Prediction Of Excitation Energies Research Articles

Predicting excitation energies in warm and hot dense matter.

In a dense plasma environment, the energy levels of an ion shift relative to the isolated ion values. This shift is reflected in the optical spectrum of the plasma and can be measured in, for example, emission experiments. In this work we use a recently developed method of modeling electronic states in warm dense matter to predict these level energies. In this model excited state energies are calculated directly by enforcing constrained one-electron occupation factors, thus allowing the calculation of specific transition and ionization energies. This model includes plasma effects self-consistently, so the effect of continuum lowering is included in an ab initio sense. We use the model to calculate the K-edge and K-alpha energies of solid density magnesium, aluminum, and silicon over a range of temperatures, finding close agreement with experimental results. We also calculate the ionization potential depression to compare to widely used models and investigate the effects of temperature on the lowering of the continuum.

Predicting Solvatochromism of Chromophores in Proteins through QM/MM and Machine Learning.

Solvatochromism occurs in both homogeneous solvents and more complex biological environments, such as proteins. While in both cases the solvatochromic effects report on the surroundings of the chromophore, their interpretation in proteins becomes more complicated not only because of structural effects induced by the protein pocket but also because the protein environment is highly anisotropic. This is particularly evident for highly conjugated and flexible molecules such as carotenoids, whose excitation energy is strongly dependent on both the geometry and the electrostatics of the environment. Here, we introduce a machine learning (ML) strategy trained on quantum mechanics/molecular mechanics calculations of geometrical and electrochromic contributions to carotenoids' excitation energies. We employ this strategy to compare solvatochromism in protein and solvent environments. Despite the important specifities of the protein, ML models trained on solvents can faithfully predict excitation energies in the protein environment, demonstrating the robustness of the chosen descriptors.

Ab initio calculations for well deformed nuclei: 40Mg and 42Si

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around N=28, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of 40Mg, 42Si, and 44S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that 40Mg and 42Si exhibit large deformations. After that, the erosion of the N=28 shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in N=28 even-even isotones ranging from 40Mg to 48Ca. Finally, the shell evolution of N=28 in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of 40Mg and 42Si.

Combining Renormalized Singles GW Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies.

We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the GRSWRS method, which uses the RS Green's function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS approach significantly outperforms BSE/G0W0 for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/GRSWRS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach.

Computational Discovery of TTF Molecules with Deep Generative Models.

We present a computational workflow based on quantum chemical calculations and generative models based on deep neural networks for the discovery of novel materials. We apply the developed workflow to search for molecules suitable for the fusion of triplet-triplet excitations (triplet-triplet fusion, TTF) in blue OLED devices. By applying generative machine learning models, we have been able to pinpoint the most promising regions of the chemical space for further exploration. Another neural network based on graph convolutions was trained to predict excitation energies; with this network, we estimate the alignment of energy levels and filter molecules before running time-consuming quantum chemical calculations. We present a comprehensive computational evaluation of several generative models, choosing a modification of the Junction Tree VAE (JT-VAE) as the best one in this application. The proposed approach can be useful for computer-aided design of materials with energy level alignment favorable for efficient energy transfer, triplet harvesting, and exciton fusion processes, which are crucial for the development of the next generation OLED materials.

Reliable transition properties from excited-state mean-field calculations.

Delta-self-consistent field (ΔSCF) theory is a conceptually simple and computationally inexpensive method for finding excited states. Using the maximum overlap method to guide optimization of the excited state, ΔSCF has been shown to predict excitation energies with a level of accuracy that is competitive with, and sometimes better than, that of time-dependent density functional theory. Here, we benchmark ΔSCF on a larger set of molecules than has previously been considered, and, in particular, we examine the performance of ΔSCF in predicting transition dipole moments, the essential quantity for spectral intensities. A potential downfall for ΔSCF transition dipoles is origin dependence induced by the nonorthogonality of ΔSCF ground and excited states. We propose and test a simple correction for this problem, based on symmetric orthogonalization of the states, and demonstrate its use on bacteriochlorophyll structures sampled from the photosynthetic antenna in purple bacteria.

New insights for titanium(iv) speciation in acidic media based on UV-visible and 31P NMR spectroscopies and molecular modeling.

