Computational%20Chemistry

1
Computational Chemistry

• Tom Grimes
• 12/13/2001

2
The Basics

• Input a molecular structure
• In some cases, electronic configuration may need
  to be known
• Three basic types of calculations
• Single-point energy
• Geometry optimization
• Frequency calculation
• Interpret the data

3
Single-point Energy

• In the simplest terms, it is the energy intrinsic
  to the structure
• Useful for determining the stability of a
  compound
• The structure may be in an excited state
• Defines a potential energy surface (PES)

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Potential Energy Surface
5
PES of HO
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Geometry Optimization

• Determination of the equilibrium geometry
• Generally, the geometry associated with the
  lowest single-point energy
• Can also be used to find transition state
  geometry by minimizing the energy in all
  coordinates on the PES except for one
• SCF theory finds a stationary point, a place
  where the energy gradient is zero
• May correspond to either a minimum or a
  saddlepoint

7
Frequency Calculation

• Predicts the intensities of the vibrations
  associated with a molecule
• This is useful for predicting the absorption
  spectra of compounds
• It can also be used to verify whether the
  structure was fully optimized
• If it was not fully optimized, reaction
  coordinates appear as imaginary frequencies.
• NMR spectra can also be predicted

8
IR Spectrum of Ethanol
Predicted IR Bands
Measured IR Spectrum
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Computational MethodsMolecular Mechanics

• Treats molecules classically
• Ball-and-spring model
• Assumes ideal bond angles and lengths
• Fastest method
• Predicts geometries well
• For normal systems, the bond angles and lengths
  will be close to ideal
• Relatively poor prediction of energies
• Total energy only takes into account deviation
  from ideal bond length, bond angles, dihedrals,
  and van der Waals interactions

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Computational MethodsSemi-empirical

• Based on quantum mechanics, but uses empirical
  data to simplify the calculations
• Fast, but not as fast as molecular mechanics
• Produces good energies and good geometries for
  simple organic compounds

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Computational MethodsAb Initio

• Calculations based on quantum mechanics, without
  use of empirical data
• Slowest method because it involves approximating
  a solution to the Schrödinger equation strictly
  from quantum mechanical principles
• Generally finds approximations using
  self-consistent field (SCF) theory
• Produces the best energies and geometries, overall

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Popular Procedures

• Molecular Mechanics
• AMBER, DRIEDING, UFF, MMFF
• Force-fields, not methods
• Semi-Empirical
• AM1, PM3, MNDO, CNDO, INDO
• Ab Initio
• Hartree-Fock, BLYP, DFT methods

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Basis Sets

• A basis set is a set of functions that restrict
  the electrons considered to specific regions of
  space
• Larger basis sets impose fewer restrictions, and
  so give better predictions
• However, larger basis sets are computationally
  more expensive

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Interpretation

• Computational data are not a replacement for
  physical experiments
• Keep the basis set and computational method in
  mind when deciding how much credence to give the
  result of a calculation
• Cross-checking each calculation with another is
  invaluable
• E.g., checking a geometry optimization with a
  frequency calculation if imaginary frequencies
  exist, the structure is not fully optimized and
  some of the numbers may not be accurate

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Implementations

• Titan
• Easy to use GUI
• Not as flexible as other programs
• Gaussian
• No native GUI, but GaussView is available as a
  front end
• Very flexible, but syntax is profuse and often
  confusing
• GAMESS
• Text-only interface, even more bare than Gaussian
• Free
• Well-known and used by researchers

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DMol3 (Accelrys)

• A DFT plugin to the Cerius2 core
• Two modules molecular systems and periodic
  systems
• Advantages
• Good implementation of DFT methods
• Allows periodic systems, surfaces, solids, as
  well as gas phase
• Parallel
• Disadvantages
• Requires SGI IRIX (UNIX) workstations

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A Problem

• One of the primary restrictions in carbon
  nanostructure research is the lack of material
• It is expensive and time-consuming to produce
  bucky-balls/nanotubes
• The process of formation is not well understood

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Nanotube Prices

• Very expensive
• Run from 300/gram to 1,200/gram
• Few sources
• Nano-Lab (nano-lab.com)
• Carbon Nanotechnologies (cnanotech.com)

360.00
300.00
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Research Project

