BF3 Valence and Rydberg States As Probed by Electron Energy Loss

Article pubs.acs.org/JPCA

BF3 Valence and Rydberg States As Probed by Electron Energy Loss Spectroscopy and ab Initio Calculations D. Duflot,† M. Hoshino,*,‡ P. Limaõ -Vieira,*,‡,§ A. Suga,‡ H. Kato,‡ and H. Tanaka‡ †

Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), UMR CNRS 8523, Université de Lille, F-59655 Villeneuve d’ Ascq Cedex, France ‡ Department of Physics, Sophia University, Tokyo 102-8554, Japan § Laboratório de Colisões Atómicas e Moleculares, CEFITEC, Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal ABSTRACT: In this contribution we probe BF3 low-lying excited singlet states measured at 100 eV, 2.8° scattering angle and triplet states at 40 eV, 40° scattering angle, while sweeping the energy loss over the range 10.0− 20.0 eV. The electronic state spectroscopy has been investigated and the assignments supported by quantum chemical calculations. This provides the first comprehensive investigation of all singlet and triplet excited electronic states of boron trifluoride up to the first ionization potential. A generalized oscillator strength analysis is employed to derive oscillator strength f 0 value and integral cross sections (ICSs) from the corresponding differential cross sections (DCSs). The f 0 value is compared with the optical oscillator strength (OOS) from photoabsorption, and the unscaled Born ICSs are then compared with relevant energy and binary-encounter and f-scaled Born cross section (BEf-scaling) results determined as a part of this investigation. The lowest n members of the Rydberg series have been assigned as converging to the lowest ionization energy limits of boron trifluoride and classified according to the magnitude of the quantum defects (δ).

1. INTRODUCTION Boron trifluoride, BF3, has attracted interest from the international scientific community in regard to its quite broad range of technological applications as a sensitive neutron detector,1 as an alternative agent for plasma doping,2 and for metal surface treatment,3 but in particular as a feed gas in plasma processing of materials through jet plasma chemical vapor deposition in gaseous mixtures.4−6 Due to its relevance at the industrial and technological levels, as well as the need to accurately model the underlying plasma chemical processes, a set of detailed electron collision cross sectional data is needed. Thus, one rationale for the present study is to present for the first time electron energy loss spectra of BF3 at different electron impact energies and scattering angles, together with a detailed interpretation of the electronic state spectroscopy of such molecule. BF3 has been extensively studied by VUV photoabsorption,7−9 fluorescence,10 and photoelectron11−16 spectroscopies, as well as by electron beam experiments associated with temporary negative ion formation and ionization17 and by electron impact vibrational excitation.18 Electron scattering experimental studies on boron trifluoride include the grand total cross section (TCS) measurements by Szmytkowski and co-workers19 covering an energy range in the 0.6−370 eV. Recently, despite those spectroscopic experiments, quantitative measurements in swarm experiments have provided absolute cross sections for electron transport and rate coefficients.20 We © 2014 American Chemical Society

note that elastic integral, differential, and momentum transfer cross sections were calculated through a Schwinger multichannel method (SCM),21,22 whereas Vinodkumar et al.23 reported total elastic and total inelastic cross sections using a spherical complex optical potential (SCOP), with Nikitovic et al.24 using a Monte Caro code to model electron kinetics in BF3. Finally, a literature survey shows that ab initio studies of BF3 are rather old.12 Along with our program for providing electron−molecule collision cross sectional data, absolute differential cross sections, integral, and momentum transfer cross sections have been determined for elastic scattering from 1.5 to 200 eV and for vibrational excitation from 1.5 to 15 eV.25 These were also compared with our independent atom model with screening corrected additivity rule (IAM-SCAR) calculations.25 In contrast to several studies reported in the literature, there are still some inconsistencies in the assignments of electronic excited states among photoabsorption and electron energy loss data, while to our knowledge, no high-resolution electron energy loss spectrum has been reported for BF3 so far. However, we report the results of an extensive study on the electronic state spectroscopy of BF3 by high-resolution electron energy loss spectroscopy. In addition, comprehensive results Received: September 16, 2014 Revised: October 22, 2014 Published: October 22, 2014 10955

dx.doi.org/10.1021/jp509375y | J. Phys. Chem. A 2014, 118, 10955−10966

The Journal of Physical Chemistry A

Article

Figure 1. Shape of the Hartree−Fock MO’s (aug-cc-pVQZ) of BF3.

from ab initio quantum chemical calculations of the vertical excitation energies and oscillator strengths for the neutral electronic transitions are also given, to accurately evaluate lowlying singlet and triplet excited states. The ionization energies (IEs) for the lowest ionic states are also estimated using different levels of theory. Furthermore, BEf-scaling26 is applied to the intense optically allowed (π, 1e″) → (2a2″, π*) transition, and thus, the integral cross section is estimated to elucidate its contribution to the total inelastic cross section. In the next section, we provide a brief summary of the structure and properties of BF3. In section 3, we present a brief discussion of the experimental methods, and in section 4 the computational details are described. Section 5 is devoted to presenting and discussing the results of our study with a comparison with others being made where possible. Finally, some conclusions that can be drawn are given in section 6.

lengths of 1.3100 and 1.3112 Å, respectively. These values are consistent with the recommended values from NIST27 (1.307 Å) and the CRC Handbook of Chemistry and Physics (1.313 Å).28 BF3 is a planar molecule and has a high symmetry (D3h) in its electronic ground state. The symmetry species available to a D3h molecule are A1′, A2′, E′, A1″, A2″, and E″ and the calculated electron configuration of the X̃ 1A1′ ground state is (core) 1e′4 1a1′2 2a1′2 and (valence) 3a1′2 2e′4 4a1′2 3e′4 1a2″2 4e′4 1e″4 1a2′2. Examination of the ground-state MOs (Figure 1) shows that the highest occupied molecular orbital (HOMO) 1a2′ and the second highest occupied molecular orbital (HOMO−1) 1e″ have F 2p lone pair in-plane and out-ofplane character, respectively, whereas the HOMO−2 4e′ has F 2p lone pair in-plane character and HOMO−3 1a2″ has π(B− F) character. The lowest unoccupied molecular orbitals (LUMO), 2a2″, the (LUMO+1), 5a1′, and (LUMO+2), 5e′, are mainly of π*(B−F), σ*(B−F), and σ*(B−F) antibonding character, respectively. The theoretical studies have shown considerable overlap of the lowest Rydberg states with valence states. The calculated transition energies, oscillator strengths, and the main character of the wave function are shown in

