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Which of the following is correct for H2+ ion ?

  • A.A possible trial wave function for the ion is \(\psi = C_{1}\,1S_{A} \pm C_{2}\,1S_{B}\)
  • B.The coefficients of the trial wave function are not equal
  • C.A possible trial wave function is \(\psi = C_{1}\,1S_{A} / C_{2}\,1S_{B}\)
  • D.The 1S orbitals are not normalised

Answer: A

The correct statement is a possible trial wave function for the ion is ψ = C11SA ± C21SB.

In the LCAO treatment of H2+, the single electron's wave function is a linear combination of the 1s orbitals on nuclei A and B. The plus combination gives the bonding orbital and the minus combination the antibonding one.

Because the two nuclei are identical, symmetry makes the coefficients equal in magnitude (C1 = ±C2), so (B) is wrong. A ratio of orbitals (C) is not a linear combination, and the 1s orbitals used are normalised hydrogen functions (D).

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