Computational Spectroscopy II. ab initio MethodsAdvanced Methods for ThermochemistryThermodynamic quantities available from a Gaussian FREQ calculationThermodynamic quantitiesRates of Chemical ReactionGaussian-1, Gaussian-2, Gaussian-3, and CBS TheoriesDetails of the G1 and G2 methodsG2 & G3 accuracyCBS vs G3Solvation methodsSolvation Methods in G03A case study on solvation effects (2-nitrovinyl)amine: NH2-CH=CH-NO2Appendix: The z-matrixComputational SpectroscopyII. ab initio Methodsfrom part (g) Advanced Methods for ThermochemistryChemistry 713Updated: February 28, 2008Advanced Methods for Thermochemistry1. Thermodynamics from Gaussian data2. Rate constants from Gaussian data3. “High accuracy” extrapolation methods- G1, G2, G3, CBS-4M, CBS-Q, CBS-QB34. Condensed phase methods- treatments of solvationThermodynamic quantities available from a Gaussian FREQ calculation# freq hf/3-21+g geom=connectivity…Vinyl fluoride frequency… ------------------- - Thermochemistry - ------------------- Temperature 298.150 Kelvin. Pressure 1.00000 Atm.... This molecule is an asymmetric top. Rotational symmetry number 1. Rotational temperatures (Kelvin) 3.05888 .50432 .43294 Rotational constants (GHZ): 63.73686 10.50837 9.02106 Zero-point vibrational energy 124526.4 (Joules/Mol) 29.76253 (Kcal/Mol) Warning -- explicit consideration of 1 degrees of freedom as vibrations may cause significant error Vibrational temperatures: 739.91 1123.38 1431.13 1558.02 1624.71 (Kelvin) 1789.79 2083.59 2245.96 2657.35 4809.86 4928.00 4962.46 Zero-point correction= .047430 (Hartree/Particle) Thermal correction to Energy= .050672 Thermal correction to Enthalpy= .051616 Thermal correction to Gibbs Free Energy= .023092 Sum of electronic and zero-point Energies= -175.909354 Sum of electronic and thermal Energies= -175.906112 Sum of electronic and thermal Enthalpies= -175.905167 Sum of electronic and thermal Free Energies= -175.933691 E (Thermal) CV S KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin Total 31.797 9.146 60.033 Electronic .000 .000 .000 Translational .889 2.981 37.405 Rotational .889 2.981 21.503 Vibrational 30.019 3.185 1.126 Vibration 1 .869 1.218 .623 Q Log10(Q) Ln(Q) Total Bot .238974E-10 -10.621649 -24.457250 Total V=0 .156464E+12 11.194414 25.776090 Vib (Bot) .174410E-21 -21.758428 -50.100631 Vib (Bot) 1 .315520E+00 -.500974 -1.153534 Vib (V=0) .114192E+01 .057635 .132710 Vib (V=0) 1 .109123E+01 .037916 .087305 Electronic .100000E+01 .000000 .000000 Translational .122716E+08 7.088902 16.322799 Rotational .111655E+05 4.047877 9.320581A portion of the G03 output “.log” file.(cont’d)….Thermodynamic quantitiesReactants Transition state (‡) ProductsDifference in electronic energy€ ΔU00Zero point energyZero point energy€ ΔU2980€ H = U + PV, ∴ ΔHT0= ΔUT0+ Δ PV( )for changes at temp T.G = H − TS, ∴ ΔGT0= ΔHT0+ TΔST0, Kc= exp −ΔGT0RT( )Avg Thermal EnergyAvg Thermal EnergySee Cramer, p 355 ff.D. A. McQuarrie, Statistical MechanicsRates of Chemical ReactionReactants Transition state (‡) ProductsDifference in electronic energyZero point energyZero point energyAvg Thermal EnergyAverage Thermal Energy of molecules that reactE0Barrier to reactionEaActivationEnergyArrhenius rate: Transition state theory: € k =kBThQQreactantsexp−E0kBT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟‡€ k = Aexp−EakBT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟See Cramer, p 519 ff.J. I. Steinfeld, J.S. Francisco, W. L. Hase, Chemical Kinetics and Reaction DynamicsFor aA + bB  products, the partition functions are€ Qreactants≡ QA( )aQB( )band Q which does NOT include the reaction coordinate.‡Transition state theory, when carefully applied with good ab initio data, can give very good rate constants. The Arrhenius expression is used mainly as a means of fitting experimental data, and is NOT commonly used to generate calculated rates from ab initio data.Gaussian-1, Gaussian-2, Gaussian-3, and CBS TheoriesBasis set and correlation extrapolation methods calibrated on a large number of species to get the thermochemistry right.G1, G2, G3, and several variants developed by Pople are available in G03. G1 & G2 in Foresman & Frisch, pp 150-153G3 in Curtis et al., J. Chem. Phys. 109, 7764 (1998). G2 gets 148 enthalpies with absolute deviations from experiment of 1.56 kcal/mol, and G3 within 0.94 kcal/mol.“Complete Basis Set” (CBS) methods (CBS-4M, CBS-Q, CBS-QB3) developed by Peterson and collaborators are also available in G03.Foresman & Frisch, pp 154-160.CBS-Q is a little better than G2; CBS-QB3 is comparable to G3, but faster.The better levels of these “high accuracy methods” are demanding on CPU time.Compromise on the level is necessary for larger systems.The calculations involved are fully ab initio, but the design of the extrapolation methods is empirical, based on a a range of test systems Gives some semiempirical character to these “high accuracy methods”Work well for the kinds of systems and for the properties on which they were calibrated, but otherwise caveat emptor.Details of the G1 and G2 methodsAll terms must be added to get the final energy (Foresman & Frisch, p 152).G3 is similar but is more complicated (Curtis et al., J. Chem. Phys. 109, 7764 (1998) ).G2 add theseG1 add theseenergiesForesman & Frisch, p 152G2 & G3 accuracy QuickTime™ and a decompressorare needed to see this picture.Curtis et al., J. Chem. Phys. 109, 7764 (1998).QuickTime™ and a decompressorare needed to see this picture.CBS vs G3CBS-QB3 is comparable in accuracy to G3, but runs faster.G3(MP2) is almost as good and is faster than CBS-B3.QuickTime™ and a decompressorare needed to see this