Ab initio and quasiclassical trajectory study of the N(2D) + NO(X2Π) → O(1D) + N2(X1Σg+) reaction on the lowest 1 A' potential energy surface

In this work we have carried out ab initio electronic structure calculations, CASSCF/CASPT2 with the Pople's 6-311G(2d) basis set on the ground singlet potential energy surface (1 1A′ PES) involved in the title reaction. Transition states, minima and one 1 1A′/2 1A′ surface crossing have been characterized, obtaining three NNO isomers with the energy ordering: NNO (1Σ+)<cyclic−C2v NON(1A1)<NON(1Σ+g). Approximately 1250 ab initio points have been used to derive an analytical PES which fits most of the stationary points, with a global root-mean-square deviation of 1.12 kcal/mol. A quasiclassical trajectory study at several temperatures (300-1500 K) was performed to determine thermal rate constants, vibrational and rovibrational distributions and angular distributions. The dynamics of this barrierless reaction presents a predominant reaction pathway (96% at 300 K) with very short-lived collision complexes around the NNO minimum, which originate backward scattering and a similar fraction of vibrational and translational energy distributed into products. At higher temperatures other reaction pathways involving NON structures become increasingly important as well as the N-exchange reaction (3.02% of the branching ratio at 1500 K), this latter in accord with experimental data. It is concluded that the physical electronic quenching of N(2D) by NO should be negligible against all possible N(2D)+NO reaction channels

Ab initio ground potential energy surface (3A'') for the O(3P) + N2O reaction and kinetics study

An ab initio CASPT2//CASSCF study of the 3A' ground potential energy surface for the O(3P) + N2O(X1+) reaction has been performed, investigating the two predominant reactive channels. Symmetry breaking is reported for some of the structures. Rate constants are calculated by means of the transition state theory yielding values in almost quantitative agreement with experiment for the 2 NO(X2∏) channel, but at variance with experiment for the N2(X1g+) + O2(X3g-) one. A preliminary study on the possible existence of surface crossings (3A'-1A', 3A'-1A' and 3A'-3A' intersections! reveals that more efforts are warranted to fully explain the origin of this discrepancy

An empirical, yet practical way to predict the band gap in solids by using density functional band structure calculations

Band structure calculations based on density functional theory (DFT) with local or gradient-corrected exchange-correlation potentials are known to severely underestimate the band gap of semiconducting and insulating materials. Alternative approaches have been proposed: from semiempirical setups, such as the so-called DFT +U, to hybrid density functionals using a fraction of nonlocal Fock exchange, to modifications of semilocal density functionals. However, the resulting methods appear to be material dependent and lack theoretical rigor. The rigorous many-body perturbation theory based on GW methods provides accurate results but at a very high computational cost. Hereby, we show that a linear correlation between the electronic band gaps obtained from standard DFT and GW approaches exists for most materials and argue that (1) this is a strong indication that the problem of predicting band gaps from standard DFT calculation arises from the assignment of a physical meaning to the Kohn-Sham energy levels rather than from intrinsic errors of the DFT methods and (2) it provides a practical way to obtain GW-like quality results from standard DFT calculations. The latter will be especially useful for systems where the unit cell involves a large number of atoms as in the case of doped or defect-containing materials for which GW calculations become unfeasible

Morphology of TiO2 nanoparticles as fingerprint for the transient absorption spectra: implications for photocatalysis

Understanding the relationship between structural properties and the character of the charged carriers in photoactive TiO2 nanoparticles is fundamental to improving their photocatalytic activity. Transient absorption spectroscopy (TAS) is often used to explore the character of the charge carriers, but carrying out experiments on well-defined nanoparticles with a given morphology and selected size is extremely difficult. Here, hybrid time-dependent density functional theory based calculations carried out for realistic TiO2 nanoparticles (NPs) with bipyramidal, truncated, and spherical morphologies reveal that the electron-trapped carriers are quite sensitive to the NP morphology. In particular, these carriers are shallowly trapped in faceted NPs whereas they are deeply trapped in those exhibiting a spherical morphology. In addition, the simulated absorption spectra can be compared directly to experimental ones obtained by TAS, thus allowing additional information to be provided regarding the morphology of the TiO2 NPs in a given sample. Note that although the present study focuses on TiO2 nanoparticles, it can be easily extended to other photoactive materials such as ZnO or WO3 NPs thus allowing the extraction of information regarding the relationship between the NP morphology and the nature of the low-lying excited states

