How are molecular orbitals determined?

Answer 1

It's a bit unclear what you're asking for, but I assume you mean how do we determine which molecular orbitals (MOs) are formed from which atomic orbitals (AOs).

Let's say we looked at methane.

Carbon uses its #2s# and #2p# AOs to bond with hydrogen's #1s# AO. As it prepares to bond with hydrogen, carbon allows its #s# and #p# orbitals to mix, slightly lowering their energy levels, and creating a hybridized #sp^3# MO from the #2p_x#, #2p_y#, #2p_z#, and #2s# orbitals, which explains why it's called #sp^3# (#1# #s#-type and #3# #p#-type AOs), and also why it is said to have roughly 75% #p# character and 25% #s# character.

The hybridization in carbon can be written out roughly like this:

When the orbital overlap occurs, carbon shares its #sp^3# electrons with hydrogen's #1s# electron to make one #sigma# bond.

The overlap between a #1s# and a #2p# looks like this diagram I drew below (suppose the #2p_x# orbital is on the x-axis):

(The carbon is positioned where the #sp^3# node is.)

The electron density increases where the #2p_("x/y/z")# and the #1s# have the same phase (#+#), and so that lobe gets bigger (think principle of superposition for standing waves).

Since a bond must be favorably made to be made often, the resulting MO must support a greater electron density in order to make the bond fairly strong (and therefore stable). Therefore, it is a bonding MO (antibonding MOs are due to opposite-phase overlap, decreasing electron density by creating nodes, and working against bonding, hence "anti").

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Answer 2

Molecular orbitals are determined using computational methods like quantum mechanics calculations or approximations such as the Hartree-Fock method or Density Functional Theory. These methods solve the Schrödinger equation for the system, providing information about the spatial distribution and energy levels of the molecular orbitals. Additionally, experimental techniques like spectroscopy can provide insight into molecular orbital structures.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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