# Why is chemistry unpredictable?

Disclaimer: I am not a chemist by any means, and I only have knowledge limited to what I learned in my university's Chemistry III course. Basic understanding of everything up to valence electron orbitals.

Why is there no set of rules to follow which can predict the product of chemical reactions? To me, it seems that every other STEM field has models to predict results (physics, thermodynamics, fluid mechanics, probability, etc) but chemistry is the outlier.

Refer to this previous question: How can I predict if a reaction will occur between any two (or more) substances? The answers given state that empirical tests are the best way we've gotten to predict reactions, because we can discern patterns or "families" of reactions to predict outcomes. Are we only limited to guessing at "family" reactions?

In other words, why am I limited to knowing my reactants and products, then figuring out the process? Can I know the reactants, hypothesize the process, and predict the product?

If the answer is "It's complicated", I would enjoy a push in the right direciton - like if valence orbitals actually do help us predict, or any laws of energy conservations etc, please give me something which I can go research.

• Your best bet would be to look at the field of theoretical chemistry which has various branches of study as highlighted in the above link. Basically, if you are given a set of reactants and products, then you can have a huge number of combinations of atoms simply by looking at all possible arrangments of atoms. But, you can significantly narrow down your options by looking at lower potential paths (which are made from ab initio calculations), simulating movements of the nuclei (molecular dynamics), theoretical kinetics and so on. Oct 19 '20 at 16:02
• BTW, just a digression: You said chemistry is the "outlier" in STEM. I have a gut feeling that maybe biology (which is also a part of STEM) may not be "predictive" enough for you as well, at least when you start out with the subject. Biology and chemistry together form an integral part of STEM, so it may be worth pondering over their seemingly "empirical" nature ;) Oct 19 '20 at 16:11
• Chemistry is neither a set of easy rules, neither set of empirical knowledge to memorize. Or, it it both, intertwined in a wild mixture of both extremes. Most non chemists are too impatient to recognize many patterns, that are hybrids of rules and evidence. Oct 19 '20 at 16:17
• doi.org/10.1016/j.drudis.2018.02.014 Oct 19 '20 at 16:24
• It's not unpredictable. It is just complex... sometimes to a point it is easier to just try (many times) and see instead of calculating something. Oct 20 '20 at 7:30

First of all, I'd ask: what do you admit as "chemistry"? You mentioned thermodynamics as being a field where you have "models to predict results". But thermodynamics is extremely important in chemistry; it wouldn't be right if we classified it as being solely physics. There is a large amount of chemistry that can be predicted very well from first principles, especially using quantum mechanics. As of the time of writing, I work in spectroscopy, which is a field that is pretty well described by QM. Although there is a certain degree of overlap with physics, we again can't dismiss these as not being chemistry.

There are several different answers to this depending on what angle you want to approach it from. All of these rely on the fact that the fundamental theory that underlies the behaviour of atoms and molecules is quantum mechanics, i.e. the Schrödinger equation.*

Addendum: please also look at the other answers, as each of them bring up different excellent points and perspectives.

### (1) It's too difficult to do QM predictions on a large scale

Now, the Schrödinger equation cannot be solved on real-life scales.† Recall that Avogadro's number, which relates molecular scales to real-life scales, is ~$$10^{23}$$. If you have a beaker full of molecules, it's quite literally impossible to quantum mechanically simulate all of them, as well as all the possible things that they could do. "Large"-ish systems (still nowhere near real-life scales, mind you — let's say ~$$10^3$$ to $$10^5$$) can be simulated using approximate laws, such as classical mechanics. But then you lose out on the quantum mechanical behaviour.

So, fundamentally, it is not possible to predict chemistry from first principles simply because of the scale that would be needed.

### (2) Small-scale QM predictions are not accurate enough to be trusted on their own

That is not entirely true: we are getting better and better at simulating things, and so often there's a reasonable chance that if you simulate a tiny bunch of molecules, their behaviour accurately matches real-life molecules.

