In this paper, we investigate HNCO by resonant and nonresonant Auger electron spectroscopy at the K-edges of carbon, nitrogen, and oxygen, employing soft X-ray synchrotron radiation. In comparison with the isosteric but linear CO2 molecule, spectra of the bent HNCO molecule are similar but more complex due to its reduced symmetry, wherein the degeneracy of the π-orbitals is lifted. Resonant Auger electron spectra are presented at different photon energies over the first core-excited 1s → 10a′ resonance. All Auger electron spectra are assigned based on ab initio configuration interaction computations combined with the one-center approximation for Auger intensities and moment theory to consider vibrational motion. The calculated spectra were scaled by a newly introduced energy scaling factor, and generally, good agreement is found between experiment and theory for normal as well as resonant Auger electron spectra. A comparison of resonant Auger spectra with nonresonant Auger structures shows a slight broadening as well as a shift of the former spectra between −8 and −9 eV due to the spectating electron. Since HNCO is a small molecule and contains the four most abundant atoms of organic molecules, the reported Auger electron decay spectra will provide a benchmark for further theoretical approaches in the computation of core electron spectra.

Isocyanic acid, HNCO, has already been in the center of many spectroscopic studies covering nearly the complete spectral range from microwaves (MW) to vacuum ultraviolet (VUV).1–14 This interest arises not only from this molecule’s importance in combustion reactions like the famous RAPRENOx process, in which HNCO is an important intermediate in the reduction of toxic nitrogen oxides,15–18 or its occurrence in the interstellar space19 but also because it represents an interesting benchmark for theoretical work. Having only 16 valence electrons, the computational cost for more precise theoretical methods is manageable. In addition, isocyanic acid has the same number of valence electrons as CO2; i.e., the two molecules are isosteric, but it has a reduced non-linear symmetry, and it contains the most abundant elements of organic molecules: carbon, hydrogen, oxygen, and nitrogen. The structure of HNCO in its neutral ground state (gs) was determined experimentally by means of IR1,2 and microwave spectroscopy3 and it was found to belong to the CS point group. The molecule’s photodissociation4–8 and photoionization9–14 have been investigated extensively using UV and VUV laser or synchrotron radiation. Here, we extend this work to the soft X-ray region at the K-edges of C, N, and O. The core-ionized or core-excited molecular states have very short lifetimes, in the order of several femtoseconds, which is on the same time scale of nuclear motions. Core-level spectroscopy is therefore a powerful tool to study the interplay between electronic de-excitation dynamics and nuclear dynamics. For recent reviews on this topic, the reader is referred to Refs. 20 and 21. Core-ionized molecular states can undergo radiative or non-radiative Auger decay. In the latter process, the core hole is filled by an electron of one of the valence orbitals, which induces the emission of the Auger electron from the valence manifold into the ionization continuum, leading to a two-hole (2h) dicationic final state. The kinetic energy of this electron is analyzed in normal (nonresonant) Auger electron spectroscopy (AES). A core-excited state occurs when the X-ray excitation induces a transition from a 1s to an unoccupied valence orbital, which leads to resonant Auger electron spectroscopy (RAES). Frequently, two pathways are distinguished for the non-radiative decay. In the so-called participator decay, the electron in the initially unoccupied valence orbital takes part in the Auger process, while in a spectator decay it remains in the excited orbital. The excess energy is in both cases again transferred to an Auger electron, leading thus either to one-hole (1h) or, in spectator decay, to two-hole one-particle (2h1p) final-state configurations. Note that this nomenclature is useful to distinguish between one-hole final states, which are dominant in photoelectron spectroscopy, and the remaining spectator part of RAES generally resembling the normal Auger spectra. However, it is not unambiguous, as the final states may have mixed 1h and 2h1p characters.22,23 In both AES and RAES, conclusions can be drawn on the characteristics of the intermediate and final states and the dynamics occurring during the de-excitation step.

The CO2 molecule, which is isosteric to isocyanic acid, has long served as a benchmark for molecular core-level spectroscopy. Normal Auger24–28 as well as K-shell energy loss29 and photoabsorption spectra30–32 were investigated by various groups. Resonant Auger spectra of CO2 at the oxygen and carbon edges were recorded33 and analyzed with theoretical support,34 which motivated several detailed studies on the first resonance in the spectrum assigned to the O1s/C1s → 2πu transition. A Rydberg state was found to contribute on the high-energy side of the resonance,35 and the vibrational structure of the Renner-Teller split Πu intermediate state was resolved both on the carbon36–38 and oxygen edges.39 Furthermore, the relaxation dynamics and thus dissociation of the molecular ions formed after Auger decay were carefully explored.40,41 Experimental and theoretical studies were also conducted on related linear molecules like CS242–45 and OCS.43,44,46–48

In this paper, we extend this work to isocyanic acid, HNCO, a non-linear molecule with the same number of electrons as CO2 and a similar electronic structure. We present the molecule’s normal Auger electron spectra after core ionization with soft X-ray synchrotron radiation at the carbon, nitrogen, and oxygen edges. In addition, the 1s core excitation NEXAFS (near-edge x-ray absorption fine structure) spectra are presented, as well as resonant Auger electron spectra for the first resonance and selected higher resonances at all three edges. The interpretation of the experimental spectra is given on the basis of a quantum chemical protocol that aims to reproduce how the underlying electronic structure as well as the most essential vibrational effects influence the spectral appearance. Related to this work, we recently reported on the ultrafast photodissociation of the nucleobase thymine probed by Auger spectroscopy with femtosecond soft x-ray pulses, in which the comparison with the HNCO AES identified isocyanic acid as the main fragmentation product.49 

The experiments were performed at the high-resolution soft X-ray beamline PLEIADES50 of Synchrotron SOLEIL. The HNCO sample was prepared following the procedure of Ashby and Werner by treating potassium cyanate with phosphoric acid, and the impurities (mainly CO2) were removed by a trap-to-trap distillation.51 The remaining CO2 impurity was found to be below 0.8% from the valence photoelectron spectrum. As the sample polymerizes above 0 °C, the liquid was held at around −40 °C during the experiment. The vapor pressure of isocyanic acid at that temperature is sufficiently high to fill a differentially pumped gas cell, through which the synchrotron beam passes. Linearly polarized soft X-ray radiation oriented at the magic angle of 54.7° to eliminate angular dependence effects of the electron emission was provided by an Apple II HU80 permanent magnet undulator, which was monochromatized using a 600 lines mm−1 grating with variable groove depth. Supplementary measurements with horizontal and vertical light polarization were conducted in order to extract electron emission asymmetry parameters by using the conventional formula βe=2(I0I90)/(I0+2I90). The photon bandwidth was 60 meV around the oxygen edge and 40 meV and 30 meV at the nitrogen and carbon edges, respectively. The electron spectra were recorded using a VG Scienta R4000 hemispherical electron analyzer with a curved entrance slit of 0.3 mm at a pass energy of 50 eV, leading to a spectrometer resolution of 37.5 meV. NEXAFS spectra were obtained by scanning the photon energy and recording the total ion yield. The Auger electron energy was calibrated using the literature spectra of CO2 and N224 and along with the NEXAFS spectra normalized to the photon flux, sample pressure, and acquisition time.

The geometry and vibrational frequencies of HNCO were computed at the B3LYP/def-TZVP level of theory using Turbomole V6.6.52 The AES and RAES spectra were calculated with a home-written program package described in detail elsewhere.38,53–55 In brief, the cc-pVTZ56 basis set was used to represent occupied Hartree-Fock orbitals of the ground state of the HNCO molecule and the virtual valence orbitals, as obtained by the modified improved virtual orbital method described in Ref. 54. These orbitals were employed in valence CI calculations to represent the respective ground, core-hole, and final electronic states. In all cases, up to two electrons were allowed in the virtual orbitals. Due to the number of required electronic states and large electron redistribution accompanying core-hole generation, all five virtual valence orbitals were taken into account for the ground and core-hole states, whereas only two virtual orbitals were used for final electronic states. The virtual valence orbitals were determined as the lowest possible virtual orbitals of a Fock operator of a doubly ionized HNCO molecule which (i) are orthogonal to the occupied Hartree-Fock orbitals and (ii) can be represented to at least 98% from the atomic orbitals (AOs), in our case the 1s, 2s, and 2p orbitals of the N, C, and O atoms as well as of the hydrogen 1s orbital.54,57 Auger decay rates (Γhf) were obtained with the one-center approximation as described in more detail elsewhere.53,58,59 In brief, the Fermi-Wentzel golden rule expression is used with the CI representations of the core-hole state wavefunction (Ψh) and that of the final-state (Ψfεlm) to which the energy-normalized Auger continuum channel (εlm) is formally coupled, leading to a rate

Γhf=2πlmΨh|Ĥ|Ψfεlm2.
(1)

The Hamiltonian matrix element is then represented in terms of two-electron matrix elements of the molecular orbitals of the continuum channel, the core (ψc) as well as the valence (ψv, ψw) molecular orbitals (MOs),