• Currently, the most efficient process for
  nanotube production is the HiPCO process
• It is thought that the disproportionation of CO
  occurs to generate CO2 and carbon, possibly in
  the form of C2
• Nanotube formation does not occur without the
  catalyst, but the mechanism of catalysis is
  unknown
• Fe clusters are found at the ends of the tubes,
  but it is not known whether these are the
  catalytic agent or whether they form after the
  tubes

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Preliminary

• Iron pentacarbonyl, Fe(CO)5
• Computational methods are ideal to discover
  possible mechanisms of catalysis because
  transition states and energetics can be
  calculated easily (relative to actually
  attempting to determine them empirically) and
  does not require the danger of handling Fe(CO)5

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Previous Goals

1. Search existing literature for previous work done
   on iron carbonyl and dicarbon
2. Evaluate the computational tools and methods
   available to us
3. Find possible iron-dicarbon structures
4. Compute properties of these compounds

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Literature Search Results

• Provided structural information for Fe(CO)5 that
  could be verified
• Provided the structure of an iron pentacarbonyl
  dimer and its formation by photolysis
• Important because one of the theories of
  catalysis is nucleation of Fe clusters
• HiPCO process expected to provide these
  conditions
• Provided information of the bonding of C2
• Suggested the best methods for computations of
  iron compounds

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Formation of the Fe(CO)5 Dimer
2 Fe(CO)5 ? Fe2(CO)9 CO
Fe3(CO)12
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Literature Search Results, contd

• C2
• No sigma orbitals available for bonding
• Eta-bonding only
• Different from CO ligand bonding

CO Bonding
C2 Bonding
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MO Diagrams
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Literature Search Results, contd

• Suggested computational methods
• DFT Density Functional Theory
• Similar to HF methods, but uses a more general
  functional for the exchange correlation term in
  the energy expression
• The functional is based on the idea that the
  minimal energy of a collection of electrons under
  the influence of an external Coloumbic field is a
  unique functional of the electron density
• CI Configuration interaction
• Is based on approximating the exchange
  correlation by replacing one or more occupied
  orbitals with virtual orbitals, basically making
  a linear superposition of the HF determinant with
  others

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Second Goal

• The next step was to try to evaluate our tools by
  reproducing literature values for the structure
  of Fe(CO)5
• Bond lengths agreed to within 0.02 Å
• Trigonal bipyrimidal geometry was stable
• Total energy also agreed with literature

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Hurdles in Attaining this Goal

• Structures containing iron are notoriously
  difficult to model because the d-orbitals become
  important in bonding
• This significantly increases the time necessary
  to complete a calculation
• Another problem was the difficulty in determining
  the spin multiplicity of the system
• At incorrect multiplicities, the geometry refused
  to converge upon a stable solution

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Iron-Dicarbon Compounds

• Did not find any in the literature that were
  helpful
• Most in the literature had a bunch of other
  ligands
• It is known that the C2 will be eta-bound to the
  iron because no sigma orbitals are available
• Two stoichiometries were proposed
• Fe(C2)4 tetragonal and square planar
• Fe(C2)5 trigonal bipyrimidal

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Iron-Dicarbon Structures
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Another Proposed Structure

• This structure was suggested by Smalley and Hauge
  of Rice University
• Optimized using UB3LYP/6-31G
• No imaginary frequencies found

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Properties of Iron-Dicarbon Compounds

• Unable to optimize the geometry of any of the
  stoichiometries
• Spin multiplicity unknown
• Time-intensive computation limits how fast we can
  search for viable structures
• Not enough time
• Since this was at the end of the Summer, there
  was no time left

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Conclusion

• Search existing literature for previous work done
  on iron carbonyl and dicarbon
• Done
• Evaluate the computational tools and methods
  available to us
• Done
• Find possible iron-dicarbon structures
• Found some, but more work in this area could be
  useful
• Compute properties of these compounds
• Begun, but far from done

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More Research Ideas

• Beowulf clusters
• Independent distributed
• More time needed on the current iron-dicarbon
  structures
• Doing an even more intensive literature search on
  dicarbon research
• Determining possible intermediates
• Finding possible pathways for their formation
• Finding ways to detect these intermediates
• Use the information to make production more
  efficient

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References

• Accelrys, www.accelrys.com
• Exploring Chemistry with Electronic Structure
  Methods, 2nd Ed., Foresman and Frisch, Gaussian,
  Inc.
• Gaussian 98 Users Reference, Gaussian, Inc.
• Titan Users Guide, Wavefunction, Inc.,
  Schrodinger, Inc.
• NIST WebBook, webbook.nist.gov/chemistry
• Previous Work