NOBEL PRIZE IN CHEMISTRY OF

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*for the discovery of the strongly attractive isovalence bond in molecular structures*

**submitted to:**

**2016 Nobel Committee for Chemistry: Prof. Sara Snogerup Linse (Chairman), Prof. Peter Brzezinski, Prof. Claes Gustafsson, Prof. Olof Ramstršm, Prof. Johan Aqvist, and Prof. Gunnar von Heijne (Secretary)**

via registered mail at

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via fax at +46 (0)8 660 38 47

and via email

http://www.nobelprize.org/nobel_organizations/nobelfoundation/contact.html

**THE NOMINEE. **

I hereby nominate for the 2016 Nobel Prize in Chemistry the Italian-American scientist **Prof. Ruggero Maria Santilli,** formerly from MIT, Harvard University, and other leading institutions, who is the author of about 250 post Ph. D. papers and 18 monographs published by refereed journals and leading publishers around the world (see the curriculum http://www.world-lecture-series.org/santilli-cv and the scientific archive http://www.santilli-foundation.org/news.html and the historical archive http://www.i-b-r.org/ir00022.htm); the founder and editor in chief of the 37 year old Hadronic Journal, Algebras, Groups and Geometries, and other post Ph. D. scientific journals (http://www.hadronicpress.com); the founder and President of the 35 year old Institute for Basic Research (http://www.i-b-r.org); a speaker or keynote lectures at numerous international scientific meetings over fifty years of research (http://www.world-lecture-series.org/); the recipient of numerous scientific prizes (http://www.santilli-foundation.org/santilli-nobel-nominations.html); the founder and Chief Scientist of the U. S. publicly traded company Magnegas Corporation (http://www.magnegas.com); the founder and Chief Scientist of the additional U. S. publicly traded company Thunder Energies Corporation (http://www.thunder-energies.com); and the originator of additional scientific and industrial activities.

**THE DISCOVERIES **

**1. Insufficiency of quantum chemistry for covalence bonds**

When he was a member of the faculty of Harvard University in the early 1980s under support from the Department of Energy (DOE contracts ER-78-S-02-47420.A000, AS02-78ER04742, DE-AC02-80ER1065, DE-AC02-80ER-1065.A001, and DE-AC02-80ER.1065), Prof. R. M. Santilli showed that the covalence bond of an electron pair in singlet coupling cannot exist according to quantum mechanics and chemistry because of the Coulomb repulsion between the two electrons, F = e^{2}/r^{2} that, at mutual distances of one Fermi - 10^{–13} cm, can reach very big values of the order of 10^{26} N.

Additional insufficiencies of quantum chemistry art short distance, including insufficiencies of "screened Coulomb potentials," are presented in Refs. [9,19] and literature quoted therein.

*Figure 1. A reproduction of the original figure used by Santilli to illustrate the fundamental novelty in the transition from the structure of the hydrogen atom to that of the hydrogen molecules which is given by the presence in the latter of the mutual penetration and overlapping of valence electron pairs. Santilli argues that quantum mechanics and chemistry are exactly valid for all distances bigger that that of covalence couplings, but said theories need in the latter care of a "completion" essentially according to the celebrated argument by Einstein, Podolsky and Rosen [9].*

**2. Need for a new non-Hamiltonian attractive force in covalence bonds**

Santilli argued that the only conceivable possibility to achieve an attractive force in covalence bonds is to admit the existence of a *new interaction* structurally beyond quantum mechanics and chemistry, since the latter theories have a Hamiltonian structure and all possible Hamiltonian interactions had failed to achieve an attractive force between identical electrons in covalence bonds.

Santilli accepted that electrons have a *point-like charge* as established by quantum electrodynamics, but he repeated in his works that *"There exist no point-like wavepackets in nature,"* since the electron is known to have a wavepacket with a radius of about one Fermi, which is quite large for particle standards.

