Development and application of statistical and quantum mechanical methods for modelling molecular ensembles

Abstract

The development of new quantum chemical methods requires extensive benchmarking to establish the accuracy and limitations of a method. Current benchmarking practices in computational chemistry use test sets that are subject to human biases and as such can be fundamentally flawed. This work presents a thorough benchmark of diffusion Monte Carlo (DMC) for a range of systems and properties as well as a novel method for developing new, unbiased test sets using multivariate statistical techniques. Firstly, the hydrogen abstraction of methanol is used as a test system to develop a more efficient protocol that minimises the computational cost of DMC without compromising accuracy. This protocol is then applied to three test sets of reaction energies, including 43 radical stabilisation energies, 14 Diels-Alder reactions and 76 barrier heights of hydrogen and non-hydrogen transfer reactions. The average mean absolute error for all three databases is just 0.9 kcal/mol. The accuracy of the explicitly correlated trial wavefunction used in DMC is demonstrated using the ionisation potentials and electron affinities of first- and second-row atoms. A multi-determinant trial wavefunction reduces the errors for systems with strong multi-configuration character, as well as for predominantly single-reference systems. It is shown that the use of pseudopotentials in place of all-electron basis sets slightly increases the error for these systems. DMC is then tested with a set of eighteen challenging reactions. Incorporating more determinants in the trial wavefunction reduced the errors for most systems but results are highly dependent on the active space used in the CISD wavefunction. The accuracy of multi-determinant DMC for strongly multi-reference systems is tested for the isomerisation of diazene. In this case no method was capable of reducing the error of the strongly-correlated rotational transition state. Finally, an improved method for selecting test sets is presented using multivariate statistical techniques. Bias-free test sets are constructed by selecting archetypes and prototypes based on numerical representations of molecules. Descriptors based on the one-, two- and three-dimensional structures of a molecule are tested. These new test sets are then used to benchmark a number of methods.