Here, thermodynamic properties are approximated only by considering the unique minima on the PES, which in the molecular case are the different conformations. 20–22 Good results can be achieved with all of the above schemes, but in practice the construction of the PES and the relevant modes is technically involved, often only possible for relatively small molecules and unfeasible for routine computational chemistry workflows.Ī stronger focus on multiple minima (molecular configurations/conformers) leads to the second class of approaches. 17–19 Another method that includes the torsional anharmonicity via 1D-PES and takes multiple structures into account is the MS-T approach (and its variants), developed by Truhlar and coworkers. Advances have also been made for approaches that investigate coupled torsional motions. 6 to include a separate treatment of vibrational and torsional modes (UM-VT). 14–16 This scheme was later adapted by Head-Gordon et al. For example, this can be done by construction of one-dimensional (1D) potential energy surfaces (PES) along the respective normal modes, as in the uncoupled normal mode approach of Sauer and coworkers. The first go beyond the HO approximation and explicitly account for anharmonicities in the description mainly for low-frequency, torsional normal modes. 7–13 However, even frequency scaling is unable to account for all of the missing contributions to the entropy.Īpproaches that compute the absolute entropy can be roughly categorized into two major classes. 3–6 Because RRHO errors are often systematic, a common strategy is linear or multi-parametric scaling of the HO vibrational frequencies to mimic the effect of anharmonicity. A comparison of entropies calculated in this way to experimental values for small molecules reveals an insufficient accuracy already for relatively rigid molecules mainly due to anharmonicity effects. This is then usually extended by the rigid-rotor model, giving rise to the rigid-rotor-harmonic-oscillator (RRHO) approach. 1,2Īs for most other thermodynamic properties, QM computations of the entropy are commonly based on frequency calculations in the harmonic oscillator (HO) approximation. Calculations of thermodynamic properties at finite temperatures are essential and if we neglect here the issue of solvation, the basic problem is an efficient computation of the molecular entropy. In order to compare theory with experiment, additional corrections and computational steps are required.
While those reactions are usually carried out at room temperature in solution, quantum mechanical (QM) calculations are primarily conducted for isolated molecules at absolute temperature zero. 1 Introduction A main goal of computational chemistry is to realistically model various chemical reactions and predict their products.
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Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.
Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Even for the hardship case of extremely flexible linear alkanes (C 14H 30–C 16H 34), errors are only about 3 cal mol −1 K −1. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol −1 K −1 (about <1–2%) for the total gas phase molecular entropy of medium-sized molecules. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs–Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations.
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