Ψh|Ĥ|Ψfεlm=vwγhfvwψhεlm|ψvψw,
(2)

where γhfvw is a transition density matrix element that is obtained from the core-hole and final-state wavefunctions by applying the Slater-Condon rules. The Slater integrals ψhεlm|ψvψw=  ψh*(1)εlm*(2)1r12ψv(1)ψw(2)dr1dr2 were approximated by expanding the valence MOs as linear combinations of AOs (χ), neglecting all contributions of AOs not located at the core-hole atom and by assuming that the continuum channel is identical to the atomic one,

ψhεlm|ψvψwμvχhεlm|χμχvcμvcνw.
(3)

The orbitals in the remaining two electron integrals are all centered at the core-hole atom and are taken from the literature.60 The representation of the virtual MOs and the occupied MOs as linear combinations of AOs makes application of the one-center approximation straightforward. Simultaneously, the AO coefficients of the valence orbitals allow us to inspect properties of the MOs. As this is required for a qualitative interpretation of the Auger electron spectrum, we depict the MOs in Fig. 1, while their AO representation is given in Table I. Accordingly, the 4a′, 5a′, and 6a′ MOs represent mostly the C–O, C–N, and N–H bonds, respectively, while the 7a′ orbital is mostly the σ lone pair on the oxygen atom. The next higher valence MOs come in pairs with about equal orbital energies and are essentially π-type orbitals. The lowest pair 8a′ and 1a″ shows no node along a plane orthogonal to the N–C–O axis, while the 9a′ and 2a″ orbitals have one node and the 10a′ and 3a″ MOs two nodes. It is worth to note that the large AO coefficients (bold face in Table I) indicate the character and preferential location of the electrons in the MO. As we shall show, this is reflected in the Auger intensities.

FIG. 1.

Computed molecular orbitals for HNCO (view along the y axis). The bent geometry of the molecule is shown in the xy-symmetry-plane in the indent at the right bottom.

FIG. 1.

Computed molecular orbitals for HNCO (view along the y axis). The bent geometry of the molecule is shown in the xy-symmetry-plane in the indent at the right bottom.

Close modal
TABLE I.

AO representation of the molecular valence orbitals of the HNCO molecule as obtained from the modified improved virtual orbital technique. The orbital energies ε of the occupied orbitals are the eigenvalues of the Fock operator of the neutral HNCO molecule, while the orbital energies of the virtual orbitals 10a′ and 3a″ are the expectation values of a Fock operator corresponding to an average of two-hole states within the occupied valence orbitals. The dominant AO orbital character is given in bold.

4a′5a′6a′7a′1a″8a′9a′2a″10a′3a″
ε (eV)−40.1−34.4−22.3−19.8−17.8−17.6−13.1−12.3−16.7−15.5
H1s 0.01 0.06 −0.32 0.13 0.00 −0.05 0.10 0.00 −0.28 0.00 
N2s −0.12 −0.62 0.33 −0.04 0.00 0.19 0.34 0.00 −0.21 0.00 
N2px −0.05 −0.16 −0.50 0.21 0.00 −0.21 −0.25 0.00 0.26 0.00 
N2py 0.01 0.08 −0.28 0.13 0.00 0.27 0.70 0.00 −0.42 0.00 
N2pz 0.00 0.00 0.00 0.00 0.29 0.00 0.00 0.77 0.00 −0.68 
C2s −0.21 −0.22 −0.31 −0.12 0.00 −0.09 −0.08 0.00 −0.17 0.00 
C2px −0.19 0.30 0.18 −0.35 0.00 0.07 0.09 0.00 −0.09 0.00 
C2py −0.02 0.01 −0.03 0.03 0.00 0.45 0.04 0.00 0.99 0.00 
C2pz 0.00 0.00 0.00 0.00 0.46 0.00 0.00 0.17 0.00 1.01 
O2s −0.72 0.13 0.22 0.56 0.00 −0.05 −0.01 0.00 0.04 0.00 
O2px 0.22 −0.02 0.22 0.71 0.00 −0.16 0.04 0.00 0.02 0.00 
O2py 0.03 0.00 −0.03 0.15 0.00 0.59 −0.59 0.00 −0.63 0.00 
O2pz 0.00 0.00 0.00 0.00 0.64 0.00 0.00 −0.62 0.00 −0.58 
4a′5a′6a′7a′1a″8a′9a′2a″10a′3a″
ε (eV)−40.1−34.4−22.3−19.8−17.8−17.6−13.1−12.3−16.7−15.5
H1s 0.01 0.06 −0.32 0.13 0.00 −0.05 0.10 0.00 −0.28 0.00 
N2s −0.12 −0.62 0.33 −0.04 0.00 0.19 0.34 0.00 −0.21 0.00 
N2px −0.05 −0.16 −0.50 0.21 0.00 −0.21 −0.25 0.00 0.26 0.00 
N2py 0.01 0.08 −0.28 0.13 0.00 0.27 0.70 0.00 −0.42 0.00 
N2pz 0.00 0.00 0.00 0.00 0.29 0.00 0.00 0.77 0.00 −0.68 
C2s −0.21 −0.22 −0.31 −0.12 0.00 −0.09 −0.08 0.00 −0.17 0.00 
C2px −0.19 0.30 0.18 −0.35 0.00 0.07 0.09 0.00 −0.09 0.00 
C2py −0.02 0.01 −0.03 0.03 0.00 0.45 0.04 0.00 0.99 0.00 
C2pz 0.00 0.00 0.00 0.00 0.46 0.00 0.00 0.17 0.00 1.01 
O2s −0.72 0.13 0.22 0.56 0.00 −0.05 −0.01 0.00 0.04 0.00 
O2px 0.22 −0.02 0.22 0.71 0.00 −0.16 0.04 0.00 0.02 0.00 
O2py 0.03 0.00 −0.03 0.15 0.00 0.59 −0.59 0.00 −0.63 0.00 
O2pz 0.00 0.00 0.00 0.00 0.64 0.00 0.00 −0.62 0.00 −0.58 

The lowest vertical double ionization potential of HNCO was computed at the Multi-Configuration reference Coupled Electron Pair Approach (MCCEPA)61 using a cc-pVTZ basis and restricted Hartree-Fock reference wavefunctions in order to obtain an independent energy scale of the calculated spectra. In preceding applications on molecular Auger electron spectra, we found that the CI approach tends to provide an appropriate ordering of the final states but systematically overestimates the energy width of the calculated spectra. Since this trend is systematic and it seems appropriate to simplify a comparison between calculated and experimental spectra, we “squeezed” the energy scale by an empirical factor. The latter was determined as 0.85 and turned out to be essentially independent of the core hole and applicable for normal as well as for resonant Auger electron spectra. The vertical binding energy (BE) of the lowest final state (0) was set to the energy difference of this state and the ground state (gs) as obtained with the MCCEPA,61 while the vertical binding energies of the next states were calculated from the valence CI-energies (ECI) as

Ebind,i=0.85(ECI,iECI,0)+EMCCEPA,0EMCCEPA,gs.
(4)

It is well established that the decay dynamics of molecular Auger spectroscopy gives rise to vibrational broadening and shifting of Auger signals. This was represented by the moment method of Cederbaum and Tarantelli62,63 using these vertical binding energies in combination with core-hole lifetimes, vibrational frequencies, and gradients along the vibrational coordinates as described before.38,54 This approach approximates a band, i.e., the spectral features due to all vibrational states connected with a transition between two electronic states, by a single Gaussian function. The width and position (band center) of the Gaussian reflect the distribution of vibrational features resulting from geometry relaxation of the molecule upon core-hole formation due to potential energy differences of the ground, intermediate, and final states. Thus, the moment theory does not represent individual vibrational transitions, which can be observed mostly at the high kinetic energy part of the Auger-type spectra. Furthermore, it assumes broadband excitation correctly reproducing the experimental conditions of Auger electron spectra (AES) but not those of the presented resonant Auger spectra, which have been obtained with a bandwidth that is about an order of magnitude smaller than the width of the band (i.e. vibrational structure) in the core excitation spectra. Nevertheless, as shown in the previous work22,38,54,62,63 and below, the moment theory generally provides a realistic and computationally feasible representation of the overall appearance of molecular AES and RAES. This creates confidence in the theoretical assignment of the observed spectral features to electronic states, which is one of the main results of the present investigation. The experimental spectrometer resolution of 30, 40, and 60 meV full width at half maximum for the C, N, and O core-hole spectra, respectively, was represented by convoluting the obtained spectra by corresponding Gaussian distributions. Unless stated otherwise, this approach is used to obtain all theoretical AES and RAES spectra shown in the following.

The experimental carbon, nitrogen, and oxygen 1s normal Auger electron spectra of isocyanic acid recorded at photon energies of 350, 465, and 570 eV, respectively, are shown in Fig. 2. Auger electrons in the energy ranges of 220–280 eV (C1s), 325–390 eV (N1s), and 460–520 eV (O1s) were analyzed in steps of 50 meV. A distinct band structure is observed at all three K-edges on the high-energy side of the spectrum, while broad and less intense bands are observed at lower kinetic energies. In order to compare bands corresponding to the same final dicationic states at the different edges among themselves as well as to the computed binding energies of Eq. (4), in the following, the band positions will be discussed in terms of binding energies of the Auger electron instead of electron kinetic energies. The binding energy is obtained from the difference of the kinetic energy of the Auger electron and the 1s ionization energy. The latter was determined to be 295.9, 405.7, and 540.2 eV for C1s, N1s, and O1s ionization, respectively.

