4809
J. Phys. Chem. 1994, 98, 4809-4813
Quasirelativistic Pseudopotential Study of Species Isoelectronic to Uranyl and the Equatorial Coordination of Uranyl? Pekka Pyykko,' Jian Li,# and Nino Runeberg Department of Chemistry, University of Helsinki, P.O.B. 19 (Et. Hesperiankatu 4), FIN-0001 4 Helsinki, Finland Received: August 23, 1993; In Final Form: January 1 1 , 1994"
The calculated trends of geometries and vibrational frequencies of several uranyl isoelectronic species, like the known N U N and CUO, and the unknown CUN-, NUO+, and NUF2+, are reported. The N U N and C U O results support the matrix spectroscopic assignments. The simplest example of equatorial coordination to uranyl is the Cb species UO3. Its calculated vibrational frequencies also support matrix spectroscopic ones. We earlier suggested that the large range of uranyl bond lengths in UO&-type systems could be interpreted in terms of a "frozen, soft e, vibrational mode". Further studies on UF6, U(OH)6, [(OUO)(F,),]("2)-, [(OUO)(NO,)3]-, and [(OUO)(C03)3]c show only small variation of R,, as function of R,. Thus, the alloxide case is a special one, where all ligands are capable of single and multiple bonding.
1. Introduction
ZZ
The uranium atom ground state is 7s26d15P and hence the U(V1) ion formally hasa closed 6p semicore shell and empty 5f, 6d, 7s, and 7p shells, in order of decreasing binding energy and chemical importance. The uranyl ion1d has a
electron configuration. The uu is the HOMO while the empty 5f 6 and @Jlevels are the LUMOs. The g and u MO's mainly bond to uranium 6d and 5f AO's, respectively, although considerable hybridization with the 6p semicore A 0 also occurs, resulting in a 6puu hole. Having six electron pairs in bonding MOs, uranyl could be said to have triple bonds:
@UE02+
(2)
and it indeed is a persistent species in various coordinating surroundings; no data are available for the free, gaseous ion. The surprise, then, is the large variation of the axial U-0,, distance, R,,, in a number of [(0,,U0,,)(0,).](2"2'systems. The shortest claimed uranyl bond distances are about 150 pm' and they grow, for the quasi-octahedral ( n = 4) systems with a D4h (two short-four long) local symmetry, up to 192 pm, and via 208-209 pm at octahedral symmetry, to 223-232 pm in an "antiuranyl" geometry (two long-four short). We7 recently found that very little energy is needed to change R,, as function of R, along the minimum-energy path of UO& and suggested that the large range of uranyl bond lengths could be seen (for n = 4) as a "frozen, soft eg mcde" of the octahedral central cluster. Analogous behavior has been found for other octahedral systems? StrBmberget a1.8cdescribedthelarge spread of Hg-0 bond lengths in Hg(I1) hexahydrates as a weak secondorder Jahn-Teller effect, increasing the vibrational amplitude. Here we study whether this notion has any validity outside the U06" type systems. Equatorial fluoride, nitrate, and carbonate groups are studied. We also consider the isoelectronic UF.5, U(NH)&, and U(OH)6 and other hydroxyl models. t Reported at the Coordination Chemistry Centennial Symposium, 205th ACS National Meeting, Denver, April 1, 1993. Author for correspondence. t On leave of absence from the Department of Chemistry, Peking University, Beijing 100871, China. Abstract published in Advance ACS Absrracts, April 1, 1994.
0022-3654/94/2098-4809$04.50/0
9
BUF
8
BUO-
7
BUN'-
6
BUC3- CUC2-
5
BUB4-
CUF+ N U F ~ + O U F ~ +FUF'+
NUO+ CUN-
5 6 7 8 Figure 1. Species, isoelectronic to uranyl.
