Unrestricted models

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) ... 

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.

Unrestricted models, for example, the unrestricted Hartree-Fock (or UHF) model, are actually simpler and generally less costly than the corresponding restricted models, and because of this are much more widely used. Results for open-shell molecules provided in this book will make use of unrestricted models. 

Since the restricted model is quite nonlinear, it would be quite cumbersome to estimate and examine the loss in fit. We can test the restriction using the unrestricted model. For this problem,... 

The Wald test is based on the unrestricted model. The statistic is the square of the usual t-ratio,... 

Minimal END has also been applied to a model system for intramolecular electron transfer. The small triatomic system LiHLi is bent C2v structure. But the linear structure presents an unrestricted Haiti ee-Fock (TJHF) broken symmetry solution with the two charge localized stmctures... 

Although not strictly part of a model chemistry, there is a third component to every Gaussian calculation involving how electron spin is handled whether it is performed using an open shell model or a closed shell model the two options are also referred to as unrestricted and restricted calculations, respectively. For closed shell molecules, having an even number of electrons divided into pairs of opposite spin, a spin restricted model is the default. In other words, closed shell calculations use doubly occupied orbitals, each containing two electrons of opposite spin. 

Here, occ means occupied and virt means virtual. In the restricted Hartree-Fock model, each orbital can be occupied by at most one a spin and one (i spin electron. That is the meaning of the (redundant) Alpha in the output. In the unrestricted Hartree-Fock model, the a spin electrons have a different spatial part to the spin electrons and the output consists of the HF-LCAO coefficients for both the a spin and the spin electrons. 

A common feature of the Hartree-Fock scheme and the two generalizations discussed in Section III.F is that all physical results depend only on the two space density matrices p+ and p, which implies that the physical and mathematical simplicity of the model is essentially preserved. The differences lie in the treatment of the total spin in the conventional scheme, the basic determinant is a pure spin function as a consequence of condition 11.61, in the unrestricted scheme, the same determinant is a rather undetermined mixture of different spin states, and, in the extended scheme, one considers only the component of the determinant which has the pure spin desired. 

Kuhlmann-Wilsdorf [7] provided a new theoretical approach in which melting was ascribed to the unrestricted proliferation of dislocations at the temperature for which the free energy of formation of glide dislocation cores becomes negative. Several physicists have shown interest in this model which has not so far been accorded similar attention in the chemical literature. 

Fig. 11a and b. Decay of the alignment echo height as a function of the mixing time x2 for different motional mechanisms, a Tetrahedral jumps as a model for conformational changes b Diffusive motion, the solid lines correspond to unrestricted rotational diffusion, the dashed lines to diffusion restricted to an angular region of 8°. Note the strong dependence of the decay curves on the evolution time t, in case of diffusive motion... 

While the first three points improve the quantity and quality of information, in silico models benefit further from their unrestricted potential for customised presentation of results. This allows addressing aspects like individual preferences in information gathering, remote usage of models, interactive teaching and training, etc. 

In addition, since the HPHF wavefunction exhibits a two-determinantal form, this model can be used to describe singlet excited states or triplet excited states in which the projection of the spin momentum Ms=0. The HPHF approximation appears thus as a simple method for the direct determination of excited states (with Afs=0)such as the usual Unrestricted Hartree Fock model does for determining triplet excited states with Ms = 1. 

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]. 

In generalized Rouse models, the effect of topological hindrance is described by a memory function. In the border line case of long chains the dynamic structure factor can be explicitly calculated in the time domain of the NSE experiment. A simple analytic expression for the case of local confinement evolves from a treatment of Ronca [63]. In the transition regime from unrestricted Rouse motion to confinement effects he finds ... 

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