Automated versus Chemically Intuitive Deconvolution of Density Functional Theory (DFT)-Based Gas-Phase Errors in Nitrogen Compounds

Abstract

Catalysis models involving metal surfaces and gases are regularly based on density functional theory (DFT) calculations at the generalized gradient approximation (GGA). Such models may have large errors in view of the poor DFT-GGA description of gas-phase molecules with multiple bonds. Here, we analyze three correction schemes for the PBE-calculated Gibbs energies of formation of 13 nitrogen compounds. The first scheme is sequential and based on chemical intuition, the second one is an automated optimization based on chemical bonds, and the third one is an automated optimization that capitalizes on the errors found by the first scheme. The mean and maximum absolute errors are brought down close to chemical accuracy by the third approach by correcting the inaccuracies in the NNO and ONO backbones and those in N−O and N−N bonds. This work shows that chemical intuition and automated optimization can be combined to swiftly enhance the predictiveness of DFT-GGA calculations of gases.

Minimum conditions for accurate modeling of urea production via co-electrolysis

“…The total error in the DFT-calculated free energy of formation of , denoted , is determined as the difference between the DFT prediction ( ) and the experimental value as shown in Eq. 12 : 36 , 38 – 40 , 44 , 45 , 53 …”

“…Interestingly, previous works have shown that when GGA, meta-GGA, and/or hybrid functionals are used to model various families of C- 40 , 43 and N-containing compounds 38 , 39 , 53 , H 2 O 2(g) and O 2(g) 36 , 44 , 45 , sizable gas-phase errors are still found. Such errors are systematic and can be mitigated by means of inexpensive semiempirical corrections 38 , 40 , 41 , 43 , 53 . This strongly suggests that a cautious and early assessment of gas-phase errors is needed to guarantee the accuracy of (electro)catalytic models based upon DFT calculations.…”

Gas-phase errors in computational electrocatalysis: a review

“…For a reaction in the gas phase, the enthalpy (Δ r H DFT ) and Gibbs energy (Δ r G DFT ) change can be estimated from DFT calculations using the following equations:Δ r G DFT = Δ r H DFT − T Δ S In eqn (1), Δ E DFT is the sum of the DFT energies of the products multiplied by their respective stoichiometric coefficients minus the DFT energies of the reactants also multiplied by their respective stoichiometric coefficients. Analogously, ΔZPE is the change in the zero-point energies of products and reactants calculated through the harmonic oscillator approximation, and is the change in the heat capacity contribution, which is usually neglected because of the cancellation of the contributions of products and reactants in the range of 0 to 298.15 K. 6,28,35 However, we anticipate that this term may not be negligible for reactions with numerous proton–electron transfers. In eqn (2), T Δ S represents the difference between the total entropies of the products and reactants, usually taken from thermodynamic tables.…”

“…This semiempirical energy can then be used to calculate the equilibrium potential of nitrate reduction reactions. Given that the error in the DFT-calculated free energy of HNO 3 is larger than 1 eV for several GGA and meta-GGA xc-functionals, 25,28,29,51 overlooking it leads to seriously impaired reaction energies and equilibrium potentials, especially for reactions with small number of transferred electrons.…”

Extracting Features of Active Transition Metal Electrodes for NO Electroreduction with Catalytic Matrices

“…The Gibbs free energy difference for the considered elementary steps (Δ G ) was approximated as Δ G ≈ Δ E DFT + ΔZPE – T Δ S + Δ E solvation , where Δ E DFT is the PBE-calculated energy difference, ΔZPE is the zero-point energy change, and T Δ S is the corresponding entropy change at 298.15 K. For gas-phase molecules the total entropies were obtained from thermodynamic tables, and their free energies were corrected semiempirically (more details on this procedure are available in section S1), − while for adsorbates Δ S only includes vibrational entropies. Δ E solvation is the contribution of solvent-adsorbate interactions to the free energy, which we evaluated using four different solvation approaches, see sections S1 and S2.…”