2. BRIEF SUMMARY OF THE STRUCTURE AND PROPERTIES OF BF3 The BF3 calculated geometry optimized at CCSD(T) level with the aug-cc-pVQZ and cc-pV6Z basis set establish R(B−F) bond 10956



Article

Table 1. Calculated Vertical Excitation Energies (EOM-CCSD Level at the aug-cc-pVQZ+R basis set) (eV) and Oscillator Strengths (Singlet States) of Boron Trifluoride (BF3) Compared with Experimental Data and Other Work (Energies in eV) (Details in Text) C2v X̃ 1A1 1 B1 1 A2 1 B2 + 1A2 1 B1 + 1A1 1 B1 + 1A1 1 B2 + 1A2 1 A2 1 B1 + 1A1 1 B1 1 B2 1 B1 + 1A1 1 B2 + 1A2 1 A2 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 A1 1 B1 + 1A1 1 A2 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 B2 + 1A2 1 B1 1 B2 1 B2 + 1A2 1 B1 1 B1 + 1A1 1 A1 1 B1 + 1A1 1 A2 1 B2 + 1A2 1 B1 + 1A1 1 B1 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 B2 1 A1 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 A2 1 A2 1 B1 + 1A1 1 B1 1 B2 + 1A2 1 B1 1 A1 1 B2 1 B1 + 1A1 1 A2 1 A2 1 B1 + 1A1

D3h X̃ 1A1′ 1 A2′ 1 A1″ 1 E″ 1 E′ 1 E′ 1 E″ 1 A1″ 1 E′ 1 A′2 1 A2″ 1 E′ 1 E″ 1 A1″ 1 A2′ 1 E″ 1 E′ 1 A1′ 1 E′ 1 A1″ 1 A2′ 1 E″ 1 E′ 1 E″ 1 A2′ 1 A2″ 1 E″ 1 A2′ 1 E′ 1 A1′ 1 E′ 1 A1″ 1 E″ 1 E′ 1 A2′ 1 A1′ 1 E″ 1 E′ 1 A2′ 1 A1′ 1 A2′ 1 E″ 1 E′ 1 A1″ A1″ 1 E′ 1 A2′ 1 E″ 1 E′ 1 E′ 1 E″ 1 E′ 1 A1″ 1 A1″ 1 E′

E (eV) 11.674 11.799 12.456 12.772 13.399 12.917 13.694 13.726 14.104 14.094 14.431 14.474 14.478 14.511 14.519 14.522 14.810 14.855 14.911 14.913 14.934 14.953 15.065 15.103 15.193 15.259 15.272 15.280 15.347 15.357 15.389 15.395 15.402 15.462 15.502 15.533 15.534 15.593 15.598 15.607 15.603 15.620 15.611 15.633 15.639 15.679 15.699 15.731 15.734 15.741 15.755 15.774 15.777 15.784

fL

⟨r2⟩a

assignment

0.000000 0.000000 0.000000 0.089056 0.402924 0.000000 0.000000 0.001068 0.000000 0.334790 0.000087 0.000000 0.000000 0.000000 0.000000 0.094892 0.000000 0.000002 0.000000 0.000000 0.000000 0.004773 0.000000 0.000000 0.113489 0.000000 0.000000 0.001068 0.000000 0.010004 0.000000 0.000000 0.000072 0.000000 0.000000 0.000000 0.001808 0.005112 0.000000 0.000000 0.000000 0.001525 0.000000 0.000000 0.003118 0.000000 0.000000 0.000000 0.000000 0.020222 0.112476 0.000000 0.000000 0.002022

46 62 47 62 64 54 47 103 100 138 88 130 134 101 169 106 101 102 235 341 200 159 279 149 447 103 514 540 549 129 350 923 160 721 1153 165 178 175 181 92 1102 746 1235 200 1721 1241 2235 197 160 156 160 200 269 328 331

ground state (5b1, 1a2′) → 3sσ/σ*(a1,a′1) (5b1, 1a2′) → (3b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → 3sσ/σ*(a1,a′1) (4b1 + 8a1, 4e′) → 3sσ/σ*(a1, a′1) (1a2 + 2b2, π, 1e″) → (3b2, 2a2″, π*) (4b1 + 8a1, 4e′) → (3b2, 2a2″, π*) (5b1, 1a2′) → 3pπ(b2, a2″) (5b1, 1a2′) → 3pσ(a1 + b1, e′) (5b1, 1a2′) → 4sσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3pσ(a1 + b1, e′) (5b1, 1a2′) → 3dδ(a1 + b1, e′) (5b1, 1a2′) → 3dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 3pσ(a1 + b1, e′) (5b1, 1a2′) → 3dσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3pσ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3pπ(b2, e′) (4b1 + 8a1, 4e′) → 3pσ(a1 + b1,e′) (5b1, 1a2′) → 4pσ(a1 + b1, e′) (5b1, 1a2′) → 4pπ(b2, a2″) (5b1, 1a2′) → 4dσ(a1, a′1) (4b1 + 8a1, 4e′) → 3pπ(b2, a2″) (5b1, 1a2′) → 4dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 4sσ(a1, a′1) (5b1, 1a2′) → 5sσ(a1,a′1) (1b2, 1a2″) → 3sσ/σ*(a1, a′1) (5b1, 1a2′) → 4dπ(a2 + b2, e″) (5b1, 1a2′) → 5dσ(a1, a′1) (5b1, 1a2′) → 5dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (4b1 + 8a1, 4e′) →4sσ(a1,a′1) (5b1, 1a2′) → 5pπ(b2, a2″) (1a2 + 2b2, π, 1e″) → 3dσ(a1, a′1) (4b1 + 8a1, 4e′) → 3pσ(a1 + b1, a′1) (5b1, 1a2′) → 6sσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 3dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 3dδ(b1 + a1, e′) (1b2, 1a2″) → (3b2, 2a2″, π*) (5b1, 1a2′) → 6dσ(a1, a′1) (5b1, 1a2′) → 5dπ(a2 + b2, e′) (5b1, 1a2′) → 5pσ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dδ(b1 + a1, e′) (5b1, 1a2′) → 6pπ(b2, a2″) (5b1, 1a2′) → 6pσ(a1 + b1, e′) (5b1, 1a2′) → 7sσ(a1,a′1) (1a2 + 2b2, π, 1e″) → 3dπ(b2 + a2, e″) (4b1, 8a1, 4e′) → 3dδ(a1 + b1, e″) (4b1 + 8a1, 4e′) → 3dδ(b1 + a1, e′) (4b1 + 8a1, 4e′) → 3dπ(b2 + a2, e′) (4b1 + 8a1, 4e′) → 3dσ(b1,a1, e″) (4b1 + 8a1, 4e′) → 3dπ(b2,a2, e″) (1a2 + 2b2, π, 1e″) → 4pσ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 4pπ(b2, e′) 10957

