Shell closed versus open

Total spin den sity reflects th e excess probability of fin din g a versus P electrons in an open-shell system. Tor a system m which the a electron density is equal to the P electron density (for example, a closed-shell system), the spin density is zero. 

The relative efficiency of the two stiffeners is compared principally on the basis of the torsional resistance. The reason for the lower efficiency rating of the sandwich-blade stiffener is its low torsional resistance (and the bending stiffness is not high) and for the high efficiency of the hat stiffener is its high torsional resistance because of the basic open-versus closed-section stiffener issue. Stiffener torsional resistance affects the buckling load of a stiffened panel or shell as shown by Card and Jones [7-3]. 

In Gaussian, open shell calculations are requested by prepending the method keyword with a U (for unrestricted) similarly, closed shell calculations use an initial R (for example, RHF versus UHF, RMP2 versus UMP2 and so on). ... 

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

The open state of YFj/PAH capsules for dextran 2000 kDa was observed at pH = 5, but at pH = 10 aU inorganic/organic capsules were closed and the dextran molecules captured inside. Changing the pH again to an acidic medium resulted in an opening of the capsule shell and release of dextran molecules into the surrounding solution (Fig. 3.10). A similar capsule permeability versus pH dependence was pre-... 

For larger clusters much spectroscopic detail is lost, but measurements of the photoionization thresholds provide information concerning cluster ionization potentials. Sodium clusters show a relatively smooth decrease in ionization potential from 5.1 eV for the atom to 3.5 eV for the 14-atom cluster. This is still significantly above the 1.6-eV work function of bulk sodium. For the smaller clusters the odd sizes have a lower ionization potential than the neighboring even-sized clusters because of effects due to open versus closed shell configurations. Recently measurements have been made of the ionization potential of iron clusters up to 25 atoms. In this experiment the ionization potentials were bracketed by the use of various ionizing lasers. There is a decrease in the ionization potential from 7.870 eV for an iron atom to the 4.4-eV work function of the bulk metal, but the trend is by no means linear. Thus, the ionization potential of Fea is about 5.9 eV, while those of Fes and Fe4 are above 6.42 eV. Clusters in the range of 9-12 atoms have ionization potentials below... 

The high %-Pl (or low %-Pnl) exhibited by numerous open- and closed-shell species gives strong (but indirect) evidence that the resonance-free world described by 4 must closely resemble the full solution 4 of Schrodinger s equation, at least in some average or overall sense. Nevertheless, we expect that the small correction 4 will play the dominant role in certain chemical phenomena of interest, such as aromaticity. In this chapter, we wish to characterize L-type versus NL-type contributions to chemical properties in more direct fashion, seeking to understand the subtle influences of resonance-type delocalization corrections to the localized 4 -based picture. The NBO program includes a powerfiil array of perturbative and... 

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