Abstract
Ionic, covalent, metallic and hydrogen bonds and the van der Waals force go by separate names. This paper asks what divides them—the answer is that a continuum of strength has been cut by the $RT$ of room temperature. Change the temperature at which one cuts, and the classification changes. No new mathematical theorem and no new law is claimed.
First, take the $RT$ of room temperature as the ruler. At $298.15$ K, $RT=\mathbf{2.4790}$ kJ/mol(Section 2).
Second, divide five bonds by it. Ionic $\mathbf{317.47}$, metallic $161.36$, covalent $\mathbf{140.38}$, hydrogen bond $8.07$, van der Waals $\mathbf{0.4034}$(Section 2).
Third, this is the core of the paper. Only the van der Waals force falls below $1$—being weaker than the thermal motion of the room, it breaks at room temperature(Section 3).
Fourth, cool it and it survives. At the temperature of liquid nitrogen, $77$ K, $RT=0.6402$ kJ/mol, and the van der Waals force becomes $\mathbf{1.5620}$ times it(Section 4).
Fifth, the boundary temperature is a single number. $1.0$ kJ/mol equals $RT$ at $T=\mathbf{120.27}$ K—and the classification changes across it(Section 4).
Sixth, the strengths themselves have no break. From $1.0$ to $787$ is a continuum spanning a factor of $\mathbf{787}$, with no jump anywhere(Section 5).
Scope (what is not claimed)
No new mathematical theorem and no new law is claimed—the representative strengths of each bond, the value of $RT$, and the picture of thermal motion breaking a bond are all standard. No chemistry is built—what is used is one division. The mechanisms of bonding are not discussed—why an ionic bond is strong and a van der Waals force weak is not treated at all. No bond energy is measured—all are cited representative values and vary between sources. The $1.0$ kJ/mol for the van der Waals force in particular is a value to show an order of magnitude, and moves by several times between pairs. “Breaking” is not defined rigorously—comparing with $RT$ is a rule of thumb; real dissociation involves activation barriers and configurational entropy. It is used here as a rule of thumb only. No revision of the classification is urged—the custom is useful. What this paper says is only that the boundary is relative to a temperature. The metallic bond is represented by a single value—it in fact varies greatly between metals; one value for iron has been posited. Relation to earlier papers: Paper 275 showed that there is no natural boundary between a semiconductor and an insulator—this paper writes the same figure for chemical bonds. There it was $E_g$ and temperature, here it is bond energy and temperature. Paper 273 counted four different quantities written in the same unit—this paper writes that five names are cutting one continuum. Paper 201 counted “complete” as four different claims—this paper is the converse, a case where there are more names than things. Paper 190 measured rare on a logarithmic scale—this paper writes in the ratio $787$. What is added is dividing five bonds by $RT$ into one table, observing that only the van der Waals force falls below $1$, computing that at $77$ K it becomes $1.5620$ and survives, and obtaining the boundary temperature $120.27$ K.
1. Notation and Placement
Setting: compare the strength of a bond with the vigour of thermal motion. The measure of thermal motion is $RT$, with $R$ the gas constant and $T$ the absolute temperature.
The rule of thumb: a bond energy well above $RT$ is not easily broken by thermal motion. Below $RT$, the thermal motion is the stronger.
Question: what divides the five names?
The answer is that a continuum of strength has been cut by $RT$. Change the temperature at which one cuts, and the classification changes.
A caution: comparison with $RT$ is a rule of thumb. Real dissociation involves activation barriers and entropy—it is used here as a rule of thumb only.
