Orbitals sizes

For molecular systems with up to thirty valence electrons, an amplitude of =t0.1 a.u. was chosen for the contour level. For systems with more than thirty valence electrons it was necessary to reduce this value to 0.08 a.u. to maintain the orbital size at a comfortable visual level. The molecular orbitals were normalized to an occupancy... 

Two JC Component System. Vahdation of Orbital Size Effect... 

S Two K Component System. Validation of Orbital Size Effect on the Magnitude of Facial Selectivity... 

The orbital size of an atomic electron (top) is correlated with its orbital energy, just as the bounce height of a tennis ball is correlated with its kinetic energy (bottom). 

Summarizing, the principal quantum number (n) can have any positive integral value. It indexes the energy of the electron and is correlated with orbital size. As U increases, the energy of the electron increases, its orbital gets bigger, and the electron is less tightly bound to the atom. 

Just as orbital size ( ) limits the number of preferred axes (Jit/ ), the number of preferred axes (/) limits the orientations of the preferred axes (ttli). When / — 0, there is no preferred axis and there is no orientation, so W = 0. One preferred axis (7=1) can orient in any of three directions, giving three possible values for mi +l, 0, and-1. Two preferred axes (/ = 2) can orient in any of five directions, giving five possible values for +2, +1, 0, -1, and -2. Each time / increases in value by one unit, two additional values of / become possible, and the number of possible orientations increases by two ... 

How large are orbitals Experiments that measure atomic radii provide information about the size of an orbital. In addition, theoretical models of the atom predict how the electron density of a particular orbital changes with distance from the nucleus, r. When these sources of information are combined, they reveal several regular features about orbital size. 

As an example, Figure 7-21 shows that the — 3 orbitals of the copper atom have their maximum electron densities at similar distances from the nucleus. The same regularity holds for all other atoms. The quantum numbers other than tt affect orbital size only slightly. We describe these small effects in the context of orbital energies in Chapter 8. 

We know that the most important factor for orbital size is the value of tt and that small orbitals screen better than large ones, so the screening sequence makes sense. 

Accessible electrons are called valence electrons, and inaccessible electrons are called core electrons. Valence electrons participate in chemical reactions, but core electrons do not. Orbital size increases and orbital stability decreases as the principal quantum number n gets larger. Therefore, the valence electrons for most atoms are the ones in orbitals with the largest value of ti. Electrons in orbitals with lower tl values are core electrons. In chlorine, valence electrons have ft = 3, and core electrons have — 1 and — 2. In iodine, valence electrons have a = 5, and all others are core electrons. 

Although they both have the s p valence configurations, selenium s least stable electrons are in orbitals with a larger ft value. Orbital size increases with tt. Selenium also has a greater nuclear charge than sulfur, which raises the possibility that nuclear attraction could offset increased tt. 

C09-0115. The H—O—H bond angle in a water molecule is 104.5°. The H—S—H bond angle in hydrogen sulfide is only 92.2°. Explain these variations in bond angles, using orbital sizes and electron-electron repulsion arguments. Draw space-filling models to illustrate your explanation. 

Another influence on the magnitude of the crystal field splitting is the position of the metal in the periodic table. Crystal field splitting energy increases substantially as valence orbitals change from 3 d to 4d to 5 d. Again, orbital shapes explain this trend. Orbital size increases as n increases, and this means that the d orbital set becomes... 

Before investigating the qualitative concepts of the VSEPR model it is worth noting that the details of the interactions between the electron pairs have been ascribed to a size-Pauli exclusion principle result . But objects do not repel each other simply because of their sizes (i.e. interpenetrations) only if the constituents of the objects interact is any interaction possible10). If we are to use the idea of orbital size at all we must avoid the danger of contrasting a phenomenon (electron repulsion) with one of its manifestations (steric effects). The only quantitative tests which we can apply to the VSEPR model are ones based on the terms in the molecular Hamiltonian specifically, electron repulsion. 

Schrodinger s equation required the use of quantum numbers to describe each electron within an atom corresponding to the orbital size, shape, and orientation in space. Later it was found that one needed a quantum number associated with the electron spin. 

The relationship between orbital size and quantum number for the hydrogen atom. 

As n increases, the electron s energy increases and orbital size increases. 

Similarly, one may ask how AF110111 would be expected to change in the series C—F, C—Cl, C—Br, and C—I or the series HF, HC1, HBr, and HI. The situation is simpler for these series, since both the electronegativity and orbital size vary but have the same effect on the bond dissociation energy. Variation in orbital size is approximately pro-... 

The numerical results are consistent with the result of an experiment in which the ion cyclotron orbit sizes of a methane (CHi, ) and benzene (C6H6 ) mixture of ions were varied. In the control experiment, the two ions were excited by low amplitude consecutive RF burst pulses of varied time. The signal ratio was essentially constant over the range of orbits for which signals were detectable. In contrast, for a chirp from 10 kHz to 2 Mhz at 2.094 kHz/usee of varied amplitude, the abundance ratio of CH t/C6H6t decreased from about 90 to about 10 as the orbit size was increased, indicating loss of the lighter ion. 

An example of the complexity of the frequency variations in the cubic cell is given in the extreme by the splitting of a peak into a doublet for ions excited to very large orbits. A similar phenomenon was noted by Marshall (47). In the example reported here, the ions were excited by a 0.385 volt peak-to-base RF burst in a 0.0254 m cubic cell with a 1 volt trap and a magnetic field of 1.2 T. Two maxima are discernible for ion-cyclotron-orbit sizes larger than the noptimaln orbit size at about 760 psec excitation time. Local centroids are measurable one increases by ca. 50 Hz and the other... 

The observations that there is an "optimum" orbit size and that peaks split for orbits not too much larger than the optimum orbit suggest that the optimum orbit occurs because of special circumstances. One possible circumstance is a coincidence of frequencies for ions with low and high z-mode amplitudes so that if there are mass discriminating differences in the way the ions populate the trap or in the way ions are excited, then systematic mass measurement errors can be expected. Excitation of the cyclotron mode does produce a spread in cyclotron radii, and mass discriminating z-mode excitation is discussed elsewhere in this chapter. Thus, frequency variations that cause systematic mass errors are due in part to trap field inhomogeneities. These effects are evident at low ion populations and may be due in part to excitation induced ion cloud deformation which increases with ion number. 

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