arXiv subjects

Gianluca Levi

Publications and source records attributed to Gianluca Levi.

At least 19 recordsLinked to original sources

arXiv2026

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States

Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations typically provide more accurate values of the excitation energy of Rydberg states than time-dependent density functional theory approaches. However, the reliability of orbital-optimized methods for properties of Rydberg excited states such as the dipole moment remains much less explored, with existing benchmarks largely limited to the lowest excited states. Here, orbital-optimized density functional calculations with a plane-wave basis set are used to compute the dipole moment of several Rydberg states of a set of small molecules. Plane waves provide a flexible representation of diffuse Rydberg orbitals, overcoming limitations of commonly used atomic orbitals basis sets. Due to overconfinement of the Rydberg orbitals, a single-augmented atomic basis set yields a magnitude of the dipole moment that disagrees with the plane-wave calculations, even when the corresponding excitation energy is in good agreement. For the most diffuse states, the orientation of the dipole moment predicted by the atomic orbitals basis set can also be incorrect, and discrepancies with plane waves calculations persist even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE used in combination with the plane-wave representation of the orbitals gives good agreement with higher-level coupled-cluster calculations performed with sufficiently diffuse basis sets, when the latter are available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction generally leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ dependence of the effective Kohn--Sham potential.

physics.chem-ph↗

arXiv2026

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations II: Absorption Spectra

Absorption spectra up to 10 eV are calculated for a set of small molecules using a variational density functional approach in which the orbitals are optimized for each excited state. A plane-wave basis set is employed to accurately describe diffuse Rydberg excitations, while the transition dipole moment is evaluated from nonorthogonal Kohn--Sham determinants within the projector augmented wave formalism. Comparison with higher-level coupled-cluster results shows that orbital-optimized calculations provide a good description of oscillator strengths for states with predominantly single-configurational character, even with the generalized gradient approximation functional PBE. The inclusion of exact exchange and self-interaction correction further improves the results, with the latter yielding the smallest errors (mean absolute relative error of $\sim$25%). In contrast, large errors for all functionals are found for multi-configurational states, due to an inability of the approach to describe the multi-configurational character. Instead, the nonorthogonality between the ground and excited states is not found to be a significant source of error. These results establish the performance of orbital-optimized density functional calculations for absorption spectra of small molecules and highlight the need for extensions that combine state-specific orbital relaxation with an explicit multi-configurational treatment.

physics.chem-ph↗

arXiv2026

Orbital-optimized density functional calculations of excited electronic states: Recent advances and perspectives

Orbital-optimized (OO) density functional calculations provide a time-independent, variational route to electronic excitations, alternative to presently widely used time-dependent density functional theory (TDDFT) approaches. As the orbitals are optimized in a state specific way, these methods can provide a balanced description of excited states with different character, thereby overcoming several limitations of practical implementations of TDDFT. Driven by recent developments in algorithms for obtaining excited states as saddle points on the electronic energy surface, OO methods have attracted increasing interest, maturing into an active and rapidly expanding area of research. Here, the theoretical foundations of the approach are clarified and an overview of recent methodological developments in excited-state orbital optimization is provided. An overview of methods for treating open-shell singlet excited states and current approaches for computing transition properties and spectra is also provided. Finally, recent applications to molecular Rydberg, charge-transfer, and core excitations are reviewed, with the aim of assessing the present accuracy and range of applicability of OO density functional calculations with common exchange and correlation functionals.

physics.chem-ph↗

arXiv2026

Valence and Rydberg excited state bond dissociation curves of CO2 from orbital-optimized density functional calculations

