Spin-flip approach

Spin-flip approaches used a reference. Computed at r(F-F) = 100 bohr. Tleference 32. Reference 12. 

J.S. Sears, C.D. Sherrill, A.I. Krylov, A spin-complete version of the spin-flip approach to bond breaking What is the impact of obtaining spin eigenfunctions J. Chem. Phys. 118 (2003) 9084. 

Dirac equation. Leading-order Lorentz violating energy shifts 61/12 and di/34 can be obtained from a Hamiltonian using perturbation theory and relativistic two-fermion techniques. For our observed transitions at the strong magnetic field of 1.7 T, dominantly only muon spin flip occurs so the energy shifts are characterized by the muon parameters alone of the extended theory. The results of this approach are [4] ... 

Harris and Jones also presented results for spin-flip energies and for ionization potentials. Again, trends are reasonably well interpreted. For the spherical GL potential used, the energy to flip an s spin is overestimated for all of the atoms except Ni and Cu, the largest discrepancies, of about 0.5 eV, occurring near the middle of the series. On the other hand, the spin-flip energy for a d electron in Cr " is underestimated in this approach by about 1 eV. Errors in ionization potentials are about 0.4 eV. 

This approach can be easily generahzed to the n spin-flip process and therefore the temperature dependence of ton is obtained by ... 

The relaxation of the dimerized chain can also be described by a stochastic approach. Assuming single spin-flips and an alternation of exchange interactions 7i and h along the chain, one obtains [27,28] ... 

In order to see the difference in the two approaches, below I focus on the excitation energies, AE, of the Be states that are discussed here. The nice thing about atomic spectra of this type is that there is accurate experimental information with which one can compare the results of a theoretical method (See, Tables of NIST, USA, in the WWW). Specifically, I compare the AE from the Be Fermi-sea energies for which cancellations on subtraction of total energies are expected, with those obtained from methods that have used one of the known basis sets. I consider two such publications. The first is in 1986 by Graham et al. [105] where a (9s9p5d) contracted GTO basis (61 basis functions) was used for different types of computations. I keep the full Cl (FCI) results. The second is in 2003 by Sears, Sherrill and Krylov [106], who studied aspects of "spin-flip" methods and compared them with FCI using the same basis set, which is a 6-31G. 

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