Distinguishing electron paramagnetic resonance signature of molecular hydrino

Summary . Quantum mechanics postulates that the hydrogen atom has a stable ground state from which it can be promoted to excited states by capture of electromagnetic radiation, with the energy of all possible states given by E n = -13.598/n 2 eV, in which n  1 is a positive integer. By contrast, it has been proposed that the n = 1 state is not the true ground state, and that so-called ‘hydrino’ states of lower energy can exist, which are characterized by fractional quantum numbers n = 1/p, in which 1 < p  137 is a limited integer 1,2 . Electron transition to a hydrino state, H(1/p) is non-radiative and requires a quantized amount of energy, 2mE 1 (m is an integer), to be transferred to a catalyst 3,4 . Since its inception 5 the hydrino hypothesis has remained highly controversial 6-17 and laboratory verification studies by its proponents have been criticised 18,19 . we an account of an independent electron paramagnetic resonance (EPR) study of molecular hydrino H 2 (1/4) that was produced by a plasma reaction of atomic hydrogen with non-hydrogen bonded water as the catalyst. A sharp, complex, multi-line EPR spectrum is found, detailed properties prove to be semi-quantitatively consistent with predictions 20 from hydrino theory with an average error less than 0.09 G (0.2%) over a 39 G span of 37 lines. sought to find reasonable alternative, ‘conventional’ interpretations for the detected paramagnetism. Fundamental relevance of the hydrino hypothesis lies in its challenging some of the foundations of the theory of quantum mechanics 1 . Very high net energy release during hydrino formation signifies technological relevance as a novel plus multiple weak signals in the low-and high-field wings. The center of the two main lines corresponds to an apparent g value of 2.0045(6) which is close to the value of 2.00464 predicted for the H 2 (1/4) S = 1/2 spin-only doublet system. The two lines are separated by circa 4 Gauss and are of equal intensity.


2
Introduction. The quantized energy levels of the hydrogen atom are En = -13.598/n 2 eV, in which the principal quantum number n is a positive integer. The electronic ground state has n = 1.
Higher states can be populated by absorption of light according to the Rydberg equation  = RH[(1/n2)-(1/n1)] with RH = 109.677 cm -1 . R. Mills has hypothesized and experimentally tested that the n = 1 state is not the absolute ground state and that lower-energy 'hydrino' states characterized by fractional quantum numbers 1/p, with 2  p  137, can exist 1,2,20,28 , and, furthermore, that H(1/p) can be produced from H(n=1) in a non-radiative process whereby a catalyst reversibly takes up an amount of energy equal to (p-1)27.196 eV such that an total amount equal to (p 2 -1)13.598 eV is ultimately released as heat 4,20,28 . These proposals have been presented as elements of a contentious theory of much wider coverage, called the grand unified theory of classical physics (here abbreviated as GUTCP) with the much wider claim to revisit the foundations of quantum mechanics 1,20,29 . Although a critical appraisal of this controversial assertion on theoretical grounds initially developed in journals of established reputation 6,7,9,10 , subsequently the works of independent opponents 8,11 , neutral observers 14 , and adherents 13,15,17 alike have slipped off either to publications with impact factors typically well below unity or to un-reviewed papers. Thus, the present verdict of the scientific community at large appears to be one of disregard, if not disdain.
Worthy of note is the fact that all cited evaluations by independent researchers thus far are exclusively concerned with theoretical arguments, while occasional independent experimental testing of the theory's predictions has not been published and has only been indirectly cited 14 .
Moreover, all of these criticisms are based on the incompatibility of hydrinos with quantum mechanics with the inherent assumption of the validity of quantum mechanics, which is circular reasoning. Mills' prediction of hydrino states of hydrogen is not based on quantum mechanics. It is based on physical laws, and the resulting physical theory is remarkably predictive over 85 orders of magnitude of scale in exact solutions having fundamental constants only 1,20 . Since Mills theory is physical/testable, we consider the bias away from experimental testing and reporting as undesirable in view of the potentially far reaching fundamental and technological implications of the GUTCP. The present study is an attempt to break a 30-year independent testing silence by providing an objective and readily reproducible spectroscopic test on a system allegedly containing molecular hydrino, H2(1/4). This work is not a test of the GUTCP as a whole; it has a 3 bearing on three sub-aspects: hydrino existence, catalytic hydrino formation, and paramagnetic properties of H2(1/4) predicted by the theory.
