Density Functional Theory Calculations on FO, OFO, and FOO Species and their Cations and Anions
3. Results and Discussion
In the case of the FO radical, the DFT functionals predict bond lengths between 1.33 Å (SVWN) and 1.38 Å (BLYP), as shown in Table 1. The best agreement with the experimental value (1.3541 Å) [49] is given by the PBEPBE calculation. The hybrid methods (B3LYP, B3PW91, and mPW1PW91) predict shorter bond lengths than the experimental value, whereas the pure DFT functionals (BLYP and PBEPBE) predict longer values. The local density approximation method (SVWN) predicts a slightly shorter value. The best theoretical prediction for this bond length is provided by coupled cluster and multi reference configuration interaction calculations (RCCSD(T)/aV6Z and iCAS-CI+Q/aV6Z) [50], which are very close to the experimental results, with values of 1.3510 Å and 1.3542 Å respectively.
In order to study the energetic properties of the species, we calculate the Ionisation Potential (IP), Electron Affinity (EA) and enthalpy of formation (∆Hof) of FO. The adiabatic electron affinity (EAa), vertical electron affinity (EAv), and vertical detachment energy (VDE) are defined as the difference in total energies of species according to the formulae [51]:
EAa = E(optimized neutral) – E(optimized anion),
EAv = E(optimized neutral) – E(anion at optimized neutral geometry);
VDE = E(neutral at optimized anion geometry) – E(optimized anion).
The lowest adiabatic electron affinity for the FO species is predicted by mPW1PW91 (2.047 eV) and the highest by SVWN (2.828 eV) as shown in Table 2. The best agreement with experimental data (2.272 eV) [52] is predicted by B3LYP, which differs from experiment by only 0.02 eV. The vertical EA is about 0.3 eV lower than the adiabatic EA, and the vertical detachment energy (VDE) is also 0.3 eV higher than adiabatic EA using pure DFT functionals and hybrid calculations.
Similar to the electron affinity definitions, the adiabatic (IPa) and vertical (IPv) ionization potentials are defined as
IPa = E(optimized cation) – E(optimized neutral),
IPv = E(cation at optimized neutral) – E(optimized neutral)
For the prediction of ionization potentials (IP), both singlet and triplet states of FO+ are included. The triplet adiabatic IP is closer to experimental data than the singlet one as shown in Table 2. The B3PW91 predicts closest agreement to the experimental data, followed by mPW1PW91. However the local density approximation method predicts a value higher than experiment by 0.4 eV.
The enthalpies of formation are calculated through isodesmic and diatomic reactions [53]
FOH
where O2 and F2 are in their triplet and singlet ground states respectively. All total energies used here have been corrected for the vibrational Zero Point Energy (ZPE) with the relevant scaling factor for each functional (1.0079, 1.0126, 0.9806, 0.9776, and 0.9800 respectively for SVWN, BLYP, B3LYP, B3PW91, and mPW1PW91) [54-57]. All calculated heats of formation by isodesmic (A) and diatomic reactions (B) are within the range of experimentalAF-106 error. For the isodesmic prediction both hybrid methods and pure DFT functionals give excellent results when compared to the experimental data. The diatomic reaction prediction differs from the experimental prediction by only 0.6 – 1.7 kcal/mol, except in the case of SVWN.
Table 1 Bond lengths of FO species (in Angstroms) Species
Experimental 1.3541 [20, 49] 1.516 [52]
Previous theoretical data for OFO is provided by Gosavi et al. [58] based on RHF-SCF optimization at the 6-31G level of basis set. The OFO structure is predicted to lie about 85 kcal/mol above FOO on those calculations. Recent theoretical data is given by Denis [11]
using CCSD(T)/aug-cc-pVTZ level of calculation, where the energy difference is 121.6 kcal/mol. The neutral OFO lies higher in energy than its asymmetric isomer FOO, by 109 – 120 kcal/mol according to DFT calculations. The SVWN predicts a difference of 119 kcal/mol, while BLYP and PBEPBE predict 109 and 115 kcal/mol respectively.
The only experimental data available for OFO energetics is the heat of formation, which is 91.20 kcal/mol [61]. The heats of formation are predicted according to diatomic and isodesmic reactions below experimental values. The estimate closest to experiment is predicted by the BLYP functional, which lies 15.8 kcal/mol higher. The PBEPBE functional predicts the highest discrepancy of around 31.9 kcal/mol. The isodesmic reaction prediction (A) is better than that of the diatomic reaction (B), especially for the hybrid methods. Only the PBEPBE functional predicts the OFO heat of formation calculation to be better for the diatomic reaction, as listed in Table 3. The high level of ab inito calculation (CCSD(T)) [11] predicts a value 40 kcal/mol higher than that of experiment [8].
