Volume 2012, Issue No.1, Dt. 14th January
2012. Time : 20h33mPM
The tri- Sulfur molecular vibrations analysis
and the possible new quanta characteristic of those vibrations.
by
Professor Dr. Kotcherlakota Lakshmi Narayana
trusciencetrutechnology@BlogSpot.com, 17-11-10, Narasimha
Ashram, Official Colony, Maharanipeta. P. O., Visakhapatnam,-530002. Andhra
Pradesh.
Mobile: 9495717723/9491902867 29th August 2011 Time: 11h21m AM
Keywords: Molecular
Vibrations, Tri- Sulfur, Moons of other Planets, Planetary volcanoes, A new
theory of Gravito-Magnetism, Novel Quanta, Astrophysics,
Astronomy,Moons, Relativity Theory, Gravitation, Quantum Theory
ABSTRACT
There is a lot of information
obtained by the various space probes
regarding the Volcanoes on the surfaces of the Moons surrounding other planets
and as well far away of the star exo-planets. The most common features of these
volcanoes observations and their lave flows have indicated the presence of
Sulfur in enormous quantities deep in the interiors of their mantle and core
structures. The symmetry considerations of the tri-sulfur with both the D3
and the D3h point groups irreducible representations have been
examined to discover that the symmetry leads to A’1+E’ vibrations
under D3h. The redundant condition on the angles reduces the degrees
of freedom to just two unlike the Water molecule of XY2 symmetry
that has three degrees of freedom. The complete
molecular vibration analysis has been made to using the Green’s function
formalism to arrive at the possible vibration frequencies, force field
characteristics and other molecular parameters which would be of great interest
to Astrophysicists. A total new vibration frequency has been found due to the
gravitational compression of the tri-sulfur deep in the interiors of the either
the Earth or the Moons of other planets. My method of study (differs from the
method of study that is based on the recently coined Gravito-magnetism, in the
sense that) we are dealing with the quanta produced due to the gravitational
affects on the molecular vibrations. Essentially we consider the current and
inductive forces produced on the bond lengths due to the gravitation. Estimates
are given of all the physical quantities that characterize the quanta. The
principle that I enunciate is “all the universal objects are subject to
gravitational currents in terms of geometric units of both the signs subject to
the response frequencies realizable under gravitational impulses acting on
them”.
==================================================================================
Submitted
to Sectional President, Physical Sciences, 99th Indian Science
Congress 3-7 January, 2012 hosted by KIIT University, and NISER, Bhubaneswar,
Odisha, India. Prof. B.N. Jagtap, outstanding Scientist & Head, Atomic
& Molecular Physics Division, Bhabha Atomic Research Centre, Mumbai
-400085: bnj@barc.gov.in, bnjagtap@gmail.com; Mobile:
09969656485; Tel. 022 2559506 .{An article
prepared for Physical Sciences section of the Indian Science Congress
Association Session to be held at KIIT University & NISER, Bhubaneswar during 1st to 7th January,
2012 by the author copy right held}
==========================================================================
The Japan
mountain volcano has several times erupted releasing large quantities of Sulfur
into the atmosphere and many a times it caused the death of several people.
Even the Venus planet possessing
sulfuric acid clouds, the atmosphere of it is mostly carbon dioxide (96
percent), nitrogen (3.5 percent), and carbon monoxide, argon, sulfur dioxide,
and water vapor (all less than 1 percent). The atmosphere is so thick and heavy
that it bends light, making the ground appear to curve upward in all
directions. The planet's atmosphere is ninety times heavier than Earth's. But
deep in the interior of the Saturn moons the sulfur exists and the beautiful
thick snowy white show occasionally the lave flows of the erupted sulfur. How
the Sulfur does exists, deep inside the Moons and the various planets, under
heavy pressure of the gravitational pull. One answer to has been provided by
the Astrophysicists stating that tri-sulfur form is possibility. This led me to
investigate its molecular vibrations since the possible vibration frequencies
would reveal not only the characteristics of such a molecule parameters but as
well to obtain if any quanta generated along with the features of the force
field vibrations and symmetry mixing. Regarding the literature on S-S bond,
it’s interesting to note that the stretching frequency of S-S bond varies from
430-520cm -1as per the papers quoted in the references [1, 2, 3]
listed below. Also the Si-S-S-Si in
disilyl sulfides have three bands of symmetric stretching while the asymmetric
stretch is at 515cm -1as reported by
Linton and Nixon[4].