9 Z 1
TABLE 1: Calculated Properties of Uranyl at the HF Level Using Four Different Pseudowtentialsa (Refs 15. 18-20) ~~
~~
PP
Z,
valencespace
b c d e
14 14 14 32
6s6p5f6d7s 6s6pSf6d7s 6s6pSf6d7s 5s5p5d 6s6p5f6d7s
~~
R 168.4 167.3 172.3 166.4
~
v1(u8)
vz(xu)
v1(uu)
1156 1164 1007 1209
264 264 238 263
1209 1242 1082 1295
Z,is thecorecharge,R (in pm) theU-0 distanceand vi the vibrational frequencies (in cm-I). Hay et al.15 U basis (4s4p3d4f)/[3s3p2d4fl. Hay1* U basis (5s4p3d4f)/[3s3p2d2fl. Ermler et aleL9U basis (5~5p4d4f)/[2~2pldlf; the 6s, 7s, 6pand 7pcontractcd functions all use five primitives. Kiichle et aLZ0U basis (12sllplOd8f)/[8s7p6d4fl. The isoelectronic principle9 is still useful for predicting new chemical species."J The species, isoelectronic to uranyl, are enumerated in Figure 1. Both NUNk1J2 and CUO" have already been observed in rare-gas matrices. We now report calculated geometries and vibrational frequencies for a number of these species. 2. Method The Gaussian 92 program14 and the 14-valence-electron (14VE) quasi-relativistic uranium pseudopotential (PP)I5 with corresponding (4s4p3d4f)/ [3s3p2d4fl basis set were used for the production runs. When the triatomic species were discussed, the main-group elements B-F were described using the (9s5p)/ [3s2p] all-electron (AE) basis sets.16 For larger systems, the atoms C-F were also described using a PP and a (4s4p)/[2s2pJ double-zeta basis.1' For hydrogen a (4s)/[2s] b a s W was used. The dependence of the results on the uranium pseudopotential 0 1994 American Chemical Society
Pyykk8 et al.
4810 The Journal of Physical Chemistry, Vol. 98, No. 18, 1994
TABLE 2 Calculated Harmonic Vibrational Frequencies (cm-1) for Z I U Z ~ NUF2+ OUOZ+
750 1156 869 874
179 264 177 253
1059 899 804.4 897 788.9 852 868.7 1168 1008 1053
247 185
-
NUO+ 12CU'60 13cul60
IZCU'*O NUN CUN-
1272 1209 93 1 962.5 952.3 1293 1185 852.6 1143 837.1 1183 844.8 1209 1051 1147
-
181
181
-
245
229
a Combined from several measurements. U02(ClO&(aq). c In argon matrix.
23" 24b 25c 13 13 13 0' n
12
Measured
from
3. Results and Discussion Triatomic Species. The calculated vibrational frequencies are given in Table 2 and the other properties in Table 3. Figure 2 gives an idea of the agreement of these HF-level frequencies for UOzz+and U 0 3 with experiment. Of the predicted species, NUO+ is surrounded in Figure 1 from three sides by observed species. Its calculated U-N and U-O bond lengths are short, 163.1 and 171.5 pm, respectively. Perhaps it could be made by insertion of U into NO+, analogously with NUN and CUO. The anion CUN-, an insertion product to cyanide, also could have a chance. The shortest calculated bond length is the 0-U of 161.0 pm in OUF3+. It is slightly
FUF4+
OUF~+
ouo2+ NUF2+ CUF+ NUO+ CUO CUO NUN BUF CUNBUO-
cuc2-
0"
Bz
BI
AI
AI
AI
HF HF HF HF HF HF HF
MP2 HF HF HF HF HF
z1-u
and UO,.
below the 164.8 calculated for uranyl. The calculated U-F of 179.2 pm indicates multiple bonding to fluorine, as well. Denning et a1.26 notice that in UOXs- (X = F, C1) the U-X bond, trans to oxygen, is shorter than the four others and discuss the "inverse trans influence" in terms of a OUX3+ unit. The asymmetric or disproportionated uranyl-like system NUF2+has calculated U-N and U-F bond lengths of 161.2 and 188.5 pm, respectively. We have earlier2' compared it with the experimentallycharacterized Me3SiN=U[N(SiMe3)2]3F, whose U=N and U-F are 185 and 201 pm, respectively.28 Note that the more electropositive ligand is calculated to have the shorter bond in both NUF2+, NUO+, and CUO. Apart from these systems, Gilje and Cramer29point out that only one system, Cp3U=CHPR3, with a U-C multiple bond is known, while several short U-N bonds, with nearly triple-bond character, are known. Total-energy comparisons at H F level between species of different total charges are not accurate. Subtracting from the total energies of XUYnin Table 3 the calculated energies of XYn, we find a
