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Die Arbeit befasst sich mit der Ab-Initio-Berechnung von molekularen Eigenschaften, beispielsweise Dipolmomenten oder Strukturen, mithilfe von explizit korrelierter Störungstheorie. Hierzu erfolgt die Herleitung, Implementierung und Analyse der Genauigkeit von analytischen Gradienten für die Methode RI-MP2-F12. Mit diesem Ansatz können Energien und Eigenschaften am Basissatzlimit berechnet werden, so dass der Fehler durch Überlagerung von Basissätzen (BSSE) drastisch reduziert wird.

Gradienten --- Integralberechnung --- molekulare Eigenschaften --- Density-Fitting --- Störungstheorie

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The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications and may be also useful for doctoral and advanced undergraduate students.

Quasistationarer Zustand --- Stochastisches System --- Storungstheorie --- Stochastic systems. --- Stochastic processes. --- Random processes --- Systems, Stochastic --- Probabilities --- Stochastic processes --- System analysis --- Markov Chains. --- Nonlinearly Perturbed Regenerative Processes. --- Renewal Equation. --- Semi-Markov Processes.