Computational Chemistry
Todd C. Gehris and Julie B. Ealy, Ph.D.
Penn State University, Lehigh Valley
Introduction
Spartan Pro is molecular modeling software. Molecular modeling is a means to predict the
structure of a molecule using a set of mathematical and chemical rules. Molecular modeling reduces
the cost of research by limiting the number of physical experiments needed to be performed. By
having a reasonable idea of the structure of a molecule a researcher will know if a molecule will
prove useful for the goals of the research or if another molecule should be tested. A variety of
modeling methods may be used in Spartan Pro. They are Molecular Mechanics, Semi Empirical,
Hartree-Fock and Density functional. The method to be used is dependent upon the molecule that is
being tested. Each of the molecular modeling methods has its strengths and weaknesses and is
parameterized and optimized for different types of molecules. Some examples of the things to be
considered when selecting modeling method are; organic vs. inorganic, metals and transition metals,
periodic row of the atoms in the molecule, ionic character of the molecule. The various molecular
modeling methods use chemical or mathematical methods such as, Huckel’s rule, molecular orbital
theory, quantum mechanics, Schrödinger’s equation, and wave functions. A breakdown of the type
of the methods used for each modeling method and what that means in terms of the final results are
presented in the center of this poster. By performing calculations using all the molecular modeling
methods available in Spartan Pro we hope to demonstrate to the reader the choices that need to be
made to use the software reliably. We also hope to demonstrate the strengths and weaknesses of the
different methods. Our final goal is to create a simple framework for novice Spartan Pro users that
will enable them to easily select the molecular model best suited to the molecules they wish to run.
Abstract
Spartan Pro was utilized to compare theoretical measurements of bond length, bond angle
and dipole to experimental data. We constructed a matrix of values obtained from each of the
theoretical models and associated error rates determined by experimental data. An error limit of
3% was used for bond length and bond angle in order to create a visual of the theoretical model
that best represents experimental data. We discovered high error rates for dipoles in most
molecular modeling methods so the 3% limit was not applied in relation to dipoles. Although
there was often a high error in dipole calculations, our data revealed that some molecular
modeling methods correctly calculate trends in dipoles.
TEST GROUPS
CH3F
CH3Cl
CH3Br
CH3I
H 2O
H 2S
H2Se
H2Te
PF3
PCl3
PBr3
PI3
HF
HCl
HBr
HI
C2H6
C2H4
C2H2
NH3
PH3
AsH3
SbH3
Molecular modeling methods outline
o
o
o
o
o
o
o
Molecular Mechanics
Can be used for molecules containing more than 1000 atoms.
Fast procedure to perform conformational analysis.
Computation of geometry, enthalpy, entropy and vibrational states.
Energy of a molecule is described as the sum of contributions arising from distortions of ideal bond
distance, bond angles, dihedral angles, and non-bonded iterations.
Experimental analogies are electron diffraction and gas phase chromatography
MMFF (molecular mechanics force field)
o Bond lengths often differ from experimental values by 0.01.
o Parameters not developed for inorganic systems.
o May reproduce trends in dipoles but values are way off.
SYBYL
 Parameterized for second row or greater elements
 Does well with organic but poorly with inorganic.
 Results are very inaccurate for some systems.
o
o
o
o
o
o
o
o
o
Semi empirical (quantum based methods)
Useful for molecules containing up to 200 atoms.
Calculations are based upon molecular orbital theory.
Uses a simplified version of Schrödinger’s equation.
Calculations only use valence shells. Inner shells are treated as a fixed core.
Will provide accurate models of a molecule if the atoms making up the molecule are included in the
data set.
Useful for equilibrium geometries: transition metal inorganic and organo-metalic compounds.
Interaction among nuclei and electrons and molecular geometry in terms of minimum energy
arrangements of nuclei.
Total electron density: corresponds to the electron density measured in an x-ray diffraction
experiment.
AM1
o Gives poor results for second row elements
o PM3
o Was specifically developed for equilibrium geometries of transition metal inorganic and
organo-metallic compounds.
o Reasonably good results for metal-carbon bond lengths.
o
o
o
o
o
o
o
o
Hartree-Fock
Impractical for molecules with greater than 100 atoms
Useful for thermodynamic and kinetic comparisons.
Provides excellent account of molecular equilibrium and transition state geometry.
Does well with equilibrium conformations.
Calculations use a simplification of the Schrödinger’s equation. A single wave function Ψ serves as a
replacement (or product) of many electron wave functions Ф. Each electron is considered to be
effected by the sum of all other electrons.
Incomplete description of coupling motions of electrons (electron correlation). Often causes greater
errors in transition metal inorganic and organo-metalic compounds.
Electron-electron repulsion may be overestimated, resulting in shorter reported bond lengths.
Poor for bond making and breaking reactions.
o Moderately successful in reproducing dipole trends but the magnitudes of the dipoles are often
overestimated.
o Hartree-Fock approximation : involves a single determinant of products of one-electron functions
o Spin orbital written as a product of a space part Ψ which is a function of the coordinates of a
single electron
o Molecular orbital has two possible spin parts α and β, only 2 electrons may occupy given
molecular orbital and they must have opposite spins.
o Size comparison of dipole values. Smallest to largest values.