METHOD
In the calculations made, I have used the
group theoretical technique to obtain the transformation properties of the
Cartesian coordinates of the three vertex Sulfur atoms occupying the corners of
the equilateral triangle. The permutation group
six transformations designated usually by A, B, C, D, and F apart from
the identity operation E satisfy the group multiplication table of a D3
group. But I have extended the group to have 12 symmetry elements to take into
account the reflection in the horizontal plane of the tri-sulfur molecular
structure of an equilateral triangle. The irreducible representations and the
Characters of the point group D3h are made use of to arrive at the
modes of the vibrations of this molecule. Since the molecule posses a redundant
constraint of angles sum must be 180 degrees we have only two degrees of
freedom for this molecular vibrations.
Calculations
For these
the coordinate axes are chosen as shown in the Figure below. Please note the
numbers given are for the schematic representation of the diagram. They don’t
correspond to the actual bond length position coordinates. Below I give the
bond lengths etc. The angle at each vertex is however 60 deg.
The D3h
symmetry has the irreducible representations A1’, A2’, E’, A1”, A2”, E” . The symmetry operations are listed as E-identity,
2C3 clockwise and anticlockwise rotations by 120 degrees of the
vertices, 3C2 the rotations along the diagonals by 180 degrees, σh the reflection in horizontal
plane, 2S3 operation involving reflection and 3σv reflections
in the vertical planes on the three diagonals.
The
tri-sulfur was found to have the molecular vibrations given by A’1
+E’. While for the D3 symmetry group the symmetry operations are
only six they are 2C3 clockwise and anticlockwise rotations by 120
degrees of the vertices, E the identity operation, 3C2 rotations by
180 degrees along the diagonals at the vertices. And the irreducible
representations of the D3 group are just four given by, A1, A2
and doubly degenerate E. The tri-sulfur was found to have the molecular
vibrations given by A1 +E.
EQUVILATERAL
TRIANGLE GROUP
A=[0
0 0 1
0 0 0
0 0;
0 0 0
0 cosd(60) sind(60) 0 0 0;
0 0
0 0 cosd(30) -sind(30) 0
0 0;
1 0 0
0 0 0
0 0 0;
0 cosd(60) sind(60) 0
0 0 0
0 0; 0
cosd(30) -sind(30) 0 0
0 0 0
0;
0 0 0
0 0 0
1 0 0;
0 0 0
0 0 0
0 cosd(60) sind(60); 0
0 0 0
0 0 0
cosd(30) -sind(30)];
B= [1 0
0 0 0
0 0 0
0; 0 -1
0 0 0
0 0 0
0; 0 0
1 0 0
0 0 0
0;
0 0 0
0 0 0
1 0 0;
0 0 0 0
0 0 0
-1 0; 0
0 0 0
0 0 0
0 1;
0 0
0 1 0
0 0 0
0; 0 0
0 0 -1
0 0 0
0; 0 0
0 0 0
1 0 0
0];
C= [0
0 0 0
0 0 0
0 0; 0
0 0 0
0 0 0
sind(30) -cosd(30); 0
0 0 0
0 0 0
-cosd(30) -sind(30); 0
0 0 1
0 0 0
0 0; 0
0 0 0
sind(30) -cosd(30) 0
0 0; 0
0 0 0
-cosd(30) -sind(30) 0
0 0; 1
0 0 0
0 0 0
0 0; 0
sind(30) -cosd(30) 0
0 0 0
0 0; 0
-cosd(30) -sind(30) 0
0 0 0
0 0];
D =
[0 0 0 0 0 0
1.0000 0 0; 0 0 0 0 0 0 0
-0.5000 0.8660; 0 0 0 0 0 0 0
-0.8660 -0.5000; 1.0000 0 0 0 0 0 0 0 0; 0
-0.5000 0.8660 0 0 0 0 0 0; 0
-0.8660 -0.5000 0 0 0 0 0 0; 0 0 0
1.0000 0 0 0 0 0; 0 0 0 0
-0.5000 0.8660
0 0 0; 0 0 0 0
-0.8660 -0.5000 0 0 0];
F =[
0 0 0
1.0000 0 0 0 0 0; 0 0 0
0 -0.5000
-0.8660 0 0 0; 0 0 0 0
0.8660 -0.5000 0 0 0; 0 0 0 0 0 0
1.0000 0 0; 0
0 0 0 0 0 0
-0.5000 -0.8660; 0 0 0 0 0 0 0
0.8660 -0.5000; 1.0000 0 0 0 0 0 0 0 0; 0
-0.5000 -0.8660 0 0 0 0 0 0; 0
0.8660 -0.5000 0 0 0 0 0 0];
E is an identity matrix of dimensions 9x9
This fact has been overlooked to my
knowledge in the literature given in many text books on group theory etc.
Therefore the molecular vibration analysis differs for the tri-sulfur molecule.