FIG. 2.

Experimental AES of isocyanic acid at the carbon (a), nitrogen (b), and oxygen (c) edges recorded at photon energies of 350, 465, and 570 eV, respectively. The upper x axis shows the binding energy common for all three spectra. The O1s spectrum in panel (c) was published previously in Ref. 49.

FIG. 2.

Experimental AES of isocyanic acid at the carbon (a), nitrogen (b), and oxygen (c) edges recorded at photon energies of 350, 465, and 570 eV, respectively. The upper x axis shows the binding energy common for all three spectra. The O1s spectrum in panel (c) was published previously in Ref. 49.

Close modal

Moddeman et al. divided the CO2 AES into three regions:24 The bands at high kinetic energies were assigned to an Auger decay, in which only weakly bound outer-valence orbitals are involved (K-WW). In the intermediate region, the final dicationic states have vacancies in one weakly bound outer-valence orbital and in one strongly bound inner-valence shell orbital (K-SW), while processes leading to final states with two inner-valence orbital holes can be assigned to bands at even lower kinetic energies (K-SS). The latter signals tend to be broader than the former ones due to (i) configurational mixing with a multitude of (shake-up) configurations and (ii) large gradients of final states containing holes in MOs with strongly chemical bonding character. As discussed above, HNCO is an isostere of CO2 and therefore similar Auger spectra are expected. Following Moddeman’s systematics for CO2, the more pronounced bands up to about 50 eV binding energy in the HNCO spectra can be assigned to K-WW final states, while the higher binding energy region in the shown spectra corresponds to K-SW final states. Direct comparison of the C1s and O1s HNCO Auger spectra with the CO2 ones as illustrated with dashed lines in Figs. 3(a) and 5(a) reveals the high similarity. The HNCO spectra are shifted to higher kinetic energies, as the orbitals in HNCO lie at lower binding energies than the corresponding ones in CO2 due to the lower electronegativity of nitrogen as compared with oxygen. In addition, the HNCO spectra feature a more complex band structure since the π-orbitals’ degeneracy and the parity of all states are lifted due to the lower symmetry. This manifests itself, for example, for the peak at the highest kinetic energy in the CO2 AES, which is assigned to the 1Δg and 1Σg+ (1πg−2) final states having two holes in the 1πg HOMO orbital of CO2. The HOMO of the non-linear CS symmetric HNCO molecule is no longer degenerate. This gives rise to the observed double peak structure in the C1s Auger spectrum at 34.6 and 35.7 eV [Fig. 3(a)] and to the high-energy shoulders to the peaks at 33.8 eV BE for N1s [Fig. 4(a)] and at 35.2 eV for O1s (Fig. 5). The high kinetic energy peak can be assigned to the 1A′ (2a″−2) HOMO−2 and the 1A″ (9a′−12a″−1) states, while the lower kinetic energy peak (shoulder) corresponds to the 1A′ (9a′−2) state with two holes in the HOMO-1 orbital. The peaks are assigned by comparison with the computed Auger spectra shown in Figs. 3(b), 4(b), and 5(b) at the carbon, nitrogen, and oxygen edges, respectively, which are in excellent agreement with the experiment.

FIG. 3.

Experimental (a) and computed (b) C1s Auger spectra of HNCO. The experimental CO2 spectrum, shifted by +2.2 eV for better illustration, is also shown for comparison [dashed line in panel (a)]. Assignments for the labeled bands are given in Table II.

FIG. 3.

Experimental (a) and computed (b) C1s Auger spectra of HNCO. The experimental CO2 spectrum, shifted by +2.2 eV for better illustration, is also shown for comparison [dashed line in panel (a)]. Assignments for the labeled bands are given in Table II.

Close modal
FIG. 4.

Experimental (a) and computed (b) N1s Auger spectra. Assignments for the labeled bands are given in Table II.

FIG. 4.

Experimental (a) and computed (b) N1s Auger spectra. Assignments for the labeled bands are given in Table II.

Close modal
FIG. 5.

Experimental (a) and computed (b) O1s Auger spectra. The dashed line in panel (a) corresponds to the experimental CO2 spectrum shifted by +3.0 eV. Assignments for the labeled bands are given in Table II.

FIG. 5.

Experimental (a) and computed (b) O1s Auger spectra. The dashed line in panel (a) corresponds to the experimental CO2 spectrum shifted by +3.0 eV. Assignments for the labeled bands are given in Table II.

Close modal

Table II summarizes computed energies of those final states that provide significant contributions to the main features indicated in Figs. 3–5. The corresponding transition rates, the adiabatic energies, and the dominating configurations are also given. This is consistent with an interpretation of the HNCO spectrum analog to the one of Moddeman’s systematics for CO2:24 The two bands at the lowest binding energies correspond to final-state configurations with vacancies in the weakly bound (W) HOMO (2a″) and HOMO-1 (9a′) orbitals, while the richly structured intermediate region (37-50 eV binding energy) is dominated by Auger decay to final states with vacancies in the 6a′, 7a′, 1a″, and 8a′ orbitals. The bands with even higher binding energies correspond predominantly to Auger decay processes leading to inner-valence shell vacancies in the 4a′ or 5a′ orbital, which have a significant 2s character.

TABLE II.

Final states contributing significantly to the signals numbered in Figs. 3–5. Transition rates (I in 10−3 au), vertical energies Evert and band centers Ebc (in eV) according to the moment theory, and the dominant configurations of the states are also indicated.

DominatingCarbonNitrogenOxygen
TermConfigurationEvertIEbcSignalIEbcSignalIEbcSignal
1A′ 2a″−2 34.6 0.03 35.2 0.40 34.7 0.23 34.9 
1A″ 9a′−1 2a″−1 34.9 0.04 35.3 0.42 35.1 0.24 35.1 
1A′ 9a′−2 35.6 0.05 36.0 0.25 35.9 0.18 35.7 
1A″ 7a′−1 2a″−1 38.7 0.04 39.3 0.03 38.8 0.16 39.1 
1A′ 7a′−1 9a′−1 38.9 0.03 39.4 0.04 39.0 0.13 39.2 
1A′ 1a″−1 2a″−1a 39.2 0.07 40.2 0.25 39.3 0.19 39.7 
1A″ 1a″−1 9a′−1a 39.3 0.06 40.3 0.29 39.5 0.18 39.8 
1A′ 8a′−1 9a′−1a 40.3 0.03 41.3  0.29 40.4  0.11 40.8 
1A″ 6a′−1 2a″−1 41.4 0.01 41.7  0.23 41.9  0.03 41.5  
1A′ 6a′−1 9a′−1a 41.6 0.03 41.9  0.17 42.2  0.08 41.6 
1A″ 1a″−1 8a′−1 42.8 0.10 43.7 0.04 43.6  0.41 42.6 
1A′ 1a″−2a 42.8 0.09 43.7 0.05 43.6  0.39 42.6 
1A′ 8a′−2a 43.5 0.06 44.4 0.03 44.3  0.35 43.4 
1A′ 6a′−1 7a′−1a 44.4 0.04 44.7 0.04 44.8  0.17 44.5  
1A″ 7a′−1 1a″−1a 44.8 0.07 45.7 0.24 45.3 0.22 45.1 
1A′ 6a′−1 8a′−1a 45.2 0.06 45.9 0.26 45.5 0.11 45.5 
1A″ 6a′−1 1a″−1a 45.5 0.02 46.1  0.07 46.2  0.40 45.4 
1A′ 6a′−1 8a′−1a 45.6 0.03 46.1  0.08 46.2  0.39 45.5 
1A′ 7a′−2a 49.1 0.01 49.6  0.00 49.8  0.40 48.7 
1A′ 6a′−2a 52.3 0.02 53.1  0.31 52.7 0.00 53.0  
1A′ 5a′−1 9a′−1a 53.3 0.01 54.6 0.07 53.8  0.00 53.8  
1A″ 5a′−1 2a″−1a 56.9 0.02 58.4 0.05 57.4  0.01 57.5 
1A′ 5a′−1 8a′−1a 59.3 0.01 61.1  0.07 59.9 0.00 59.9  
1A′ 5a′−1 6a′−1a 64.7 0.01 65.8 0.19 65.3  0.02 65.1  
1A″ 4a′−1 1a″−1a 64.9 0.00 66.6  0.00 65.9 0.04 65.1  
1A′ 4a′−1 7a′−1a 66.9 0.00 68.5  0.00 67.8  0.11 67.1 
1A′ 4a′−1 7a′−1a 67.1 0.00 68.8  0.00 68.0  0.07 67.4 
DominatingCarbonNitrogenOxygen
TermConfigurationEvertIEbcSignalIEbcSignalIEbcSignal
1A′ 2a″−2 34.6 0.03 35.2 0.40 34.7 0.23 34.9 
1A″ 9a′−1 2a″−1 34.9 0.04 35.3 0.42 35.1 0.24 35.1 
1A′ 9a′−2 35.6 0.05 36.0 0.25 35.9 0.18 35.7 
1A″ 7a′−1 2a″−1 38.7 0.04 39.3 0.03 38.8 0.16 39.1 
1A′ 7a′−1 9a′−1 38.9 0.03 39.4 0.04 39.0 0.13 39.2 
1A′ 1a″−1 2a″−1a 39.2 0.07 40.2 0.25 39.3 0.19 39.7 
1A″ 1a″−1 9a′−1a 39.3 0.06 40.3 0.29 39.5 0.18 39.8 
1A′ 8a′−1 9a′−1a 40.3 0.03 41.3  0.29 40.4  0.11 40.8 
1A″ 6a′−1 2a″−1 41.4 0.01 41.7  0.23 41.9  0.03 41.5  
1A′ 6a′−1 9a′−1a 41.6 0.03 41.9  0.17 42.2  0.08 41.6 
1A″ 1a″−1 8a′−1 42.8 0.10 43.7 0.04 43.6  0.41 42.6 
1A′ 1a″−2a 42.8 0.09 43.7 0.05 43.6  0.39 42.6 
1A′ 8a′−2a 43.5 0.06 44.4 0.03 44.3  0.35 43.4 
1A′ 6a′−1 7a′−1a 44.4 0.04 44.7 0.04 44.8  0.17 44.5  
1A″ 7a′−1 1a″−1a 44.8 0.07 45.7 0.24 45.3 0.22 45.1 
1A′ 6a′−1 8a′−1a 45.2 0.06 45.9 0.26 45.5 0.11 45.5 
1A″ 6a′−1 1a″−1a 45.5 0.02 46.1  0.07 46.2  0.40 45.4 
1A′ 6a′−1 8a′−1a 45.6 0.03 46.1  0.08 46.2  0.39 45.5 
1A′ 7a′−2a 49.1 0.01 49.6  0.00 49.8  0.40 48.7 
1A′ 6a′−2a 52.3 0.02 53.1  0.31 52.7 0.00 53.0  
1A′ 5a′−1 9a′−1a 53.3 0.01 54.6 0.07 53.8  0.00 53.8  
1A″ 5a′−1 2a″−1a 56.9 0.02 58.4 0.05 57.4  0.01 57.5 
1A′ 5a′−1 8a′−1a 59.3 0.01 61.1  0.07 59.9 0.00 59.9  
1A′ 5a′−1 6a′−1a 64.7 0.01 65.8 0.19 65.3  0.02 65.1  
1A″ 4a′−1 1a″−1a 64.9 0.00 66.6  0.00 65.9 0.04 65.1  
1A′ 4a′−1 7a′−1a 66.9 0.00 68.5  0.00 67.8  0.11 67.1 
1A′ 4a′−1 7a′−1a 67.1 0.00 68.8  0.00 68.0  0.07 67.4 
a

