Predicting the generation of singlet oxygen
Molecular orbitals are actually, to the best of my knowledge, not really helpful in explaining this observation. Instead, a much more fundamental concept does a much better job: the conversion of (electronic) spin.

The reacion you mentioned can be analysed in terms of spin states. Nobody will disagree that hydrogen peroxide, sodium hypochlorite, sodium chloride and water are singlet compounds. Therefore, using generic Greek letters as placeholders for the different compound to illustrate the point that their true doesn’t matter much, we can write the equation as:

$$\ce{^1\unicode{x391}\ + ^1\unicode{x392}\ -&gt; ^?\Gamma\ + ^1\Delta\ + ^1\unicode{x395}}\tag{1}$$

We see that we are reacting two singlet compounds two three compounds and two of the products are also singlets. This means, every spin on the left-hand side of the equation is paired and most of the spins on the right-hand side, too. To generate a triplet product, we would need to flip a few spins but that is a slow process on the timescale of a chemical reaction. (Note that the conversion from singlet oxygen back to triplet can be observed as a faint red glow demonstrating that it is not instant but delayed.) Thus, in the moment of the particle collision, generating all-singlet products from all-singlet reactants (if only a single product potentially can have an unpaired spin) is the only option. Thus:

$$\ce{^1\unicode{x391}\ + ^1\unicode{x392}\ -&gt; ^1\Gamma\ + ^1\Delta\ + ^1\unicode{x395}}\tag{2}$$