Mixed quantum-classical dynamics (MQCD) methods are effective models for excited-state processes in quasi-classical molecular systems, in which nuclear motion is described by classical trajectories while electronic populations undergo quantum nonadiabatic transitions. This article presents Newton-X 26, a new generation of the Newton-X platform that consolidates two decades of development into a modular ecosystem for generating spectra and initial conditions, propagating dynamics, and analyzing, postprocessing, and archiving data. Newton-X 26 supports multiple MQCD strategies, including surface hopping, decoherence-corrected Ehrenfest dynamics, and ab initio multiple spawning, and connects to a range of electronic-structure engines through dedicated interfaces. The platform emphasizes efficient execution for large trajectory ensembles, enabling systematic convergence analyses and uncertainty estimation. Complementary tools support automated data curation, machine-learning-assisted workflows, and reproducible FAIR-oriented reporting and sharing. Taken together, Newton-X 26 provides an open-source environment for routine MQCD applications and continued method development across multiple electronic-structure levels.

We performed a simulation of the time-resolved photoelectron spectrum (TRPES) of trans-azobenzene after ππ∗ excitation in a mixed quantum–classical framework. The electronic structure of the molecule and of its cation was obtained with a semiempirical multireference configuration interaction approach, the nonadiabatic dynamics was simulated with the surface hopping algorithm, and the TRPES was determined by computing the relevant Dyson orbitals. According to our results, the TRPES obtained with a probe photon energy of 6.0 eV shows two bands, the one at higher energy being due to the S2 electronic state of the molecule and the other one to the S1 state. For both bands, the main contribution to the spectrum originates from the D0 state of the cation. Our simulated TRPES is in very good agreement with the available experimental data, both in terms of the energetic positions of the bands and their lifetimes. Our findings confirm that the wavelength dependence of the photoisomerization quantum yields of trans-azobenzene is not due to a peculiar nonadiabatic decay process, as previously inferred from the experimental TRPES. Rather, the reason for the violation of Kasha’s rule is that different regions of the nuclear phase space are explored in S1, whether this state is populated by direct excitation or by the radiationless decay of S2.

Nonadiabatic molecular dynamics simulations provide a theoretical understanding of various excited-state processes in photochemistry, offering access to band widths, radiative or nonradiative relaxation and corresponding lifetimes, excited-state energies, and charge transfer. The range of method developments within the framework of time-dependent density functional theory is exceedingly large for molecular quantum chemistry. Still, it shrinks significantly when aiming to treat periodic boundary conditions. To address this gap and complement existing software packages for solid-state nonadiabatic molecular dynamics, we present an interface between the CP2K electronic structure and the NEWTON-X surface hopping codes. The interface features the generation of initial conditions, as well as adiabatic and nonadiabatic molecular dynamics, based on phenomenological or numerical time-derivative couplings. Setups are validated on gas-phase pyrazine, with electronic absorption spectra and excited-state populations for transitions between the lowest singlet states being in agreement with established molecular quantum chemistry methods. Extending the system size to crystalline pyrazine, limitations of approximate couplings are discussed, and the efficiency and applicability of the interface are demonstrated by computing broad spectra over several eV and 100 fs trajectories, considering couplings between all 80th lowest excited states, at low computational cost with a mixed semiempirical density functional theory setup.

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1 A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

We describe a method to run simulations of ground or excited state dynamics under extremely high pressures. The method is based on the introduction of a fictitious ideal gas that exerts the required pressure on a molecular sample and is therefore called XP-GAS (eXtreme Pressure by Gas Atoms in a Sphere). The algorithm is most suitable for approximately spherical clusters of molecules described by quantum chemistry methods, Molecular Mechanics or mixed QM/MM approaches. We compare the results obtained by the algorithm here presented and by the XP-PCM approach, based on a continuum description of the environment. As a test case, we study the conformational dynamics of 1,3-butadiene either as an isolated molecule ("naked" butadiene) or embedded in a cluster of argon atoms, under pressures up to 15 GPa. Overall, our results show that the XP-GAS QM/MM simulation method is in good agreement with the XP-PCM QM/Continuum model (Cammi model) in describing the effect of the pressure on static properties as the equilibrium geometry of butadiene in the ground state. Furthermore, the comparison of XP-GAS simulations with naked butadiene and butadiene in argon shows the importance, for XP-GAS and related methods, of a realistic representation of the medium in modelling pressure effects.

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.

