Self-consistent field, spin density

Self-consistent field, spin density, 43 183 Self-dissociation reactions, sulfuric acid and, 1 387-389... 

The computational model capable of yielding accurate spin-spin coupling constants is the multiconfigurational self-consistent field (MCSCF) model, and before the advent of density functional theory, spin-spin coupling constants in small systems were often... 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

In this substection we will shortly discuss the computational methods used for calculation of the spin-spin coupling constants. Two main approaches available are ab initio theory from Hartree-Fock (or self-consistent field SCF) technique to its correlated extensions, and density function theory (DFT), where the electron density, instead of the wave function, is the fundamental quantity. The discussion here is limited to the methods actually used for calculation of the intermolecular spin-spin coupling constants, i. e. multiconfigurational self consistent field (MCSCF) theory, coupled cluster (CC) theory and density functional theory (DFT). For example, the second order polarization propagator method (SOPPA) approach is not... 

The inter-fragment coupling occurs through the interaction of their atomic multipoles which are determined from the fragment electron densities within the self-consistent-field (SCF) procedure. The a-spin Fock matrix for region A with inclusion of this coupling is... 

AMI Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF) and the Self-consistent Field Diradicals Electronic Wavefunctions Analysis G2 Theory M0ller-Plesset Perturbation Theory Natural Bond Orbital Methods Spin Contamination. 

As a matter of fact, as in the Hartree-Fock (HF) scheme, the KS equation is a pseudo-eigenvalue problem and has to be solved iteratively through a self-consistent field procedure to determine the charge density p(r) that corresponds to the lowest energy. The self-consistent solutions 4>ia resemble those of the HF equations. Still, one should keep in mind that these orbitals have no physical significance other than in allowing one to constitute the charge density. We want to stress that the DFT wavefunction is not a Slater determinant of spin orbitals. In fact, in a strict sense there is no A -electron wavefunction available in DFT. ... 

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60]. 

---