Calculations of the lowest valence π* as well as the 3s and higher energy 3pσ Rydberg excited states of the CO2 molecule are carried out using density functionals with variational optimization of the orbitals, an approach involving relatively little computational effort. Five functionals with varying degree of exchange are used in combination with real or complex-valued orbitals that are optimized by finding saddle points on the electronic energy surface corresponding to the excited states. When the PBE functional is used in combination with complex orbitals, the calculated excitation energy is found to be within 0.3 eV of multireference configuration interaction reference values, and the results are further improved with hybrid functionals. In contrast, linear-response time-dependent density functional theory calculations give errors up to 1.9 eV for the most diffuse 3pσ excitation and exhibit stronger dependence on both the excitation character and the functional used. Calculated C-O dissociation curves using the PBE functional and the orbital-optimized approach compare remarkably well with the reported multireference configuration interaction and equation-of-motion coupled-cluster singles and doubles calculations. Thanks to the low computational cost, these results demonstrate that orbital-optimized density functional calculations can be a promising route for modelling photorelaxation in condensed-phase CO2, for example in the context of interstellar cosmic-ray radiation driven process involving high-energy Rydberg states.

physics.chem-ph↗

arXiv2026

Orbital Optimization and Neural-Network-Assisted Configuration Interaction Calculations of Rydberg States

Rydberg excited states of molecules pose a challenge for electronic structure calculations because of their highly diffuse electron distribution. Even large and elaborate atomic basis sets tend to underrepresent the long-range tail, overly confining the Rydberg state. An approach is presented here where the molecular orbitals are variationally optimized for the excited state using a plane wave basis set in a Hartree-Fock calculation, followed by a configuration interaction calculation. The use of excited state optimized orbitals greatly enhances the convergence of the many-body calculation, as illustrated by a full configuration interaction calculation of the $2s$ Rydberg state of H$_2$. A neural-network-based selective configuration interaction approach is then applied to calculations of $3s$ and $3p$ states of H$_2$O and NH$_3$. The obtained values of excitation energy are in close agreement with experimental measurements as well as previous many-body calculations where sufficiently diffuse atomic basis sets were used. Calculations using atomic basis sets lacking extra diffuse functions, such as aug-cc-pVTZ, give significantly higher estimates due to confinement of the Rydberg states.

physics.chem-ph↗

arXiv2026

Freeze-and-release direct optimization method for variational calculations of excited electronic states

Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy landscape. The optimization can be particularly difficult if the excitation involves significant rearrangement of the electron density, as for charge transfer excitations. A simple strategy for variational orbital optimization of excited states is presented. The approach involves minimizing the energy while freezing the orbitals directly involved in the excitation, followed by a fully unconstrained saddle point optimization. Both steps of this freeze-and-release strategy are carried out using direct optimization algorithms with the same computational scaling as ground state calculations. The performance of the method is extensively assessed in calculations of intramolecular and intermolecular charge transfer excited states of organic molecules and molecular dimers using a generalized gradient approximation functional. It is found that the freeze-and-release direct optimization approach can avoid variational collapse to spurious, charge-delocalized solutions for cases where conventional algorithms based on the maximum overlap method fail. For intermolecular charge transfer, the orbital-optimized calculations are found to provide the correct dependency of the energy on the donor-acceptor separation without requiring long-range exact exchange, something common time-dependent density functional theory approaches fail to achieve.

physics.chem-ph↗

arXiv2025

Natural-Orbital-Based Neural Network Configuration Interaction

Selective configuration interaction methods approximate correlated molecular ground- and excited states by considering only the most relevant Slater determinants in the expansion. While a recently proposed neural-network-assisted approach efficiently identifies such determinants, the procedure typically relies on canonical Hartree-Fock orbitals, which are optimized only at the mean-field level. Here we assess approximate natural orbitals - eigenfunctions of the one-particle density matrix computed from intermediate many-body eigenstates - as an alternative. Across our benchmarks for H$_2$O, NH$_3$, CO, and C$_3$H$_8$ we see a consistent reduction in the required determinants for a given accuracy of the computed correlation energy compared to full configuration interaction calculations. Our results confirm that even approximate natural orbitals constitute a simple yet powerful strategy to enhance the efficiency of neural-network-assisted configuration interaction calculations.

physics.chem-ph↗

arXiv2025

Fine Tuning of the Rotational Rate of Light-Driven, Second Generation Molecular Motors by Fluorine Substitutions

