arXiv subjects

Filippo Lipparini

Publications and source records attributed to Filippo Lipparini.

At least 19 recordsLinked to original sources

arXiv2026

Use of Cholesky decomposition in the CFOUR program package

An overview is given about our efforts to speed up high-level computations of molec- ular energies and properties using Cholesky decomposition (CD). We describe the cor- responding developments in the CFOUR quantum-chemical package with a focus on (a) the use of CD in complete-active space self-consistent-field (CASSCF) and coupled- cluster (CC) computations, (b) the implementation of analytic CC gradients using CD, (c) the efficient calculation of magnetic properties (NMR shieldings and magnetizabili- ties) using CD when carried out with explicit magnetic-field dependent basis functions, i.e., the so-called gauge-including atomic orbitals (GIAOs), (d) the efficient computa- tion of CASSCF response properties using CD, (e) the use of CD in relativistic two- and four-component computations, as well as (f) computations for molecules in finite magnetic fields using GIAOs together with CD. An outlook on future developments concerning the CFOUR package is given.

physics.chem-ph↗

arXiv2026

Critical point search and linear response theory for computing electronic excitation energies of molecular systems. Part II. CASSCF

The computation of excited states within the Complete Active Space Self-Consistent Field (CASSCF) framework remains a significant challenge in quantum chemistry, both theoretically and algorithmically. In this work, we extend the K\"ahler manifold formalism introduced in Part I of this series to the CASSCF theory, and draw a geometrical connection from the time-dependent CASSCF equations to state-specific and linear response methodologies for excited states. This is achieved by first investigating the underlying CASSCF manifold and identifying its K\"ahler structure, which is complicated by the nontrivial coupling of CI and orbital degrees of freedom. Building on these theoretical findings, we derive the CASSCF linear response equations in a straightforward manner, and develop a robust state-specific method that relies solely on first-order derivatives of the CASSCF energy functional. Numerical results on representative molecular systems-water, formaldehyde, and ethylene-demonstrate the effectiveness of the proposed state-specific method, while revealing the difficulty of reliable identification of excited states due to nonlinearity induced by the CASSCF theory.

physics.chem-ph↗

arXiv2026

Experimental proof of strong $\Pi$-$\Sigma$ mixing in the Renner-Teller and Pseudo-Jahn-Teller affected CCH$^+$ ($^3\Pi$) ion

The ethynyl radical cation, CCH$^+$ ($^3\Pi$), offers a unique system for fundamental spectroscopic studies of non-adiabatic effects due to its open-shell linear structure and the presence of a low-lying $^3\Sigma^-$ state, which induces notable perturbations in the (ro-)vibrational spectrum. To probe these effects, we recorded the broadband vibrational spectrum of CCH$^+$ from 350-3450 cm$^{-1}$ using leak-out spectroscopy. The spectrum reveals a complex splitting pattern in the CCH bending mode, attributed to Renner-Teller and pseudo-Jahn-Teller coupling effects between the $^3 \Pi$ and $^3 \Sigma^-$ electronic states. A three-state diabatic model, validated here against high-resolution IR data of the CH stretching mode, facilitated assignments within the broadband infrared (IR) spectrum, including an additional $\Pi$ vibronic feature observed in the aforementioned high-resolution spectrum. Our results highlight a pronounced sensitivity of the splitting pattern to the $\Pi$-$\Sigma$ energy gap, with couplings so large that even the zero-point vibrational motion of the bending vibration is sufficient to disrupt the vibronic structure of this ion. This compact ion, with strong coupling effects and high-quality spectroscopic data, serves as an exemplary system for evaluating non-adiabatic models.

physics.chem-ph↗

arXiv2026

Solvation Lies Within: Simulating Condensed-Phase Properties from Local Electronic Structures

In transitions between different environmental settings, a molecular system inevitably undergoes a range of detectable changes, and the ability to accurately simulate such responses, e.g., in the form of shifts to molecular energies, remains an important challenge across physical chemistry. Based on an exact decomposition of total energies from Kohn--Sham density functional theory in a basis of spatially localized molecular orbitals, the present work outlines a robust protocol for sampling the effect of solvation within homogeneous condensed phases by focusing on perturbations to local electronic structures only. We report chemically intuitive results for binding energies of water, ethanol, and acetonitrile that all display fast convergence with respect to the bulk size. Results stay largely invariant with respect to the choice of basis set while reflecting differences in density functional approximations, and our protocol thus allows for a physically sound and efficient estimation of general effects related to bulk solvation.