The theoretical F-O bond distance in the neutral 2A″ FOO radical is predicted to be in the range of 1.59 to 1.67 Å. The predicted bond length is close to the experimental value (1.649 Å) [62]. The best agreement with the experimental data is given by PBEPBE which differs by only 0.006 Å. Previous theoretical predictions at high level of ab initio calculation [12, 44] produce values of 1.6282 and 1.6420 Å respectively. Only for the FOO bond angle do the pure DFT functionals predict poorer results compared with the hybrid and local density approximations. The hybrid methods and the SVWN predict 111.06 to 111.85o, while the experimental data is 111.19o [62], and the pure DFT functionals predict a value one degree higher. This asymmetric FOO is also predicted to lie lower in energy than its symmetric isomer by 118.7, 109.3, 114.6, 115.5, 119.1, and 120.4 kcal/mol according to the SVWN, BLYP, PBEPBE, B3LYP, B3PW91, and mPW1PW91 calculations respectively.
FOO is known as molecule that is difficult to study theoretically [12]. The heat of formation for the neutral FOO is calculated from the reactions
AF-107
2
22
3 F O F
FOO + → +
(A)FOO O
F
2+ 2
2→ 2
(B)The prediction of the local density approximation and pure DFT functionals lie far from the experimental value, particularly based on the diatomic reaction (B). The experimental values lie in a wide range from 5 to 12 kcal/mol [12]. The high level ab initio calculation [10] predicts a value far from this experimental value. The best result for this heat of formation is predicted by the B3LYP on the diatomic reaction calculation, and another by the B3PW91 using the isodesmic reaction approach.
The calculated ionization potentials are also shown in Table 4. The reported adiabatic ionization potential is 12.600 eV [62]. The B3PW91 again predicts a value for IP closest to this experimental result. The pure DFT functionals, BLYP and PBEPBE predict an IP lower than that of experiment, while the hybrid methods and local density approximation predictions lie higher. The vertical IP is also predicted to lie higher than the adiabatic IP by up to 0.4 eV.
The electron affinity properties are distinguished as adiabatic EA, vertical EA, and vertical detachment energy (VDE). The DFT predicted data of these properties are shown in Table 4. Vertical EA is lower than adiabatic EA and the VDE. Unfortunately there is no experimental data available for these properties for the purpose of comparison. The local approximation method SVWN predicts these EAs to lie higher than those predicted by other DFT functionals.
The harmonic vibrational frequencies for the FOO species are also listed in Table 4.
The frequencies for the ionic species in the Table relate to the singlet state only. All frequencies are corrected by suitable correction factors [53-56] for each functional except for the PBEPBE. The predicted harmonic frequencies for FOO are in very good agreement with the experimental estimates, with the exception of SVWN. For the frequencies of the ionic species, the predictions of the DFT functionals vary according to the functional.
Unfortunately there are no experimental data available for these species.
AF-108 Table 2 Energies and harmonic vibrational frequencies of FO species (parentheses energy at 298.15K)
Methods EA (eV)
VDE (eV)
IP (eV)
FO [∆Hf (0 K)]
(kcal/mol)
Harmonic Vibrational Frequencies
(cm-1)
a v Triplet-a Singlet-a Triplet-v Singlet-v A B FO (2Π) FO+ (3Σ) FO- (1Σ) SVWN 2.828 2.575 3.228 13.191 15.179 13.474 15.537 16.78 28.99 1148.6 1398.0 845.3 BLYP 2.236 1.954 2.664 12.678 14.680 12.968 15.018 22.60 24.74 1034.8 1281.3 733.8 PBEPBE 2.129 1.858 2.656 12.570 14.648 12.867 15.000 21.11 25.92 1088.6 1350.0 779.7 B3LYP 2.292 1.991 2.697 12.922 15.060 13.270 15.447 24.00 24.41 1074.3 1357.4 763.2 B3PW91 2.117 1.828 2.514 12.770 14.985 13.120 15.376 23.27 25.02 1100.0 1388.4 788.2 mPW1PW91 2.047 1.758 2.444 12.741 15.014 13.077 15.428 23.65 24.63 1110.4 1406.6 798.1
G3 2.251 14.508