Sample production. A common feature of a hydrino state with an excited H state is that both comprise an electron, a proton, and a photon. In an excited state, the photon superimposes the proton field to decrease the central field at the electron to +e/n (e is the fundamental charge) and creates a radial dipole instability that results in radiation. Conversely, the photon of a hydrino state increases the central field at the electron to +(1+m)e and creates a radial monopole that is radiatively stable. According to Mills ground-state (n=1) atomic hydrogen can be converted to atomic hydrino (n=1/(1+m)) by means of a nonradiative resonant energy transfer to a catalyst with potential energy = m27.2 eV (that is 2mE1) according to the reaction m27.2 eV + H(1) + Cat  H*(1/(1+m)) + Cat* + m27.2 eV in which the energy term on the left is energy absorbed by the catalyst (typically by resonant ionization) and the term on the right is the energy released by the increase in the potential energy of the hydrogen atom to form H*(1/(1+m)), an intermediate of the hydrino atom of radius aH.
Subsequently the ionized catalyst, Cat*, regenerates by recombination, with the release of its previously gained ionization energy, and the hydrino intermediate converts to stable H(1/(m+1)) having a radius of aH/(1 + m) by release of additional energy such that the overall release of energy is [(m+1) 2 -1]13.6 eV. By considering quantum state p = m +1 the reaction may be written The Rydberg formula with the inclusion of the hydrino states is E = 13.6 eV/n 2 ; n = 1/137, 1/136…1/4, 1/3, ½,1,2,3… The hydrino transition reaction requires atomic H and a single catalyst species which is typically formed chemically or by a plasma reaction 20,28 . Further reactivity produces molecular hydrino 4 H2(1/p) from atomic hydrino H(1/p) when the bond energy is removed by collision with a third body, which can be a reactor-wall constituent (cf 30 ). A variety of species can resonantly and nonradiatively accept m27.2 eV from atomic hydrogen to serve as catalyst for hydrino formation (Ref- 1,Chp 5 & 20 ); in the present case we use the nascent (that is, in situ prepared, not hydrogen-bonded) water molecule with potential energy 327.2 eV wherein the solutions of the water molecule and hydrogen bonded water molecules were given previously (Ref-1, Chps13 and 16). Details of the sample preparation are given in the METHODS section. Briefly, the reactor is a closed vessel in which a low-voltage discharge is created between a liquid gallium electrode and a solid tungsten electrode with water and hydrogen introduced from a supported-Pt H2/O2 recombiner supplied with H2 gas and trace O2 to form trace nascent or non-H-bonded water catalyst. Either additional oxygen or water vapor are introduced to produce gallium oxide that is the negative ion spectrum wherein the hydride ion was elevated compared to control GaOOH. No hydrocarbons above adventitious levels were present and no nitrogen was found indicating the unlikeliness for EPR signals to originate from organic radicals. Equally, in the positive spectrum no potentially paramagnetic transition ions were present. Selected area electron diffraction (SAED) with the transmission electron microscope (Extended Data Fig. 3) revealed the samples to comprise two different morphological and crystalline forms of GaOOH: rods with orthorhombic diffraction pattern matched control GaOOH, which lacks molecular hydrino, in morphology and crystalline structure 31 , and were not sensitive to the TEM electron beam; on the other hand, morphologically polymeric crystals comprising hexagonal crystalline structure were very electron-beam sensitive, and were assigned to novel GaOOH:H2(1/4). X-ray diffraction 5 (XRD) showed a phase shift from the GaOOH control lines with different deviations between NaOH and KOH formed GaOOH:H2(1/4) as illustrated in Extended Data Fig. 4.

Paramagnetism.
