Explicitly correlated random-phase approximation: Development and application of a wave-function method

Entwicklung und Anwendung einer Wellenfunktionsmethode Gegenstand der vorliegenden Arbeit ist die Entwicklung der Random-Phase-Approximation-Methode, mit dem Ziel deren langsame Basissatzkonvergenz durch Kombination mit dem explizit korrelierten Wellenfunktionsansatz der F12-Theorie zu überwinden. Die Random-Phase-Approximation hat sich als leistungsfähiger Ansatz zur Erfassung der Elektronenkorrelation erwiesen, da sie langreichweitige Wechselwirkungen beschreiben kann und gleichzeitig eine vorteilhafte Skalierung der Rechenzeit mit der Systemgröße aufweist. Zur weiteren Verbesserung der Recheneffizienz der Random-Phase-Approximation-Methoden werden im Rahmen dieser Arbeit zwei Ansätze eingeführt und anhand einer Zusammenfassung der Arbeitsgleichungen, der zugehörigen Implementierungen und Benchmark-Ergebnisse vorgestellt. Es wird gezeigt, dass die Basissatzkonvergenz drastisch beschleunigt werden kann, wenn der Ring-Coupled-Cluster-Doubles-Ansatz zugrunde liegt. Benchmark-Ergebnisse veranschaulichen, dass triple-zeta-Basissätze ausreichen um Korrelations- und Atomisierungsenergien bis zu 99% des Basissatzlimits zu konvergieren. Eine vergleichbare Verbesserung wird für verschiedene explizit korrelierte Ring-Coupled-Cluster-Doubles-Ansätze erzielt, welche exakten Austausch berücksichtigen. Die Verbindung zur Coupled-Cluster-Theorie wird zudem verwendet um Diagnostiken zu entwickeln, die es ermöglichen die Anwendbarkeit der Random-Phase-Approximation in Abhängigkeit des zu untersuchenden Systems zu überprüfen

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension

Traces of trauma – a multivariate pattern analysis of childhood trauma, brain structure and clinical phenotypes

Background: Childhood trauma (CT) is a major yet elusive psychiatric risk factor, whose multidimensional conceptualization and heterogeneous effects on brain morphology might demand advanced mathematical modeling. Therefore, we present an unsupervised machine learning approach to characterize the clinical and neuroanatomical complexity of CT in a larger, transdiagnostic context. Methods: We used a multicenter European cohort of 1076 female and male individuals (discovery: n = 649; replication: n = 427) comprising young, minimally medicated patients with clinical high-risk states for psychosis; patients with recent-onset depression or psychosis; and healthy volunteers. We employed multivariate sparse partial least squares analysis to detect parsimonious associations between combinations of items from the Childhood Trauma Questionnaire and gray matter volume and tested their generalizability via nested cross-validation as well as via external validation. We investigated the associations of these CT signatures with state (functioning, depressivity, quality of life), trait (personality), and sociodemographic levels. Results: We discovered signatures of age-dependent sexual abuse and sex-dependent physical and sexual abuse, as well as emotional trauma, which projected onto gray matter volume patterns in prefronto-cerebellar, limbic, and sensory networks. These signatures were associated with predominantly impaired clinical state- and trait-level phenotypes, while pointing toward an interaction between sexual abuse, age, urbanicity, and education. We validated the clinical profiles for all three CT signatures in the replication sample. Conclusions: Our results suggest distinct multilayered associations between partially age- and sex-dependent patterns of CT, distributed neuroanatomical networks, and clinical profiles. Hence, our study highlights how machine learning approaches can shape future, more fine-grained CT research

A variational formulation of the Harris functional as a correction to approximate Kohn–Sham density functional theory

Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn–Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures

Excited-state properties for extended systems: Efficient hybrid density functional methods.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02–0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm–Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2–0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes

Excited-state properties for extended systems: Efficient hybrid density functional methods.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials due to its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis-set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.2 pm for excited-state bond lengths and in the range of 0.02 - 0.06 eV for vertical excitation, adiabatic excitation and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least one order of magnitude can be achieved for ES geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semi-empirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation and fluorescence energies are in the range of 0.2 - 0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by one order of magnitude, suggesting its potential use for large-scale screening purposes

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes

Accurate computations of the structures and binding energies of the imidazole ... benzene and pyrrole ... benzene complexes

Using explicitly-correlated coupled-cluster theory with single and double excitations, the intermolecular distances and interaction energies of the T-shaped imidazole⋯⋯benzene and pyrrole⋯⋯benzene complexes have been computed in a large augmented correlation-consistent quadruple-zeta basis set, adding also corrections for connected triple excitations and remaining basis-set-superposition errors. The results of these computations are used to assess other methods such as Møller–Plesset perturbation theory (MP2), spin-component-scaled MP2 theory, dispersion-weighted MP2 theory, interference-corrected explicitly-correlated MP2 theory, dispersion-corrected double-hybrid density-functional theory (DFT), DFT-based symmetry-adapted perturbation theory, the random-phase approximation, explicitly-correlated ring-coupled-cluster-doubles theory, and double-hybrid DFT with a correlation energy computed in the random-phase approximation

Identification and Quantification of Coumarins by UHPLC-MS in Arabidopsis thaliana Natural Populations

Coumarins are phytochemicals occurring in the plant kingdom, which biosynthesis is induced under various stress factors. They belong to the wide class of specialized metabolites well known for their beneficial properties. Due to their high and wide biological activities, coumarins are important not only for the survival of plants in changing environmental conditions, but are of great importance in the pharmaceutical industry and are an active source for drug development. The identification of coumarins from natural sources has been reported for different plant species including a model plant Arabidopsis thaliana. In our previous work, we demonstrated a presence of naturally occurring intraspecies variation in the concentrations of scopoletin and its glycoside, scopolin, the major coumarins accumulating in Arabidopsis roots. Here, we expanded this work by examining a larger group of 28 Arabidopsis natural populations (called accessions) and by extracting and analysing coumarins from two different types of tissues–roots and leaves. In the current work, by quantifying the coumarin content in plant extracts with ultra-high-performance liquid chromatography coupled with a mass spectrometry analysis (UHPLC-MS), we detected a significant natural variation in the content of simple coumarins like scopoletin, umbelliferone and esculetin together with their glycosides: scopolin, skimmin and esculin, respectively. Increasing our knowledge of coumarin accumulation in Arabidopsis natural populations, might be beneficial for the future discovery of physiological mechanisms of action of various alleles involved in their biosynthesis. A better understanding of biosynthetic pathways of biologically active compounds is the prerequisite step in undertaking a metabolic engineering research