Broken-symmetry method

Fe—S dimers, 38 443-445 map, four-iron clusters, 38 458 -functional theory, 38 423-467 a and b densities, 38 440 broken symmetry method, 38 425 conservation equation, 38 437 correlation for opposite spins and Coulomb hole, 38 439-440 electron densities, 38 436 exchange energy and Fermi hole, 38 438-439... 

In pursuit of suitable models and theories for the WOC manganese cluster, Noodleman and Hendrickson 140) have used LCAO Xa density function calculations, employing the broken symmetry method (see Section III,E,3), to calculate J(Mn Mn ) and J(Mn Mn ) values in the chloro-oxo cubane [Mn Mn sOsClYlOaCCHalg]. The /a/T behavior of this complex was different in detail from the others described earlier, and good agreement with was obtained using the Xa calculations, with parameter values of = 2.02, e/(Mn - -Mn ) = -t-19.3 cm", J(Mn - -Mn ) = -46.6 cm", and Sf = f. 

Table 1. shows the total energies obtained using the RHF method for 1. LCAO minimal basis set STO-IG for the sake of comparison with FSGO, 2. FSGO in its symmetric and broken symmetry solutions and, 3. LCAO minimal basis set STO-3G in order to allow a safer comparison with the quality of the subminimal basis used in the FSGO technique. The dissociation curves are given in Figure 1. 

Although P3 procedures perform well for a variety of atomic and molecular species, caution is necessary when applying this method to open-shell reference states. Systems with broken symmetry in unrestricted Hartree-Fock orbitals should be avoided. Systems with high multireference character are unlikely to be described well by the P3 or any other diagonal approximation. In such cases, a renormalized elec-... 

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. 

Lindgren et al. studied the excited state and phosphorescence of platinum(II) acetylides (5.9) with the DFT/B3LYP method [103], The calculated UV/Vis absorption spectra revealed that the orientation of the phenyl rings relative to the P-Pt-P axis has a strong correlation with the intensity of the absorption band. The broken symmetry phenomenon was also confirmed in the lowest triplet excited state, which leads to a OC-Ph bond on one side and a C=C=C bond on the opposing side. Quadratic response calculations of spin-orbit coupling showed that the intensity of the phosphorescence of these complexes arises mainly from the a—>n type T- l) transitions localized at the OC-Pt-P fragment, but not from the delocalized 7t—type transitions. The quadratic response calculations also reproduced an increase of xR from PEj to PE2 (5.9), which was also determined experimentally. 

In the majority of calculations, the RHF electron density shows (at molecular geometry close to the equilibrium) spatial symmetry identical with the point symmetry group (the nuclear configuration) of the Hamiltonian. But the RHF method may also lead to broken symmetry solutions. For example, a system composed of the equidistant H atoms uniformly distributed on a circle shows bond alternation, i.e. symmetry breaking of the BOAS type. ... 

To remove the BSSE we may consider the use of the basis set ft not only for ab but also for a and This procedure called the counter-poise method, was first introduced by Boys and Bernardi. Application of the full basis set ft when calculating a results in the wave function of A containing not only its own atomic orbitals, but also the atomic orbitals of the ( absent ) partner B, the " ost orbitals (Fig. 13.3b). As a by-product, the charge density of A exhibits broken symmetry... 

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