Vibronic coupling in molecules and in solids

We utilize the experience gained in our previous studies on the chemistry of vibronic coupling in simple homonuclear and heteronuclear molecules to begin assembling theoretical guidelines for the construction of potentially superconducting solids exhibiting large electron-phonon coupling. For this purpose we analyze similarities between vibronic coupling in isolated molecules and in extended solids. In particular, we study vibronic coupling along the antisymmetric stretch coordinate (Q(as)) in linear symmetric AAA molecules, and along the optical phonon pairing mode coordinate (Q(opt)) in corresponding one-dimensional [A](infinity) chains built of equidistant A atoms. This is done for a broad range of chemical elements (A). The following similarities between vibronic coupling in molecules and phonon coupling in solids emerge from our calculations: 1) The HOMO/ LUMO electronic energy gap in an AAA molecule increases along Q(as), and the highest occupied crystal orbital/lowest unoccupied crystal orbital gap in [A](infinity) chain increases along Q(opt). 2) The maximum vibronic instability is invariably obtained for a half-filled, singly occupied molecular orbital in AAA molecules, and for a corresponding half-filled band in [A](infinity) chains. 3) The vibronic stability of an AAA molecule increases with a decrease of the AA bond length, as does the vibronic stability of [A](infinity) chains (external pressure may lead to a reversal of a Peierls distortion). 4) The high degree of s-p mixing and ionic/covalent forbidden curve crossing dramatically enhance the vibronic instability of both AAA molecules and [A](infinity) chains. We also introduce one quantitative relationship: The parameter log(R) (where R is molar refractivity, a parameter used by Herzfeld to prescribe the conditions for the metallization of the elements) correlates with a parameter f(AA) (defined as twice the electronegativity of A, divided by the equilibrium AA bond length), used by two of us previously to describe vibronic coupling in AAA molecules for a broad range of elements (A=halogen, H, or an alkali metal). We hope to illustrate that key chemical aspects of vibronic coupling in simple molecules may thus be profitably transferred to corresponding materials in the solid state.