LCAO-MO Theory In molecular orbital theory the MOs, {ψ µ}, are usually expanded as combinations of atomic orbitals, {φ i}. The p x and p y are affected by the C 3v point group operations by equal amounts and hence are degenerate. For diatomic molecules, AB, these LCAO MOs have the general form Ψ1 = aψA + bψB Ψ2 = aψA – bψB! These atomic orbitals have e symmetry as defined by the character table. Shropshire Association of Local Councils - Signed up to the Armed Forces Covenant We Commit to honor the Armed Forces Covenant and support the Armed Forces Community. Specific combinations of atomic orbitals are use to build molecular orbitals. If S > 0, a bonding MO … Formulating SALCs with Projection Operators U The mathematical form of a SALC for a particular symmetry species cannot always be deduced by inspection (e.g., e1g and e2u pi-MOs of benzene). Approximate method: It's a bit tedious to write out. The gist is to set up each of the combinations you have (eg 3x1-x2-x3-x4) equal to a linear combination of the three p orbitals (since they are the T2 AO's). For the µth MO, we write this expansion as The MOs are solutions to an effective Schrödinger equation: ψ µ =c iµ φ i i ∑=c 1µ φ 1 +c 2µ φ 2 +c 3µ φ A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. U A projection operator is a function that acts on one wave function of the basis set of functions that comprise the SALCs (e.g., one of the $\begingroup$ This is worked out in David Bishop's book "Group Theory and Chemistry" on p. 238 and 239, which you might be able to view in Google Books. As seen here the p z orbital, like the 1s and 2s orbitals, has A 1 symetry; they are totally symmetric to the operations of the C 3v point group. The SALC of a molecule can be constructed in the same manner as the LCAO, Linear Combination of Atomic Orbitals, however the basis set differs. Solution will involve molecular orbitals - similar to atomic orbitals - but centred around all of the nuclei in molecule. Each defined by sets of quantum numbers, with electron probability density determined by ψ2, where ψ = molecular wave function. In quantum mechanics, electron configurations of atoms are described as wavefunctions. Linear Combination of Atomic Orbitals (LCAO).! While looking for the SALCs of a molecule, one uses vectors represented by b j , on the other hand, while looking for the LCAO of a molecule, one uses atomic orbitals as the basis set. We recognise the value of serving personnel, both Regular and Reservists, Veterans and … LCAO: From Hydrogen Atom to Hydrogen Molecule Consider a Hydrogen atom with one electron in the 1s orbital: 0 r V r 1s energy level Potential of a Hydrogen atom One can solve the Schrodinger equation: r V r r E r m 2 2 2 and find the energy of the 1s orbital and its wavefunction


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