A GAUSSIAN 80(6-311G**) study of the species NHn and NHn+ (n = 1–3)

Journal of Molecular Structure (Theochem), Elsevier Science Publishers B.V., Amsterdam

110 (1984) 155-166 -Printed in The Netherlands

A GAUSSIAN 80(6-311G**) STUDY OF THE SPECIESNH, and NH, (n = l-3)

DEIRDRE

POWER, PAUL BRINT and TREVOR

Chemistry Department, (Received

R. SPALDING

University College, Cork (Republic of Ireland)

16 March 1984)

ABSTRACT GAUSSIAN 80(6-311G**) calculations were performed in both Hartree-Fock and configuration interaction modes on the complete series of molecules NH, and NH*, (a = l-3). In general the agreement between the calculated and experimentally determined structures of the NH, species is very good and leads to confidence in the corresponding results for NH; ions. Calculated thermochemical quantities (AH;, IPs and APs) are in good agreement with the available experimentally determined values. INTRODUCTION

Although there have been a large number of molecular orbital calculations of species based on NH3 previously, there does not appear to have been a complete set calculated with the same MO program. This paper reports the calculation of all molecules NH, and ions NW, using the GAUSSIAN 80 program [l] with the 6-311G ** basis set used in both Hartree-Fock (H-F) and configuration interaction (CI) modes. In some cases excited states were calculated as well as the ground state of each species. The electronic and molecular structures, and thermochemical data such as A@, ionisation potential (Ip), or appearance potential (AP) from NH3 are calculated and compared with experimental data where available. CALCULATIONAL

METHODS

The Gaussian 80 suite of programmes of Pople et al. [l] was used for all calculations with the 6-311G** basis set of Krishnan et al. [ 21. Geometries were optimised at the single configuration H-F level (unrestricted H-F where applicable), using the analytical Berny optimisation procedure. CI calculations were performed on the optimised geometries and involved all double substitutions. Conversions of calculated total energies (ET) to values comparable with experimental data were achieved in various ways. Heat of formation AHj’ of species were calculated in the same manner as used by Dewar [3] in the MIND03 semi-empirical calculations, i.e., for NH, 0166-1280/84/$03.00

8 1984 Elsevier Science Publishers B.V.

156

A@(NH,)

=Er(NH,)

-ET(N)

-nE,(H)

+ AI+(N) + nA@(H)

(1)

where A@(N) and A@(H) were taken as 113.0 and 52.1 kcal mol-’ respectively and ET is the calculated total energy of each species. In general both H-F and CI calculations were performed on the species studied. In both cases the same level of calculation was used for molecules and atoms in (1). It should be noted that the above equation ignores any kinetic energy contribution due to the atoms or molecules involved in the formal process. Such contributions are small. Values for ionisation potentials (IP) were obtained using the general formula (2) IPWL)

= E,W+,)

-ErW,)

(2)

For the calculation of the adiabatic IP the E,(NW,) was the lowest energy value of NH’,, i.e., an optimised calculation was performed. In the case of the vertical IP calculation the total energy of NH+, was obtained by restricting the geometry of NW, to be the same as that for NH,. Appearance potential values were calculated using the general formula AP(NH;) = ET(NJ$,)

- ET(NHB) + (3 - n)E,(H)

(3)

Again both adiabatic and vertical values were calculated. Adiabatic values used the lowest ET values obtained from an optimised geometry calculation for NH;. The vertical values used a restricted geometry calculation on NH+,, the restricted geometry was based on the ground state geometry of NH3 by using the same bond lengths and angles and omitting the required number of hydrogens for the ions NW,. APs and IPs were calculated without recourse to empirical data. RESULTS AND DISCUSSION

Table 1 contains the calculated and experimentally derived structural parameters for the ground states of the species NH,, and NH*, (n = 1-3) together with the calculated total energies of the species. Table 2 gives details of some important excited states of the neutral and ionic species. Table 3 gives the calculated and experimental values of A@ and IPs. The adiabatic and vertical APs of the ions NH+, (n = 2-O) and the corresponding experimental values determined mass spectrometrically are given in Table 4. The greater accuracy of the CI calculation relative to the H-F calculation is demonstrated clearly in Table 3. From a computing efficiency viewpoint it would seem that a calculation at the CI level utilizing the H-F optimised geometry is a very economical method for determining thermochemical data for molecules containing elements from the first row of the Periodic Table. Further discussion will concentrate on the CI results.

