Electronic Correlation

Dear Colleagues,

Electronic correlation arises from the quantum nature of electrons. Electrons interact with each other through Coulomb repulsion, and their motion, which in quantum theory cannot be exactly studied, is influenced by mutual relationships. The so-called Coulomb correlation, referring to the independent particle model of the Hartree–Fock theory, plays a big role in this. Consequently, the exact solution of the non-relativistic Schrödinger equation of the electronic system of interest is of great significance. Since the seminal work of Wigner, who first introduced the concept of “correlation energy” for an electron gas, a huge number of developments have been carried out so far; however, the exact solution of Schrödinger equation still remains not possible in general. The search for a correct estimation of correlation energy has led to the development of methods that also include the calculation of properties, often related to the derivatives of energy with respect to external parameters, and of the two-particle density and related functions. The inclusion of electronic correlation then becomes very important for excited states whose wave function is more complex than that of the ground state. In this context, accurate computation can greatly support the interpretation and implementation of experiments. Correlation energy is normally conceived as the sum of two contributions, namely, dynamic and non-dynamic or static. The non-dynamic contribution is associated with the multi-determinant character of the ground state, and its inclusion is fundamental for the construction of energy surfaces. The dynamic contribution derives instead from the small contributions coming from the complementary space and assumes an important role in obtaining quantitative results.

Although the state-of-the-art has reached a high standard to date, there are at least three lines of development that can still allow for further improvement. First of all, the new computing architectures allow faster calculations and make more and more complex calculations available. Then, there is the need for the development of new computer codes in line with these innovations. Finally, the theory is important to find new methodological routes to design how to combine exact physics with such new computing resources.

Prof. Dr. Claudio Amovilli
Guest Editor

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