Extensive background information for this paragraph is provided in Supplementary information 20 . Alternative to the probabilistic matter waves of quantum mechanics, the electron in a hydrogen atom is modelled in GUTCP as a two-dimensional spherical membrane of infinitesimal thickness in which current flows along two infinite, nested rotation sets of great circle filaments. This current pattern naturally gives rise to both orbital and spin angular momentum wherein the latter defines a g factor equal to 29 2 + 0.0023193. In the hydrogen molecule the spherical current pattern becomes a prolate spheroid in which the pairing of two electrons leads to a diamagnetic ground state. Atomic hydrino differs from H(n>1) states in that rather than the absorption of a photon to form an excited state, H(n=1/p) it is formed by a non-radiative energy transfer to a resonant energy acceptor followed by continuum extreme ultraviolet radiation to the final stable hydrino atomic state. The continuum EUV radiation was recorded in the laboratory at the 20 MW optical power level with a predicted 10.1 shortwave cutoff, and this radiation is observed astrophysically over all space 20,32,33 . Two hydrino atoms react to form molecular hydrino having two photons that are phase-locked to the electron current and circulate in opposite directions. Consequently, the molecule has a diamagnetic and a paramagnetic electron, the latter with g equal to 2 + 20.0023193 = 2.0046386 (Ref- 1,Chp16 & 20,28 ). This fundamental prediction from first principles provides a simple and accurate testing criterion for the existence of molecular hydrino. EPR spectroscopy. A wide magnetic field scan EPR spectrum of the Ga(O)OH solid powder taken at ambient temperature, exhibits a single derivative feature only against an essentially flat background, and with g value close to the free-electron value (Fig. 2a). Zooming-in on this feature (Fig. 2b) shows it to consist of two separate lines plus multiple weak signals in the lowand high-field wings. The center of the two main lines corresponds to an apparent g value of 2.0045 (6) which is close to the value of 2.00464 predicted for the H2(1/4) S = 1/2 spin-only doublet system. The two lines are separated by circa 4 Gauss and are of equal intensity. 6 Microwave power saturation plots (Extended Data Fig. 5) are very similar for the two peaks and are consistent with inhomogeneous broadening 34 (see below).
Concentrating on resolving fine structure in the main peaks we reduce the magnetic-field modulation amplitude to 25 mGauss (that is, below the bandwidth of the 100 kHz modulation frequency). The spectral amplitude in a single scan drops to below a signal-to-noise ratio of unity and extensive averaging over six hours and filtering is required to afford the high-resolution pattern in Fig. 2c. Each line has resolved in an isotropic equidistant beat pattern with sub-line separation of circa 0.32 Gauss.
For individual sub-lines we observe an apparent peak-to-peak width of circa 170 mGauss which is highly unusual for solid-state samples. Such narrow lines have been found for (i) organic radicals in organic solvents at ambient temperature 35 ; (ii) small paramagnetic molecules in matrices of noble gasses solidified at cryogenic temperatures 36 ; (iii) single hydrogen atoms encapsulated in molecular cages 37 ; and (iv) paramagnetic molecules in the gas phase at low pressure 38 . Excluding the first two options on obvious grounds (no organic solvents and no cryogenic temperatures) and the third one on spectroscopic grounds (atomic hydrogen EPR is a single line at the free electron g value split widely by proton hyperfine interaction), the narrow line width that we observe would be consistent with the detection of a low-pressure paramagnetic gas occluded in a solid.
We recorded the spectrum in Fig. 2d under optimized conditions for the detection and resolution of satellite lines whose existence was indicated by the small periodic peaks in the wings of the spectrum in Fig. 1b. Thus, the fine structure of the two central lines was slightly deformed by over-modulation and by mild microwave power saturation, and the data collection was extended to 40 hours with constant frequency monitoring for subsequent correction of individual 4-min traces for minor frequency drift.
