This work describes a program for computing and analyzing the ultrafast (attosecond and femtosecond) nonlinear X-ray spectra of molecules at the multiconfigurational quantum chemistry level, called MCNOX. It is aimed at cutting-edge current and future photochemistry/photophysics applications enabled by X-ray free-electron lasers and high harmonic generation light sources. It can compute steady-state X-ray absorption spectroscopy (XAS) and three types of ultrafast nonlinear X-ray spectra: transient XAS, all-X-ray four-wave mixing, and stimulated Raman spectra. It is especially capable of picking out major electronic transitions, and further computing the natural transition orbitals for these transitions, which help finally yield the physical and chemical insights from complex signals. Following a research paradigm of "electronic structure-*molecular dynamics-*signal", in this paper, methods for the former two steps are reviewed, and then the theory, implementations, and technical details for signal simulations are presented along illustrative examples on uracil.

Vibrationally resolved C 1s X-ray photoelectron spectra (XPS) of a series of six polycyclic aromatic hydrocarbons (PAHs; phenanthrene, coronene, naphthalene, anthracene, tetracene, and pentacene) were computed by combining the full core hole density functional theory and the Franck–Condon simulations with the inclusion of the Duschinsky rotation effect. Simulated spectra of phenanthrene, coronene, and naphthalene agree well with experiments both in core binding energies (BEs) and profiles, which validate the accuracy of our predictions for the rest molecules with no high-resolution experiments. We found that three types of carbons i (inner C), p (peripheral C bonded to three C atoms), and h (peripheral C bonded to an H atom) show decreasing BEs. In linear PAHs (the latter four), h-type carbons further split into h1 or h2 (on inner or edge benzene ring) subtypes with chemical shifts of ca. 0.2–0.4 eV. All major Franck–Condon-active modes are characterized to be in-plane vibrations: low-frequency (<800 cm–1) C–C ring deformation modes play an essential role in determining the peak asymmetries; and for each h-type carbon a high-frequency (ca. 3600 cm–1) C*–H stretching mode is responsible for the high-energy tail. We found that core ionization leads to reduction of all C*–C and C*–H bond lengths and ring deformation with a definite direction. Based on theoretical spectra of four linear PAHs, we found asymptotic relations and anticipated possible spectral features for even larger linear PAHs. Our calculations provide accurate reference spectra for XPS characterizations of PAHs, which are useful in understanding the vibronic coupling effects in this family. 

Vibronic coupling plays a pivotal role in molecular spectroscopy. We present a theoretical study on vibrationally resolved x-ray photoelectron spectra (XPS) of seven azines (CxHyNz; pyridine, three diazines, two triazines, and one tetrazine) at the nitrogen 1s edge, to explore the vibronic coupling effects as influenced by consecutive replacement of the CH group with a N atom. Franck-Condon simulations were performed with the Duschinsky rotation effect included, where the electronic structure was calculated by the density functional theory. Validations on pyrimidine show good agreement with the experiment, weak functional dependence, and weak mode mixing effect. We observed an evident blue shift in binding energies with the increasing number of N atoms in this series, together with molecule-dependent vibronic fine structures. These molecules have either C2v or Cs molecular symmetry at the optimized core-ionized geometries. Franck-Condon-active vibrational modes were identified to be low frequency (500–1650 cm−1), totally symmetric (A1 or A′), in-plane ring deformation modes. Core ionization on N∗ always leads to elongation of the N∗−N bond length, accompanied by an increase of the ∠C−N∗−X bond angle (X=C, N). Our study predicts accurate theoretical reference spectra for the azine family and provides useful information on the properties of the core-ionized states as influenced by the structural change of CH↔N replacement.

We performed a density functional theory (DFT) study on X-ray photoelectron (XPS) and absorption (XAS) spectra of graphitic carbon nitride (g-C3N4) nanosheets at the N and C K-edges. A combined cluster-periodic approach was employed to calculate XPS spectra, in which the core ionic potential (IP) of the solid 2D material was computed by subtracting the work function (obtained with periodic conditions) from the gas phase IP (obtained with large cluster models). With amino-terminated supermolecules of different sizes, we obtained convergent spectra and provide new assignments for 5 nitrogen [1 sp(2); 4 sp(3) (bridging, tertiary, and primary/secondary amino nitrogens)] and 4 carbon (all bonded with three nitrogens) local structures. A good agreement with experiments was obtained, with the N1s (C1s) main peak position differing by 0.1-0.2 eV (0.5-0.8 eV). Our simulations show that N1s XPS of pure g-C3N4 contains only two major features at 398.6 and 401.2 eV, contributed from sp(2)-N and sp(3)-N, respectively. The chemical shifts of all sp(3)-N are so close (deviating by 0.3-0.6 eV) that terminal amino groups -NHx (x = 1, 2) will only be distinguished in high-resolution measurements. In C1s XPS, all carbons show similar (deviation < 0.2 eV) IPs, as determined by the same nearest neighbors. We further excluded the effect of shake-up satellites that may change our XPS interpretations by equivalent core hole time-dependent DFT (ECH-TDDFT) simulations. The effect of vibronic coupling is small (redistribution is only 0.1-0.3 eV to the higher-energy region) in the N1s edge as estimated from the asymmetric main peak shape, and negligible in the C1s edge. Quicker size convergence was found in XAS than XPS. In N1s XAS, we identified a weak pi* spectral feature at 400-401 eV for both -NHx and tertiary nitrogens. Our study provides a clear theoretical reference for X-ray spectral fingerprints of different local structures, which is useful for analysis of g-C3N4 based materials with various designed or unavoidable structural modifications. We also highlight our combined cluster-periodic approach in calculating the K-edge XPS spectra of general 2D materials which predicts accurate absolute values.