Titanium chemistry in aqueous acidic media has been extensively investigated over the last decades. Hydrolyzed species such as Ti(OH)3+, TiO2+, Ti(OH)22+ or Ti(OH)3+ have been identified and their equilibria have been studied in nitric and perchloric acid. A predominance of the divalent cations was found for low pH (i.e., pH <2). Nonetheless, recent literature reports the existence of small titanium oxo-clusters in aqueous acidic media for large titanium(iv) concentration (typically., >0.1 mol L−1), as stable precursors for the formation of condensed titanium dioxide. The present paper reconsiders firstly previous knowledge about the speciation of titanium(iv) in non-complexing acidic media by giving evidence for the presence of polynuclear hydrolyzed species, even at very low Ti(iv) concentration (i.e., typically <0.1 mmol L−1). UV-visible absorbance spectra recorded for diluted nitric acid solutions (a model of non-complexing acidic medium) containing titanium(iv) were compared to time-dependent density functional theory (TD-DFT) predicted excitation energies. Experimental and predicted maximal absorbance wavelengths showed significantly improved matches when polynuclear species were considered in TD-DFT calculation. Then, 0.1–12.7 mol L−1 phosphoric acid solutions containing titanium(iv) were studied by means of spectroscopic techniques (UV-visible, NMR) in order to identify qualitatively the presence of titanium(iv) complexes and to link this speciation to the acid concentration. Two different titanium(iv) orthophosphate complexes, potentially polynuclear, were detected, and the presence of free titanium(iv) is also expected for low phosphoric acid concentration (i.e., <0.1 mol L−1). A general complexation scheme for a large range of H3PO4 concentration was thus formulated.

Dipole Moment Variation Clears Up Electronic Excitations in the π-Stacked Complexes of Fluorescent Protein Chromophores.

We propose a quantitative structure-property relationship (QSPR) model for prediction of spectral tuning in cyan, green, orange, and red fluorescent proteins, which are engineered by motifs of the green fluorescent protein. Protein variants, in which their chromophores are involved in the π-stacking interaction with amino acid residues tyrosine, phenylalanine, and histidine, are prospective markers useful in bioimaging and super-resolution microscopy. In this work, we constructed training sets of the π-stacked complexes of four fluorescent protein chromophores (of the green, orange, red, and cyan series) with various substituted benzenes and imidazoles and tested the use of dipole moment variation upon excitation (DMV) as a descriptor to evaluate the vertical excitation energies in these systems. To validate this approach, we computed and analyzed electron density distributions of the π-stacked complexes and correlated the QSPR predictions with the reference values of the transition energies obtained using the high-level ab initio quantum chemistry methods. According to our results, the use of the DMV descriptor allows one to predict excitation energies in the π-stacked complexes with errors not exceeding 0.1 eV, which makes this model a practically useful tool in the development of efficient fluorescent markers for in vivo imaging.

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations.

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT.

Synthesis, electronic structure and NH-tautomerism of novel mono- and dibenzoannelated phthalocyanines

Novel low-symmetry benzoannelated metal-free phthalocyanines of A3B-, ABAB- and AABB-types were synthesized by statistical condensation of phthalonitrile bearing bulky solubilizing groups (fragment A) and new naphthalonitrile with OH-terminated diethylene glycol anchors (fragment B). Comprehensive physical-chemical characterization of the synthesized macrocycles allowed to reveal the electronic effects associated with the extension of π-system. The interpretation of the observed effects was performed by theoretical calculations where simplified TD-DFT approach at CAM-B3LYP/6-31G(d) level was successfully used for the first time to predict excitation energies of Q-band region in UV–Vis spectra of low-symmetry phthalocyanines with errors not exceeding 0.03 eV. Altogether it allowed to identify the spectroscopic signatures of various tautomers including energy-unfavourable forms.

Excitons in Solids from Periodic Equation-of-Motion Coupled-Cluster Theory.

We present an ab initio study of electronically excited states of three-dimensional solids using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The explicit use of translational symmetry, as implemented via Brillouin zone sampling and momentum conservation, is responsible for a large reduction in cost. Our largest system studied, which samples the Brillouin zone using 64 k-points (a 4 × 4 × 4 mesh), corresponds to a canonical EOM-CCSD calculation of 768 electrons in 640 orbitals. We study eight simple main-group semiconductors and insulators, with direct singlet excitation energies in the range of 3 to 15 eV. Our predicted excitation energies exhibit a mean signed error of 0.24 eV and a mean absolute error of 0.27 eV when compared to experimental values. Although this error is similar to that found for EOM-CCSD applied to molecules, it may also reflect the role of vibrational effects, which are neglected in the calculations. Our results support recently proposed revisions of experimental optical gaps for AlP and cubic BN. We furthermore calculate the energy of excitons with nonzero momentum and compare the exciton dispersion of LiF with experimental data from inelastic X-ray scattering. By calculating excitation energies under strain, we extract hydrostatic deformation potentials to quantify the strength of interactions between excitons and acoustic phonons. Our results indicate that coupled-cluster theory is a promising method for the accurate study of a variety of exciton phenomena in solids.

