Broken-symmetry description

BS means broken symmetry DFT. See Refs. 56 and 59 for a description of the details of the calculations. 

The second approach to treating nondynamical correlation has an air of the ostrich about it ignore the spin symmetry of the wave function and use unrestricted Haxtree-Fock (UHF) theory as the single configuration description [7]. Since the UHF wave function comprises one spin-orbital for each electron, a molecular UHF wave function should dissociate to atomic UHF wave functions, for example. This is certainly not the case for spin-restricted Hartree-Fock (RHF) molecules and atoms in general. And there is an attractive simplicity about UHF — no active orbitals to identify, and so forth. However, where nondynamical correlation would be important in an RHF-based treatment, the UHF method will suffer from severe spin-contamination, while where nondynamical correlation is not important the RHF solution may be lower in energy than any broken-symmetry UHF solution, so potential curves and surfaces may have steps or kinks where the spin symmetry is broken in the UHF treatment. 

We also performed symmetry-adapted calculations for the hexuply bonded configuration. While the calculated values of and are reasonably close to the broken-symmetry results, the vibrational frequency is far too high and the anharmonicity far too low. In the final analysis, Cr2 should be regarded neither as a hexuply bonded nor as an antiferromagnetic dimer. Its correct description... 

The specific examples chosen in this section, to illustrate the dynamics in condensed phases for the variety of system-specific situations outlined above, correspond to long-wavelength and low-frequency phenomena. In such cases, conservation laws and broken symmetry play important roles in the dynamics, and a macroscopic hydrodynamic description is either adequate or is amenable to an appropriate generalization. There are other examples where short-wavelength and/or high-frequency behaviour is evident. If this is the case, one would require a more microscopic description. For fluid systems which are the focus of this section, such descriptions may involve a kinetic theory of dense fluids or generalized hydrodynamics which may be linear or may involve nonlinear mode coupling. Such microscopic descriptions are not considered in this section. 

If the surface tension is a function of position, then there is an additional term, daldx, to the right-hand side in the last equation. From the above description it can be shown that the equation of motion for the Fourier component C(y,0 of the broken symmetry variable is... 

Hamiltonian, but in practice one often begins with a phenomenological set of equations. The set of macrovariables are chosen to include the order parameter and all other slow variables to which it couples. Such slow variables are typically obtained from the consideration of the conservation laws and broken symmetries of the system. The remaining degrees of freedom are assumed to vary on a much faster timescale and enter the phenomenological description as random thermal noise. The resulting coupled nonlinear stochastic differential equations for such a chosen relevant set of macrovariables are collectively referred to as the Langevin field theory description. 

The current calculations, which are not yet routine, but which can now be performed on relatively simple computers, are based on DFT models for the description of the MOs of magnetic molecules, and on the so-called broken-symmetry approach, first suggested by Noodleman in 1981. ... 

As a consequence of their size, conjugated polymers exhibit some physical properties more associated with solid state physics than molecular physics. One of these concepts is broken symmetry ground states. Another is the quasi-particle description of excited states, widely used in solid physics, which is also appropri-... 

The most widely applied approximation to extract / within a single determinant description of the spin states is the so-called Broken Symmetry approach which uses two determinants ... 

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