Resolved Absorption Spectra Research Articles

Calculation of vibrationally resolved absorption spectra of acenes and pyrene.

The absorption spectra of naphthalene, anthracene, pentacene and pyrene in the ultraviolet-visible (UV-Vis) range have been simulated by using an efficient real-time generating function method that combines calculated adiabatic electronic excitation energies with vibrational energies of the excited states. The vertical electronic excitation energies have been calculated at the density functional theory level using the PBE0 functional and at the second-order approximate coupled-cluster level (CC2). The absorption spectra have been calculated at the PBE0 level for the studied molecules and at the CC2 level for naphthalene. The transition probabilities between vibrationally resolved states were calculated by using the real-time generating function method employing the full Duschinsky formalism. The absorption spectrum for naphthalene calculated at the PBE0 and CC2 levels agrees well with the experimental one after the simulated spectra have been blue-shifted by 0.48 eV and 0.12 eV at the PBE0 and CC2 level, respectively. The absorption spectra for anthracene, pentacene and pyrene simulated at the PBE0 level agree well with the experimental ones when they are shifted by 0.49 eV, 0.57 eV and 0.46 eV, respectively. The strongest transitions of the main vibrational bands have been assigned.

Infrared spectroscopy of jet-cooled HCCl singlet chlorocarbene diradical: CH stretching and vibrational coupling dynamics.

Quantum shot noise limited laser absorption methods are used to obtain first high-resolution infrared rovibrational spectra of jet cooled chlorocarbene (HCCl) diradical in a supersonic slit-jet discharge expansion spectrometer. The rotationally resolved absorption spectra of the C-H stretch ν1 fundamental are analyzed in the framework of a Watson non-rigid asymmetric rotor Hamiltonian model. Further analysis of the mid-infrared data reveals the additional presence of what has nominally been assigned as the combination band with one quantum of the H-C-Cl bend (ν2) and two quanta of the C-Cl stretch (2ν3). Rovibrational constants are obtained from least squares fits for each of the four excited vibrational states built on the ν1 fundamental and the combination mode for each 35Cl and 37Cl atom isotopologue. The four bands occur within a narrow spectral window, requiring detailed comparison of multiple spectral properties (e.g., rotational constant dependence on vibrational excitation, band types/transition dipole moment alignment in the body-fixed frame, etc.) to aid in the vibrational assignment. Indeed, the IR transition intensities arise from strong anharmonic mixing between the "bright" ν1 C-H stretch and "dark" H-C-Cl bend/C-Cl stretch combination modes, resulting in nearly equal amplitudes for the zeroth order and harmonic states. Finally, to aid the spectral search for HCCl in the interstellar medium, ground state two-line combination differences are combined with previous laser-induced fluorescence results to predict precision microwave transitions for HC35Cl and HC37Cl.

Photodissociation dynamics in the first absorption band of pyrrole. I. Molecular Hamiltonian and the Herzberg-Teller absorption spectrum for the A21(πσ*)←X̃1 A1(ππ) transition.

This paper opens a series in which the photochemistry of the two lowest πσ* states of pyrrole and their interaction with each other and with the ground electronic state X̃ are studied using ab initio quantum mechanics. New 24-dimensional potential energy surfaces for the photodissociation of the N-H bond and the formation of the pyrrolyl radical are calculated using the multiconfigurational perturbation theory (CASPT2) for the electronic states X̃(ππ), 11A2(πσ*), and 11B1(πσ*) and locally diabatized. In this paper, the ab initio calculations are described and the photodissociation in the state 11A2(πσ*) is analyzed. The excitation 11 A2←X̃ is mediated by the coordinate dependent transition dipole moment functions constructed using the Herzberg-Teller expansion. Nuclear dynamics, including 6, 11, and 15 active degrees of freedom, are studied using the multi-configurational time-dependent Hartree method. The focus is on the frequency resolved absorption spectrum as well as on the dissociation time scales and the resonance lifetimes. Calculations are compared with available experimental data. An approximate convolution method is developed and validated, with which absorption spectra can be calculated and assigned in terms of vibrational quantum numbers. The method represents the total absorption spectrum as a convolution of the diffuse spectrum of the detaching H-atom and the Franck-Condon spectrum of the heteroaromatic ring. Convolution calculation requires a minimal quantum chemical input and is a promising tool for studying the πσ* photodissociation in model biochromophores.