The relaxation time of several second generation molecular motors is analysed by calculating the minimum energy path between the metastable and stable states and evaluating the transition rate within harmonic transition state theory based on energetics obtained from density functional theory. Comparison with published experimental data shows remarkably good agreement and demonstrates the predictive capability of the theoretical approach. While previous measurements by Feringa and coworkers [Chem.\,Eur.\,J.\,(2017) 23, 6643] have shown that a replacement of the stereogenic hydrogen by a fluorine atom increases the relaxation time because of destabilization of the transition state for the thermal helix inversion, we find that a replacement of CH$_3$ by a CF$_3$ group at the same site shortens the relaxation time because of elevated energy of the metastable state without a significant shift in the transition state energy. Since these two fluorine substitutions have an opposite effect on the relaxation time, the two combined can provide a way to fine tune the rotational speed of a molecular motor.

physics.chem-ph↗

arXiv2025

Decoherence and vibrational energy relaxation of the electronically excited PtPOP complex in solution

Understanding the ultrafast vibrational relaxation following photoexcitation of molecules in a condensed phase is essential to predict the outcome and improve the efficiency of photoinduced molecular processes. Here, the vibrational decoherence and energy relaxation of a binuclear complex, [Pt$_2$(P$_2$O$_5$H$_2$)$_4$]$^{4-}$ (PtPOP), upon electronic excitation in liquid water and acetonitrile are investigated through direct adiabatic dynamics simulations. A quantum mechanics/molecular mechanics (QM/MM) scheme is used where the excited state of the complex is modelled with orbital-optimized density functional calculations while solvent molecules are described using potential energy functions. The decoherence time of the Pt-Pt vibration dominating the photoinduced dynamics is found to be $\sim$1.6 ps in both solvents. This is in excellent agreement with experimental measurements in water, where intersystem crossing is slow ($>10$ ps). Pathways for the flow of excess energy are identified by monitoring the power of the solvent on vibrational modes. The latter are obtained as generalized normal modes from the velocity covariances, and the power is computed using QM/MM embedding forces. Excess vibrational energy is found to be predominantly released through short-range repulsive and attractive interactions between the ligand atoms and surrounding solvent molecules, whereas solute-solvent interactions involving the Pt atoms are less important. Since photoexcitation deposits most of the excess energy into Pt-Pt vibrations, energy dissipation to the solvent is inefficient. This study reveals the mechanism behind the exceptionally long vibrational coherence of the photoexcited PtPOP complex in solution and underscores the importance of short-range interactions for accurate simulations of vibrational energy relaxation of solvated molecules.

physics.chem-ph↗

arXiv2025

A Neural-Network-Based Selective Configuration Interaction Approach to Molecular Electronic Structure

By combining Hartree-Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method's performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N$_2$ molecule is compared with published full CI calculations that included nearly $10^{10}$ Slater determinants, and the results are reproduced with only $4\cdot10^{5}$ determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method's high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.

physics.chem-ph↗

arXiv2024

Orbital-optimized versus time-dependent density functional calculations of intramolecular charge transfer excited states

The performance of time-independent, orbital optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. $-2$ eV for TD-DFT, no correlation is observed for the orbital optimized approach. The orbital optimized calculations with the LDA and the GGA functionals provide a mean absolute error of $\sim$0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with long-range charge transfer character. Orbital optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

physics.chem-ph↗

arXiv2024

GPAW: An open Python package for electronic-structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE) providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation (BSE), variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support of GPU acceleration has been achieved with minor modifications of the GPAW code thanks to the CuPy library. We end the review with an outlook describing some future plans for GPAW.

cond-mat.mtrl-sci↗

arXiv2024

Saddle Point Search Algorithms for Variational Density Functional Calculations of Excited Electronic States with Self-Interaction Correction

