Dual-Level Method for Estimating Multistructural Partition Functions with Torsional Anharmonicity

For molecules with multiple torsions, an accurate evaluation of the molecular partition function requires consideration of multiple structures and their torsional-potential anharmonicity. We previously developed a method called MS-T for this problem, and it requires an exhaustive conformational search with frequency calculations for all the distinguishable conformers; this can become expensive for molecules with a large number of torsions (and hence a large number of structures) if it is carried out with high-level methods. In the present work, we propose a cost-effective method to approximate the MS-T partition function when there are a large number of structures, and we test it on a transition state that has eight torsions. This new method is a dual-level method that combines an exhaustive conformer search carried out by a low-level electronic structure method (for instance, AM1, which is very inexpensive) and selected calculations with a higher-level electronic structure method (for example, density functional theory with a functional that is suitable for conformational analysis and thermochemistry). To provide a severe test of the new method, we consider a transition state structure that has 8 torsional degrees of freedom; this transition state structure is formed along one of the reaction pathways of the hydrogen abstraction reaction (at carbon-1) of ketohydroperoxide (KHP; its IUPAC name is 4-hydroperoxy-2-pentanone) by OH radical. We find that our proposed dual-level method is able to significantly reduce the computational cost for computing MS-T partition functions for this test case with a large number of torsions and with a large number of conformers because we carry out high-level calculations for only a fraction of the distinguishable conformers found by the low-level method. In the example studied here, the dual-level method with 40 high-level optimizations (1.8% of the number of optimizations in a coarse-grained full search and 0.13% of the number of optimizations in a fine-grained full search) reproduces the full calculation of the high-level partition function within a factor of 1.0 to 2.0 from 200 to 1000 K. The error in the dual-level method can be further reduced to factors of 0.6 to 1.1 over the whole temperature interval from 200 to 2400 K by optimizing 128 structures (5.9% of the number of optimizations in a fine-grained full search and 0.41% of the number of optimizations in a fine-grained full search). These factor-of-Two or better errors are small compared to errors up to a factor of 1.0 × 10³ if one neglects multistructural effects for the case under study.