E (eV) exp

ref 9

ref 10

13.13 13.13

13.200 13.130

13.19

13.98

13.973

13.98 14.70

14.654

14.70 15.016

15.23

15.289

15.23/15.56

15.56

15.640

15.56

16.10



Article

Table 1. continued D3h

E (eV)

fL

⟨r2⟩a

assignment

E″ 1 E′ 1 A2″ 1 A2′ 1 E′ 1 A1″ 1 E″ 1 E″ 1 E′ 1 A2′ 1 E″ 1 A1′ 1 E″ 1 E′ 1 A1′ 1 A1′ 1 E″ 1 E′ 1 A2′

15.789 15.803 15.827 15.830 15.867 15.906 15.923 15.974 15.977 16.039 16.064 16.088 16.112 16.118 16.128 16.150 16.169 16.170 16.194

0.000000 0.001054 0.000934 0.000000 0.000028 0.000000 0.000000 0.000000 0.011852 0.000000 0.000000 0.000000 0.000000 0.005926 0.000000 0.000000 0.000000 0.001002 0.000200

337 350 337 2274 950 1407 147 443 632 622 386 346 516 457 507 539 577 561 588

(1a2 + 2b2, π, 1e″) → 4pσ(a1, a′1) (4b1 + 8a1, 4e′) → 3dσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 4pσ(b1 + a1,e ′) (5b1, 1a2′) → 8sσ(a1,a′1) (5b1, 1a2′) → 7pσ(a1 + b1, e′) (5b1, 1a2′) → 7pπ(b2, a2″) (7a1 + 3b1, 3e′) →(b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → 5sσ(a1, a′1) (5b1, 1a2′) → 8pσ(a1 + b1, e′) (5b1, 1a2′) → 9sσ(a1, a′1) (4b1 + 8a1, 4e′) → 4pπ(b2, a2″) (4b1 + 8a1, 4e′) → 3pσ(b1 + a1, e′) (1a2 + 2b2, π, 1e″) → 4dσ(a1, a′1) (4b1 + 8a1, 4e′) → 4dσ(a1 + b1, e″) (1a2 + 2b2, π, 1e″) → 4dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 4dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 4dδ(a1, b1, e′) (1a2 + 2b2, π, 1e″) → 4dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 4dδ(b1 + a1, e′)

C2v 1

B2 1 B1 1 B2 1 B1 1 B1 1 A2 1 B2 1 B2 1 B1 1 B1 1 B2 1 A1 1 B2 1 B1 1 A1 1 B1 1 B2 1 B1 1 B2 a

1

+ A2 + 1A1

+ 1A1 + 1A2 + 1A1 + 1A2 + 1A2 + 1A1

+ 1A2 + 1A1

1

E (eV) exp 16.10

ref 9

ref 10

≈16

Mean value of r2 (electronic radial spatial extents).

ensure their Knudsen numbers are approximately equal, so that the gas beam profiles remain similar. The actual head pressures behind the nozzle were about 0.5 Torr for BF3 and 2.5 Torr for He, which have been derived from the values of the hard sphere diameters for BF3 and He as 6.04 and 2.18 Å, respectively. 3.2. BF3 Sample. The gas sample used in the EELS experiment was purchased from Takachiho Chemical Company, with a stated purity of >99%. The sample was used as delivered.

Tables 1−3 for singlet and triplet states (EOM-CCSD results). The lowest vertical ionization energies have been experimentally obtained at 15.95 (1a2′)−1, 16.67 (1e″)−1, 17.122 (4e′)−1, 19.18 (1a2″)−1, 20.09 (3e′)−1, and 21.50 eV (4a1′)−1.15 The calculated vertical IEs at the CCSD(T) geometry are presented in Table 4 and agree reasonably well with the experimental data. The experimental values have been used to calculate the quantum defects associated with transitions to Rydberg orbitals (section 5.3). Finally, the components of the polarizability tensor, obtained at the Hartree−Fock level using the aug-ccpVQZ basis set at the CCSD(T) geometry are α∥ = 2.17 × 10−24 cm3 and α⊥ = 1.75 × 10−24 cm3, in reasonably good agreement with the recommended value of 3.31 × 10−24 cm3.28

4. COMPUTATIONAL SECTION 4.1. Ab Initio Calculations. Calculations were performed to determine the geometry and excitation energies of the neutral molecules (Tables 1−3) and the vertical ionization energies (Table 4) using the MOLPRO program.36 Because MOLPRO cannot handle nonabelian symmetry groups, the calculations are performed using the smallest abelian subgroup of D3h, i.e., C2v. The ground state geometry was optimized at the frozen core coupled cluster single−double with perturbative triples (CCSD(T))37 level using Dunning’s aug-cc-pVQZ38 and aug-cc-pV6Z atomic basis sets.39 The electronic spectra were computed at the equation of motion EOM-CCSD level38 at the obtained CCSD(T) geometries. For a better description of Rydberg excited states, a set of diffuse functions (6s, 6p, 4d), taken from Kaufmann et al.,40 localized on the B atom, was added to the original basis set (aug-cc-pVQZ+R and cc-pV6Z +Rbasis sets). The oscillator strengths of the electric dipole transitions were calculated using the length gauge after obtaining the dipole transition moment between the ground and excited states using the standard formula (in au):

3. EXPERIMENTAL DETAILS 3.1. Electron Energy Loss Spectroscopy. The electron energy loss spectrometer used in this work has been described sufficiently in previous publications.29−31 In brief, the system is of a crossed electron-molecular beam type with a hemispherical monochromator (differentially pumped) and analyzer with an electron lens system controlled by computer-driven voltages. The setup was operated at impact energies from 20 to 300 eV and an angular range from −20° to +150°, with typical energy resolution of 100 meV, full width at half-maximum (fwhm). The electron energy scale was calibrated against the 19.37 eV Feshbach resonance in He. The angular scale and resolution (3.0° (fwhm)) were determined from the symmetry in the intensity profile of the He 21P excitation measured at the 0° nominal-scattering angle. The molecular beam was produced effusively from a nozzle, a simple tube (L = 5 mm, D = 0.3 mm), kept at slightly elevated temperatures (50−70°) throughout the measurements to avoid nozzle surface contamination by BF3. The observed elastic scattered electrons were converted into absolute cross sections by using the standard relative flow technique with He differential cross sections (DCSs) as the reference species.32 For a comprehensive description of this technique see refs 33−35. This implies adjustment of the relative gas (BF3, He) pressures to

fL =

2 ΔE |⟨Ψgs|r|Ψexc⟩|2 3

Finally, the lowest vertical ionization energies of BF3 were also obtained at the restricted RCCSD(T) level (Table 4), using partial third-order (P3) propagation and outer valence green function (OVGF)41 calculations,42 as implemented in the Gaussian 09 package.43 Gaussian 09 was also used to obtain the 10958



