The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.

A compilation relevant for the contents of Contribution to ISC107

Discover the best professional documents and content resources in AnyFlip Document Base.
Published by aram1121944, 2019-09-19 04:07:50


A compilation relevant for the contents of Contribution to ISC107

Keywords: NMR,Computational Chemistry,Simulations,interpretations

Emeritus Professor
Department of Chemistry
North Eastern Hill University
PO NEHU Campus
SHILLONG 793022 Meghalaya
Email: [email protected]

Sankarampadi Aravamudhan
Tower T3, Door no. M-S13
Ashiana Shubham Project
Melrosapuram Road
S.P. Koil Sub Post office
Maraimalinagar municipal limit
Govindapuram 603204
Kanchipuram Dist.
Tamil Nadu

Chemical Sciences –Sectional

Chemical Prof. Diwan S. Rawat, Dr. Anand S. Aswar, Dr. N. B. Prakash, 1)Chemical
Sciences Department of Chemistry, Professor & Head, Sciences
University of Delhi, Department of Professor, in Human
Delhi-110 007; Chemistry, Dept. of SS&AC, Health
Res. : 38/6, Probyn Road, Sant Gadge Baba Care.
Opposite Law Faculty, Amravati College
University of Delhi, Delhi- University, Amravati- of Agriculture, UAS,
110 007; 444 602 (M.S.);
Res. : Sarthak Layout, GKVK,
Christ Colony, Camp, Bangalore – 560 065;
Amravati-444 602;
Mobile : 09448686638;

Tel : 011-27667501 (O); Email :
Mobile : 09810232301; [email protected]
E-mail : Tel : 0721-2662206
[email protected] / Extn. 262 /
[email protected] 2553016 (O), 0721-
2666769 (R); Mobile :
09421790866 /
Fax : 0721-2660949 /

E-mail :
[email protected]
[email protected]




Sankarampadi Aravamudhan

Department of Chemistry
North Eastern Hill University
SHILLONG 793022 Meghalaya


Key Words: Shielding Tensor , NMR, Combined Molecules

By “Shielding”, in the context of Nuclear Magnetic Resonance, an electronic property of the
nucleus is referred to. Since this shielding of nuclei in molecule arises due to variations in the
electron circulations in the molecule, it turns out to be a Tensor Property, which has reference
to molecular point group symmetry. Retrieving the output of shielding tensors from QM
calculations on combined molecular systems requires an attention to both point group
symmetries of the two molecules are reported in a common coordinate axes system which is
the concern in this report. Illustration is with combination of benzene and hydrogen.

Word Count=100


Sankarampadi Aravamudhan

Department of Chemistry
North Eastern Hill University
SHILLONG 793022 Meghalaya


Key Words: Shielding Tensor, NMR, Combined Molecules

By “Shielding”, in the context of Nuclear Magnetic Resonance,
an electronic property of the nucleus is referred to. Since this
shielding of nuclei in molecule arises due to variations in the
electron circulations in the molecule, it turns out to be a Tensor
Property, which has reference to molecular point group
symmetry. Retrieving the output of shielding tensors from QM
calculations on combined molecular systems requires an
attention to both point group symmetries of the two molecules
are reported in a common coordinate axes system which is the
concern in this report. Illustration is with combination of
benzene and hydrogen.


It has been a well established method to calculate susceptibility anisotropy values by
measuring the proton chemical shift variations due to neighboring groups. Mostly, it is only
the isotropic chemical shift values had been used, and in particular for the “ring-current”
effects. However, magnetic dipole model used for the ring current effects can be used for
determining the full susceptibility tensor elements provided the shielding tensor element
values are known. One of the early HR PMR in solid-state determination did reveal the
usefulness of such a procedure. The HR-PMR in solid state single crystals is a difficult
experiment and all molecular crystals may not be amenable for such a study. For any
molecule, quantum mechanical computations can yield full proton shielding tensor values,
and this theoretical shielding tensor values along with the magnetic dipole model can be
utilized for susceptibility tensor values. When the molecule has not only an aromatic ring
function, but also other functional groups which can have significant susceptibility values, the
molecular fragments are the targets to find susceptibility values not merely the full molecule.
All these have been mentioned in the earlier contributions and presentations [1]. In the
presentation [(1) (a)], the aspect of calculations on combined molecular system and finding
the possible coordinate axes system relevant for the reported proton shielding tensors was

also highlighted. In this contribution, the different point group symmetry of isolated
molecules with reference to shielding tensor elements and the combined molecular systems
are discussed so that when molecular fragments are targeted, these considerations would not
be impediments in making progress.

