# Quantum Chemistry - bonding

1. Jan 13, 2010

### sineontheline

I posted this elsewhere but I wasn't sure if physics people were lurking on the chem forum.

I want to understand MO and LCAO. The chapters in Levine weren't enough. Are there other books on bonding that people know of?

2. Jan 14, 2010

### DrDu

A classic is the book by Eyring, Walter and Kimball. A book with emphasis on the numerical implementation is Szabo and Ostlund (Dover Publications). However, I think that Levine is very clear on that subject so that you should get all the basics from it. What exactly didn't you understand?

3. Jan 14, 2010

### sineontheline

oh it wasn't that i didn't understand. its that he doesn't go into enough detail calculating the hydrogen ion. I looked up the orginal paper where it was derived. and when he starts talking about higher order bonds. i mean, i read it a while ago too. this is just what i just remember. but still aside from levine and mccuarie, i dont know of any other books that i can look at.

like you know how griffiths QM walks through calculations when hes deriving stuff. I want something like that.

4. Jan 15, 2010

### Modey3

The LCAO approach is a MO-theory approach to solving the SE atomic/molecular systems. The best books for learning MO-theory are Elementary Methods Of Molecular Quantum Mechanics (Magnasco) and Modern Quantum Chemistry Intro to Advanced Electronic Structure Theory (Szabo). What exactly don't you understand about the H2+ model?

modey3

5. Jan 17, 2010

### cgk

The best overview over current techniques in quantum chemistry is "Molecular Electronic-Structure Theory" by Helgaker, Jörgensen and Olsen.

About "LCAO": The term "LCAO" should not be understood too literally. "Atomic orbitals" in the modern terminology are simply any kind of local basis functions placed on atoms. Some of the functions in a basis set are actually built to resemble atomic orbitals (i.e., solutions of the Hartree-Fock equations for atoms), but most are not.

A "molecular orbital" is then a one-particle function satisfying some kind of mean-field one-particle Schrödinger equation (usually the Hartree-Fock equation, or the Kohn-Sham equation). Molecular orbitals are typically expanded as linear combination of non-orthogonal local basis functions like this:
$$\phi_r(\vec x) = \sum_{\mu} C^\mu_r \phi_\mu(\vec x),$$
where $$r$$ indexes the molecular orbitals (occupied or virtual) and $$\mu$$ the basis functions (which are often called atomic orbitals''), and $$C^\mu_r$$ is the orbital coefficient matrix.
This matrix is what is actually determined in a calculation of orbitals (like Hartree-Fock or Kohn-Sham).

If doing wave function methods, these orbitals are then used as input for a so called correlation calculation'' (e.g., some coupled cluster method), in which accurate wave functions are determined based on the Hartree-Fock wave function as a initial approximation to the electronic structure of the system.
The orbitals themselves usually do not have any strict physical interpretation. The most one can hope to get from them are (unimpressive) ionization energies via Koopman's theorem.