Quantifying the Performances of DFT for Predicting Vibrationally Resolved Optical Spectra: Asymmetric Fluoroborate Dyes as Working Examples.

This article aims at a quantitative assessment of the performances of a panel of exchange-correlation functionals, including semilocal (BLYP and PBE), global hybrids (B3LYP, PBE0, M06, BHandHLYP, M06-2X, and M06-HF), and range-separated hybrids (CAM-B3LYP, LC-ωPBE, LC-BLYP, ωB97X, and ωB97X-D), in predicting the vibrationally resolved absorption spectra of BF2-carrying compounds. To this end, for 19 difluoroborates as examples, we use, as a metric, the vibrational reorganization energy (λvib) that can be determined based on the computationally efficient linear coupling model (a.k.a. vertical gradient method). The reference values of λvib were determined by employing the CC2 method combined with the cc-pVTZ basis set for a representative subset of molecules. To validate the performances of CC2, comparisons with experimental data have been carried out as well. This study shows that the vibrational reorganization energy, involving Huang-Rhys factors and normal-mode frequencies, can indeed be used to quantify the reliability of functionals in the calculations of the vibrational fine structure of absorption bands, i.e., an accurate prediction of the vibrational reorganization energy leads to absorption band shapes better fitting the selected reference. The CAM-B3LYP, M06-2X, ωB97X-D, ωB97X, and BHandHLYP functionals all deliver vibrational reorganization energies with absolute relative errors smaller than 20% compared to CC2, whereas 10% accuracy can be achieved with the first three functionals. Indeed, the set of examined exchange-correlation functionals can be divided into three groups: (i) BLYP, B3LYP, PBE, PBE0, and M06 yield inaccurate band shapes (λvib,TDDFT < λvib,CC2), (ii) BHandHLYP, CAM-B3LYP, M06-2X, ωB97X, and ωB97X-D provide accurate band shapes (λvib,TDDFT ≈ λvib,CC2), and (iii) LC-ωPBE, LC-BLYP, and M06-HF deliver rather poor band topologies (λvib,TDDFT > λvib,CC2). This study also demonstrates that λvib can be reliably estimated using the CC2 model and the relatively small cc-pVDZ basis set. Therefore, the linear coupling model combined with the CC2/cc-pVDZ level of theory can be used as a very efficient approach to determine λvib values that can be used to select the most adequate functional for more accurate vibronic calculations, e.g., including more refined models and environmental effects.

High-Resolution Mapping of Thermal History in Polymer Nanocomposites: Gold Nanorods as Microscale Temperature Sensors.

A technique is reported for measuring and mapping the maximum internal temperature of a structural epoxy resin with high spatial resolution via the optically detected shape transformation of embedded gold nanorods (AuNRs). Spatially resolved absorption spectra of the nanocomposites are used to determine the frequencies of surface plasmon resonances. From these frequencies the AuNR aspect ratio is calculated using a new analytical approximation for the Mie-Gans scattering theory, which takes into account coincident changes in the local dielectric. Despite changes in the chemical environment, the calculated aspect ratio of the embedded nanorods is found to decrease over time to a steady-state value that depends linearly on the temperature over the range of 100-200 °C. Thus, the optical absorption can be used to determine the maximum temperature experienced at a particular location when exposure times exceed the temperature-dependent relaxation time. The usefulness of this approach is demonstrated by mapping the temperature of an internally heated structural epoxy resin with 10 μm lateral spatial resolution.

On the order reduction of the radiative heat transfer model for the simulation of plasma arcs in switchgear devices

An approach to derive low-complexity models describing thermal radiation, employed to simulate the behavior of electric arcs in switchgear systems, is presented. The idea is to approximate the (high dimensional) full-order equations, describing the propagation of the radiated heat intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order one are presented.

Fast photodynamics of azobenzene probed by scanning excited-state potential energy surfaces using slow spectroscopy.

