Computational Methods Summary
MGCF - College of Chemistry, University of California, Berkeley
Energy Models (QM or MM)
Molecular mechanics (MM)
- Useful for initial calculations on small organics, can do any size up through proteins.
- Uses classical ball-and-spring laws where each force constant, ideal bond length, angle and dihedral angle are empirical parameters. Electrostatic and VDW interactions are included.
- Only useful if parameters (the force field) closely match atom type and linkages in your system.
- Programs available in MGCF: Macromodel, AMBER, NAMD, Desmond, Gromacs, more……
- Mainly used as a starting point for high-level ab initio calculations or mixed with DFT (below).
- Approximate solution of Schrödinger equation neglecting instantaneous electron-electron interactions (correlation) unless post-HF corrections are applied.
- Energy and orbital coefficients solved for by iterative self consistent field (SCF) method.
- High-level calculations (configuration interaction, coupled cluster, G3, etc.) can correct for correlation and achieve chemical accuracy but only possible for small molecules, very time consuming.
- Programs available in MGCF: Gaussian, Jaguar, QChem, Gamess, NWChem, more ……
Density functional theory (QM)
- Appropriate for up to about 200 atoms (sometimes larger), best choice for most organometallics
- In the Schrödinger equation, energy is a functional of electron density, not the true wavefunction. Iterative SCF procedure is similar to that of HF.
- Implicitly includes electron correlation, so much more accurate than HF, but behavior is sometimes unpredictable because the electronic density functional cannot be derived ab initio.
- Many functionals exist. B3LYP includes some HF exchange (hybrid DFT) and has good performance for organic molecules, but may not suitable for metal complexes and structures with non-covalent interactions. Some newer functionals are ωB97X-D, M06, HSE06, BMK, TPSSh, etc…
- Programs available in MGCF: Gaussian, Jaguar, QChem, Gamess, NWChem, more......
Basis Sets (for QM calculations):
- The set of atomic orbitals whose coefficients are optimized in SCF.
- Each orbital usually represented by a linear combination of Gaussian functions.
- The number of Slate-type orbital (STO) determines the size of a basis set. The bigger the basis set, the better the results, but for DFT not much gain beyond triple-zeta level (three STO).
- 6-31G is a popular double-zeta level split-valance basis set using 6 Gaussian functions for inner shell orbitals, with 3 and 1 Gaussian functions for the 1st and the 2nd valance STO, respectively.
- Polarization functions (** or (d,p) after G) add d functions to p shells (carbon, phosphorus, etc.) and p functions to hydrogen. Use at least d functions on p shells (one *) for acceptable results!
- Diffuse functions (++ before G) add next-principal-quantum-number shell. In DFT, useful for anions, excited states or sometimes late transition metals.
- Effective core potentials (ECP) replace core electrons with a potential felt by valence electrons, simplifies calculation of heavy atoms. The relativistic effect of core electrons can be included in the ECP. Normally needed for atoms heavier than 1st-row transition metals.
- For metals/heavy atoms, start with LANL2DZ but see our page for suggestions about better basis sets: http://glab.cchem.berkeley.edu/glab/faqs/gauss_custombasis.html
- Can include molecular orbital energy and shape, excitation energies, partial charges, dipole and multipole moments, polarizabilities, NMR shielding and coupling constants, etc.
Common Geometry Algorithms
Molecular energy (aka Single Point - calculates energy of input geometry – no geometry change)
- Can be used on a previously optimized geometry
- MM: Energy is relative to a hypothetical unstrained system.
- QM: SCF energy, relative to a separated collection of electrons and nuclei.
- Add up energies of species on each side of a balanced chemical equation and calculate reaction energy (Make sure the total number of basis functions are the same in the whole reaction).
Geometry optimization (also called minimization)
- Finds local minimum: the bottom of whichever potential energy well in which a molecule is drawn.
- Iterative process, with the molecular energy calculated between each optimization cycle.
- Can optimize all coordinates or constrain one or more coordinates.
- Default convergence criteria are arbitrarily set, you might allow looser or need tighter criteria.
- Can be used to manually adjust a distance, angle or torsion systematically. Commonly used for searching torsions (dihedral drive) or as a manual method to locate transition states (TS).
- Best methods randomly sample potential energy surface to find global minimum-energy structure.
- Nearly always confined to MM methods due to number of structures generated/minimized.
- For flexible organic species, perform conformational search before QM geometry optimization.
Transition state search
- Needed to model chemical kinetics, locates an energy maximum along a reaction coordinate while minimizing energy w.r.t. all other coordinates for a reaction mechanism study.
- Normally used with QM methods, locating correct TS in the reaction pathway is much more difficult to be successfully achieved than optimization for intermediates.
- A converged TS must have exactly one imaginary vibrational frequency.
- Perform intrinsic reaction coordinate (IRC) calculation for a TS and confirm reactant and product.
6. Vibrational frequencies
- Normally with QM methods, calculates molecular vibrational frequencies, IR and/or Raman intensities.
- Also calculates zero-point energies (ZPE), thermal enthalpies and thermal Gibbs free energies which should be added to SCF energies when studying reaction kinetics or thermodynamics.
- A minimum has all real valued frequencies, a transition state has exactly one imaginary frequency.
7. Molecular dynamics
- Applicable to MM (up to macromolecules) and sometimes QM methods (very small systems).
- Models molecular motion over time, response to forces acting on molecule.
- Will eventually sample all accessible conformations at a given temperature, if the simulation is run long enough (this can be very long and in some cases impractical).
- For large systems (proteins, DNA, etc.) more useful than conformational searching.
- Takes into account that reaction trajectories do not always follow the exact minimum-energy path.