Accurate Prediction of Core Properties for Chiral Molecules using Pseudo Potentials

Pseudo potentials (PPs) constitute perhaps the most common way to treat relativity, often in a formally non-relativistic framework, and reduce the electronic structure to the chemically relevant part. The drawback is that orbitals obtained in this picture (called pseudo orbitals (POs)) show a reduced nodal structure and altered amplitude in the vicinity of the nucleus, when compared to the corresponding molecular orbitals (MOs). Thus expectation values of operators localized in the spatial core region that are calculated with POs, deviate significantly from the same expectation values calculated with all-electron (AE) MOs. This study describes the reconstruction of AE MOs from POs, with a focus on POs generated by energy consistent pseudo Hamiltonians. The method reintroduces the nodal structure into the POs, thus providing an inexpensive and easily implementable method that allows to use nonrelativistic, efficiently calculated POs for good estimates of expectation values of core-like properties. The discussion of the method proceeds in two parts: Firstly, the reconstruction scheme is developed for atomic cases. Secondly, the scheme is discussed in the context of MO reconstruction and successfully applied to numerous numerical examples. Starting from the equations of the state-averaged multi-configuration self- consistent field method, used for the generation of energy consistent pseudo potentials, the electronic spectrum of the many-electron Hamiltonian is linked to the spectrum of the effective one-electron Fock operator by means of various models systems. This relation and the Topp–Hopfield–Kramers theorem, are used to show the shape-consistency of energy-consistent POs for atomic systems. Shape-consistency describes POs that follow distinct AOs exactly outside a core-radius r_core . In the cases presented here, shape-consistency holds to a high degree and it follows that in atomic systems every PO has one distinct partner in the set of AOs. The overlap integral between these two orbitals is close to one, as it is determined mainly by the spatial orbital parts outside r_core . Expanding, e.g., a 5s PO in occupied AOs, the 5s AOs will have the highest contribution. The POs itself contains contributions from high-energy unoccupied AOs as well (e.g. 15s), which damp the nodal structure of the POs near the nucleus. Consequently, neglecting contributions from unoccupied orbitals in a projection of the POs reintroduces the nodal structure. This approach is not directly suitable for the reconstruction of MOs, as they often need to be expanded in a full set of AOs at each atomic center, including all unoccupied orbitals, to properly account for the electron density distribution in the molecule. However, it is shown that the occupied MOs are well described by occupied and low-energy unoccupied AOs only and a mapping of the POs onto a basis containing only these orbitals reconstructs the nodal structure of the MO. The approach uses only standard integrals available in most quantum chemistry programs. The computational cost of these integrals scales with N^2 , where N is the number of basis functions. The most time consuming step is a Gram-Schmidt orthogonalization, which scales in this implementation with MN^2 , M being the number of reconstructed orbitals. The reconstruction method is subsequently tested: Valence orbitals of atomic, closed-shell systems were reconstructed numerically exactly. The influence of numerical parameters is investigated using the molecule BaF . It is shown that the method is basis set dependent: One has to ensure that the PO basis can be expanded exactly in the basis of AOs. Violating this rule of thumb may degrade the quality of reconstructed orbitals. Additionally, the representation of MOs by a linear combination of occupied and unoccupied AOs is investigated. For the exemplary systems, the shells included in the fitting procedure of the PP were sufficient. Reconstruction of the alkaline earth monofluorides showed that periodic trends can be reconstructed as well. Scaling of hyperfine structure parameters with increasing atomic number is discussed. For hydrogenic atoms, the scaling should be linear, whereas small deviations from the linear behavior were observed for molecules. The scaling laws computed from reconstructed and reference orbitals were almost identical. In this context, the failure of commonly used relativistic enhancement factors beyond atomic number 100 is discussed. Applicability of the method is also tested on parity violating properties for which the main contribution is generated by the valence orbitals near the nucleus. Symmetry-independence of the method is shown by successful reconstruction of orbitals of the tetrahedral PbCl_4 and chiral NWHClF. The reliable reconstruction of chemical trends is shown with the help of the NWHClF derivatives NWHBrF and NWHFI. The study of chiral compounds as, e.g., NWHClF and its group 17 derivatives, which have been proposed as paradigm for the detection of parity-violation in chiral molecules, remains of great importance. Especially the direct determination of absolute configuration of chiral centers is still non-trivial. The author contributed to this field with a self-written molecular dynamics (MD) program to simulate Coulomb explosions and thus to provide an insight especially into the early explosion stages directly after an instantaneous multi-ionization of the molecule CHBrClF, comparable to experiments using the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technique. An algorithm for the determination of the investigated molecule’s absolute configuration from time-of-flight data and detection locations of molecular fragments is included in the program. The program was used to generate experiment-equivalent data which allowed for the first time the investigation of non-racemic mixtures by the analysis routines of the experiment. The MD program includes harmonic and anharmonic bond potentials. A charge-exchange model can model partial charges in early phases of the Coulomb explosion. Furthermore, Born–Oppenheimer MD simulations and statistical models are used to explain the relative abundance of products belonging to competing reaction channels, as obtained by photoion coincidence measurements. Additionally, qualitative statements about reaction branching ratios are made by comparing the partition functions of involved degrees of freedom. Analytic equations for partition functions of simple models are used to provide a simple formula allowing fast estimates of reaction branching ratios

Compuchem applied to the study of semiconductive transition metal complexes architectures.

