Atomic and molecular orbitals a) What do graphical representations of orbitals t
ID: 996112 • Letter: A
Question
Atomic and molecular orbitals
a) What do graphical representations of orbitals typically show? How is this related to the statements often found in general chemistry textbooks about a large fraction of the electron density being enclosed in some three-dimensional surfaces ?
b) For many-electron atoms and molecules, why do we describe the electronic structure in terms of orbitals. Shouldn’t we just solve the Schrödinger equation and use the many-electron wavefunction instead?
c) In the context of orbital theory as taught in this course, what does ‘orbital occupation’ really mean?
d) State the Pauli principle in its most general form, and its consequences in molecular orbital theory.
e) Is there a unique set of molecular orbitals for a given molecule? Give a reason for your answer, not just Yes or No.
f) Describe an electronic configuration that cannot be correctly described with a single Slater-determinant wavefunction
g) In molecular orbital calculations based on the self-consistent field (SCF) concept, how are the orbital energies and the total energy related?
h) Describe an example for an unintuitive outcome when you change the occupation numbers of the orbitals of a system.
Explanation / Answer
What do graphical representations of orbitals typically show? How is this related to the statements often found in general chemistry textbooks about a large fraction of the electron density being enclosed in some three-dimensional surfaces ?
answer: They represent boundary surfaces. From the nucleus to that surface the probability to find the electron is about 90 %, this probability changes radial and angular in the inner volume, but it is only an integrated probability in all the volume.
b) For many-electron atoms and molecules, why do we describe the electronic structure in terms of orbitals. Shouldn’t we just solve the Schrödinger equation and use the many-electron wavefunction instead?
The Schrödinger equation can only being solved for atoms of 1 electrons due the three bodies problem. For 1 e- atoms the solution of the equation produce the orbitals and we used them as an aproximation in multi electronic atoms.
c) In the context of orbital theory as taught in this course, what does ‘orbital occupation’ really mean?
means the distribution of the electrons in the different orbitals according to pauli principle, energy minimization principles and hund rule.
d) State the Pauli principle in its most general form, and its consequences in molecular orbital theory.
That principle states that an electron has an unique set of quantum numbers, this means that for two electrons occupy the same orbital their spins must be paired.
e) Is there a unique set of molecular orbitals for a given molecule? Give a reason for your answer, not just Yes or No.
No, because in first approach you can use any combination of orbitals to create the molecular orbital, that not imply that the initial set is the energetically optimum. Generally the atomic orbitals are taken as first approach
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