Figure-1 Benzene Molecule

From this structure editor the coordinate information can be extracted by saving this as a file
with xyz format. This format is one of the common formats encountered while working with
structure editors. The contents of such a file look like what is displayed in the next page:


C -0.012388877 1.391427583 0.000000000
C 1.202113124 0.712149583 0.000000000
C 1.221091124 -0.679278417 0.000000000
C -1.207911877 0.679278583 0.000000000
C -1.188934877 -0.712149417 0.000000000
C 0.025567123 -1.391427417 0.000000000
H -0.027322877 2.486260584 0.000000000
H 2.142800124 1.272498583 0.000000000
H 2.176711124 -1.213763417 0.000000000
H -2.163532877 1.213761583 0.000000000
H -2.129622877 -1.272496417 0.000000000
H 0.040498123 -2.486261417 0.000000000

Table-1 Coordinates of benzene structure

From the above table one can find the Benzene ring plane is XY plane and the perpendicular
to the ring is Z- axis. This xyz file as above can be used to input at the to
display the structure. This geometry was not optimized but still structure had a D6h symmetry.

Figure-2: Benzene structure webmo output.

Thus till now complications all looks simple procedure wise and output wise. For such an
input of xyz file, the webmo enlists numerically two sets of coordinates. One is referred to as
“input orientation” and the next s “standard orientation” as below when a simple Energy
calculation is made. Thus sets in an ambiguity, which set of axes system is to prevail for

output properties like Shielding Tensor. Seems the “standard orientation” axes system is
prevailing for the properties, and the need for the “input orientation” seems an internal matter

for software/programming and in this context need not be considered in detail.


Input orientation:


Center Atomic Atomic Coordinates (Angstroms)

Number Number Type XYZ


16 0 0.000000 0.000000 0.000000

26 0 0.000000 0.000000 1.391557

36 0 1.205124 0.000000 2.087335

46 0 2.410247 0.000000 1.391557

56 0 2.410247 0.000000 0.000000

66 0 1.205124 0.000000 -0.695778

71 0 1.205124 0.000000 -1.790713

81 0 3.358489 0.000000 -0.547467

91 0 3.358489 0.000000 1.939024

10 1 0 1.205124 0.000000 3.182270

11 1 0 -0.948241 0.000000 1.939024

12 1 0 -0.948241 0.000000 -0.547467


Standard orientation:


Center Atomic Atomic Coordinates (Angstroms)

Number Number Type XYZ


16 0 0.000000 1.391557 -0.000000

26 0 1.205124 0.695778 -0.000000

36 0 1.205124 -0.695778 -0.000000

46 0 -0.000000 -1.391557 -0.000000

56 0 -1.205124 -0.695778 -0.000000

66 0 -1.205124 0.695778 0.000000

71 0 -2.153365 1.243246 0.000000

81 0 -2.153365 -1.243246 -0.000000

91 0 -0.000000 -2.486492 0.000000

10 1 0 2.153365 -1.243246 0.000000

11 1 0 2.153365 1.243246 0.000000

12 1 0 0.000000 2.486492 0.000000


Quantity Value

Route #N B3LYP/3-21G SP Geom=Connectivity

Gaussian Stoichiometry C6H6
Job description: Symmetry D6H
Basis 3-21G

RB3LYP Energy -230.975141331 Hartree

Dipole Moment 0.0000 Debye

Server (13158)

CPU time 1.8 sec

Even with the reconciliation as above within benzene molecule itself, a situation arises which
does not appear to be uniform for all protons that is the principal axes system of proton
shielding tensor does not coincide with molecular axes system.