Therefore, Santilli indicated that the only conceivable physical origin of the needed new interaction is the *total mutual penetration of the wavepackets of the electrons in singlet coupling.* Santilli then proved that this interaction is *variationally non-selfadjoint* or, equivalently, *non-Hamiltonian,* [1] in the sense that it violates the integrability conditions to admit a representation with a Hamiltonian, thus being beyond any hope of quantitative treatment via quantum mechanics and chemistry.

More specifically,. Santilli showed that the emerging new interaction (Figure 3) is *non-linear* in all variables including the wavefunction, *non-local* because it is distributed in a volume not reducible to a finite collection of isolated points, and *non-unitary* in the sense that its time evolution U(t) characterizes a non-unitary transform [1]

(1) UU^{† ≠ I,}

on a Hilbert space over a conventional numeric field.

*Figure 3. Santilli has shown that the use of all interactions admitted by quantum chemistry leads to a null force between the atoms of the hydrogen molecule, thus identifying the need for basically new, non-Hamiltonian interactions responsible for molecular structures that can only originate in the deep mutual penetration and overlapping of valence electron pairs.*

**3. The birth of isomathematics**

The non-linear, non-local and non-Hamiltonian character of the needed new interactions established in a final form beyond scientific doubt the need of a *new mathematics* in order to achieve a consistent and effective representation of covalence bonds with a true attractive force.

Santilli knew that non-unitary theories are afflicted by serious mathematical and physical insufficiencies, or sheer inconsistencies, such as the violation of causality since they admit solutions in which the effect precedes the cause.

Also, the mathematics underlying quantum mechanics and chemistry is local-differential thus being structurally unable to represent the needed non-local interactions. Besides, quantum mechanics and chemistry cannot consistently represent composite systems with non-linear internal interactions due to the violation of the superposition principle, and have other shortcomings.

The Hamiltonian H(r, p) can only represent linear, local-differential and Hamiltonian, that is, *variationally self-adjoint* interactions [1]. Santilli saw the need of introducing in the basic dynamical equations a *second operator* for the representation of non-linear, non-local and non-Hamiltonian interactions which he denoted T and assumed to be positive-definite, T &gf; 0 for topological consistency, but possess otherwise an arbitrary functional dependence T = T(t, r, p, ψ, ∂ψ, ...).

In order to introduce the new operator T in a mathematically consistent way, Santilli suggested in his monographs [1] the generalization of the conventional associative product AB between generic quantities A, B (numbers, functions, operator, etc.) into the form

(2) AB → A×B = ATB, T > 0,

Mrs. Carla Santilli suggested for the new product the name of *isoproduct* where the prefix "iso" is intended in the Greek meaning of preserving the original axiom of associativity. Since that proposal, the terms "isotopic liftings" are referred to axiom-preserving mathematical maps or physical theories.

In monographs [1], Santilli presented the first known isotopic lifting of 20th century mathematics via the use of isoproduct (2) applied to numbers, functions, operators, etc. In particular, Santilli achieved in Refs. [1] the first known structural generalization of the various branches of Lie's theory, including the isotopies of universal associative algebra, Lie algebras with generalized commutation rules

(3) [A, B]* = A×B - B×A = ATB - BTA,

today known as *Lie-Santilli isocommutators,* and Lie groups, such as the isotopies in one dimension

(4) U(t) = e^{HTti} U(0)e^{-itTH}

today known as the *Lie-Santilli isogroups.*

Subsequently, Santilli recognized that the above non-unitary theory remained afflicted by major mathematical and physical insufficiencies because still formulated on a conventional Hilbert space over a conventional numeric field. In particular, the above isotopic theories were unable to predict the same numerical values under the same conditions at different times.

In order to resolve the impasse, while visiting in the summer of 1993 the *Joint Institute for Nuclear Research* in Dubna, Russia, Santilli was forced to reinsert the historical classification of numbers by Gauss, Cailey, Hamilton and other illustrious mathematicians, and discovered that said classification was incomplete since the basic numeric axioms also admit numbers with arbitrary positive-definite multiplicative units [2].