Article

Table 2. Calculated Vertical Excitation Energies (EOM-CCSD Level at the cc-pV6Z+R Basis Set) (eV) and Oscillator Strengths (Singlet States) of Boron Trifluoride (BF3) Compared with Experimental Data and Other Work (Energies in eV) (Details in Text) C2v X̃ 1A1 1 B1 1 A2 1 B2 + 1A2 1 B1 + 1A1 1 B2 + 1A2 1 B1 + 1A1 1 A2 1 B1 + 1A1 1 B2 1 B1 1 B1 + 1A1 1 A2 1 B2 + 1A2 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 A1 1 B1 + 1A1 1 A2 1 B1 1 B2 + 1A2 1 B1 + 1A1 1 B2 + 1A2 1 B1 1 B2 1 B2 + 1A2 1 B1 1 B1 + 1A1 1 B1 + 1A1 1 A1 1 B1 + 1A1 1 B2 + 1A2 1 B1 1 B1 1 B1 + 1A1 1 B2 + 1A2 1 B2 1 B1 + 1A1 1 B1 1 A2 1 A2 1 B2 + 1A2 1 B1 + 1A1 1 B1 1 B2 + 1A2 1 A1 1 B1 + 1A1 1 A2 1 B1 1 B2 1 B2 + 1A2 1 A1 1 A1 1 B2

D3h X̃ 1A1′ 1 A2′ 1 A1″ 1 E″ 1 E′ 1 E″ 1 E′ 1 A1″ 1 E′ 1 A2″ 1 A′2 1 E′ 1 A1″ 1 E″ 1 A2′ 1 E″ 1 E′ 1 A1′ 1 E′ 1 A1″ 1 A2′ 1 E″ 1 E′ 1 E″ 1 A2′ 1 A2″ 1 E″ 1 A2′ 1 E′ 1 E′ 1 A1′ 1 E′ 1 E″ 1 A2′ 1 A1′ 1 E′ 1 E″ 1 A2′ 1 E′ 1 A2′ 1 A1″ 1 A1″ 1 E″ 1 E′ 1 A2′ 1 E″ 1 A1′ 1 E′ 1 A1″ 1 E′ 1 E″ 1 E″ 1 A1′ 1 E′ 1 A2′

E (eV) 11.728 11.850 12.514 12.830 12.972 13.462 13.759 13.787 14.160 14.175 14.516 14.555 14.575 14.588 14.593 14.600 14.883 14.914 14.969 14.973 14.997 15.011 15.132 15.160 15.255 15.331 15.338 15.343 15.421 15.445 15.464 15.489 15.519 15.606 15.622 15.622 15.667 15.681 15.683 15.686 15.689 15.693 15.710 15.737 15.804 15.835 15.835 15.838 15.839 15.843 15.848 15.851 15.883 15.888

fL

⟨r2⟩a

assignment

0.000000 0.000000 0.000000 0.088948 0.000000 0.399564 0.000000 0.000911 0.329662 0.000000 0.000058 0.000000 0.000000 0.000000 0.000000 0.093168 0.000000 0.000026 0.000000 0.000000 0.000000 0.005000 0.000000 0.000000 0.113332 0.000000 0.000000 0.000598 0.012788 0.000000 0.000914 0.000000 0.000000 0.000000 0.001744 0.000000 0.004102 0.000128 0.000000 0.000000 0.000000 0.000000 0.003632 0.000000 0.000000 0.000194 0.092272 0.000000 0.000000 0.013328 0.000000 0.004988 0.000736 0.001212

46 62 47 62 64 47 53 104 101 88 144 135 103 130 171 125 103 103 241 345 205 156 278 153 459 105 560 567 573 488 132 601 168 1188 182 188 189 189 1574 1226 446 1500 728 878 2063 200 170 252 336 181 176 340 292 391 340

(5b1, 1a2′) → 3sσ/σ*(a1, a′1) (5b1, 1a2′) → (3b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → 3sσ/σ(a1, a′1) (4b1 + 8a1, 4e′) → 3sσ/σ*(a1, a′1) (4b1 + 8a1, 4e′) → (3b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → (3b2, 2a2″, π*) (5b1, 1a2′) → 3pπ(b2, a2″) (5b1, 1a2′) → 3pσ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3pσ(b1 + a1, e′) (5b1, 1a2′) → 3dσ(a1, a′1) (5b1, 1a2′) → 3dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3pσ(a1 + b1,e ′) (5b1, 1a2′) → 3dπ(a2 + b2, e″) (5b1, 1a2′) → 4sσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3pσ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3pπ(b2, e′) (4b1 + 8a1, 4e′) → 3pσ(a1 + b1,e′) (5b1, 1a2′) → 4pσ(a1 + b1, e′) (5b1, 1a2′) → 4pπ(b2, a2″) (5b1, 1a2′) → 4dσ(a1, a′1) (4b1 + 8a1, 4e′) → 3pπ(b2, a2″) (5b1, 1a2′) → 4dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dσ(a1, a′1) (5b1, 1a2′) → 5sσ(a1, a′1) (1b2, 1a2″) → 3sσ/σ*(a1, a′1) (5b1, 1a2′) → 4dπ(a2 + b2, e″) (5b1, 1a2′) → 5dσ(a1, a′1) (5b1, 1a2′) → 5pσ(a1 + b1, e′) (4b1 + 8a1, 4e′) → 4sσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (5b1, 1a2′) → 5dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (5b1, 1a2′) → 6sσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 3dπ(a2 + b2, e″) (1a2 + 2b2, π, 1e″) → 3dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 3dδ(b1 + a1, e′) (5b1, 1a2′) → 6dδ(a1 + b1, e′) (5b1, 1a2′) → 6dσ(a1, a′1) (1a2 + 2b2, π, 1e″) → 4pσ(b1 + a1, e′) (5b1, 1a2′) → 6pπ(b2, a2″) (5b1, 1a2′) → 5pσ(a1 + b1, e′) (5b1, 1a2′) → 6pσ(a1 + b1, e′) (5b1, 1a2′) → 7sσ(a1, a′1) (4b1 + 8a1, 4e′) → 3dπ(b2 + a2, e″) (4b1 + 8a1, 4e′) → 3pσ(b1, a1, e′) (4b1 + 8a1, 4e′) → 3pσ(b1 + a1, e′)/ 3dδ(a1 + b1, e′) (4b1 + 8a1, 4e′) → 3dπ(b2 + a2, e′) (4b1 + 8a1, 4e′) → 3dδ(a1 + b1, e′) (4b1 + 8a1, 4e′) → 3dπ(b2 + a2, e′) (1a2 + 2b2, π, 1e″) → 4pσ(b1, e′) (1a2 + 2b2, π, 1e″) → 4dπ(a2 + b2, e″) (4b1 + 8a1, 4e′) → 3dδ(a1 + b1, e′) (1a2 + 2b2, π, 1e″) → 4dδ(a1 + b1, e′) 10959