Investigating the character of excited states in TiO2 nanoparticles from topological descriptors: implications for photocatalysis

Titanium dioxide (TiO2) nanoclusters (NCs) and nanoparticles (NPs) have been the focus of intense research in recent years since they play a prominent role in photocatalysis. In particular, the properties of their excited states determine the photocatalytic activity. Among the requirements for photocatalytic activity, low excitation energy and large separation of the charge carriers are crucial. While information regarding the first is straightforward from either experiment or theory, the information regarding the second is scarce or missing. In the present work we fill this gap through a topological analysis of the first singlet excited state of a series of TiO2 NCs, and anatase and rutile derived NPs containing up to 495 atoms. The excited states of all these systems in vacuo have been obtained from time-dependent density functional theory (TDDFT) calculations using hybrid functionals and the influence of water was taken into account through a continuum model. Three different topological descriptors based on the attachment/detachment one-electron charge density, are scrutinized: (i) charge transfer degree, (ii) charge density overlap, and (iii) distance between centroids of charge. The present analysis shows that the charge separation in the excited state strongly depends on the NP size and shape. The character of the electronic excitations, as arising from the analysis of the canonical Kohn-Sham molecular orbitals (MOs) or from natural transition orbitals (NTOs), is also investigated. The understanding and prediction of charge transfer and recombination in TiO2 nanostructures may have implications in the rational design of these systems to boost their photocatalytic potential

Electronic properties of realistic anatase TiO2 nanoparticles from G(0)W(0) calculations on a Gaussian and plane waves scheme

The electronic properties of realistic (TiO2)n nanoparticles (NPs) with cuboctahedral and bipyramidal morphologies are investigated within the many-body perturbation theory (MBPT) G0W0 approximation using PBE and hybrid PBEx (12.5% Fock contribution) functionals as starting points. The use of a Gaussian and plane waves (GPW) scheme reduces the usual O4 computational time required in this type of calculation close to O3 and thus allows considering explicitly NPs with n up to 165. The analysis of the Kohn-Sham energy orbitals and quasiparticle (QP) energies shows that the optical energy gap (Ogap), the electronic energy gap (Egap), and the exciton binding energy (ΔEex) values decrease with increasing TiO2 NP size, in agreement with previous work. However, while bipyramidal NPs appear to reach the scalable regime already for n = 84, cuboctahedral NPs reach this regime only above n = 151. Relevant correlations are found and reported that will allow one to predict these electronic properties at the G0W0 level in even much larger NPs where these calculations are unaffordable. The present work provides a feasible and practical way to approach the electronic properties of rather large TiO2 NPs and thus constitutes a further step in the study of realistic nanoparticles of semiconducting oxides

Theoretical modeling of electronic excitations of gas-phase and solvated TiO2 nanoclusters and nanoparticles of interest in photocatalysis

The optical absorption spectra of (TiO2)n, nanoclusters (n = 1-20) and nanoparticles (n = 35, 84) have been calculated from the frequency-dependent dielectric function in the independent particle approximation under the framework of density functional theory. The PBE generalized gradient approach based functional, the so-called PBE+U method and the PBE0 and PBEx hybrid functionals containing 25% and 12.5% of nonlocal Fock exchange, respectively have been used. The simulated spectra have been obtained in the gas phase and in water on previously PBE0 optimized atomic structures. The effect of the solvent has been accounted for by using an implicit water solvation model. For the smallest nanoclusters, the spectra show discrete peaks, whereas for the largest nanoclusters and for the nanoparticles they resemble a continuum absorption band. In the gas phase and for a given density functional, the onset of the absorption (optical gap, Ogap) remains relatively constant for all nanoparticle sizes although it increases with the percentage of nonlocal Fock exchange, as expected. For all tested functionals, the tendency of Ogap in water is very similar to that observed in the gas phase with an almost constant upshift. For comparison, the optical gap has also been calculated at the TD-DFT level with the PBEx functional in the gas phase and in water. Both approaches agree reasonably well although the TD-DFT gap values are lower than those derived from the dielectric-function. Overall, the position of the spectral maxima and the width of the spectra are relatively constant and independent of particle size which may have implications in the understanding of photocatalysis by TiO2

Theoretical investigation of the eight low-lying electronic states of the cis- and trans-nitric oxide dimers and its isomerization using multiconfigurational second-order perturbation theory (CASPT2)