Contribution of this configuration to the state is less than 50%.

Comparing the three spectra at the C, N, and O edges, several differences become obvious: While the bands at the lowest binding energy have only low intensity in the C1s case, they dominate the spectrum for N1s and also show a significant intensity in the O1s spectrum. This is understood by inspection of the hole orbitals (9a′ and 2a″) of the corresponding final states in Fig. 1 and Table I. These MOs have nodes in a plane perpendicular to the NCO axis near to the carbon atom and thus only very small AO coefficients at the latter. As the Auger decay is mostly an intra-atomic process, the transition probability for an Auger decay, in which a HOMO or HOMO-1 electron fills the C1s core hole, is relatively low. By contrast, it is significantly higher for oxygen, and even more so for nitrogen, as the electron density at the respective atoms in the HOMO and HOMO-1 increases in that order.

The K-WW region in the C1s spectrum is dominated by a pronounced peak centered at 39.2 eV BE and a several eV broad band centered around 45 eV. The former is assigned to final dicationic state configurations with one hole in the 2a″ HOMO or 9a′ HOMO-1 and one in the 1a″ HOMO-4 or 7a′ HOMO-5 orbital. The latter is mostly due to final states with two vacancies in the HOMO-3 and HOMO-4 orbitals 8a′ and 1a″. By contrast, transitions to final states with vacancies in lower lying outer-valence orbitals are rather well resolved in the N1s and O1s spectra. The well-localized electron densities at the N and O atoms for the 6a′ and 7a′ molecular orbitals explain this observation, as it leads to higher transition probabilities for Auger decay filling a N1s or O1s core hole than a C1s core hole and thus to more pronounced bands. This becomes, for example, obvious for the well-resolved band in the O1s spectrum at 49.8 eV, which can be assigned to a decay to the 7a′−2 final-state configuration. The latter corresponds to the σ lone pair orbital on the oxygen atom, which has a high electronic density localized at the oxygen atom.

The computations confirm that the spectral regions below 50 eV BE can indeed be assigned to K-SW Auger decay processes involving the inner-valence shell orbitals 4a′ and 5a′. Here, doubly excited dicationic final states also play more important roles leading to a high number of accessible final states and thus broad bands in the experimental spectra.

Figure 6 shows NEXAFS spectra of isocyanic acid near the carbon, nitrogen, and oxygen edges. Each of the spectra was obtained by recording the total ion yield while scanning the photon energy in steps of 20 meV between 287 and 297 eV for the carbon spectrum and 399-408 eV and 532-541 eV for nitrogen and oxygen, respectively.

FIG. 6.

NEXAFS spectra for excitation of carbon (a), nitrogen (b), and oxygen (c) 1s electrons. The vertical arrows indicate the photon energies for which resonant Auger spectra will be discussed in Sec. III C. The bands are assigned in Table III.

FIG. 6.

NEXAFS spectra for excitation of carbon (a), nitrogen (b), and oxygen (c) 1s electrons. The vertical arrows indicate the photon energies for which resonant Auger spectra will be discussed in Sec. III C. The bands are assigned in Table III.

Close modal

By comparing these spectra once again with the respective ones of CO2, the reduced symmetry of HNCO manifests itself in the band structure. While the C1s and O1s absorption spectra of CO2 are dominated by a single broad band centered around 290.8 and 535.3 eV, respectively, which have been assigned to the 1s → π* transition,29,31 the HNCO spectra at all three edges feature two broad bands separated by about 1.5 eV. The LUMO 10a′ and LUMO+1 3a″ orbitals lie close in energy and excitation from the 1s orbital to either of these unoccupied orbitals explain the occurrence of the observed double bands. This assignment is consistently supported by all quantum chemical calculations at Hartree-Fock, valence CI, and MCCEPA/cc-pVTZ levels of theory. The reported excitation energies were obtained at the latter. Besides these broad features, further peaks are visible on the high-energy side, especially in the carbon and nitrogen spectra. These are assigned to Rydberg states. Although only transitions from 1s core orbitals to np Rydberg orbitals are allowed, a close lying molecular state can lend intensity to a ns Rydberg state by configuration mixing or by vibronic coupling.29 A possible assignment of the small peaks at 291.5 eV and 293.0 eV in the C1s spectrum is therefore the 3s and 3p Rydberg states, respectively. In the N1s spectrum, intensity lending of the 10a′ core-excited state to the 3s Rydberg state might explain the occurrence of a double peak at 401.2 and 401.7 eV, while the double peak around 403 eV can be assigned to a 3p Rydberg state. In the oxygen spectrum, Rydberg states are probably concealed by the 1s → 10a′ and 3a″ bands, which are visibly broader compared with C1s and N1s. An overview of the band maxima and the possible assignments are given in Table III. Resonant Auger spectra can give an indication whether a band in the absorption spectrum originates from a molecular or a Rydberg state, as discussed in the supplementary material on the example of the first five bands in the nitrogen spectrum.

TABLE III.

Peak positions in eV and possible assignments of the bands in the NEXAFS spectra of HNCO. Calculated vertical core excitation energies at the MCCEPA/cc-pwCPTZ level are given in brackets.

C1sN1sO1sPossible assignment
288.9 (289.5) 400.1 (400.8) 534.0 (534.0) 1s−1 10a′1 
290.3 (290.8) 401.7 (402.0) 535.5 (535.5) 1s−1 3a″1 
291.5 401.2 … 3s Rydberg 
293.0 403.0 … 3p Rydberg 
… 403.9 … 4s, 4p Rydberg 
C1sN1sO1sPossible assignment
288.9 (289.5) 400.1 (400.8) 534.0 (534.0) 1s−1 10a′1 
290.3 (290.8) 401.7 (402.0) 535.5 (535.5) 1s−1 3a″1 
291.5 401.2 … 3s Rydberg 
293.0 403.0 … 3p Rydberg 
… 403.9 … 4s, 4p Rydberg 

In the next step, resonant Auger spectra were recorded at each of the photon energies indicated by the vertical arrows in Fig. 6 to get a better understanding of the nature of these resonances and to identify regions where interesting molecular dynamics occur. A series of RAES corresponding to the C1s → 10a′ excitation is depicted in Fig. 7. Besides the photon energy on top of the resonance at 288.8 eV [panel (c)], resonant Auger electron spectra on the resonance’s low-energy flank (b) and high-energy flank (d) were recorded, as well as an off-resonance photoelectron spectrum at 287.1 eV (a). Auger electrons with energies between 220 and 295 eV were detected by scanning the electron analyzer in steps of 50 meV. Binding energies were calculated from the difference of the photon energy and the Auger electron kinetic energy.