The 12 parameter matrices of the group of D3 are designated as a, b,
c, d, e, f, g, h, i, j, k, and l. In these the e representation is the identity
matrix with character as 12. Certain
coordinate relations under the D3h
point symmetry group are given below for example a*v , where v is the
matrix of Cartesian coordinates (x1, x2, x3, y1, y2, y3, z1, z2, z3 respectively for the x, y and z axes of
the three vertex sulfur atoms designated as 1, 2 and 3) explicitly
.5000*x2+.8660*y2; .8660*x2-.5000*y2; z2
.5000*x1+.8660*y1; .8660*x1-.5000*y1; z1
.5000*x3+.8660*y3; .8660*x3-.5000*y3; z3
In which the z-axes quantities
remain unperturbed while the x and y coordinates of all the three atoms get
mixed up due to the group operation given by the matrix A.
 |
| Fig.1 of Tri-Sulfur vibration and the possible new quanta |
With n= 26328.64894 atmospheres and the tri-sulfur new frequency as
148.69 cm^-1 at a radius of earth 6.3992e+06m and gravitational acceleration at
800m as 9.80245m/sec^2 we have a graphical presentation of the new
gravito-molecular vibration theory with a governing equation as given below:
14.0489-3.5818*w.^2+ 0.2283*w.^4+0.36*w^2*b^2-F0^2=0.
Impulsive force F0 is dimensionless of the order 0.826e-53 but in
dimension analysis it is varied from 0.3e-08 to .06e-14.
This leads to
2.3265e-10*((.39079e+16) + (.39803e+15*w. ^4-.61009e+18*w. ^2
+.23379e+21)/w.^2)^(1/2)-(0.13918e+14)*0.3e-08)
and
2.3265e-10*((.39079e+16) + (.39803e+15*w. ^4-.61009e+18*w. ^2
+.23379e+21)/w.^2)^(1/2)-(0.13918e+14)*.6e-14) respectively.
The amplitude of oscillations that constitutes a gravitational
current due to the impulsive force is the finer aspect of the present theory in
the sense that the net gravito-impedance is given by the expression within the brackets. Note that it involves F0.
F0 values result in frequency of
response about w = ±5 with the current values in dimensionless units is listed
below. Note the infinite super-gravitational current at zero response
frequency.
w=0 y=INF: w=1 y=3.469144 w=2 y=1.685901
w=3 y=1.088412 w=4 y=0.787363 w=5 y=0.604891
 |
| Fig.2 This gives the triangle up and down of Tri-Sulfur vibration and the possible new quanta |
Numerical
Data
The bond
distance at one-bond strength is taken to be 1.04angstroms. This gives us two
types of outer and inner circles of the tri-sulfur with the respective radii as
0.6 and 0.3 angstroms respectively. The possible gravitational displacement due
to the attraction and subsequent restoration by the gaseous & solid upward
thrust sets the tri-sulfur to vibrate in a radial direction to the surface of
the mantle/core material of the Earth. Figure given in conclusions and results
section of this article, illustrates the two possible configurations with the
centroid of the tri-sulfur molecule displaced in a vertical direction. The
displacement is around .3angstroms corresponding to the inner circular radius
of the equilateral tri-sulfur molecule.
 |
| Fig.3 depicts new theory of a gravitational current due to the impulsive force |
This results
in frequency of response about w = ±5 with the current values in dimensionless
units is listed below. Note the infinite super-gravitational current at zero
response frequency. w=0 y=INF: w=1 y=3.469144 w=2 y=1.685901 w=3 y=1.088412 w=4
y=0.787363 w=5 y=0.604891
Geometric
inductance, capacitance, resistance and the possible impact force have been
used to arrive at the response frequency values. Therefore the principle that I
enunciate is “all the universal objects are subject to gravitational currents
in terms of geometric units of both the signs subject to the response
frequencies realizable under gravitational impulses acting on them”. It is
found that a mean free path of λ=.3e-08cm then the density of the tri sulfur
gas would be 117.42gm/cm^3 and this length leads to the 26.328e+03 atmospheres
pressure. Such quantities are quite feasible inside an astronomical object such
as a moon of Saturn or the Jupiter.
 |
| Fig.4 some visitors to the article on Tri-Sulfur |
CONCLUSIONS
AND RESULTS
The most
common features of these volcanoes observations and their lave flows have
indicated the presence of Sulfur in enormous quantities deep in the interiors
of their mantle and core structures. The symmetry considerations of the
tri-sulfur with both the D3 and the D3h point groups
irreducible representations have been examined to discover that the symmetry
leads to A’1+E’ vibrations under D3h. The redundant
condition on the angles reduces the degrees of freedom to just two unlike the
Water molecule of XY2 symmetry that has three degrees of freedom.