E (eV) exp

ref 9

ref 10

13.13

13.200

13.19

13.13

13.130

13.98 13.98

13.973

14.70

14.654

14.70 15.016

15.23

15.289

15.23/15.56

15.56

15.640

15.56

16.10



Article

Table 2. continued D3h

E (eV)

fL

⟨r2⟩a

A1″

15.929

0.000069

841

C2v 1

a

1

A1

E (eV) exp

assignment

ref 9

ref 10

(5b1, 1a2′) → 7pπ(b2, a2″)

Mean value of r2 (electronic radial spatial extents).

Table 3. Lowest Valence and Rydberg Triplet Transition Energies (eV) of Boron Trifluoride (BF3) Calculated at the EOMCCSD/aug-cc-pVQZ+R Level (Details in Text)a C2v

D3h

3

3

B1 3 A2 3 A1 + 3B1 3 A2 + 3B2 a

A′2 3 A″1 3 E′ 3 E″

assignment

E(T)

E(S)

exp

quantum defect

(5b1; 1a2′) → 3sσ/σ*(a1; a1′) (5b1; 1a2′) → (3b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → (3b2, 2a2″, π*) (1a2 + 2b2, π, 1e″) → 3sσ/σ*(a1; a1′)

11.497 11.664 12.207 12.260

11.674 11.799 13.399 12.262

11.90

1.17

12.55

1.18

E(T) and E(S) stem from the energy of triplet and singlet states, respectively. E(S) values are obtained with MOLPRO.36

Table 4. (a) Calculated Vertical Ionization Energies (eV) and (b) Vertical Ionization Energies (eV) and Intensities (Pole Strengths, PS) (CCSD(T) Geometry) of Boron Trifluoride, BF3, Obtained at the CCSD(T) Geometry Using the cc-pV6Z Basis Set (a) Vertical Ionization Energies B2 (1a2−1)

1e″−1 PS

18.045 16.403 16.422 15.95 15.94 16.0 15.70 16.26 15.95

A2 (2b2−1)

2

E″ (1e″ )

0.94 0.92

0.94

energy 18.704 17.234 17.291 16.67 16.67 16.7 16.71 17.14 16.67

PS 0.94 0.92

0.94

energy 19.070 17.540 17.578 17.14 17.10 17.2 16.89 17.48 17.122

PS

energy 20.780 19.390 19.446 19.13 19.13 19.2 19.02 19.42 19.180

0.94 0.93

0.94

2

−1

E′ (4e′−1)

2

E″ (1e″ ) 18.704 17.087 16.865 17.149 17.017

1a2″

4e′4

A1 (8a1−1)

2

−1

18.045 18.704 16.896 15.817 15.791 17.569 16.450 17.128 16.157 17.112 (b) Vertical Ionization Energies and Intensities

1a2′−1 energy

a

2

A′2 (1a2′ )

Koopmans′ theorem ROHF ROMP2 RCCSD RCCSD(T)

Koopmans OVGF P3 expa expb expc GFc OVGFd expe

2

−1

2

D3h

D3h

B1 (5b1−1)

2

C2v

19.070 17.751 17.190 17.556 17.323 4a1′

3e′ PS

energy

PS

energy

PS

0.93

21.5 21.29 21.81

0.93

0.94 0.93

0.93

20.09 19.98 20.2 20.08 20.63 20.038

Reference 12. bReference 9. cReference 13. dReference 52. eReference 14.

where ki and kf are the initial and final momenta of the incident electron, a0 is the Bohr radius (0.529 Å), R is the Rydberg energy (13.61 eV), E0 is the energy of the incident electron, E is the excitation energy, and GOSexpt(K2) is the experimental generalized oscillator strength (GOS), and K2 is the momentum transfer squared defined by

lowest triplet transitions at the EOM-CCSD level, because this type of calculation is not available through MOLPRO. Due to the excitation of doubly degenerate orbitals, the energy ordering of the Rydberg states does not necessarily follow the order ns < np < nd. Thus, the assignment of the calculated transitions was made by using the calculated spatial extensions of the wave function ⟨r2⟩, as well as by examining the shape of the EOM-CCSD natural orbitals (for the aug-cc-pVQZ calculations only, because cc-pV6Z MO’s cannot be visualized). 4.2. Fitting Procedures. The corresponding integral cross sections were derived by applying a generalized oscillator strength analysis and then assessed against the BE and f scaling. The values of the DCS (E0, θ) determined by the present measurements for the intense optically allowed transition 1e″(π) → 2a2″(π*), are transformed to GOSexpt by the standard formula:26 GOSexpt (K 2) =

(E /R )k ia0 2

4a0 k f a0

Ka 2 = (k ia 0)2 + (k f a0)2 − 2(k ia0)(k f a0) cos θ

The experimental data are fitted with a semitheoretical formula proposed by Vriens44 for a dipole allowed excitation as G (x ) =

⎡ ∞ fm x m ⎤ 1 ⎢∑ ⎥ m (1 + x)6 ⎢⎣ m = 0 (1 + x) ⎥⎦

(3)

where x=

Q

K 2 DCS(E0 ,θ )

(2)

(1)

K2 α2

(4)

and 10960


The Journal of Physical Chemistry A α=

B + R

Article

B−E R

K 2 max = 2

(5)

with B the binding energy of the target electron being excited. The f m values are fitting constants to be determined in a leastsquares fit analysis of the experimental GOSs (Gexpt), as seen in Figure 2a. The experimental optical oscillator strengths (OOSs)

E0 ⎡ E ⎢1 − + R ⎢⎣ 2E0

can now be extracted from the f 0 coefficient that was determined from the fit in each case, as K → 0. A comparison of the f 0 value with the photoabsorption data shows another assessment for verification and validation of the measurements. The present f 0 value (0.21) agrees reasonably well with the OOS of 0.26.9 Finally, estimates of the ICSexpt (corresponding to the unscaled Born integral cross section shown as a dashed line in Figure 2 bottom), at 100, 200, and 300 eV, can be obtained from eqs 3−5 using the standard formulas45 by integrating Gexpt(K2) over the limits of K2 corresponding to θ = 0° and 180°:

