Santilli’s 2001 Completion of Quantum Chemistry According to Einstein’s 1935 Argument

A PubRelco Interview of Sir Ruggero Maria Santilli. with Scientific and Industrial implications.New York, N.Y., April 15, 2019
Q1. Prof. Santilli, could you please review in a language accessible to the general audience Einstein’s 1935 historical prediction that quantum mechanics and, therefore, quantum chemistry are incomplete theories

A1. Einstein did not accept the uncertainty principle of quantum mechanics, namely, the impossibility to identify the position of a particle with classical precision. For that reason, he made his famous quote “God does not play dice with the universe.” Einstein believed that quantum mechanics is an “incomplete theory,” in the sense that it could be broadened into such a form to recover classical determinism at least under special conditions. The same argument evidently applies to quantum chemistry.

Q2. We understand that you proved Einstein’s vision in physics.

A2. Yes, as reported in your preceding interview, I provided three physical broadening of quantum mechanics along Einstein’s vision, the first was done by including irreversibility over time of energy releasing processes, the second was done via the representation of particles as they are in the physical reality (extended, deformable and hyperdense), and the third was done via the use of a suitable mathematics showing the existence of the so-called ‘hidden variables’ in quantum axioms, such as those for spin and angular momentum. I also provided examples of particle pairs whose mutual distance recovers indeed classical determinism under extreme conditions, as predicted by Einstein.

Figure 2. A conceptual rendering of the hydrogen molecule at absolute zero degree temperature without the bond of valence electrons showing no attractive or repulsive force between the two hydrogen atoms..

Figure 2. A conceptual rendering of the hydrogen molecule at absolute zero degree temperature without the bond of valence electrons showing no attractive or repulsive force between the two hydrogen atoms..

Q3. Are you claiming to have proved Einstein’s vision also in chemistry?

A3. Einstein’s vision on the lack of final character of quantum mechanics has implications for all of 20th century sciences. Therefore, the lack of confirmation of Einstein’s argument in chemistry would imply the lack of actual achievement of Einstein’s vision.

Figure 3. A conceptual rendering of the hydrogen molecule according to quantum chemistry showing the repulsion (rather than a bond) between two point-like valence electrons due to their equal charge..

Figure 3. A conceptual rendering of the hydrogen molecule according to quantum chemistry showing the repulsion (rather than a bond) between two point-like valence electrons due to their equal charge..

Q4. Can you please outline the main aspect of the confirmation in chemistry?

A4. With the understanding that quantum chemistry did achieve historical advances, I did not accept quantum chemistry as being a final theory since my graduate studies at the University of Torino, Italy, in the mid 1960s, because of a truly fundamental insufficiency, namely, the inability by quantum chemistry to identify the attractive force bonding together atoms into molecules. Consider for simplicity the hydrogen molecule H2 at absolute zero degree temperature. When the two electrons move in independent orbits (Figure 1), the hydrogen molecule cannot exist due to the absence of any possible bond. In fact, the two hydrogen atoms are bonded into H2 by the bond between the two valence electrons with antiparallel spin. By following Einstein,, I could not consider quantum chemistry to be a complete theory because according to the basic axioms of quantum chemistry, valence electrons should ‘repel’ each other due to their equal charge, without any known possibility of admitting their attraction

(Figure 2).

There was no doubt in my mind that the understanding of the attractive force between valence electrons required a ‘completion’ of quantum chemistry precisely along Einstein’s vision. Following decades of research including contributions by various colleagues, quantum chemistry was completed into a covering theory known as hadronic chemistry; the attractive force between valence electrons was clearly identified; and the ‘completed’ theory was proved to verify molecular experimental data..

Figure 4. A conceptual rendering of the hydrogen molecule according to the completion of quantum chemistry into hadronic chemistry illustrating the first and only known attractive force between valence electrons caused by non-potential interactions due to deep penetration of extended wavepackets .

Figure 4. A conceptual rendering of the hydrogen molecule according to the completion of quantum chemistry into hadronic chemistry illustrating the first and only known attractive force between valence electrons caused by non-potential interactions due to deep penetration of extended wavepackets .

Q5. Can you please outline the main steps of the indicated achievements?

A5. I had to accept the chemical evidence establishing the existence of a strongly attractive force between valence electron pairs. This can only occur via a new interaction not representable with quantum chemistry which interaction can only be non derivable from a potential. In turn, the representation of the new attractive force could only be done by ‘completing’ quantum chemistry into a broader theory.

Q6. How did you achieve the needed ‘completion’ of quantum chemistry?

