Quantum mechanics field notes

We have previously defined the one-electron spin-density matrix in the context of standard HF methodology (Eq. (6.9)), which includes semiempirical methods and both the UHF and ROHF implementations of Hartree-Fock for open-shell systems. In addition, it is well defined at the MP2, CISD, and DFT levels of theory, which permits straightforward computation of h.f.s. values at many levels of theory. Note that if the one-electron density matrix is not readily calculable, the finite-field methodology outlined in the last section allows evaluation of the Fermi contact integral by an appropriate perturbation of the quantum mechanical Hamiltonian. 

A note of caution must be inserted at this point. It appears, at first sight, that there is a meaning that can be attached to the absolute phase of the field and to the phases of the molecular expectation values. However, it must be remembered that the phase of the molecular quantity is induced by the radiation field prior to the present time. Therefore all phases must be related to the phase of a previous pulse that synchronizes the molecular clock with the field clock. With this synchronization it is possible to understand how quantum mechanical interference between events induced in the past propagates and can be used to control energy and/or population transfer at a later time. 

Here we give an overview of the current status and perspectives of theoretical treatments of solvent effects based on continuum solvation models where the solute is treated quantum mechanically. It is worth noting that our aim is not to give a detailed description of the physical and mathematical formalisms that underlie the different quantum mechanical self-consistent reaction field (QM-SCRF) models, since these issues have been covered in other contributions to the book. Rather, our goal is to illustrate the features that have contributed to make QM-SCRF continuum methods successful and to discuss their reliability for the study of chemical reactivity in solution. 

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