arXiv subjects

Giorgio Domenichini

Publications and source records attributed to Giorgio Domenichini.

6 recordsLinked to original sources

arXiv2026

Machine learning predictions of the Hessian matrix for peptides chains and small proteins

Molecular Hessians have a key role in describing molecular vibrations, trajectories and optimization paths. An explicit calculation of them through standard quantum mechanical methods can be computationally expensive for medium-large systems, and in many applications not even needed. Machine learning methods can be a shortcut to tackle efficiently the computational difficulties. This paper will present a ML model able to predict the Hessian matrix of biological system made of thousands of atoms. The method, based on learning the Hessian in internal coordinates is intrinsically invariant to molecular rotations and translations, and has a very good scaling with the systems' size. The training was performed on a dataset of simple aminoacids, as they constitute the building blocks of larger proteins. From the predicted Hessian matrix it is possible to calculate thermochemical properties within the harmonic approximations, among them enthalpies, entropies, Gibbs' free energies, and zero point vibrational energies.

physics.chem-ph↗

arXiv2025

Alchemical diastereomers from antisymmetric alchemical perturbations

The energy difference between two iso-electronic systems can be accurately approximated by the alchemical first order Hellmann-Feynmann derivative for the averaged Hamiltonian. This approximation is exact up to third order because even-order contributions cancel out. This finding holds for any iso-electronic compound pair (dubbed `alchemical diastereomers'), regardless of differences in configuration, composition, or energy, and consequently, relative energy estimates for all possible iso-electronic alchemical diastereomer pairs, require only O(1) self-consistent field cycles for any given averaging reference Hamiltonian. We discuss the relation to the Verlet algorithm, alchemical harmonic approximation (AHA) [J. Chem. Phys. 162, 044101 (2025)], relative properties such as forces, ionization potential or electron affinities, and Levy's formula for relative energies among iso-electronic systems that uses the averaged electron density of the two systems [J. Chem. Phys. 70, 1573 (1979)]. Numerical estimates accurately reflect trends in the charge-neutral iso-electronic diatomic molecule series with 14 protons (N$_2$, CO, BF, BeNe, LiNa, HeMg, HAl), with systematically increasing errors. Using alchemical Hellmann-Feynman derivatives for toluene, we demonstrate the concept's broader applicability by estimating relative energies for all 36 possible alchemical diastereomer pairs from vertical iso-electronic charge-neutral antisymmetric BN doping of toluene's aromatic ring, with mean absolute errors of a few milli-Hartrees.

physics.chem-ph↗

arXiv2024

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 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 is 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.

physics.chem-ph↗

arXiv2023

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 data set, but is shown to be applicable to larger molecules picked from the QM9 data set. 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.

physics.chem-ph↗

arXiv2022

Alchemical geometry relaxation

We propose to relax geometries throughout chemical compound space (CCS) using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrödinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both, nuclear charges and nuclear positions (named "alchemical force"), within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analysed the convergence of the alchemical force perturbation series, as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH$_4$, NH$_3$, H$_2$O, and HF yield mean absolute errors of of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 Bohr for 4$^\text{th}$ order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree Fock derivative for benzene we provide numerical predictions of equilibrium energies and relaxed structures of all the 17 iso-electronic charge-netural BN-doped mutants with averaged absolute deviations of $\sim$27 mHa and $\sim$0.12 Bohr, respectively.

physics.chem-ph↗

arXiv2020

Effects of perturbation order and basis set on alchemical predictions

Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and perturbation order,introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis-set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on CCSD reference results, and is limited to all neutral diatomics with 14 electrons (AlH ... N$_2$). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighbouring out-of-sample diatomics with near CCSD quality using perturbations up to 5$^{th}$ order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.

physics.chem-ph↗