*Figure 3. An illustration of the notion at the foundation of this nomination, namely, the deep mutual penetration and overlapping of the wavepackets of valence electrons in singlet coupling, with ensuing non-linear, non-local, and non-Hamiltonian interactions whose quantitative treatment requested Prof. Santilli to conduct decades of studies, first, for the construction of the new isomathematics [1-3], and then the construction of the novel isomechanics [7] and isochemistry [9].*

In this way, Santilli discovered new numeric fields F*(n*,×,I*),, today known as *Santilli isofields,* admitting the positive-definite, but otherwise arbitrary, generalized multiplicative unit

(5) I* = 1/T >. 0,

today known as *Santilli isounit.*

with associated isoproduct (2) resulting in the discovery of the new *isoreal, isocomplex, or isoquaternionic numbers*

(6) n* = nI*,

where n is an ordinary real, complex or quaternionic number.

Recall that physical quantities, such as coordinates r, Linear linearmomenta p, energy E, etc., can be called "scalars" when their values are on a conventional field. For consistency, all physical quantities of isotopic theories must be *isoscalars,* that is, must have value in an isofield, thus leading to *isocoordinates* r* = rI*, *isomomenta* p* = pI*, * isoenergy* E* = EI*, etc.

Despite the reformulation o isofields, isotopic theories remained afflicted by inconsistencies. In particular, they were unable to predict the same numeric values under the same conditions at different times.

Following extensive efforts, during the heat of the sessions of the 1995 *Second International Conference on non-potential Interactions* held at the Castle Prince Pignatelli in Italy, Santilli was left with no additional option than that of re-inspecting the most fundamental calculus of 20th century theories, the Newton-Leibnitz differential calculus.

in this way, Santilli discovered that, contrary to a general belief in mathematics for over four centuries, the ordinary differential calculus does indeed depend on the unit of the base field. the conventional differential calculus hold for the particular case when said unit is not dependent on the differential valuable. However, when said unit dopes indeed depend on the differential variable, Santilli discovered the generalized form [3],

(7) d*r* = Td r* = T d [rI*(t, r,p, ...)] = dr + TdI*,

In the same memoir [3], Santilli reformulated the isotopies of the main aspects of 20th century mathematics, including the isotopies of numeric fields, functional analysis, differential calculus, metric spaces, geometries, algebras, symmetries, etc. and showed the achievement of the needed mathematical and physical consistency.

Nowadays, *isomathematics* is referred to a mathematics characterized at all levels by an arbitrary, positive-definite, multiplicative unit I* = 1/T >. 0 and isoproduct (2), thus including the isotopies of all aspects of 20th century mathematics without exceptions (see Refs. [4-6] for independent studies). The isodifferential calculus is today called the *Santilli-Georgiev isodifferential calculus* in view of the monumental series of six volumes ion the field written by S. Georgiev [6].

*Figure 4. A view of the isochemical model of the hydrogen molecule at absolute zero degree temperature, thus without rotations, showing the Santilli strong isovalence bond between electron pairs into the isoelectronium quasiparticle. Note the oo-shaped orbit of the isoelectronium with consequential representation of the diamagnetic character of the hydrogen molecule and its reduction to a restricted three-body system [9,14,15] thus admitting analytic solutions [16,17].*

**4. The birth of isomechanics and isochemistry**

Following the proposal of isoproduct (2) and of the isotopies of Lie's theory, Santilli introduced in monograph [1b], page 260, the isotopic generalization of Heisenberg equation for the time evolution of an observable A in the finite form

(8) idA/dt = A×H - H×A = ATH - HTA,

and the isotopic generalization of Schroedinger equations

(9) H×|ψ > = E* × |ψ > = E |ψ>>,

The above isoequations were then studied in detail in memoir [3] as well as in monographs [7] and they are today known as the *Heisenberg-Santilli isoequations* and the *Schroedinger-Santilli isoequation,* respectively.

Santilli introduced in Ref. [1b], page 112, the name *hadronic mechanics* for the new mechanics with the most general possible covering of quantum mechanics which is irreversible over time and its algebraic structure is characterized by *Santilli Lie-admissible theory.* Ref. [1b] then introduced the name of *isomechanics* for the particular branch of hadronic mechanics characterized by isoequations (8) and (9) whose algebraic structure is given by the *Lie-Santilli isotheory.* In Refs. [3,7], the isoequations achieved the final form of being formulated on *Hilbert-Myung-Santilli isospaces* [8] over Santilli isofields [2].