A6. I accepted the evidence hat valence electrons are not point -particles as represented by quantum chemistry (Figures 1 and 2), because they are characterized by wavepackets as big as nuclei. I also accepted the experimental evidence that the wavepackets of valence electrons are in conditions of deep mutual penetration (Figure 3). This allowed me to identify the new force as being of contact type, thus not being derivable from a potential.

Q7. How did you develop these ideas into a viable ‘completion’ of quantum chemistry?

A7. The biggest difficulty was mathematical, rather than chemical, because the mathematics of quantum chemistry can only represent potential forces between point particles. A mathematics for the representation of non-potential forces between extended valence electrons did not exist and, therefore, had to be built. When I was at the Department of Mathematics of Harvard University inn the late 1970s under DOE support, I proposed a new mathematics based on the generalization of all products AB between arbitrary quantities A, B, into the form A*B = ATB called ‘isotopic’ in the sense of being axiom-preserving, where T represents precisely the new non-potential forces (see my 1978 monographs with Springer-Verlag Foundation of Theoretical Mechanics, particularly Volume II). This allowed Einstein’s ‘completion’ ofd the mathematical structure of quantum chemistry into a form admitting the d new forces. Applications and verifications could only be done thereafter.

Q8. Please outline the main chemical aspects with links to technical publication for interested chemists.

A8. The new forces were first identified in physics and verified with the representation of the synthesis of mesons (see Section 5 of the 1978 Harvard paper). Following that, In collaboration with the University of Cambridge Ph. D. physicist A. O. E. Animalu, we applied the new mathematics to the representation of the attractive force between the identical electrons of the Cooper pair in superconductivity (see the 1985 paper). In view of encouraging results in superconductivity, I conducted systematic studies that lead to the first and only known ‘attractive’ force between a valence electrons pair in molecular structures nowadays known as the isoelectronium (see the 2001 monograph Foundations of Hadronic Chemistry, see also the independent reviews byV. M. Tandge, and by E. Trell). In collaboration with the chemist Don D. Shillady of Virginia Commonwealth University, we proved that the ‘completion’ of quantum l molecular models into the form admitting an explicitly attractive force between valence electron pairs permitted the first known exact representation of experimental data of the hydrogen molecule, and of the water molecule.

Prof. R. M. Santilli

Prof. R. M. Santilli
Prof.  A. O. E. Animalu

Prof. A. O. E. Animalu
Prof.  D. D. Shillady.

Prof. D. D. Shillady.

Q9. Could you please indicate how the representation of the hydrogen molecule according to Figure 3 verifies Einstein’s argument?

A9. When the two valence electrons have independent orbits as in Figure 1, quantum mechanics is exactly valid and so is the uncertainty principle, namely. it is impossible to identify with classical precision their mutual distance. By contrast, when the two valence electrons are represented as extended particles in conditions of deep mutual penetration with ensuing non-potential forces as in Figure 3. the mathematics (let alone the physics) underlying the uncertainty principle is inapplicable (see Post 10 of thepreceding interview), and the mutual distance between the two valence electrons approaches classical determinism.

Q10. Does the academic community admit the lack of an actual bond in the hydrogen molecule according to quantum chemistry?

A10. No. The indicated insufficiency is one of several best kept secrets in the best graduate schools in chemistry around the globe.

Q11. Can you indicate the reaction by chemists to your achievement of an explicitly attractive force between valence electrons?

A11. With due exceptions, the reaction by chemists has generally been that of extreme repulsion because, in academia, basic novelty is an enemy to be assassinated at whatever cost. But I believe that such a negative reaction is a rather normal part of the scientific process for basically new vistas because, sooner or later, scientific evidence always emerges.



Post 1
Dear Editors, please ask Prof. Santilli how he achieved an attractive force between identical valence electrons. An outline for non-experts would be appreciated. Vdr39yu

Post 2
Hello Vdr39yu – Post 1, thanks for the important question. The isoelectronium is studied in details in Chapter 4 of Foundations of Hadronic Chemistry. The subsequent chapters provide verifications with molecular experimental data for the hydrogen and water molecules. Here is a rudimentary outline. After years of trials and failures with conventional methods, I had to conclude that there is no possibility to achieve an attractive force between identical electrons via the use of the Schroedinger equation of quantum chemistry,H(r, p) ψ = E ψ,   H = K + V,     (1)

where H is the Hamiltonian of the valence electron pair as the sum of the kinetic energy K and the repulsive potential energy V. I achieved the needed attractive force via the use of the covering iso-schroedinger equation of hadronic chemistryH(r, p) T(ψ*, …)ψ* = E* ψ*,   H = K + V,     (2)

