The author replies to Weinhold.

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 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 (b_xo) 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 density 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-Lewis-type 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” (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, 1013–1018.
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.