157

Neutral molecules Ammonia in its ground electronic state has a pyramidal (C,) geometry as determined by infrared [4-61 and electron diffraction analysis [7] with a orbital configuration. The lowest spectroscopically (lal)2(2al)2(le)4(~1)2 observed excited singlet state is planar (D%) and is formed by promoting an electron from the “lone pair” (3aI in C3” or la;’ in Da) orbital to a Rydberg 3s ai orbital, resulting in an electronic state with Ai symmetry [ 81. The Gaussian 80 6-311G** calculated ET values for NH3 (-56.21040 a.u., H-F, and -56.42240 a.u., CI) compare favourably with all previous values. There is only one set of values which are lower in energy and hence probably provide a more accurate A@ than the present values. The lower values were -56.43497 a.u. (STO/CI) and -56.44796 a.u. (STO/CI + EQ) calculated by Eades et al. [9] using the POLYCAL programme [lo] (the ST0 basis set is summarised as [ 5, 4, 2/2, 11. The CI calculations were carried out with ah single and double excitations from the valence space into the virtual space excluding the top virtual orbital (E > 10 a.u.) in each calculation. Previous GAUSSIAN 80 calculations employed STO-3G and 4-31G basis sets [ 111. The geometries obtained from these calculations are not as good as the geometries from the 5-31G [ 12],6-31G [ 13],6-31G* [ 141, 6-31G** [12, 131 and 6-311G** calculations. There is very little difference between the geometry obtained at the 6-31G* [14] level and that calculated in the present study at the 6-311G** level. The calculated bond lengths and bond angles are 100.1 pm and 107.5”, and 100.1 pm and 107.4” respectively. They are both in excellent agreement with the experimental values of 101.2 pm [4-6] (101.38 pm [15]) and 106.7” [4-61 (107.23’ [15]). The absorption spectrum of the NH, amino radical was first observed during flash photolysis experiments with ammonia [ 161 and hydrazine [ 171. It has been of great interest to spectroscopists for some time because of the Renner-Teller [18, 191 interactions shown by the two lowest electronic states, 2B1 and 2A 1, which produces interesting vibrational structure. In its linear form it has a degenerate ground state with three ?r electrons

Bending to CzVgeometry leads to two states (la1)2(2a,)2(lb,)2(3a1)2(1~1)1:

2B1

According to the scheme suggested by Walsh [20] the 3al molecular orbital lies below lb1 so that the 2Bl state will be lower in energy. This is confirmed by the present calculation (see Tables 1 and 2). Previous calculations on NH, have been performed by many workers [ 11, 21-231. For the 2Bl state the only calculation which obtained a lowerET than the present one (-55.75025 a.u.) was a calculation by Peyerimhoff and Buenker [21] ; they obtained a

158

value of -55.78432 a.u. They used a basis set comprising 56 contracted Cartesian Gaussian functions with a configuration interaction treatment of the general MRD-CI [24-261 type and configuration selection and energy extrapolation. They also obtained better results for the 2Al state with an ET value of -55.72898 au. compared with -55.69560 a.u. from the present work. Table 1 summarises the geometrical data resulting from the Gaussian 80 6-311G** calculation for NH, in the ‘B1 state. The bondlength was 101.2 pm and the H-N-H angle was 104.0”. For the 2A1 state the bond length was 98.64 pm with a H-N-H angle of 143.07”. Experimental information is available on both the 2B 1 and 2A 1 states of NH2 due mainly to the work of Dressler and Ramsay [27] who reported a spectroscopic study of NH2 with special emphasis on the RennerTeller [18, 191 effect for the 2Bl state. In general there is excellent agreement between the calculated and experimentally determined values. The determined N-H bond length was 102.4 f 0.5 pm [27] which is only 1.2 pm larger than the calculated value; similarly the calculated bond angle of 104.0” is only 0.7” larger than the experimental angle of 103.3 + 0.5” [27], Table 1. Using additional spectroscopic data 1281, Dixon [29] m-examined the vibronic interactions and concluded, contrary to Dressler and Ramsay [27], who indicated that the 2A1 excited state of NH2 is linear, that it was bent, with a bond angle of 144 f. 5’ and bond length 101.0 pm (other values quoted in the literature for the N-H length include 97.5 + 1 pm [27] and 100 pm [30] ). The calculated values were, N-H bond length 98.64 pm, and H-N-H bond angle 143.07”, which are in good agreement with the experimental results. Many workers have investigated the splitting energy between the 2Bl and 2A 1 states. Bender and Schaefer [ 231 calculated it to be 12 800 cm-’ (SCF, 36.6 kcal mol-‘) and 14 500 cm-’ (CI, 41.46 kcal mol-I). The value was recalculated by Bell and Schaefer [ 221, using a basis set of similar quality to that used by Bender and Schaefer [23] (i.e., using double zeta plus polarization) TABLE 1 Calculated and experimental structures and total energies of NH, and NH; Snedes