where H represents the conventional Coulomb interaction and T represents the new non-Hamiltonian interaction. Out of a variety of solutions, the simplest one occurs for (see. Eq. (4.7), loc, cit.)T ≈ N eψ/ψ* ≈ 1 + N ψ/ψ* > 0     (3)where N is a positive constant, ψ is the wavefunction of the quantum electron pair (1) and ψ* is an isowavefunction selected in such a way to achieve the desired attraction. Simple calculations yield the following solutionψ* = M(1 – e– b r)/ r     (4)

where b = 1/rhh is the inverse of the ‘hadronic horizon’ rhh (the radius after which quantum mechanics is recovered identically because particles return to have sole potential interactions). Additional simple calculations via the use of Eq. (2) yieldH(r, p) T(ψ*, …) ψ* ≈ (p2/m + e2/r + VHulten) ψ* = E’ ψ*,     (5)VHulten = 1 – Q[1 – e– br/(1 – e-br)/r]     (6)

where m is the mass of an electron.The following points are then important for the plausibility of the model:

    1) The attractive Hulten potential behaves like the Coulomb one at short distance, thus absorbing the repulsive Coulomb potential in Eq. (5) resulting in the desired attraction with a mere re-definition of the Hulten constant Q.

   2) As it is well known, the Hulten potential has a finite number of energy states. Hence, there can only exist a finite number of isoelectronia.| E’ | = A(B/n – n)2 > 0,     (7)

where A and B are positive quantities depending on various local values, see for details Eq.s (5,15) page 171 of [loc. cit.].

   3) The application of the model, which i did with Don Shillady, to the representation of the experimental data of the hydrogen molecule, and of the water molecule yields numerical values of the A and B quantities, in particular, the value B = 1 under which spectrum (7) is reduced to one single value for n = 1. Therefore, the isoelectronium can assume one and only one configuration.

A few words of caution are now in order. The isoelectronium can only be formulated via hadronic chemistry and its underlying new isomathematics. The lack of knowledge of these methods generally results in inconsistencies that often remain unknown to users of conventional methods In fact, rudimentary Eqs. (2) to (7) are expressed via conventional mathematics but they are the projection of the actual equations on isospaces over isofields.

For instance, for the correct formulation of Eq. (2), coordinates r have to be isocoordinates r* – rU, where U is the isounit, U = 1/T; momenta p have to be isomomenta p* formulated via the isodifferential calculus; the Hamiltonian and other operators have to be isooperators defined on an iso-Hilbert isospace over the isofield of isocomplex isonumbers, etc. My suggestion is to understand first the mechanism for achieving the needed attractive forces between identical electrons and then pass to its rigorous formulation. Best wishes. Ruggero M. Santilli (Email:

Post 3
Prof. Santilli, please indicate how the isoelectronium constitutes a verification of the EPR argument. Thanks. Lwe29ty

Figure 6. A conceptual rendering of the structure of the isoelectronium denoting two valence electrons with antiparallel spins under deep penetration of their wavepackets, as occurring in reality.

Figure 6. A conceptual rendering of the structure of the isoelectronium denoting two valence electrons with antiparallel spins under deep penetration of their wavepackets, as occurring in reality.

Post 4
Lwe29ty – Post 3, I am glad to see that this open exchange does indeed stimulate important questions. Here is my view. When the electrons are represented as point-like particles, quantum mechanics applies, and the EPR argument is inapplicable. However, when the electrons are represented with extended wavepackets in condition of mutual penetration, the sole existence of one energy level of the Hulten spectrum, Post 2, their mutual distance (see Figure 6) can only have one value, such as 10-15 cm, thus recovering classical determinism in clinet with Einstein’s vision. Ruggero Maria Santilli (Email:

Post 5
Prof. Santilli, thank you for the clear outline of Post 2 and congrats for a rather difficult achievement. I would appreciate more details on the structure of the isoelectronium, for instance, how you handle the non-linear interactions of hadronic chemistry clearly expressed in Eq. (2). Vdr39yu

Post 6
Hello Vdr39yu – Post 5, I appreciate your interest. You are sharp in seeing that a most crucial aspect of Eq. (2) is its non-linearity in the wavefunction ψ* . It should be recalled here that non-linear equations in quantum chemistryH(r, p, ψ)ψ = E ψ     (8)

violates the superposition principle, thus preventing the decomposition of the wavefunction ψ of the isoelectronium into those of the two valence electrons,ψ ≠ Col.(ψ1, ψ2)    (9)

This insufficiency prevents the identification of the characteristics of the constituents of a bound state with non-linear interactions (in our case, the valence electrons when members of a valence bond). This and other limitations have caused the general lack ion consideration of non-linear interactions in quantum chemistry.