However, we are not at the stage where people would take this for granted. Therefore, the ultimate test of whether a prediction is correct or wrong is to do the experiment in the lab. If the computation matches experiment, great: if not, then the computation is wrong. (Obviously, in this hypothetical and idealised discussion, we exclude unimportant considerations such as "the experimentalist messed up the reaction").

In a way, that means that you "can't predict chemistry": even if you could, it "doesn't count", because you'd have to then verify it by doing it in the lab.

### (3) Whatever predictions we can make are too specific

There's another problem that is a bit more philosophical, but perhaps the most important. Let's say that we design a superquantum computer which allowed you to QM-simulate a gigantic bunch of molecules to predict how they would react. This simulation would give you an equally gigantic bunch of numbers: positions, velocities, orbital energies, etc. How would you distil all of this into a "principle" that is intuitive to a human reader, but at the same time doesn't compromise on any of the theoretical purity?

In fact, this is already pretty tough or even impossible for the things that we can simulate. There are plenty of papers out there that do QM calculations on very specific reactions, and they can tell you that so-and-so reacts with so-and-so because of this transition state and that orbital. But these are highly specialised analyses: they don't necessarily work for any of the billions of different molecules that may exist.

Now, the best you can do is to find a bunch of trends that work for a bunch of related molecules. For example, you could study a bunch of ketones and a bunch of Grignards, and you might realise a pattern in that they are pretty likely to form alcohols. You could even come up with an explanation in terms of the frontier orbitals: the C=O π* and the Grignard C–Mg σ.

But what we gain in simplicity, we lose in generality. That means that your heuristic cannot cover all of chemistry. What are we left with? A bunch of assorted rules for different use cases. And that's exactly what chemistry is. It just so happens that many of these things were discovered empirically before we could simulate them. As we find new theoretical tools, and as we expand our use of the tools we have, we continually find better and more solid explanations for these empirical observations.

### Conclusion

Let me be clear: it is not true that chemistry is solely based on empirical data. There are plenty of well-founded theories (usually rooted in QM) that are capable of explaining a wide range of chemical reactivity: the Woodward–Hoffmann rules, for example. In fact, pretty much everything that you would learn in a chemistry degree can already be explained by some sort of theory, and indeed you would be taught these in a degree.

But, there is no (human-understandable) master principle in the same way that Newton's laws exist for classical mechanics, or Maxwell's equations for electromagnetism. The master principle is the Schrödinger equation, and in theory, all chemical reactivity stems from it. But due to the various issues discussed above, it cannot be used in any realistic sense to "predict" all of chemistry.

* Technically, this should be its relativistic cousins, such as the Dirac equation. But, let's keep it simple for now.

† In theory it cannot be solved for anything harder than a hydrogen atom, but in the last few decades or so we have made a lot of progress in finding approximate solutions to it, and that is what "solving" it refers to in this text.

Let me contribute two more reasons which make chemistry hard to analyse from a purely theoretical standpoint.

The first one is that, viewed very abstractly, chemistry essentially relies on the study of geometry in very high-dimensional spaces, and even from a purely mathematical point this can be extremely difficult. An important part of chemistry is bond breaking and bond formation, which is behind most reactions. This turns out to require knowledge of the vibrational modes of a molecule. For a general molecule with $$N$$ atoms, there are $$3N - 6$$ vibrational modes. Each of these vibrational modes are a "spatial dimension" in what is called phase space. In principle, if we knew the potential energy in every point of the phase space for a molecule, we would know virtually everything there is to know about how it might react. For an idea of what this looks see, see the figure below:

