Computational Chemistry

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					Computational Chemistry
         Tom Grimes
         12/13/2001
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
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)
Potential Energy Surface
PES of HO*
                              Ground State         1st Excited State

                -74.5

               -74.55
 E, Hartrees




                -74.6

               -74.65

                -74.7
                        0.1    0.6           1.1            1.6
                                     r, Angstroms
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
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
IR Spectrum of Ethanol

                            0




                                  Relative Intensity
                            0.2

                            0.4

                            0.6

                            0.8

                             1
 3500   2500       1500   500
        Wavenumber

    Predicted IR Bands                                 Measured IR Spectrum
Computational Methods:
Molecular 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
Computational Methods:
Semi-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
Computational Methods:
Ab 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
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
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
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
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
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
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
Nanotube Prices
 Very expensive
 Run from $300/gram to
  $1,200/gram
 Few sources
     Nano-Lab (nano-lab.com)
     Carbon Nanotechnologies
      (cnanotech.com)
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
    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
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
    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
Formation of the Fe(CO)5
Dimer



    2 Fe(CO)5  Fe2(CO)9 + CO




           Fe3(CO)12
Literature Search Results,
cont’d
   C2
        No sigma orbitals available for bonding
        Eta-bonding only
        Different from CO ligand bonding




     CO Bonding                     C2 Bonding
MO Diagrams
Literature Search Results,
cont’d
   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
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
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
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
Iron-Dicarbon Structures
Another Proposed Structure
 This structure was
  suggested by Smalley
  and Hauge of Rice
  University
 Optimized using
  UB3LYP/6-31G
       No imaginary
        frequencies found
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
Conclusion
1.       Search existing literature for previous work
         done on iron carbonyl and dicarbon
          Done
2.       Evaluate the computational tools and methods
         available to us
          Done
3.       Find possible iron-dicarbon structures
          Found some, but more work in this area could be
           useful
4.       Compute properties of these compounds
          Begun, but far from done
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
References
Accelrys, www.accelrys.com
Exploring Chemistry with Electronic Structure
   Methods, 2nd Ed., Foresman and Frisch,
   Gaussian, Inc.
Gaussian 98 User’s Reference, Gaussian, Inc.
Titan User’s Guide, Wavefunction, Inc.,
   Schrodinger, Inc.
NIST WebBook, webbook.nist.gov/chemistry
Previous Work

				
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