Molecular orbital theory: basic elements (updated)

Term:molecular Orbital theory, MO

"Starting point" Schrodinger equation: operator/Hamiltonian – Orbital/wave function – intrinsic value

The "Hamiltonian" energy operator, in the absence of external field, is written into two parts of kinetic energy and potential energy, the total atomic energy (negative), the kinetic energy (negative) of the electron monomer, the repulsion potential energy (positive) between the nuclei, the repulsion potential energy (positive) between the electrons, and the nuclear electron attraction potential energy (negative) five items In the Born-oppenheimer approximation, the electron is able to achieve a balanced position instantaneously when the nucleus is shifted, that is, the nucleus can be regarded as fixed when discussing the electron motion. Given the position of the nucleus at the time of calculation (for example, a single point calculation or a search given by a potential energy surface), the energy of the nucleus is a definite value, and the coordinates (as the parameter of the electron motion as a single point/structure) are also determined values. At this point, we can write out the Schrodinger equation, which excludes only two of the atomic nuclei, and the remaining electrons-related three, which is known as the "net electron energy", plus that the nuclear machinery can become the total energy.

"Orbital" by using the Variational method to solve the Schrodinger equation, the molecular orbits can be derived from the linear combination of atomic orbitals (Lcao), wherein the combination coefficients are variational parameters. But it is obvious from a mathematical point of view that any function group can be used to combine the molecular orbits. (To be precise, it is preferable to have a set of eigen-equations/intrinsic vectors/vectors of the system Hamiltonian, but the base vectors of the Hamiltonian are generally infinitely many, so they can only be truncated to a certain degree of progress.) ）

Note that there is no discussion of the opening and closing shells, spatial orbital, and spin orbital.

The intrinsic value of the "intrinsic value" Hamiltonian is the system energy corresponding to the eigen vector.

To solve the Schrodinger equation idea: After a given system (the nucleus attribute and coordinate of the system), the Hamiltonian can be written out, and the Hamiltonian can be written out for the long-term equations, and the eigen-values and the eigen-vectors are obtained by solving the equations.

Difficulty: Multivariate calculus, and difficult to separate variables (electron interaction between the generation of 1/rij), difficult to write analytic solutions.

Solution Ideas:

1. Ignoring the electron interaction, the Hamiltonian is divided into the kinetic energy and potential energy of each electron, so that the independent Schrodinger equation can be written in the degree of freedom of each electron coordinate, and the molecular orbital (Hartree product) obtained by the product of the monomer wave function is obtained. This is the original hartree-fork equation.

2. On the basis of 1, the average field term is added, that is, adding other electrons (densities) to this electron's repulsive potential energy in the monomer Schrodinger equation, and using the SCF idea to cycle the accurate energy. This energy does not respond well to the interaction of electrons, but is a basic compensation. This is hartree-fork theory.

3. On the basis of 1, the electronic interaction is considered to be a perturbation, i.e. MP theory (to be added to confirm).

4. On the basis of 1, by the Hartree products molecular orbital particles occupy the various states of the system (configuration), these States are a group of bases, theoretically the correct state can be linear expansion/table out, this is CI (to be added).

5. And coupled Cluster theory, etc. (to be added).

Molecular orbital theory: basic elements (updated)