The first quantum theory of molecules

Nenad Trinajstić

J. Jahanpanah, M. Esmaeilzadeh

The vibrational motion equations of both homo- and hetero-nuclei diatomic molecules are here derived for the first time. A diatomic molecule is first considered as a quantum mechanics oscillator. The second- and third-order Hamiltonian operators are then formed by substituting the number operator for the quantum number in the corresponding energy eigenvalues. The temporal variations of relative position and linear momentum of two oscillating atoms are calculated by solving Heisenberg's equations of motion. The results indicate that the oscillatory behaviour of diatomic molecules are described by the wave packets which consisted of two different frequencies. The stability theory of optical oscillators (lasers) is then exploited to determine the stability conditions of an oscillating diatomic molecule in the different energy levels of Morse potential. It peculiarly turned out that the diatomic molecules are exactly dissociated at the energy level in which their equations of motion become unstable. We also determine the minimum oscillation frequency (cut-off frequency) of a diatomic molecule at the dissociation level of Morse potential.

Vanessa A. Seifert

The investigation of the relation between chemistry and quantum mechanics includes examining how the two theories each describe an isolated molecule. This paper focuses on one particular characteristic of chemistry's and quantum mechanics' descriptions of an isolated molecule; namely on the assumptions made by each description that an isolated molecule is stable and has structure. The paper argues that these assumptions are an idealisation. First, this is because stability and structure are partially determined by factors that concern the context in which a molecule is considered (i.e. thermodynamic conditions, time-range of experiment, environment, etc.). Secondly, the stability and structure of a molecule can only be empirically identified with reference to those factors. This paper examines these assumptions in the context of the philosophical literature on idealisations. This examination is a novel contribution that raises interesting questions about the relation between the two theories, the nature of stability and structure, and the function of these assumptions in the two theories.

Linus Carl Pauling

Christian Fey, Markus Kurz, Peter Schmelcher +2 more

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an s -wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically explained.