In this work we have carried out ab initio electronic structure calculations, CASSCF/CASPT2 and CASSCF/MRCI-SD+Q with several Pople's and correlation-consistent Dunning's basis sets, of the planar cis- and trans-NO dimers for the lowest eight electronic (singlet and triplet) states. The geometry, frequencies, dipole moment, binding energy, and vertical excitation energies are predicted with an accuracy close to or even better than the best reported ab initio previous results for some of these properties, and in very good agreement with the available experimental data. CASPT2 optimized geometries show the existence of at least four shallow NO-dimers (i.e., two cis-(NO)2 (1A1 and 3B2) and two trans-(NO)2 (1Ag and 3Au)), although CASSCF optimization with CASPT2 pointwise calculations indicate the existence of other less stable dimers, on the excited states. Vertical excitation energies were calculated for these four dimers. For the cis-NO dimer, the ordering and the energy spacings between the excited states (i.e., 1A1, 3B2, 1B2, 2nd 1A1, 1A2, 3A2, 3B1, 2nd 3B1) are very similar to those found in a recent MRCI-SD study. The singlet cis-NO dimer (1A1) is the most stable one in almost quantitative accord with the experimental data, and in disagreement with previous density functional theory studies. A nonplanar transition state for the singlet trans ↔ cis isomerization has also been fully characterized. This leads to an almost negligible energy barrier which would originate a rapid isomerization to the most stable cis-NO dimer at low temperatures, in accord with the experimental difficulties to measure the properties of the trans-NO dimer. Not only are basis set superposition error corrections necessary to evaluate accurately the binding energies, but also to determine the NN distance of these symmetrical dimers. Some problems regarding the symmetry of the wave function were found for the symmetrical NO dimers and for the NO+NO asymptote, and several approximate solutions were proposed

Ab initio 1A' ground potential energy surface and transition state theory kinetics study of the O(1D) + N2O → 2NO, N2 +O2(a1Δg) reactions

An ab initio study of the 1A' ground potential energy surface (PES) of the O(1D) + N2O(X1+) system has been performed at the CASPT2//CASSCF (complete active space second-order perturbation theory//complete active space self-consistent field) level with Pople basis sets. The two reactions leading to 2 NO(X2) [reaction (1)] and N2(X1g+) + O2(a1∆g) [reaction (2)] products have been investigated. In both reactions a trans-approach of the attacking oxygen to the N2O moiety is found to be preferred, more markedly in reaction (1). For this reaction also a cis-path is feasible and is possibly connected with the trans -path by a transition state placed below reactants. A thorough characterization of the entrance zone has been performed to allow for subsequent kinetics calculations. Fixed angle and minimum energy paths have been constructed and transition state geometries have been refined at the CASPT2 level, thus obtaining approximate structures and frequencies for the latter. From these calculations it can be inferred that both reactions proceed without an energy barrier. Rate constant calculations in the 100-1000 K temperature range based on CASPT2 structures and using the transition state theory yield values in good agreement with experiment for the two reactions, especially when a proper scaling of the energy barriers is performed. Also, for comparative purposes quasiclassical trajectory calculations were performed on reaction (1) in the same temperature range, using a previous pseudotriatomic analytical potential energy surface, obtaining good agreement with experiment

Barnes Update Applied in the Gauss−Newton Method: An Improved Algorithm to Locate Bond Breaking Points

A mechanochemical reaction is a reaction induced by mechanical energy. A general accepted model for this type of reactions consists in a first order perturbation on the associated potential energy surface (PES) of the unperturbed molecular system due to mechanical stress or pulling force. Within this theoretical framework, the so-called optimal barrier breakdown points or optimal bond breaking points (BBPs) are critical points of the unperturbed PES where the Hessian matrix has a zero eigenvector that coincides with the gradient vector. Optimal BBPs are 'catastrophe points' that are par- ticularly important because its associated gradient indicates how to optimally harness tensile forces to induce reactions by transforming a chemical reaction into a barrierless process. Building on a previous method based on a nonlinear least squares minimiza- tion to locate BBPs (Bofill et al., J. Chem. Phys. 2017, 147, 152710-10), we propose a new algorithm to locate BBPs of any molecular system based on the Gauss-Newton method combined with the Barnes update for the nonsymmetric Jacobian matrix, which is shown to be more appropriate than the Broyden update. The efficiency of the new method is demonstrated for a multidimensional model PES and two medium size molec- ular systems of interest in enzymatic catalysis and mechanochemistry