We present two different computational approaches to design covalently bound dimers for singlet fission. Both designs aim at maximizing the effective coupling between the initial singlet excited state S* and the double triplet state TT, by tuning the interaction (mainly through-space) between the chromophore units. Design I is based on a preliminary search for the optimal relative arrangements of chromophores in a space of possible stacked pair geometries. Then, the optimized dimeric arrangements are used as targets for the covalent connection of the two chromophores. In design II, all viable ways to covalently bind the two chromophores are considered, using a given set of linkers. Next, the most promising covalent dimers for singlet fission, among our tested candidates, are identified. The application of our approaches to a locked 1,3-diphenyl-isobenzofuran chromophore and a diamino-fluoroquinone compound allowed to design several promising dimers for singlet fission, featuring large S*-TT effective couplings and favorable energetics.

We tested the effect of different ways of sampling the initial conditions in surface hopping simulations, with a focus on the initial energy distributions and on the treatment of the zero point energy (ZPE). As a test case, we chose the gas phase photodynamics of azomethane, which features different processes occurring in overlapping time scales: geometry relaxation in the excited state, internal conversion, photoisomerization, and fast and slow dissociation. The simulations, based on a semiempirical method, had a sufficiently long duration (10 ps) to encompass all of the above processes. We tested several variants of methods based on the quantum mechanical (QM) distributions of the nuclear coordinates q and momenta p, which yield, at least on the average over a large sampling set, the correct QM energy, namely the ZPE when starting from the ground vibrational state. We compared the QM samplings with the classical Boltzmann (CB) distribution obtained by a thermostated trajectory, whereby thermal effects are taken into account, but the ZPE is utterly ignored. We found that most QM and CB approaches yield similar results as to short time dynamics and decay lifetimes, whereas the rate of the ground state dissociation reaction CH3NNCH3 → CH3NN + CH3 is sharply affected by the sampling method. With QM samplings a large fraction of trajectories dissociate promply (<1 ps) after decay to the ground state and with rates of the order of 10-1 ps-1 after the first ps. Instead, the CB samplings yield a much smaller fraction of prompt dissociations and much lower rates at long times. We provided evidence that the ZPE "leaks" from high frequency modes to the reactive ones (N-C bond elongations), therefore unphysically increasing the dissociation rates with QM samplings. We show that an effective way to take into account the ZPE and to avoid the "leaking" problem is to add the ZPE to the potential energy surfaces as a function of the most relevant internal coordinates. Then, Boltzmann sampling can be done as usual, so this approach is suitable also for condensed state dynamics. In the tests we present here, the ZPE correction method yields dissociation rates intermediate between QM and uncorrected Boltzmann samplings.

The photoisomerization of chromophores embedded in biological environments is of high importance for biomedical applications, but it is still challenging to define the photoisomerization mechanism both experimentally and computationally. We present here a computational study of the azobenzene molecule embedded in a DPPC lipid membrane, and assess the photoisomerization mechanism by means of the quantum mechanics/molecular mechanics surface hopping (QM/MM-SH) method. We observe that while the trans-to-cis isomerization is a slow process governed by a torsional mechanism due to the strong interaction with the environment, the cis-to-trans mechanism is completed in sub-ps time scale and is governed by a pedal-like mechanism in which both weaker interactions with the environment and a different geometry of the potential energy surface play a key role.

Structural characterization of transient electrochemical species in the sub-millisecond time scale is the all-time wish of any electrochemist. Presently, common time resolution of structural spectro-electrochemical methods is about 0.1 seconds. Herein, a transient spectro-electrochemical Raman setup of easy implementation is described which allows sub-ms time resolution. The technique studies electrochemical processes by initiating the reaction with an electric potential (or current) pulse and analyses the product with a synchronized laser pulse of the modified Raman spectrometer. The approach was validated by studying a known redox driven isomerization of a Ru-based molecular switch grafted, as monolayer, on a SERS active Au microelectrode. Density-functional-theory calculations confirmed the spectral assignments to sub-ms transient species. This study paves the way to a new generation of time-resolved spectro-electrochemical techniques which will be of fundamental help in the development of next generation electrolizers, fuel cells and batteries.

We present three different computational designs of potential singlet fission chromophores. In the first two cases, we propose structural modifications of two biradicaloid compounds already known with regard to singlet fission, namely 1,3-diphenyl-isobenzofuran (DPBF) and 2,3-diamino-1,4-benzoquinone (DABQ). In the former case, the introduction of methylene bridges between the phenyl rings and the isobenzofuran core of DPBF leads to an improvement of the singlet fission energetics and confers a higher degree of rigidity to the resulting molecule. In the second case, structural modifications of DABQ are proposed in order to overcome its fast nonradiative excited state decay and to improve its singlet fission energetics. The resulting diamino-fluoroquinone compounds fulfill the desired energy criteria and represent new potential chromophores for singlet fission. Finally, in the third proposed design we exploit the captodative effect to tune the energy levels of small biradicaloid molecules, leading to propose several compounds presented for the first time as suitable chromophores for singlet fission.