AJ?? = E,(XUY") - E,(XY")
(3) of -52.676, -52.761, -52.827, and -53.157 au for XYn = CN-, CO, NN and NO+, respectively. UOJ. The calculated structure of uranium trioxide is shown in Figure 3. All vibrational frequencies (Table 4) are positive. The D3h species, with R = 180.6 pm, is a saddle point, 49 kJ mol-' above the C a minimum. The single, slightly longer U-O bond could be seen as the simplest example of equatorial oxide coordination to uranyl. It lengthens the axial bond length from 165 to 175 pm. Here the coordination number CN, = 1. A 20 pm variation of R, changes the R,, by only -2.2 pm. In other words, the ratio (4)
is about -0.11,
174.3 161.0 164.8 161.2 174.1 163.1 170.7 177.4 168.2 188.0 175.5 194.8 182.0
Mulliken population Zz-U
179.2 188.5 203.7 171.5 180.5 182.7
-
207.4 174.2 180.7
-
I
uo3
Calculated Properties for Uranyl-like Compounds, ZIUZZ method
Bz
Figure 2. Calculated and experimental vibrational frequencies for UOzz+
bond length species
ag
uop
was tested by using three other pseudopotentials18-20 for the uranyl ion. The results are compared in Table 1. The Ermler et al. PP19 gives a longer bond length and smaller frequencies than the three others, perhaps due to the contraction of s and p functions to minimal basis level. The Kiichle et al. PP20 has a larger valence space but gives R and vi closer to the Hay15-18 ones. The experimental bond length of UOz2+is not known. Earlier calculations with the uranium PP from ref 15 and a (4f)/[2fl contraction with a (9sSpld)/[3~2pld]basis for oxygen give a U-O distance of 162.5 and 173.2 pm at H F and MP2 levels, respe~tively.~J* A density functional calculation by van Wezenbeek et ala6gives an U-0 of 170.0 pm. As the uranium basis contained no gtype polarization functions, only HF-level and almost no MP2-level results are reported. Care had to be taken to converge to the electron configuration (1); the NUN results in ref 7 pertain to a 6, excited singlet state. Thevibrational frequenciesof the three- and four-atomicspecies were calculated using the H F force fields and the MOLVIB 6.0 program.22
TABLE 3
tlM
42,
QU
0.30 0.25 -0.04 0.13 -0.1 1 -0.12 -0.35 -0.46 -0.38 -0.83 -0.70 -1.39 -0.99
3.41 2.74 2.08 2.14 1.61 1.46 0.97 1.03 0.77 1.41 0.33 1.03 -0.01
92,
0.02
-
-0.26 -0.51 -0.34 -0.62 -0.63
-
-0.58 -0.63 -0.65
-
Elau -249.057693 -225.692932 -201.966257 -206.041690 -189.805006 -181.982973 -1 65.446462 -166.125187 -1 61.697730 -176.691555 -144.909049 -1 52.143444 -127.926811
Uranyl Isoelectronic Species -0.13
ol
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4811 240
2+
Cdc.(tYmrk) A Cdc.(Ref7) .Exp
0 230 .
220 .
Figure 3. Calculated structures for U02*+and UO3.
B 9210 .
TABLE 4 Calculated and Experimental Vibration Frequencies for UO, expjcalc mode calc expa 0.71 b2 214 151.5 bi 242 211.6 0.88 a1 262 186.2 0.7 1 al 838 745.5 0.90 a1 964 bi 99 1 852.5 0.86 References 25 and 30.
2
200 .
.2
:5
190
\
.e,
.
11
TABLE 5 Comparison of Results Using Pseudopotentials and All-Electron Treatment for Oxygen and Fluorine species method Rlpm va,,lcm-l U06” PP 216.4 594 AE
expO UF.5
PP AE
expo U(NH)s”
PP
214.8 208 195.9 192.6 199 230.3b 223.lC
587 797 706 764 667
180
’
1 7 16
200
210
220 %/Pm
230
240
Figure 4. Optimized R, as function of 4 for UO6&. The dashed line corresponds to cubic geometry. This work uses a pseudopotential at oxygen, ref 7 did not. For the experimental points, see ref 7. 205
- UF6
a References 1-6. b U-N-H angle flexible, optimized at 102.5’. UN-H 180’.