Unfortunately, there is simply too much space to explore in very high-dimensional objects, so it's very difficult to get a picture of it as a whole. Also disappointingly, almost all of this space is "tucked away in corners", so it is also very difficult to get a reliable picture of the whole space by looking at small bits of it at a time. This has been called "the curse of dimensionality". Something as simple as benzene ($$\ce{C6H6}$$) has a $$\mathrm{3 \times 12-6 = 30}$$-dimensional vibrational phase space (though this particular phase space is highly symmetric, as benzene itself has a high symmetry). Now consider a general reaction which requires two reagents, and forms one product:

$$\ce{A + B -> C}$$

Each of the three molecules has its own phase space, and combining them all together means adding all the number of dimensions of each. In this view, a chemical reaction is nothing but a particular set of trajectories of points (for each atom) in the combined phase space of all molecules, such that the potential energy of the system is locally minimised throughout the trajectory. As such, one would easily find themselves trying to describe trajectories in objects with over 100 dimensions. Few people talk about chemistry at this level of abstraction because it is so complex, but it is a conceptual hurdle in describing chemistry "exactly". Thankfully, there is research into it, such as the CHAMPS collaboration.

The second complication is that, while many important reactions are direct reactions like the one shown above, in the general case, what really exists is a network of reactions, potentially forming a complicated, highly interconnected graph with dozens or even hundreds of intermediates and possible products (graph vertices) and as many reaction arrows connecting them (graph edges). The field of chemical reaction network theory uses graph theory to study these networks. It appears that some of the problems they grapple with are NP-hard.

Of course, this second issue compounds on the first!

So given these two dizzyingly complex problems, even from a purely mathematical standpoint, how can we do chemistry at all? Well, with enough experimental parametrization (e.g. equilibrium constants, rate constants, enthapies and entropies of formation, etc.) and approximations, you can drastically simplify the description of a system. Fortunately, even after throwing away so much detailed information, we can still make decent predictions with what is left. You really should count ourselves lucky!

• This is a really insightful and absolutely fantastic answer and extremely helpful to those outside of or not immersed in chemistry. I see stable manifolds in satellite trajectories and in papers about them in Chaos but never stopped to think of how general the concept was. Instead of doing what I was supposed to today I will go hide somewhere and (try to) read all of your linked sources :-)
– uhoh
Oct 20 '20 at 3:44
• @uhoh There are a number of articles studying chemical oscillators (which can display mathematical chaos) from a reaction network theory perspective. That alone is probably quite a rabbit hole to go down. You have my blessing! Oct 20 '20 at 3:57

Parts of chemistry have predictability but the combinatorial complexity of what is possible leaves a large amount of space for things that don't follow the rules

Some of the ways chemistry differ from physics in unpredictability are an illusion. Take gravity, for example. There is a strong rule–sometimes described as a law–that all objects near the surface of the earth fall with the same acceleration. That is a cast iron rule isn't it? Apparently not. Flat pieces of paper and feathers don't fall as fast as cannon balls and the exact way they fall is very unpredictable. "But we know why that is, don't we?" Yes, a bit, it is air resistance. But that doesn't enhance the predictability at all as any useful prediction would have to solve the equations for fluid flow and there is a \$1m prize for even proving that those basic equations even have a solution all the time.

Arguably, physics is only predictable in school where only idealised versions of real problems are considered.

And it is unfair that chemistry is completely unpredictable. A good deal of physical chemistry is quite like physics in its laws and predictions.

I suspect that you are talking about general organic and inorganic chemistry where there are many predictable properties of compounds but a dictionary full of exceptions to even simple rules.

Or synthetic chemistry where reactions sometimes work but often don't. But, there are plenty of chemical reactions that work fairly reliably (Grignard reactions make C-C bonds fairly reliably with many compounds; Diels Alder reactions create two at once with predictable stereochemistry.)

But this predictability is limited by a fundamental problem: the unfathomably large variety of possible compounds that could be made. Take a ridiculously small subset of possible compounds: all those that can be made just from carbon and hydrogen using only single bonds and disallowing any rings. For simple compounds where the 3D nature of the compounds does not interfere by constraining their existence in real space (atoms have finite volumes in 3D space and can't overlap in real structures) these are mathematically equivalent to simple trees (or the carbon skeleton is: we assume the hydrogens fill out the remaining bonds so each carbon ends up with 4). at the point where 3D space becomes a constraint on which can exist, there are already about 25k distinct possible compounds and by the time you get to 25 there are more possibilities than all the chemicals that have ever been characterised in the history of chemistry.