∫K

K 2 max 2 min

Gexpt(K 2) E/R

d(ln K 2)

E0 ⎡ E ⎢1 − − R ⎢⎣ 2E0

1−

E ⎤ ⎥ E0 ⎥⎦

faccur E0 fBorn (E0 + B + E)

σBorn(E0)

(9)

5. ELECTRONIC STATE SPECTROSCOPY: RESULTS AND DISCUSSION The present full ranges of the EEL spectra of boron trifluoride (BF3) are shown in Figure 3, together with the calculated oscillator strengths. Generally speaking, we observe a ∼0.5 eV shift between experiment and theory, which is reasonable for the level of accuracy. Moreover, the calculations with the two basis sets are very similar for both energy and intensities. Some tentative members of the Rydberg series are assigned for the first time. The major EEL bands, generally speaking, can be classified mainly as valence transitions of 1(π → π*), 1(nF → σ*), and 1(π → σ*) character and members of Rydberg series converging to the lowest ionization energies. A detailed analysis of Figure 3 DCSs from 100 eV, 2.8° and 40 eV, 40° (bottom figure), reveals a rather identical intensity characteristics showing the nature of the singlet transitions involved in the electronic excitation of boron trifluoride. However, of particular relevance, is the clear experimental evidence of the triplet character in the low-lying transitions in the 10−13 eV energy region and fully supported by theoretical calculations

(6)

with K 2 min = 2

(8)

where faccur is an accurate value obtained from experiments (photoabsorption) or calculations with accurate wave functions, B + E is the scaling factor, and f Born is the value from the calculation with the wave function employed in the calculation of the unscaled Born cross section σBorn. In the present study, however, we have employed our own high energy “experimental” results as the unscaled σBorn at E0 =200 and 300 eV in eq 9 because no Born calculation was available in the literature. The f-scaling process has the effect of replacing the wave function used for σBorn with an accurate value, but in the present study, we employ the experimental f 0 value of 0.21 for faccur and f Born, thus faccu/f Born = 1. The BEf scaling corrects the deficiency of the Born approximation at low E0, without losing its well-known validity at high E0 values. This method has been applied successfully to atoms and molecules in our group (see, e.g., ref 47). As shown in Figure 2 bottom, it is found that the BEf-scaled Born method seems to generate more reliable values than the unscaled Born ICS over the intermediate collision energies for BF3 intense optically allowed transition 1e″(π) → 2a2″(π*) transition.

Figure 2. BF3 electron impact excitation for the 1e″(π) → 2a2″(π*) transition: (a) generalized oscillator strengths; (b) integral cross sections (10−18 cm2). See text for further details.

4πa0 2 E0 / R

E ⎤ ⎥ E0 ⎥⎦

The result for the main π* electronic state (13.13 eV) is plotted in Figure 2a. This is discussed in more detail in section 5. 4.3. BEf-Scaling Method. Scaled (plane wave) Born cross sections for dipole-allowed excitations f-scaling and BE-scaling, and BEf-scaling are described in detail in Kim26 so only a brief description is given for the points relevant to the present study. It is well-known that the Born approximation gives fairly good agreement for the excitation cross section in optically allowed transitions at high collision energies. However, by modifying the Born approximation, Kim developed a new, simple scaling method for the excitation cross section of atoms over the entire range of collision energies46 and also extended to the case of molecular target. The BEf-scaled Born cross section, σBEf, is given by σBEf (E0) =

ICSexpt (E0) =

1−

(7)

and 10961



Article

between the 1a2′ and 3e′ states of BF3+.9,10,12,14,15 The electronic absorption spectrum of BF3 has been investigated by Maria et al.7 reporting a weak feature at 7.89 eV and assigned to a singlet−triplet transition (3Γnπ* ← 1Γ1). Meanwhile, Durrant et al.48 EELS data assigned the 7.9 eV feature, later revised to 8.2 eV,49 to the 1(1a2′) → 1(2a2′,π*) transition. This interpretation is ruled out by the present calculations (Tables 1 and 2) predicting this transition at ∼11.8 eV with both basis sets. Unfortunately, the present EELS data, obtained in single collision conditions by keeping the pressure lower than 10−3 Torr, does not reproduce this feature, which we attribute to a possible contamination (impurity)50 in the earlier measurements. However, to discard an unlikely contribution from BF3 dimer formation in the nozzle tube or even polymerization, we have performed with Gaussian 09 at the TD-DFT/ωB97-XD/aug-cc-pVQZ level of theory a set of calculations on the lowest-lying excited states of the D2h B2F6 dimer (not shown here). The result shows without ambiguity no contributions from dimer electronic transitions below 11 eV. Nevertheless, our data are generally speaking consistent with previous VUV absorption data8−10 reporting the lowest-lying features above ∼11 eV. High-resolution synchrotron radiation experiments of Hagenow et al.9 and Suto et al.10 agree well in the wavelength region where they overlap, 62−180 nm (20−6.5 eV) and 45−113 nm (27.6−11 eV), respectively. However, Hagenow et al9 report an ascending branch in the energy region below 11 eV, which is reproduced neither in the present EELS data (Figure 3) nor in Suto’s.10 This can be attributed to second-order light effect contributing to the baseline spectrum. Yet, a close inspection of Figure 3 reveals that under particular electron impact energies and scattering angle detection, another interesting behavior in the EELS cross section becomes perceptible. We will address this issue further below. The major EELS bands centered at 13.13, 13.98, 14.70, 15.56, and 16.10 eV can be classified mainly as a mixture of Rydberg−valence transitions due to the promotion of an electron from the occupied to unoccupied MOs (assignments in Tables 1, 2, and 5). The lowest lying singlet excited state has been reported by Hagenow et al.9 and Suto et al.10 with a maximum at 13.13 and 13.19 eV, respectively, in very good agreement with the present value of 13.13 eV. This feature is assigned to the transition (1A1′ → 1E′, π(1e″) → π*(2a2″)) (Tables 1 and 2) with the highest calculated oscillator strength (∼0.4). The calculated value is much higher than the photoabsorption result of Hagenow et al. (0.26)9 and the present experimental derivation (0.210 ± 0.065) (Figure 3). A possible explanation for such a discrepancy (a factor of 2 between the two independent experimental values and the calculations) can be due to vibronic effects, i.e., due to the significant Jahn−Teller distortion, since the π(1e″) → π*(2a2″) excited state should be pyrimidalized. It is possible that the inclusion of Jahn−Teller effects can affect the vibrational Franck−Condon factors so that the oscillator strength would be lowered. However, a detailed study of these effects is beyond the scope of the present work. Moreover, the calculations also predict a rather intense oscillator strength (0.09) at a slightly lower energy (∼12.8 eV), assigned to the mixed valence− Rydberg transition 4e′ → 3sσ/σ*(a1′) (Tables 1 and 2). This corresponds to the same transition assigned by Hagenow et al.9 at 13.200 eV with an oscillator strength estimated to be about 0.1. So, for this transition, the calculated value is in very good agreement with the experimental data. This is not surprising because, for a Rydberg state, vibronic effects are not expected to

Figure 3. Electron energy loss spectra (EELS) in the range 10.0−20.0 eV for boron trifluoride (BF3) obtained at 100 and 40 eV electron impact energy and 2.8° and 40° scattering angle, respectively. The vertical bars are the calculated oscillator strengths.

