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We're commonly taught that when atoms want to hybridize in for instance methane, an electron is excited from $2s$ to $2p$ to allow for four unpaired electrons, which is necessary for bonding.

Where does the energy for this excitation come from?

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  • $\begingroup$ If you are talking about the sp3 hybridization: there is no excitation involved... $\endgroup$ – Greg Aug 17 '16 at 5:03
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Ab initio hybridisation is a concept taught in schools to help understand how carbon with its one s- and three p-orbitals can achieve a tetrahedral environment. As part of this process, it is required to formally excite an electron.

Formally is the key word here. The entire process is a formal process that has practically nothing to do with real-life atoms (especially because these real-life atoms rather rarely end up in a vacuum without anything around them as the theory assumes). Thus, in real life this formal energy is not needed.

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In this process the energy of s orbital increases, but the energy of three p orbitals decrease.

This is like irl two hungry friends one of them having spam. The one with spam will share it with a friend and (if you look at him alone) his state worsens (say -1). On the other hand his friend benefits (say +2). Sharing still brings the benefit to the system.

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