And this is for very constrained rules for making the compounds that use only two elements and deny a huge variety of interesting structures.

The real issue making chemistry apparently complex is that unfathomably large combinatorial variety of possible chemicals that might exist. In such a large space there is very little possibility that simple rules will always work. And this complexity is just about the possible structures. There are a very large number of reactions that get you from one structure to another and those add another midbuggeringly large layer of complexity.

And this, I think, is the reason why many find chemistry so hard to generalise about. There are simply too many possible things that can exist and even more possible ways to make them for any simple set of rules to always work. And I thought physicists had a problem not being able to fully solve the Navier Stokes equations.

Predictabilty is essentially determined by the level of detail you need to accurately model the phenomenon you're trying to predict. Models that require little detail to capture the phenomenon of interest typically can give reliable predictions, while those requiring enormous detail typically cannot.

The level of detail needed is determined by the complexity of the system, and the fineness at which you wish to model it; the amount of detail needed to model a complex system can be reduced if you only wish to make coarse-grained predictions.

This is true for all the sciences—biology, chemistry, physics, and geology. Thus, in this fundamental way, they all have the same predictability. I.e., there is no fundamental difference in the nature of prediction among these fields. Allow me to illustrate:

Physics:

1. Bending of light from a distant star by the sun's gravitational field. Predictable. Requres very little detail to model the phenomenon accurately: Just the mass of the sun, and the assumption that the distant star is a point particle at a distance much greater than the earth-sun distance.

2. The temperature of the sun's corona. Not yet predictable. This problem requires far more detail to model correctly. The system is so complex that we don't have a model to predict the temperature of the sun's corona, and thus can't explain why the corona is far hotter than the surface of the sun.

Chemistry:

1. Osmotic presure of a highly dilute solution. Predictable. Requires very little detail to model the phenomenon accurately: Just the concentration of the solute.

2. Folding of long (1000's of nucleotides) RNAs. Coarse-grained predictions (the relative radius of gyration) can be made; fine predictions (the ensemble-average probability of each individual base pair) cannot be made (at least not reliably).

Biology:

1. Possible blood types (O, A, B, AB) of offspring, and their odds. Predictable. Requires only the blood type of each parent.

2. Size at which cells divide. Not yet predictable. Cells are enormously complex, and thus a model capable of predicting this would require enormous detail.

Granted, there is a practical difference among the fields, in that physics has more phenomena that can be predicted with simple models than chemistry, and chemistry more than biology, because as one goes from physics → chemistry → biology, one is typically studying successively higher levels of organization of matter. But I regard that as practical difference rather than a fundamental one.

• Reminds me of Rumsfeld's famous "known unknowns and unknown unknowns". Another classic example: the weather. In some cases it is not detail that matters (nonlinear dynamics), in fact accurate simple models can fail to provide useful predictions even when all parameters are known exactly. Oct 20 '20 at 7:11

"it seems that every other STEM field has models to predict results (physics, thermodynamics, fluid mechanics, probability, etc) but chemistry is the outlier"

This is only partially true, but there are areas of all of those fields where predictive power is difficult in practice due to the complexity of the system and convolution of features. In simplified cases, yes, we can do quite well, but once the systems grow in size and complexity, we do less well.

Physics is a good example of this. The laws of mechanics are quite well-understood. But how well can you handle a chaotic 3-body system? There may be features that are predictable, but not probably not the entire system.

With thermodynamics, how well do we handle mesoscopic systems? Computationally, they can be quite difficult. In thermodynamics, we're able to deal with this complexity by discarding features that we don't care about to focus on bulk properties that rapidly converge in ever-larger systems, but we can't handle the entire system.

Fluid mechanics. OK. We have Navier-Stokes. Have you tried solving Navier-Stokes? Entire volumes have been written about how to deal with Navier-Stokes, and we still don't have great understanding of all of its features.

