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Every 4.5 V lantern batteries are a series of three 1.5 V cells. It would have more capacity if it consisted of single 4.5 V cell. But I don't see any 4.5 V cell.

According to Wikipedia's Standard Electrode Potential data page, there are vast possibilities of a 4.5 V cell. The one I think most plausible is:

$$ \begin{align} \text{Anode:} &\quad &\ce{Ca + 2 H2O &→ Ca(OH)2 + 2 H+ + 2 e-} \quad|\cdot 5\\ \text{Cathode:} &\quad &\ce{2 BrO3- + 12 H+ + 10 e- &→ Br2 + 6 H2O}\\ \hline \text{Overall:} &\quad &\ce{5 Ca + 2 HBrO3 + 4 H2O &→ 5 Ca(OH)2 + Br2} \end{align} $$

Have anyone tried this or anything else 4.5 V?

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    $\begingroup$ To put it mildly, I'd say that your perspective on what is and what isn't plausible in chemistry is rather skewed. $\endgroup$ – Ivan Neretin Aug 20 at 10:18
  • $\begingroup$ @IvanNeretin Well, to be honest, I thought it's plausible because it's a calcium battery. $\endgroup$ – Dannyu NDos Aug 20 at 10:19
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    $\begingroup$ Calcium is not that good in a battery, for it will react with water by itself. (Sure, some workaround might be possible.) Bromine is not good anywhere near you. HBrO3 is even worse, and moreover, it doesn't even exist in a pure form. $\endgroup$ – Ivan Neretin Aug 20 at 10:22
  • $\begingroup$ @IvanNeretin HBrO3 is in aqueous solution. (The cathode reaction was edited accordingly.) $\endgroup$ – Dannyu NDos Aug 20 at 10:34
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    $\begingroup$ Would it really 'have more capacity' if it were a single 4.5V cell? That depends on many factors that have nothing to do with the electrode potentials. Engineering a useful product is way harder than you think. $\endgroup$ – Jon Custer Aug 20 at 12:34
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Perhaps you consider the volume allotted to the batteries as equivalent to capacity. A better measure would be ampere-hours at 4.5v, or watt-hours. And weight might be a factor to consider.

An electrochemical cell with a high voltage (4.5v) that requires complicated or dilute ingredients could better fill the volume allotted, but if it runs out of power in a shorter time, it has less capacity. You could consider 6 cells in a 9v battery to be a complicated device, but it seems so simple. Three 1.5v cells in a package would give you a simple overall structure, and could give you high capacity due to the simple internal composition of each cell.

One reason that lithium ion batteries are so highly regarded is their high electrochemical capacity. "The more energy a [rechargeable] battery can hold when charged, the less often you need to charge it. No one wants to be replacing the batteries in their wireless keyboard every week or to have their kid’s toy conk out after just 15 minutes. Whereas a common disposable AA battery’s capacity is anywhere from 800 mAh for budget brands up to 2,000 mAh for premium versions, most rechargeable batteries start at around 1,800 mAh and go up to nearly 3,000 mAh. Most trustworthy companies right now make AA batteries around 2,000 mAh. We don’t consider batteries with stated capacities lower than 1,700 mAh, which is too underpowered, or higher than 2,500 mAh, which makes us suspicious that a company is overpromising." https://thewirecutter.com/reviews/best-rechargeable-batteries/

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