Figure-3 Benzene Molecular axes system and proton shielding principal directions.
At the C-H bond one of the proton shielding principal axes is along the C-H bond, then for
Proton 12 and Proton 11 the situations would be different as shown in Figure-3. Thus the
standard orientation set of coordinates and molecular axes are not characteristic axes for
shielding tensor of proton 11. This situation was reported much earlier while presenting the
magnetic dipole model for benzene protons .; One can find in the calculated results [2] at
each proton the shielding tensor element values and axes disposition are identical with
respect to the C-H bond. But with respect to Molecular axes system, the shielding principal
directions do not coincide with the symmetry axes for D6h. It is evidently seen in the Figure-
4, that the Principal values of all the six protons are equal with a one-to-one correspondence.
The Principal directions of the tensor are all not along the molecular X,Y,Z system. But for
each proton, as a simple appreciation of chemical point group symmetry, all the protons have

one of the PAS axes along the C-H bond, perpendicular to
the C-H bond in the molecular plane, and the third axis is
perpendicular to the molecular plane for all of the protons

Figure-4: Results of Intra molecular Chemical shift
with magnetic dipole model [2]


Below, are the Shielding tensor values in the X,Y,Z system (the standard orientation axes
system). Proton 11 tensor is non-diagonal because of the non-zero xy and yx components
while the proton 12 tensor is diagonal. And for Proton 11 and 12 the “eigenvalues” given are
same indicating the symmetry equivalence. The eigenvalues are listed in the increasing of the
magnitudes without referring to the axis designation X,Y, or Z. The 9 values of full-matrix
elements do not bear any one-to-one correspondence for the proton11 and proton 12. It is this
feature which makes it difficult to recognize the existing C6 rotation equivalence, this
situation is highlighted in greater detail in the next section. If there could be such
precautionary notes for the case of isolated C6H6, the attention to the symmetry aspects would
be much less straight forward in the case of combination of C6H6 and H2.

Figure-5: The tensor shielding tensor element values for proton-11 and Proton-12

The zz components for proton 11 and 12 are of the same magnitude, and not the
corresponding xx and yy components. Does this in any way violate the assertion that the H11
and H12 are symmetry equivalent due to the C6 symmetry axis in Benzene? What is required
is an appropriate rotation of molecule/or axes by the 60⁰ angle corresponding to the C6
symmetry rotation. Then Proton 11 and Proton 12 equivalence would be ensured by the Non-
diagonal proton-11 tensor becomes a diagonalized tensor, and the diagonal elements would
be the same values as that of proton-12 diagonalized values. This numerical matrix
transformation is illustrated in the following diagram. R60 refers to the matrix for rotating by
60 degrees angle, R60-1 is the inverse matrix of R60. By the equation R60 x R60-1 = 1, results on
a Unit Matrix. The above illustration of symmetry equivalence holds good because the
electronic structure pattern in the molecules adhere to the point group symmetries, hence
symmetry equivalent sites have same effective result even if the tensors at the outset are
diagonal/non-diagonal depending upon the disposition of C-H bond with reference to the
molecular frame of reference. Most of these symmetry manifestations and required
transformations were implicit in the results of earlier presentations, and some aspects were
given explicit mention at each context. Before venturing into molecular fragments with such
results, it was found necessary to highlight in a greater detail for the extra care required in
processing the numerical outputs of QM shielding tensor computations.

Figure-6: Transforming non-diagonal tensor to diagonalized form

Figure-7. Symmetry equivalences

The above details on symmetry aspects, diagonal and non diagonal tensors, are not usually
required for attention of chemists who are mostly concerned with the isotropic values of
chemical shifts. But the calculation of Susceptibility Tensor of aromatic molecule using H2
molecule as a probe around the aromatic ring requires an incisive awareness of the symmetry
aspects which cannot be generalized in any simple way, as for the isolated molecules. Making
this more transparent is the purpose in this contribution, again to a limited extent since the
complete details in one such contribution would not be within the stipulated limits.
To begin with the system of C6H6 and H2, the coordinate system for two dispositions are
displayed in Figure-8 just as much as the isolated benzene in Figure-2. At this stage the

careful consideration of the numerical tables and the visual image for the corresponding
numerical values would acquaint with the situation for the combined system, in view of the
discussion for benzene molecule in the previous sections.

As seen in Figure-8 the perpendicular to molecule is the X-axis of the molecular coordinate
system. Y and Z axes are in the molecular plane. The six protons are related by C6 symmetry
axis, but the Y-, and Z- axes are not related by the same C6 rotation axis.

With this exposure to the symmetry aspects and the diagonal and non-diagonal tensors, the
discussions of calculating the susceptibility tensors from proton shielding tensor (as in ref.
[1]) results in the Susceptibility Tensor of aromatic ring, using the corresponding H13, and
H14 shielding Tensors, provisional results are in Figure-9.