In spin quantification (METHODS) we find that a complete spectrum of high resolution, such as in Fig. 2d, represents an S = 1/2 concentration of circa 2.6 M if the paramagnet would be homogeneously distributed over the sample volume. Transmission electron microscopy (Fig 1) and XRD show the Ga(O)OH polymer to comprise micro-spherical particles of the order of 100 nm diameter with an estimated spatial occupancy of roughly 10%. This would make the actual The unique electronic structure results in one paramagnetic and one diamagnetic electron.
The former induces a current in the latter by means of spin-orbit coupling resulting in a split of the original resonance into two lines separated by a frequency-independent interaction, which is for H2(1/4) predicted to be of magnitude 3.9943 Gauss with the field center of the two lines corresponding to the original g value of 20 2.00464. Experimentally we observe two lines of equal intensity separated by 3.9 Gauss whose center is found at g = 2.0045 (6).  Table-4).

Consistency controls.
Unequivocal interpretation of complex EPR spectra typically requires analysis of data taken at more than one microwave frequency. The magnetic model of molecular hydrino H2(1/4), providing a basis for interpretation of the EPR, predicts a number of features to be either dependent or independent of microwave frequency. These predictions can be checked in separate experiments as consistency tests. The g value of 2.00464 in between the two main lines is a real g value and thus its field position should be linear in the microwave frequency.
Contrarily, all fine structure splittings are predicted to be constant in field units and thus independent of the frequency.
As a check we have taken data in Q-band at circa 35 GHz. Here, practical complications arise resulting in reduced signal-to-noise ratios. For S = 1/2 systems, any spectrometer operating in a frequency band different from X-band is generally found to exhibit a significantly lower concentration sensitivity. Furthermore, the maximal applicable intensity of the microwave is 9 found to be limited (that is, the spectrometer is not tunable at higher microwave powers) apparently due to a relatively high dielectric permittivity of the Ga(O)OH samples. Fig 3a shows two traces resulting from extensive averaging, one taken under over-modulating conditions to emphasize the main two-line pattern, and one taken at lower modulation amplitude in an attempt to resolve fine structure. Consistent with the interpretation of the X-band spectrum we find a doublet of lines whose spectral center has a real g value of 2.0046 and with a frequencyindependent splitting of circa 4 Gauss. Under the employed conditions, the underlying broad signal has turned dispersive and thus shows up as an absorption-shape feature. A lower modulation amplitude does not afford resolution of the two-lines' fluxonal fine structure, which indicates that the spectral line width has increased with frequency. This is in fact consistent with our previous conclusion (cf. Fig 2c and Extended Data Fig. 6) that the line shape is Gaussian due to inhomogeneous broadening, which implies a line width in field units linear in the frequency 40 .
Since the signal-to-noise ratio in Q-band was insufficient to detect the satellite lines, and since attempts to measure the samples in other frequency bands were hitherto unsuccessful (not shown), we took data at two, well-separated frequencies within the X-band thus allowing for comparison of high-resolution spectra with the trade-off of reduced frequency resolution (Fig.   3bc). Data taken at 9.46 GHz were transformed for comparison with data taken at 9.85 GHz in two ways: (1) frequency-ratio conversion of every digital point of the field axis, and (2) singlevalued overall field shift to create maximal overlap of the two spectra. In the first method all real g values will overlay while features constant in the field will mismatch. In the second method all features of a fine-structure pattern constant in the field will overlay when the selected field point of conversion corresponds to the g value of that pattern. Fig. 3b gives the result of the first method: all features mismatch except for the spectral center at g = 2.0046, therefore the latter is the only real g value and all other features are from frequency-independent hyperfine interactions. Fig 3c gives  We consider this alternative explanation of the EPR highly unlikely on the following grounds. The reaction mixture only contains H2, O2, H2O, and Ga. Even in the presence of trace contaminants of, e.g., C, N, we cannot envision how the high-temperature plasma reaction conditions and sample formation in strong aqueous base could lead to the formation of