The complete molecular vibration
analysis has been made to using the Green’s function formalism to arrive at the
possible vibration frequencies, force field characteristics and other molecular
parameters which would be of great interest to Astrophysicists.
A total new
vibration frequency has been found due to the gravitational compression of the
tri-sulfur deep in the interiors of the either the Earth or the Moons of other
planets. My method of study (differs from the method of study that is based on
the recently coined Gravito-magnetism, in the sense that) we are dealing with
the quanta produced due to the gravitational affects on the molecular
vibrations. Essentially we consider the current and inductive forces produced
on the bond lengths due to the gravitation.
Estimates
are given of all the physical quantities that characterize the quanta.
Geometric inductance, capacitance, resistance and the possible impact force
have been used to arrive at the response frequency values. The principle that I
enunciate is “all the universal objects are subject to gravitational currents
in terms of geometric units of both the signs subject to the response
frequencies realizable under gravitational impulses acting on them”.
ACKNOWLEDGMENT
I am indebted to late Professor K. Rangadhama
Rao D.Sc. (Madras). D.Sc. (London) at the J.V.D College of Science Technology,
his laboratories in Andhra University, Waltair, Visakhapatnam, for making me
aware of the Group theory structural approach, in the study of molecular force
fields and in the Subject of Nuclear Physics spectroscopy analysis. I have used
symmetry group tabulae based on the partitions of a number, for the analysis of
Fluorine-18, and Oxygen-19 etc nuclei in my Ph.D. thesis. The p orbital hybridization with d-orbital
along with s-orbital for the analysis of BrCl isotope molecules has been
calculated by me to obtain the Quadrupole resonance frequencies a work of
significance in the sense that Prof K R Rao has analyzed the atomic p-orbital
transitions in the Arc and in Spark Spectra in his D Sc Thesis presented to
Madras University in 1924. Further research is imminent.
REFERENCES
& NOTES
1. J Cymerman and J.B. Willis. J.Chem.Soc p1332, 1951
2. S.N.Nabi and N. Sheppard. J.Chem Soc. P.3439, 1059
3. D.W.Scott and J.P.McCullough. JAmer.Chem.Soc.80, p3554, 1958.
4. H.R.Linton and E.R.Nixon. J.Chem Phys. 29, p.921, 1958.
5. B. Malekolkalami and M. Farhoudi September
2nd, 2008 in arXiv:gr-qc/0610095v2 dated 13 November 2009 says that “The gravitomagnetic field is the
force exerted by a moving body on the basis of the intriguing interplay between
geometry and dynamics which is the analog to the magnetic field of a moving
charged body in electromagnetism.”
6.
trusciencetrutechnology, Vol.2009, No.7, Wednesday, 15 July 2009:
11:25:45 PM On the nature and possible existence of Collapsing Gravitational
Superconducting Currents of a Cosmic Entity and the generation of Bilinear
Physical Entities of Ghost Fields. by Professor Dr. Kotcherlakota Lakshmi
Narayana says that “ The coupled Einstein-Dirac-like equations, have a richness
of variety of solutions, by use of the detailed Energy Momentum Tensor
quantities of free magnetic strengths, bare mass-less electrostatic ghost
charges and the mass-less ghost neutrino, subject to pressure and other field
contributions.”
7.
trusciencetrutechnology@blogspot.com
Vol.2010, Issue No.3, Dt: 01 March 2010: 10:12:04 AM : A NEW THEORY OF INTERPLAY OF RAO AND
ANTI-RAO QUANTA WITH THE GRAVITATIONAL FIELDS by Professor Kotcherlakota
Lakshmi Narayana, (Retd.Prof.ofPhysics, Shivaji University), 17-11-10, Official
Colony, Maharanipeta.P.O, Visakhapatnam-530002. Mobile: 9491902867: Email ID: Kotcherlakota_l_n@hotmail.com
says that “A new theory of interplay of Rao and Anti Rao quanta with the
gravitational fields has been formulated and modelled within the frame work of
Einstein’s General Theory of Relativity. These quanta of ubiquitous occurrence
in the universe are not massless but could as well exist with certain effective
charge. The non-vanishing Ricci tensor has been utilized to arrive at the
possible mass range of these quanta. This tensor yielded two sets of the Rao
and the anti-Rao quanta masses ±2.85 & ±0.65 that justify their physical
existence as massive quanta of both positive and negative energy. This is
unlike the Dirac Sea of negative energy since we have both r and t variables to
obtain the variable that portraits the mass magnitude. The non-vanishing
diagonal components of Einstein Equations of General Relativity exhibit the
pressure and the density features of the fluid of these quanta. A constraint
has been made use of to simplify the only non-vanishing non-diagonal component
of the Einstein Tensor to obtain an expression for a charge-like quantity as a
function of the variables wt, r and t. The time dependent charge expression is
a noteworthy departure from the static charge characteristic of
Reissner-Nordstrom metric.”