STO-3G < 6-31G* approx= 6-311+G(2D,P) < 6-31G(*)
o 3-21G, 6-31G, and 6-311G
o Function representing valence regions are split into components
o Inner and outer shell orbitals used.
o 6-31G, 6-31G*, and 6-31G**
o Polarization basis sets
o Allows for small displacement of the center of electronic charge
o STO-3G
o Uses 3 Gaussian type orbitals to estimate 1 Slater Type Orbital
o Has high errors for hypervalent compounds
o Bond lengths are longer than experimental values.
o Minimal basis set. Uses only the number of functions required to represent all of the electrons
of the atom.
 H and He use 1 function
o
o
o
o
o
o
 Li and Be use 2 functions.
o Properly accounts for O and N compounds but not P and S compounds.
3-21G
o Bond lengths are longer than experimental values.
o Superior to STO-3G in regards to bond length and ordering bond distance.
6-31G*
o Superior to STO-3G in regards to bond length and ordering bond distance.
o Results are approximately equal to 6-311+G which indicates that 6-31G* may represent the
limit for Hartree-Fock calculations.
3-21G*
o Good for structure determination of 2nd row elements.
3-21G(*)
o Has a basis set for second row and heavier group elements
o Good for structure determination of 2nd row elements.
o Similar to 3-21G but has d-type functions add on second row and heavier elements.
o Yields dipole results higher than expected, but will give improved results with a basis extension
set.
6-31G
o Often have significant error in bond length.
6-31+G*
o Basis sets incorporate diffuse functions.
o Useful for calculations involving anions.
o Diffuse functions are added to some atoms for calculations.
o 6-311+G
o Yields dipole results higher than expected.
Density functional
o Most processor intensive of all the methods.
o Electron correlation taken into account explicitly.
o Uses numerical integration that may cause greater magnitudes of uncertainties.
o Accounts explicitly for many-electron effects by including a correlation term based on an
idealized many electron problem.
o Calculations should be superior to Hartree-Fock and comparable to mp2
o Treats a molecule as a functional of the electron density.
o Treats the molecule as an energy functional of the molecular system. The energy functional is a
combination of the following energy components: Kinetic energy of electrons, Attraction of
electrons by the nuclear potential and electron interaction, classical Coulomb repulsion of charge
density, and an exchange correlation term that accounts for many body and quantum effects.
o Local Density Approximation is reduced to one-electron densities in Density Functional Theory.
Good results are produced from atoms with large or constant electron densities, such as metals and
transition metals.
Conclusion
Our data revealed that all the Density Functional methods proved effective for angle and bond
length measurements for the following groups: group 5 elements (NH3,PH3…), group 6 elements
(H2S, H2O…), hydrogen halides, and all the carbon groups tested. Density Functional theory,
svwn/dn* and svwn/dn** proved effective for the phosphorous halide groups but with a slight
anomaly between different angles and lengths that should be equal to one another. Density
Functional methods duplicated dipole trends for hydrogen halides.
Hartree-Fock 3-21G(*) proved to be a useful method for phosphorous halides, group 5, and
hydrogen halides. The added d-type functions for higher atomic weight elements makes 3-21G(*) a
slightly more useful Hartree-Fock method. Hartree-Fock 3-21G(*) duplicated dipole trends for our
group 5 test elements and hydrogen halides.
Semi-empirical PM3 was effective for all group 6 molecules in our test group except Te which
had extreme errors.
All methods produced reasonable results for our carbon-based test molecules. All the HartreeFock methods except STO-3G and 3-21G(*) gave errors for methyl bromide and methyl iodide. This
is the result of these methods having an incomplete basis set for atoms below the second row of the
periodic table.
References
1) N. N. Greenwood and A. Earnshaw (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann:
Jordan Hill, Oxford.
2) Francis A. Carey (2003). Organic Chemistry (5th ed.). McGraw-Hill Companies, Inc.: Boston, MA.
3) Linus Pauling (1960). The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An
Introduction to Modern Structural Chemistry (3rd ed.). Cornell University Press: Ithaca, NY.
4) John P. Lowe (1978). Quantum Chemistry (2nd ed.) Academic Press, Inc.: Boston, MA.
5) Compiled by H. J. M. Bowen; J. Donohue; D.G. Jenkin; Olga Kennard; P.J. Wheatley; D. H. Whiffen (1958)
Table of Interatomic Distances and Configuration in Molecules and Ions. The Chemical Society: London.
6) Charles D. Hodgman (Ed.) (1961). Handbook of Chemistry and Physics. The Chemical Rubber Publishing
Co.: Cleveland, OH.
7) W. J. Hehre; Jianguo, Yu; P. E. Klunzinger (1997). A Guide to Molecular Mechanics and Molecular Orbital
Calculations in Spartan. Wavefunction, Inc.: Irvine, CA.
8) W. J. Hehre; B. J. Deppmeier; P. E. Klunzinger (1999). A PC Spartan Pro Tutorial. Wavefunction, Inc.: Irvine,
CA.
9) A. Streitweiser, Jr. (1961). Molecular Orbital Theory for Organic Chemists. John Wiley & Sons, Inc.: New
York.