Schrodinger equation electronic structure methods

Electronic structure methods use the laws of quantum mechanics rather than classical physics as the basis for their computations. Quantum mechanics states that the energy and other related properties of a molecule may be obtained by solving the Schrodinger equation ... 

For any but the smallest systems, however, exact solutions to the Schrodinger equation are not computationally practical. Electronic structure methods are characterized by their various mathematical approximations to its solution. There are two major classes of electronic structure methods ... 

Electronic structure methods are aimed at solving the Schrodinger equation for a single or a few molecules, infinitely removed from all other molecules. Physically this corresponds to the situation occurring in the gas phase under low pressure (vacuum). Experimentally, however, the majority of chemical reactions are carried out in solution. Biologically relevant processes also occur in solution, aqueous systems with rather specific pH and ionic conditions. Most reactions are both qualitatively and quantitatively different under gas and solution phase conditions, especially those involving ions or polar species. Molecular properties are also sensitive to the environment. 

Electronic structure methods are aimed at solving the Schrodinger equation for a single or a tew molecules, infinitely removed front all other molecules. Physically... 

The basis set convergence error is separate from the accuracy of the particular electronic structure method used to solve the Schrodinger equation (Hartree-Fock, singles and doubles configuration interaction, second-order perturbation theory, etc.). The methods error is defined by... 

To complete the list of errors involved in the solution of the electronic Schrodinger equation, we must also define the error associated with a given calculation, i.e., a given choice of electronic structure method and basis set. The calculational error is given by... 

The Variation Principle is the main point of departure all questions of symmetry, approximation etc. are judged from the point of view of their likely effect on the variational form of the Schrodinger equation. We attempt to take the minimal basis AO expansion method as far as possible while remaining within a family of well-defined conceptual models of the electronic structure which is theoretically and numerically underpinned by the variation principle. 

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