The ratio of experimental to theoretical vibrational frequencies (see Table 4) varies from 0.71 to 0.90; the average of 0.81 is typical of HF calculations. The results support the symmetry assignments in refs 25 and 30. No experimental information is available on the geometry of UO3(g), apart from the C, symmetry in an argon matrix. Its atomization enthalpy, AHo’,~, is estimated to be 2065( 14) kJ mol-’ and ionization potential 10.4(6) eV.3’ The corresponding calculated Koopmans’ ionization potential is 11.1 eV. UO& and UF6. The effect of using a PP for the ligands 0 or F was tested on these bond lengths and breathing frequencies in Table 5 and found small. All subsequent results use PP. The optimized R,, as function of R, is shown in Figures 4 and 5, respectively. The present variation of U-0,, as function of U-0,, using an oxygen PP, is similar to that of ref 7 with an AE oxygen. The variation for fluorine turned out to be much smaller. The r-values are about -1.5 and -0.32, for 0 and F, respectively. The octahedral minima have the bond lengths in Table 5 . The Mulliken overlap populations are 0.222 and 0,161, and the uranium charges 2.252 and 2.036, respectively. Figure 6 shows the equipotential surfaces for these two cases and demonstrates clearly that the “soft eBmode” of UO& has disappeared in the isoelectronic UF6. It is interesting to ask whether such a mode should be included in simulations of oxide phases.32 U(NH)&. TheNH2-group is polarizable and capableof single and multiple bonding, like 02-. We therefore carried out exploratory calculations on these unknown systems. The octahedral case (U-N-H = 180’) has a U-N distance of 223.1 pm, 6.7 pm above the analogous U-0 distance. In this particular case, the ratio r = -2.1, even larger than for U06”. If the U-N-H angle is optimized, the U-N distance increases to 230.3 pm. The r is comparable but R,, diverges for R, I 225 Pm*
190 185
195
190
200
205
%/Pm
Figure 5. Optimized R , as function of ROpfor UF6.
2.3
2.2
& 2.1 2.0
1.9
1.8 1.8
1.9
2.0
2.1
2.2
2.3
R , Figure 6. Equipotential contours of UF6 and the UO& cluster model. UOz(NH)46. In this case the optimized U-0 is 186.5 pm whileU-N islong,258.8pm,andU-N-H = 101.7’. Therratio is small, -0.29.
U(OH)6 We now saturate the oxygen valencies by hydrogens.
4812
Pyykk6 et al.
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 [(OUO)Fn](n-2t 178
I
+
HF 0 minimum H Exp 1 RbUOz(N03)3 .
177 .
176 .
175 .
+' 173
171 . 170
1
i
J I
'
2
3
4 CN,=n
5
6
7
Figure 7. Calculated uranyl bond lengths in uranyl fluorides as function of the equatorial coordination number, n = CN,. See Table 6 for experimental references.
.
170 240
245
250 255 U-O,/Pm
260
265
Figure 8. Calculated uranyl bond lengths as function of the equatorial U-O(nitrate) distance in [(OUO)(NO3)3]-. The experimental point is from ref 40.
TABLE 6
Optimized Geometries for Uranyl Fluorides' symmetry U-O U-F point ref 209.4 Dzhb 171.3 U02Fz 173.7 214.8 D3h U02F3176.2 220.7 D4h U02Fd2229.8 177.6 ~ 0 ~ ~ ~ Ds3h 176.Y 224.5 1 36 175d 220 2 37 3 e 176(3) 178(1) 223.5 4 38 UO2F6& D6h 177.4 248.3 174(2) 242.9(2) 5 39 a Distancesgivenin pm. Experimental points from Figure 7. Terminal U-F distances chosen. A symmetry lowering to Cb lowers the energy from-132.145 39 to-1 32.148 62 au, but has small effectson thedistances. Average of 173(4) and 180(4)pm. Average of 174 and 176 pm. As quoted in ref 1. species
This system is analogous to the known U(OMe)6, whose U-0 = 210 pm and U-0-C 153.7°.33 The present optimized geometry is U-0 199.1 pm, 0-H 95.5 pm and U-0-H 180'. The r is about -0.3 8. [(OUO)(OH)4]~. Under D4h symmetry, the optimized geometry is U-0,, 178.4 pm, U-0,220.4 pm, and U-0-H 180'. The r is about -0.36. Experimentally, in U02(0-t-Bu)2(Ph3PO)z, the average U-0,, is 179 pm, the alkoxide U-0,215 pm, and the phosphine oxide U-0, 241 ~ m . 3 ~ Uranyl Fluorides. Uranyl fluoride species [ (OUO)(Fcq)n](*2)with n = 5 and 6 are structurally characterized.' In addition, one n = 7 system has been reported.35 Figure 7 shows the optimized U-0 distances for n = 2-6. The symmetries and U-F distances are given in Table 6. For U02F5* (Dsh), the calculated U-0 and U-F distances in Table 6 and Figure 7 are close to experiment. Note that the vertical scale is very narrow. For U02F6+ ( D d , with the highest negative charge, the U-0 distance is comparable with the previous case (n = 5 ) but the U-F distance larger. Uranyl Nitrate and Carbonate. The calculated R,, versus R, curves are shown in Figures 8 and 9. D3h symmetry was assumed for the complex and for the individual anions (N-0 128.4 pm,