stable radical structures of considerable complexity. The ToF-SIMs, EDS, and XRD analyses also eliminate alternatives. Furthermore, since the sample is a solid, for complex radicals one would expect to see anisotropy in the spectra. In particular absorption-shaped peaks that come with axial or rhombic symmetry of the spin Hamiltonian are not observed. A broad signal underlies the molecular-hydrino assigned spectrum. Its spectral center corresponds to the g value of 2.0046 within experimental error. Its temperature behaviour is very different from that of the hydrino-assigned spectrum (Extended Data Fig. 8). The origin and nature of the broad signal are presently unknown, however, a reasonable hypothesis would be to assume that there are two phases of GaOOH that encapsulate H2(1/4) wherein H2(1/4) is a near free gas in only one phase 20,28 . A scanning/transmission electron microscope (SEM/TEM) used for imaging and selected area electron diffraction (SAED) (Extended Data Fig. 3) showed that the GaOOH:H2(1/4) sample comprised two different morphologically polymeric crystals of GaOOH, a hexagonal crystalline structure that was very sensitive to the TEM electron beam, and rods having orthorhombic crystalline structure that were not electron beam sensitive. The rod crystal morphology and crystalline structure match those of the literature for control GaOOH that lacks gaseous molecular hydrino inclusion 31 . The XRD crystal system for Tsumgallite (control GaOOH) is orthorhombic. The hexagonal phase is likely the source of the fine structure EPR spectrum, and the orthorhombic phase is likely the source of the broad background EPR feature. Cooling may selectively eliminate, e.g., by microwave power saturation, the observed near free-gas-like EPR spectral behavior of H2(1/4) trapped in the hexagonal crystalline matrix. In addition to wall interactions, deviations from theory could be due to the influence of the proton of GaOOH and those of absorbed water. Also, matrix orientation in the magnetic field, matrix interactions, and interactions between one or more H2(1/4) could cause some shifts.
Deuterium substitution was performed to eliminate an alternative assignment of any EPR spectral lines as being nuclear split lines. The deuterated analog of GaOOH:H2(1/4), GaOOH:HD(1/4), was confirmed by Raman spectroscopy 20,28 . The EPR spectrum of the deuterated analog showed a singlet with no fine structure; thus, eliminating any possible nuclear splitting assignment. The g factor and profile matched that of the singlet of GaOOH:H2(1/4) wherein the singlet in both cases was assigned to the orthorhombic phase. The XRD of the deuterated analog matched that of the hydrogen analog, both comprising gallium oxyhydroxide. TEM confirmed that the deuterated analog comprised 100% orthorhombic phase (cf 31 ). The phase preference of the deuterated analog may be due to a different hydrino concentration and kinetic isotope effect which could have also reduced the concentration.
Lastly, further investigation is warranted to assign a peak slightly downfield from the central g value of 2.0046 the X-band spectra having a small signal of apparent axial symmetry (cf Fig. 2d). This peak is likely the pure spin-flip (no spin orbital coupling or fluxon linkage splitting) transition peak of the orthorhombic GaOOH phase with entrapped H2(1/4) molecules that are constrained relative to the free gas state or near free gas state of the hexagonal phase.

Conclusions.
A plasma reaction has been carried out intended to produce molecular hydrino using non hydrogen bonded water as the catalyst and with liquid gallium as one of the electrodes.
Polymeric Ga(O)OH with a spherical particle structure, presumably containing H2(1/4), was purified from the reaction mixture. H2(1/4) is proposed to be an S = 1/2 paramagnet with complex fluxonal and spin-orbital coupling level structure. The solid Ga(O)OH compound exhibits a complex gas-phase-like X-band EPR spectrum at ambient temperature whose fine structure semi-quantitatively agrees with hydrino-theory predictions. This analysis is consistent with frequency-dependent studies, while alternative, conventional interpretations are judged to be extremely unlikely. In summary, the present study provides compelling EPR spectroscopic evidence for the existence of hydrino. In view of the possible far-reaching implications of this conclusion for the theory of quantum mechanics, for hydrogen-related chemistry, for astronomy, and for energy transduction and production technology (Refs 1,20 and references therein), it is also offered as an urgent invitation to academia at large to repeat and extend the described experiments in lieu of refutation on quantum mechanical theoretical grounds.

