In Part II of a three-part series, we discuss two factors absent from textbooks of general chemistry that are important in a discussion of teaching orbitals. First, atomic orbitals are shown systematically to comprise algebraic formulae in coordinates of not one but four sets (spherical polar, paraboloidal, ellipsoidal, spheroconical coordinates). Each formula has its corresponding shape as a surface of constant amplitude; some visual examples are provided. Second, the argument that molecular structure is incompatible with quantum mechanics is presented. Despite the utility of orbitals as mathematical functions in various calculations, they are intrinsically complicated for the traditional purpose of qualitative explanation of molecular structure.

In Part I of a three-part series, we present an objective survey of the technical literature discussing the inclusion of orbitals in high-school and post-secondary general chemistry. We start with the definition of orbitals. The presentation of orbitals in secondary (high) school is presented with arguments for and against. The content of orbitals in the curriculum of general chemistry is presented and summarized in terms of 1) electron configuration, 2) periodic table, 3) molecular structure and 4) reactivity. Previous discussion in favor of and against each theme is presented. Recent research in chemical education is also reviewed.

The importance of hybrid atomic orbitals, both historically and mathematically, is reviewed. Our new analysis of the original derivation of the sp3, sp2, sp model reveals serious errors. Based on a critical survey of the literature, we submit six formal criteria that deprecate the use of hybrid orbitals in a pedagogical context. A sound mathematical basis of sp3 and sp2 formulae does not exist; hybrid atomic orbitals have hence no legitimate role in the teaching of organic chemistry.

The importance of hybrid atomic orbitals, in both general and organic chemistry, is reviewed. Every contemporary textbook of organic chemistry introduces the directed-valence (e.g. sp3, sp2, sp) model, but the suitability of these hybrid orbitals for use in the teaching of molecular structure has been increasingly questioned. Based on a critical survey of the literature, we submit seven practical criteria that deprecate the use of hybrid orbitals in a pedagogical context. We suggest how the teaching of organic chemistry without hybrid orbitals will provide students with an enhanced education.