2. Dividing Five Bonds by $RT$
Check 2.1: at $298.15$ K, $RT=8.314462618\times298.15/1000=\mathbf{2.4790}$ kJ/mol.
| Bond | Representative strength [kJ/mol] | Times $RT$ |
|---|---|---|
| Ionic (the NaCl lattice) | $787$ | $\mathbf{317.4722}$ |
| Metallic (iron) | $400$ | $161.3582$ |
| Covalent (C--C) | $348$ | $\mathbf{140.3816}$ |
| Hydrogen bond (O--H$\cdots$O) | $20$ | $8.0679$ |
| van der Waals | $1.0$ | $\mathbf{0.4034}$ |
Observation 2.2 the upper four run from $8$ to $317$ times $RT$, and none of them breaks at room temperature. The last alone falls below $\mathbf{1}$.
Observation 2.3 the strengths themselves form a continuum spanning a factor of $787$, from $1.0$ to $787$. Between ionic and metallic, and between metallic and covalent, there is no jump—$400$ and $348$ differ by only $1.15$.
3. The Core: Only the van der Waals Force Falls below $1$
Observation 3.1 the number $0.4034$ means that the thermal motion is some $2.5$ times the stronger. So at room temperature what is held by van der Waals forces is continually breaking and re-forming.
Check 3.2: see where the line at $1$ is crossed.
| Bond | Times $RT$ | Against $1$ |
|---|---|---|
| Ionic | $317.4722$ | above |
| Metallic | $161.3582$ | above |
| Covalent | $140.3816$ | above |
| Hydrogen bond | $8.0679$ | above |
| van der Waals | $\mathbf{0.4034}$ | below |
Observation 3.3 the line at $1$ is crossed in one place only. And that one place coincides exactly with the customary boundary between “a chemical bond” and “an intermolecular force”—the line of the classification has been drawn at the position of room-temperature $RT$.
Observation 3.4 the separator—what has to be changed for the classification to change. The temperature. Not one bond energy has been moved.
4. Cool It and It Survives
Check 4.1: lower the temperature and recompute $RT$.
| Temperature | $RT$ [kJ/mol] | van der Waals ($1.0$) is $RT$ times |
|---|---|---|
| $298.15$ K (room) | $2.4790$ | $\mathbf{0.4034}$ (it breaks) |
| $120.27$ K | $1.0000$ | $\mathbf{1.0000}$ (the boundary) |
| $77$ K (liquid nitrogen) | $0.6402$ | $\mathbf{1.5620}$ (it survives) |
Observation 4.2 across $120.27$ K the van der Waals force moves from the side weaker than thermal motion to the side stronger. The temperature is $T=1000/R=\mathbf{120.27}$ K—a simple number, the bond energy divided by the gas constant.
Observation 4.3 at $77$ K it becomes $1.5620$. Inside liquid nitrogen, what is held by van der Waals forces stays held—one and the same force is a “bond” or a “fluctuation” according to the temperature.
Observation 4.4 Paper 275 wrote that the boundary between a semiconductor and an insulator moves with temperature. This paper is the same figure—there it was $E_g$ and $kT$, here bond energy and $RT$, and in both the classification is made by the same operation of dividing an energy by a temperature.
5. The Strengths Themselves Have No Break
Check 5.1: set out the five values by the ratio between neighbours.
| Neighbours | Ratio | A jump? |
|---|---|---|
| Ionic $787$ over metallic $400$ | $1.97$ | not a jump |
| Metallic $400$ over covalent $348$ | $\mathbf{1.15}$ | not a jump |
| Covalent $348$ over hydrogen bond $20$ | $17.4$ | large but continuous |
| Hydrogen bond $20$ over van der Waals $1.0$ | $20.0$ | large but continuous |
| Whole span, $787$ over $1.0$ | $\mathbf{787}$ | — |
Observation 5.2 the metallic and covalent bonds differ by only $\mathbf{1.15}$. And still they carry separate names—what separates the names is not the strength (it is the mechanism).
Observation 5.3 meanwhile the hydrogen bond and the van der Waals force differ by $20$, and both are sometimes called “intermolecular forces”. The ordering of strengths and the ordering of names do not agree.
