Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

Structures and Spectroscopic Properties of Polysulfide Radical Anions: A Theoretical Perspective

The potential involvement of polysulfide radical anions Sn•- is a recurring theme in discussions of the basic and applied chemistry of elemental sulfur. However, while the spectroscopic features for n = 2 and 3 are well-established, information on the structures and optical characteristics of the larger congeners (n = 4-8) is sparse. To aid identification of these ephemeral species we have performed PCM-corrected DFT calculations to establish the preferred geometries for Sn•- (n = 4-8) in the polar media in which they are typically generated. TD-DFT calculations were then used to determine the number, nature and energies of the electronic excitations possible for these species. Numerical reliability of the approach was tested by comparison of the predicted and experimental excitation energies found for S2•- and S3•-. The low-energy (near-IR) transitions found for the two acyclic isomers of S4•- (C2h and C2v symmetry) and for S5•- (Cs symmetry) can be understood by extension of the simple HMO π-only chain model that serves for S2•- and S3•-. By contrast, the excitations predicted for the quasi-cyclic structures Sn•- (n = 6-8) are better described in terms of σ → σ* processes within a localized 2c-3e manifold.

Probing Intermolecular H-Bonding Interactions in Cyanuric Acid Networks: Quenching of the N K-Edge Sigma Resonances

The electronic characterization of the cyanuric acid both in gas phase and when embedded within an H-bonded scheme forming a monolayer on the Au(111) surface has been performed by means of X-ray Photoelectron Spectroscopy (XPS) and Near Edge X-ray Absorption Fine Structure (NEXAFS) spectroscopy. The experimental spectra at the N, O, and C K-edges have been assigned with the support of DFT calculations, and the combination between theory and experiment has allowed to us investigate the effect of the H-bonding intermolecular interaction on the spectra. In particular, the H-bond formation in the monolayer leads to a quenching of the N 1s NEXAFS resonances associated with transitions to the sigma empty orbitals localized on the N–H portion of the imide group. On the other hand, the π* empty states remain substantially unperturbed. From a computational point of view, it has been shown that the DFT-TP scheme is not able to describe the N 1s NEXAFS spectra of these systems, and the configuration mixing has to be included, through the TDDFT approach in conjunction with the range-separated XC CAM-B3LYP functional, to obtain a correct reproduction of the N 1s core spectra.

Carbon and Nitrogen K-Edge NEXAFS Spectra of Indole, 2,3-Dihydro-7-azaindole, and 3-Formylindole

The near-edge X-ray absorption fine structure (NEXAFS) spectra of indole, 2,3-dihydro-7-azaindole, and 3-formylindole in the gas phase have been measured at the carbon and nitrogen K-edges. The spectral features have been interpreted based on density functional theory (DFT) calculations within the transition potential (TP) scheme, which is accurate enough for a general description of the measured C 1s NEXAFS spectra as well as for the assignment of the most relevant features. For the nitrogen K-edge, the agreement between experimental data and theoretical spectra calculated with TP-DFT was not quite satisfactory. This discrepancy was mainly attributed to the many-body effects associated with the excitation of the core electron, which are better described using the time-dependent density functional theory (TDDFT) with the range-separated hybrid functional CAM-B3LYP. An assignment of the measured N 1s NEXAFS spectral features has been proposed together with a complete description of the observed resonances. Intense transitions from core levels to unoccupied antibonding π* states as well as several transitions with mixed-valence/Rydberg or pure Rydberg character have been observed in the C and N K-edge spectra of all investigated indoles.

Analysis of the kinetic energy functional in the generalized gradient approximation

A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

Valence ππ* Excitations in Benzene Studied by Multiconfiguration Pair-Density Functional Theory

We explore the valence singlet and triplet ππ* excitations of benzene with complete active pace self-consistent field (CASSCF) theory, complete active space perturbation theory (CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT) for four different choices of active space. We propose a new way to quantify the covalent and ionic character of the electronic states in terms of the components of the total electronic energy. We also explore the effect of scaling the exchange and correlation components of the on-top density functional used in MC-PDFT; we observe that increasing the exchange contribution improves the MC-PDFT excitation energies for benzene.

Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance

We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches. NCAP is constructed by reconsidering the imposition of the asymptotic correctness of the X potential (-1/ r) as a constraint. Inclusion of derivative discontinuity and approximate integer self-interaction correction treatments along with first-principles determination of the effective second-order gradient expansion coefficient yields a major advance over our earlier correct asymptotic potential functional [CAP; J. Chem. Phys. 2015 , 142 , 054105 ]. The new functional reduces a spurious bump in the CAP atomic exchange potential and moves it to distances irrelevantly far from the nucleus (outside the tail of essentially all practical basis functions). It therefore has nearly correct atomic exchange-potential behavior out to rather large finite distances r from the nucleus but eventually goes as - c/ r with an estimated value for the constant c of around 0.3, so as to achieve other important properties of exact DFT exchange within the restrictions of the GGA form. We illustrate the results with the Ne atom optimized effective potentials and with standard molecular benchmark test data sets for thermochemical, structural, and response properties.

