Formal charge and oxidation state are two means of estimating the charge of an atom in a molecule. Though these concepts have very different origins—formal charge is derived from the ball-and-hook model of bonding and oxidation state is based on the ionic approximation of molecules—they are used to predict reactivity and other molecular properties through their properties as charges. In this submission, it is shown that formal charge and oxidation state are two extreme descriptions of bonding: formal charge represents zero (...) charge transfer between atoms while oxidation state represents complete charge transfer in each bond. These ‘localised electron approximations’ form an incomplete picture of atomic charge. Electronegativity measures the extent of polarity in real bonds; this concept can be introduced to polarise bonds relative to the ‘equal sharing model’. It is shown that the various electronegativity models are fundamentally related. We chose two models to demonstrate numerically that polar bonds yield charges intermediate between the localised electron approximations: Pauling and Mulliken. It is shown that probabilistic interpretation of the Pauling scale (‘scaled Pauling’ method) and use of asymmetric chemical potential (‘modified Mulliken’ method) lead to atomic charges that closely approximate experimental values using simple ‘back of the envelope’ calculations. It is seen that formal charge, oxidation state, and electronegativity-interpolated charge lie on a continuum and are mathematically related. It is therefore concluded that electronegativity introduces (quantum) delocalisation to the localised (classical) picture of electron bonding. (shrink)

This manuscript explores the orthogonality constraints on configurations and orbitals subject to the property that states are mutually orthogonal. The orthogonality constraints lead to properties that affect the description of chemical systems. When states are described as linear combinations of configurations, the coefficient matrix diagonalises S−1H. Therefore, single-configuration states are only possible in one-electron systems: non-orthogonal configurations yield single-configuration states only if S−1H is diagonal, but this would violate the orthonormalisation constraint. Further, the coefficient matrix is not constrained to be (...) square. Similarly, the orbitals used to construct configurations may also be orthogonal or non-orthogonal; orbitals are only required to be mutually orthogonal at the one-electron limit. Orthogonal orbitals are generally preferred due to their mathematical and conceptual simplicity, leading to fictitious unoccupied orbitals. Since the Fock operator is orthogonality agnostic, non-orthogonal orbitals can be generated by solving the Fock equation independently for each electron; the virtual orbitals produced by this conception are true excitation orbitals as they are eigensolutions of the Fock operator. Additionally, we show that the number of molecular orbitals generated is not restricted to the number of atomic orbitals employed in the computation. This manuscript explores the mathematical relationships that need to be satisfied under the various orthogonality regimes. We also present mathematical relationships that provide results that are independent of the orthogonality approximation within a particular computational method. (shrink)

Slater’s method is an integral part of the undergraduate experience. In actuality, Slater’s method is part of an atomic model and not simply a set of rules. Slater’s rules are a simple means for computing the effective nuclear charge experienced by an orbital. These rules are based on the shell-like structure of the Slater atom in which outer shell electrons are incapable of shielding inner electrons. Slater’s model provides a qualitative description of the valence electrons in multi-electron atoms with tremendous (...) ease. The model is useful for explaining atomic properties such as ionisation energy, electron affinity and atomic radius qualitatively. Slater’s rules also correctly reproduce the Madelung rule of filling and the ionisation sequence (4s before 3d); however, these rules are not able to reproduce the anomalous configurations of atoms such as Cr and Cu. It is found that the atomic properties that Slater’s model reproduces are all related to the exponential decay factor of the Slater orbital. We find—from estimating the polarity of a diatomic molecule using a simple model—that molecular polarity is related to the difference in the exponential decay factors of the valence orbitals of the two atoms, implying that the decay factor acts as the electronegativity of the atom. (shrink)