As DNA is a highly hydrophilic molecule, it usually cannot pass through the cell membrane of bacteria. Hence, to make bacteria capable of internalizing genetic material, they must be made competent to take up the DNA. This can be achieved by making small holes in bacterial cells by suspending them in a solution containing a high concentration of calcium. Extra-chromosomal DNA will be forced to enter the cell by incubating the competent cells and the DNA together on ice followed by a brief heat shock that causes the bacteria to take up the DNA. Additionally, a poorly performed procedure may lead to insufficient competent cells to take up DNA. The divalent cations generate coordination complexes with the negatively charged DNA molecules and LPS, the monovalent that you mentioned can’t. DNA, being a larger molecule, cannot itself cross the cell membrane to enter into the cytosol. The heat shock step strongly depolarizes the cell membrane of CaCl2-treated cells. Thus, the decrease in membrane potential lowers the negativity of the cell’s inside potential, ultimately allowing the movement of negatively charged DNA into the cell’s interior.