Discussion
1sA and 1sB are the normalized eigenfunctions of two hydrogen atoms HA and HB, respectively. If \(S = \langle 1s_{A} | 1s_{B} \rangle\), the option that is ALWAYS CORRECT is
Answer: D
The statement that is always correct is \(0 \le S \le 1\).
The 1s functions are real, positive everywhere and normalised. Their overlap integral is therefore a real number that cannot be negative, and by the Schwarz inequality it cannot exceed the product of the norms, 1. It equals 1 only when the two nuclei coincide and approaches 0 as they move far apart.
\(S = 1\) holds only at zero separation and \(S = 0\) only at infinite separation, so neither is always true. The overlap of two real functions is real, so it is never an imaginary constant.
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