Spiers Memorial Lecture : Quantum chemistry: The first seventy years

Abstract

Present-day theoretical chemistry is rooted in Quantum Mechanics. The aim of the opening lecture is to trace the evolution of Quantum Chemistry from the Heitler-London paper of 1927 up to the end of the last century, emphasizing concepts rather than calculations. The importance of symmetry concepts became evident in the early years: one thinks of the necessary antisymmetry of the wave function under electron permutations, the Pauli principle, the aufbau scheme, and the classification of spectroscopic states. But for chemists perhaps the key concept is embodied in the Hellmann-Feynman theorem, which provides a pictorial interpretation of chemical bonding in terms of classical electrostatic forces exerted on the nuclei by the electron distribution. Much of the lecture is concerned with various electron distribution functions-the electron density, the current density, the spin density, and other 'property densities'-and with their use in interpreting both molecular structure and molecular properties. Other topics touched upon include Response theory and propagators; Chemical groups in molecules and the group function approach; Atoms in molecules and Bader's theory; Electron correlation and the 'pair function'. Finally, some long-standing controversies, in particular the EPR paradox, are re-examined in the context of molecular dissociation. By admitting the concept of symmetry breaking, along with the use of the von Neumann-Dirac statistical ensemble, orthodox quantum mechanics can lead to a convincing picture of the dissociation mechanism.

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix

“…27,28 This definition intuitively corresponds to the physical situation of processes such as the mentioned electron rearrangements during chemical reactions; dissociation processes are particular cases of central importance in understanding the nature of chemical bond. 29 In such cases, it is necessary to specify the pure states of the system as being spin-adapted, i.e., the wave functions are eigenfunctions of the squaredand projection-spin operators, Ŝ 2 and Ŝ z , with eigenvalues S͑S +1͒ and S z , respectively. We will restrict ourselves to such kind of states because spin purity is of fundamental importance for a correct interpretation of highly correlated entangled states, despite in general a pure state may not be necessarily spin-adapted 20,21 for most of cases in which entanglement is defined.…”