What you are suggesting there is essentially what is already done in MM-MD: molecular structures are parameterized with respect to structural features and that is used to generate thermochemical data. So, everything you pitched is already implemented in corresponding software packages.

Additionally, there are people working on machine learning to further automate such calculations and for organic molecules they are quite far.

However, this is only an approximation to reality. Actually, the electrons do not have the information whether they are part of a bond or a core orbital, all they "know" is that they are indifferentiable parts of a wavefunction that is defined by the locations of atomic nuclei. All other parameters such as bond orders, strain etc. are derived from this wavefunction. For structures which resemble the set of molecules to which the MM force field was fit, the resulting energies are good approximations to the quantum mechanical results, but the further you go away from the defining set, the worse it gets and then there is no way around and ab initio calculation.

Entropy is not related to disorder, it is related to heat and work.

Organic Chemists have evaluated if a reaction has an ore red transition state or disordered one. The Diels -Alder in a very ordered transition state . There is enzyme rate enhancement theory that out a molecule in a certain configuration lowers the transition state since it may cause a strain in the molecule and a certain bond to break. I assume you should ask what the gaps are in such work? Or how to better calculate catalysis with the current models and software packages. Check out molecular glue and how that is a paradigm shift here also.

ER,

Then what I learned in Thermodynamics in college is not true. While it's true that entropy can be defined without reference to disorder, most definitions I've seen refer to it as an increase in disorder in a system. Therefore, in terms of visualizing what's happening in a system, entropy 𝒊𝒔 related to disorder.

So I think I'm going to need clarification to your statement:

𝘌𝘯𝘵𝘳𝘰𝘱𝘺 𝘪𝘴 𝘯𝘰𝘵 𝘳𝘦𝘭𝘢𝘵𝘦𝘥 𝘵𝘰 𝘥𝘪𝘴𝘰𝘳𝘥𝘦𝘳, 𝘪𝘵 𝘪𝘴 𝘳𝘦𝘭𝘢𝘵𝘦𝘥 𝘵𝘰 𝘩𝘦𝘢𝘵 𝘢𝘯𝘥 𝘸𝘰𝘳𝘬.

JS

James Schulte

The metaphor 'Entropy as disorder' comes out when one consider Boltzmann's equation for mono-atomic ideal gas. But the world does not look like a mono-atomic ideal gas.

See the paper

Styer, Dan. "Entropy as disorder: History of a misconception." The Physics Teacher 57, no. 7 (2019): 454-458.

A good starting point to understand entropy is JANAF Themochemical Tables, they are available nowadays online:

https://janaf.nist.gov/

Look at couple of substances - there is a column with the entropy values. To understand entropy means is at least to understand how these values are obtained. Also you can try to interpret them as disorder.

Thank you ER!

Not sure I can agree wit any statement that says entropy is not disorder . at constant pressure delta G is (free energy) is maximized in chemical reaction and determines it a reaction is spontaneous. If there is no heat loss or delta H is zero and the free energy could be the maximum work obtained ( as in an electrical system). G=H-TS where this us a tradeoff of enthalpic energy enough energy to break bonds minus the entropic (orientation factor ) to see if a reaction occurs. So a sI add enerfy the mlecule might adapt a configuration where a conclusion with enough kinetic energy will not produce the ddeisred reaction as an E2 does when a bulky base tries to do a SN2 displacment on a sterically hindered carbon. So entropy is disorder and to minimize this as a chemist is flatly wrong.

Regarding "is entropy disorder": in most cases, analyzing phenomena handwavingly from the disorder perspective checks out which is why in introductory classical thermodynamics classes this is still the option of choice. For most reactions e.g. in organic chemistry that is completely sufficient.

However, there are some materials for which there are phase transitions in which a seemingly more ordered structure still has the higher entropy; for these, the "disorder" approach no longer succeeds while the statistical approach still checks out.

Robert Doti

Say, we compute equilibrium composition at given T and P by minimizing the total Gibbs energy of the system - min G (mass, T and P, remains constant). Let us take reaction

CO2 = CO + 0.5 O2

The chemical variable is defined as

n(CO2) = 1 - x

n(CO) = x

n(O2) = 05.x

The figure below shows the change of the Gibbs energy with x. I have recently made this computation to demonstrate the adiabatic flame temperature. By T = 2518 К and p = 1 atm at equilibrium x = 0.213:

https://blog.rudnyi.ru/ru/wp-content/uploads/2025/04/C_02_C02.png

So, how do you prove that the disorder is at maximum by x = 0.213?

Evgenii Rudnyi

The disorder is at maximum with the largest number of individual molecules, therefore at x=1.

The entropy at standard conditions is by Hess' law [213,6*(1-x)+(198+0.5*205)x]J/molK which also has its maximum at x=1.

This is how the disorder thing is meant to be interpreted. As I said, it fails in some cases, but this reaction is a classical example where it works nicely.

Jürgen Weippert

I am not sure if I understand. Take an isolated system with CO2, CO and O2. The entropy in such a system at equilibrium is at maximum, isn't it? Yet, at equilibrium you do not have CO+O2, hence the maximal entropy of such a system has nothing to do with the state of disorder that you have suggested. In other words, according to your logic entropy is not related to disorder at all.

In your graph you minimized the Gibbs free energy within the system. There is no reason why within the system the minimum of G would at the same time be the maximum of S within the system.

