Chapter 6

Foundation of Multi-Configurational Quantum Chemistry

Giovanni Li Manni

Giovanni Li Manni

Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

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Kai Guther

Kai Guther

Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

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Dongxia Ma

Dongxia Ma

Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

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Werner Dobrautz

Werner Dobrautz

Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

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First published: 23 November 2020
Citations: 7

Summary

After introducing the fundamental goals—solving the Schrödinger equation—and the associated problems of quantum chemistry, we describe the basics of multiconfigurational approaches to solve the latter. As an exact—or full configuration interaction (FCI)—solution, even in a finite basis set, comes with an exponential scaling cost, the importance of an efficient representation in either a Slater determinant or configuration state function basis is discussed. With the help of such an efficient representation it is possible to apply iterative techniques, like the Davidson method, to obtain the exact solution of the most important low-lying eigenstates of the Hamiltonian, describing a quantum chemical system. As the exponential scaling still restricts these direct approaches to rather modest system sizes, we discuss in depth the multi-configurational extension of the self-consistent field method (MCSCF), which captures the static correlation of a problem and serves as a starting point for many more elaborate techniques. In addition, we present the complete active space approach—and the generalized and restricted extensions thereof—, which allows an intuitive construction of the chemically important reference space and enables a much more compact description of the important degrees of freedom of a problem at hand. We explain the state-specific and state-averaged approaches to obtain excited states within the MCSCF method and conclude this chapter by presenting stochastic Monte-Carlo approaches to solve the FCI problem for unprecedented active space sizes.

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