physics.chem-ph↗

arXiv2025

A novel implementation of CCSD analytic gradients using Cholesky decomposition of the two-electron integrals and Abelian point-group symmetry

We present a novel and efficient implementation of coupled-cluster with singles and doubles (CCSD) analytic gradients that combines the Cholesky decomposition (CD) of electron-repulsion integrals with the exploitation of Abelian point-group symmetry. This approach is particularly effective for medium-sized and large symmetric molecular systems. The CD of two-electron integrals is performed using a symmetry-adapted two-step algorithm, while the derivatives of the Cholesky vectors are computed with respect to symmetry-adapted nuclear displacements and contracted on-the-fly with the CCSD density matrices. Geometry optimizations of symmetric systems with several hundreds of basis functions have been carried out to assess the efficiency of our implementation and to quantify the computational gain provided by the exploitation of point-group symmetry.

physics.chem-ph↗

arXiv2025

The QUEST Database of Highly-Accurate Excitation Energies

We report theoretical best estimates of vertical transition energies (VTEs) for a large number of excited states and molecules: the \textsc{quest} database. This database includes 1489 \emph{aug}-cc-pVTZ VTEs (731 singlets, 233 doublets, 461 triplets, and 64 quartets) for both valence and Rydberg transitions occurring in molecules containing from 1 to 16 non-hydrogen atoms. \textsc{Quest} also includes a significant list of VTEs for states characterized by a partial or genuine double-excitation character, known to be particularly challenging for many computational methods. The vast majority of the reported values are deemed chemically-accurate, that is, are within $\pm0.05$ eV of the FCI/\emph{aug}-cc-pVTZ estimate. This allows for a balanced assessment of the performance of popular excited-state methodologies. We report the results of such benchmarks for various single- and multi-reference wavefunction approaches, and provide extensive supporting information allowing testing of other models. All corresponding data associated with the \textsc{quest} database, along with analysis tools, can be found in the associated \textsc{GitHub} repository at the following URL: https://github.com/pfloos/QUESTDB.

physics.chem-ph↗

arXiv2024

A polarizable CASSCF/MM approach using the interface between OpenMMPol library and CFour

We present a polarizable embedding quantum mechanics/molecular mechanics (QM/MM) framework for ground- and excited-state Complete Active Space Self-Consistent Field (CASSCF) calculations on molecules within complex environments, such as biological systems. These environments are modeled using the AMOEBA polarizable force field. This approach is implemented by integrating the OpenMMPol library with the CFour quantum chemistry software suite. The implementation supports both single-point energy evaluations and geometry optimizations, facilitated by the availability of analytical gradients. We demonstrate the methodology by applying it to two distinct photoreceptors, exploring the impact of the protein environment on the structural and photophysical properties of their embedded chromophores.

physics.chem-ph↗

arXiv2024

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/$GW$ and Wave Function Methods

To expand the QUEST database of highly-accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly-accurate excitation energies. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both $G_0W_0$ and ev$GW$ quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models amongst those with respective $\mathcal{O}(N^5)$ and $\mathcal{O}(N^6)$ scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, $\omega$B97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-$\omega$B88PP86 and SOS-$\omega$PBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/ev$GW$ calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

physics.chem-ph↗

arXiv2024

Cholesky decomposition in spin-free Dirac-Coulomb coupled-cluster calculations

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their non-relativistic counterparts. While for non-relativistic CC calculations atomic-orbital (AO) based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost on that case. Here, molecular-orbital (MO) based algorithms exploiting the CD of the two-electron integrals allow to reduce disk-space requirements, and lead to computational cost in the CC step that are more or less the same as in the non-relativistic case. The only remaining overhead in a CD-SFDC-CC calculation are due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15 % of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)$_4$ molecules with X = Ni, Pd, Pt.

physics.chem-ph↗

arXiv2024

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wavefunctions

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called flag manifolds, we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests Riemannian optimization as a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

math.OC↗

arXiv2024

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

physics.chem-ph↗

arXiv2024

The OpenMMPol Library for Polarizable QM/MM Calculations of Properties and Dynamics

