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 from measured dipole moments (e.g., in the form |q_A| = [µ_AB/R_AB]^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

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 µ_z^(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 closed-shell 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 (accessed Feb 2005).
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, 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; (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.

See the author's reply.