Molecular orbitals functions

Xhe corresponding molecular orbital function for this system is ... 

Multiplying a molecular orbital function by a or P will include electron spin as part of the overall electronic wavefunction i /. The product of the molecular orbital and a spin function is defined as a spin orbital, a function of both the electron s location and its spin. Note that these spin orbitals are also orthonormal when the component molecular orbitals are. 

Wave functions for the orbitals of molecules are calculated by linear combinations of all wave functions of all atoms involved. The total number of orbitals remains unaltered, i.e. the total number of contributing atomic orbitals must be equal to the number of molecular orbitals. Furthermore, certain conditions have to be obeyed in the calculation these include linear independence of the molecular orbital functions and normalization. In the following we will designate wave functions of atoms by % and wave functions of molecules by y/. We obtain the wave functions of an H2 molecule by linear combination of the Is functions X and of the two hydrogen atoms ... 

It is interesting that the molecular-orbital functions give an alternative... 

The first approximation made in simplifying the task of solving for F is the orbital approximation. Each of the M electrons of the molecule is assumed to be described by a molecular orbital function ip the total wave function for the electronic state is the product of 0 s for the individual electrons (Equation A2.2).c... 

Fortunately, the same rules apply to interaction between two molecular orbitals as apply to interaction between two atomic orbitals. We shall be able to make a new model to cover the interacting situation by adding and subtracting the molecular orbital functions that were correct for the separate molecules before the interaction occurred. 

The H2 molecular orbital function is designated ols the designation o tells us that the MO has... 

A wave function of an electron configuration is generally approximated as a product of molecular orbital functions, which are eigenfunctions of a one-electron Hamilton operator. When 2n electrons occupy n molecular orbitals, the wave function of electron configuration of the lowest energy is written as... 

The starting point for most high-level molecular computations is the Hartree-Fock method. This is based on a Slater determinant of molecular orbital functions, analogous to Eq (9.1) for atoms ... 

If we consider the nuclei A and B to be both hydrogen nuclei, then the atomic orbitals of A and B will be Is orbitals. Solution of this molecular orbital function leads to two molecular functions of the form ... 

The wavefunction W(X,b) will be given as a single Slater determinant made from spin-unrestricted Hartree-Fock (UHF) molecular orbital functions which are eigenfunctions of the perturbed Fock matrices... 

The coefficients for the properly symmetrized molecular orbital functions can be obtained by using the idempotent character operator The reducible... 

This configuration is represented by a wavefunction that is a product of six molecular orbital functions (tt electrons only). 

The functions are already products of molecular orbital functions ... 

The molecular-orbital functions, "0/3(r), are constructed in exact analogy to the Bloch functions of the last section. Thus, we have. 

These molecular-orbital functions are particle-in-a-box solutions, and not surprisingly, the molecular-orbital states satisfy the following condition under the operation of the inversion operator i,... 

Under what conditions are the molecular-orbital and valence-bond descriptions of the c bonding in an octahedral complex equivalent Derive the valence-bond functions shown in Fig. 9-7 from the general molecular-orbital functions. 

Molecular orbital functions given by the linear combination of yi, and are as follows ... 

A one-electron function used in the expansion of the molecular orbital function. The basis functions are commonly represented by atomic orbitals centered on each atom of the molecule. 

The approximation of the molecular orbital function as a linear combination of atomic orbitals chosen as the basis functions. 

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