Probability. This is trickier to talk about, but I think the difficulty and complexity is building an underlying probabilitistic model. When you build your machine learning model, there are generally hyper-parameters to set. What makes a good hyper-parameter and how do you pick one? Just the one that works?

The thing with chemistry is that real-life examples are already incredibly complex. Pick any reaction you want. Liquids or solids? You're already dealing with bulk properties, phase interfaces, and boundary effects. Or solutions and solution effects. Gases? Once you have non-trivial reactions, how many atoms are there? How many electrons? Now, consider the fact that your typical organic reaction involves compounds with tens or hundreds of atoms in solution. There may be multiple models of reactivity, some productive, some not. And in the laboratory, reactions can be quite sensitive to any number of reaction conditions, which a generalized reactivity model does not begin to account for.

But in chemistry, as with the other disciplines, we aim to find simplifications that allow us to deal with complexity. We've been able to find patterns of reactivity, which are somewhat general but don't capture the full complexity of the system.

There are some great answers to this question already, but I'd like to provide a more practical boots-on-the-ground answer from my own perspective as an organic chemistry PhD who did computational chemistry on the side.

## Most fields at their cutting edge are unpredictable

It has been my observation that when you come up against the frontier of what is possible, progress comes by and large only through a long grinding process of Trial and Error. When a breakthrough in understanding is made and the process all of a sudden becomes easy, rapid progress is made until things become hard again. This is true of all sorts of complex projects. The theory helps you along so far, but at some point you have to go off the beaten track and make your own way.

## Chemistry gets mathematically hard, fast

Someone who's completing their undergraduate in a STEM field is likely to have a bit of a skewed impression of the first fact, because they will have already reached that point of unpredictability with chemistry but not with physics. It takes a long time to learn the differential equations associated with things like mechanics, stress-strain, heat transfer, fluid dynamics, electromagnetism and quantum fields. These topics often have solutions for idealised situations that are amenable to being written on paper in closed form.

The (comparative) simplicity of these solutions along with the difficulty of learning the necessary maths along the way may give the undergrad physicist the mistaken idea that this is what all physics is like. Hard-but-tractable differential equations that yield elegant solutions. In reality once you get past the idealised conditions physics becomes much more about computer simulation and experimentation.

In contrast, the equations that describe what happens in the flask (kinetics and thermodynamics) go from trivial to mind-bendingly difficult with only a little bit of added complexity. Other answerers have gone into this part in more detail, so I won't talk but about it here. Suffice to say I spent many fruitless hours of my education trying to find a generalised maths approach to the problems I was facing.

In practice, at least for organic chemistry, the main objective is to synthesise compounds from other compounds, typically complex ones from simple ones. The theory sort of devolves into a broad, massive decision tree.

Want to make intermediate A? try reaction B, if that doesn't work try reaction C. C normally works for this kind of thing, so if it's not working, check that your reagents are pure. You could try D but that's likely to deprotect the other side of A.

Systematic studies of certain reaction patterns exist, and they can certainly be helpful. Take the substitution patterns of aromatic rings, for instance. Using a bit of orbital theory, you can predict the outcome of reactions on aromatic rings based on what's already on the ring and in what position. But again, these studies were done on simple substrates and may not necessarily apply to whatever synthetic behemoth you're working on.

## Lab work is hard

Finally on to the practical aspect. Chemical reactions may fail for any number of reasons that aren't theoretical. There's basic stuff like the cleanliness of your equipment and the purity of your reagents. You can lose heaps of your material by choosing the wrong solvents to work up (extract the product from the reaction mixture) with. Most of the material has gone into the aqueous layer without you knowing it, and you've either discarded it (rookie mistake) or it's degraded or turned into something else before you realised.