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photo -physical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

We performed computational simulations of the photodynamics of a self-assembled monolayer (SAM) of an azobenzene derivative (azobiphenyl, ABPT) on a gold surface. An excitonic approach was adopted in a semiempirical framework, which allowed us to consider explicitly the electronic degrees of freedom of 12 azobenzene chromophores. The surface hopping scheme was used for nonadiabatic molecular dynamics simulations. According to our results for an all trans-ABPT SAM, the excitation energy transfer between different chromophores, very fast in the ππ∗ manifold, does not occur between nπ∗ states. As a consequence, the excitation transfer does not play an important role in the quenching of the azobenzene photoisomerization in the SAM (experimentally observed and reproduced by our calculations) which, instead, has to be attributed to steric effects.

In this chapter we deal mainly with nonadiabatic independent trajectory approaches to the simulation of excited state dynamics. We focus on a ubiquitous shortcoming of such methods, namely overcoherence, or lack of decoherence, in the time-evolution of the electronic wavefunction and density matrix. In the mean-field approach the overcoherence affects the average potential energy surface on which the trajectory runs, yielding unphysical results, while in the surface hopping dynamics it leads to an overestimation of the couplings between electronic states. In the introduction we frame the theme of decoherence as a fundamental element of quantum theory and a real process affecting molecular dynamics. In the next section, we introduce the overcoherence problem in independent trajectory methods for nonadiabatic dynamics. In the third section, we shortly review the mean-field and surface hopping approaches, we show how decoherence can be described in the framework of Liouville-von Neumann equation, and we introduce several formulas and procedures to compute decoherence rates. In the fourth section we examine a variety of algorithms that have been proposed to correct the overcoherence in mean-field and surface hopping methods, dividing them in two classes: those based on stochastic sudden decoherence events, and those introducing smooth modifications of the (over)coherent electronic dynamics. Finally, in the last section we recall the most popular and/or promissing decoherence correction methods, and we focus on tests showing how such corrections really improve the accuracy of the nonadiabatic trajectories simulations.

We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented.

We present an implementation of the Frenkel exciton model in the framework of the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method, aimed at simulating the dynamics of multichromophoric systems, in which excitation energy transfer can occur, by a very efficient approach. The nonadiabatic molecular dynamics is here dealt with by the surface hopping method, but the implementation we proposed is compatible with other dynamical approaches. The exciton coupling is computed either exactly, within the semiempirical approximation considered, or by resorting to transition atomic charges. The validation of our implementation is carried out on the trans-azobenzeno-2S-phane (2S-TTABP), formed by two azobenzene units held together by sulfur bridges, taken as a minimal model of multichromophoric systems, in which both strong and weak exciton couplings are present.

Surface hopping investigation of singlet fission in covalently linked dimers: impact of the mutual arrangement.

The strong coupling between molecules and photons in resonant cavities offers a new toolbox to manipulate photochemical reactions. Although the quenching of photochemical reactions in the strong coupling regimen has been demonstrated before, their enhancement has proven to be more elusive. Here, by means of a state-of-the-art approach, we show how the trans- cis photoisomerization quantum yield of azobenzene embedded in a realistic environment can be higher in polaritonic conditions than in the cavity-free case. We characterize the mechanism leading to such enhancement and discuss the conditions to push the photostationary state toward the unfavored reaction product. Our results provide a signature that the control of photochemical reactions through strong coupling can be extended from selective quenching to improvement of the quantum yields.

We present surface hopping simulations of singlet fission in 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF). In particular, we performed simulations based on quantum mechanics/molecular mechanics (QM/MM) schemes in which either two or three ThBF molecules are inserted in the QM region and embedded in their MM crystal environment. Our aim was to investigate the changes in the photodynamics that are brought about by extending the delocalization of the excited states beyond the minimal model of a dimer. In the simulations based on the trimer model, compared to the dimer-based ones, we observed a faster time evolution of the state populations, with the largest differences associated with both the rise and decay times for the intermediate charge transfer states. Moreover, for the trimer, we predicted a singlet fission quantum yield of similar to 204%, which is larger than both the one extracted for the dimer (similar to 179%) and the theoretical upper limit of 200% for the dimer-based model of singlet fission. Although our study cannot account for the effects of extending the delocalization beyond three molecules, our findings clearly indicate how and why the singlet fission dynamics can be affected.

The strong coupling regime between confined light and organic molecules turned out to be promising in modifying both the ground state and the excited states properties. Under this peculiar condition, the electronic states of the molecule are mixed with the quantum states of light. The dynamical processes occurring on such hybrid states undergo several modifications accordingly. Hence, the dynamical description of chemical reactivity in polaritonic systems needs to explicitly take into account the photon degrees of freedom and nonadiabatic events. With the aim of describing photochemical polaritonic processes, in the present work, we extend the direct trajectory surface hopping scheme to investigate photochemistry under strong coupling between light and matter.