(discussion below). It is worth noting that our EELS at low impact energy and relatively high scattering angle enhance the singlet to triplet transitions in detriment of the singlet to singlet transitions (Figure 3 and Table 3). The calculated vertical ionization energies (IEs) are presented in Table 4. Generally speaking all the theoretical methods agree with each other with the exception of Koopman’s theorem. The measured lowest vertical IE of boron trifluoride (15.95 eV)14 agrees reasonably well with the RCCSD(T) and ROMP2 theoretical predictions (Table 4a). As far as the ROHF method is concerned, the value is noticeably high, reflecting the difficulties of the Hartree− Fock method to obtain accurate molecular properties, especially for open shell systems. Regarding the Koopmans’ theorem, the lack of agreement with the other methods is not surprising in view of the deficiency in electron correlation and relaxation. The P3 and OVGF results are very close to each other and reproduce reasonable well, to within 0.5 eV, the experimental data (Table 4b). We will now discuss in turn our results of BF3 electronic excitation in the following sections. Any comparisons drawn will be made with the available data in the literature. 5.1. Valence Singlet Excitation of Boron Trifluoride (BF3). The energy loss spectrum at 100 eV and 2.8° scattering angle consists of several bands assigned to transitions from occupied molecular orbitals to valence-and/or Rydberg orbitals. Some bands, peaking at 13.98, 14.70, and 15.56 eV, are superimposed by vibrational progressions,9 which unfortunately are not visible here because of the energy resolution limited inherently in the EELS measurement. The band at 15.56 eV has been interpreted as a strong pseudo-Jahn−Teller interaction 10962



Article

curves (although not shown here) to resolve the underlying transitions. The maximum values are obtained at 11.90 and 12.55 eV and listed in Table 3. The theoretical calculations in Table 3 report on the BF3 lowest valence and Rydberg triplet transition energies calculated at the EOM-CCSD/aug-cc-pVQZ +R level. We tentatively assign the feature at 11.90 eV to the mixed valence−Rydberg X̃ 1A1′ → 3A2′, 1a2′ → 3sσ/σ*(a1′) transition (Table 3) with a quantum defect δ = 1.17 converging to ionic electronic ground state. However, a careful analysis of Figure 3 (bottom) shows that this band becomes discernible at low impact energy and relatively high scattering angle denoting an underlying broad dissociation structure which may confer a more valence-like character. As shown in Tables 1 and 2, the calculations report the dipole-forbidden valence singlet excitation 1a2 → (2a2″, π*) feature at ∼11.8 eV. This means that singlet excitation is not predominant at this energy and so, the 11.90 eV may be assigned to the (1A1′ → 3A2′, 1a2′ → 3sσ/ σ*(a1, a′1)) transition as in Table 3. As far as the 12.55 eV feature is concerned, this may correspond to the (1A1′ → 3E″, (1e″, π) → 3sσ/σ*(a1′)) transition with a quantum defect δ = 1.18 converging to the ionic electronic first excited state (Table 3). Such π valence excitation character assumption seems reasonable because the intensity of this feature does not change appreciably as in the case of the 11.90 eV feature when comparing the EELS data at 100 eV, 2.8° scattering angle and at 40 eV, 40° scattering angle. 5.3. Rydberg Features. The EELS data consist of structures superimposed on diffuse features extending to the lowest ionization energies (IEs). The peak positions, En, have been compared using the Rydberg formula:

Table 5. Energies (eV), Quantum Defects, and Assignments of the ns, np, and nd Rydberg Series Converging to the Ionic Electronic Ground (1a2′)−1, First (1e″)−1, Second (4e′)−1, Third (1a2″)−1, Fourth (3e′)−1, and Fifth (4a1′)−1 Excited States of Boron Trifluoride, BF3 vertical energy

ref 9

quantum defect (δ)

assignment

IE1 = 15.95 eV 13.98

13.973

0.37

14.70 15.23

14.654 15.289

−0.30 −0.35 IE2 = 16.67 eV

13.98

0.75

14.70

0.37

15.56

−0.50 IE3 = 17.122 eV

13.14 15.56

13.200 15.640

1.15 1.05

16.10

−0.65 IE4 = 19.18 eV

15.23

1.14 IE5 = 20.09 eV

17.55 18.81

17.892 18.814

0.68 0.74

18.12

17.991

0.37

18.51

18.499

0.06 IE6 = 21.50 eV

18.12

0.99

18.81

0.75

1a2′ → npσ 3p 1a2′ → ndδ 3d 4d 1e″ → npσ 3p 1e″ → npπ 3p 1e″ → ndδ 3d 4e′ → nsσ 3s 4s 4e′ → ndσ 3d 1a2″ → nsσ 3s 3e′ → npσ 3p 4p 3e′ → npπ 3p 3e′ → ndδ 3d

En = E i − R /(n − δ)2

where Ei is the ionization energy (vertical values), n is the principal quantum number of the Rydberg orbital of energy En, R is the Rydberg constant (13.61 eV), and δ the quantum defect resulting from the penetration of the Rydberg orbital into the core. The proposed first members (n = 3) of the Rydberg structures are presented in Tables 1, 2, and 5. Assignments in the spectra for higher members of the Rydberg series, where n ≥ 4 members are expected to lie, is rather complex due to the presence of other valence transitions, and the limited resolution of the present experiments. No attempts have been made to find other high energy members. Therefore, with quantum defect calculations as our only guide, we cannot propose assignments for these bands with confidence, so Table 5 is just a tentative assignment. The identification of Rydberg states was based more firmly on the symmetry and shape of the mono-occupied orbitals and the values of the oscillator strengths. The second band with a maximum at 13.98 eV is mainly Rydberg in character assigned to the (1a2′) → 3pσ(e′) transition (converging to the ionic electronic ground state) in agreement with the former value 13.973 eV.9 However, a high oscillator strength (∼0.16) allows to assign this feature to the (π, 1e″) → 3pσ(e′) transition converging to the second ionization limit (Table 5). The third band at 14.70 eV is assigned to the (1a2′) → 3dδ(e′) transition converging to the ionic electronic ground state of BF 3 with a Rydberg contribution to the ionic first excited state (Table 5). The feature at 15.56 eV tentatively assigned to 1a2″ → 3sσ/σ*(a1′) can also has a Rydberg contribution converging to third excited ionic state of BF3 (Table 5).

