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Theoretical method development

Method Development

Dr. Róbert Izsák
hat im Jahr 2020 ans Middlebury College gewechselt. Nähere Informationen zu seiner jetzigen Tätigkeit finden Sie hier. Diese Seite dokumentiert die Forschung seiner Gruppe in der Abteilung Molekulare Theorie und Spektroskopie bis 2020.
What follows is a more general view on (wave function based) method development. As with any attempt that tries to give a bird’s eye view of a large research area, not everything can be fitted neatly into the scheme presented here. Nevertheless, the purpose of theoretical science is to build theories with quantitative predictive power from only a few principles taken for granted. These predictions can then be checked experimentally, the underlying assumption being that an ideally perfect experiment should match the predictions coming from an ideally ‘exact’ theory. In practice there are many obstacles both on the experimental and on the theoretical side. As there are no experiments without error, there are no theories without some flaws. A realistic goal is to keep these under control. In quantum chemistry, the ‘exact’ side of the coin basically consist of the principal assumptions of quantum theory and (special) relativity. The resulting equations are often not amenable to practical computations, and, therefore, a system of approximations is designed to arrive at something ‘computable’, something that can be practically evaluated. This role is taken by Hartree-Fock theory in quantum chemistry. In order to arrive at this theory, various approximations were made, but since in principle we know what we neglected, we know what effects this may cause, see Fig. 1. For example, if we ignore relativity, we cannot expect our method to account for the color of gold, which we then consider as a ‘relativistic effect’. On the other hand in principle we are also able to correct for what we neglected, i.e., we have control over the error we allow. This may not be an easy task, however. While Hartree-Fock theory recovers 98% of the total electronic energy, the recovery of the remaining few percents can be an extremely costly computational assignment, and yet a necessary one since most chemistry is affected by this ‘correlation energy’. For this reason, the purpose of method development is to devise efficient methods which allow us to accurately describe chemically interesting systems.

Róbert Izsák

Dr. Róbert Izsák

Gruppenleiter am Max-Planck-Institut für Kohlenforschung
Gruppenleiter am MPI für Chemische Energiekonversion
Postdoc am MPI für Bioanorganische Chemie; heute MPI CEC
Postdoc an der Universität Bonn
Ph.D. (Chemie) an der Cardiff University, UK
Diplom (Chemie), Universität Szeged, Ungarn


Resolution of Identity and Chain of Spheres
Resolution of Identity and Chain of Spheres

Resolution of Identity and Chain of Spheres

Hartree-Fock theory plays a central role in Quantum Chemistry. It serves on the one hand as a basis for electron correlation approaches while on the other it is also essential for density functional theory. The evaluation of the HF exchange term is a rather time consuming operation for larger molecules and as a result for a wide range of chemically or biologically interesting systems. This motivates the development of various efficient approaches to exchange evaluation. The Chain of Spheres exchange (COSX) algorithm, one of the most efficient methods available for this purpose today, has been developed in the institute since 2009. The algorithm has favorable scaling and contraction properties which makes it especially suitable for larger systems. In combination with the resolution of identity for the Coulomb term (RI-J) it enables large scale HF and DFT calculations. To realize the full potential of any approximation to the SCF energy, it is inevitable to obtain the corresponding gradients and the Hessian. These can then be used in geometry optimizations and to calculate various properties. Gradients are determined in an approximate manner for the COSX algorithm, while for Hessian calculation its main advantage is in the CP-SCF step. The COSX method can also be used beneficially in correlation methods. In these cases the SCF density is replaced by an effective density in which the amplitudes of various excited determinants are contracted with molecular orbital coefficients. Thus, the evaluation of the so called singles Fock term in the LPNO-CCSD method, and the external exchange term in the SCS-MP3, CCSD and EOM-CCSD methods can both be significantly accelerated without significant loss of accuracy. In the former case the contraction involves the singles, in the latter case the doubles amplitudes, but in both cases the approximated terms are form the bottleneck of the corresponding method.

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Excited States
Excited States

Excited States

 In 2014, our group began to investigate various ways of implementing the equation of motion (EOM) coupled cluster (CC) theory for large molecules. Our first effort involved using COSX for the evaluation of the external exchange term, which lowered the costs of the calculation but did not change the scaling of the method which remained proportional to the sixth power of some measure of the system size. Similarly, domain-based local pair natural orbitals (DLPNO) can be employed to accelerate the ground state CC step, but since the amplitudes are back-transformed into the canonical basis before the EOM-CCSD code makes use of them, the overall scaling of the method remains unaffected. While the excited states would require state specific DLPNOs, it turns out that the ground state DLPNOs can be used to implement efficient methods for the evaluation of ionization potentials and electron affinities. These on the other hand are necessary ingredients for the so-called similarity transformed EOM or STEOM method, which reduces the the excitation manifold to the space of single excitations without neglecting terms based on a perturbative basis, as second order methods such as CC2 or ADC(2) do. Thus, DLPNOs for the ionization process and the STEOM method for the reduction of the excitation manifold in the canonical basis can be combined to yield the DLPNO-STEOM method, which can be used to obtain excitation energies and some of the spectroscopic properties of molecular systems using several thousand basis functions. In addition, the effect of nuclear vibrations can be included into our description of molecular spectra. Our group has been involved in the efficient implementation of a simple propagator approach to describe various rate constants that appear in the Jablonski diagram shown in Fig. 2. While the fluorescence rate (kF) is determined by the transition dipole moment, which between singlets is only zero if spacial symmetry demands it, transitions between singlet and triplet states are spin forbidden in non-relativistic quantum mechanics. In this picture, the radiative process only competes with non-radiative internal conversion (kIC) in fluorescent materials. If relativistic effects are important, singlet-triplet transitions may become allowed depending on the strength of the SOC connecting the two states. Phosphoresce rates (kP) as well as intersystem crossing rates are proportional to SOC, and the challenge of designing strong emitters lies in ensuring that populating the triplet states and their radiative decay are fast (kISC and kP are large), while the non-radiative decay of the triples is slow (k0ISC is small). Thus, the combination of this propagator scheme with the DLPNO-STEOM method for the computation of vertical excitation energies and transition dipoles is an approach we plan to pursue in the future in what we hope to be a fruitful combination of method development and practical applications.