A reason I could not accept quantum chemistry as a final theory is that it is linear in the wavefunction, while chemical reality is expected to be non-linear, particularly in the case of deep mutual penetration of the wavepackets in valence bonds where interactions are non-linear, non-local and non-Hamiltonian. Isomathematics was constructed in such a way to reconstruct linearity on isospaces over isofields. In fact, when you go to the abstract level, the non-linear isoproduct H(r, p)T(ψ*,…)ψ* can be written in the isolinear form , H(r, p) × ψ*, namely, a form which is linear on isospaces over isofields, but its projection tin on conventional spaces over conventional fields is non-linear.

This is due to the fact that all non-linear terms are embedded in the isounit I(ψ*,…) =1/T(ψ*,…) > 0 that, being positive-definite, is topologically equivalent to the conventional unit “1”, thus explaining why non-linearity disappear at the abstract level. I hope these comments have been of assistance in your study of a basic aspect in the search of new advances. Ruggero Maria Santilli (Email;

Post 7
Prof. Santilli, hoping not to abuse your courtesy and time, please provide some information on the structure of the isoelectronium, such as the characteristics of the valence electrons when members of the isoelectroniumc. Vdr39yu<.p>

Post 8
Hello Vdr39yu – Post 7, thanks for an additional quite important question. Unfortunately, my knowledge of the structure of the isoelectronium is rather limited because I was satisfied by the fact that the isoelectronium as a quasi-particle allowed an exact representation if molecular data that could only be approximately represented with quantum chemistry. However, most of the research done for the constituents in the synthesis of the neutron from the proton and the electron applies to the constituents of the isoelectronium. Here are a few comments.According to the 20th century physics of point-particles in vacuum, ‘particles’ are unitary irreducible representation of the Lorentz-Poincare’ symmetry,. 

The neutron synthesis has established that, in the transition from motion in vacuum to motion within hyperdense hadronic matter, particle experience a mutation of their ‘intrinsic’ characteristics including mutations of their rest energy, spin, charge, magnetic moments, etc., in amount depending on local characteristics of the medium. As an example, for hadronic media of low density (such as that in the interior of mesons), conventional spin is expected to be conserved, while I consider purely political the idea that an electron maintains the spin 1/2 when immersed within media of very high density, such as that in the core of a star or in the interior of a black hole. The hierarchy of spin mutations is quantitatively treated in my 1998 proof of the EPR argument

In view of the indicated mutations, the constituents of the isoelectronium are not conventional electrons, but new particles called isoelectrons defined as isounitary isoirreducible isorepresentations of the Lorentz-Poincare’-Santilli isosymmetry on the the iso-Hilbert space over isofields, see the 1995 monograph Elements of Hadronic Mechanics, Volume II. As far as I can see, the spin and magnetic moment of the isoelectrons in the isoelectronium have conventional values, but I expect a mutation of their chargebecause potentially necessary to turn a Coulomb repulsion into an attraction. Hence the identical isoelectrons constituting the isoelectronium can be identified rather accurately via the isoirrep of the Lorentz-Poincare’-Santilli isosymmetry under the subsidiary constraints of recovering chemical molecular data. Sincerely, Ruggero Maria Santilli (Email: 9
Can anybody tell what is the rest energy of the isoelectronium? Ker34ui

Post 10
I studied Santilli’s monograph on hadronic chemistry as well as his paper with Shillady, and my understanding is that the rest energy of the isoelectronium is not precisely known. This is due to the fact that: the sum of the rest energy of the two electron in vacuum is 1.022 MeV; binding energy (7) is very close to zero (for B = 1, n = 1, | E| = 0) because it is the binding energy caused by a “contact” interaction “not” derivable by a potential; and the contribution to the rest energy of the isoelectronium caused by the potential Coulomb interaction – at the risk of saying a “betise” – should give an “excess rest energy” over the value 1.022 MeV, since the interaction is repulsive (the contribution would be a routine mass defect in the event of an attraction). In any case, when compared to the stuffiness of orthodox chemistry, this is a quiet cool and refreshing problem indeed! Thank you, Santilli for peeking deep into nature. Swe57wo

Post 11
I Nominated Prof. Santilli for the Nobel Prize in Physics for his proof of the EPR argument, Post 13 of the preceding interview After reading this interview and studying the related technical literature, I have Nominated Prof. Santilli also for the Nobel Prize in Chemistry hoping that he will be the second Nobel Laureate in both Physics and Chemistry after Madame Curie. Xer22uu

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