Santilli proposed isomechanics for the representation of closed-isolated bound stems of extended particles/wavepackets with non-linear, non-local and non-Hamiltonian internal forces, because the Lie-Santilli isocommutator is antisymmetric, thus allowing the conservation of conventional total physical quantities, such as that of the total energy

(10) idA/dt = H×H - H×H = 0.

Following, and only following the achievement of sufficient mathematical and physical maturity treated in expected new nominations, Santilli published in 2001 monograph [9] dedicated to *hadronic chemistry* with particular emphasis on the particular branch of *isochemistry* which is the subject of this nomination.

The most salient features of isomechanics and isomechanics can be summarized as follows [3,7,9]:

1. Isomechanics and isochemistry are a non-unitary "completion" of quantum mechanics and chemistry, respectively, essentially according to the celebrated argument by Einstein, Podolsky and Rosen.

2. The basic axioms of isomechanics and isochemistry are the same as those of quantum mechanics and chemistry, to such an extend that all distinctions disappear at the abstract, realization-free level.

3. Isomechanics and isochemistry are solely valid at one Fermi mutual distances and recover conventional mechanic s and chemistry, respectively, for mutual distances sufficiently bigger than one Fermi.

4. Isomechanics and isochemistry are the only known theories allowing a consistent treatment of bound states of extended particles/wavepackets with non-linear internal forces thanks to the verification of the superposition principle on isospaces over isofields that allow a consistent treatment of the individual constituents.

5. The ultimate significance of isomathematics in the resolution of the inconsistencies of non-linear, non-local and non-unitary theories is that of allowing the reconstruction of locality, linearity and unitarity when formulated on isospaces over isofields, resulting in new notions today known as * Santilli isolocality, isolinearity, isolocality and isounitarity.*

*Figure 5. A view of the water molecule H _{2}O H-O-H at absolute zero degree temperature, thus without any rotational degree of freedom, showing Santilli strong isovalence bonds H-O and O-H that have allowed a numerically exact and time invariant representation of the binding energy and other features of the water molecule [9,15].*

**5. Santilli strong isovalence bond**

Santilli has stated in Ref. [9] that *Even though scientifically valuable, the quantum chemical notion of covalence is a 'nomenclature' because it is essentially conceptual and misses a quantitative treatment producing an fully identified 'attractive' force between valence electrons in singlet coupling.* Consequently, Santilli initiated long-term studies to achieve a representation of covalence electron bonds verifying the following conditions:

**Condition I:** Be quantitative, that is, the bond is treated via equations;

**Condition II:** Produce an explicit force which is so attractive to overcome the Coulomb repulsion; and

**Condition III:** Be in agreement with molecular binding energies and other molecular data.

Conditions I and II were solved by Santilli in 1978 [12] when he was in the faculty at Harvard Universe, by proving that the representation of non-linear, non-local, and non-Hamiltonian interactions via isoequations (9) with the simple isotopic element

(11) T = e^{–Γ(ψ,...) ∫ ψ ψ† d3,}

creates an explicit *attractive* force represented by a Hulten potential which is so *strong* at short distances to "absorb" Coulomb forces (because the Hulten potential is known to behave like the Coulomb potential at one Fermi mutual distances).

Santilli then applied this mechanism (see Ref. [12], Section 5 in particular) to reach the first (and only) known representation of *all* characteristics of the π^{0} meson as a *compressed positronium,* namely, as a bound state at one Fermi mutual distance of one electron and one positron.

The historical significance of Santilli π^{0} model (hat will be treated in details in a separate forthcoming nomination) is that paper [12] established the existence of a component of the strong interactions which is of non-liar, non-local, and non-Hamiltonian. In fact, strong interactions can only act at one Fermi mutual distances, thus implying the necessary mutual penetration and overlapping of the wavepackets of particles.

