Perspective: Quantum Hamiltonians for optical interactions.

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Comment on "Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field" [J. Chem. Phys. 144, 044109 (2016)].

The 'problem' identified in the paper [J. Chem.Phys. 144, 044109 (2016)] does not arise in a properly formulated non-relativistic Hamiltonian formalism for both classical and quantum electrodynamics.

On the quantum theory of molecules.

Transition state theory was introduced in 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that such a surface could be constructed using eigensolutions of the Schrödinger equation for the molecular (Coulomb) Hamiltonian but at that time such calculations were not possible. Nowadays quantum mechanical ab initio electronic structure calculations are routine and from their results PESs can be constructed which are believed to approximate those assumed derivable from the eigensolutions. It is argued here that this belief is unfounded. It is suggested that the potential energy surface construction is more appropriately regarded as a legitimate and effective modification of quantum mechanics for chemical purposes.

Molecular structure calculations without clamping the nuclei.

A number of recent papers have considered ways in which molecular structure may be calculated when both the electrons and the nuclei are treated from the outset as quantum particles. This is in contrast to the conventional approach in which the nuclei initially have their positions fixed and so merely provide a potential for electronic motion. The usual approach is generally assumed to be justified by the 1927 work of Born and Oppenheimer. In this paper we discuss what precisely might be anticipated in the way of molecular structure from a mathematical consideration of the spectral properties of the full Coulomb Hamiltonian, to what extent the very idea of molecular structure might be dependent upon treating the nuclei simply as providing a potential and the extent to which the work of Born and Oppenheimer can be used to support this position.