# Presentation: 193964

## Theoretical Structure and Spectra of Gallium Arsenide Clusters

*hira@nnmc.edu*

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**Northern New Mexico College**
**Espanola, New Mexico 87532**

## Introduction

-     have become a subject of great scientific and technological interest.
-  The group III-V semi-conducting materials have been studied
-     extensively in the bulk phase.
-  Recent focus has been on the GanAsn clusters in view of the
-     possibility of novel applications.
-  Experimental results on gas phase gallium arsenide clusters reveal
-     interesting similarities, as well as interesting dissimilarities, with the
-     bulk materials.
-  One significant trend revealed by the cluster studies is the even-odd
-     alternation in their electron affinities and ionization potentials.

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**Introduction**

## Introduction Continued

**Introduction Continued**

## Theory

**Theory**

## Theory Continued

**Theory Continued**

-  The wavefunction  for a particle is, in general, a function of its
-     position and time.
-  The symbol       is the mathematical operator “del”. The del
-     operator is defined as a sum of the partial derivatives with
-     respect to x, y and z co-ordinates.
-  If the total energy of a particle, does not change over time, then
-     the form of the Schrödinger Equation is simpler:
- 					.... (2)
-  Despite the simple form of equation (2), it is impossible to solve
-     the Time-Independent Schrödinger Equation exactly for most
-     molecules. Thus we are forced to make several simplifying
-     assumptions, to obtain an approximate solution.

## Computational Scheme

**Computational Scheme**

- The simplifying assumptions are:
- The electrons are moving in a field of fixed nuclei. This allows us to separate the motion of the nuclei from the motion of the electrons. This is the Born-Oppenheimer Approximation.
- The square of the norm  of the electronic wavefunction for the molecule is the probability density for the electrons in the system.
- The molecular orbitals  for the electrons in the molecule are restricted to be linear combinations of a pre-defined set of one-electron functions  known as basis functions.
- The resulting equations are nonlinear and must be solved iteratively. The
-       procedure to solve them is called the Self-Consistent Field (SCF)
-       method.

## Computational Scheme Continued

-        1. Compute the integrals.
-        2. Construct an initial guess and form the density matrix.
-        3. Construct the Fock matrix *F* and calculate the term *E**XC* on a grid.
-        4. Solve for the coefficient matrix *C* and form the electron density
-            matrix.
-        5. Test for convergence. If test fails, go back to step 1. Else, finalize
-            output.
** **
-  Our computational model consists of complete geometry optimizations
-     at B3LYP/LANL2DZ level for all the clusters:
-     BLYP = Becke-Lee-Yang-Parr Functional,
-     LANL2DZ = Los Alamos National Laboratory 2 Double Zeta basis** **set.

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**Computational Scheme Continued**

## Results:

**Results:**
** ****Binding Energy/Atom**

## Results:

**Results:**
** ****Binding Energy/Atom**

## Results:

**Results:**
** ****Binding Energy/Atom**

## Results: Energy Graphs

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

## Results: IR Spectra

**Results: IR Spectra**

## Conclusions

**    ****yet have found the most stable forms for these clusters.**
** ****The binding energy per atom for the small gallium arsenide clusters**
**    ****increases, in general, as the number of pairs n increases. It dips slightly**
**    ****from n =8 to n=10.**
** ****37.6 % of the bulk cohesive energy of 6.67 eV is recovered at  n =12.**
-  **There is a possible magic number for cluster stability at n = 8****.**
** ****The number of IR spectral peaks increase as the cluster size is increased, **
**    ****from 1 peak for GaAs to 9 peaks for Ga****4****As****4****.**

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**Conclusions**

## References

-      GanAsn Clusters with CGaAs Cages: Possible Nanostructures”, Bull. Am. Phys. Soc. _52_**, **1006 (March 2007).
- 2. Daniel Bulnes, Nichole Moya-Leyba, Erica Velarde
-     and Ajit Hira, " Theoretical Study of Na3C60 and
-     Na4C60 Clusters: Pathways to Nanoscale Contacts",
-     *Bull. Am. Phys. Soc*. _50_, 1475 (March 2005**).**
- 3. A. S. Hira and A. K. Ray, "Interactions of the Na2
-     dimer with a C60 Molecule", *Phys. Rev.* A _54_, 2205
-     (1996).

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**References**

## Acknowledgements

**Theoretical Structure and Spectra of Gallium Arsenide Clusters**

**Acknowledgements**