Such calculated values for C6H6 from the probe H2 molecular protons are available in
reference [1],


Then if an analysis for Susceptibility Tensors for molecular fragments is to be envisaged,
then as in Figure-10, the probe molecule may be conveniently placed at a specific distance
and this Hydrogen molecule can be placed around the central ring (may be even substituted
aromatic molecule) along several points on the radius of a circle, ensuring from the center of
gravity of the molecule the radial vector distance of hydrogen molecule is the same. Then the
changes in the shielding tensor of protons of hydrogen molecule must vary reflecting the
induced field angular dependence. Depending upon the symmetry at the aromatic molecule
these angular variations can be possibly traced to the functional group nearest to the hydrogen
molecule. And an appropriate statistical procedure may give the breakup of shielding tensor
in terms of fragment contributions so that the total whole molecule susceptibility tensor can
be sum of fragmented values. Such a processing reduces uncertainty of empirical methods
and must be consistent. Subsequently referring to experimental values of NMR shielding
appropriate rationalization would be possible on the soundeness of this approach.

Figure-8: The coordinate system and coordinate values for 2-dispostion of H2

Figure-9: The Susceptibility Tensor Elements for Benzene from H2 Proton Shieldings

Figure-10: C6H6 and H2 / H2 rotated around C6H6 in 30 deg interval


(1) (a)

(2) (a)
(b) On page -290, Event-16 in the contents of book by Sankarampadi Aravamudhan, “
A Monograph of Contributions of Dr. S. Aravamudhan to Scientific Events”. Publisher
of the book: Scholars Press, Omniscriptum Publishing Group, Mauritus.


Isolated hydrogen molecule has diagonal tensor with the axes system as in inset above with ZZ being the
most shielded [27.5205] direction coinciding with H-H
bond direction. The diagonal tensor is also axially

symmetric since in the plane perpendicular to the ZZ symmetry axis, the tensor elements are same. In
the combined system above, H13 and H14 are the protons of hydrogen molecule. Unlike in isolated
molecule the two protons are not equivalent, though each one of the protons has diagonal tensor; there
are two distinct tensors the two protons of hydrogen, one for nearer proton H13 the other tensor for
farther proton H14.

The combined system with H-H bond line at 10 deg rotated from (an axis) of the combined molecular
system is depicted on this sheet. The hydrogen molecule protons have non diagonal tensors. Associating
the tensor elements for subtraction of corresponding isolated molecule tensor elements requires the
correspondences of tensor elements, and a reconciliation of the differences of symmetry dispositions.




Department of Chemistry
NEHU Campus Mawkynroh Umshing
SHILLONG 793022 Meghalaya INDIA

[email protected]


Theme: THEME CT: Chemistry Across the Themes
Symposium: 1. Advanced Methodologies for Matter Characterization and Better Knowledge

Presentation Type: Poster Communication

Poster Presentation No: P530

Session 1 BLUE Code
Poster Session Schedule: From Monday, July 8, 2019 at 12;00 AM to Tursday, July 9m 2019 at 6:00 PM
Poster Format: A0 – Portrait

At the web page (URL given below) the events related to IUPAC2019 PARIS have been
enumerated with hotlinks to open up for details.:


Initial documentation


A message received from

The Congress Secretariat

on Friday 3rd May 2019 at 9:21PM

Personal Indian Passport is to be renewed ---/10th May 2019/

A message from Program Manger on behalf of Congress Secretariatreceved on 14th May 2019, 08:38

Invitation Letter received attached to message on 20th May2019 2:50 PM
Invitation Letter received on 11th June 2019

On 20th May 2019 by evening the passport renewal process initiated. Outcome to be known in a week's

Application submitted successfully (on 23rd May 2019 ; 11:47 AM) for Passport/Renewal
Secured Valid Passport 11th June 2019 ; 10:22 PM

Communication from Conference Secretariat-acceptance & mode of presentation (on 23rd May 2019

IUPAC2019 - General Participant Registration Confirmed as on 28th May 2019 9:52 PM --- Confirmation
of Registration 11th June 2019

Also click & find here Registration updates



Department of Chemistry, NEHU Campus Mawkynroh Umshing, SHILLONG 793022 Meghalaya INDIA

