Linear Scaling High-spin Open-shell Local Correlation Methods

Human beings use different methods to understand the world, religiously or scientifically, empirically or theoretically, synthetically or analytically. Quantum chemistry is one of the these methods. Starting from first principles of quantum mechanics, applying different mathematical and physical approximations, the behaviors of molecules are described. Before the discussion of the complex theories in quantum chemistry, it is better to answer two questions first. One is for which kind of system quantum chemistry is needed? The other is what is the accuracy needed for the results of quantum chemistry calculations? Quantum chemistry is used to study the molecular world, but it is not true that quantum chemistry is needed for all molecules. It is not possible and also not necessary to apply quantum chemistry to huge molecules, for example, a DNA or a protease molecule. To study very large systems, there are bio-chemical databases, molecular dynamics based on molecular mechanics (MM), and semi-empirical methods. If the electron structure in the system changes smoothly and slowly, the above methods generally provide acceptable results. However, there are also rapid changes of electron structure, for example, in chemical reactions such as bonding breaking, bonding forming, charge transfer, etc. To describe chemical reactions, using quantum chemistry is necessary and important. Fortunately, even for a complex biological chemical reaction, the active region where the electron structure changes rapidly is rather local, i.e., the region has a size of maximum up to two or three hundred atoms, but usually less than 100 atoms. Using quantum chemistry to study the active region in combination with other methods which describe the remaining system is the basic methodology to study very large molecules. The quantum mechanics / molecular mechanics (QM/MM) approach is a good example of such methodologies. The accuracy needed for the energies calculated by quantum chemistry depends on how far a calculation is from reality or experiment. A single energy calculated by quantum chemistry (for example, a Hartree-Fock (HF) or a density functional theory (DFT) calculation) can be applied to “bare” and “static” molecules. These are molecules in vacuum or in a gas field, at zero kelvin, without excited levels of vibrations and rotations, without relativistic effects, and under adiabatic and BornOppenheimer approximations. The aim of quantum chemistry research is to find different methods, based on first principle, or experience, to bring traditional quantum chemistry calculations back to reality. Basically, to perform a calculation to a