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Firstly, I found the RHF expansion of $\Phi_2$ and $\Phi_3$ is not symmetric at equation (4.29). Then I expand $\Phi_2$ by myself, the results showed it's

$ \Phi_2 = (\chi_A\chi_A-\chi_B\chi_B)(\alpha\beta-\beta\alpha) - (\chi_A\chi_B-\chi_B\chi_A)(\alpha\beta+\beta\alpha) $

Moreover, even with this the equation (4.30)~(4.31) is also inconsistent, which the righthand side of the equation should be switched.

But this is a famous book in its third edition, so am I misunderstood or there is an error?

The UHF Dissociation and the Spin Contamination Problem

Reference:

(1) Jensen, F. Introduction to Computational Chemistry, 3rd ed.; John Wiley & Sons: Nashville, TN, 2017.

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    $\begingroup$ @Nisarg There may be people viewing this on mobile screens, for those it may be very, very inconvenient to read the smaller font that you are trying to fake with <sup> ... </sup> tags. There is also not really any point to it, since it actually increases line spacing and it does not save any screen real estate. And given that the source is a major point of this question, the choice to present it smaller than the rest is actually worse. $\endgroup$
    – Martin - マーチン ♦
    Commented Jan 16, 2022 at 16:01

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There is an updated list of errata* for the 3rd edition of Jensen's book at https://chem.au.dk/~frj/corrections_ICC3.html, which includes the mistake you pointed out (and more).

It reads:

page 138, (4.29), third line should read: [chiAchiA - chiBchiB](alpha.beta - beta.alpha) - [chiAchiB - chiBchiA](alpha.beta + beta.alpha)
page 138, (4.29), fourth line should read: -[chiAchiA - chiBchiB](alpha.beta - beta.alpha) - [chiAchiB - chiBchiA](alpha.beta + beta.alpha)
page 138, (4.31), a minus sign is missing, or change to (chiBchiA - chiAchiB)(alpha.beta + beta.alpha)

Or, put into maths:

$$\begin{align} \Phi_2 &= [\chi_\mathrm{A} \chi_\mathrm{A} - \chi_\mathrm{B}\chi_\mathrm{B}](\alpha\beta - \beta\alpha) - [\chi_\mathrm{A} \chi_\mathrm{B} - \chi_\mathrm{B}\chi_\mathrm{A}](\alpha\beta + \beta\alpha) \tag{4.29} \\ \Phi_3 &= -[\chi_\mathrm{A} \chi_\mathrm{A} - \chi_\mathrm{B}\chi_\mathrm{B}](\alpha\beta - \beta\alpha) - [\chi_\mathrm{A} \chi_\mathrm{B} - \chi_\mathrm{B}\chi_\mathrm{A}](\alpha\beta + \beta\alpha) \tag{4.29} \\[10pt] ^3\Phi_+ = \Phi_2 + \Phi_3 &= - [\chi_\mathrm{A} \chi_\mathrm{B} - \chi_\mathrm{B}\chi_\mathrm{A}](\alpha\beta + \beta\alpha) \tag{4.31} \end{align}$$

* Annoyingly, this was quite difficult to find, as Wiley only provides a link to a four-year-old list of errata. You need to go to Frank Jensen's homepage to get the updated link.

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