Spin-unrestricted

Choose LHH(spin Unrestricted Hartree-Fock) or RHF (spin Restricted Ilartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-sh el I and closed-shell calcii lation s an d RHF for cUised-shell calculation s on ly, Th e closed-shell LHFcalculation may be useful for studyin g dissociation of m olectilar system s. ROHF(spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ah initio calculations). 

UFF (universal force field) a molecular mechanics force field unrestricted (spin unrestricted) calculation in which particles of different spins are described by different spatial functions VTST (variational transition state theory) method for predicting rate constants... 

Open shell systems—for example, those with unequal numbers of spin up and spin down electrons—are usually modeled by a spin unrestricted model (which is the default for these systems in Gaussian). Restricted, closed shell calculations force each electron pair into a single spatial orbital, while open shell calculations use separate spatial orbitals for the spin up and spin down electrons (a and P respectively) ... 

In a crystal-field picture, the electronic structure of iron in the five-coordinate compounds is usually best represented by a (d yf idyz, 4cz) ( zO configuration [66, 70], as convincingly borne out by spin-unrestricted DFT calculations on the Jager compound 20 [68]. The intermediate spin configuration with an empty d 2 yi orbital in the CF model, however, has a vanishing valence contribution to the... 

Both Fe(ll)(TPP) and Fe(II)(OEP) have positive electric quadrupole splitting without significant temperature dependence which, however, cannot be satisfactorily explained within the crystal field model [117]. Spin-restricted and spin-unrestricted Xoi multiple scattering calculations revealed large asymmetry in the population of the valence orbitals and appreciable 4p contributions to the EFG [153] which then was further specified by ab initio and DFT calculations [154,155]. 

Just as in the unrestricted Hartree-Fock variant, the Slater determinant constructed from the KS orbitals originating from a spin unrestricted exchange-correlation functional is not a spin eigenfunction. Frequently, the resulting (S2) expectation value is used as a probe for the quality of the UKS scheme, similar to what is usually done within UHF. However, we must be careful not to overstress the apparent parallelism between unrestricted Kohn-Sham and Hartree-Fock in the latter, the Slater determinant is in fact the approximate wave function used. The stronger its spin contamination, the more questionable it certainly gets. In... 

Pople, J. A., Gill, P. M. W., Handy, N. C., 1995, Spin-Unrestricted Character of Kohn-Sham Orbitals for Open-Shell Systems , Int. J. Quant. Chem., 56, 303. 

In the case of paramagnetic complexes their experimental magnetic parameters are determined by computer simulation of the powder spectra [59], Together with the corresponding calculated values, obtained using a relativistic spin-unrestricted ZORA approach, they all are collected in Table 2.8. 

Equation (4.34) is sometimes called the spin-unrestricted HFA, because it allows solutions in which self-consistent adatom orbitals of opposite spin have different energies... 

An initial equilibrium structure is obtained at the Hartree-Fock (HF) level with the 6-31G(d) basis [47]. Spin-restricted (RHF) theory is used for singlet states and spin-unrestricted Hartree-Fock theory (UHF) for others. The HF/6-31G(d) equilibrium structure is used to calculate harmonic frequencies, which are then scaled by a factor of 0.8929 to take account of known deficiencies at this level [48], These frequencies are used to evaluate the zero-point energy Ezpe and thermal effects. 

Apart from the selection of basis set and correlation procedure, an additional consideration arises in open-shell systems because of the presence of one or more unpaired electrons. This leads to treatments that are referred to as spin-restricted (R), spin-unrestricted (U), and spin-projected (P). 

It has been argued [12] that DFT calculations on open-shell systems should always be performed with spin-unrestricted methods. However, it is still of practical interest to compare the performance of procedures such as UB3LYP and RB3LYP in thermochemical predictions [13]. 

Several of the methods referred to in this chapter use the URCCSD(T) procedure in which a spin-unrestricted CCSD(T) calculation is performed on a high-spin RHF reference wavefunction, as implemented in the MOLPRO program. H. J. Werner, P. J. Knowles, R. D. Amos, A. Bemhardsson, A. Beming, P. Celani, D. 

Figure 5. Ethylene torsion, DZP basis. All curves are shifted such that the energy at 0 is zero. The spin-flip curves do not exhibit an unphysical cusp and are closer to the reference TC-CISD curve than the corresponding spin-restricted and spin-unrestricted models.

Here a is an adjustable parameter, usually determined by comparing Hartree-Fock and Xa atomic calculations. In the spin-unrestricted version, the spin-up and spin-down orbitals are distinct, so that in general the resulting wavefunction is not a spin eigenfunction. 

Figure 1 shows the one-electron energies of iron(II) porphine in both spin-restricted and spin-unrestricted (different orbitals for different spins) form. The geometry used has a planar porphine with an Fe-N distance of 2.01 A and no axial ligands. This calculation assumes a high-spin quintet state with the configuration (dxy) ... 

In this chapter, we later consider spin-polarized systems. One avenue of approach is to apply the spin unrestricted formalism, where SOs have different spatial orbitals for different spins. However, this procedure can introduce important spin contamination effects through the last term of Eq. (27) since the overlap matrix (5. These effects can be avoided by the use of spin-restricted theory. In this case only a single set of orbitals is used for a and / spins. 

Due to the spin polarization effect, the magnetic orbitals can be difficult to identify from a spin-unrestricted calculation. Since the total energy of a Kohn—Sham determinant is invariant under unitary transformations between the spin-up orbitals among each other and spin-down orbitals among each other, one can arrange each spin-up orbital to overlap at most with each spin-down orbital on the basis of the corresponding orbital transformation (COT) (88—90). Then, the molecular orbitals (MOs) are ordered into pairs of maximum similarity between spin-up and spin-down orbitals and can be separated into three groups (i) the MOs with spatial overlap close to one (doubly occupied MOs),... 

The simplest approximate wavefunction for an open-shell molecule is the spin-unrestricted Hartree-Fock function... 

An initial equilibrium structure is obtained by geometry optimization at the Hartree-Fock (HF) level with the 6-31G(d) basis.68 69 Spin-restricted Hartree-Fock (RHF) theory is used for singlet states and spin-unrestricted Hartree-Fock theory (UHF) for others. 

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