*Figure 6. A reproduction of Tables 4.1 and 4.2 of monograph [9] showing the achievement by isochemistry of a numerically exact representation of all features of the hydrogen molecule. The invariance over tie stems from the invariance of isochemistry under the Galileo-Santilli isosymmetry for relativistic motion and under the Lorentz-Poincare'-Santilli isosymmetry for relativistic motions that are treated in separate nominations.*

Subsequently, A. O. E. Animalu and R. M. Santilli [13] noted that the Hulten potential emerging from the isotopic element (11) is so strong to overcome the known Coulomb repulsion of Cooper pairs in superconductivity. Animalu then introduced a new model of superconductivity, today known as *Animalu isosuperconductivity* to be treated in a future nomination, which is in full agreement with experimental data, as well as having remarkable predictive capacities not available in conventional superconductivity.

Following this preparatory research, Santilli conducted systematic studies [9] to verify Condition III resulting in a new model of covalence bonds, today known as *Santilli strong isovalence bond.* Detailed studies on the verification of Condition III were done by Santilli and D. D. Shillady who established that the strong isovalence bond allows a numerically exact and time-invariant representation from first axiomatic principles (that is, without ad hoc parameters or functions) of the binding energy and other data of the hydrogen [14] and water molecules [15].

An important advance in Refs. [9,14,125] is that isomathematcs allows the remove of the singularity at the origin r = 0 of the Dirac distribution thanks to the *Dirac-Myung-Santilli isodelta isofunction* [19]

(13) δ*(r) = ∫ e^{ikT(r, ...)r} dk,

and the conversion of weakly convergent series, such as the canonical one

(14) A(w) = I + w (AH - HA)/1! + ...

into strongly convergent isoseries, e.g., of the isocanonical type,

(15) A(w) = I* + w (ATH - HTA)/1! + ...

Consequently, the time currently needed for computer calculations of molecular data can be reduced by at least 1,000 times [9,14,15].

*Figure 7. A reproduction of Table 5-1 of Ref. [9] summarizing the achievement of the first numerically exact representation of the binding energy, electric and magnetic moments of the water molecule.*

Santilli isovalence bond is so strong to turn a valence electron pair into a quasi-particles called *isoelectronium* [9,14,15] with significant implications, such as the first (and only) quantitative representation of the diamagnetic character of the hydrogen molecule [9].

In turn, the isoelectronium has allowed the first and only known reduction, in good approximation, of the of the hydrogen molecule to a restricted three-body systems, thus allowing analytic solutions that have been studied by A. K. Aringazin and M.G. Kucherenko [16], R. Perez-Enriquez and R. Rivera [17], and otehrs.

Among a rapidly expanding bibliography on Santilli strong isovalence bond, we mentions Refs. [18,19] and lectures [20,21].

_____________________________

The signature available in the

original nomination has been withheld

in the internet for privacy.

**REFERENCES**

[1] R. M. Santilli, * Foundation of Theoretical Mechanics,* Volumes I (1978) [3a], and Volume II (1982) [3b], Springer-Verlag, Heidelberg, Germany,

http://www.santilli-foundation.org/docs/Santilli-209.pdf

http://www.santilli-foundation.org/docs/santilli-69.pdf

[2] R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and "Hidden Numbers" of Dimension 3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993)

http://www.santilli-foundation.org/docs/Santilli-34.pdf

[3] R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures, P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996)

http://www.santilli-foundation.org/docs/Santilli-37.pdf

[4] Chun-Xuan Jiang, * Foundations of Santilli Isonumber Theory,* International Academic Press (2001),

http://www.i-b-r.org/docs/jiang.pdf

[5] Raul M. Falcon Ganfornina and Juan Nunez Valdes, * Fundamentos de la Isdotopia de Santilli,* International Academic Press (2001),

http://www.i-b-r.org/docs/spanish.pdf

English translation Algebras, Groups and Geometries Vol. 32, pages 135-308 (2015),

http://www.i-b-r.org/docs/Aversa-translation.pdf

[6] S. Georgiev, * Foundations of the IsoDifferential Calculus,* Volumes, I, II, III, IV, V and VI, Nova Scientific Publisher (2015 on).

