Physical Chemistry , 1st ed.

Example 12.5 The third electron in Li goes into the 2sorbital. Assuming a (re)normaliza- tion constant of 1/ 6 , construct a p ...

and 1, so that the possible subshells are 2sand 2p. Because of the slightly higher energy of the 2psubshell, the electrons occ ...

Written as a determinant, this wavefunction is indeed antisymmetric. If the determinant were evaluated, it would expand into 24 ...

be the only factor determining the order of orbital occupation. But in multi- electron atoms, there is an additional factor. Not ...

the order in which orbitals are filled by electrons. Perhaps the most common is shown in Figure 12.6. This ordering of orbitals, ...

12.6 Perturbation Theory 387 H1s^1 He 1s^2 Li 1s^22 s^1 Be 1s^22 s^2 B1s^22 s^22 p^1 C1s^22 s^22 p^2 N1s^22 s^22 p^3 O1s^22 s^22 ...

That does not mean that there is no understanding of, or recourse for, such systems. Nor does it imply that quantum mechanics is ...

where E(0)is the average energy of the ideal or model system (that is, an eigenvalue energy, usually) and E(1)is the first-o ...

a.Using perturbation theory, estimate the average energy of a particle having mass mand whose motion is described by the lowest- ...

real (0)(1) (12.18) It should be understood by now that there is not just one wavefunction for a model system. There are a l ...

Using equation 12.21, the nth real wavefunction n,realis written as n,realn(0) m^  ( E m ( n ( 0 0 ) ) )Hˆ   E  m (0 ...

Solution a.The system looks like this: where the sloped line indicates the true bottom of the box. b.In order to determine a 2 , ...

For a cyanide species where the mass is me,k 1 10 ^7 kgm/s^2 , and a 1.15 Å (that is, 1.15 10 ^10 m), we can evaluate th ...

meters, and then the expression is minimized with respect to those parameters. In calculus terms, if the energy is some expressi ...

Example 12.11 shows how variation theory works with a variable that al- lows one to minimize the energy of a system. It uses the ...

The total energy of the helium atom is therefore Etrial 2   8 Z   (^20) 2 h e 2 (^4)   8 Z 1 8 0 Z  8  e (^ ...

12.8 Linear Variation Theory Computer-assisted variation theory is especially powerful when there are a large number of variable ...

The minimization condition represented by equation 12.26 must now be fulfilled according to variation theory. Because of the sub ...

determinable.) In evaluating this determinant one will get a polynomial of or- der n, in which the highest power ofEwill be En. ...

Solution According to equation 12.31, the nontrivial solution of the simultaneous equations found by minimizing the energy will ...