MOLECULAR FORCE FIELDS AND CONSTANTS OF LIGHT, MASSIVE AND SUPER MASSIVE WATER-LIKE MOLECULES* Kotcherlakota L Narayana, NIO, Donapula, Goa 1993.

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Volume 2013, Issue No.12, December 13, 2013, Time: 7h42m.P.M.

Molecular Force Fields and Constants of light, Massive and Super Massive Water-like Molecules*

by

Kotcherlakota . L. Narayana,

General Physics Laboratories, 

Shivaji University, Kolhapur-416004.

&

(Paper No.246, Page 139-140, Section IV, Chemistry,

Proc. 80^th Ind. Sci. Cong. Part III, NIO, Donapula, Goa 1993.)

and

[Professor Dr. Kotcherlakota Lakshmi Narayana]

{Retd. Prof. of Physics, SU, Kolhapur}, 17-11-10, Narasimha Ashram, Official

Colony, Maharanipeta. P.O, Visakhapatnam-530002 cell no: 9491902867.

               Key Words:  Newer water molecules,  Force Constants. SHO molecule

ABSTRACT

The Japaneese Scientist Y.N. Kim suggested that formation of muonium and mesonium water molecules is feasible with the new accelerators for production of high intensity positive kaon and muon beams. Mesonium, Muonium and Kaonium water molecules can exist over a life time of 10E-08 much longer time than electron orbital time of 10E-14 secs. The massive water molecule was ruled out by Kim based on the observation that the Baryon Σ ⁺ might also form a ΣHO water molecule. Since its life time is shorter and its formation would thus be a rare event.

These new rules are obtained to suit the requirements Of the molecules πHO,  κHO, μHO and SHO where S stands for the super-water molecular mass, for example under an SU(3) symmetry formula of Elementary Particle Physics.[Data for SHO given in Table IV below]

             Adopting  the same structure constants and force field data of H₂O molecule given by Nakamoto, the fundamental vibration frequencies for κHO and πHO were obtained by Kim as 

          for  κHO  v₁=3708 cm^-1  v₂=1886 cm^-1  and v₃ =5704 cm^-1 
and  
        for πHO v₁= 3707cm^-1  v₂=3488 cm^-1  and v₃  = 9413 cm^-1.

        Since this data reported the more rigorous calculations for the vibration frequencies of (μHO), (κHO), (πHO) have not become readily available in literature.

          Kim sought the formation and existence of these water-like molecules under the notion of production of these by high intensity beams of μ+, κ+, π+ particles by accelerators. The pulse duration of 10E-14 secs allows capture of 10 molar water molecules of NaOH, and then Kim estimates for minimum values of n particles of the beam to produce about one water-like molecule for each pulse as approximately 6E+07 for π+ and 9E+07 for κ+ and under the assumption of maximum concentration of μ+s in the NaOH solution. The later is given by [μ+] = n*τ/ (t* N₀ ) where the muon mean life time τ = 2.2E - 06 secs, with the probability of their formation by v, with  τv ≫1,  N₀= Avogadro’s number and with n= 1E+06 and a pulse of duration t= 1E-04 results in about one muonium water might be formed for each pulse of the beam. Temperature increase would result in substantial increase of formation of muonium water-like molecules.

          Vibration spectra may be used to identify the formation of the muonium water.  Using the force constants K_HO  =  K_μO = 7.76E+05 dyn/cm K_α/r^2 = 0.69E+05 dyn/cm with bond length as  r = r_HO = r_μO  and  alpha=angle is 105⁰ Kim reports in Physical Rev letters calculated by Wilson FG-method that vibrational frequencies in wave number as; v₁=3686cm^-1  v₂=3448cm^-1  and v₃=10809cm^-1. The larger value of v₃ due to the smallness of muon mass, however leads to a frequency sums of 

v₁ + v₃ =    14495cm ^{- 1} and  

  v₂ + v₃ =   14257cm^-1 

remarkably very close to the visible region (red). The typical vibration pattern has been suggested as a means to confirm the formation of the muonium-water in the typical production of it with high-intensity accelerator muon beams.

DATA USED

Z X Y     mx     my       mz                 w₁        w₂          w₃                   

κHO  15.995 1.0081  0.530102   3708     1886      5074

πHO 15.995 1.0081  0.1498474  3707     3448      9413

μHO 15.995 1.0081  0.1176484  3686     3448      10809     
     

ΣHO 15.995 1.0081  1.27688

 K_HO  =  K_μO = 7.76E+05 dyn/cm

K_α/r^2 = 0.69E+05 dyn/cm;   r = r_HO = r_μO  and  α = 105⁰.

