IV. Theoretical Chemistry

We have noticed during our studies on vibronic coupling, that for a large class of molecules, M, there exists an unexpectedly simple relationship between the calculated values of bond lengths in M0 (its ground singlet state), MT (its first excited triplet state), M* (the ground state doublet of its radical anion) and M*+ (the ground state doublet of the related radical cation). An estimate of the equilibrium bond length R for given bond in MT may be obtained as follows: R(MT) = R(M*) + R(M*+) – R(M0); see   paper7.pdf.   This “remarkably simple relationship connecting the calculated geometries of isomolecular states of three different multiplicities”, called by Ayers and Parr “the Grochala-Albrecht-Hoffmann rule”, has been initially explained within the molecular orbital framework. It has been later analyzed using the DFT formalism, as well; see more on the:   GAH rule.pdf. Recently, we have extended this study to show that the GAH rule holds only for alternant, but fails for non-alternant hydrocarbons; properties defined as aromaticity/anti-aromaticity are not connected to applicability of this relationship (POL J CHEM, invited paper in press 2007).

  • We all used to describe quantum world assuming its sort of “onion-like” nuclear/electronic/vibrational/rotational struture. We often assume for simplification that there are so large differences in energies of nuclear/electronic/vibrational/rotational levels, that they do not communicate with one another. Yet, this is a rough assumption only. Vibronic coupling (vibrational/electronic coupling) is an interesting physical phenomenon, which describes coupling of electrons with movements of (much heavier than an electron) nuclei. Vibronic coupling reveals its presence for many observables. It attracted us because of its significance for a traditional explanatory theory of superconductivity, the BCS theory.
  • Together with Roald Hoffmann we wrote a 5-part series on “chemistry of vibronic coupling”. We were looking for a place for chemical intuition in thinking about superconductivity, so as to provide a reasonable direction to the experimental search for new materials. In part 1 (part1) we investigated how to maximize vibronic coupling constants in a diabatic harmonic potential model. In part 2 (part2) we analyzed the dynamic diagonal vibronic coupling constant for T1 ligand-to-metal charge-transfer (LMCT) states in AB systems (A, B = alkali metal, H, halogen); in part 3 (part3) we studied the off-diagonal dynamic vibronic coupling constants for intervalence charge-transfer (IVCT) states in ABA systems (A, B = alkali metal, H, halogen). In part 4 (part 4) we generalized observations on off-diagonal vibronic coupling constants for systems built of elements from the whole Periodic Table. In the last contribution in the series (part 5) we learned to transfer knowledge on vibronic coupling from molecules to the solids in the context of qualitative and quantitative features of coupling.
  • The most important general conclusions from these investigations are the following:

(i) Molecular systems built of hard Lewis acids/bases should be vibronically more unstable than systems built of soft Lewis acids/bases.
(ii) The more pronounced s-p mixing, the larger the vibronic instability.
(iii) An “ionic/covalent curve crossing” significantly increases the vibronic instability of a molecule.
(iv) There are numerous analogies between vibronic coupling in molecules and phonon coupling in solids; knowledge of vibronic coupling in molecules helps to predict metallization of solids.

I am currently developing a general approach to superconductivity, valence tautomerism, bond isomerism, valence fluctuations in f13 compounds, and molecular devices for data storage. It is based on theory of the avoided crossing, and it provides practical indications on how to use chemistry in order to desing new systems exhibiting these fascinating phenomena.