Azobenzene, a versatile and polymorphic molecule, has been extensively and successfully used for photoswitching applications. The debate over its photoisomerization mechanism leveraged on the computational scrutiny with ever-increasing levels of theory. However, the most resolved absorption spectrum for the transition to S1(nπ*) has not followed the computational advances and is more than half a century old. Here, using jet-cooled molecular beam and multiphoton ionization techniques we report the first high-resolution spectra of S1(nπ*) and S2(ππ*). The photophysical characterization reveals directly the structural changes upon excitation and the timescales of dynamical processes. For S1(nπ*), we find that changes in the hybridization of the nitrogen atoms are the driving force that triggers isomerization. In combination with quantum chemical calculations we conclude that photoisomerization occurs along an inversion-assisted torsional pathway with a barrier of ~2 kcal mol−1. This methodology can be extended to photoresponsive molecular systems so far deemed non-accessible to high-resolution spectroscopy.

Influence of Duschinsky and Herzberg-Teller effects on S₀→ S₁ vibrationally resolved absorption spectra of several porphyrin-like compounds.

The S0 → S1 (Q band) high-resolved absorption spectra of three porphyrin-like compounds, porphycene, magnesium porphyrin, and zinc tetraazaporphyrin, were simulated in the framework of the Franck-Condon approximation including the Duschinsky and Herzberg-Teller (HT) contributions. Substitution of meso-aza on porphyrin macrocycle framework could change severely the absorption energy, vibrational intensity, and spectral profile of Q band. Therefore, we focused attention on the spectral similarities and contrasts among the three compounds based on the density functional theory and its time-dependent extension calculations. The simulated spectra agreed well with the experimental ones and further confirmed that the HT and Duschinsky effects have significant influence on the weakly allowed or forbidden transition of sizable organic molecules. The pure HT and Duschinsky effects were explored separately to clarify their contributions on changing vibrational intensities of different modes. Moreover, we tentatively assigned most of the vibrational modes which appeared in the experimental spectra but corresponding assignments were not given. The present work provided a useful method to simulate and interpret the absorption spectra of porphyrin-like compounds.

The lineshape of the electronic spectrum of the green fluorescent protein chromophore, part I: gas phase.

In this work we present the vibrationally resolved optical absorption spectrum of p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI), the green fluorescent protein (GFP) chromophore, computed at several levels of theory, including time-dependent DFT with various functionals and basis sets, CASSCF, CASPT2 and XMCQDPT2. We also investigated what happens to the spectrum if the ground- and excited-state geometries are optimized at different levels of theory (mixed approach), as has been used previously. The vibrationally resolved absorption spectra obtained by DFT, CASPT2 and XMCQDPT2 are very similar and consist of a main absorption peak and a shoulder that is ∼1500 cm(-1) higher in energy. The vibrational progression increases moderately with temperature. These spectra are in qualitative agreement with experimental action spectra, but much narrower and lack the long tail in the blue, even at high temperatures. Because our calculated emission spectra, which are equally narrow, are in good agreement with the emission of green fluorescent protein at 253 K, we argue that the action spectrum are too broad to be considered as the absorption spectrum. The CASSCF method and the mixed approaches overestimate the vibrational progressions with respect to CAM-B3LYP, CASPT2 and XMCQDPT2, due to inaccuracies in the geometric S0 →S1 displacements. Finally, we computed the vibronic spectra of four chromophore analogues with different substitutions on the rings and found that these substitutions hardly affect the lineshape in vacuum.

Erratum: Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures.

When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curv...

NIR dual luminescence from an extended porphyrin. Spectroscopy, photophysics and theory.