FIG. 7.

Resonant Auger spectra measured at photon energies corresponding to a C1s → 10a′ excitation [panels (b)–(d)]. An off-resonance spectrum is shown in (a) (note the different scale of the intensity axis). Panel (e) depicts the calculated resonant Auger spectrum where vibrational broadening was described with the moment theory, while the spectrum in panel (f) shows the stick spectrum resulting from vertical transitions at the ground state structure. The red line in (f) is a convolution of this stick spectrum with a Gaussian with full width at half maximum of 1 eV. Peaks marked with asterisks originate from core ionization by second-harmonic synchrotron light.

FIG. 7.

Resonant Auger spectra measured at photon energies corresponding to a C1s → 10a′ excitation [panels (b)–(d)]. An off-resonance spectrum is shown in (a) (note the different scale of the intensity axis). Panel (e) depicts the calculated resonant Auger spectrum where vibrational broadening was described with the moment theory, while the spectrum in panel (f) shows the stick spectrum resulting from vertical transitions at the ground state structure. The red line in (f) is a convolution of this stick spectrum with a Gaussian with full width at half maximum of 1 eV. Peaks marked with asterisks originate from core ionization by second-harmonic synchrotron light.

Close modal

The off-resonant spectrum shows the valence photolines of HNCO. Several of these lines become enhanced by resonant Auger decay at particular photon energies. It becomes obvious that there is a very strong enhancement of the two bands at binding energies of 15.9 and 17.8 eV (signals 3 and 4), when the on-resonance spectra are compared with the off-resonance ones. By contrast, a comparable enhancement is not observed for the lowest lying bands at 11.8 and 12.5 eV (signals 1 and 2). In addition, broad spectral features with a binding energy above 20 eV are enhanced by resonant excitation into the 10a′ orbital. Comparison with the computed RAES spectrum depicted in panel (e) of Fig. 7 shows similarities but a rather unsatisfactory agreement with the experimental spectrum. However, the theoretical data can be used to interpret the spectrum as indicated in panel (f) of Fig. 7, which shows a Gaussian convolution of the stick spectrum obtained by plotting the one-center resonant Auger transition rates at the calculated binding energies of all final states obtained at the ground state structure of the HNCO molecule. This “vibration-free” RAES spectrum compares much better with its experimental counterpart than the moment theory analog where the band positions and widths are individually determined by modeling the time evolution of vibrational motions initiated upon core excitation. As all other calculated spectra are in much better agreement with the experiment (see below and above), we deduce that the theoretical protocol employed in this work is unusually inappropriate for the C1s RAES in the first resonance. This failure seems to be related to the simulation of vibrational broadening by the moment method and is most probably due to errors in the gradients that are used to estimate line widths and shifts by the moment theory. Please note that the broadband approximation in the moment theory cannot be the reason for the overestimation of the bandwidths in the theoretical spectra, as the experimental RAES spectra obtained with different excitation energies give rise to very similar RAES spectra with much narrower signals. The sum of all these spectra weighted with the respective absorption intensities is the broadband-excited RAES spectrum, which is thus not well reproduced with the moment theory. All other AES and RAES spectra presented in this work compare much more favorably with the experimental data (see above and below).

Nevertheless, the calculated spectrum allows for a reasonable assignment of the bands, which is given in Table IV. Bands below 21 eV binding energy correspond primarily to participator Auger transitions leading to 1h final states, while bands at higher binding energy are mostly correlated to spectator Auger decay processes to 2h1p final states. The two lowest lying bands (1 and 2) at 11.8 and 12.5 eV are assigned to the states with dominant 2a″−1 and 9a′−1 configurations and experience no enhancement in RAES. The 2a″ and 9a′ molecular orbitals are composed mostly of oxygen and nitrogen p-orbitals, while the contribution of the carbon AOs is almost negligible (see Table I). In analogy to the explanation for the weak bands for 2h final states with vacancies in these orbitals in the normal AES, the partial resonant Auger rate is consequently low. By contrast, the carbon AOs have a larger contribution to the 8a′ and 1a″ molecular orbitals leading to a strong enhancement of the band at 15.9 eV (signal 3) due to participator decay into these single-hole states. A less pronounced signal is found for the band at 17.8 eV (4) correlated to the 7a′−1 final state which is in line with the carbon AO contribution of the 7a′ orbital. By scanning the photon energy over the first resonance in the C1s NEXAFS spectrum, the enhancement of these participator states is significantly reduced on the high-energy flank (289.4 eV) and the band assigned to the 8a′−1 and 1a″−1 final-state configurations (3) at 15.9 eV experiences a significant broadening. This indicates that the Franck-Condon overlap between the core-excited intermediate and ionic final state changes when scanning the photon energy along the first resonance. A high resolution study focused on this energy region should provide more details on these nuclear dynamics during core excitation. As stated above, the RAES is dominated by spectator Auger decay in the binding energy region above 21 eV. This is supported not only by the theoretical results but also by the fact that the electron angular distribution β-parameter for these bands is very small (0.0 ± 0.3), while it is clearly positive (β ≈ 0.4 ± 0.2) for the participator transitions at lower binding energies. The most prominent features in the high-energy region, the broad bands centered around 24.4 and 29.9 eV (signals 6 and 7), can be assigned mainly to final-state configurations with the spectator electron left in the 10a′ orbital and one hole in either the 1a″ or 8a′ (6) or the 7a′ and 6a′ (7) and a second hole in another outer-valence shell orbital. Shake-up processes, in which the spectator electron is excited to another virtual orbital or a third electron experiences an excitation, lead to the observed broadening in the high binding energy region. In general, the spectral characteristics are very similar to the CO2 C1s → 2Πu resonant Auger spectrum33,36,37,64 as well as the one of the related OCS molecule.48 For CO2, the A2Πu participator state is clearly dominating, which corresponds to the strongly enhanced 8a′−1 and 1a″−1 final-state configurations for HNCO. The 1πu−2u1 state has an important contribution in the lower energy spectator state region in the CO2 spectrum, while at higher energies final states like 3σu−1u−1u1 or 4σg−1u−1u1 occur.33 These final states correspond also to the ones identified to be contributing to the spectral structure in HNCO.

TABLE IV.

Final states contributing significantly to the signals in the resonant Auger spectra in Figs. 7–9. Transition rates (I in 10−3 a.u.),69 vertical energies Evert and band centers Ebc (in eV), and the dominating configurations of the states are also indicated.