NHa

NH, NH

species

ExmrimentaI data

CaIcuIateddata

B~otal (a.=)

Bondlength (pm)

Bondlength (pm)

H-N-H ande(0)

H-F

100.1

107.4

-56.21040

-56.42240

101.2 102.3

104.0

-56.57893 -54.97606

-55.76026 -56.10685

101.2 102.2 106.3 105.1

120.0 150.3

-56.89800 -56.23066 -54.63909 -54.50604

-56.06814 -56.36930 -54.62862 -54.62420

101.2 14-61 101.3s [ISI 102.4 *0.6 C311 104.8 Cl11 103.8 1321

NH+ f Z&4) NH+ (2)a aThis is the experimental

106.7 C4-61

107.23 Cl61 103.3 iO.6 Call

ground state - see text.

CI

159

to give a value of 11 830 cm-’ (33.82 kcal mol”). Peyerimhoff and Buenker [21] calculated the energy difference between the two states to be 12 148 cm-l (34.73 kcal mol-‘) for a fixed N-H bond length of 102.4 pm, but if the “corrected” distance of 98.5 pm for the upper state is used then the value is lowered to 11 048 cm-’ (31.59 kcal mol-l). Lathan et al. [ll] using a 4-31G basis set calculated the separation to be 9282.4 cm-’ (26.5 kcal mol-‘). Table 2 gives the energy separation calculated using the 6-311G** basis set. At the H-F level the value obtained is 11 583.6 cm-’ (33.12 kcal mol-‘) and the CI calculation gives a value of 11 994.64 cm-’ (34.29 kcal mol-‘). Experimental values for the splitting enzrgy have been obtained by Johns et al. [ 311. The analysis of the ~2A,-PBl absorption system was extended and vibronic levels of the 2Al state were identified from u’ = 1 to u’ = 8. Although the vibrational-rotational origin is not observed, extrapolation of rotational branches gave a value of 11 122 cm-’ (31.8 kcal mol” ) indicating excellent agreement between the present theoretical value from the 6311G* * basis set and experiment. The NH radical is well known spectroscopically. It has been observed in flames, electric discharges, flash photolysis and extraterrestrially in sunspots, comets, etc. The neutral molecule has a lowest energy configuration of (1o)~(20)2(3u)2(177)~ and this leads to three states 3Z; ‘A and ‘Z+. Experimental observations show that 32- is the lowest energy state [32]. In the present work the 32- and ‘A states were studied at the H-F and CI levels. The results indicate that the 3Z- is lower in energy than the ‘A state, the ET values being -55.10685 a.u. (CI) and -55.02758 a.u. (CI) respectively, Tables 1 and 2. Table 2 gives details of the excited states for the NH radical and also gives energy differences between the ground and excited states. Lathan et al. [ 111 using a 4-31G basis set predict that the separation between the ‘X- and ‘A states is 46 kcal mol-‘. Another treatment by Cade [ 331 including an estimate of the correlation differences gave a value of 38 kcal mol-‘. Kuba and Ohm [ 341 reported the gap to be 43.8 kcal mol-l from their TABLE 2 Excited States for NH, and NH+, Species

Multiplicity

NH, NH NH; NH; NH; NH+

2(=-4,) WA) WA,) U’B,) V-4,) 4a

-55.69560 -55.02758 -55.30616 -55.26908 -55.23170 -54.62852

NH+

2b

-54.6

ET (a.u.)

aThis is the experimental excited state - see text. bThis is the experimental ground state - see text.

