Geochemical Modeling ShortCourse

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Geochemical Modeling Short-Course

• By Matthew C. F. Wander

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Course Instructor

• Matthew Wander
• email mwander_at_notes.cc.sunysb.edu
• Office ESS 205
• Web Site www.cems.sunysb.edu/Gaussian/
  index.html
• Thanks to Andrea!

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Course Materials

• Text Foresman and Frisch Exploring Chemistry
  with Electronic Structure Methods
• Supplemental Background Cramer Essentials of
  Computational Chemistry
• Program Gaussian 03W and GaussView Win, includes
  manuals

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Course Outline

• Theoretical Introduction and GaussView
• Single Point Energy Calculations
• Geometry Optimizations
• Frequency Spectra Calculations
• Basis Set Effects
• Model Effects

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Optional Topics

• High Accuracy Techniques
• Solvation
• IRC and Transition State Calculations
• Excited States
• Crystals and Periodic Boundary Conditions
• Surface Effects

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Schrodenger Equation

• Contains one kinetic term (electrons)
• Potential nuclear-nuclear, nuclear-electronic,
  electron-electronic terms

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Born-Oppenheimer Approximation

• Assumes nucleus motion is slow relative to
  electrons.
• Therefore Nuclei can be treated as frozen
  classical particles.

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Variation vs. Perturbation

• Variation change basis functions
• Perturbation mix basis functions
• All quantum mechanics utilize a combination of
  both.
• Variational Theorem Ecalc gt Etrue.
• Does not hold for differences.

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The Double Pendulum

• Closest classical analogue to solving the
  Schrodenger equation

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Hartree-Fock Formulation (HF)

• One single product wavefuntion of one electron
  orbitals.
• Gives rise to Exchange Correlation

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Density Functional Theory (DFT)

• Kohn-Sham Theorem states 1 to 1 correspondence
  between density and energy.
• Unfortunately relationship not known

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DFT and HF

• Work essentially the same way.
• Electrons replaced by Density Functionals
• Sometimes two are combined.
• DFT overestimates where HF underestimates.

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What does Gaussian Actually Do?

• Solves Determinates

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Spin

• Does not explicitly Appear in Equation
• Two approaches Restricted vs. Unrestricted
• Restricted means a b.
• Pauling Rule Electrons anti-commute.

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Other Methods

• Multi Determinential CI, CC, CASSCF
• Counts components of molecular excited states.
• Electrons not strictly separable.
• MP2, MP4 approximations of above.

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Periodic Table