DominantCarbonNitrogenOxygen
TermConfigurationEvertIEbcSignalIEbcSignalIEbcSignal
2A″ 2a″−1 11.5 0.02 13.1 0.11 12.0 0.07 12.2 
2A′ 9a′−1 12.0 0.01 14.6 0.11 12.8 0.10 12.9 
2A′ 8a′−1 14.9 0.28 16.5 0.01 15.3 0.05 15.3 
2A″ 1a″−1 15.0 0.17 16.6 0.01 15.4 0.03 15.4 
2A′ 7a′−1 16.6 0.08 18.6 0.01 17.2 0.07 17.2 
2A″ 9a′−1 2a″−1 10a′1 18.9 0.02 19.9  0.10 19.0 0.06 19.1 
2A′ 2a″−2 10a′1 19.0 0.01 19.2  0.26 18.9 0.16 19.0 
2A′ 6a′−1 19.2 0.05 18.7 0.10 19.5 0.00 19.5  
2A″ 9a′−1 2a″−1 10a′1a 19.5 0.01 20.5  0.11 19.6 0.08 19.7 
2A′ 9a′−1 2a″−1 3a″1a 19.7 0.02 21.5 0.06 20.1  0.05 20.1 
2A″ 7a′−1 2a″−1 10a′1 22.8 0.03 22.7 0.02 22.6  0.08 22.8 
2A′ 1a″−1 2a″−1 10a′1a 24.4 0.06 25.5 0.23 24.5  0.07 24.8 
2A″ 9a′−1 2a″−1 10a′1a 24.5 0.01 25.3  0.22 24.6 0.00 24.8  
2A′ 1a″−1 2a″−1 10a′1a 24.8 0.04 26.0 0.14 25.0 0.03 25.2 
2A″ 1a″−1 2a″−1 3a″1a 25.0 0.03 26.2 0.15 25.1 0.04 25.3 
2A′ 9a′−1 2a″−1 3a″1a 25.3 0.03 27.2 0.10 25.7 0.01 25.8  
2A′ 8a′−1 9a′−1 10a′1a 25.9 0.01 27.8  0.24 26.2 0.02 26.4  
2A′ 6a′−1 9a′−1 10a′1a 26.2 0.03 24.6 0.10 25.8 0.05 25.7 
2A″ 1a″−1 8a′−1 10a′1a 27.3 0.03 27.6  0.01 27.2  0.12 27.1 
2A′ 8a′−2 10a′1a 27.6 0.04 28.4 0.07 27.7  0.09 27.7 
2A″ 1a″−1 2a″−1 3a″1a 27.9 0.00 28.4  0.00 28.0  0.17 27.9 
2A′ 8a′−1 9a′−1 10a′1a 28.1 0.01 28.6  0.01 28.0  0.31 28.0 
2A″ 1a″−1 8a′−1 10a′1a 28.6 0.01 29.3  0.01 28.5  0.17 28.4 
2A′ 1a″−1 8a′−1 3a″1a 28.7 0.01 29.4  0.01 28.7  0.14 28.6 
2A′ 8a′−1 9a′−1 2a″−1 3a″1 10a′1a 29.2 0.01 30.1  0.04 29.2  0.13 29.3 
2A′ 6a′−1 7a′−1 10a′1a 29.2 0.05 27.5 0.02 28.9  0.09 28.7 
2A′ 1a″−2 10a′1a 29.3 0.03 29.6  0.01 29.3  0.18 29.1 
2A′ 7a′−1 8a′−1 10a′1a 30.3 0.01 31.1  0.00 30.4  0.13 30.3 
2A″ 6a′−1 1a″−1 10a′1 30.3 0.01 29.0  0.14 30.1 0.01 30.0  
2A′ 6a′−1 7a′−1 10a′1a 30.3 0.01 30.7  0.00 30.5  0.08 30.3 
2A′ 6a′−1 7a′−1 10a′1a 30.4 0.01 29.5  0.00 30.3  0.12 30.2 
2A″ 7a′−1 1a″−1 10a′1a 30.7 0.04 29.7 0.16 30.3 0.19 30.3 
2A′ 7a′−1 9a′−1 10a′1a 30.8 0.00 31.2  0.02 30.9  0.11 30.8 
2A′ 6a′−1 9a′−1 10a′1a 31.0 0.07 30.2 0.26 30.8 0.01 30.9  
2A″ 6a′−1 1a″−1 10a′1a 31.2 0.01 31.7  0.02 31.2  0.24 31.1 
2A″ 6a′−1 1a″−1 10a′1a 31.3 0.01 31.7  0.02 31.2  0.13 31.2 
2A′ 7a′−2 10a′1a 34.7 0.02 34.9  0.00 34.6  0.44 34.3 
2A′ 1a″−1 8a′−1 9a′−1 3a″1 10a′1a 37.9 0.01 37.6  0.09 37.7 0.00 37.7  
2A′ 6a′−2 10a′1a 38.1 0.03 36.2  0.22 37.6 0.00 37.6  
2A′ 5a′−1 9a′−1 10a′1a 43.4 0.01 43.8  0.17 43.3 10 0.01 43.5  
2A″ 4a′−1 1a″−1 10a′1a 49.9 0.01 49.6  0.00 49.5  0.14 49.3 
2A′ 4a′−1 8a′−1 10a′1a 49.9 0.00 49.4  0.00 49.7  0.11 49.4 
2A″ 4a′−1 1a″−1 10a′1a 50.2 0.01 50.1  0.00 49.9  0.15 49.7 
2A′ 4a′−1 7a′−1 2a″−1 3a″1 10a′1a 53.5 0.00 53.0  0.00 53.1  0.14 52.9 
2A′ 4a′−1 1a″−1 9a′−1 3a″1 10a′1a 53.5 0.00 53.4  0.00 53.2  0.12 53.0 
2A′ 4a′−2 10a′1a 69.5 0.00 68.9  0.00 69.1  0.08 68.7 
DominantCarbonNitrogenOxygen
TermConfigurationEvertIEbcSignalIEbcSignalIEbcSignal
2A″ 2a″−1 11.5 0.02 13.1 0.11 12.0 0.07 12.2 
2A′ 9a′−1 12.0 0.01 14.6 0.11 12.8 0.10 12.9 
2A′ 8a′−1 14.9 0.28 16.5 0.01 15.3 0.05 15.3 
2A″ 1a″−1 15.0 0.17 16.6 0.01 15.4 0.03 15.4 
2A′ 7a′−1 16.6 0.08 18.6 0.01 17.2 0.07 17.2 
2A″ 9a′−1 2a″−1 10a′1 18.9 0.02 19.9  0.10 19.0 0.06 19.1 
2A′ 2a″−2 10a′1 19.0 0.01 19.2  0.26 18.9 0.16 19.0 
2A′ 6a′−1 19.2 0.05 18.7 0.10 19.5 0.00 19.5  
2A″ 9a′−1 2a″−1 10a′1a 19.5 0.01 20.5  0.11 19.6 0.08 19.7 
2A′ 9a′−1 2a″−1 3a″1a 19.7 0.02 21.5 0.06 20.1  0.05 20.1 
2A″ 7a′−1 2a″−1 10a′1 22.8 0.03 22.7 0.02 22.6  0.08 22.8 
2A′ 1a″−1 2a″−1 10a′1a 24.4 0.06 25.5 0.23 24.5  0.07 24.8 
2A″ 9a′−1 2a″−1 10a′1a 24.5 0.01 25.3  0.22 24.6 0.00 24.8  
2A′ 1a″−1 2a″−1 10a′1a 24.8 0.04 26.0 0.14 25.0 0.03 25.2 
2A″ 1a″−1 2a″−1 3a″1a 25.0 0.03 26.2 0.15 25.1 0.04 25.3 
2A′ 9a′−1 2a″−1 3a″1a 25.3 0.03 27.2 0.10 25.7 0.01 25.8  
2A′ 8a′−1 9a′−1 10a′1a 25.9 0.01 27.8  0.24 26.2 0.02 26.4  
2A′ 6a′−1 9a′−1 10a′1a 26.2 0.03 24.6 0.10 25.8 0.05 25.7 
2A″ 1a″−1 8a′−1 10a′1a 27.3 0.03 27.6  0.01 27.2  0.12 27.1 
2A′ 8a′−2 10a′1a 27.6 0.04 28.4 0.07 27.7  0.09 27.7 
2A″ 1a″−1 2a″−1 3a″1a 27.9 0.00 28.4  0.00 28.0  0.17 27.9 
2A′ 8a′−1 9a′−1 10a′1a 28.1 0.01 28.6  0.01 28.0  0.31 28.0 
2A″ 1a″−1 8a′−1 10a′1a 28.6 0.01 29.3  0.01 28.5  0.17 28.4 
2A′ 1a″−1 8a′−1 3a″1a 28.7 0.01 29.4  0.01 28.7  0.14 28.6 
2A′ 8a′−1 9a′−1 2a″−1 3a″1 10a′1a 29.2 0.01 30.1  0.04 29.2  0.13 29.3 
2A′ 6a′−1 7a′−1 10a′1a 29.2 0.05 27.5 0.02 28.9  0.09 28.7 
2A′ 1a″−2 10a′1a 29.3 0.03 29.6  0.01 29.3  0.18 29.1 
2A′ 7a′−1 8a′−1 10a′1a 30.3 0.01 31.1  0.00 30.4  0.13 30.3 
2A″ 6a′−1 1a″−1 10a′1 30.3 0.01 29.0  0.14 30.1 0.01 30.0  
2A′ 6a′−1 7a′−1 10a′1a 30.3 0.01 30.7  0.00 30.5  0.08 30.3 
2A′ 6a′−1 7a′−1 10a′1a 30.4 0.01 29.5  0.00 30.3  0.12 30.2 
2A″ 7a′−1 1a″−1 10a′1a 30.7 0.04 29.7 0.16 30.3 0.19 30.3 
2A′ 7a′−1 9a′−1 10a′1a 30.8 0.00 31.2  0.02 30.9  0.11 30.8 
2A′ 6a′−1 9a′−1 10a′1a 31.0 0.07 30.2 0.26 30.8 0.01 30.9  
2A″ 6a′−1 1a″−1 10a′1a 31.2 0.01 31.7  0.02 31.2  0.24 31.1 
2A″ 6a′−1 1a″−1 10a′1a 31.3 0.01 31.7  0.02 31.2  0.13 31.2 
2A′ 7a′−2 10a′1a 34.7 0.02 34.9  0.00 34.6  0.44 34.3 
2A′ 1a″−1 8a′−1 9a′−1 3a″1 10a′1a 37.9 0.01 37.6  0.09 37.7 0.00 37.7  
2A′ 6a′−2 10a′1a 38.1 0.03 36.2  0.22 37.6 0.00 37.6  
2A′ 5a′−1 9a′−1 10a′1a 43.4 0.01 43.8  0.17 43.3 10 0.01 43.5  
2A″ 4a′−1 1a″−1 10a′1a 49.9 0.01 49.6  0.00 49.5  0.14 49.3 
2A′ 4a′−1 8a′−1 10a′1a 49.9 0.00 49.4  0.00 49.7  0.11 49.4 
2A″ 4a′−1 1a″−1 10a′1a 50.2 0.01 50.1  0.00 49.9  0.15 49.7 
2A′ 4a′−1 7a′−1 2a″−1 3a″1 10a′1a 53.5 0.00 53.0  0.00 53.1  0.14 52.9 
2A′ 4a′−1 1a″−1 9a′−1 3a″1 10a′1a 53.5 0.00 53.4  0.00 53.2  0.12 53.0 
2A′ 4a′−2 10a′1a 69.5 0.00 68.9  0.00 69.1  0.08 68.7 
a

Contribution of this configuration to the state is less than 50%.