Excited electronic states of molecules and solids play a fundamental role in fields such as catalysis and electronics. In electronic structure calculations, excited states typically correspond to saddle points on the surface described by the variation of the energy as a function of the electronic degrees of freedom. A direct optimization algorithm based on generalized mode following is presented for density functional calculations of excited states. While conventional direct optimization methods based on quasi-Newton algorithms usually converge to the stationary point closest to the initial guess, even minima, the generalized mode following approach systematically targets a saddle point of a specific order l by following the l lowest eigenvectors of the electronic Hessian up in energy. This approach thereby recasts the challenging saddle point search as a minimization, enabling the use of efficient and robust minimization algorithms. The initial guess orbitals and the saddle point order of the target excited state solution are evaluated by performing an initial step of constrained optimization freezing the electronic degrees of freedom involved in the excitation. In the context of Kohn-Sham density functional calculations, typical approximations to the exchange-and-correlation functional suffer from a self-interaction error. The Perdew and Zunger self-interaction correction can alleviate this problem, but makes the energy variant to unitary transformations in the occupied orbital space, introducing a large amount of unphysical solutions that do not fully minimize the self-interaction error. An extension of the generalized mode following method is proposed that ensures convergence to the solution minimizing the self-interaction error.

physics.chem-ph↗

arXiv2023

Orbital-optimized Density Functional Calculations of Molecular Rydberg Excited States with Real Space Grid Representation and Self-Interaction Correction

Density functional calculations of Rydberg excited states up to high energy are carried out for several molecules using an approach where the orbitals are variationally optimized by converging on saddle points on the electronic energy surface within a real space grid representation. Remarkably good agreement with experimental estimates of the excitation energy is obtained using the generalized gradient approximation (GGA) functional of Perdew, Burke and Ernzerhof (PBE) when Perdew-Zunger self-interaction correction is applied in combination with complex-valued orbitals. Even without the correction, the PBE functional gives quite good results despite the fact that corresponding Rydberg virtual orbitals have positive energy in the ground state calculation. Results obtained using the TPSS and r2SCAN meta-GGA functionals are also presented, but they do not provide a systematic improvement over the results from the uncorrected PBE functional. The grid representation combined with the projector augmented-wave approach gives a simpler and better representation of the diffuse Rydberg orbitals than a linear combination of atomic orbitals with commonly used basis sets, the latter leading to an overestimation of the excitation energy due to confinement of the excited states.

physics.chem-ph↗

arXiv2023

Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations

Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 511 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely ${}^{3}A_2 < {}^{1}E < {}^{1}A_1 < {}^{3}E$. Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.

cond-mat.mtrl-sci↗

arXiv2023

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following

Variational calculations of excited electronic states are carried out by finding saddle points on the surface that describes how the energy of the system varies as a function of the electronic degrees of freedom. This approach has several advantages over commonly used methods especially in the context of density functional calculations, as collapse to the ground state is avoided and yet, the orbitals are variationally optimized for the excited state. This optimization makes it possible to describe excitations with large charge transfer where calculations based on ground state orbitals are problematic, as in linear response time-dependent density functional theory. A generalized mode following method is presented where an $n^{\text{th}}$-order saddle point is found by inverting the components of the gradient in the direction of the eigenvectors of the $n$ lowest eigenvalues of the electronic Hessian matrix. This approach has the distinct advantage of following a chosen excited state through atomic configurations where the symmetry of the single determinant wave function is broken, as demonstrated in calculations of potential energy curves for nuclear motion in the ethylene and dihydrogen molecules. The method is implemented using a generalized Davidson algorithm and an exponential transformation for updating the orbitals within a generalized gradient approximation of the energy functional. Convergence is found to be more robust than for a direct optimization approach previously shown to outperform standard self-consistent field approaches, as illustrated here for charge transfer excitations in nitrobenzene and N-phenylpyrrole, involving calculations of $4^{\text{th}}$- and $6^{\text{th}}$-order saddle points, respectively. Finally, calculations of a diplatinum and silver complex are presented, illustrating the applicability of the method to excited state energy curves of large molecules.

physics.chem-ph↗

arXiv2023

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

physics.chem-ph↗

arXiv2021

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density dependent functionals (ODD) including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate $π^\ast$ orbitals where the importance of complex orbitals is illustrated. An application of the method to several metal-to-ligand charge-transfer and metal-centred excited states of an Fe$^{\rm II}$ photosensitizer complex is described and the results compared to reported experimental estimates. The method is also used to study the effect of Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

physics.comp-ph↗