[7] R. M. Santilli, * Elements of Hadronic Mechanics,* Vol. I and Vol. II (1995) [15b], Academy of Sciences, Kiev,

http://www.santilli-foundation.org/docs/Santilli-300.pdf

http://www.santilli-foundation.org/docs/Santilli-301.pdf

[8] H. C. Myung and R. M. Santilli, "Modular-isotopic Hilbert space formulation of the exterior strong problem," Hadronic Journal {\bf 5}, 1277-1366 (1982),

http://www.santilli-foundation.org/docs/Santilli-201.pdf

[9] R. M. Santilli, *Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels,* Kluwer Academic Publishers (2001),

http: //www.santilli-foundation.org/docs/Santilli-113.pdf

Russian translation by A. K. Aringazin

http://i-b-r.org/docs/Santilli-Hadronic-Chemistry.pdf

[10] E. Trell, "Review of Santilli Hadronic Chemistry," International Journal Hydrogen Energy Vol. 28, p. 251 (2003),

http://www.scientificethics.org/Hadronic Chemistry.pdf

[11] V. M. Tangde, "Advances in hadronic chemistry and its applications," Foundation of Chemistry, DOI 10.1007/s10698-015-9218-z (March 24, 2015)

http://www.santilli-foundation.org/docs/hadronic-chemistry-FC.pdf

[12] R. M. Santilli, "Need of subjecting to an experimental verification the validity within a hadron of Einstein special relativity and Pauli exclusion principle," Hadronic J. **1**, 574-901 (1978),

http://www.santilli-foundation.org/docs/santilli-73.pdf

[13] A. O. E. Animalu and R. M. Santilli, "Nonlocal isotopic representation of the Cooper pair in superconductivity," Intern. J. Quantum Chemistry Vol. 29, 185 (1995)

http://www.santilli-foundation.org/docs/Santilli-26.pdf

[14] R. M. Santilli and D. D. Shillady, "A new isochemical model of the hydrogen molecule," Intern. J. Hydrogen Energy Vol. 24, pages 943-956 (1999)

http://www.santilli-foundation.org/docs/Santilli-135.pdf

[15] R. M. Santilli and D. D. Shillady, "A new isochemical model of the water molecule," Intern. J. Hydrogen Energy Vol. 25, 173-183 (2000)

http://www.santilli-foundation.org/docs/Santilli-39.pdf

[16] A. K. Aringazin and M.G. Kucherenko, "Exact variational solution of the restricted three-body Santilli-Shillady model of the hydrogen molecule," Hadronic J. Vol. 23, 1-56 (2000) (physics/0001056)

www.santilli-foundation.org/docs/3body.pdf

[17] R. Perez-Enriquez and R. Riera, "Exact analytic solution of the restricted three-body Santilli-Shillady model of the hydrogen molecule, " Progress in Physics Vol. 2, 34-41 (2007) (physics/0001056)

www.santilli-foundation.org/docs/3body2.pdf

[18] S. S. Dhondge and A. A. Bhalekar, "Hadronic Chemistry and Binding Energies," American Institute of Physics, in press 2013

http://www.santilli-foundation.org/docs/SSD-Rhodes.pdf

[19] I. Gandzha and J. Kadeisvili, *New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli,* Sankata Printing Press, Nepal (2011),

http://www.santilli-foundation.org/docs/RMS.pdf

[20] R. M. Santilli, *An Introduction to Hadronic Chemistry,* Invited Lecture delivered at the Institute for UltraFast Spectroscopy and Laser City College of New York on October 19, 2012

http://www.world-lecture-series.org/lecture-iv-a

[21] R. M. Santilli, *An Introduction to Hadronic Chemistry,* Keynote speech at the International Workshop on Hadronic Chemistry, Mathematics and Physics October 21 to 26, 2013, India Department of Chemistry Rashtrasant Tukadoji Maharaj Nagpur University

http://www.world-lecture-series.org/santilli-india-2013

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