Physical Chemistry , 1st ed.

Figure 12.9 shows a representation of the energies of the initial basis func- tions compared to the approximate energies for the ...

part of the overall wavefunction, so the complete wavefunction is the sum of many simple parts. Computers are also useful in per ...

electron and nucleus 2, and a repulsive electrostatic potential between nucleus 1 and nucleus 2. The complete Hamiltonian for H ...

where ^2 p 1 and ^2 p 2 are the Laplacian operators for the two nuclei (which are just protons) and Eel(R) is the electronic p ...

electronic wavefunctions are. Electrons in molecules are described approxi- mately with orbitals just like electrons in atoms ar ...

Because the molecular orbitals must be normalized, we can determine ex- pressions for c 1 and c 2. Normalizing the first equatio ...

With the substitutions, the expressions for the average energies become E 1  H 1 11   S H 12 ^12 E 2  H 1 22   S H 12  ...

Example 12.14 Using R1.32 Å, evaluate S 12 ,H 12 ,E 1 ,E 2 , and the wavefunctions for H 2 . Use 13.60 eV as the value for th ...

nodal surface between the nuclei; the electron’s probability of being at that point is exactly zero. If all atomic orbitals were ...

spin-orbital wavefunction must be antisymmetric with respect to exchange of the two electrons. Recall that the wavefunction for ...

2 selectrons will occupy the g 2 sbonding molecular orbital (and have oppo- site spins). A molecular orbital diagram for Li 2 i ...

erate antibonding orbitals. (In filling degenerate orbitals, Hund’s rules still apply.) Because of their symmetry properties, bo ...

and variation theory are two tools used in quantum mechanics to approxi- mate the behavior and energy of multielectron systems. ...

12.14 Summary 415 2 p 2 s 2 p 2 s NONO 1 s 2 p HFHF 2 s Figure 12.24 Molecular orbitals of the heteronuclear diatomic molecules ...

12.2 Spin 12.1.In the Stern-Gerlach experiment, silver atoms were used. This was a good choice, as it turned out. Using the elec ...

ground state of the anharmonic oscillator in terms of c, as- suming that ˆHH° is the ideal harmonic oscillator Hamiltonian opera ...

12.12 & 12.13 Molecular Orbitals; More Diatomic Molecules 12.39.Explain how we know that the first in equation 12.43 is the ...

13 419419 S YMMETRY IS ONE OF THE MOST POWERFUL TOOLS that can be ap- plied to quantum mechanics and wavefunctions. Most people ...

describe molecular wavefunctions more easily (like the example of the quadri- lateral and square above). Symmetry considerations ...

elements such that operation on that molecule by the corresponding symme- try operations will produce a “new” orientation in spa ...