the configuration (Q2s)2 (Q2s*)2 (pie2py)1 (pie2px)1 is the molecular orbital description for the ground state of:
Li2 (+)
B2
C2
Be2
B2 (-2)
To determine the molecular orbital description for each molecule, we need to understand the molecular orbital (MO) diagram for each molecule and identify the number of electrons present in the system.
First, let's start with Li2(+):
Li2(+) has one more electron compared to the neutral Li2 molecule. The neutral Li2 MO diagram has a total of 8 electrons, so Li2(+) will have 9 electrons.
Using the Aufbau principle, we start filling the MO diagram with the lowest energy orbitals first. Based on the given molecular configuration, (Q2s)2 (Q2s*)2 (pie2py)1 (pie2px)1, we can conclude the following:
- (Q2s)2 represents two electrons in the σ2s bonding MO.
- (Q2s*)2 represents two electrons in the σ2s* anti-bonding MO.
- (pie2py)1 represents one electron in the π2py bonding MO.
- (pie2px)1 represents one electron in the π2px bonding MO.
Combining these electron configurations, we have:
- 2 electrons in σ2s bonding MO
- 2 electrons in σ2s* anti-bonding MO
- 1 electron in π2py bonding MO
- 1 electron in π2px bonding MO
This gives us a total of 6 electrons. Since Li2(+) has 9 electrons, the remaining 3 electrons are placed in the remaining available orbitals, which are the π2py* anti-bonding MO and the π2px* anti-bonding MO. Therefore, the molecular orbital description for Li2(+) is (Q2s)2 (Q2s*)2 (pie2py)1 (pie2px)1 (pie2py*)1 (pie2px*)1.
Moving on to B2:
B2 is a neutral molecule, so it has a total of 10 electrons. Based on the given molecular configuration, we can again conclude:
- (Q2s)2 represents two electrons in the σ2s bonding MO.
- (Q2s*)2 represents two electrons in the σ2s* anti-bonding MO.
- (pie2py)1 represents one electron in the π2py bonding MO.
- (pie2px)1 represents one electron in the π2px bonding MO.
Combining these electron configurations, we have:
- 2 electrons in σ2s bonding MO
- 2 electrons in σ2s* anti-bonding MO
- 1 electron in π2py bonding MO
- 1 electron in π2px bonding MO
This gives us a total of 6 electrons. Since B2 has 10 electrons, the remaining 4 electrons are placed in the remaining available orbitals, which are the π2py* anti-bonding MO and the π2px* anti-bonding MO. Therefore, the molecular orbital description for B2 is (Q2s)2 (Q2s*)2 (pie2py)1 (pie2px)1 (pie2py*)2 (pie2px*)2.
Using a similar approach, you can determine the molecular orbital descriptions for C2, Be2, and B2(-2) by considering their respective electron configurations and molecular orbital diagrams.