180
R
\
0" 5
175
240
245
250 255 U-O,/pm
260
265
Figure 9. Calculated uranyl bond lengths as function of the equatorial U-O(carbonate) distancein [(OUO)(C03)3]c. The experimentalpoints 1 and 2 are taken from refs 41 and 42, respectively. The horizontal error limits correspond to the experimental extremes. C-0 132.4pm). The encircled points correspond tooptimization of both R, and Rax. The available experimental points are included. As seen, both the calculated U-O(urany1) and U-O(nitrate or carbonate) are near experimental values in crystals. Note again that the scale is very narrow. The uranium in seawater occurs as [(OUO)(C03)3lc. It has
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4813
Uranyl Isoelectronic Species Nitrate
Nitrater
Uranyl
.;ed
I
-..-. I I
,*‘
I
,‘
Academy of Finland. The calculations were carried out on the Convex 3840 and Cray X-MP EA1432 of CSC, Espoo. We are indebted to Dr. Michel Dupuis for kindly producing the test results for the Ermler et al. PPI9 using the HONDO 8.4 program and to the referees for their comments.
References and Notes la’s HOMO
5f$ LUMO
Figure 10. The la2’ HOMO of NO,- and the
LUMO of uranyl.
TABLE 17: Calculated Mulliken Overlap Populations between Uranium and the Axial and Equatorial Oxygens breakdown species
oxygens
U02(NOa),ax
U02(C03)3C
q ax
total
U(s)
U(p)
U(d)
U(f)
0.232 0.830 0.234 0.826
0.028
0.074
0.100
0.031
0.032
0.070
0.100
0.032
been suggested that ligands with axial hydrogen bonds to 0,, could be used to extract it.43 Nature of Equatorial Bonding. Coulson and Lestefl considered the eventual roleof f orbitals in the secondary, equatorial bonding in uranyl nitrate and pointed out that the uranium f+ (ml = f 3 ) AO’s span the bl, and b2” irreps of the D3h complex. As seen in Figure 10,a HOMO(nitrate)-to-LUMO(urany1) donation is then a logical proposal for the nature of the equatorial bond. To our knowledge, this proposal has not been critically examined. We give the calculated Mulliken overlap populations for uranyl nitrate and carbonate in Table 7. As seen, the U(5f)-O, ones are very small, about 0.03 (for each U-O). The total U-0, population of 0.23 involves uranium AO’s in the order d > p > s = f, which would suggest that the U(5f) AO’s play only a minor role in the equatorial coordination of these particular species.
4. Conclusions 1. The calculations summarized in section 2 suggest that the bond length of the free uranyl ion could be of the order of 166 pm(1argest-basisHF) to 170pm ( D n ) . As theequatorialligands are found to lengthen U-O,,, the experimental values below 166 pm should be checked. 2. We have predicted a number of further, so far unknown, species isoelectronic with uranyl and provided theoretical support to the vibrational assignments of the observed NUN, CUO and U 0 3 molecules. 3. Our previous idea that the large variation of R,, in uranyl oxides could be determined by an “innermostclockwork”of UO& bonding is still there and awaits confirmation from full-crystal calculations. It turns out, however, to be a special case. The only comparable case is the model system U(NH),f-. In the other U(V1) compounds examined, some or all of the axial and equatorial ligands are less polarizable and not capable of single and multiple bonding, and indeed these R,, variations are small, both theoretically and experimentally. The older experimental (R,, RaX)points further outside the present curves for thevarious ligands are suspicious. 4. A Mulliken population analysis of the uranyl nitrate and carbonate complexes suggests that the 5f is n o t an important uranium AO, involved in the equatorial coordination. Acknowledgment. We thank Professor L. L. Lohr for bringing us intocontact with Professor L. Andrews. Dr. T. Sundius kindly provided access to his vibrational frequency program MOLVIB 6.0. J.L. was supported by Centre for International Mobility, Finnish Ministry of Education. N.R.is supported by The
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