Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data.

We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

Optimizing the Local Chemical Environment on a Bifunctional Helical Peptide Scaffold Enables Enhanced Enantioselectivity and Cooperative Catalysis.

We describe a proof-of-concept study in which peptide-bound enamine and thiourea catalysts are used to facilitate the conjugate addition of cyclohexanone to nitroolefins. Our bifunctional peptide scaffold is modified to optimize the local environment around both catalysts to enhance both reactivity and enantioselectivity, affording selectivities of ≤95% ee. Circular dichroism, nuclear magnetic resonance nuclear Overhauser effect studies, and molecular dynamics simulations verify the helical structure of our catalyst in solution and the importance of the secondary structure in catalysis.