Capturing multireference excited states by constrained-density-functional theory

The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean field method that extends the previously proposed eXcited Constrained DFT (XCDFT) from single Slater determinants to ensemble 1-RDMs for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal DFT calculation while at the same time is capable of approaching states with multireference character. We benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal TDDFT.

Efficient determination of excitation energies and absorption spectra for quantum dots and large systems from ab initio data

A semi-empirical Hamiltonian with the INDO approximation and CIS was parameterized to reproduce EOM-CCSD excitation energies for diatomic silicon Si2 with different inter-atomic separations. The model Hamiltonian is transferable, producing excitation energies for clusters, Sin(n=3,4,5) with mean absolute errors (MAEs) of 0.26, 0.18, and 0.09 eV, respectively, from the EOM-CCSD energies. The absorption spectra are also in qualitative agreement with the EOM-CCSD spectra. For clusters Si19 and Si40, comparison with TDDFT gave MAEs of 0.32 and 0.12 eV, respectively. Predictions of excitation energies and absorption spectra are also given for Sin (n=124,147,172,779) using the model Hamiltonian.

Searching for states analogous to the C12 Hoyle state in heavier nuclei using the thick target inverse kinematics technique

Identification of alpha cluster states analogous to the 12C Hoyle state in heavier alpha- conjugate nuclei can provide tests of the existence of alpha condensates in nuclei. Such states are predicted for 16O, 20Ne, 24Mg, 28Si etc. at excitation energies slightly above the multi-alpha particle decay threshold, but have not yet been experimentally identified. The Thick Target Inverse Kinematics (TTIK) technique can be used to study the breakup of excited self-conjugate nuclei into many alpha particles. The reaction 20Ne+{\alpha} was studied using a 20Ne beam at 12 MeV/nucleon from the K150 cyclotron at Texas A&M University. The TTIK method was used to study both single {\alpha}-particle emission and multiple {\alpha}-particle decays. Events with alpha multiplicity up to four were analyzed. The analysis of the three {\alpha} - particle emission data allowed the identification of the Hoyle state and other 12C excited states decaying into three alpha particles. The results are shown and compared with other data available in the literature. Although the statistics for events with alpha multiplicity four is low, the data show a structure at about 15.2 MeV that could indicate the existence in 16O of a state analogous to the 12C Hoyle state. This structure is confirmed by the re-analysis of alpha multiplicity four events from a previous experiment performed at 9.7 MeV/nucleon with a similar setup but lower granularity. Moreover, the reconstructed excitation energy of 24Mg for these events peaks at around 34 MeV, very close to the predicted excitation energy for an excited state analogous to the 12C Hoyle state in 24Mg.

Low-lying excited states by constrained DFT.

Exploiting the machinery of Constrained Density Functional Theory (CDFT), we propose a variational method for calculating low-lying excited states of molecular systems. We dub this method eXcited CDFT (XCDFT). Excited states are obtained by self-consistently constraining a user-defined population of electrons, Nc, in the virtual space of a reference set of occupied orbitals. By imposing this population to be Nc = 1.0, we computed the first excited state of 15 molecules from a test set. Our results show that XCDFT achieves an accuracy in the predicted excitation energy only slightly worse than linear-response time-dependent DFT (TDDFT), but without incurring into problems of variational collapse typical of the more commonly adopted ΔSCF method. In addition, we selected a few challenging processes to test the limits of applicability of XCDFT. We find that in contrast to TDDFT, XCDFT is capable of reproducing energy surfaces featuring conical intersections (azobenzene and H3) with correct topology and correct overall energetics also away from the intersection. Venturing to condensed-phase systems, XCDFT reproduces the TDDFT solvatochromic shift of benzaldehyde when it is embedded by a cluster of water molecules. Thus, we find XCDFT to be a competitive method among single-reference methods for computations of excited states in terms of time to solution, rate of convergence, and accuracy of the result.

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo.

In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states' accuracies become desirable. As a direct measure of a wave function's accuracy, the energy variance offers one route to achieving such a balance. Here, we develop and test a variance matching approach for predicting excitation energies within the context of variational Monte Carlo and selective configuration interaction. In a series of tests on small but difficult molecules, we demonstrate that the approach is effective at delivering accurate excitation energies when the wave function is far from the exhaustive flexibility limit. Results in C3, where we combine this approach with variational Monte Carlo orbital optimization, are especially encouraging.

