Orbital picture in molecular inner-shell excited states of Rydberg-valence mixed character

Abstract

The core-to-sigma* excited state is repulsive for the bond elongation; on the other hand, the core ionized state and the core-to-pi* state are bound and the core-to-Rydberg states are almost parallel to the potential energy curve of the core ionized state. Thus, the core-electron excitation to the unoccupied sigma* orbital can be mixed with the one-electron Rydberg or continuum orbital, as dependent on the bond distance, and even with the unoccupied pi* orbital in some cases. Within the framework of one-electron picture, we show sigma* orbitals mixed with Rydberg character in the 1s excitation of O2 and CH3F, and Rydberg orbitals mixed with valence character in the 1s excitation of CH4, CO2, and N2O.

Orbital picture in molecular inner-shell excited states of Rydberg-valence mixed character

Nobuhiro Kosugi

UVSOR, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan

ABSTRACT

The core-to-s* excited state is repulsive for the bond elongation; on the other hand, the core ionized state and the core-to-p* state are bound and the core-to-Rydberg states are almost parallel to the potential energy curve of the core ionized state. Thus, the core-electron excitation to the unoccupied s* orbital can be mixed with the one-electron Rydberg or continuum orbital, as dependent on the bond distance, and even with the unoccupied p* orbital in some cases. Within the framework of one-electron picture, we show s* orbitals mixed with Rydberg character in the 1s excitation of O₂ and CH₃F, and Rydberg orbitals mixed with valence character in the 1s excitation of CH₄, CO₂, and N₂O.

I. INTRODUCTION

The atomic and molecular core-to-Rydberg excitation is converging to a certain core ionization threshold (E_th). In addition, most molecules have unoccupied molecular orbitals of anti-bonding valence character such as s* and p*. These anti-bonding orbitals can also accept an excited electron from the inner shell. The potential energy curve of the core-to-s* valence excited state [1] is repulsive for a specified s bond; then, the core-to-s* excited state is lower than the continuum and Rydberg region at the longer bond distance and is embedded in the continuum at the shorter distance. That is, two kinds of interaction involving the valence state should be discussed along the potential energy curve for a specified s bond[1]: the Rydberg-valence interaction below E_th and the continuum-valence interaction above E_th. In the present work, we discuss the former interaction within one-electron picture and show how the valence and/or Rydberg orbitals look like through the interactions.

II. RYDBERG CONTRIBUTION IN CORE-TO-s* EXCITATION

A. O₂

N₂ has a triple covalent bond and the 3s_u* molecular orbital is of strong antibonding character; then, the N1s excitation to this s* orbital is observed above E_th as a well-known shape resonance. In molecules having weak covalent bonds, the 1s ® s* excited state is possibly observed below E_th. We can expect Rydberg-valence (RV) mixings in the case of the same p-symmetry as the 2ps* orbital. As already discussed [1,2], the strong RV mixing results in new potential energy curves due to the avoided curve crossing of the Rydberg (p-type) and valence (2ps*) states.

The Rydberg features in the O 1s excitation spectrum of O₂ with a triplet ground state are very complicated due to two ionization thresholds, ⁴S⁺ and ²S⁺ [2,3]. The angle-resolved photoion spectroscopy (ARPIS) has shown that the core-to-s* (3s_u*) excited states give exchange-split two strong resonances in the Rydberg region [2,3] and that the ⁴S⁺ channel gives vibrational enhancements in the 3ps Rydberg state and the ²S⁺ channel has no distinct evidence for the RV mixing [2]. Fig. 1 shows (a) this 3s_u* orbital before the RV mixing and ^(b) the RV-mixed 3ps-3s_u* orbital in the Franck-Condon region. This kind of the RV mixing is not effective for the s-type or d-type Rydberg states with different symmetry from the 2ps* orbital.

B. CH₃ F

In N₂, the N1s excitation to the p* orbital is located lower than the Rydberg region. Even in saturated molecules, the excitation to the s* orbital is possibly located below the Rydberg region in the case of very weak s covalent bonds. In CH₃F with a very weak s covalent bond between CH₃ and F, we have observed a broad and strong s* (6a₁) band below the Rydberg region and a weak shoulder arising from the 3sa₁ Rydberg [4]. The s* (6a₁) and 3sa₁ Rydberg orbitals are shown in Fig. 2, indicating that the 3sa₁ orbital of the CH₃ fragment is deformed by orthogonalization to the valence electrons of the F atom. There might be more or less RV mixing due to the avoided crossing for the same a₁ symmetry.

III. VALENCE CONTRIBUTION IN CORE-TO-RYDBERG EXCITATION

A. CH₄

A simple molecular orbital picture predicts that the CH₄ molecule has the 2t₂* and 3a₁* antibonding molecular orbitals. In the case of inner-shell excitation, the C1s (1a₁) ® 3a₁ excitation is dipole forbidden but the C1s (1a₁) ® 2t₂ excitation is dipole allowed. However, no distinct 2t₂* resonance is observed in the C1s photoabsorption of CH₄ [5]. The C1s photoabsorption spectrum shows many distinct Rydberg states, vibronically allowed 3sa₁, strong npt₂ series, and ndt₂ series. The Rydberg region in CH₄ (C1s) [5] seems to be almost the same as in CH₃F (C1s) [4]. It is noticed that the C1s (1a₁) ® 3pt₂ Rydberg excited state with three-fold degeneracy should be affected by Jahn-Teller (JT) distortion. Fig. 3 shows one of the three degenerate 3pt₂ Rydberg orbitals in CH₄ in comparison with the 3sa₁ Rydberg orbital. Considering that the 3pt₂ orbital has no valence contribution and is purely atomic-like, we could expect a very weak JT distortion in the 3pt₂ Rydberg state [6]. However, recent high-resolution C1s photoabsorption spectra of CH₄ [7,8] have shown that the 3pt₂ Rydberg state shows strong vibrational contributions in addition to the total symmetric vibration. This vibrational enhancement should arise from the JT effect in CH₄. Fig. 4 shows ^(b) a C_3v-distorted 3p Rydberg orbital, together with (a) the 2t₂* orbital obtained without any diffuse function. The JT distorted 3pt₂ orbital can get a large 2t₂* contribution. This valence mixing gives intensities to the vibronically excited states of the C1s (1a₁) ® 3pt₂ excitation.