Then there's the more subtle stuff. The reaction might only work with one particular stir bar because it was impregnated by a palladium catalyst at some point. Reactions often need rigorous exclusion of oxygen and water to work, but occasionally you actually need some oxygen present to make it go, and the only way you'd ever find this out is by noticing the sloppily set up reactions always seem to perform better than the rigorous ones. You have one bottle of reagent from the sixties from a company that no longer exists, and once that's used up, the new bottle of the same reagent just doesn't work (this one happened to me). The surface of your glassware is slightly too acidic for your reaction, and you need to silanise it to get it to work (also happened to me). Some reactions don't work because your country is just too damn humid. The procedure you're following was written by a student desperate to impress/placate their adviser, and the yields are inflated. Your current lot of acetonitrile solvent is lower quality because China shut down their polluting acrylonitrile plants in order to improve the air quality in preparation for the Olympics. And so on and so forth.

Chemistry as a subject is very bitsy and messy. The best chemists I've known often had excellent memories. But all subjects tend to be messy and bitsy once you get past the basic theory and into the fine details.

To me, it seems that every other STEM field has models to predict results (physics, thermodynamics, fluid mechanics, probability, etc) but chemistry is the outlier.

What about structural engineering? Within that field, it's quite easy to predict the strength of a beam of known material and dimension, like a steel I-beam or dimensional lumber. But what about some new material, like a composite of toothpicks embedded in Elmer's glue?

Whether the material is steel or toothpick-glue composite, couldn't one "just" predict the strength from more basic physical properties?

Well yes, but that would be very complex. But I think more importantly, that wouldn't be structural engineering anymore. It would be some more basic field of physics.

You argue chemistry is "unpredictable" because reactions are described by rules and patterns rather than being derived from first principles. I posit these rules and patterns are chemistry. Without them, you no longer have chemistry. So chemistry is "unpredictable" (in your sense) by definition.

This isn't unique to chemistry, really. Most fields of study are based on the application of more pure fields, adding their own rules and patterns to enable higher-level reasoning about more complex systems:

The answer is dimensionality reduction: a reaction has billions and billions of atoms interacting with one another, but we create analogies to the interactions using just a few symbols which we manipulate using rules; a symbolic analogy of countless atoms interacting, but this process implies loss of information about reality. The simpler the analogy, the higher the loss of information and the less accurate the analogy. The results of symbol manipulation will differ from the reality of the reaction. The average of a set of numbers is a good example: you reduce a set of n dimensions onto a single dimension. There is a loss in information.

Another example: Newtonian physics did not predict what scientist saw with the famous Double Slit experiment. The moment that happens, the rules and symbols you use to make predictions(like the yield of a chemical reaction) become useless. So, it's not that Chemistry is unpredictable, the symbols we use to make predictions about chemistry are not good enough. The only way to make 100% accurate predictions is to simulate every single atom and subatomic particle and be certain the rules we use to define the interactions are 100% analogous to what happens in reality. We know this to be impossible due to the uncertainty principle.

Quantum chemistry has much more complex models that are a better analogy to a reaction, thus it is a *better predictor, but never 100% accurate.

Any basic text in Organic Chem has a table of contents.So for a given transformation such as reduction it will list reagents( the chemicals or conditions,eg heat ,light,that appear above the arrow connecting reactants with products) For a simple reactions such as the sodium borohydride reduction of acetone to isopropanol I have absolute faith that if I carry this out in the laboratory it will work.If it didn't work I would check the labels on the reagent bottles and confirm the identity/purity of the chemicals used.If these checked out and the reaction still failed ,it would be in the category of dropping an apple and watching it ascend up toward the sky.It is not a matter of a failed opinion.Now if I change the substrate to a large polyfunctional molecule,the analogous reduction may not occur at all or yield a highly rearranged product.Retroanalysis may provide a rationale but for the bench chemist doing the reduction,it is an opinion as to whether it is worth trying the reaction in the first place.

Simply put, it is because we don't have complete or near complete understanding of the forces that drive chemical reactions, every few atoms added to the structure of the compounds will add new forces and layers of complexity that we haven't accounted for in our simple 300 years of chemistry knowledge. You can sense this when you learn the theories show their limitation at some point where complexity surfaces (for instance Lewis, Huckel ... etc).