Alchemical geometry relaxation

Extending the definition of atomic basis sets to atoms with fractional nuclear charge

Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a non-physical system in which an atom possess a non-integer nuclear charge. A correct quantum mechanical treatment of these systems is limited by the fact that finite size atomic basis sets do not define exponents and contraction coefficients for fractional charge atoms. This paper proposes a solution to this problem and shows that a smooth interpolation of the atomic orbital coefficients and exponents across the periodic table is a convenient way to produce accurate alchemical predictions, even using small size basis sets.

Molecular Hessian matrices from a machine learning random forest regression algorithm

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

Optimization of General Molecular Properties in the Equilibrium Geometry Using Quantum Alchemy: An Inverse Molecular Design Approach

Inverse molecular design allows the optimization of molecules in chemical space and is promising for accelerating the development of functional molecules and materials. To design realistic molecules, it is necessary to consider geometric stability during optimization. In this work, we introduce an inverse design method that optimizes molecular properties by changing the chemical composition in the equilibrium geometry. The optimization algorithm of our recently developed molecular design method has been modified to allow molecular design for general properties at a low computational cost. The proposed method is based on quantum alchemy and does not require empirical data. We demonstrate the applicability and limitations of the present method in the optimization of the electric dipole moment and atomization energy in small chemical spaces for (BF, CO), (N₂, CO), BN-doped benzene derivatives, and BN-doped butane derivatives. It was found that the optimality criteria scheme adopted for updating the molecular species yields faster convergence of the optimization and requires a less computational cost. Moreover, we also investigate and discuss the applicability of quantum alchemy to the electric dipole moment.

Relative energies without electronic perturbations via alchemical integral transform

We show that the energy of a perturbed system can be fully recovered from the unperturbed system’s electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2 p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree–Fock reference numbers.

Exploration of Chemical Space for Designing Functional Molecules Accounting for Geometric Stability

The design of functional molecules is regarded as searching for molecules with desired functionalities in chemical space populated by candidate molecules. Considering the geometric stability of molecules during the search process is crucial for designing realistic molecules. Here, we propose a method for designing functional molecules by exploring chemical space while explicitly accounting for geometric stability based on computational quantum alchemy. The proposed design method allows the simultaneous prediction of functional molecule in the equilibrium structure and its target desired property in an inverse design fashion without preparing the molecular geometries and performing brute-force screening. The applicability of the design method is proven by obtaining molecules with the desired atomization and electronic energies in various chemical spaces: (BF, CO), (CH₄, NH₃), 18 BN-doped benzene derivatives, and 3.1 × 10⁵ BN-doped phenanthrene derivatives.