DFT as Operational Foundation of Chemistry?

Connecting to the previous post, recall the common idea that Density Functional Theory DFT as a form of StdQM: 

• serves as Operational Foundation of Chemistry OFC. 
• does not serve as Conceptual Foundation of Chemistry CFC. 

Recall that DFT is based on electron (charge) density $\rho (r)$ defined in StdQM as a mean-value of the wave function squared by integration over all 3d variables of configuration space, except one denoted by $r$. The idea of dimensional reduction to electron density in 3d by massive integration was taken up by Thomas-Fermi already in 1927, but was quickly abandoned because it did not work out, but the idea then resurfaced in more advanced form as DFT the 1960s to now serve as OFC but not CFC,  described by Nobel Laureate Roald Hoffman: DFT gives numbers but not stories. 

But is it possible to produce numbers as OFC without stories as CFC?  

Recall that electron density is defined as a massive mean-value where massive information is destroyed by integration. In particular electron-electron repulsion potential energy and electron kinetic energy are not computable from $\rho (r)$ and so not total energy. 

To derive total energy from electron charge density $\rho (r)$ requires modeling of exchange/correlation seeking to eliminate effects of massive integration as a form of information recovery, which is the role of DFT to deliver.  

The foundation of DFT is the Hohenberg-Kohn Theorem HKT stating that ground state total energy is uniquely determined by electron density, however without any specific information about the connection since HKT is based on a non-constructive logical mathematical contradiction argument without physical meaning. The difficult task assigned to DFT is to recover information lost by integration and so serve as OFC. Does it work? Is it really possible to recover information after formation of mean value?

Basic questions:

1. Can DFT serve as Foundation of Chemistry FoC as only OFC and not CFC?
2. What is the role of HKT for DFT?

RealQM is an alternative to StdQM displaying full information about individual electron charge distribution with direct delivery of electron-electron repulsion energy and electron kinetic energy. It appears that RealQM can deliver both OFC and CFC?

The Nobel Prize in Chemistry 1998 (1/2) was awarded to Walter Kohn "for his development of the density-functional theory (within computational quantum chemistry)" and more precisely because he 

• Demonstrated that electron density is sufficient to determine ground-state properties.
• Replaced the intractable many-body wavefunction with a tractable density-based formulation.
• Enabled first-principles calculations for real chemical systems. It was recognition of a foundational structural innovation in quantum chemistry.

Here is a comment by ChatGPT taking two positions and comparing:

Here are the strongest versions of (A) the post’s critique and (B) the standard DFT/StdQM defense — then a direct comparison, focused exactly on the two “basic questions” in the post.

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A. Strongest version of the post’s critique

Core thesis (post): DFT may deliver numbers (OFC) but cannot be a real foundation because it lacks a constructive, physically meaningful route from electron density to total energy.

1. “Density is a lossy mean-value”

• In StdQM, the one-particle density $\rho (r)$ is obtained by integrating square of wave functions over the other $3N-3$ coordinates; the post emphasises this is a massive averaging that “destroys information.”

• Therefore, the post argues: you cannot, in general, reconstruct electron–electron repulsion and kinetic energy from $\rho (r)$ alone.

2. “HK is non-constructive and ‘without physical meaning’”

• HK is portrayed as a contradiction-style existence theorem: it asserts uniqueness of $E[\rho ]$ for the ground state but gives no constructive map from $\rho$ to energy.

• So: HK cannot “found” DFT in a physical sense; it only licenses the hope.

3. “DFT = information recovery after compression”

• The post frames exchange–correlation modeling as an attempt to recover what was lost by integration (information recovery after forming a mean).

• Skeptical question: Is it even possible in principle to recover what was destroyed? If not, then DFT cannot be a true foundation—only a patchwork fit machine.

4. “Numbers without stories is unstable”

• Invokes Hoffmann’s line: “DFT gives numbers but not stories,” then asks whether OFC without CFC is coherent: can chemistry be “founded” on a tool that yields outputs without mechanism?

5. “RealQM as the constructive alternative”

• The post claims RealQM provides “full information about individual electron charge distribution” and directly yields e–e repulsion and kinetic energy, hence could deliver both OFC and CFC.

Bottom line of the critique: DFT’s practical success does not equal foundational status; lacking a constructive physical link from density to energy, it is not a foundation but an effective numerical workaround.

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B. Strongest version of the standard defense

Core thesis (defense): DFT is grounded in rigorous variational structure; “non-constructive” doesn’t mean “non-physical,” and Kohn–Sham provides the constructive machinery. DFT is therefore a legitimate foundation in the modern scientific sense (predictive + principled).

1. **“Information loss” is the wrong lens

• Yes, $\rho (r)$ is a reduced description — but reduction is not automatically “lossy” in the relevant sense.

• HK’s point is precisely that, for ground states, the reduced object $\rho$ is sufficient to determine the external potential and thus all ground-state observables (even if the mapping is unknown in closed form).

2. Non-constructive existence theorems can still be foundational

• Physics routinely uses existence/variational principles as “foundation” (least action; ground-state variational principles; stability as minimization).

• “Physical meaning” comes from what is empirically testable: energies, structures, forces.

3. HK is not the whole foundation; Kohn–Sham is the workhorse

• The defense agrees HK doesn’t give the functional — but says: that’s not a fatal flaw because Kohn–Sham turns the problem into a tractable scheme and the remaining unknown is packaged into $E_{xc}[\rho$.

• So HK = legitimacy/structure, KS = construction.

4. “Numbers without stories” is a feature of mature science, not a bug

• Plenty of correct scientific frameworks explain via structure rather than narrative mechanism (thermodynamics, variational mechanics).

• Chemistry itself thrives on layered explanation: DFT provides the quantitative layer; “bond,” “lone pair,” etc. are higher-level stories built atop it.

5. The decisive criterion: predictive adequacy at scale

• DFT works broadly across molecular and materials chemistry, yielding usable energies and geometries. That’s why it functions as the effective foundation of modern computational chemistry.

Bottom line of the defense: DFT is a foundation because it gives a principled route from first principles (Hamiltonian + variational structure) to testable predictions, even though the exact functional is unknown and explanation is largely variational/structural.

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C. Direct comparison on the post’s two questions

The post’s questions	Strong critique answer	Strong defense answer
1. Can DFT serve as FoC as only OFC and not CFC?	No (or only in a weakened sense). A “foundation” must be constructive/ontological; DFT gives outputs but not mechanism, and depends on ad hoc recovery of lost information.	Yes. “Foundation” in science can be operational + structural. DFT underwrites the quantitative backbone; chemical “stories” are higher-level models, not required at the fundamental level.
2. What is the role of HKT for DFT?	Mostly rhetorical legitimation. HK asserts uniqueness but gives no constructive link, so it cannot ground DFT physically; it’s a non-constructive permission slip.	Structural cornerstone. HK justifies density primacy for ground states; KS supplies construction; functionals are approximations but systematically improvable and empirically constrained.

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D. Where the dispute really sits

It’s not mainly about whether DFT “works.” It’s about what you require from a “foundation.”

• If you require constructive ontology + local mechanism, the post’s critique has real bite.

• If you accept variational/structural grounding + predictive success as foundational, the standard defense is strong.

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E. One sharp “meeting point” question

A single question cleanly separates the camps:

Is it legitimate that the exact $E[\rho]$ exists and the theory is variationally well-posed, even if the exact functional is unknown and we rely on approximations?

• The post leans no (insufficiently constructive).

• The establishment leans yes (this is normal in many-body physics).