B. CO₂(C1s)

In the C1s (2s_g) excitation spectrum of CO₂, the strongest Rydberg state is of 3ss_g symmetry [8,9]. However, the C1s (2s_g) ® 3ss_g Rydberg excitation is dipole-forbidden. Fig. 5 shows a contour map of the 3ss_g Rydberg orbital (Fig. 5(a)), which is mixed with the 5s_g* antibonding orbital (Fig. 5(b)). This valence mixing does not give any intensity from the C1s (2s_g). On the other hand, Fig. 6 shows an orbital map for the same 3s Rydberg orbital at a bent geometry. The 3s Rydberg state has a large p* contribution. The C1s (2s_g) ® 2p_u* valence excited state has a stable bent geometry due to the Renner-Teller effect on electronically degenerate states in linear polyatomic systems [10]. This bending geometry, or bending motion in terms of molecular dynamics, is related to the vibronically induced 3ss_g Rydberg transition. In high-resolution ARPIS spectra, bending vibrational fine structures are resolved in the C1s (2s_g) ® 3ss_g and 4ss_g Rydberg bands [8,9].

C. N₂O and CO₂ (terminal N and O)

N₂O and CO₂ are isoelectronic and the molecular orbitals look similar. The lowest s* (8s*) and 3s Rydberg orbitals excited from the central N (N_c) are shown in Fig. 7. The orbital character is nearly the same as in CO₂ (C1s) shown in Fig. 5. The N_c 1s excitation of N₂O is expected to be similar to the C1s excitation of CO₂. Unfortunately, the N1s excitation spectra include contributions from two N 1s edges and do not show clear evidence for bending mode coupling in the N_c manifold [11]. On the other hand, the lowest s* orbitals (8s* of N₂O in Fig. 7(a) and 5s_g* of CO₂ in Fig. 5(a)) have a large ps component on the terminal N (N_t) and O. Fig. 8 shows a contour map of the "4s" Rydberg orbital excited from the N_t 1s. The N_t 4s Rydberg orbital has a large 8s* contribution with a ps component as shown in Fig. 7(a) and get its intensity from the N_t 1s ® ps component [1,11]. Although the s-type Rydberg series is generally expected to be weak in the 1s photoabsorption, the Rydberg regions of the N_t 1s and O1s excitations of N₂O and CO₂ are dominated in the observed spectra [7,8,11] by the s-type Rydberg states (4s most dominant) due to the lowest s* mixing with the ps component on the terminal atoms. However, it is noted that the 1s ® 8s* excitation of N₂O and 1s ® 5s_g* excitation of CO₂ are not definitely identified as the 1s ® 2t₂* of CH₄. In these cases, it is reasonable to think that the valence contribution is dissolved in the Rydberg sea [1,6,12].

IV. SUMMARY

Using molecular orbitals, we have discussed how the 1s ® s* excited state looks like in the 1s excitation of O₂ and CH₃F, and how we know evidence for the 1s ® s* contribution in photoabsorption spectra of CH₄, CO₂, and N₂O. In the former molecules, the excitation to the s* orbital is identified in the Franck-Condon region from the ground state; in the latter molecules, the excitation to the s* orbital is not clearly identified but its evidence is observed through the Rydberg-valence mixing in the Franck-Condon region. In O₂, the s* (3s_u*) orbital is mainly mixed with the 3ps_u Rydberg orbital converging to the ⁴S⁺ ionization. In CH₃F, the excitation to the s* (6a₁*) orbital is observed below the 3sa₁ Rydberg state. On the other hand, in CH₄, the Jahn-Teller distortion of the 3pt₂ Rydberg transition induces contribution from the s* (2t₂*) orbital component. In the 1s excitations from the terminal atoms in CO₂ and N₂O, some lower s-type Rydberg states get intensities from the s* (5s_g* and 8s*) component. In the 1s excitations from the central atoms in CO₂ and N₂O, the 1s ® s* excited state with gerade-gerade transition is a dipole-forbidden (dark) state (not exactly from N_c in N₂O). In CO₂, the C1s excitation to the 3ss_g Rydberg orbital is vibronically enhanced through mixing with the C1s excitation to the p* (2p_u*) orbital with the Renner-Teller effect.

Acknowledgements

The author acknowledges fruitful discussion with Dr. Miyabi Hiyama from a theoretical point of view and with Dr. Jun-ichi Adachi from an experimental point of view. The present work was partly supported by Grant-in-Aid for Scientific Research (B) from the Japan Society for the Promotion of Science (JSPS).

Received on 14 January, 2005

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Publication Dates

• Publication in this collection
  17 Jan 2006
• Date of issue
  Dec 2005

History

• Received
  14 Jan 2005