The Hückel theory, introduced nearly a century ago, is often regarded as mainly an educational tool, too simplistic for making quantitative predictions of molecular reactivity and structure. In this talk, I present arguments and demonstrate numerical results suggesting that this paradigm needs revision. By adopting the method of redefining a reference state from statistical mechanics, I introduce the new independent atom ansatz of density functional theory. The formally exact ansatz allows for representing electron density of a molecule in terms of densities of perturbed atoms and provides the eigenvalue problem for atomic states in a molecule – so-called atomions. A very simple total energy functional is derived, which can be regarded as a Hückel theory with linear overlap, electrostatic, and dynamic correlation terms.
This derived framework, referred to as the nonempirical tight binding theory (NTB), is parameter-free, describes bond dissociation to free atoms correctly, and incorporates energy decomposition and charge analyses at no additional cost. The first-generation NTB, involving local resonance integrals, is found to be superior to the current heavily parameterized tight binding and reactive force field methods for hydrogenic model systems [1]. The second-generation NTB, with non-local resonance integrals, yields a first-of-a-kind analytical expression for difficult-to-compute dynamic correlation energy in H2: . It also accurately predicts the bond energy, bond length, and the vibrational wavenumber of an H2 molecule with absolute errors of 0.002 Å, 0.19 eV, and 13 cm-1 relative to experiment [2]. The model is generalized to period-2 diatomics, for which equally high accuracy is achieved using either no parameters (He2, Be2) or with optimized core and valence basis set exponents (Li2, B2, N2, O2, and F2) [3]. Implications of NTB to understanding the origin and generality of chemical bonding and interpretations of quantum mechanics are discussed.
References:
- Mironenko, A. V. Analytical and Parameter-Free Hückel Theory Made Possible for Symmetric Hx Clusters. The Journal of Physical Chemistry A, 2023, 127 (37), 7836-7843.
- Leung, L. and Mironenko, A. V. Analytical Correlation in the H2 Molecule from the Independent Atom Ansatz. https://arxiv.org/abs/2405.15809.
- Mironenko A. V., Leung L., and Zhuang J. Self-consistent Equations for Nonempirical Tight-Binding Theory. https://arxiv.org/abs/2204.04554.