Electron-Electron Interaction, DMRG, TNS, and DFT

The reliability of quantum chemical methods for the description of molecular systems is determined by the treatment of the electron-electron interaction. Tackling this so-called electron-correlation problem is thus at the heart of quantum chemistry. We have investigated the analytical behaviour of electron-electron interaction potentials, density functional parameterizations, model potentials, and spin-spin interactions in polynuclear clusters. Although some methods - like the notorious B3LYP hybrid density functional theory - became standard models in computational chemistry, they may yield unreliable results for special classes of molecules. In particular transition metal complexes containing metals like iron, manganese or nickel pose a true challenge for quantum chemical first-principles methods. It is desirable to uncover pathological cases in order to discover ways for a general improvement of these methods.

For a review see:

C. R. Jacob, M. Reiher, external pageSpin in Density-Functional Theory, Int. J. Quantum Chem. 112 2012 3661-3684.

New parametrizations of the electronic wave function are promising for the description of complicated (multi-reference) electronic structures. We pioneered the applicability of the density matrix renormalization group (DMRG) algorithm for studies in transition metal chemistry. One goal is to derive a set-up that allows for routine black-box DMRG calculations with a number of renormalized states that is as small as possible in order to considerably reduce the computational demands. With this methodology we were able to calculate accurate ab initio reference spin densities. We also develop tensor-network parametrizations and presented the first investigation on tensor-network states for molecules described by the full quantum chemical Hamiltonian. Our latest development is a second-generation, matrix-product-operator based, multi-purpose DMRG program.

For reviews see:

S.F. Keller, M. Reiher, external pageDetermining Factors for the Accuracy of DMRG in Chemistry, CHIMIA 68 2014 200-203.

K. H. Marti, M. Reiher, The Density Matrix Renormalization Group Algorithm in Quantum Chemistry (PDF, 356 KB), Z. Phys. Chem. 224 2010 583-599.

K. H. Marti, M. Reiher, New Electron Correlation Theories for Transition Metal Chemistry (PDF, 1.7 MB), Phys. Chem. Chem. Phys. 13 2011 6750-6759.