Calculating excited-state gradients and derivative couplings using time-dependent density functional theory (TDDFT) remains a computationally demanding task. An efficient variant, TDDFT with resolution of the identity and a minimal auxiliary basis (TDDFT-ris), has been developed to accelerate excitation energy calculations. However, the formulation and implementation of analytical derivatives for this method have not yet been reported. In this work, we present an implementation of analytical excited-state gradients and derivative couplings within the TDDFT-ris framework. Benchmark calculations on medium-sized organic molecules demonstrate a two- to 3-fold speedup for both gradients and derivative couplings compared to standard TDDFT. The accuracy of the TDDFT-ris approach is assessed for gradient-dependent applications, including geometry optimizations, emission energy calculations, and the localization of minimum-energy crossing points. Overall, the TDDFT-ris method provides reliable approximations for most cases, with noticeable errors mainly occurring in derivative couplings between nearly degenerate states.
Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional representations of conformational landscapes and cluster trajectories into relevant metastable states. Most of these algorithms require the selection of a small number of features that describe the problem of interest. Although deep neural networks can tackle large numbers of input features, the training costs increase with input size, which makes the selection of a subset of features mandatory for most problems of practical interest. Here, we show that random nonlinear projections can be used to compress large feature spaces and make computations faster without a substantial loss of information. We describe an efficient way to produce random projections and then exemplify the general procedure for protein folding. For our test cases NTL9 and the double-norleucin variant of the villin headpiece, we find that random compression retains the core static and dynamic information of the original high-dimensional feature space, making trajectory analysis more robust.
The multiscale model combining the multiconfigurational self-consistent field (MCSCF) method with the fully atomistic polarizable Fluctuating Charges (FQ) force field (Sepali, C.; et al. J. Chem. Theory Comput. 2024, 20, 9954-9967) is here extended to the calculation of analytical nuclear gradients. The gradients are derived from first-principles, implemented in the OpenMolcas package, and validated against numerical references. The resulting MCSCF/FQ nuclear gradients are employed to simulate vibronic absorption spectra of aromatic molecules in aqueous solution, namely benzene and phenol. By integrating this approach with molecular dynamics simulations, both solute conformational flexibility and the dynamical aspects of solvation are properly captured. The computed spectra reproduce experimental profiles and relative band intensities with remarkable accuracy, demonstrating the capability of the MCSCF/FQ model to simultaneously describe the multireference character of the solute and its interaction with the solvent environment.