2420

AE (kcal mol-‘) 34.29 49.74 33.35 56.61 80.08 2.71

160

CI calculations. O’Neill and Schaefer [ 351 obtained a similar gap of 46.1 kcal mol” using a CI calculation. A very extensive SCF calculation was reported by Huo [36] using a basis set involving d and f functions for nitrogen andp functions for hydrogen, the value obtained for the energy gap was 42.1 kcal mol-*. A very recent calculation by Fueno et al. [ 371 using a full CI calculation with double zeta basis augmented by polarization functions (9s 5p 2d/4s lp) [ 5s 3p ld/Bs lp] obtained a value of 42.2 kcal mol-‘. The present calculations obtained a value of 49.74 kcal mol-’ at the CI level for the energy gap. The experimental value for the separation between the two states is 36.0 kcal mol’ [ 381. Calculations by Lathan et al. [ll] produced a N-H bond length of 108.2 pm (STO-3G) and 103.3 pm (4-31G). The 6311G** calculations gave 102.3 pm and the experimental value is 103.8 pm [36]. Ions Most of the available data on NH4 comes from photoelectron spectroscopic (PES) studies [39-461. Removal of an electron from the 2ul orbital of NH3 gives rise to planar NH: in the 2Ay ionic state and results in a long vibrational progression of the u2 vibration with no clearly detectable excitations of other vibrations. Structure which has been observed in the 3s and 3p Rydberg bands of NH3 was extensively studied by Douglas and Hollas [39] and by Humphries et al. [ 401. These studies show that the excited molecule is planar and the N-H bond distance increased from 101.2 pm [4-61 to 102.2 pm. The close similarity between the Rydberg band patterns and PE spectrum indicates that these features persist in the (2al)-’ 2Ay state of the ion. The Franck-Condon factor for the transition from the ground state of ammonia to the 2A; ionic state has been calculated [47-491. Harshbarger [ 501 used the result to show that NH: has a planar configuration and the N-H bond length for the 2Ay state of the ion is 107 f 1 pm. In another study of the electronic band shape Avouris et al. [51] concluded that the planar NH; has a N-H bond length longer than in the ground state by about 6 pm. Lathan et al. [ll] using the STO-3G and 4-31G basis sets found that the ammonia cation is planar with D 3h symmetry. The optimised 4-31G bond length was 101 pm in NH; compared with the NH3 value of 99.1 pm. The 6-311G** calculation gave a planar structure for NH: and an increase in the bond length on ionization of NH3, the bond length calculated for NH; at this level being 101.2 pm compared with the bond length of 100.1 pm calculated for NH3. This result is in good agreement with those of Douglas and Hollas [ 391 and Humphries et al. [40]. The present calculations provide a lower value for total energy than any previously reported, Table 1. The cation NH: is isoelectronic with methylene, CH, and therefore it has analogous electronic states. The lowest state is predicted to be a triplet with the molecule in a non-linear structure. The calculated H-N-H angle of 150.3” (6-311G**) is larger than the experimentally determined angle

161

H-C-H in CH2 of 136” which was found from electron spin resonance [52, 531, and spectroscopic work [ 541. This is in line with the general prediction of widening angles in cations compared to neutral species [ll] . The first excited state ‘Al is also found to have a bent structure but with a smaller angle, 109.4”. Measurement of the first two adiabatic ionization potentials of NH2 gave an exp_erimental value for the separation of the ground vibrational levels in NH; (xjBi) and NHi(‘A,) of 0.99 + 0.02 eV (22.8 + 0.5 kcal mol-‘) [55]. This is apparently the only reported experimental value for this separation, however, there have been some theoretical predictions. The 6-311G** calculation gave the separation as 33.3 kcal mol-’ (CI) which is lower and nearer to the experimental result than all other calculated values which lie in the range 47.6-59 kcal mol-’ [ 11, 56,571. Two other excited states ‘B1 and 3A2 have been observed in the PE spectrum of NH2 by Dunlavey et al. [55], however, there are no more experimental details available on these states. The calculations at the 6-311G** level suggest that they lie 56.6 and 80.1 kcal mol-’ respectively above the ground state, Table 2. The NH+ species is isoelectronic with CH. Both the doublet state (1~)~(2~)~(3u)~(la)’

