Understanding LCAO Matrix Solutions for Molecules

In summary, LCAO (Linear Combination of Atomic Orbitals) can be used to construct the matrix for solving molecular orbitals in two cases: small molecules (such as H3, HF2-, H2O, CH4) and groups or parts of molecules with delocalized pi-systems. This can be done using Huckel theory, which is readily available but only applies to conjugated pi-systems in hydrocarbons. To generalize this method, one can use extended Huckel theory or freely available programs like YAeHMOP. Further explanations and resources can be found online.
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I would like to understand how LCAO may be used to construct the matrix to be solved for the molecular orbitals of two cases of molecules:

1) small molecules like H3 (or H3+, HF2-, H2O, CH4, etc.
2) groups or parts of molecules with delocalized pi-systems (including linear and cyclic hydrocarbons, crown ethers, carboxylate ions, etc.)

Huckel theory instruction is readily available, but it is only supposed to apply to the case of conjugated pi-systems in hydrocarbons, i.e. a special case of part 2 of what I'm looking for.

I wish to generalize this, to all very small molecules like the ones I listed, and also to delocalized pi-systems (within the framework of arbitrary larger molecules, which I presume need not be considered to affect that system much).

Can anyone suggest where I should read or look (Internet sources are welcome too) to find this explanation laid out?
 
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Related to Understanding LCAO Matrix Solutions for Molecules

1. What is LCAO matrix solution for molecules?

LCAO (Linear Combination of Atomic Orbitals) matrix solution is a method used to calculate the electronic structure and properties of molecules. It involves combining atomic orbitals of individual atoms to form molecular orbitals, which describe the distribution of electrons in a molecule.

2. How does LCAO matrix solution work?

LCAO matrix solution works by solving the Schrodinger equation for a molecule using a linear combination of atomic orbitals as a basis set. The coefficients of the atomic orbitals in the linear combination are determined by minimizing the energy of the system, resulting in a set of molecular orbitals that describe the electronic structure of the molecule.

3. What information can be obtained from LCAO matrix solution?

LCAO matrix solution can provide information on the electronic structure of a molecule, including the energy levels of the molecular orbitals, the distribution of electrons in the molecule, and the bonding and antibonding interactions between atoms.

4. What are the limitations of LCAO matrix solution?

LCAO matrix solution assumes that the molecular orbitals are composed of a linear combination of atomic orbitals, which may not always accurately describe the electronic structure of a molecule. Additionally, it does not take into account the effects of electron correlation, which can be significant in certain molecules.

5. How is LCAO matrix solution used in practical applications?

LCAO matrix solution is often used in computational chemistry to predict the properties of molecules and to aid in the design of new compounds. It can also be used to analyze experimental data, such as spectroscopic data, to gain insight into the electronic structure of a molecule.

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