In this work, we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-off errors, it may not be positive definite. The dimensionality, given by the number of auxiliary functions, also poses a challenge in terms of memory and time demand since the coefficient matrix is dense. The methodology presented is based on a preconditioned Krylov subspace method able to deal with indefinite ill-conditioned equation systems. To assess its potential, it has been combined with double asymptotic electron repulsion integral expansions as implemented in the deMon2k package. A numerical study on a set of problems with up to 130,000 auxiliary functions shows its effectiveness to alleviate the abovementioned problematic. A comparison with the default methodology used in deMon2k based on a truncated eigenvalue decomposition of the coefficient matrix indicates that the proposed method exhibits excellent robustness and scalability when implemented in a parallel setting.

We recently adapted the Auxiliary DFT framework as implemented in deMon2k to the simulation of time-dependent problems via the Runge and Gross equations. Our implementation of the so-called Real-Time-Time-Dependent ADFT (RT-TD-ADFT) fully benefits from the algorithms available in deMon2k to carry out variational density fitting, notably the MINRES algorithm recently proposed for self-consistent-field calculations. We test here MINRES for the first time in the context of RT-TD-ADFT.We report extensive benchmarks calculations to assess the reliability of the ADFT framework. These encompass the construction of absorption spectra in the gas phase and in solvent, the calculation of electronic stopping power curves, the irradiation of zeolites by swift ions and the investigation of charge migrations with attosecond time resolution. All our results are very encouraging. We show that even small auxiliary basis sets are sufficient to obtain results almost undisguisable from those obtained with large and flexible auxiliary bases. Overall, we establish the reliability of RT-TD-ADFT to simulate electronics dynamics in large or very large molecular systems.

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola–Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree–Fock and Kohn–Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.

Machine learning approaches can drastically decrease the computational time for the predictions of spectroscopic properties in materials, while preserving the quality of the computational approaches. We studied the performance of kernel-ridge regression (KRR) and gradient boosting regressor (GBR) models trained on the isotropic shielding values, computed with density-functional theory (DFT), in a series of different known zeolites containing out-of-frame metal cations or fluorine anion and organic structure-directing cations. The smooth overlap of atomic position descriptors were computed from the DFT-optimised Cartesian coordinates of each atoms in the zeolite crystal cells. The use of these descriptors as inputs in both machine learning regression methods led to the prediction of the DFT isotropic shielding values with mean errors within 0.6 ppm. The results showed that the GBR model scales better than the KRR model.