The key to understanding molecular electronic structure and dynamical behavior of molecules is an accurate assessment of the many-electron correlation effects. Our group focuses on the development and applications of new quantum-mechanical methods that include correlation, particularly on the coupled-cluster theory and its renormalized, active-space, extended, multi-reference, and response variants that allow us to study chemical reaction pathways and potential energy surfaces involving bond breaking, covalent as well as non-covalent interactions, radicals, biradicals, and other open-shell species, molecular electronic excitations, electron-transfer processes, properties in vibrationally and electronically excited states, and transition probability coefficients for various types of spectroscopy. We examime ways of achieving high-level coupled-cluster or numerically exact energetics by combining determinstic computations with stochastic wave function sampling. We also develop approximate coupled-pair approaches for strongly correlated systems, which can be used to model metal-insulator transitions, and local correlation coupled-cluster methods and their multi-level extensions that can be applied to large molecular systems with hundreds of atoms, which are characterized by the linear or sublinear scaling of the computational time with the system size and coarse-grain parallelism, while preserving high accuracies coupled-cluster theories offer for smaller molecules. Our goal is to design and apply robust and yet affordable computational approaches that enable precise modeling of molecular processes and properties relevant to combustion, catalysis, light harvesting, and photochemistry. Our main interest is in methods that are predictive and systematically improvable, while offering high accuracy, ease of use, and relatively low computer costs compared to other quantum-chemistry approaches that aim at similar precision, so that one can use them to study chemical processes and phenomena involving complex molecular problems, in addition to more traditional smaller systems. We write our own computer codes for the standard and new coupled-cluster methods which are distributed world-wide through a popular electronic structure package GΛMESS and plugins to PSI4 available on GitHub. Our methods are also available in NWChem and, in the original or modified form, Q-Chem and MRCC.