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Valence bond, chemical term, 1927 WH. Heitler and FW. London's first quantum mechanical treatment of electron pair bonds in hydrogen molecules.
The valence bond theory is consistent with the classical concept of electron pair bond that chemists are familiar with, and has developed rapidly since its appearance.However, the calculation of valence bond theory is relatively complicated, which makes the later development slow.With the increasing improvement of computing technology, the theory will have new development.
1927 WH. Heitler and FW. London completed the quantum mechanical approximation of electron pair bonds in hydrogen molecule for the first time, which is the basis of modern valence bond theory.50. C. Pauling and others introduced the concept of hybrid orbitals, synthesized the valence bond theory, and successfully applied it to the structure of diatomic molecules and polyatomic molecules.
In 1927, Heitler and London used quantum mechanics to deal with hydrogen molecule H2, solving the essential problem of chemical bond between two hydrogen atoms, so thatCovalent Bond Theory From the typical Lewis theory to today's modern covalent bond theory.
Where rA1, rB1 are the distances between nucleus A, B and electron 1;R12 is the distance between two electrons;RAB is the distance between two nuclei... (Figure 1);1/RAB represents the potential energy between two atomic nuclei (both hydrogen nucleus and electronic charge are 1 basic charge unit);1/rA1, 1/rB1,... are also potential energy;Eu is the Laplacian operator.
The key point of the Heitler London method is how to properly select the approximate wave function Ψ (1,2) (or trial wave function) of the ground state H2, and then use the variational formula to minimize the energy E of the hydrogen molecule (assuming that Ψ is normalized):
Where * represents complex conjugate.Consider the system composed of two hydrogen atoms, if the ground state wave function of two hydrogen atoms A (with electron 1) and B (with electron 2) is:
φA⑴=πexp（-rA1）
φB⑵=πexp（-rB2）
If two hydrogen atoms are far apart, the wave function of the system is:
Φ1（1,2）=φA⑴φB⑵
In fact, the two electrons are indistinguishable.Also suitable functions are:
Φ2（1,2）=φB⑴φA⑵
Both functions Φ 1 and Φ 2 correspond to the same energy.Heitler and London took the equal weight linear combination of two functions as the variational function of H2:
Ψ（1,2）=c1Φ1+c2Φ2
Solve the secular equation and get c1=± c2. The wave function and energy are:
Where
S is the overlapping integral of atomic orbits.Calculate the items in the energy formula and integrate them to get:
Where Q, J and s are all functions of R.If Δ E ± is used to represent the difference between the molecular energy and the energy of two separated atoms (Figure 2):