μ 105.659 MeV;       κ 493.78MeV;        π 139.58MeV;

INTRODUCTION

       The Japaneese scientist Kim [Ref.1] suggested the formation of the muonium and mesonium water molecules is feasible with the new accelerators for production of high intensity positive Kaon and Muon beams. Mesonium, Muonium and Kaonium water molecules can exist over a life time of 1E-08sec comparatively longer time than the orbital speed of an electron approximately 1E-14sec. The massive water molecule was ruled out by him based on the observation that the Baryon though can form a ΣHO water molecule its life time being shorter its formation would thus be a rare event.

          Adopting the same structure constants and force fields data of H₂O molecule as given by Nakamoto, the fundamental vibration frequencies for κHO and  HO were obtained by Kim as :

κHO    3708cm ^{- 1} : 1886 cm^{- 1}:   5074cm^{- 1}

     HO    3707cm^{- 1}   : 3448 cm^{- 1}:  9413 cm^{- 1}.

          Since this data reported by Kim to-date the vibration frequencies made by rigorous calculations for the  πHO,  κHO, μHO have not been readily available in literature and the present work therefore aims a reasonable set of Molecular Force Fields and molecular constants for the Light πHO, Massive κHO, and the presently defined Super (massive) SHO water-like molecules, determined by Green’s function and partitioning techniques and formulae earlier derived by the present author.

            Actually Kim sought the formation and existence of these water-like molecules under the notion of production of these by the high intensity beams of K+, π+, Ξ+ and Σ+ particles by accelerators.

            The pulse duration of 1E-14 sec allows capture of 10 molar water molecules of NaOH, and Kim estimated for the minimum values of n particles of the beam to produce about one water-like molecule for each pulse as approximately 6E+07 for pions and 9E+07 for Kaons and under the assumption of maximum concentration of μ in the NaOH solution. The later is given by by [μ+] = n*τ/ (t* N₀ ) where muon mean life time  τ =2.2E-06sec , No Avogadro’s number and with n= 1E+06 particles and pulse time of duration t= 1E-14. He also found that the temperature increase would result in substantial increase of formation of muonium water-like molecules.

                                Vibration spectra may be used to identify the formation of the muonium water. In fact Kim using force constants K_HO  =  K_μO = 7.76E+05 dyn/cm K_α/r^2 = 0.69E+05 dyn/cm with bond length as  r = r_HO = r_μO  and  alpha=angle is 105⁰ finds a  larger value of v₃  for μHO due to the smallness of muon mass, and then the frequency sums of 

           v₁ + v₃ =14495cm^-1 

and  v₂ + v₃  =14257cm^–1

remarkably very close to the visible region (red).

METHOD AND PROCEDURE ADOPTED 

IN THE PRESENT WORK

                   In the present work new sum and product rules of vibration spectroscopy have been adopted distinctly different from similar ones reported earlier by the present author in a series of papers in the early 1970 and the 1980s.[Ref. 2-13].

          These new rules are obtained to suit the requirements Of the molecules πHO,  κHO, μHO and SHO where S stands for the super-water molecular mass, for example under an SU(3) symmetry formula of Elementary Particle Physics.

            The procedure involves the use of the Green’s function and the partitioning techniques outlined by the author in the above said papers published previously.

RESULTS

                   κHO  molecule

-----------------------------Table I-------------------------------

Freq:   3708   2256.06    5236.37   (in cm ^-1)

Force

Fields 6.376  1.121        11.7963   (mdyne/Å)

Corolis

Coeff:             2.62           -8.37

------------------------------------------------------------------------

                      πHO  molecule

-----------------------------Table II ---------------------------

Freq:    3707   3759.25     8745.547 (in cm ^-1)

Force

Fields: 3.117  1.546          17.4946  (mdyne/Å)

Corolis

Coeff.            -7.051         -2.078

-----------------------------------------------------------------------

                μHO molecule

----------------------Table III-------------------------------------

Freq:     3686      4154.754    9630.152 (in cm ^-1)

Force

Fields:  3.138      1.3932        18.456  (mdyne/Å)

Coriolis

Coeff.   2.516           -7.868

--------------------------------------------------------------------------

                     SHO molecule

---------------------------Table IV--------------------------------------

Freq:    3020.1   1926.69     3617.324 (in cm ^-1)

Force

Fields:   6.35      1.196          8.531   (mdyne/Å)

Coriolis

Coeff.                 2.516      -7.868

----------------------------------------------------------------------------

The Tables 1 to 4 summarize the data obtained.