The ring-opening channel and the influence of Rydberg states on the excited state dynamics of furan and its derivatives

One important relaxation pathway for photo-excited five-membered heterocyclic organic molecules is ring-opening via a dissociative πσ^* state. In this study, we investigate the influence of this pathway in furan and several hydrogenated and methylated derivatives by combining time-resolved photoelectron spectroscopy with time-dependent density functional theory and coupled cluster calculations. We find strong experimental evidence that the ring-opening channel is the major relaxation channel in furan, 2,3-dihydrofuran, and 2-methylfuran (2-MF). In 2,5-dimethylfuran (25-DMF), however, we observe that the molecules relax either via a π3s Rydberg state or through a direct return to the ground state by undergoing ring-puckering motions. From the supporting calculations, for 2-MF and 25-DMF, we predict that there is strong mixing between the πσ^* state and the π3s Rydberg state along the ring opening pathway. However, in 25-DMF, no crossing between the πσ^*/π3s state and the initially excited ππ^* state can be found along the ring opening coordinate, effectively blocking this channel.

TD DFT insights into unusual properties of excited sandwich complexes: structural transformations and vibronic interactions in Rydberg-state bis(η6-benzene)chromium

TD DFT calculations reveal specific features of the Jahn–Teller effect in the lowest Rydberg p state of a prototypical sandwich molecule.

HLE16: A Local Kohn-Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies

Local exchange-correlation functionals have low cost and convenient portability but are known to seriously underestimate semiconductor band gaps and the energies of molecular Rydberg states. Here we present a new local approximation to the exchange-correlation functional called HLE16 that gives good performance for semiconductor band gaps and molecular excitation energies and is competitive with hybrid functionals. By the simultaneous increase of the local exchange and decrease of the local correlation, electronic excitation energies were improved without excessively degrading the ground-state solid-state cohesive energies, molecular bond energies, or chemical reaction barrier heights, although the new functional is not recommended for optimizing lattice constants or molecular bond lengths. The new functional can be useful as-is for calculations on semiconductors or excited states where it is essential to control the cost, and it can also be useful in establishing a starting point for developing even better new functionals that perform well for excited states.

Dependence of Adenine Raman Spectrum on Excitation Laser Wavelength: Comparison between Experiment and Theoretical Simulations

We acquired the Raman spectra of adenine in powder and aqueous phase using excitation lasers with 532, 633, and 785 nm wavelengths for the region between 300 and 1500 cm^-1. In comparison to the most distinct peak at 722 cm^-1, the peaks between 1200 and 1500 cm^-1 exhibited a characteristic increase in cross-section with decreasing excitation wavelength in both phases. This trend can be reproduced by different density functional theory (DFT) calculations for the adenine molecule in the gas phase as well as in the aqueous phase. Furthermore, from the calculation on the π-stacked dimer, hydrogen-bonded dimer, and trimer, we find that this trend toward excitation laser wavelength is not sensitive to the packing. When comparing the Raman spectra given by different excitation wavelength, one should take care in analyzing the cross-section, and present day DFT calculations are able to capture general trends in the excitation laser wavelength dependence of the Raman activity.

MN15: A Kohn-Sham global-hybrid exchange-correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions

Kohn-Sham density functionals are widely used; however, no currently available exchange-correlation functional can predict all chemical properties with chemical accuracy. Here we report a new functional, called MN15, that has broader accuracy than any previously available one. The properties considered in the parameterization include bond energies, atomization energies, ionization potentials, electron affinities, proton affinities, reaction barrier heights, noncovalent interactions, hydrocarbon thermochemistry, isomerization energies, electronic excitation energies, absolute atomic energies, and molecular structures. When compared with 82 other density functionals that have been defined in the literature, MN15 gives the second smallest mean unsigned error (MUE) for 54 data on inherently multiconfigurational systems, the smallest MUE for 313 single-reference chemical data, and the smallest MUE on 87 noncovalent data, with MUEs for these three categories of 4.75, 1.85, and 0.25 kcal mol-1, respectively, as compared to the average MUEs of the other 82 functionals of 14.0, 4.63, and 1.98 kcal mol-1. The MUE for 17 absolute atomic energies is 7.4 kcal mol-1 as compared to an average MUE of the other 82 functionals of 34.6 kcal mol-1. We further tested MN15 for 10 transition-metal coordination energies, the entire S66x8 database of noncovalent interactions, 21 transition-metal reaction barrier heights, 69 electronic excitation energies of organic molecules, 31 semiconductor band gaps, seven transition-metal dimer bond lengths, and 193 bond lengths of 47 organic molecules. The MN15 functional not only performs very well for our training set, which has 481 pieces of data, but also performs very well for our test set, which has 823 data that are not in our training set. The test set includes both ground-state properties and molecular excitation energies. For the latter MN15 achieves simultaneous accuracy for both valence and Rydberg electronic excitations when used with linear-response time-dependent density functional theory, with an MUE of less than 0.3 eV for both types of excitations.

Assessment of the LFAs-PBE exchange–correlation potential for high-order harmonic generation of aligned H2+ molecules

We examine the performance of the LFAs-PBE exchange-correlation potential for the HHG spectra and related properties of H₂⁺ molecules aligned parallel and perpendicular to the polarization of an intense linearly polarized laser pulse.

Multiconfiguration Pair-Density Functional Theory Spectral Calculations Are Stable to Adding Diffuse Basis Functions

Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.