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Thermochemistry

Thermochemistry#

Thermochemical contributions are calculated in autodE using the ideal gas model and variants thereof. The molar enthalpy is,

\[H = E_\text{elec} + E_\text{internal} + E_\text{ZPE} + RT\]

and Gibbs free energy,

\[G = H - TS\]

where \(T\) is the temperature and \(R\) the gas constant. See here for a more in-depth mathematical background. With a completed electronic structure calculation free energies can be obtained using either RRHO, shifted-RRHO (from Truhlar[1]) and qRRHO (from Grimme[2]). Global parameters can also be set in autode.Config, which apply to all thermochemical calculations including those when calculating a profile with rxn.calculate_reaction_profile(free_energy=True)

General#

To calculate thermochemical contributions (enthalpy, Gibbs free energy) in autodE the minimal required input is

import autode as ade

water = ade.Molecule(smiles='O')
water.calc_thermo()
print(f'E = {water.energy:.6f}',
      f'H = {water.enthalpy:.6f}',
      f'G = {water.free_energy:.6f}',
      f'units = {water.energy.units}')

Out: E = -76.269260 H = -76.245955 G = -76.264398 units = Unit(Ha)

For a non-default set method and keywords:

import autode as ade

water = ade.Molecule(smiles='O')
water.calc_thermo(method=ade.methods.G09(),
                  keywords=['PBEPBE', 'def2SVP', 'Freq'])

ORCA#

To calculate thermochemical contributions from a completed ORCA Hessian file (H2O_hess_orca.hess):

import autode as ade

mol = ade.Molecule('H2O_hess_orca.xyz')
orca = ade.methods.ORCA()

calc = ade.Calculation(name='H2O',
                       molecule=mol,
                       method=orca,
                       keywords=orca.keywords.hess)
calc.output.filename = 'H2O_hess_orca.hess'

mol.calc_thermo(calc=calc, temp=298.15, ss='1atm', sn=1)
print(mol.g_cont)

Out: 0.00145779587867773

which differs from the ORCA-calculated value (0.00145673 Ha) by <0.001 kcal mol-1. To calculate a total free energy including \(E_\text{elec}\) both a .out and .hess file need to be present with the same basename. For example:

import autode as ade

mol = ade.Molecule('H2O_hess_orca.xyz')
orca = ade.methods.ORCA()

calc = ade.Calculation(name='H2O',
                       molecule=mol,
                       method=orca,
                       keywords=orca.keywords.hess)
calc.output.filename = 'H2O_hess_orca.out'

mol.calc_thermo(calc=calc)
print(f'H = {mol.enthalpy:.6f} Ha\n'
      f'G = {mol.free_energy:.6f} Ha')

Out:

H = -76.249086 Ha
G = -76.267526 Ha

where, without any arguments to calc_thermo, the default method uses room temperature (298.15 K), a one molar (1 M) standard state (appropriate for molecules in solution), Grimme’s qRRHO treatment of low frequency vibrational modes and a calculated symmetry number, which in this case is two (C2v symmetry).

Gaussian#

Likewise from a Gaussian output file of butane (butane_hess_g09.log):

import autode as ade

mol = ade.Molecule('butane.xyz')
g09 = ade.methods.G09()

calc = ade.Calculation(name='butane',
                       molecule=mol,
                       method=g09,
                       keywords=g09.keywords.hess)
calc.output.filename = 'butane_hess_g09.log'

mol.calc_thermo(calc=calc, temp=298.15, ss='1atm', sn=1, lfm_method='igm')
print(mol.g_cont)

Out: 0.10419152589407932

which differs from the Gaussian-calculated value (0.104216 Ha) by ~0.01 kcal mol-1.

Note

Gaussian 09 has very tight tolerances on symmetry and uses a pure harmonic oscillator treatment of low frequency modes.

Frequency scaling#

Default methods use frequency scaling automatically to generate the most accurate thermochemistry possible. Unscaled frequencies can be obtained by setting

ade.Config.freq_scale_factor = 1.0

Note

The above examples were generated using unscaled frequencies.

References#

[1] R. F. Ribeiro, A. V. Marenich, C. J. Cramer and D. G. Truhlar, Phys. Chem. B 2011, 115, 14556.

[2] S. Grimme, Chem. Eur. J. 2012, 18, 9955.

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