Observation 5.4 a point to state honestly—the five names are divided by mechanism, not by strength. What this paper says is that only the higher division, between “a chemical bond” and “an intermolecular force”, is cut by room-temperature $RT$.
6. Roll Call and Closing
- Room-temperature $RT$(Check 2.1): $2.4790$ kJ/mol.
- Five divided by $RT$(Check 2.1): from $317.47$ down to $0.4034$.
- The line at $1$ is crossed once(Check 3.2): by the van der Waals force alone.
- It coincides with the custom(Observation 3.3): the line sits at $RT$.
- The boundary is $120.27$ K(Check 4.1): $T=1000/R$.
- $1.5620$ at $77$ K(Check 4.1): it moves to the surviving side.
- Metallic and covalent differ by $1.15$(Check 5.1): and carry separate names.
- A continuum spanning $787$(Check 5.1): with no jump.
- Names divide by mechanism(Observation 5.4): not by strength.
Closing: the strengths of bonds form a continuum spanning a factor of $787$, from $1.0$ to $787$ kJ/mol. The metallic and covalent bonds differ by only $\mathbf{1.15}$ and carry separate names, while the hydrogen bond and the van der Waals force differ by $20$ and are both called intermolecular forces—the ordering of strengths and the ordering of names do not agree. In one place only does a name coincide with the strength. Divide the five by the room-temperature $RT=2.4790$ kJ/mol and the van der Waals force alone falls below $1$ (at $\mathbf{0.4034}$)—and that is exactly the customary boundary between “a chemical bond” and “an intermolecular force”. But that boundary is a line drawn by a temperature and not something the matter carries—cool to $\mathbf{120.27}$ K and the line is crossed, and at $77$ K it stands at $1.5620$ and survives. One thing separates them—writing down at which temperature's $RT$ one divided. Write it down, and names divided by mechanism separate from names divided by temperature. Do not write it down, and one reads a line drawn at room temperature as a line drawn by nature.
References
- Pauling, L. (1960). The Nature of the Chemical Bond, 3rd edition. Ithaca: Cornell University Press.
- Atkins, P. and de Paula, J. (2010). Physical Chemistry, 9th edition. Oxford: Oxford University Press.
- Israelachvili, J. N. (2011). Intermolecular and Surface Forces, 3rd edition. Amsterdam: Academic Press.
- Jeffrey, G. A. (1997). An Introduction to Hydrogen Bonding. Oxford: Oxford University Press.
- Kittel, C. (2005). Introduction to Solid State Physics, 8th edition. New York: Wiley.
- Stone, A. J. (2013). The Theory of Intermolecular Forces, 2nd edition. Oxford: Oxford University Press.
- Yamagishi, Y. (2026). “Rare” Is Measured on a Logarithmic Scale [Paper 190]. Zenodo. 10.5281/zenodo.22106182
- Yamagishi, Y. (2026). “Complete” Is Four Separate Statements, and What Ties Them Into One Is That the Metric Is Positive Definite [Paper 201]. Zenodo. 10.5281/zenodo.22109052
- Yamagishi, Y. (2026). Four Different Quantities, All Written in $\mathrm{J/kg}$ [Paper 273]. Zenodo. 10.5281/zenodo.22169983
- Yamagishi, Y. (2026). There Is No Natural Boundary between a Semiconductor and an Insulator [Paper 275]. Zenodo. 10.5281/zenodo.22170039
Reference
Yamagishi, Y. (2026). The Classes of Chemical Bond Are a Continuum of Strength Cut by a Temperature [Paper 278]. YOI: https://www.yamagishiyuuki.com/yoi/278
DOI: 10.5281/zenodo.22170205
ORCID: 0009-0006-8587-3450
PDF (English) · PDF (Japanese) · Date proof of the English PDF (OpenTimestamps .ots) · SHA256SUMS
The record page for this paper (in Japanese, with the PDFs in each language and the date proof): YOI 278. This paper is a preprint and has not been peer reviewed.