4a1′ → ns 3s 4a1′ → np 3p

be strong. The other two bands at 13.98 and 14.70 eV have been assigned to Rydberg excitations that are discussed in section 5.3. The feature at 15.56 eV is tentatively assigned to the 1a2″ → 3sσ/σ*(a1′) transition. The feature at 17.55 eV is assigned to the 4a1′ → 2a2′(π*) transition in good agreement with the 17.520 eV from Hagenow et al.9 and 17.52 eV from Suto et al.10 Interesting to note, Suto et al.10 threshold energies for BF3 photodissociation processes, in particular at 10.58 and 11.44 eV assigned to BF + F2 and BF2* + F, respectively, with the former showing a nonradiative character. These mechanisms may be prevalent in the spectra contribution to the underlying dissociative behavior of the low-lying EELS states. 5.2. Valence Triplet Excitation of Boron Trifluoride (BF3). Here we report on the first measurements of the lowest lying triplet states as studied by electron energy loss spectroscopy and theoretical calculations (Table 3). Figure 3 (bottom) shows the EELS recorded at 100 eV, 2.8° scattering angle and at 40 eV, 40° scattering angle, where in the energy region 10.0−13.0 eV we note considerable changes in the shape of the DCSs. These have been fitted with Gaussian profile 10963



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5.4. BEf-Scaling. The experimental (apparent) generalized oscillator strength (GOS) in eq 1 is derived from the “measured” DCS at 100, 200, and 300 eV with an integral Born cross section obtained “empirically” through eq 3. Then, the BEf-scaling approach is applied to obtain the scaled integral cross section of the strong optically allowed (π, 1e″) → (2a2″, π*) transition. Note that we do not calculate the first order plane-wave Born cross section in the present work but calculate the vertical excitation energies for bound states as mentioned in section 4.1. A comparison of the f 0 value (0.210 ± 0.065, Figure 2 top) with the photoabsorption data shows another assessment for verification and validation of the present measurement, although our present value is around 30% lower than the oscillator strength (0.26) reported from Hagenow et al.,9 but it falls within the experimental uncertainty when computing the ICS.25 In Figure 2 bottom, we now compare our unscaled (dashed line) and scaled (solid line) ICS results for the (π → π*) band together with three experimental points, only one for the experimental (unscaled) ICS at 100 eV and the two for the scaled Born at 200 and 300 eV. However, unfortunately, we are not aware of any other data in the literature to compare with; that is, both ICSs are first predicted for the intermediate energy region below 100 eV by the present scaling. So, in comparison with the Born ICSs, our BEf-scaling results might be appropriate for use in any modeling studies in which BF3 is an important constituent, because, in general, the Born approximation produces lager cross section values than expected. Furthermore, the cross section is really critical below 30 eV for the modeling. Here, this is an interesting speculation as it suggests that the π → π* transition is intense and relatively unperturbed by the Rydberg−valence interactions, characterizing a typically optical allowed transition for the BEf-scaling. However, it is in contradiction to the present calculations showing a considerable contribution of strong Rydberg−valence mixing affecting the 4e′ → 3sσ/σ*(a′1) E′ state in BF3. Such a contribution would lend support to a deviation in the applicability of the BEf-scaling method. Namely, that any vibrational sublevel of an electronic state in any molecule, where avoided level crossings and other perturbation effects are important, might not have their cross sections reliably calculated within the BEf-scaling approach. Actually, Hagenow et al.9 report extensive vibrational excitation in the vicinity of the (π → π*) transition with a Rydberg contribution at 13.2 eV, as discussed above. It is interesting to note that we have recently observed a similar behavior of such disagreement in the applicability of the BEfscaling for the O2 longest band due to the curve crossing.51 Finally, under those circumstances, further investigations are needed to clarify the validity of the BEf-scaling in BF3 for the intermediate energy region.

of boron trifluoride. The broad nature of the low-lying bands in BF3 may be closely related to a dissociative character. This transition potentially results in dissociation yielding a source of BF and F2 species. We have also reported Born and BEf-scaling ICS results for the most intense (π → π*) transition, where we noted that the BEf-scaling approach is effective to reduce the Born ICS in magnitude in the intermediate energy region below 100 eV. Therefore, these BEf-scaling results may be more useful for modeling the behavior of BF3 in industrial applications at the present stage when no other reliable data are available to compare with.

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AUTHOR INFORMATION

Corresponding Authors

*M. Hoshino. Tel: (+81) 3 3238 4227. E-mail: masami-h@ sophia.ac.jp. *P. Limão-Vieira. Tel: (+351) 21 294 78 59. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.D. acknowledges support from the CaPPA project (Chemical and Physical Properties of the Atmosphere), funded by the French National Research Agency (ANR) through the PIA (Programme d’Investissement d’Avenir) under contract ANR10-LABX-005. This work was granted access to the HPC resources of CINES under the allocation 2014-088620 made by GENCI (Grand Equipement National de Calcul Intensif). The Centre de Ressources Informatiques (CRI) of the Université Lille1 also provided computing time for part of the calculations. P.L.-V. acknowledges the Portuguese Foundation for Science and Technology (FCT-MEC) for partial support from the research grants PEst-OE/FIS/UI0068/2014 and PTDC/FISATO/1832/2012. P.L.-V. also acknowledges his Visiting Professor position at Sophia University, Tokyo, Japan. This work was conducted under the support of the Japanese Ministry of Education, Sport, Culture. and Technology.

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REFERENCES

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6. CONCLUSIONS The present work provides the first complete EELS of BF3 from 10.0 to 20.0 eV together with sophisticated calculations providing more reliable assignment in the spectra. Due to the DCS behavior from 100 eV, 2.8° and 40 eV, 40° scattering angle, transitions are assigned to singlet−singlet and singlet− triplet states to a combination of valence and Rydberg transitions supported by ab initio calculations on vertical excitation energies and oscillator strengths. The present electron spectroscopy data provide the first experimental evidence of the triplet state nature of the lowest lying excitation 10964



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BF3 Valence and Rydberg States As Probed by Electron Energy Loss

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