Reactor setup
The plasma reactor (SunCell®) 20  Prior to operation, the pressure gauges were verified for accuracy within +/-1% using the same unit that was vendor calibrated.

Reaction control
The reaction within the cell was maintained using two separate electrical systems: an electromagnetic (EM) pump system to complete the circuit between the two electrodes within the cell, and an ignition system to supply electrical input energy to initiate the reaction. The

Product processing
Either water or additional oxygen was flowed into the reaction cell chamber to form gallium oxide to entrap H2(1/4) gas formed in the cell wherein the production of the H2(1/4) gas was confirmed by gas chromatography following cryogenic collection as well as thermal release of gas from gallium-oxide trapped H2(1/4) product 20 . Gallium oxide material was collected from a hydrino reaction run in the SunCell®, and the gallium oxide material (50 g) was dissolved in 4 M KOH solution (500 ml). After 0.5-1 hour, the solution was filtered to remove any insoluble solid phases. A white polymeric material began to nucleate from the clear filtrate after 24 hours.
Using a Buchner funnel, side-arm flask, and filter paper (Whatman TM , Grade 50, 09-865C), the 19 ultrafine precipitate was suction filtered from the solution. The filtered compound was carefully removed from the filter paper with a spatula without contacting the filter paper. To wash the recovered compound, it was suspended in deionized (DI) water, and filtered out a second time using the prior procedure while applying additional DI water while filtering. The compound was dried in air at 60-80 °C for 12 hours. XRD showed that the resulting white polymeric material comprised GaOOH with an average particle size of 111 nm. EPR spectroscopy X-band spectra were recorded at 9.4-9.9 GHz with a Bruker EMX-plus spectrometer using the equipped with an extra-long axial probe, and data were logged with a LabVIEW program. 21 Individual scans for signal averaging were normalized for drifts in field and/or frequency with a LabVIEW program before averaging.

EPR data analysis
The Bruker spectrometer can be set to automatically collect 2D data sets for varying microwave power intensity (that is, EPR amplitude versus magnetic field and microwave power), but the manufacturer's software lacks an option to analyze these data in terms of inhomogeneous broadening. Therefore, a LabVIEW program was written for non-linear Levenberg-Marquardt fitting to Portis' theory 34 .
EPR spectra taken at two different frequencies were compared in a LabVIEW program that afforded frequency normalization versus field scan shift normalization in order to separate frequency-dependent from frequency-independent spectral components.
To generate simulations of EPR spectra two programs were written in Intel   Gauss, and whose center is distinctly shifted from the free electron value to g = 2.0045. Trace c: further zoom-in on one of the lines now recorded with a very small modulation amplitude reveals a fine structure of multiple lines with apparent peak-to-peak derivative line width of 0.17 Gauss and separated by circa 0.32 Gauss. Trace d: extensively averaged spectrum taken under conditions optimized for maximal signal-to-noise ratio at the expense of minor over-modulation and power saturation, exhibits a complex pattern of triplet satellite lines. Data collection times for traces a-d were 10, 16, 375, and 2400 min, respectively. All spectra were taken at ambient temperature. Trace e is a simulation using field positions predicted by hydrino theory.
Other experimental conditions and simulation parameters are given in the METHODS section.

Fig.3 Multi-frequency experiments as checks on consistency of the EPR interpretation.
Trace a: extensively averaged Q-band spectra taken at two different modulation amplitudes of 1 Gauss (red) or 250 mGauss (blue). No fine structure is resolved in addition to the two main lines consistent with an inhomogeneous line width linear in the microwave frequency. The central g value and the splitting between the two lines in field units are identical to those observed in X-band. Trace b: extensively averaged intra X-band experiment at two frequencies, 9.4629 GHz (red) and 9.8209 GHz (black). Each field point of the red spectrum is frequency transformed to that of the black spectrum where the overlay shows that only the center of the two main lines is a real g value. In trace c the red spectrum is shifted in its entirety to a higher field for maximal overlap with the black spectrum. Here the overlay proves that there is only a single real g value and that all other features are constant in the field. See METHODS for experimental conditions.