The second law of thermodynamics says that the global entropy must be maximized. ΔG that has two contributions: ΔG=ΔH-TΔS. The ΔS part accounts for the entropy changes within the system while the ΔH part accounts for enthalpy exchange which can be connected to the entropy change in the environment.

The entropy I was calculating in my previous post was the entropy within the system. That one, as the equation shows, always increases when you go to the right side of the reaction formula because more molecules=more disorder. That's what all of this is about.

Regarding the enthalpy part: let's assume the environment as a gaseous bath. An enthalpy release into this environment results in more motion of the gaseous bath which is more chaotic (statistically spoken, due to a larger variety of possible energy distributions).

Therefore what you calculated in your graph can be interpreted as the competition between disorder inside due to more gas molecules vs. more disorder outside due to more motion. For each temperature, this competition ends differently and that result is chemical equilibrium.

Therefore, the reaction you presented is an example in which the disorder interpretation of entropy works perfectly fine.

Side note: if you want a less handwaving deduction of "more molecules/atoms in the gas phase= (normally) more entropy", check the derivation of the Sackur-Tetrode equation.

Jürgen Weippert

Let us consider an isolated system. After all the metaphor "entropy as disorder" comes from Boltzmann's treatment of an ideal mono-atomic gas in the isolated system. You are right that in this case it is necessary to change the math but it should not be too difficult. Take 1 mole CO and 0.5 mole of O2, put them in the isolated system and find maximum of the total entropy. If you take the heat capacities constant, you will have two equations with two unknowns - temperature and x. But at equilibrium x will not be one - so the entropy has no relationship to the criterion of disorder that you have suggested.

I really don't know what part of it you don't want to understand. This was the explanation I got in school (not even university). Admittedly, it is "optimized" for an closed system since school chemistry is rarely done in isolated systems.

If you insist upon an isolated system, the transfer isn't that hard, either: if you have more molecules, you get more entropy out of that, while if you go to the exothermic side, the CO2 molecules will have to store this energy internally and that, once again, opens up a larger variety of options for distributing the energy among the vibrational states. So you have a competition between two statistical (disorder) phenomena again.

Earlier, I clearly acknowledged that this interpretation has its limitations (or call it failure scenarios if you want) which are encountered in the graduate lectures, but I don't find the disorder interpretation to understand and for the scenario you brought up it works perfectly fine.

Jürgen Weippert

You have written before:

"The disorder is at maximum with the largest number of individual molecules, therefore at x=1."

Do you agree now that this was the wrong conclusion?

My point is that we do not know what is disorder - it is not well defined notion. Hence, when people rely on this notion they usually get wrong conclusion - an example is the original question to this thread.

I repeat - entropy is connected with heat and work. This is the starting point to discuss entropy - the second law. Only this way one can achieve good results.

The original question was related to suggestion to change the notion of the entropy. In this case my answer was that we should look at the second law - it does not make sense to try to change it.

Jawad Alzeer

I have opened your paper. The very first sentence is unfortunately not correct:

"Chemical reactivity has traditionally been analyzed using thermodynamic variables as abstract concepts separate from molecular structure."

Thermodynamics entropy is connected with molecular structure by the partition function. And this connection via equilibirium statistical mechanics is in full agreement with the second law in classical thermodynamics. The best is to forget about disorder while discussing entropy - one must just follow the equations that define entropy.

Evgenii Rudnyi, it would be great if you read the entire article and get your final feedback

Jawad Alzeer

I have browsed the paper but I would say that I do not understand it, sorry. Well, my knowledge in organic chemistry is limited, this could be the reason.

Let me start with

ΔG = ΔH - T ΔS

ΔH is not related to potential energy directly, it includes the contribution from heat capacities. Also this equation does not depend on the mechanism of chemical reaction. I am afraid, one cannot predict the path of the reaction based on enthalpies and entropies of reagents and products. To compute the equilibrium constants one should know ΔH and ΔS, I have not understood how you evaluate them, sorry.

If you do not change the equation above, that is, the meaning of the enthalpy and entropy, then everything should be okay. Well, in my knowledge, no one computes the entropy based on the ideas of disorder, as this is impossible because one cannot evaluate the numerical value of disorder.

You wrote ;

Constitution: how many bonds and atoms form the core of a molecule

• Configuration: spatial arrangement, such as chirality or E/Z isomerism
• Conformation: flexibility or rigidity due to rotations or strain

Chemists have been doing this since I studied chemistry in grad school since the 1950s from Saul Winstein and HC Brown.

Any theory for a chemist has a chemist asking does it help me to predict reactivity better?

For instance, to get to the transition state -the high point in a reaction path (the height of the mountain) one supplies heat (enthalpy) however in order for the reaction to proceed we may need proper 180-degree attack of leaving group in nucleophilic attack in SN2). So if I cannot achieve the order of that orientation, I may have side reactions take place. This result in an E-2 attack with the nucleophile (loosely a strong Lewis base) on the C-H bond abstracting a Proton and causing a beta elimination to the alkene and not the substitution. This has been described by organic chemists since Ingold's time from 1930s.

So any new way of looking at entropy is one does it help me understand this better to make sense when i take organic chemistry (education value) or does it help me make better predictions to avoid E2 reactions? Or to predict how i can make better catalysts to but bond strain on a molecule. Chemists have been doing this for years.