[email protected]

The bulk magnetic susceptibility induced field distribution within the magnetized materials is dependent
upon the particular specimen shape. For certain regular shapes like sphere and ellipsoids, the induced
field distribution is homogeneous within the entire specimen. This well known homogeneity within a
sample combined with the zero induced fields prevailing inside spherically shaped specimen enabled a
customary procedure to make spherically shaped single crystal specimen for purposes of determination
of shielding tensor of protons by high resolution PMR in solids by selective averaging (1). In spite of such
experiments on carefully made spheres, there were still ambiguities in the shielding tensor values
determined. This ambiguity could be resolved at stage of determination proton shielding tensor values
in single crystal of pyromelliticacid dianhydride (2).
This resolution came about because of the realization that at a proton site in a crystal lattice, both the
intra molecular and inter molecular contributions are present and the symmetry determining these two
contributions are different. This aspect has been given a detailed consideration (2). Importantly if
contributions from sources two different symmetries are to be disentangled, since in principle more
than a merely two symmetries can be invoked within a molecule, disentangling such components leads
to fragmenting molecule into as many varying symmetries as there can be to disentangle. There can be
combined molecular systems drawn in structure editors which can be submitted for quantum chemical
calculation of shielding tensors. These aspects with preliminary calculated results are reported and the
possible outcomes for interpretation of chemical structure are indicated (3, 4 & 5).

1. High Resolution NMR in Solids Selective Averaging , 1st Edition ,
Supplement 1 Advances in Magnetic Resonance, Authors: Ulrich Haeberlen , eBook ISBN:
9780323160254 , Imprint: Academic Press , Published Date: 28th January 1976, Page Count: 204
2. Pyromellitic acid dianhydride: crystal structure and anisotropic proton magnetic shielding S.
Aravamudhan , U. Haeberlen , H. Irngartinger & C. Krieger , Pages 241-255 | Volume 38, 1979 - Issue 1,
Published online: 23 Aug 2006,
----ebook link :



1. What is the root source for these Questions? Sheet 2

2. What are the Contributions to Induced Fields at the site of the nucleus from the different parts of

the specimen that makes up the Experimentally Measured Shielding Tensor?. Sheet 3
3. Why is the Bulk Susceptibility Contribution zero for Spherical Samples? Sheet 4

4. How is the Intermolecular Contribution calculated by the Discrete Summation Procedure? Sheet 5

5. How to ensure that all the neighboring molecules of significance have been considered in the
summation? How can the boundary of Lorentz Sphere [the semi micro volume element] be

constructed? Sheet 6

6. Can the Semi micro Volume element be Ellipsoidal instead of being Spherical; can there be Lorentz

Ellipsoids? Sheet 7

7. What is the Intermolecular contribution to the Shielding Tensor if the neighboring molecules are

enclosed within a Ellipsoidal Volume Element instead of Spherical volume Element? Sheet 8

8. Can the Experimentally measured Values of the Shielding Tensor for the spherical shape and the

Ellipsoidal shape be related by an equation? Sheet 9
9. What are the questions still remain at this stage to be answered? Sheet 10

10. What are the considerations when the induced fields within the specimen can be inhomogeneous?

Sheet 11

11. Why the Discrete Summation procedure cannot be extended to the entire extent of the

macroscopic specimen? Sheet 12

12. Where are the sources for finding a description of the simpler summing method of calculating

demagnetization factors? Sheet 13

13. Can the simple method be useful for tackling the difficult calculations for the case of

inhomogeneous magnetization? Have there been any specific shapes considered till date? Sheet

14. Can there be zero Induced Fields inside a specimen of inhomogeneous magnetization, if the shape
of inner volume element and the outer specimen shapes are same as argued out for ellipsoids?

Sheet 15

15. Can the Shielding tensor results be obtained with simple calculations in the case of an
experimental determination in the inhomogeneously magnetized specimen even when provided

that the shapes are describable by regular eqautions? Sheet 16

Appendix: on Sheet 17 ; Sheet 18 ; Sheet 19 & Sheet 20






The correction for inter molecular contribution required
the fragmentation of molecule and lead to consider the
chemical aspects of fragmentation by theoretical methods.