Low-lying dark nÏ€∗ states play an important role in many photophysical and photochemical processes of organic chromophores. Transient X-ray absorption spectroscopy (TXAS) provides a powerful technique for probing the dynamics of valence states by exciting the electrons into high-lying core excited states. We employ multiconfigurational self-consistent field calculations to investigate the TXAS of uracil along its nonradiative photodecay pathways. An open issue is whether dark nÏ€∗ state S1 (n is the lone pair localized on an oxygen atom) is accessible when bright ππ∗ state S2 is selectively excited. Vertical core excitations were calculated along the potential energy surfaces of the three lowest states, S0-S2, interpolated between two minima and two minimum-energy conical intersections. Computed TXAS data from the C, N, and O K edges show distinct spectral fingerprints of the dark state in all spectral regimes. At the O 1s edge, the nÏ€∗ state has a very strong absorption at 526-527 eV, while at the C (N) 1s edge, by contrast, there is almost zero (very weak) absorption at 279-282 eV (397-398 eV). All K-edge spectra can be used to sensitively detect the dark states. Our proposed O 1s feature has already been observed in a recent TXAS experiment with thymine. Natural transition orbital analysis is used to interpret all dominant features of the three lowest-valence states along the reaction coordinate and reveal some important valence fine-structure information from the core excitation.

Doping is an efficient way to open the zero band gap of graphene. The control of the dopant domain size allows us to tailor the electronic structure and the properties of the graphene. We have studied the electronic structure of boron nitride doped graphenes with different domain sizes by simulating their near-edge X-ray absorption fine structure (NEXAFS) spectra at the N K-edge. Six different doping configurations (five quantum dot type and one phase-separated zigzag-edged type) were chosen, and N K-edge NEXAFS spectra were calculated with large truncated cluster models by using the density functional theory with hybrid functional and the equivalent core hole approximation. The opening of the band gap as a function of the domain size is revealed. We found that nitrogens in the dopant boundary contribute a weaker, red-shifted pi* peak in the spectra as compared to those in the dopant domain center. The shift is related to the fact that these interfacial nitrogens dominate the lowest conduction band of the system. Upon increasing the domain size, the ratio of interfacial atom decreases, which leads to a blue shift of the pi* peak in the total NEXAFS spectra. The spectral evolution agrees well with experiments measured at different BN-dopant concentrations and approaches to that of a pristine h-BN sheet.

New x-ray free electron laser (XFEL) and high harmonic generation (HHG) light sources are capable of generating short and intense pulses that make x-ray nonlinear spectroscopy possible. Multidimensional spectroscopic techniques, which have long been used in the nuclear magnetic resonance, infrared, and optical regimes to probe the electronic structure and nuclear dynamics of molecules by sequences of short pulses with variable delays, can thus be extended to the attosecond x-ray regime. This opens up the possibility of probing core-electronic structure and couplings, the real-time tracking of impulsively created valence-electronic wavepackets and electronic coherences, and monitoring ultrafast processes such as nonadiabatic electron-nuclear dynamics near conical-intersection crossings. We survey various possible types of multidimensional x-ray spectroscopy techniques and demonstrate the novel information they can provide about molecules.

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-activespace self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

We have calculated the N 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of nitrogen-doped monolayer graphene (NG) using density functional theory (DFT) with the equivalent core hole approximation. The hexavacancy (6V) defect and its dependence on the nitrogen-doping concentration have been analyzed in detail via both N 1s -> pi* and N 1s -> sigma* transitions. The NEXAFS spectra are sensitive to the doping concentration of N in the pi* region: diluted doping weakens the main pi* peak and smears the oscillations in this region. The vacancy defect leads to a red-shift in both the pi and sigma spectra. A pyridinic nitrogen at the 6V defect center exhibits a sharp pi* peak at 398.4 eV, which agrees well with the experimental pre-edge structure at 398.6 eV. The sigma* peak is split in two, which can serve as the fingerprint to reveal the nature of the defect. A structural change from pyridinic to pyrrolic NG results in a distinctive difference in the spectral shape. The ground-state band structure has also been simulated at the DFT level with periodic boundary conditions. Similar profiles are found in the N 2p projected density of states above the Fermi level and in the N 1s NEXAFS spectra.

We performed a combined experimental and theoretical study of the C1s Near-Edge X-ray Absorption Fine-Structure (NEXAFS) spectroscopy and X-ray Photoelectron Spectroscopy in the gas phase of two polycyclic aromatic hydrocarbons (phenanthrene and coronene), typically formed in combustion reactions. In the NEXAFS of both molecules, a double-peak structure appears in the C1s -> LUMO region, which differ by less than 1 eV in transition energies. The vibronic coupling is found to play an important role in such systems. It leads to weakening of the lower-energy peak and strengthening of the higher-energy one because the 0 - n (n > 0) vibrational progressions of the lower-energy peak appear in nearly the same region of the higher-energy peak. Vibrationally resolved theoretical spectra computed within the Frank-Condon (FC) approximation and linear coupling model agree well with the high-resolution experimental results. We find that FC-active normal modes all correspond to in-plane vibrations.