the basis of Lewis-structural influences are therefore wholly illusory and unsupportable. The key assumption underlying Purser’s remaining arguments is that “experimental atomic charges” can be inferred 526

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from measured dipole moments (e.g., in the form |qA| = [µAB/RAB]1/2 for diatomic molecule A–B). This assumption reflects fundamental theoretical misunderstanding. The correct expression for the electronic contribution µ(el) to the dipole moment along chosen direction z is given (in atomic units) by µz(el) = ∫z ρ(r)d3r

(1)

Equation 1 is not a matter of opinion, but of rigorous mathematical definition. As seen in the integrand of eq 1, each increment of electron density (“population”) at point r must be weighted by z (its “moment” along the chosen direction) to give the electronic contribution to µz(el). The dipole moment integral inherently gives greater weighting to portions of the electron density lying far from the nucleus, and is thus fundamentally distinct from the “democratic’’ population counting (zeroth moment of the charge distribution) of NPA and other standard population analyses. Although it is a common conceptual error to assume that atomic charges and distances are related to experimental dipole moments in the simple-minded way envisioned by Purser, such a mathematical collapse could only occur in the unphysical limit that the electron density has no spatial distribution around nuclei (i.e., electronic collapse to Dirac delta function form). The conceptual perils of estimating dipole moments without reference to the actual dipole moment integral have been authoritatively discussed in the literature over many years (6). Still other misstatements can be traced to unfortunate errors or oversights in the performance of the Spartan calculations. The ozone molecule is treated as a restricted closedshell system, whereas the actual ground-state O3 species is of open-shell singlet diradical character. Purser’s numerical values and discussion for this species are thus based on a specious RHF “solution” that lies about 300 kJ/mol above the actual equilibrium UHF/6-31G** ground state, with little or no relevance to the presented experimental data. This itemization of leading misstatements, errors, and oversights may sufficiently indicate that Purser’s conclusions do not warrant the scholarly consideration that is normally accorded to publications in this Journal. Notes 1. Spartan is a product of Wavefunction, Inc., 18401 Von Karmen Ave., Suite 370, Irvine, CA 91711 (http://www.wavefun. com; accessed Feb 2004). 2. According to Purser, “It is beyond the scope of this paper to discuss the details of the various methods of calculating bond orders...” (ref 1, p 1014). 3. The following statements from ref 1 are illustrative: “[N]atural population analysis (from which values of the natural bond order are calculated) forces electron density into orbitals generally localized between two nuclei or on a single nucleus” (p 1014); “Natural population analysis partitions electron density into lone pairs and 2-center bonds, producing a Lewis structure” (p 1015); “Natural population analysis fails because, like a Lewis structure, it partitions the electron density into lone pairs and 2-center bonds,

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Letters underestimating the true delocalization of the electron density over the molecule” (pp 1015–1016). None of these statements is even partially true.

Literature Cited 1. Purser, G. H. J. Chem. Educ. 1999, 76, 1013–1018. 2. Suidan, L.; Badenhoop, J. K.; Glendening, E. D.; Weinhold, F. J. Chem. Educ. 1995, 72, 583. 3. Reed, A. E.; Weinhold, F.; Curtiss, L. A. Chem. Rev. 1988, 88, 899; Weinhold, F. Natural Bond Orbital Methods. In Encyclopedia of Computational Chemistry; Schleyer, P. v. R; Allinger, N. L.; Clark, T.; Gasteiger, J.; Kollman, P. A.; Schaefer, H. F.; Schreiner, P. R., Eds.; John Wiley & Sons: Chichester, UK, 1998; Vol. 3, pp 1792–1811. Natural Bond Orbital NBO 5.0 Home; http://www.chem.wisc.edu/~nbo5 (accessed Feb 2005). 4. Glendening, E. D.; Weinhold, F. J. Comput. Chem. 1998, 19, 593, 610; Glendening, E. D.; Badenhoop, J. K.; Weinhold, F. J. Comput. Chem. 1998, 19, 628. 5. Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 1736. 6. Mulliken, R. S. J. Chem. Phys. 1935, 3, 573; Coulson, C. A. Trans. Faraday Soc. 1942, 38, 433; Pople, J. A. Proc. R. Soc. London Ser. A 1950, 202, 323; Gibbs, J. H. J. Phys. Chem. 1955, 59, 644; Coulson, C. A.; Rogers, M. T. J. Chem. Phys. 1961, 35, 593; Coulson, C. A. Valence, 3rd ed.; Oxford: New York, 1961, pp 152–154, 218–222; Reed, A. E.; Weinhold, F. J. Chem. Phys. 1986, 84, 2428. Frank Weinhold Theoretical Chemistry Institute and Department of Chemistry University of Wisconsin–Madison Madison, WI 53706 [email protected]

The author replies: Weinhold makes four major criticisms of my article (1). These are 1. Atomic charges were determined inappropriately from dipole moments 2. The ozone calculation was not for the ground state, open-shell, diradical species 3. Spartan does not use an appropriate algorithm for calculating natural atomic charges and bond orders 4. There is a misunderstanding of how NBO and NRT lead to identifying appropriate electron dot structures

I shall address each of these criticisms. Even though it is stated in the article that, “the charge on an atom in a polyatomic ion or molecule is not a property that can be defined uniquely or measured directly” (ref 1, p 1014), Weinhold suggests a logical error is committed by calculating atomic charges using a classical definition of dipole moment rather than the quantum mechanical dipole www.JCE.DivCHED.org