Figure 8 shows the experimental and theoretical resonant Auger spectra after N1s → 10a′ excitation. Here, a very good agreement between experiment and theory is obtained for the complete calculation in which all vibrational degrees of freedoms are considered in the moment theory approach. In the following, only the spectra recorded on top and on the rising edge of this transition at a photon energy of 400.1 and 399.9 eV, respectively, will be discussed due to the complex NEXAFS spectrum at higher photon energies (see Fig. 6). The spectra were recorded for an Auger electron energy range between 320 and 400 eV and a step size of 50 meV was employed.

FIG. 8.

Resonant Auger spectra measured on the low-energy side (b) and the peak (c) of the N1s → 10a′ resonance. Also shown is an off-resonance spectrum in panel (a) as well as the computed resonant Auger spectrum (d). Peaks marked with asterisks originate from core ionization by second-harmonic synchrotron light.

FIG. 8.

Resonant Auger spectra measured on the low-energy side (b) and the peak (c) of the N1s → 10a′ resonance. Also shown is an off-resonance spectrum in panel (a) as well as the computed resonant Auger spectrum (d). Peaks marked with asterisks originate from core ionization by second-harmonic synchrotron light.

Close modal

Contrary to the C1s excitation, though rather weak, an enhancement of the two lowest bands at 11.5 and 12.2 eV binding energy (signals 1 and 2) is observed when comparing the intensity for the spectrum recorded on top of the resonance with the off-resonance spectrum, which are both normalized to the same scale. As discussed above, these bands originate from participator Auger decay to final-state configurations with vacancies in the 2a″ HOMO and 9a′ HOMO-1 molecular orbitals. Since these MOs have significant contributions of nitrogen AOs but only small ones of the carbon analogs, the corresponding final states are strong in the nitrogen RAES but weak in the carbon spectrum as predicted by the theoretical spectrum shown in panel (d) of Fig. 7. Theory predicts a stronger enhancement than observed experimentally, most likely because the direct photoionization channel is not explicitly included in our theoretical framework. The bands observed at 15.6 and 17.3 eV (signals 3 and 4), which are assigned to final-state configurations with vacancies in the 8a′, 1a″, and 7a′ orbitals, experience no enhancement by the resonant excitation as the electron density in the vicinity of the N atom is low in these orbitals due to a nodal plane. By contrast, the electron density at the nitrogen atom is high for the 6a′ orbital and the calculation thus predicts a stronger enhancement. However, the latter transition cannot be clearly resolved in the experimental spectrum being superimposed with the lowest lying 2h1p final-state configurations from spectator Auger decay. A rather broad band is thus observed at 19.2 eV (signal 5). The N1s RAES spectrum is dominated by spectator states above this binding energy. Here, again final-state configurations with vacancies in the 9a′, 2a″, and 6a′ orbitals play a more important role than configurations with only 8a′, 1a″, or 7a′ vacancies due to the larger contributions of the nitrogen AOs to these molecular orbitals. The comparison of the resonant spectra recorded on the low-energy flank and on top of the 3a″ resonance reveals no major changes of spectral features. This indicates that the core excitation does not produce the intermediate state in a large manifold of vibrational levels as there are only minor changes in the geometry upon core excitation.

Although the general spectrum structure is rather different, the observed enhancement of bands in the resonant Auger spectrum for the O1s → 10a′ excitation, which is depicted in Fig. 9, is very similar to the one observed at the N edge. The oxygen spectrum was recorded at 534.0 eV and Auger electrons in the kinetic energy range of 450–530 eV were analyzed in 50 meV steps.

FIG. 9.

Experimental (a) and computed (b) resonant Auger spectra measured at the peak of the O1s → 10a′ resonance. The feature marked with an asterisk originates from core ionization by second-harmonic synchrotron light.

FIG. 9.

Experimental (a) and computed (b) resonant Auger spectra measured at the peak of the O1s → 10a′ resonance. The feature marked with an asterisk originates from core ionization by second-harmonic synchrotron light.

Close modal

Spectator state transitions clearly dominate the spectrum, whereas participator Auger decay leading to final-state configurations with vacancies in the highest molecular orbitals is relatively weak. This is consistent with the theoretical spectrum [panel (b) of Fig. 9], again obtained for the complete approach, and can be explained by the small contribution of oxygen AOs to the 10a′ orbital. It owes to the high electron affinity of the oxygen atom whose AOs have thus large contributions to the occupied molecular orbitals and correspondingly small contributions of the energetically higher virtual orbitals (10a′ and 3a″). This effect is increased by electronic rearrangement due to core-hole generation. The 2a″ HOMO and 9a′ HOMO-1 molecular orbitals of HNCO are nearly symmetric on the oxygen side with respect to the nitrogen side and the electron density is only slightly higher on the nitrogen side. Therefore, similar behavior in the enhancement of Auger decay processes involving these orbitals is expected for nitrogen and oxygen, whereupon the relative enhancement in the oxygen spectrum should be slightly lower. The experimental spectrum matches in general these expectations for the 2a″−1 and 9a′−1 final states (signals 1 and 2). Furthermore, the bands observed at 16.1 and 17.7 eV (features 3 and 4), which are assigned to 8a′−1 or 1a″−1 and 7a′−1, respectively, show also a similar enhancement pattern when comparing the N1s and the O1s RAES spectra. However, an increased intensity is not observed for the 2a″−1 and 9a′−1 final-state signals in the HNCO O1s → 10a′ RAES. The latter could have been expected from the CO2 O1s → 2πu spectrum, in which the X2Πg state is well pronounced.33,35 Since the photon energy was not scanned across this excitation band, the role of nuclear motion in the excited state39,41 or the contribution of a Rydberg state35 as in CO2 cannot be discussed any further for now.

So far in the discussion, the assignment of the observed bands in the resonant Auger spectra was done by comparison with the theoretical results as summarized for all three edges in Table IV. Since there is a convincing agreement for both the binding energies and the relative intensities between experiment and theory, these assignments seem to be consistent. An additional check is the comparison of the resonant Auger spectra with the valence shell and normal Auger spectra. The bands in valence shell photoelectron spectra are correlated to a transition of an electron from an occupied molecular orbital into the ionization continuum leading to 1h final states. The same final state, which is characterized by a defined binding energy, i.e., the difference between photon energy and kinetic energy of the emitted electron, is reached in a participator Auger decay. 1h final states in photoelectron spectroscopy are, however, only accessible inside the Franck-Condon region, whereas this limitation is much less strict in non-direct Auger decay processes. The comparison between the resonant Auger spectra and the well-studied valence shell photoelectron spectrum of HNCO,10–13 which was recorded at a photon energy of 100 eV, yields a convincing agreement for the spectral positions of the bands assigned to participator Auger decay with transitions leading to final-state vacancies in the HOMO, HOMO-1, HOMO-2, etc., orbitals (Fig. 10). The differences in peak shapes can be explained by the evolution of vibrational wave packets in the context of the Kramers-Heisenberg formula as discussed, e.g., in Refs. 22, 23, 36, and 65. The latter is, for example, clearly observed for the band centered at a binding energy of 15.9 eV, which is significantly broader than the respective one in the valence spectrum. This band contains contributions of the 2A′ 8a′−1 and 2A″ 1a″−1 final states and a vibrational progression is visible in the valence spectrum. The origin of this progression has not yet been unambiguously resolved due to the close proximity of the 2A′ and 2A″ states,12 but it is obvious that the vibrational envelope of this band is significantly broadened in the C1s RAES. In general, our assignments of the low BE bands in the HNCO resonant Auger spectra are consistent with the valence spectrum.

FIG. 10.

Comparison between the Auger spectra measured at the peak of the 1s → 10a′ resonances [(a)–(c)] and the valence photoelectron spectrum recorded at 100 eV (d).

FIG. 10.

Comparison between the Auger spectra measured at the peak of the 1s → 10a′ resonances [(a)–(c)] and the valence photoelectron spectrum recorded at 100 eV (d).

Close modal

The bands originating from spectator Auger decay, on the other hand, can be compared with the bands observed in normal Auger spectroscopy, as observed previously for several di- and triatomic molecules.33,66–68 This is shown in Fig. 11. Spectator Auger decay produces 2h1p final states, whereas 2h final states are reached in normal Auger decay. The binding energy of the electrons in the neutral spectator intermediate state is lower than in the cationic intermediate state involved in normal Auger decay. This leads to a screening effect of the electron residing in the virtual orbital on the emitted Auger electron and thus to a shift of the RAES spectator bands to higher kinetic energies compared with normal Auger decay. The screening effect is found to be 8 eV in the C1s RAES and 9 eV in the N1s and O1s spectra, respectively. Shifting the Auger kinetic energy spectrum by that amount leads to an almost perfect agreement of line positions and shapes between the spectator decay part of the resonant Auger spectrum and the normal Auger one.

FIG. 11.

Comparison between the 1s → 10a′ resonant Auger spectra (RAES) with the respective normal one (AES) at the carbon (a), nitrogen (b), and oxygen (c) K-edges. The RAES are shifted to higher kinetic energies due to the screening effect of the spectator electron.

FIG. 11.