: 21-1

and the quartet state (1~)~(2~)~(3u)~(ln)~:

42

were calculated in the present study. Cohn and Douglas [58] studied the emission spectrum of NH+, which they obtained by passing rapidly flowing mixtures of either helium and hydrazine, or helium and ammonia through a conventional hollow cathode discharge apparatus. They determined that the doublet was lower in energy than the quartet by 1 kcal mol-‘. All calculations have found that the quartet is the lower energy state. Lathan et al. [ 111 using the 4-21G basis set found the quartet to be lower in energy by 28 kcal mol-‘. A treatment by Liu and Verhaegen [59] using a larger basis set gave similar results, approaching the H-F limit. They reported the quartet to be 18 kcal mol-’ more stable. The present calculations at the 6-311G** level also gave the quartet to be the more stable state. However, the difference between the doublet and quartet state was only 2.7 kcal mol-’ (CI). This represents the most accurate calculation to date even though the ordering of electronic states predicted is still incorrect. Thermodynamics Calculation of heat of formation data Table 3 gives A@ data obtained from the H-F and CI calculations and the experimental values from the literature. For the ionic species, mass spectrometrically derived data are omitted because they probably refer to processes which involve an initial vertical ionization of NH, whereas the

162 TABLE 3

AH; and IP Values for NH, and NH: Species

A H#'(kcal mol-’ )

Calc. H-F

NH,

72.91 103.42

-1.63 54.48

NH

115.99

92.48

268.94 321.96 390.19

Vertical IP (eV)

Expt.

talc.

Exp t.

MC.

Expt.

-11.04 [ 601 41 [61] 42.3 [62] 81 [62] 79.2 [60] 92 [ 631 224 [64] 305.18 [65] 392.1 [66] 390.28 [66] 403.08 [66]

9.64 10.64

10.15 [46] 11.46 [55] 11.19 [67]

10.38 11.50

13.02

13.49 [55]

13.10

10.88 [46] 12.00 [55] 11.25 [68] 11.4-12.2 [69] 12.2-12.7 [69] 13.1 [701

CI

NH,

NH; NH; NH+

Adiabatic IP (eV)

220.74 299.80 392.64

corresponding calculated values refer to an adiabatic ionization. It is clear from Table 3 that the errors involved are quite small. In the case of the neutral molecules the average error is approximately 10 kcal mol-’ and for the cationic species the average error is approximately 4 kcal mol-‘. Ionization potentials Table 3 gives details of the calculated (CI) values for both vertical and adiabatic IPs and also experimental values from the literature. Potts and Price [46] determined the adiabatic IP of NH3 to be 10.15 eV. The calculated value is 9.64 eV which is in error by 0.5 eV. They also determined the vertical IP to be 10.88 eV; the calculated value is again lower by 0.5 eV, being 10.38 eV. The adiabatic IP of the NH2 radical has been reported by Dunlavey et al. [ 551 when they studied the photoelectron spectrum of NH2. Their value of 11.46 eV is 0.72 eV higher in energy than the 6-311G** calculated (CI) value of 10.64 eV. McCulloh [67], in his photoionization-mass spectrometric study, used the differences between ionic and neutral heats of formation to derive the IP of NH2 (11.17 ? 0.05 eV). Another value for the vertical IP (12.00 eV) has been reported by Dunlavey et al. [ 551. The corresponding 6311G** calculated (CI) value is 11.50 eV. Other much earlier values quoted in the literature include 11.25 eV [68] and 11.4-12.2 eV [69]. Since these values were determined from electron impact studies they may be considered to be vertical and not adiabatic IPs. The adiabatic IP for NH has been tentatively assigned at 13.49 eV by Dunlavey et al. [55]. This value is again approximately 0.5 eV higher in energy than the calculated value of 13.02 eV. Bradley et al. [69] estimated the value to be 12.2-12.7 eV. Since this was derived mass spectroscopically,