Metalloporphyrins, although trackable in abiotic systems, play a central role in fundamental biological processes, such as oxygen transport and storage, photosynthesis and electron transport during cellular respiration and photosynthesis. The relevance of this class of molecules is not limited to the biological environment, but it extends to important technological fields such as electronics, solar cells and sensors. Thus, it explains the continuously growing interdisciplinary interest for them and the push to develop novel porphyrin-like molecules, whose electronic and optical properties may be tuned through molecular engineering. In this thesis it is presented an experimental and theoretical study of the occupied/unoccupied electronic structure of two π-conjugated organic macrocycles [5,10,15,20-tetraphenylporphyrin (H2TPP) and 5,10,15,20-tetrakis(pentafluorophenyl) porphyrin (H2TPP(F))] and their Cu(II) complexes (CuTPP e CuTPP(F)) deposited as films on metallic surfaces. Several papers have been published in the past on this issue; on the other hand, I believe that my study represents a significant advance because, for the first time, all the relevant electronic shells (from the core levels of C, N, F and Cu to the occupied and unoccupied molecular orbitals) are consistently investigated with unprecedented detail. The agreement between experiments and theory is noticeable, allowing the assignment of the main features of the valence and core level spectra, as well as to correlate these features with the different atomic contributions. Moreover, new insights into the empty states of the investigated molecules and the metal-ligand bonding scheme have been gained by combining XAS data at the C, N, F K-edge and Cu L2,3-edges with open-shell relativistic ZORA TD-DFT calculations. The excellent agreement between experimental evidence and theoretical results encourages us to apply the open-shell TD-DFT approach to different ligands and corresponding Cu complexes

Relativistic DFT calculation and their effect on the accuracy of results

This study explores the significance of density functional theory (DFT) calculations with relativistic effects for two ethylenediaminetetraacetate (edta) type complexes: trans(O5)-[M(eddadp)]- (M = Rh3+, Co3+). Relativistic effects affect the electronic structure of a molecule and, thus, its chemical and spectroscopic properties. With the use of scalar relativistic corrections (SR-ZORA), as implemented in the ADF package, with the B3LYP functional, the TZP basis set and the COSMO solvation model, structural analyses show improved predictions for the geometries of both complexes. In the case of the Rh3+ complex, the differences in metal-ligand bond lengths with and without the relativistic effects were small. In the case of the Co3+ complex, the changes in metal-ligand bond lengths due to the relativistic effects were slightly more pronounced. Compared to experimental values, excitation energies are better when including relativistic corrections, especially for the Rh3+ complex. These results indicate the importance of relativistic DFT calculations for heavy element compounds

The zero order regular approximation for relativistic effects: the effect of spin-orbit coupling in closed shell molecules.

In this paper we will calculate the effect of spin–orbit coupling on properties of closed shell molecules, using the zero‐order regular approximation to the Dirac equation. Results are obtained using density functionals including density gradient corrections. Close agreement with experiment is obtained for the calculated molecular properties of a number of heavy element diatomic molecules

Relativistic Douglas-Kroll-Hess Calculations of Hyperfine Interactions within First Principles Multireference Methods

Relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field (RASSCF) formalism with restricted active space state interaction (RASSI) for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativitic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs) such as Tb(III)Pc$_2$ and Tb(II)(Cp$^\text{iPr5}$)$_2$ without ligand truncation using well-converged basis sets. In particular, for the divalent SMM which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).Comment: 40 pages, 4 figure

Accurate Prediction of Core Properties for Chiral Molecules using Pseudo Potentials

