ASSIGNMENT

1
ASSIGNMENT

• To find structures of all possible Na clusters
  upto atom no 6 and study them.
• and their IP, internal energy and free energy and
  compare with that of bulk by HF/6-31G(d)
  B3LYP/6-31G(d).

2
INTRODUCTION

• CLUSTERS
• HF
• B3LYP
• 6-31G(d)
• GAUSSIAN 03

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CLUSTERS

• clusters are the structures intermediate to
  molecules and bulk eg. fullerene
• metallic clusters have metal bonds as a
  stabilizing force and inter atomic repulsions as
  destabilizing force.
• certain properties like inter atomic distances,
  IP, free energy vary in clusters as compared to
  that of the bulk.
• stable conformers have lower energy as compared
  to unstable ones.

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Exactness....the desire Inexactness....the
need

• The underlying physical laws necessary for the
  mathematical theory of a large part of physics
  the whole of chemistry are completely known,
  the difficulty is only that the exact
  applications of these laws leads to equations
  much too complicated to be solvable.
  
  - DIRAC

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HF

• In Hartree-fock theory each electron is described
  by an orbital and the total wave functions is
  given as a product of orbitals .
• HF theory only accounts for the average
  electron-electron interactions, consequently
  neglects the correlations between electrons.
• HF gives results that are 99 correct.

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B3LYP

• Becke's three parameter formulation is a
  Density functional method . They calculate elec
  correlation via elec density functional .
• DFT functionals partition the electronic energy
  into several components ,which are computed
  separately the KE , the elec-nuclear
  interaction the coulomb repulsion an exchange
  correlation term accounting for the remainder of
  elec-elec interaction.

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6-31G(d)

• Split valence basis set like 6-31G have two sizes
  of basis functions for each valence orbital. eg H
  C are represented as
  H
  1s, 1s
  
  C1s,2s,2s,2px,2py,2pz,2px,2py,2pz
  where starred unstarred orbitals
  differ in size and can form all MOs from linear
  combinations for each atomic orbitals.
• 6 functions are used for core electrons ,3 for
  more diffused valence electrons 1 for less
  diffused valence electron.

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• d is polarized basis. Split valence sets allow
  orbitals to change size but not shape. Polarized
  basis set removes this.
• p is added to H ,d to 2nd period elements f to
  transition metals.

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GAUSSIAN

• It is connected to a system of programs for
  performing variety of semi-empirical ab-initio
  MO calculations.
• Automated geometry optmizes to either minima or
  saddle points . Optmization is performed by
  default using internal coordinates regardless of
  the input coordinates used .
• Gaussian programs use gaussian functions as basis
  set. Their general form -
  g(a,r) c
  xn ym zl e(-ar2)

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a is a constant determining size (radial extent)
of the function.
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APPROACH TO THE PROBLEM

• Initial verification of non-existence of highly
  unsymmetrical structures.
• Trying out different possible structures by HF
  method and next doing freq opt.
• Ruling out of some more structures
• Using the output given by HF files in B3LYP .
  (why not the converse ???)
• Repeating a similar process for the cations.

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OBSERVATIONS

• The values of IP, E G and the structure
  given by HF B3LYP are almost same (lt0.5).
• So the structure of all the conformers we have
  shown in the following slides are from B3LYP.
  Only those structures which are different in HF
  are shown.
• Some cations with interesting geometry are also
  shown.

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• n2
• HF/B3LYP
• Linear

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E,G IP Values for n2
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• n3
• B3LYP
• Linear
• Initial input
  90 or 109
  degrees

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• n3
• B3LYP
• Bent(168.)
• Initial input
  175 degrees

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• n3
• B3LYP
• Triangular
  96 degrees
• Initial input
  58 degrees

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• n3
• HF
• Triangular
  46 degrees
• Initial input
  58 degrees

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E,G IP Values for n3
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• n4
• HF
• Rhombus
• Only stable
  conformer

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• n4()
• Linear
• HF

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E,G IP Values for n4
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• n5
• HF/B3LYP
• Planar
• Only stable
  conformer

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• n5()
• Distorted
  tetrahedral
• B3LYP

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E,G IP Values for n5
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• n6
• B3LYP
• Planar

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• n6
• Pentagonal
  pyramidal
• B3LYP
• Most stable
  conformer

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• n6()
• Trapezoidal
  bipyramidal
• B3LYP

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E,G IP Values for n6
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IP PLOT OF MOST STABLE CONFORMER FOR EACH n

• HF B3LYP (IP in
  1000kcal/mol)
  
  
  
  
  
  
  
  
  IP of bulk sodium is
  118.589kcal/mol

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G PLOT OF MOST STABLE CONFORMER FOR EACH n

• Mod of G of the most
  stable conformer has been
  plotted for
  each n
• G in 1000kcal/mol

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Internal energy plot of the most stable
conformer for each n

• Mod of E of the most
  stable conformer has
  been
  plotted for each n
• E in 1000kcal/mol

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General symmetry in structures

• Na clusters do not form the geometry that are
  very common like tetrahedral, trigonal
  bipyramidal, square pyramidal.
• Na clusters upto n5 try to form planar
  structures that are composed of distorted
  triangular units.
• For n6 also , a planar geometry made of
  triangular units exists though it is not the most
  stable one.
• The most stable is pentagonal pyramidal,with the
  vertex atom going a little bit out of the plane.

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POSSIBLE REASONS-

• The absence of highly symmetrical structures may
  be due to the fact that this will help in
  increasing the average atom-atom distance which
  in turn may help in reducing the repulsions.
• For larger systems like n6, the geometry leaves
  planarity as this makes metal-metal bonding more
  favorable.

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Problems Faced....

• The most common problem was error by link 9999.
  This occurs if the initial guess is
  far apart from a minima. The program ,after
  making several iterations, is unable to find an
  optimum position reports an error.
• When input had perfect symmetry, the convergence
  could not be achieved .

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What to do then ???

• The input should be as close as possible.
  But in large systems it is
  difficult to be too close to the optimized
  geometry. So the last optimized geometry given
  by the error file can be used again.
• Viewing the movie of error file and the frequency
  in molden can help in eliminating the structures
  which are not possible.
• Avoid exact symmetry .

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THANK YOU

BY- Aditya Somani Ashish
Kumar