Degenerate mixing

Orbital mixing. Simple spherical orbitals are shown to illustrate the concept. A. The first-order, degenerate mixing. B. The second-order, nondegenerate mixing. 

Joo T and Albrecht A C 1993 Electronic dephasing studies of molecules in solution at room temperature by femtosecond degenerate four wave mixing Chem. Phys. 176 233—47... 

For a steady-state ciystallizer receiving sohds-free feed and containing a well-mixed suspension of ciystals experiencing neghgible breakage, a material-balance statement degenerates to a particle balance (the Randolph-Larson general-population balance) in turn, it simplifies to... 

At the start, the relative energies of the four orbitals are represented in Fig. 33. The correct procedure requires that we first interact the degenerate orbitals nj and n2, and then mix the resulting combinations with orcc and significantly different energies. This is true even though the overlap between n and n2 is extremely small, because n, and n2 are symmetry-equivalent orbitals. The... 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

Conventional presentaticsis of DFT start with pure states but sooner w later encounter mixed states and d sities (ensemble densities is the usual formulation in the DFT literature) as well. These arise, for example in formation or breaking of chemical bonds and in treatments of so-called static correlation (situations in which several different one-electron configurations are nearly degenerate). Much of the DFT literature treats these problems by extension and generalization from pure state, closed shell system results. A more inclusively systematic treatment is preferable. Therefore, the first task is to obtain the Time-Dependent Variational Principle (TDVP) in a form which includes mixed states. 

---