We present a new library designed to provide a simple and straightforward way to implement QM/AMOEBA and other polarizable QM/MM methods based on induced point dipoles. The library, herein referred to as OpenMMPol, is free and open-sourced and is engineered to address the increasing demand for accurate and efficient QM/MM simulations. OpenMMPol is specifically designed to allow polarizable QM/MM calculations of ground state energies and gradients, and excitation properties. Key features of OpenMMPol include a modular architecture facilitating extensibility, parallel computing capabilities for enhanced performance on modern cluster architectures, and a user-friendly interface for intuitive implementation and a simple and flexible structure for providing input data. To show the capabilities of fered by the library we present an interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry optimization and excited state calculation based on (TD)DFT.

physics.chem-ph↗

arXiv2023

A novel coupled-cluster singles and doubles implementation that combines the exploitation of point-group symmetry and Cholesky decomposition of the two-electron integrals

A novel implementation of the coupled-cluster singles and doubles (CCSD) approach is presented that is specifically tailored for the treatment of large, symmetric systems. It fully exploits Abelian point-group symmetry and the use of the Cholesky decomposition of the two-electron repulsion integrals. In accordance with modern CCSD algorithms, we propose two alternative strategies for the computation of the so-called particle-particle ladder term. The code is driven towards the optimal choice depending on the available hardware resources. As a large-scale application, we computed the frozen-core correlation energy of buckminsterfullerene (C$_{60}$) with a polarized valence triple-zeta basis set (240 correlated electrons in 1740 orbitals).

physics.chem-ph↗

arXiv2023

Heptazine, Cyclazine, and Related Compounds: Chemically-Accurate Estimates of the Inverted Singlet-Triplet Gap

Molecules that violate Hund's rule and exhibit an inverted gap between the lowest singlet $S_1$ and triplet $T_1$ excited states have attracted considerable attention due to their potential applications in optoelectronics. Amongst these molecules, the triangular-shaped heptazine, and its derivatives, have been in the limelight. However, conflicting reports have arisen regarding the relative energies of $S_1$ and $T_1$. Here, we employ highly accurate levels of theory, such as CC3, to not only resolve the debate concerning the sign but also quantify the magnitude of the $S_1$-$T_1$ gap. We also determine the 0-0 energies to evaluate the significance of the vertical approximation. In addition, we compute reference $S_1$-$T_1$ gaps for a series of 10 related molecules. This enables us to benchmark lower-order methods for future applications on larger systems within the same family of compounds. This contribution can serve as a reliable foundation for the design of triangular-shaped molecules with enhanced photophysical properties.

physics.chem-ph↗

arXiv2023

A Cholesky decomposition-based implementation of relativistic two-component coupled-cluster methods for medium-sized molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules have been performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of $10^{-4}$ is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF$_6$, with up to quadruple-zeta basis sets, and the lowest excitation energy in solvated uranyl ion [UO$_2^{2+}$(H$_2$O)$_{12}$].

physics.chem-ph↗

arXiv2023

CASSCF response equations revisited: a simple and efficient iterative algorithm

We present an algorithm to solve the CASSCF linear response equations that is both simple and efficient. The algorithm makes use of the well established symmetric and antisymmetric combinations of trial vectors, but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric, block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Preliminary numerical tests show that the algorithm is robust and stable.

physics.chem-ph↗

arXiv2023

A Quasi Time-Reversible scheme based on density matrix extrapolation on the Grassmann manifold for Born-Oppenheimer Molecular Dynamics

This article proposes a so-called Quasi Time-Reversible (QTR G-Ext) scheme based on Grassmann extrapolation of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics simulations. The method shows excellent results on four large molecular systems, ranging from 21 to 94 atoms simulated with Kohn-Sham density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations, while keeping a similar energy drift as in the extended Lagrangian Born-Oppenheimer method.

physics.chem-ph↗

arXiv2023

A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry

We present two open-source implementations of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) algorithm to find a few eigenvalues and eigenvectors of large, possibly sparse matrices. We then test LOBPCG for various quantum chemistry problems, encompassing medium to large, dense to sparse, wellbehaved to ill-conditioned ones, where the standard method typically used is Davidson's diagonalization. Numerical tests show that, while Davidson's method remains the best choice for most applications in quantum chemistry, LOBPCG represents a competitive alternative, especially when memory is an issue, and can even outperform Davidson for ill-conditioned, non diagonally dominant problems.

math.NA↗