163

it could be considered to be the vertical IP. Similarly, Reed and Sneddon [ 701 determined the IP to be 13.10 eV. The calculated value for the vertical IP is 13.10 eV. Appearance potentials. Morrison and Traeger 1711 studied the electron impact induced ionization and dissociation of ammonia using a quadrupole mass spectrometer. Table 4 summarises their results and work reported earlier and the corresponding 6-311G** calculated values. Two sets of values were calculated. The first was an “adiabatic” AP obtained using the ground state electronic structure of NH3 and the various NH; ions involved. A higher energy “vertical” AP was determined using the ground state structure of NH, but calculating the ionic species with bond length and angles of NHB. This was done because it is not clear if the AI% observed in the mass spectrometric experiments were “adiabatic” or “vertical” APs, although it is commonly assumed that they are the latter. Morrison and Traeger [ 711 quote a value of 15.8 eV for the process (4) forming NH; from NH3 as follows NH,+e+NHd+

H+ 2e

NH,+ e+NH*+

2H+ 2e

(5)

NH,+ e+NH’+

H,+ 2e

(6)

(4) Two calculated values for this process are 15.33 eV (adiabatic) and 16.07 eV (vertical). Other workers who have reported values for process (4) include McCulloh [ 671, who is in exact agreement with Morrison and Traeger [ 711. Powis [72] in his PES study of the influence of angular momentum in the dissociation of NH: quotes the AP to be 15.5 eV, a value nearer the calculated adiabatic AP. There are two possible processes, (5) and (6) which lead to the formation of NH+

TABLE 4 Appearancepotentials Process

Calculated(CI) (eV)

NH,+ e+NH:+ 2e NH,+e+NH;tH+2e NH,te-+NH++ NH,+

e+NH+

NH,te+N+t NH,+ e+N++

Adiabatic

Vertical

9.64 15.33

10.38 16.07( 3)* 16.86( 1) 21.73(4) 21.8( 2) 17.15(4) 17.23( 2)

2Ht

2e

21.61

t H,+

2e

17.03

3Ht 2e H,t H+ 2e

26.00 21.40

Expt. (eV)

Ref.

10.2 15.8 16.5 21.6

71 67 72 70

17.2 17.1 26.7 22.5

71 70 70 71

164

Reed and Sneddon [70] using the mass spectrometric extrapolated voltage difference technique found an appearance potential of 17.1 eV for NH+ and a further increase in NH’ ion current at 21.6 eV consistent with the dissociation processes (6) and (5) respectively. An appearance potential corresponding to (6) was detected by Morrison and Traeger at 17.2 eV, however, they did not detect a break in the curve consistent with an AP for process (5). The calculated values for processes (5) are 21.6 eV (adiabatic) and 21.73 eV (vertical). Both values are in reasonable agreement with Reed and Sneddon [70]. For process (6) the calculated values are 17.03 eV (adiabatic) and 17.15 eV (vertical). Both are in reasonable agreement with the experimental values [ 70,711. There are two processes possible for the production of N’, (7) and (8) NH,+e+N++

3H+ 2e

(7)

NH,+ e+N++

H,+ H+ 2e

(8)

Morrison and Traeger [71] commented that they were restricted by the very low level of signal for N’ (< 1% of the parent ion curve). Their onset potential for the N+ ion, which should correspond to process (8), was not clearly defined and they stated that it may have been extended below the value of 22.5 eV reported. This could then correspond to the 6-311G** value of 21.4 eV for process (8). Previous work reported that breaks in the ionization efficiency curve for N’ have been observed at 24.1, 26.7 and 28.6 eV [70]. The calculated value for process (7) is 26.00 eV which may well correspond with one of Reed and Sneddon’s values (26.7 eV). CONCLUSIONS

The electronic and molecular structures calculated with the Gaussian 80 molecular orbital program at the 6-311G ** level with configuration interaction are in general in very good agreement with experimental determined structural and electronic data. Comparing the results of H-F calculated values with CI calculated values shows the CI calculations to be clearly superior as expected. Thermodynamic data such as heats of formation, ionization potentials and appearances potentials calculated with 6-311G** (CI) are in good agreement with experimental values. ACKNOWLEDGEMENT

One of us (D.P.) wishes to thank the Department of Education of the Irish Republic for a maintenance grant. REFERENCES 1 J. S. Binkley, R. Whiteside, R. Krishnan, R. Seiger, H. B. Schlegel, S. Topiol, Kahn and J. A. Pople, GAUSSIAN 80, Q.C.P.E., 11 (1981) 406.

L. R.

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IP = 10.16 eV

NH; = IP + AH; NH,

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