52Physics Formulary by ir. J.C.A. WeversForNparticles the symmetric spatial function is given by:ψS(1, ..., N) =ψ(all permutations of1..N)The antisymmetric wavefunction is given by the determinantψA(1, ..., N) =1√N!|uEi(j)|10.15.2MoleculesThe wavefunctions of atomaandbareφaandφb. If the 2 atoms approach each other there are two possibilities:the total wavefunction approaches the bonding function with lower total energyψB=12√2(φa+φb)orapproaches the anti-bonding function with higher energyψAB=12√2(φa-φb). If a molecular-orbital issymmetric w.r.t. the connecting axis, like a combination of two s-orbitals it is called aσ-orbital, otherwise aπ-orbital, like the combination of two p-orbitals along two axes.The energy of a system is:E=ψ|H|ψψ|ψ.The energy calculated with this method is alwayshigherthan the real energy ifψis only an approximation forthe solutions ofHψ=Eψ. Also, if there are more functions to be chosen, the function which gives the lowest
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Orbital hybridisation, lower total energy, symmetric spatial function, determinant |H ij, symmetry axes