DISCUSSIONS

                        A very large value of v₃ may be understood as originating from the small mass of the muon, but the product and sum rules used by me led only to a frequency of v₃ = 9630.152 cm ^-1 which is considerably low compared to the value given by Kim 

 Viz., 10809 cm ^-1.

   Thus the sums I have obtained as follows:

v₁ + v₃ = 13316.152 cm ^{- 1}

v2 + v3 = 13784.906 cm ^{– 1}

are distinctly different from the values reported by Kim:

v₁ + v₃ = 14495 cm^{- 1}

v₂ + v₃ = 14257 cm ^{– 1}  

      The vibration spectra frequency pattern is found to be quite different from what Kim has obtained by Wilson Force Field calculations. The exact and rigorous calculations adopted in the present work also hints at a different set of symmetry force fields.

            Our experimental observations on Muon vibration frequency pattern of atmospheric disturbed conditions of Indian Peninsular region due to the recent volcanic eruptions indicate the frequency pattern obtained by us is more physically reasonable than the one predicted by Kim.

ACKNOWLEDGEMENT

            The author is deeply indebted to Late Prof. Dr. K. R. Rao D.Sc.(Madras) D.Sc. (London) at whose laboratories in Andhra University, Waltair the work on Force Fields was initiated and several people have won their Doctorate Degrees.

* Kotcherlakota L. N, “Molecular Force Fields and Molecular Constants of Light, Massive and Super Water Like Molecules”, Paper No.246, Page 139-140, Section IV, Chemistry,
Proc. 80^th Ind. Sci. Cong. Part III, NIO, Donapula, Goa 1993.
[listed as Paper No.187]

REFERENCES

1. Y.N. Kim, Phy. Rev. Lett, Vol.20, p.359, 1968.
2. K. L. Narayana,”The Mean Square Amplitude Matrices in some XY₂ type Molecules”, Shivaji University Journal, Vol.2, No.4, pages 115-122, 1969.
3.  K. L. Narayana and B. P. Sabale,” Determination of Molecular Constants by Green’s Function analysis of XY₂ type molecules”,   Shivaji University, Vol.7, Number 14, Pages 107-126, 1974.
4.  K. L. Narayana and M. K. Soudagar,”A Study of Lone-Pair Electron Contribution And Molecular Force Field Ellipses for SnCl₂”, Shivaji University Journal, Vol.7, No.14, Pages 225-231, 1974.
5. K. L. Narayana and M. K. Soudagar,”The lone pair electrons contributions and         Constraint method within Green’s function formalism for XY₂ structures Molecular   Vibrations”, 61^st Sess. of Ind. Sci. Cong. Nagpur, Paper No.16, Chemistry Section, January 1974.
6. K. L. Narayana and M. K. Soudagar,”A study of The Molecular Force Field ellipses for SnCl₂ with Lone Pair”,  Current Science  February 20, Vol.44,    p.118-119, 1975.K
7. K. L. Narayana and M. K. Soudagar,”Molecular Force Ellipses of Co-ordinated Water in Titanium Complexes”, J. Inorg. Nucl. Chem. Vol.39, Pages 19-24, 1977.
8. K. L. Narayana and M. K. Soudagar,”Lone Pair Electron contributions to the nature of force field ellipses and spectroscopic constants of dihalides of group  IV-A  elements and NO₂”,  Acta. Chim, Acad. Sci. Hungary, Tomus 84,   No.2,   Pages 103-118,   1977.
9. K. L. Narayana and M. K. Soudagar,”The dependence of mixing of symmetry  vibrations of bent XY₂ molecules on the product of relative mass ratio and the electronegativity”, p.59, Paper No.51, Section III, Abstracts, Physics, 64^th Sess.Ind. Sci. Cong. Bhubaneswar,  January 1977.
10. K. L. Narayana and M. K. Soudagar,” The Crystalline perturbation effects on the localized modes of NO₂ ion in NaNO₂ Crystal”,        Phy.Stat. Solidi. (submitted)
11. . K. L. Narayana, Kolhapur, ”Spinorial Optics of structural vibrations of Ions (atoms) and The Quasi-particle Quantization of Rangadhama Effect”, Paper No.147, Section IV, Chemistry Section, p.65-66, 70^th Proc. Ind. Sci. Cong. Part III, Shri Venkateswara University, 6^th January 1983.
12. K. L. Narayana,”Renormalization of Vibrational Energy by Rangadhama Quanta and Spinorial Phase Transitions”, Ranchi Session of 71^st session Ind. Sci. Congress, Sect IV, Chemistry  Section, Paper No.216, p.102,  1984.