Spectroscopic and photophysical properties of an extended Zn porphyrin with fused bis(tetraazaanthracene) arms including a 2,9-diphenyl-1,10-phenanthroline incorporated in a polyether macrocycle are investigated in solvents of different polarity pointing to the presence of two emitting singlet excited states. The absorption and emission features are identified and ascribed, on the basis of solvent polarity dependence, to a π-π* and to a charge transfer (CT) state, respectively. Whereas the intraligand π-π* transition is assigned to the intense absorption observed at 442-455 nm, the CT states contribute to the bands at 521-525 nm and 472-481 nm. The theoretical analysis of the absorption spectrum confirms the presence of two strong bands centered at 536 and 437 nm corresponding to CT and π-π* states, respectively. Weak CT transitions are calculated at 657 and 486 nm. Two emission maxima are observed in toluene at 724 nm from a (1)π-π* state and at 800 nm from a (1)CT state, respectively. (1)CT bands shift bathochromically by increasing the solvent polarity whereas the energy of the (1)π-π band is less affected. Likewise, the emission yield and lifetime associated with the low energy (1)CT band are strongly affected by solvent polarity. This is rationalized by a (1)π-π* → (1)CT internal conversion driven by solvent polarity, this process being competitive with the (1)π-π* to ground state deactivation channel. Time resolved absorption spectra indicate the presence of two triplet states, a short-lived one (nanoseconds range) and a longer lived one (hundreds of microsecond range) ascribed to a (3)π-π* and a (3)CT, respectively. For them, a conversion mechanism similar to that of the singlet excited states is suggested.

Nanometer-resolved radio-frequency absorption and heating in biomembrane hydration layers.

Radio-frequency (RF) electromagnetic fields are readily absorbed in biological matter and lead to dielectric heating. To understand how RF radiation interacts with macromolecular structures and possibly influences biological function, a quantitative description of dielectric absorption and heating at nanometer resolution beyond the usual effective medium approach is crucial. We report an exemplary multiscale theoretical study for biomembranes that combines (i) atomistic simulations for the spatially resolved absorption spectrum at a single planar DPPC lipid bilayer immersed in water, (ii) calculation of the electric field distribution in planar and spherical cell models, and (iii) prediction of the nanometer resolved temperature profiles under steady RF radiation. Our atomistic simulations show that the only 2 nm thick lipid hydration layer strongly absorbs in a wide RF range between 10 MHz and 100 GHz. The absorption strength, however, strongly depends on the direction of the incident wave. This requires modeling of the electric field distribution using tensorial dielectric spectral functions. For a spherical cell model, we find a strongly enhanced RF absorption on an equatorial ring, which gives rise to temperature gradients inside a single cell under radiation. Although absolute temperature elevation is small under conditions of typical telecommunication usage, our study points to hitherto neglected temperature gradient effects and allows thermal RF effects to be predicted on an atomistically resolved level. In addition to a refined physiological risk assessment of RF fields, technological applications for controlling temperature profiles in nanodevices are possible.

The excited state behavior of cytosine in the gas phase: A TD-DFT study

We report a TD-DFT study of the three lowest energy tautomers of Cytosine in the gas phase, focussing on the Franck–Condon region and on the excited state minima and comparing the performances of three different density functionals, namely CAM-B3LYP, M052X and PBE0. For what concerns the oxo-amino tautomer, the one present in water and within DNA, CAM-B3LYP and M052X provide a picture close to that of recent CCSD(T) calculations. In particular, in the Franck–Condon region the electronic transition involving the Lone Pair of the Nitrogen atom corresponds to S2 and is the lowest energy nπ∗ transition (SNπ∗), being significantly more stable than that involving the Carbonyl Lone Pair (SOπ∗), whose stability is instead overestimated by PBE0. CAM-B3LYP and M052X also provide minima fully consistent with those of the most recent MCSCF methods: different relative minima are present on the lowest energy adiabatic state and the most stable corresponds to the SNπ∗ diabatic state. PBE0 predicts instead a strong coupling of SOπ∗ with the lowest energy ππ∗ state. Calculations of the vibrationally resolved absorption spectra of the three lowest enegy tautomers, including Duschinsky effects, provide spectra in very good agreement with the experiments.

