Our research is devoted to the development of electronic structure methods and numerical algorithms for accurate prediction of molecular properties. We combine methodological advances with efficient computational strategies to enable the efficient calculation of analytic energy gradients, response properties, and higher-order derivatives within wavefunction-based electronic structure theory. Our developments span both multireference (CASSCF) and coupled-cluster methods and place particular emphasis on computational efficiency, numerical robustness, and scalability. Many of our implementations exploit the Cholesky decomposition of the two-electron integral matrix, allowing high-accuracy calculations on molecular systems that would otherwise be computationally prohibitive. This work is done in close collaboration with the groups of Jürgen Gauss and Stella Stopkowicz in Mainz and Saarbrücken. All the developments are contained in a development version of the CFOUR suite of programs.
A significant part of our research focuses on the formulation and implementation of robust numerical algorithms for large-scale eigenvalue problems arising in electronic structure theory, particularly in linear response calculations. This effort has led to the development of the open-source DiagLib library, which includes SMO-GD, an efficient iterative eigensolver specifically designed for response eigenvalue problems.
More recently, we have been exploring the application of differential geometry to electronic structure theory. This research has resulted in the development of the Grassmann Extrapolation (GExt) method for accelerating ab initio molecular dynamics simulations and in the application of Riemannian optimization techniques to the CASSCF wavefunction. These developments are carried out in close collaboration with applied mathematicians, particularly with the groups of Benjamin Stamm and Eric Cancès in Stuttgart and Paris.
Three selected publications
Pes, F.; Polack, E.; Mazzeo, P.; Dusson, G.; Stamm, B. & Lipparini, F.
A Quasi Time-Reversible Scheme Based on Density Matrix Extrapolation on the Grassmann Manifold for Born–Oppenheimer Molecular Dynamics
J. Phys. Chem. Lett., 14, 9720–9726 (2023)
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Nottoli, T.; Lapi, L.; Alessandro, R.; Giannì, I; Pes, F. & Lipparini, F.
An Efficient and Robust Implementation of CASSCF Linear Response Theory
J. Phys. Chem. A 129, 8441-8452 (2025)
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Melega, L. Nottoli, T. Gauss, J., Lipparini, F.
A Novel Implementation of CCSD Analytic Gradients Using Cholesky Decomposition of the Two-Electron Integrals and Abelian Point-Group Symmetry
J. Phys. Chem. A 130, 2097-2111 (2026)
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