Pseudo potentials (PPs) constitute perhaps the most common way to treat relativity, often in a formally non-relativistic framework, and reduce the electronic structure to the chemically relevant part. The drawback is that orbitals obtained in this picture (called pseudo orbitals (POs)) show a reduced nodal structure and altered amplitude in the vicinity of the nucleus, when compared to the corresponding molecular orbitals (MOs). Thus expectation values of operators localized in the spatial core region that are calculated with POs, deviate significantly from the same expectation values calculated with all-electron (AE) MOs. This study describes the reconstruction of AE MOs from POs, with a focus on POs generated by energy consistent pseudo Hamiltonians. The method reintroduces the nodal structure into the POs, thus providing an inexpensive and easily implementable method that allows to use nonrelativistic, efficiently calculated POs for good estimates of expectation values of core-like properties. The discussion of the method proceeds in two parts: Firstly, the reconstruction scheme is developed for atomic cases. Secondly, the scheme is discussed in the context of MO reconstruction and successfully applied to numerous numerical examples. Starting from the equations of the state-averaged multi-configuration self- consistent field method, used for the generation of energy consistent pseudo potentials, the electronic spectrum of the many-electron Hamiltonian is linked to the spectrum of the effective one-electron Fock operator by means of various models systems. This relation and the Topp–Hopfield–Kramers theorem, are used to show the shape-consistency of energy-consistent POs for atomic systems. Shape-consistency describes POs that follow distinct AOs exactly outside a core-radius r_core . In the cases presented here, shape-consistency holds to a high degree and it follows that in atomic systems every PO has one distinct partner in the set of AOs. The overlap integral between these two orbitals is close to one, as it is determined mainly by the spatial orbital parts outside r_core . Expanding, e.g., a 5s PO in occupied AOs, the 5s AOs will have the highest contribution. The POs itself contains contributions from high-energy unoccupied AOs as well (e.g. 15s), which damp the nodal structure of the POs near the nucleus. Consequently, neglecting contributions from unoccupied orbitals in a projection of the POs reintroduces the nodal structure. This approach is not directly suitable for the reconstruction of MOs, as they often need to be expanded in a full set of AOs at each atomic center, including all unoccupied orbitals, to properly account for the electron density distribution in the molecule. However, it is shown that the occupied MOs are well described by occupied and low-energy unoccupied AOs only and a mapping of the POs onto a basis containing only these orbitals reconstructs the nodal structure of the MO. The approach uses only standard integrals available in most quantum chemistry programs. The computational cost of these integrals scales with N^2 , where N is the number of basis functions. The most time consuming step is a Gram-Schmidt orthogonalization, which scales in this implementation with MN^2 , M being the number of reconstructed orbitals. The reconstruction method is subsequently tested: Valence orbitals of atomic, closed-shell systems were reconstructed numerically exactly. The influence of numerical parameters is investigated using the molecule BaF . It is shown that the method is basis set dependent: One has to ensure that the PO basis can be expanded exactly in the basis of AOs. Violating this rule of thumb may degrade the quality of reconstructed orbitals. Additionally, the representation of MOs by a linear combination of occupied and unoccupied AOs is investigated. For the exemplary systems, the shells included in the fitting procedure of the PP were sufficient. Reconstruction of the alkaline earth monofluorides showed that periodic trends can be reconstructed as well. Scaling of hyperfine structure parameters with increasing atomic number is discussed. For hydrogenic atoms, the scaling should be linear, whereas small deviations from the linear behavior were observed for molecules. The scaling laws computed from reconstructed and reference orbitals were almost identical. In this context, the failure of commonly used relativistic enhancement factors beyond atomic number 100 is discussed. Applicability of the method is also tested on parity violating properties for which the main contribution is generated by the valence orbitals near the nucleus. Symmetry-independence of the method is shown by successful reconstruction of orbitals of the tetrahedral PbCl_4 and chiral NWHClF. The reliable reconstruction of chemical trends is shown with the help of the NWHClF derivatives NWHBrF and NWHFI. The study of chiral compounds as, e.g., NWHClF and its group 17 derivatives, which have been proposed as paradigm for the detection of parity-violation in chiral molecules, remains of great importance. Especially the direct determination of absolute configuration of chiral centers is still non-trivial. The author contributed to this field with a self-written molecular dynamics (MD) program to simulate Coulomb explosions and thus to provide an insight especially into the early explosion stages directly after an instantaneous multi-ionization of the molecule CHBrClF, comparable to experiments using the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technique. An algorithm for the determination of the investigated molecule’s absolute configuration from time-of-flight data and detection locations of molecular fragments is included in the program. The program was used to generate experiment-equivalent data which allowed for the first time the investigation of non-racemic mixtures by the analysis routines of the experiment. The MD program includes harmonic and anharmonic bond potentials. A charge-exchange model can model partial charges in early phases of the Coulomb explosion. Furthermore, Born–Oppenheimer MD simulations and statistical models are used to explain the relative abundance of products belonging to competing reaction channels, as obtained by photoion coincidence measurements. Additionally, qualitative statements about reaction branching ratios are made by comparing the partition functions of involved degrees of freedom. Analytic equations for partition functions of simple models are used to provide a simple formula allowing fast estimates of reaction branching ratios