8. trusciencetrutechnology, Vol.2009, No.7,
Wednesday, 15 July 2009: 11:25:45 PM On the nature and possible existence of
collapsing gravitational superconducting currents of a cosmic entity and the
generation of bilinear physical entities of Ghost Fields. by Professor Dr.
Kotcherlakota Lakshmi Narayana, (Retd. Prof.of Phys, S. U), 17-11-10, Narasimha
Ashram, Official Colony, Maharanipeta. P. O, Visakhapatnam-53002, AP, India.
trusciencetrutechnology@blogspot.com, Mobile: 9491902867, Email ID:
kotcherlakota_l_n@hotmail.com says that “{the coupled Einstein-Dirac-like
equations have a richness of variety of solutions, by use of the detailed
Energy Momentum Tensor quantities of free magnetic strengths, bare (mass-less)
electrostatic ghost charges and the (mass-less) ghost neutrino, subject to
pressure and other field contributions. In this paper, I have investigated the
Taub space-time universes, with two different versions, of its exponent metric
parameters, that admit a conformal Group of Motions. The Einstein-Dirac-like
Field Equations and as well the Dirac-like field Equations have been solved and
their relation with a full set of killing vector fields has been established. A
new find is the set of non-vanishing partial derivative currents.
Also the
set of current densities of the bilinear physical entities have been obtained.
In principle, these allow the observation of the bilinear physical entities.
This opens a new vista of quantum observables, as well of other types of bilinear
physical entities of ghost fields. The associations of the ghosts allow the
three symmetric X ±, X 0 and one pseudo-symmetric ζ0 states that constitute the 4 component
Spinor Dirac-like wave field. Further it is found that X0 and ζ0 could generate
mixed bilinear physical entities, with a mixing angle designated as θcsc where
csc stands for collapsing superconducting currents. The General Theory of
Relativity approach has been designed, to a fresh understanding of the infinite
electrical conductivity, in terms of the possible existence of collapsing
gravitational superconducting currents. A significant finding is the generation
of bilinear physical entities, near the defined “Current Surface”. A pairing
mechanism, of the two ghost electrostatic charges, via the ghost neutrino
interactions, has been formulated with a Lagrangean that is endowed with
universal coupling constants. The formulation is characterized by the possible
ground states of 16–band gaps resulting from the pair combinations of a Dirac-like
4-component Spinor function. Introduction of color and flavor characterization
adds to the enchanting variety of collapsing superconducting current densities.
Of interest, is the characteristic wave patterns, produced by a string and
membrane solutions of the Einstein-Dirac-like field equations that exist
projected in a 3D phase space over ” Current Cones”.}
9.Sunday,
May 3, 2009 ON THE NATURE OF
MAGNETO-STRANGE FIELD FLUID FILLED COLLAPSABLE COSMIC ENTITY, KILLING VECTORS
AND A SET OF EXACT SOLUTIONS trusciencetrutechnology Vol.2009, No.5, Dated: 4th
May 2009: Time 10:12AM trusciencetrutechnology@blogspot.com says that “ In this paper ,I have investigated the
magneto-strange field fluid filled cosmic entity with strange quark matter
(like a super star), in the lateral dependent space-time metric that admits a
Group of Motions and collineations. The Einstein Field Equations have been
solved and their relation with a full set of killing vectors has been
established. The strange fluid mass (to be termed the strange charge) and the
strange quark mass expressions, use of them in judicious way, led to the New
Gravitational Red Shift formulas. Also the vertical lift in an embedded
cylindrical symmetry has been obtained for the several set of the cases, with
and without the cosmological constants. The numerical data and the graphical
illustrations are given for a discussion on the features of the set of exact
solutions obtained. These are presented to support the claim of existence of
magneto-strange holes (Magstra holes) concomitant with the worm hole solutions.
The General Relativity approach designed, to a fresh understanding of the
Elementary Particle and High Energy Physics is given.
 |
| Fig.5 Physical Sciences Section X Proc of ISCA 2012 at Bhubaneswar Odisha |
ADDENDUM
In Fig.4 The two visitors have
thrilled to look at the paper since it is something totally different from the
conventional understanding of Molecular Vibrations & the much known
attended famous EFFECT.
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