Comparison between the 1s → 10a′ resonant Auger spectra (RAES) with the respective normal one (AES) at the carbon (a), nitrogen (b), and oxygen (c) K-edges. The RAES are shifted to higher kinetic energies due to the screening effect of the spectator electron.

Close modal

The similarity between the spectator region in the RAES and the corresponding spectral features in AES may be explained by the argument that the spectating electron does not influence the electronic structure of the final states. Investigation of Tables II and IV shows that this argument is frequently valid, but it is in general an oversimplification. It holds for the lowest binding energy feature (signal 1) in the N1s AES, which is assigned to decay into the 1A′ (2a″−2) and the 1A″ (9a′−1 2a″−1) states (see Table II) and corresponds to the feature in the N 1s-110a′ excited RAES spectrum (signal 5), where it is assigned to the 2A′ (2a″−2 10a′) and the 2A″ (9a′−1 2a″−1 10a′) final states with vertical energies of 19.0 eV and 18.9 eV. A more detailed inspection shows that the AES contains also a very weak signal due to the 3A″ (9a′−1 2a″−1) state, for which a vertical energy (Evert) of 33.8 eV was calculated. The Auger transition to this state is very weak as the nitrogen atoms contributes mostly 2p AOs to the 9a′ and 2a″ MOs and as in KLL Auger decay to 2p−2 final states is parity forbidden. In the RAES final states, the spectator electron mixes the singlet and triplet configurations causing that several 9a′−1 2a″−1 10a′ configurations contribute to this spectrum and two further ones with vertical energies of 19.5 eV and 24.5 eV are found in Tables IV. Both of these states contain significant admixtures of other configurations. This example shows that RAES and AES final states and their appearance in the spectra show similarities, but the former can be affected by additional splitting due to the interaction of the two-hole configurations with the spectator electron. Actually, a more detailed analysis of the RAES and AES spectra in Fig. 11 shows that the former are generally more blurred than the latter. The carbon AES shows a pronounced minimum at 255 eV kinetic energy, for example, whereas the corresponding RAES feature shows only a slight dip in a broad band. Similar features are found in the N AES at a kinetic energy of about 368 eV and in the broad structure between 494 and 500 eV kinetic energy of the O AES.

As discussed above, the main difference between HNCO and CO2 is the reduced symmetry lifting the degeneracy of the π orbitals in CO2. Thus, a difference in the resonant Auger spectrum might be expected, depending on whether the core electron is excited to the LUMO 10a′ orbital, which has a nodal plane perpendicular to the molecular plane, or the LUMO+1 3a″ orbital with a nodal plane coinciding with the molecular plane. Resonant Auger spectra were hence recorded on top of the corresponding resonances as determined in the NEXAFS spectrum at 290.4, 401.2, and 535.3 for C1s, N1s, and O1s excitations, respectively. Apart from this change in photon energy, the experimental settings were identical to the ones for the respective first resonances. The obtained experimental spectra are depicted in Fig. 12 and a comparison with computed spectra is shown in the supplementary material.

FIG. 12.

Resonant Auger spectra recorded at the peak of the carbon (a), nitrogen (b), and oxygen (c) 1s → 3a″ resonances at photon energies of 290.4, 401.2, and 535.5 eV, respectively. The corresponding 10a′ RAES spectra are shown in light colors for comparison.

FIG. 12.

Resonant Auger spectra recorded at the peak of the carbon (a), nitrogen (b), and oxygen (c) 1s → 3a″ resonances at photon energies of 290.4, 401.2, and 535.5 eV, respectively. The corresponding 10a′ RAES spectra are shown in light colors for comparison.

Close modal

The main spectral features are very similar for 1s → 10a′ and 1s → 3a″ excitations, which is unsurprising considering the small energy difference and very similar electronic densities around the N, C, and O atoms for the LUMO and LUMO+1 orbitals. However, if the geometries of the intermediate core-excited state and the final ionic states differ slightly for the two Auger decay pathways, a change in the width and intensity of the observed bands in the resonant Auger spectra is expected due to a different vibrational overlap. This is observed in the C1s RAES spectrum in the sharper band associated with the 8a′−1 and 1a″−1 final-state configurations at 15.9 eV binding energy, whose intensity normalized on the photon flux and gas sample pressure is also greater by a factor of about 1.5 compared with the core excitation into the 10a′ molecular orbital. Similar but less pronounced sharpening of the N1s and O1s resonant Auger spectra indicates that the geometries of the corresponding intermediate and final states are also more similar in the 3a″ case than in the 10a′ resonance, leading to Auger decay with fewer vibrational levels. While the shape of participator signals does not exhibit much change when going from the first to the second resonance, a significant band broadening is visible in particular in the N1s and O1s spectra above 20 eV, a region dominated by spectator decay. Furthermore, the NEXAFS spectra in Fig. 6 show a second peak near the N1s-3a″ resonance pointing to nearby Rydberg states. Such a Rydberg resonance may also exist in the featureless second peak of the O1s NEXAFS spectrum. Thus, the band broadening of the spectator features in the resonant Auger spectra in Figs. 12(b) and 12(c) is probably due to the excitation into Rydberg states which leads to additional unresolved features in the resonant Auger spectra.

As expected, the participator part of the 1s → 3a″ and 1s → 10a′ spectra in Fig. 12 appears at the same binding energy but with slightly different vibrational progressions. On the contrary, the spectator part of the 1s → 3a″ Auger spectra is found at lower binding energy than the corresponding signals in the 1s → 10a′ decay. This indicates that energetically higher states are populated in the latter decay processes due to the higher energy of the spectator electron. This interpretation is supported by the calculated resonant Auger spectra (see the supplementary material), which show the same features. Furthermore, a discussion on RAES measured on top of the first five N1s resonances is also included in the supplementary material, which allowed for a preliminary investigation of the Rydberg character of those bands.

Normal Auger, NEXAFS, and resonant Auger spectra of HNCO were recorded at the carbon, nitrogen, and oxygen K-edges, employing soft X-ray synchrotron radiation provided by the high-resolution beamline PLEIADES at Synchrotron SOLEIL. An ab initio approach was used to compute the normal and the resonant Auger electron spectra employing the configuration interaction approach combined with Auger transition rates from the one-center approximation and the moment theory to represent vibrational features. In general, an excellent agreement of experiment and theory is obtained, supporting the newly introduced, partially empiric scaling of the computed final-state energies. Comparison of theoretical and experimental spectra allows for a reliable assignment of the dominant bands in all regions of the normal and resonant Auger spectra. Since isocyanic acid is isosteric to CO2, the C1s and O1s Auger spectra of the molecules are very similar. However, as the degeneracy of the CO2 π-orbitals is lifted in HNCO, a more complex band structure is observed in the latter spectrum. Only minor changes are visible in the resonant Auger spectra of the C, N, and O 1s → 10a′ transitions when scanning the photon energy over the first resonance. The resonant Auger spectra resulting from the decay of the corresponding 1s → 3a″ excited states (second resonance) are rather similar to the first resonance (10a′) counterparts. The former show slightly less vibrational features pointing to smaller structural changes and broader spectator features, which are explained by a mixed Rydberg-valence character of the second resonance.

As HNCO is a small molecule and contains the most abundant elements of organic molecules, the reported spectra will be very helpful when testing the performance of new theoretical methods with reasonable computational cost. The detailed comparison of our theoretical approach with consistent experimental data demonstrates the potential of our theoretical protocol to become a routine tool for the interpretation and analysis of normal and resonant Auger electron spectra. However, the approach for describing vibrational features would profit from a more balanced description of details of the related potential energy surfaces and the moment theory should be adapted for RAES cases with narrow bandwidth excitations and for Renner-Teller coupling in the core-excited states that were discussed for RAES spectra of the CO2 molecule.36,39 Further challenges lie in the description of Rydberg-excited states and development of efficient methods for more extended systems. The latter seems feasible as the computations shown in the present work can be reproduced within less than 1 h on a single node of an ordinary PC. As a result of this work, theoretical approaches with improvements in these points are presently developed.

See supplementary material for the comparison between the experimental and the calculated resonant Auger electron spectra for the carbon, nitrogen, and oxygen 1s → 3a″ resonances as well as for the experimental resonant Auger electron spectra for selected N1s resonances.

The experiments were performed at the PLEIADES beamline at Synchrotron SOLEIL, France. We thank E. Robert for technical assistance and the SOLEIL staff for stable operation of the equipment and storage ring during the experiments. We acknowledge E. Kukk, M.-N. Piancastelli, R. Püttner, and O. Travnikova for fruitful discussion. M. Gühr acknowledges funding via the Office of Science Early Career Research Program through the Office of Basic Energy Sciences, U.S. Department of Energy and NB under Grant No. DE-SC0012376. M. Gühr is funded by a Lichtenberg Professorship from the Volkswagen foundation. I. Fischer acknowledges DFG, Project Nos. FI 575/7-3 and 13-1, for funding. T. J. A. Wolf thanks the German National Academy of Sciences Leopoldina for a fellowship (Grant No. LPDS2013-14).

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Auger intensities are given in lifetime width contributions; i.e., the sum of these contributions for one core-hole state corresponds to the lifetime width due to Auger decay.

Supplementary Material