Configuration state functions , direct

All necessary formulas for Hamiltonian matrix elements in the table-CI method are presented in computationally amenable form. In contrast to the initial variant of the method, as developed by Buenker, the obtained formulas allow one to avoid intermediate calculations of separate determinantal matrix elements but instead allows calculation of the Hamiltonian matrix elements directly in the basis of configuration state functions (CSFs). The recently suggested variant of a genealogical scheme for constructing CSFs in the context of table-CI is used, which results in reducing the number of contributions to typical matrix elements by approximately a factor of 2. 

Example 1.3 Entropy and distribution of probability Entropy is a state function. Its foundation is macroscopic and directly related to macroscopic changes. Such changes are mostly irreversible and time asymmetric. Contrary to this, the laws of classical and quantum mechanics are time symmetric, so that a change between states 1 and 2 is reversible. On the other hand, macroscopic and microscopic changes are related in a way that, for example, an irreversible change of heat flow is a direct consequence of the collision of particles that is described by the laws of mechanics. Boltzmann showed that the entropy of a macroscopic state is proportional to the number of configurations fl of microscopic states a system can have... 

Eq. (8.94) represents an exact expression for the quantum mechanical state of a many-electron system. Note that the expansion coefficients Cj of the N-particle basis states are directly related to the expansion coefficients of the one-particle states. It is sufficient to know either of them (and this fact is related to the observation made below that a full configuration interaction wave function does not require the optimization of orbitals see the next section). 

---