G3B3 2.257 12.721 24.54 25.86
BHLYP 2.04a 1191a 847a
B3PW91 25.2b
RCCSD(T) 27.9c 1069c
ICAS-CI+Q 1056c
CCSD(T) 27.30d 1072d 1331d
Expt. 2.272e, j 12.78±0.03f, j (26.08 ± 2.39)g
25.84±2.39g
1029h 1053i
1300h 769±95e a = adiabatic; v = vertical
a reference [16] b reference [15] c reference [12]
d reference [11] e reference [52] f reference [60]
g reference [59] h reference [58] i reference [48]
j reference [62]
AF-109 Table 3 Energies and harmonic vibrational frequencies of OFO species (parentheses energy at 298.15K)
Methods EA (eV)
VDE (eV)
IP (eV)
OFO [∆Hf (0 K)]
(kcal/mol)
Harmonic Vibrational Frequencies (cm-1)
a v a v A B OFO (2B1) OFO+ (1A1) OFO- (1A1)
SVWN 3.842 3.878 4.002 13.559 13.667 123.22 108.28 433.1, 537.9, 848.9 491.0, 537.1, 901.8 351.3, 463.1, 742.8 BLYP 3.325 3.324 3.492 13.037 13.118 105.60 106.57 382.1, 402.4, 749.7 410.7, 436.6, 807.0 302.7, 359.2, 638.4 PBEPBE 3.236 3.239 3.402 12.989 13.074 112.05 110.46 408.7, 437.6, 794.1 453.7, 466.7, 853.6 325.3, 377.7, 679.7 B3LYP 3.798 3.786 4.003 13.762 13.883 118.16 122.12 403.7, 621.1, 789.3 468.4, 701.2, 865.4 318.3, 552.7, 662.7 B3PW91 3.642 3.636 3.775 13.657 13.782 122.62 126.14 418.1, 654.2, 813.7 484.8, 730.0, 890.7 330.6, 566.5, 687.2 mPW1PW91 3.684 3.675 3.899 13.766 13.901 124.61 128.95 422.0, 598.7, 822.6 491.1, 770.4, 904.6 331.6, 607.7, 691.2
G3 3.802 14.442
G3B3 3.737 11.955 121.27 124.68
CCSD(T) 129.19a
Exp. (90.57 ± 4.78)b
91.20 ± 4.78c a = adiabatic; v = vertical
a reference [11]
b reference [8]
c reference [62]
AF-110 Table 4 Energies and harmonic vibrational frequencies of FOO species (parentheses energy at 298.15K)
Methods EA (eV)
VDE (eV)
IP (eV)
FOO [∆Hf (0 K)]
(kcal/mol)
Harmonic Vibrational Frequencies (cm-1)
a v a v (A) (B) FOO (2A″) FOO+ (1A′) FOO- (1A′)
SVWN 2.576 2.341 3.082 12.802 13.094 10.12 -10.41 446.3, 694.8, 1556.7 535.1, 825.3, 1763.4 292.6, 482.5, 1311.6 BLYP 2.175 1.886 2.753 12.379 12.660 2.79 -2.77 394.6, 621.1, 1455.1 477.5, 755.5, 1666.4 237.8, 399.7, 1212.9 PBEPBE 2.036 1.748 2.536 12.297 12.583 8.06 -4.10 414.7, 648.7, 1522.0 502.8, 787.0, 1731.3 250.4, 420.3, 1277.9 B3LYP 2.314 2.012 2.557 12.869 13.297 5.58 6.57 319.6, 553.3, 1493.2 548.1, 812.6, 1685.1 246.5, 400.1, 1300.2 B3PW91 2.138 1.801 2.414 12.743 13.150 5.97 7.06 392.6, 608.3, 1510.3 561.3, 827.5, 1708.5 248.7, 406.4, 1330.7 mPW1PW91 2.078 1.760 2.275 12.781 13.232 5.83 8.55 302.3, 570.1, 1521.4 579.2, 840.9, 1711.8 251.0, 406.4, 1353.1
G3B3 2.865 12.285 6.20 6.81
RCCSD(T) 10.0a 400.4, 616.5, 1522.9a
iCAS-CI+Q 335.0, 546.8, 1512.2a
CCSD(T) (7.47)b
MP4 22.3c
QCISD(T) 8.9c 504, 766, 1648d
B3LYP 6.28e
Exp. 12.600f (6.08 ± 0.48)g
(5.5 ± 0.4)h 6.51± 0.48i 12 ± 3i
376, 579, 1487j
a = adiabatic; v = vertical
a reference [12] b reference [11] c reference [14] d reference [64]
e reference [15] f reference [45] g reference [61] h reference [63]
i reference [54] j reference [51]
AF-111 4. Conclusions
The performances of DFT functionals for the properties of fluorine oxides and dioxides have been assessed. Generally, for diatomic structures, the hybrid method B3LYP, followed by B3PW91, always gives very good agreement with experiments. In the case of FO the PBEPBE functional yields best agreement with experiment. The BLYP functional usually predicts longer bond lengths, while the SVWN functional shorter bond lengths. In the triatomic FOO species, the pure DFT functionals (BLYP and PBEPBE) predict results better than those of B3LYP calculations. In the case of OFO, there is no significant different between results from pure DFT functionals and hybrid methods, but the latter methods are in better agreement with available experimental data.
The energetic properties have also shown that B3PW91 and B3LYP functionals give excellent results. Both functionals predict the best ionisation potentials, electron affinities, and vertical detachment energies for species of diatomic and triatomic halogen oxides.
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