Of Electrons and Molecules

Jing Kong

A physically motivated equation that determines the number of electrons of a molecule is proposed based on some generally accepted basic chemical knowledge. It permits a complete local definition of molecules and shows that all molecules are entangled in the number of electrons. It also results in the extensivity and convexity of molecular energy, which underpin molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case and reveals an intrinsic relationship between molecular locality, size consistency, and energy convexity. Application of wavefunction theory to the new principle shows that an individual molecule with a noninteger number of electrons is locally physical. The energy of a molecule is piecewise linear with respect to its number of electrons. The realness of the number of electrons allows the definition of the electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable and used to express the physical principle as a simple additivity. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing one chemical potential. When the energy of a molecule with a definite number of electrons is not convex with respect to the number of electrons, the state of the molecule is not always locally determinable even with a known number of electrons.

R. B. Jordan

N. S. Maslova, Vladimir N. Mantsevich, P. I. Arseyev +1 more

In the present work we theoretically analyze the emergence appearance of entanglement between electronic and vibrational states in a system of two coupled molecules after switching on the interaction between them. In the framework of the adiabatic approach this effect appears because the equilibrium position of one of the molecules is sensitive to its electron occupation. The time evolution of the system shows multiple changes between its entangled and unentangled states. If this evolution starts from a pure coherent vibrational mode state and a state of a single electron localized in one of the molecules, the Schr\"odinger-cat states can appear during the system's time evolution. The Schr\"odinger-cat states can arise as a quantum superposition of distinct coherent states of molecule vibrational mode. Such states are entangled with empty and singly occupied electronic states of the molecule. The presence of entanglement between electronic and vibrational molecule states can be revealed by measuring the electron occupation (charge) of a particular molecule.

Luca Salasnich, Francesco Lorenzi

Xiaohui Ling

In the present work very-high-n Rydberg-atoms $(n \\sim 100 - n \\sim 400)$ are used to probe electron-molecule collisions at ultra-low electron energies. Based on the essentially-free-electron model, for sufficiently high n, Rydberg atom-molecule collisions can be described in terms of a binary interaction between the target molecule and the essentially-free Rydberg electron. Since the average kinetic energy of the Rydberg electron is ultra-low $\\rm({\\sim}85\\mu eV - {\\sim}1.4meV),$ analysis of the very-high-n Rydberg-atom collision data can provide information on electron-molecule scattering at electron energies corresponding to electron temperatures of only $\\sim$1$\\sp\\circ$K, which are far below those accessible using any alternate approach.\nRate constants for destruction of very-high-n Rydberg atoms in collisions with various target molecules have been measured. This study focuses on Rydberg electron transfer to an electron-attaching molecule which results in negative ion formation via the reactions $$\\rm K({\\it np\\/}) + XY \\to K\\sp+ + (XY)\\sp{-*}\\ or\\ \\to K\\sp+ + X\\sp- + Y\\eqno(1)$$and on rotational energy transfer from polar molecules which leads to Rydberg atom ionization $$\\rm K({\\it np\\/}) + XY({\\it J\\/}) \\to K\\sp+ + {\\it e}\\sp- + XY({\\it J\\/}-1)\\eqno(2)$$\nThe n dependence of the rate constants for Rydberg-atom destruction depends on the reactions involved. In reaction (1) the rate constant is independent of n whereas in reaction (2) it increases nearly linearly with n. When both reactions are possible, the measured n dependence can be explained in terms of contributions from each process.\nThe essentially-free-electron model suggests that the n dependence of the rate constants for Rydberg-atom destruction reflects the energy dependence of the cross sections of the corresponding free electron-molecule collision processes which are $$\\eqalignno{&e\\sp- + \\rm XY \\to (XY)\\sp{-*}\\ or\\ \\to X\\sp- + Y&(1\\sp\\prime)\\cr &e\\sp- + \\rm XY({\\it J\\/}) \\to {\\it e}\\sp- + XY({\\it J\\/}-1)&(2\\sp\\prime)\\cr}$$Analysis of the data therefore provides the behavior of cross sections for these processes at ultra-low electron energies.