Choice of Theoretical Method
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1 Choice of Theoretical Method 1 General Considerations PResources < Software < Computer P Expense (Time and Money) < Optimization/Single Point Calculations < Basis Set Choice < Method Choice P < Comparison < Recommendations 2 Resources Software P Methods packaged with software < See software comparison sheet P Basis functions packaged with software < Can download from PAvailable parameters for atom types PSize of molecule 3
2 Resources Computer PSpeed < Fast chips/io < Parallel processors PMemory use for optimization algorithm (D = degrees of freedom like bond length, bond angle, etc.) < Scales as D for Conjugate Gradient, Fletcher- Reeves, Polak-Ribiere < Scales as D 2 for Simplex, Powell, quasi-newton, Fletcher-Powell 4 Expense Time and Money P Optimization < t(optimization). 5 D 2 t(single point) PBasis Set (N = number of orbitals, M = number of atoms) < MM / MD scales as M 2 < AM1 / PM3 scales as N 2 to N 4 < HF scales as N 2 to N 4 < DFT scales as N 3 < MP2 scales as N 5 < MP4 scales as N 7 < Full CI scales as N! 5 PMethod < For single point calculation of C 6 H 6 using cc-pvtz basis set on Cray SVI (Young): PM3 11 s 11 Mb HF 10 min 42 Mb MP2 32 min 43 Mb MP4 36 hr 2.1 Gb G2 37 hr 2.5 Gb CBS-APNO 63 hr 6.5 Gb QCISD 10 hr 1.9 Gb G3 20 hr 1.6 Gb CBS is Complete Basis Set QCISD is Quadratic Configuration Interaction 6
3 References PJ B Foresman and Æ Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd ed, Gaussian (1996), ISBN , pp and PD C Young, Computational Chemistry, Wiley (2001), ISBN , pp PR Janoschek, Pure Appl Chem, 73 (9), (2001). PNIST Computational Chemistry Comparison and Benchmark Data Base at < 7 Considerations PMolecule Set < G2 Originally 125 calculations 1st and 2nd row heavy atoms < Extended G2 sets < G3 299 calculations from G2/97 set P Parameters < Mean Absolute Deviation (MAD) Average of deviations neglecting sign < Standard Deviation ~2/3 results lie within StdDev of experimental value < Largest Errors Worst case values 8 Energy Comparision for Basis Functions [MAD/(kcal mol -1 ), Foresman/Frisch] PHF < 93.3 for STO-3G < 58.4 for 3-21G(d) < 51.0 for 6-31G(d) < 46.7 for 6-31+G(d,p) PB3LYP < 7.9 for 6-31G(d) < 3.9 for 6-31+G(d,p) < 3.1 for G(2d,p) 9
4 Energy Comparision for Standard Methods [MAD/(kcal mol - 1 ), Young] PMechanics < E not calculated in MM2 / MM3 P Semi-empirical < 18.8 for AM1 < 17.2 for PM3 Pab initio < 51.0 for HF/6-31G(d) < 7.9 for B3LYP/6-31G(d) 10 Energy Comparision for Mixed Methods [MAD/(kcal mol -1 ), Foresman/Frisch] PAM1 optimization followed by single point < 54.2 for HF/6-31G(d) < 18.8 for AM1 < 10.5 for B3LYP/6-31G(d) P B3LYP/6-31G(d) optimization followed by single point < 7.9 for B3LYP/6-31G(d) < 4.0 for B3LYP/6-31+G(d,p) < 3.2 for B3LYP/6-311+G(2d,p) < 2.7 for B3LYP/6-311+G(3df,2df,2p) 11 Observations (Foresman/Frisch) PSemi-empirical energies are more accurate than HF PDFT energies are rather insensitive to geometry optimization used PDFT energies are more accurate using highly diffuse/polarized basis sets PAdditional basis sets are not as important for optimization as for predicting properties 12
5 Other Comparisions for Standard Methods (Young) P f H [StdDev/(kcal mol -1 )] < 0.5 for MM2 < 0.6 for MM3 < 8 for AM1 / PM3 < 4 for HF/6-31G(d) PBond Lengths (rms/å) < 0.01(StdDev) for MM2 / MM3 < for AM1 < for PM3 < for HF/6-31G(d) < for MP2/6-31G* < for B3LYP/6-31G(d) 13 PBond Angles (rms/e) < 1.0(StdDev) for MM2 / MM3 < 3.3 for AM1 < 3.9 for PM3 < 1.4 for HF/6-31G(d) < 1.5 for MP2/6-31G* < 1.4 for B3LYP/6-31G(d) PDipole Moments (StdDev/D) < 0.1 for MM2 < 0.07 for MM3 < 0.5 for AM1 < 0.6 for PM3 < 0.2 for HF/6-31G(d) 14 Recommendations PUse DFT with largest basis set for energy calculations following an optimization using < DFT with largest basis set < DFT with good basis set < HF with good basis set < HF with small basis set < Semi-empirical methods 15
6 P Use Multilevel Methods < G2 Initial geometry optimization and zero point vibrational energy (E 1 ) using HF/6-31G(d) Final geometry optimization at MP2/6-31G(d) Diffuse energy term (E 2 ) using E[MP4/6-311+G(d,p)] - E[MP4/6-311G(d,p)] Polarization energy term on heavy atoms (E 3 ) using E[MP4/6-311G(2df,p)] - E[MP4/6-311G(d,p)] Residual correlation effect energy term (E 4 ) using E[QCISD(T)/6-311G(d)] - E[MP4/6-311G(d)] Additional correction for assumption that 2df and diffuse corrections are additive and for 3rd set of f functions on heavy atom and 2nd set of p functions on H atom (E 5 ) using E[MP2/6-311G+G(3df,2p)] -E[MP2/6-311G(2df,p)] - E[MP2/6-311+G(d,p)] + E[MP2/6-311G(d,p)] 16 Empirical estimate of remaining correlation energy (E 6 ) using ( ) (# valence electron pairs) - ( ) (# unpaired valence electrons) E = (0.8929)E 1 + E[MP4/6-311G(d,p)] + E 2 + E 3 + E 4 + E 5 + E 6 MAD for E = 1.1 kcal mol -1, f H = 1.6 kcal mol -1 Several flavors of G2 17 < G3 E 2 using E[MP4/6-31+G(d)] -E[MP4/6-31G(d)] E 3 using E[MP4/6-31G(2df,p)] - E[MP4/6-31G(d)] E 4 using E[QCISD(T)/6-31G(d)] - E[MP4/6-31G(d)] E 5 using E[MP2/G3large] -E[MP2/6-31G(2df,p)] - E[MP2/6-31+G(d)] + E[MP2/6-31G(d)] E 6 using ( ) (# valence electron pairs) - ( ) (# unpaired valence electrons) E = (0.8929)E 1 + E[MP4/6-31G(d)] + E 2 + E 3 + E 4 + E 5 + E 6 t(g3). t(g2)/2 MAD for f H = 0.9 kcal mol -1 Several flavors of G3 18
7 < CBS-Q is similar to G2 using MP2/6-31G(d ) for geometry G(2df,2p) for HF and MP2 MP4/6-31+G(d,p) and QCISD/6-31+G(d )] for higher order corrections HF/6-31G(d ) for thermo with scale factor Empirical correction for electron correlation Empirical correction for spin contamination t(cbs-q). t(g3) MAD for E = 1.0 kcal mol -1, f H = 1.2 kcal mol -1 Several flavors of CBS 19
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