Rotationally resolved spectra of the 4051 Å comet band of C3 for all six 12C and 13C isotopologues

Rotationally resolved absorption spectra of the A∼1Πu–X∼1Σg+ origin band of the tricarbon molecule (C3) are reported for 12C3 and its 13C-substitued isotopologues. The 4051Å electronic transition, also identified in cometary tails and in translucent interstellar clouds, has been measured using cavity ring-down spectroscopy and a supersonically expanding planar plasma. Previous spectroscopic studies of 12C3 are extended and the electronic origin band is re-investigated including a perturbation analysis of the upper state. The rotational analysis of spectra originating from 13C mono- and di-substituted C3 yields accurate spectroscopic parameters for all six isotopologues, including ground state molecular constants for 13C12C13C and 12C13C13C.

Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures.

When large structural displacements take place between the ground state (GS) and excited state (ES) minima of polyatomic molecules, the choice of a proper set of coordinates can be crucial for a reliable simulation of the vibrationally resolved absorption spectrum. In this work, we study two carotenoids that undergo structural displacements from GS to ES minima of different magnitude, from small displacements for violaxanthin to rather large ones for β-carotene isomers. Their finite-temperature (77 and 300 K) spectra are simulated at the harmonic level, including Duschinsky effect, by time-dependent (TD) and time-independent (TI) approaches, using (TD)DFT computed potential energy surfaces (PES). We adopted two approaches to construct the harmonic PES, the Adiabatic (AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate frames: Cartesian and valence internal coordinates. Our results show that when large displacements take place, Cartesian coordinates dramatically fail to describe curvilinear displacements and to account for the Duschinsky matrix, preventing a realistic simulation of the spectra within the AH model, where the GS and ES PESs are quadratically expanded around their own equilibrium geometry. In contrast, internal coordinates largely amend such deficiencies and deliver reasonable spectral widths. As expected, both coordinate frames give similar results when small displacements occur. The good agreement between VH and experimental line shapes indicates that VH model, in which GS and ES normal modes are both evaluated at the GS equilibrium geometry, is a good alternative to deal with systems exhibiting large displacements. The use of this model can be, however, problematic when imaginary frequencies arise. The extent of the nonorthogonality of the Dushinsky matrix in internal coordinates and its correlation with the magnitude of the displacement of the GS and ES geometries is analyzed in detail.

Hard x-ray absorption spectroscopy for pulsed sources

We present a method suitable for the measurement of a high-energy resolved absorption spectrum in the emission mode upon target excitation with an intense monochromatic pulse of x-ray light. The approach is based on a measurement of a single resonant Raman x-ray spectrum at a fixed off-resonant excitation energy by a dispersive-type high-resolution emission spectrometer. Using a simple Lorentzian tail correction function and an energy-scale transformation, we reconstructed the ${L}_{3}$ absorption edge of Xe from the $3d$-$2{p}_{3/2}$ resonant Raman x-ray spectrum recorded at excitation energy 25 eV below the ${L}_{3}$ edge. The energy resolution is well below the ${L}_{3}$ core-hole lifetime broadening and allows for a straightforward extraction of the $[2{p}_{3/2}]n\ensuremath{\ell}$ resonance energies and emission strengths. The reconstructed spectrum is nearly equivalent to the high-energy resolution fluorescence detected absorption spectrum, which is recorded by scanning the photon excitation energy across the absorption edge.

High-resolution observation and analysis of the ${\rm I}^{+}_2$I2+ A2Π3/2,u–X 2Π3/2,g system

Rotationally resolved absorption spectra of I(2)(+) were recorded in 12,065-13,062 cm(-1) region by employing optical heterodyne velocity modulation absorption spectroscopy. In total, 4054 lines were assigned to 24 bands in the A(2)Π(3/2,u)-X(2)Π(3/2,g) system spanning the vibrational levels υ'' = 1-4 and υ(n)' = 11-19. The assigned lines were globally fitted and an error of 0.003 cm(-1) was obtained. Rotational constants, B(υ), were used to derive equilibrium parameters B(e)'' = 0.03977725(77) cm(-1), a(e)'' = 1.1819(24)×10(-4) cm(-1), r(e)'' = 2.584386(25) Å of the X(2)Π(3/2,g) state, and B(e)' = 0.0305787(37) cm(-1), a(e)' = 1.2353(23)×10(-4) cm(-1), r(e)' = 2.94758(18) Å of the A(2)Π(3/2,u) state. Vibrational energies were used to derive ω(e)'' = 239.0397(55) cm(-1), ω(e)x(e)'' = 0.64951(87) cm(-1) of the X(2)Π(3/2,g) state and ω(e)' = 138.103(11) cm(-1), ω(e)x(e)' = 0.45027(34) cm(-1) of the A(2)Π(3/2,u) state. The A(2)Π(3/2,u) (υ(n) = 13) state was found to be rotationally perturbed by the a(4)Σ(1/2,u)(-) (υ(n) = 17) state through second-order spin-orbit coupling.

