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Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.
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A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster reduction that is capable of providing very accurate solutions of the many-body Schrodinger equation is then initiated employing screenings to the projection manifold and commutator operations. The projection manifold is iteratively updated through the single commutators $leftlangle kappa right| [hat H,hat T]left| 0 rightrangle$ comprised of the primary clusters $hat T_{lambda}$ with substantial contribution to the connectivity. The operation of the commutators is further reduced by introducing a correction, taking into account the so-called exclusion principle violating terms, that provides fast and near-variational convergence in many cases.
To investigate inelastic electron scattering, which is ubiquitous in various fields of study, we carry out ab initio study of the real-time dynamics of a one-dimensional electron wave packet scattered by a hydrogen atom using different methods: the exact solution, the solution provided by time-dependent density functional theory (TDDFT), and the solutions given by alternative approaches. This research not only sheds light on inelastic scattering processes but also verifies the capability of TDDFT in describing inelastic electron scattering. We revisit the adiabatic local-density approximation (ALDA) in describing the excitation of the target during the scattering process along with a self-interaction correction and spin-polarized calculations. Our results reveal that the ALDA severely underestimates the energy transferred in the regime of low incident energy particularly for a spin-singlet system. After demonstrating alternative approaches, we propose a hybrid ab initio method to deal with the kinetic correlation alongside TDDFT. This hybrid method would facilitate first-principles studies of systems in which the correlation of a few electrons among many others is of interest.
We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent field equations of Kohn-Sham density functional theory. The algorithm is robust, requires relatively little finetuning and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.
WloopPHI is a Python code that expands the features of WIEN2k, a full-potential all-electron density functional theory package, by the characterization of Weyl semimetals. It enables the calculation of the chirality (or monopole charge) associated with Weyl nodes and nodal lines. The theoretical methodology for the calculation of the chirality is based on an extended Wilson loop method and a Berry phase approach. We validate the code using TaAs, which is a well-characterized Weyl semimetal, both theoretically and experimentally. Afterwards, we applied the method to the characterization of YRh$_6$Ge$_4$ and found two sets of Weyl points (ca. 0.2 eV below the Fermi energy) together with a topological nodal line (protected by mirror symmetry) crossing the Fermi energy and mapped their chiralities.
For the prototypical diatomic-molecule - diatomic molecule interactions H2-HX and H2-X2, where X = F, Cl, Br, quantum-chemical ab initio calculations are carried out on grids of the configuration space, which permit a spherical-harmonics representation of the potential energy surfaces (PESs). Dimer geometries are considered for sets of representative leading configurations, and the PESs are analyzed in terms of isotropic and anisotropic contributions. The leading configurations are individuated by selecting a minimal set of mutual orientations of molecules needed to build the spherical-harmonic expansion on geometrical and symmetry grounds. The terms of the PESs corresponding to repulsive and bonding dimer geometries and the averaged isotropic term, for each pair of interacting molecules, are compared with representations in terms of a potential function proposed by Pirani et al. (see Chem. Phys. Lett. 2004, 394, 37-44 and references therein). Connections of the involved parameters with molecular properties provide insight into the nature of the interactions.
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