Computational SpectroscopyII. ab initio Methodsfrom part (g) Advanced Methods for ThermochemistryChemistry 713Updated: February 28, 2008Advanced Methodsfor 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 availablefrom 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 inelectronic energy! "U00Zero point energyZero point energy! "U2980! H = U + PV, "#HT0= #UT0+ # PV( )for changes at temp T.G = H $ TS, "#GT0= #HT0+ T#ST0, Kc= exp $#GT0RT( )Avg Thermal EnergyAvg Thermal EnergySee Cramer, p 355 ff.D. A. McQuarrie, Statistical MechanicsRates of Chemical ReactionReactants Transition state (‡) ProductsDifference inelectronicenergyZero point energyZero point energyAvg Thermal EnergyAverage Thermal Energy of molecules that reactE0Barrierto reactionEaActivationEnergyArrhenius rate: Transition state theory: ! k =kBThQQreactantsexp"E0kBT# $ % & ' ( ‡! k = A exp"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 NOTinclude the reaction coordinate.‡Transition state theory, when carefully applied with good ab initio data, can give very goodrate constants. The Arrhenius expression is used mainly as a means of fitting experimentaldata, 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 speciesto 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 G3within 0.94 kcal/mol. “Complete Basis Set” (CBS) methods (CBS-4M, CBS-Q, CBS-QB3) developed byPeterson 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 methodsis 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 werecalibrated, 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 accuracyCurtis et al., J. Chem. Phys. 109, 7764 (1998).CBS vs G3 CBS-QB3 is comparable inaccuracy to G3, but runs faster. G3(MP2) is almost as good and isfaster than CBS-B3.(protonaffinity)Montgomery, Frisch, Ochterski, and Peterson,J. Chem. Phys. 112, 6532 (2000).(electronaffinity)(ionizationpotential)(heat offormation)Solvation methods Solvation of the subject molecules can have an important, sometimes dramatic, effect oncalculated properties, including relative energies, molecular geometries and spectra. Different kinds of solvents can have very different effects: hydrogen-bonding solvents vspolar solvents vs non-polar solvents. Explicit (or “discrete”) methods treat a collection of individual solvent molecules as partof the molecular system. Treat interactions between solute and solvent molecules explicitly. Configurational sampling is necessary. Computationally