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moment integral. In fact, quantum calculations of dipole moments for “hypervalent” molecules are notoriously poor. The mean absolute error in calculated dipole moments using the Hartree–Fock 6-31G* method for a representative sampling of “hypervalent” species is on the order of 0.4 Debye (2)! As such I would argue that ignoring the quantum definition of dipole moment and using an observable and measurable property to calculate charge is legitimate. This position is further supported by simple inspection of the results. General chemistry students are taught that the charge separation between two atoms of similar electronegativity is expected to be quite small. To the contrary, Weinhold suggests that the atomic charge on the sulfur atom in SO2 is +1.86 (3). This value demands scrutiny in light of the fact that other “accepted” methods of calculating atomic charge, the Mulliken and electrostatic methods for the same molecule, result in significantly lower, and more reasonable values of charge, +1.08 and +0.69, respectively. Weinhold correctly points out that ozone is a singlet diradical rather than the spin-paired species used in my article. Attempts to obtain the diradical structure using the UHF method in Spartan were unsuccessful, even when using the keyword “Mix” which is designed to start with an unpaired electron solution helpful in finding diradicals. Unfortunately, in the Spartan calculations, this condition does not hold and the solution collapses into the RHF solution. Consequently, as Weinhold suggests, the values for ozone in Tables 2 and 3 in ref 1 are suspect. I am unaware of any specific differences between the algorithms used to calculate natural atomic charges and natural bond orders by Spartan and Weinhold in ref 3. After examining my original data, I did find that there is one error in Table 3 of ref 1. As Weinhold correctly pointed out, the Natural C-T value for NO2 in that table should have been reported as 1.75. (Since the ozone data are based on different electronic structures, I cannot comment on Weinhold’s value for ozone.) All other values are correct. However, Weinhold’s assertion that my natural bond order numbers do not contribute usefully to discussion of ref 3 unequivocally is incorrect. Upon examining the values of atomic charges obtained from Spartan and those reported by Weinhold in ref 3, the values are identical to three decimal places! Similarly, the natural bond orders obtained from Spartan are identical to those reported by Weinhold (bxo) in Table 1 in ref 3. Either this is an astronomical coincidence, or contrary to Weinhold’s assertion, the algorithms are intrinsically related. Thus contrary to Weinhold’s assertion, the calculated natural charges reported in my paper are the results of the same analysis Weinhold describes in ref (3). Weinhold is concerned about my presentation of how NBO and NRT lead to identifying appropriate electron dot structures and in particular an assertion that NBO analysis occurs before the Natural Population Analysis (NPA). [Although it is not clear how Weinhold could come to this conclusion since it is stated in the article, “…natural population analysis (from which values of natural bond order are calculated)…” (emphasis added) ref 1, p 1014]. As I understand it, NPA involves the description of molecular electron den-


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Letters sity distribution based on a set of orthonormal atomic orbitals. This suggests that NPA takes delocalized electron density and confines it into localized “natural” atomic orbitals. Weinhold acknowledges that natural bond orbitals are an orthonormal set of localized 1- and 2-center functions that allow the electron density to be partitioned into Lewis-type and non-Lewistype components (ref 3, p 583). The fact that NPA “precedes” NBO analysis, which of course it does, is unimportant. The inherent problem with NPA appears to be that it partitions what should be delocalized electron density into localized orbitals resulting in excessive separation of charge. Lastly, I apologize for a misplaced reference (reference 22 in ref 1, p 1014), which made it look as though the deficiencies of the Mulliken and Lowdin population analysis methods were addressed in the paper by Reed, et al. That reference should have been placed two sentences below in reference to the NPA method. The hypothesis espoused to educators in my article is that Lewis structures are classical models for predicting molecular properties like shape, bond strength, bond length, and dipole moments, and that they bear little relationship to the actual electronic structure as determined by quantum calculations. Weinhold provides no evidence to suggest that that hypothesis is incorrect. In fact, by raising the issue of the electronic structure of ozone, Weinhold provides support for my position. As reported recently, “The electronic structure of ozone can be viewed as two single O–O bonds plus two singlet-coupled π electrons, one on each terminal oxygen atom”

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(4). When was the last time a general chemistry student was encouraged to draw the Lewis structure for ozone with two O–O single bonds? Furthermore, a more recent article (5) provides additional support to the supplementary conclusion of ref 1 that, in general chemistry, the ability to accurately predict molecular properties for molecules containing elements beyond the second period is only possible when the octet is expanded and formal charges are minimized. I believe that if readers consider the arguments presented here and elsewhere (5), they will come to the same conclusion. Literature Cited 1. Purser, G. H. J. Chem. Educ. 1999, 76, 1013. 2. Hehre, W. J. A Guide to Molecular Mechanics and Quantum Chemical Calculations; Wavefunction, Inc.: Irvine, CA, 2003; pp 334–335. 3. Suidan, L.; Badenhoop, J. K; Glendening, E. D.; Weinhold, F. J. Chem. Educ. 1995, 72, 583. 4. Leininger, M. L,; Schaefer, H. F., III. J. Chem. Phys. 1997, 107, 9059. 5. Purser, G. H. J. Chem. Educ. 2001, 78, 981. Gordon H. Purser Department of Chemistry The University of Tulsa Tulsa, OK 74104 [email protected]


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Comments on Purser's Article: "Lewis Structures are Models for

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