Can elements replace Hydrogen in polar molecules & act similarly?

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In a recent 9th grade advanced biology class, students learned about the unique properties of water, particularly how the two hydrogen atoms in a water molecule exhibit a relatively positive charge compared to the oxygen atom due to differences in electronegativity. This unequal electron distribution leads to weak hydrogen bonds formed through electrostatic attraction with other polar molecules, which contributes to water's unusual characteristics, such as cohesion and adhesion, as well as the stability and flexibility of DNA.A question arose regarding the behavior of other atoms with similar electronegativity to hydrogen, such as Astatine, Osmium, Arsenic, or Phosphorus, in polar covalent bonds with oxygen. The inquiry focused on whether these atoms would exhibit similar hydrogen bonding properties as hydrogen, considering their size and effective charge. It was noted that while these atoms can form polar covalent bonds, they do not create the same hydrogen bonds with other molecules, highlighting the unique role of hydrogen in molecular interactions.
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Today in 9th grade ADV Biology, we learned about how the two Hydrogen atoms in a Water molecule are relatively positive compared to the Oxygen atom. This is because the Oxygen's pull on Hydrogen's electron is greater than the Hydrogen's, or that its Electronegativity is greater. This unequal distribution in electrons is why Hydrogen is positive compared to Oxygen. Thus, they form very weak bonds, in which there is no exchange of electrons, with the negative pole of other polar molecules. This is purely the result of electrostatic attraction. This is the cause for the unusual characteristics of water, and its phases, and why things are adhesive & cohesive, as well as why our DNA is held together but split apart easily etc. I truly understand all this.

But I asked a question my teacher couldn't answer, if all this is the result of H-Bonding, and that is the result of the electronegativity of Hydrogen, than what about atoms with similar electronegativity? What if Astitane (If it wasn't radioactive) Osmium Arsenic or Phosphorus replaced the Hydrogen atoms? Would they behave similarly in a polar covalent bond with Oxygen or other atoms, as hydrogen? WOuld they partake in At-or P-Bonding for example? I'm really curios.
 
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Hydrogen is very small, so other atoms can come close to the effective charge. That is different for all other atoms.
They form polar covalent bonds in molecules, but they don't give the same hydrogen bonds to other molecules.
 
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