No single DFT method can predict Raman cross-sections, frequencies and electronic absorption maxima of oligothiophenes

Density functional theory (DFT) is a popular method for modeling the properties of organic photovoltaic materials. The ability of various functionals to predict the electronic absorption and Raman spectra of oligothiophenes is assessed. Time-Dependent DFT (TD-DFT) is commonly used for modeling electron absorption spectra but often gives spurious results. We show here that a linear relationship between the percentage of Hartree–Fock exchange (%HF) used by a density functional and the predicted excitation energy exists. This allows for tuning of hybrid functionals which can accurately predict the bandgap of four different oligothiophenes. For instance, 33% HF is required for a four unit oligothiophene which absorbs at 379nm (3.27eV) while 46% HF is required for a ten unit oligothiophene absorbing at 458nm (2.71eV). Raman spectroscopy is also used to understand conjugation in highly conjugated molecules. The Raman scattering cross-sections and frequencies of the same four oligothiophenes were measured and compared to those modeled by DFT. We show that the DFT models tuned to correctly the visible absorption bands overestimate the Raman cross-sections and underestimate their frequencies. These results should be taken into account when modeling future conjugated materials.

Phase transition studies of the odd-mass 123−135Xe isotopes based on SU(1,1) algebra in IBFM

In this paper, we have investigated the positive-parity states in the odd-mass transitional [Formula: see text]Xe isotopes within the framework of the interacting boson–fermion model. Two solvable extended transitional Hamiltonians which are based on SU(1,1) algebra are employed to provide an investigation of quantum phase transition (QPT) between the spherical and deformed gamma — unstable shapes along the chain of Xe isotopes. The low-states energy spectra and B(E2) values for these nuclei have been calculated and compared with the experimental data. The predicted excitation energies and B(E2) transition rates of the odd isotopes are found to agree well with the experimental data. We have also analyzed the critical behavior of even–odd Xe isotopes via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces and special isotopes which are the best candidates for the critical point are identified.

An integrated first principles and experimental investigation of the relationship between structural rigidity and quantum efficiency in phosphors for solid state lighting

We outline an integrated approach for exploring novel near-UV excited phosphors. To test the hypothesis of whether high host structural rigidity results in phosphors with high quantum efficiency (Φ), we calculated the Debye temperatures (Θ) for 27 host materials using density functional theory calculations. We identified Eu2+-activated Ca7Mg(SiO4)4 and CaMg(SiO3)2 as having a relatively high Θ=601K and 665K, respectively, and predicted excitation energies of 3.18eV (337nm) and 3.29eV (377nm), respectively, both of which are in good agreement with the results of photoluminescence spectroscopy. However, the measured Φ for these two phosphors was < 30%, which indicates that Θ alone is not a sufficient condition for a high Φ. This work demonstrates the potential of combined first-principles calculations and experiments in the discovery and design of novel near-UV excited phosphors.

Sticking to (first) principles: quantum molecular dynamics and Bayesian probabilistic methods to simulate aquatic pollutant absorption spectra.

This work explores the relationship between theoretically predicted excitation energies and experimental molar absorption spectra as they pertain to environmental aquatic photochemistry. An overview of pertinent Quantum Chemical descriptions of sunlight-driven electronic transitions in organic pollutants is presented. Second, a combined molecular dynamics (MD), time-dependent density functional theory (TD-DFT) analysis of the ultraviolet to visible (UV-Vis) absorption spectra of six model organic compounds is presented alongside accurate experimental data. The functional relationship between the experimentally observed molar absorption spectrum and the discrete quantum transitions is examined. A rigorous comparison of the accuracy of the theoretical transition energies (ΔES0→Sn) and oscillator strength (fS0→Sn) is afforded by the probabilistic convolution and deconvolution procedure described. This method of deconvolution of experimental spectra using a Gaussian Mixture Model combined with Bayesian Information Criteria (BIC) to determine the mean (μ) and standard deviation (σ) as well as the number of observed singlet to singlet transition energy state distributions. This procedure allows a direct comparison of the one-electron (quantum) transitions that are the result of quantum chemical calculations and the ensemble of non-adiabatic quantum states that produce the macroscopic effect of a molar absorption spectrum. Poor agreement between the vertical excitation energies produced from TD-DFT calculations with five different functionals (CAM-B3LYP, PBE0, M06-2X, BP86, and LC-BLYP) suggest a failure of the theory to capture the low energy, environmentally important, electronic transitions in our model organic pollutants. However, the method of explicit-solvation of the organic solute using the quantum Effective Fragment Potential (EFP) in a density functional molecular dynamics trajectory simulation shows promise as a robust model of the hydrated organic pollutant. Furthermore, the described protocol can be extended using higher-level equilibration and vertical excitation methods to increase the numerical accuracy and describe multi-reference electronic transitions. Finally, a measure of the accuracy of theoretically derived absorption spectra is discussed as a tool to further develop our capacity to produce accurate a priori simulations of sunlight-driven photochemistry in natural waters.