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
/ CH3FCH3Cl
CH3Br
CH3I / / H2O
H2S
H2Se
H2Te
/ PF3
PCl3
PBr3
PI3 / / HF
HCl
HBr
HI
/ C2H6
C2H4
C2H2 / / NH3
PH3
AsH3
SbH3
Molecular modeling methods outline
Molecular Mechanics
o Can be used for molecules containing more than 1000 atoms.
o Fast procedure to perform conformational analysis.
o Computation of geometry, enthalpy, entropy and vibrational states.
o 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.
o Experimental analogies are electron diffraction and gas phase chromatography
o 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.
o SYBYL
· Parameterized for second row or greater elements
· Does well with organic but poorly with inorganic.
· Results are very inaccurate for some systems.
Semi empirical (quantum based methods)
o Useful for molecules containing up to 200 atoms.
o Calculations are based upon molecular orbital theory.
o Uses a simplified version of Schrödinger’s equation.
o Calculations only use valence shells. Inner shells are treated as a fixed core.
o Will provide accurate models of a molecule if the atoms making up the molecule are included in the data set.
o Useful for equilibrium geometries: transition metal inorganic and organo-metalic compounds.
o Interaction among nuclei and electrons and molecular geometry in terms of minimum energy arrangements of nuclei.
o Total electron density: corresponds to the electron density measured in an x-ray diffraction experiment.
o 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.
Hartree-Fock
o Impractical for molecules with greater than 100 atoms
o Useful for thermodynamic and kinetic comparisons.
o Provides excellent account of molecular equilibrium and transition state geometry.
o Does well with equilibrium conformations.
o 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.
o Incomplete description of coupling motions of electrons (electron correlation). Often causes greater errors in transition metal inorganic and organo-metalic compounds.
o Electron-electron repulsion may be overestimated, resulting in shorter reported bond lengths.
o 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
§ Li and Be use 2 functions.
o Properly accounts for O and N compounds but not P and S compounds.
o 3-21G
o Bond lengths are longer than experimental values.
o Superior to STO-3G in regards to bond length and ordering bond distance.
o 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.
o 3-21G*
o Good for structure determination of 2nd row elements.
o 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.
o 6-31G
o Often have significant error in bond length.
o 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 Hartree-Fock 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
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