Q90 · CSIR-NET Chemistry, June 2014

Paper: CSIR-NET June 2014 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Hydrogen Atom · Marks: 2 · Difficulty: Medium

A Slater determinant corresponding to the ionic part of the ground state valence bond wave function of $\mathrm{H}_{2}$ molecule is $\left(1 \mathrm{s}_{\mathrm{a}} \alpha, 1 \mathrm{s}_{\mathrm{a}} \beta, 1 \mathrm{s}_{\mathrm{b}} \alpha, 1 \mathrm{s}_{\mathrm{b}} \beta\right.$ are atomic spin-orbital's of hydrogen atoms a and b of the hydrogen molecule)
(a)$\left|\begin{array}{cc}1 \mathrm{s}_{\mathrm{a}} \alpha(1) & 1 \mathrm{s}_{\mathrm{a}} \beta(1) \\ 1 \mathrm{s}_{\mathrm{a}} \alpha(2) & 1 \mathrm{s}_{\mathrm{a}} \beta(2)\end{array}\right|$
(b)$\left|\begin{array}{cc}1 \mathrm{s}_{\mathrm{a}} \alpha(1) & 1 \mathrm{s}_{\mathrm{b}} \beta(1) \\ 1 \mathrm{s}_{\mathrm{a}} \alpha(2) & 1 \mathrm{s}_{\mathrm{b}} \beta(2)\end{array}\right|$
(c)$\left|\begin{array}{cc}1 \mathrm{s}_{\mathrm{a}} \alpha(1) & 1 \mathrm{s}_{\mathrm{b}} \alpha(1) \\ 1 \mathrm{s}_{\mathrm{a}} \alpha(2) & 1 \mathrm{s}_{\mathrm{b}} \alpha(2)\end{array}\right|$
(d)$\left|\begin{array}{cc}1 \mathrm{s}_{\mathrm{a}} \alpha(1) & 1 \mathrm{s}_{\mathrm{b}} \beta(1) \\ 1 \mathrm{s}_{\mathrm{a}} \alpha(1) & 1 \mathrm{s}_{\mathrm{b}} \beta(2)\end{array}\right|$
Answer
Answer: A ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation
The ionic structure H_a⁻H_b⁺ has both electrons on atom a with opposite spins: the determinant built from the spin-orbitals 1s_aα and 1s_aβ (option a).

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