Fast and accurate excited states predictions: machine learning and diabatization.

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

Excitation and fragmentation of the dielectric gas C4F7N: Electrons vs photons.

C4F7N is a promising candidate for the replacement of sulfur hexafluoride as an insulating medium, and it is important to understand the chemical changes initiated in the molecule by collision with free electrons, specifically the formation of neutral fragments. The first step of neutral fragmentation is electronic excitation, yet neither the absorption spectrum in the vacuum ultraviolet (VUV) region nor the electron energy loss spectrum have previously been reported. Here, we experimentally probed the excited states by VUV photoabsorption spectroscopy and electron energy loss spectroscopy (EELS). We found that the distribution of states populated upon electron impact with low-energy electrons is significantly different from that following photoabsorption. This difference was confirmed and interpreted with ab initio modeling of both VUV and EELS spectra. We propose here a new computational protocol for the simulation of EELS spectra combining the Born approximation with approximate forms of correlated wave functions, which allows us to calculate the (usually very expensive) scattering cross sections at a cost similar to the calculation of oscillator strengths. Finally, we perform semi-classical non-adiabatic dynamics simulations to investigate the possible neutral fragments of the molecule formed through electron-induced neutral dissociation. We show that the product distribution is highly non-statistical.

Optimal Representation of the Nuclear Ensemble: Application to Electronic Spectroscopy.

Nuclear densities are frequently represented by an ensemble of nuclear configurations or points in the phase space in various contexts of molecular simulations. The size of the ensemble directly affects the accuracy and computational cost of subsequent calculations of observable quantities. In the present work, we address the question of how many configurations do we need and how to select them most efficiently. We focus on the nuclear ensemble method in the context of electronic spectroscopy, where thousands of sampled configurations are usually needed for sufficiently converged spectra. The proposed representative sampling technique allows for a dramatic reduction of the sample size. By using an exploratory method, we model the density from a large sample in the space of transition properties. The representative subset of nuclear configurations is optimized by minimizing its Kullback-Leibler divergence to the full density with simulated annealing. High-level calculations are then performed only for the selected subset of configurations. We tested the algorithm on electronic absorption spectra of three molecules: (E)-azobenzene, the simplest Criegee intermediate, and hydrated nitrate anion. Typically, dozens of nuclear configurations provided sufficiently accurate spectra. A strongly forbidden transition of the nitrate anion presented the most challenging case due to rare geometries with disproportionately high transition intensities. This problematic case was easily diagnosed within the present approach. We also discuss various exploratory methods and a possible extension to dynamical simulations.

Limits of the Nuclear Ensemble Method for Electronic Spectra Simulations: Temperature Dependence of the (E)-Azobenzene Spectrum.

We explore the range of applicability of the nuclear ensemble method (NEM) for quantitative simulations of absorption spectra and their temperature variations. We formulate a "good practice" for the NEM based on statistical theory. Special attention is paid to proper treatment of uncertainty estimation including the convergence with the number of samples, which is often neglected in the field. As a testbed, we have selected a well-known chromophore, (E)-azobenzene. We measured its temperature difference UV-vis absorption spectra in methanol, which displayed two dominant features: a moderate increase in the intensity of the nπ* band and a pronounced decrease in intensity of the low-energy part of the ππ* band. We attributed both features to increasing non-Condon effects with temperature. We show that the NEM based on the path integral molecular dynamics combined with range-separated hybrid functionals provides quantitatively accurate spectra and their differences. Experimentally, the depletion of the absorption in the ππ* band showed a characteristic vibrational progression that cannot be reproduced with the NEM. We show that hundreds of thousands of samples are necessary to achieve an accuracy sufficient for the unambiguous explanation of the observed temperature effects. We provide a detailed analysis of the temperature effects on the spectrum based on the harmonic model of the system combined with the NEM. We also rationalize the vibrational structure of the spectrum using the Franck-Condon principle.

Vibrationally Mediated Stabilization of Electrons in Nonpolar Matter.

We explore solvation of electrons in nonpolar matter, here represented by butadiene clusters. Isolated butadiene supports only the existence of transient anions (resonances). Two-dimensional electron energy loss spectroscopy shows that the resonances lead to an efficient vibrational excitation of butadiene, which can result into the almost complete loss of energy of the interacting electron. Cluster-beam experiments show that molecular clusters of butadiene form stable anions, however only at sizes of more than 9 molecular units. We have calculated the distribution of electron affinities of clusters using classical and path integral molecular dynamics simulations. There is almost a continuous transition from the resonant to the bound anions with an increase in cluster size. The comparison of the classical and quantum dynamics reveals that the electron binding is strongly supported by molecular vibrations, brought about by nuclear zero-point motion and thermal agitation. We also inspected the structure of the solvated electron, finding it well localized.

Do water's electrons care about electrolytes?

Ions have a profound effect on the geometrical structure of liquid water and an aqueous environment is known to change the electronic structure of ions. Here we combine photoelectron spectroscopy measurements from liquid microjets with molecular dynamical and quantum chemical calculations to address the reverse question, to what extent do ions affect the electronic structure of liquid water? We study aqueous solutions of sodium iodide (NaI) over a wide concentration range, from nearly pure water to 8 M solutions, recording spectra in the 5 to 60 eV binding energy range to include all water valence and the solute Na+ 2p, I- 4d, and I- 5p orbital ionization peaks. We observe that the electron binding energies of the solute ions change only slightly as a function of electrolyte concentration, less than 150 ± 60 meV over an ∼8 M range. Furthermore, the photoelectron spectrum of liquid water is surprisingly mildly affected as we transform the sample from a dilute aqueous salt solution to a viscous, crystalline-like phase. The most noticeable spectral changes are a negative binding energy shift of the water 1b2 ionizing transition (up to -370 ± 60 meV) and a narrowing of the flat-top shape water 3a1 ionization feature (up to 450 ± 90 meV). A novel computationally efficient technique is introduced to calculate liquid-state photoemission spectra using small clusters from molecular dynamics (MD) simulations embedded in dielectric continuum. This theoretical treatment captured the characteristic positions and structures of the aqueous photoemission peaks, reproducing the experimentally observed narrowing of the water 3a1 feature and weak sensitivity of the water binding energies to electrolyte concentration. The calculations allowed us to attribute the small binding energy shifts to ion-induced disruptions of intermolecular electronic interactions. Furthermore, they demonstrate the importance of considering concentration-dependent screening lengths for a correct description of the electronic structure of solvated systems. Accounting for electronic screening, the calculations highlight the minimal effect of electrolyte concentration on the 1b1 binding energy reference, in accord with the experiments. This leads us to a key finding that the isolated, lowest-binding-energy, 1b1, photoemission feature of liquid water is a robust energetic reference for aqueous liquid microjet photoemission studies.