Franck-Condon simulation of vibrationally resolved optical spectra for zinc complexes of phthalocyanine and tetrabenzoporphyrin including the Duschinsky and Herzberg-Teller effects

High resolved absorption and fluorescence spectra of zinc complexes of phthalocyanine (ZnPc) and tetrabenzoporphyrin (ZnTBP) in the region of Q states were reported. Few theoretical investigations were performed to simulate the well-resolved spectra and assigned the vibrational bands of the large molecules, especially for high symmetrical characteristic molecules, on account of the difficulties to optimize the excited states and analyze a large number of final vibrational-normal modes. In the present work, the S(0) ↔ S(1) absorption and fluorescence spectra (that is, the Q band) of ZnPc and ZnTBP were simulated using time-dependent density functional theory with the inclusions of Duschinsky and Herzberg-Teller contributions to the electronic transition dipole moments. The theoretical results provide a good description of the optical spectra and are proved to be in excellent agreement with experimental spectra in inert-gas matrices or in supersonic expansion. This study focused attentions on the optical spectral similarities and contrasts between ZnPc and ZnTBP, in particular the noticeable Duschinsky and Herzberg-Teller effects on the high-resolved absorption and fluorescence spectra were considered. Substitution of meso-tetraaza on the porphyrin macrocycle framework could affect the ground state geometry and alter the electron density distributions, the orbital energies that accessible in the Q band region of the spectrum. The results were used to help interpret both the nature of the electronic transitions in Q band region, and the spectral discrepancies between phthalocyanine and porphyrin systems.

Impact of Vibronic Couplings on Perceived Colors: Two Anthraquinones as a Working Example.

The accurate simulation of the dye colors remains a significant challenge for theoreticians, notably due to the sensitivity of the human eyes that are able to distinguish variations of hues corresponding to trifling energetic shifts. Using time-dependent density functional theory and two hybrid functionals, we have simulated vibrationally resolved absorption spectra of two anthraquinone derivatives (solvent blue 35 and solvent green 3) solvated in cyclohexane. Comparisons with recent experiments demonstrate the efficiency of the ωB97X-D/6-31++G(d,p) approach for these structures. The impact of microscopic vibronic couplings on the macroscopic chromatic coordinates of the dyes is quantified. This work unravels the key role of these couplings and is consequently a step further in the modeling of human-perceived colors from purely ab initio models.

Symmetry and vibrationally resolved absorption spectra near theN Kedges ofN2O: Experiment and theory

In this study, angle-resolved energetic-ion yield spectra were measured in the N $1s$ excitation region of ${\mathrm{N}}_{2}$O. A Franck-Condon analysis based on ab initio two-dimensional potential energy surfaces of the core-excited Rydberg states, which were calculated by the symmetry-adapted cluster-configuration interaction method, reproduced observed vibrational excitations specific to the individual Rydberg states well and enabled quantitative assignments. Geometric changes in the terminal nitrogen ${\mathrm{N}}_{\mathrm{t}}$ $1s$ and the central nitrogen ${\mathrm{N}}_{\mathrm{c}}$ $1s$ excited states with respect to the $3p$\ensuremath{\pi}, $3p$\ensuremath{\sigma}, and $4s$\ensuremath{\sigma} transitions were analyzed. The coupling of these valence and Rydbergs states was examined based on the second moment analysis. Irregular Rydberg-state behavior in the ${\mathrm{N}}_{\mathrm{c}}$ $1{s}^{\ensuremath{-}1}$ $4s$\ensuremath{\sigma} state was observed.