SHEET No: 10

The consideration of QM theoretical study of chemical shifts were undertaken mainly to
find the causes of lack of complete consistency between atom and bond susceptibility
values as reported by Flygare cited in

SHEET No: 11

With distance of separation the dipole moment changes and it can reverse direction.

SHEET No: 12

Thus for this system of CH2O and H2, depending on the disposition of
H2 in the neighborhood of CH2O the dipole moment vector changes.

SHEET No: 13

SHEET No: 14

Assigning the X, Y, Z avis as per the conventions adapted
in the QM soft ware for shielding directions critically
determines the success of handling magnetic dipole
approximation for calculating susceptibility tensors.

SHEET No: 15

The results in table above is the susceptibility anisotropy values for benzene obtained by
magnetic dipole model based on the shielding tensor values obtained from QM calculations.
This result provides the required confidence to proceed with the systems as displayed below
- C6H5F and H2

SHEET No: 16

Page 1 of 11

ICRTST-2018 S.S.S.K.R. Innani Mahavidyalaya Karanja (Lad)

Relevant Conference Themes:

Mathematical Physical & Chemical Sciences, Computer Science, Information Technology

Theory, Computation and Simulations can be Stand Alone
Methodology as much as the Reproducible Experimental

Determination of Physical Quantities.

Sankarampadi Aravamudhan

Department of Chemistry


s a ra va mu d ha [email protected] h ot ma i l. c o m

Keywords: Quantum Theory, Quantum Mechanical Methods, Computational Chemistry,
Calculation of Physical Quantities, Theoretical Modelling of Physical Systems,
Simulation, Inferences on Trends, Insights into Phenomena and Mechanisms,
Spectroscopic Techniques, Determination of Spectral Properties.

(ABSTRACT Text in -492 words- the following sheet)
Paper organization



Page 2 of 11


Generally, with references to Chemical Sciences, theory is meant for explaining
experimental observations, theoretical calculations are made to sort out
experimentally observed anomalous trends and exceptional material characteristics
besides in connection with the supportive spectroscopic features. Theory more are
less gets validated by the extent to which the calculations and conclusions are
helpful in interpreting experimental findings. The perspective in this contribution
is to learn how to be consistent within the theoretical frame work and confi dently
establish trends in calculated results to gain insights into the physical systems
under study so that these inferences can be transferred to the experimental
domains to design novel experiments.
ht t p: / / www. ugc - inno - ne hu. co m/ ser - s a/ S E R- 1- S t ack ing_ be nze ne_d i mer . do c
Three different instances are being enumerated to highlight the points of view as
implied in the title of this contributed paper.

(1) The instance of reconciling with the fact that the PMR spectrum of a
Polymer chain can become interpretable by invoking a cyclic dimeric
structure referred to as the “fictitious spin book keeping” structure.
ht t p://www. ugc - inno - ne hu. co m/e ve nt s - 20 18. ht ml# bhc

(2) The Quantum Mechanical Calculation for Geometry Optimization (G.O.)
can handle not only isolated molecules, but also ensemble of structures. I
certain cases when the G.O. is applied to an ensemble of molecules, this can
conveniently indicate what is the energy optimized equilibrium arrangement
of the ensemble of molecules, sometimes even unusual bonding between
units or break up of units are possible when there are more number of
identical units. Simple example to quote is a cluster of ‘n’ number of water
molecules drawn in structure with arbitrary locations. In such a cluster of
material mostly known in liquid state, random diffusions of various degrees
of freedom are possible which have to be explicitly taken into account
during the energy minimization applying calculus of variations. Such a
requirement may be to get results by the G.O. calculations which are
apparently much closer to reality.
ht t p://www. ugc - inno - ne hu. co m/e ve nt s - 20 17. ht ml#E 0 9

(3) To this context, two molecules of totally different compounds (which in
reality are never considered together for forming useful compounds) can be
drawn on structure editor and submitted for a Q.M. calculation of physical
properties of the combined system. Certain quantities like the atomic
charges, dipole moment and spectroscopic properties (specifically Proton
NMR patterns) can reveal the possible nature of interactions which may be
revealing certain trends for compounds which really matter in the
ht t p: / / www. ugc - inno - ne hu. co m/ I S C 105 - O S U/ isc1 05 - do c. pd f

Click to View FlipBook Version
Previous Book
Next Book
47 - Junio 2010