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The electronic structure and spectra of UO+
CHEhHCAL PHYSICS LETTERS
Volume 99, number 5,6
19 Aqyst 1983
THE ELECTRONIC STRUCTURE AND SPECTRA OF UO* M_ KRAUSS
and W_J_ STEVENS
Molecular Spectroscopy
Division, National Bureau of Standards, Washington. DC 20234, USA
Received 25 April 1983; in final foti
13 June 1983
Relativistic effective potentials are used to calculate the electronic structure and spectroscopic properties of UO+_ The lowest-energy states are very ionic and the molecular orbitals substantially localized so that the molecule is described by the ionic fmgments. U 3+ (f 3 , 41) and 02-(1S). TheR, and we of theground n = 9/2 state have been determined to be 3-48 bohr and 925 cm-‘_ The vibrational and electronic states are interleaved with the lowest excited electronic state, Q = 7/2, at 13 15 cm-’ _ The excitation energies of the excited states of UOi were calculated using a restricted valence configuration interaction. Strong radiative transitions are predicted in the red part of the visible.
1. Introduction The study of the positive ions oflzanium oxide dates from the observation of UO” and UOZ from the interaction of U + 0, in a molecular beam experiment [ 1,2]. Althougb the infrared spectra of matrix-isolated neutral uranium oxide species from UO to UO, [3-51 and the spectra of UO: have been assigned [6], there is no reported spectrum of UO*. In order to assist in the search for the IR and visible spectra of this ion, we have cafculated the electronic stmcture and energies of the lowest 41 and 4H states of the ion and selected excited states which can couple radiatively with the 41 ground state. The use of relativistic effective potentials (REPS) makes these calculations possible. Recent work on low2 molecules with non-relativistic effective potentials has shown that the energy curves compare well with all-electron ab initio curves [7,8]. Lee et al. [9] have described the method for calculating the j-dependent REPS based on pseudospinors. The 6s1/2,6p1/2,6~31~, 5fsjz, 5f~~~,6d3/~, and 6dsi2 spinors were obtained from a Dirac-Fock solution [IO] of a degeneracyweighted energy average of the (core)6s26p65f36d open-shell configuration of U2+ and the 6g spinors were obtained from the (core)6sz6p66g ionic configurations. The spin-orbit interaction is very large for uranium, but the large components of the 6d and 5f spinors with differentj values are not SubstantiaIly dif0 009-2614/83/0000-0000/S
03.00 0 1983 North-Iiolland
ferent. The positions of the peaks of the outermost maxima of the 5fsj2 and 5f7iz orbitals differ by 0.020 bohr and the 6d312 and 6ds11 differ by 0.092 bohr. The calculation of the electronic structures of the ground states of the actinide metal oxides are more readily done initially with neglect of the spin-orbit interaction using Z-dependent relativistic effective potentials, and subsequently introducing the spin-orbit interaction through configuration mixing. The spin-orbit components, or j dependence, of the REPS is eliminated by taking a weighted average [ 1 I] of thej=Z+ l/2 andj=Z - l/2 potentials: UlAREp = I
21+ 1
The average potential has been designated AREP. Using the ALCHEMY system of codes *, modified to use the AREP, we performed preliminary self-consistent-field (SCF) calculations which determined that the electronic structure of the lowest-energy states is very ionic, and the molecular orbitals are substantially localized. AlI of the lowest-energy states arise from the maximum projection of the angular momentum of the ionic fragments, U3’(f3,41) 02-(IS), on the molecular axis. The * ALCHEMY is a system of programs for the calculation of molecular wavefunctions developed by P-S. Bagus, B. Liu, A.D. McLean and hl. Yoshimine at IBM-San Jose, California.
417
CHEMICAL PHYSICS LETTERS
Volume 99, number 5.6
lowest energy state at the SCF level is the 41. All of the SCF quartet states from S- to 1 are found to be similar in electronic structure with the f orbitals being highly iocalized. Radiative transitions from the 41 state will be assumed to be representative of the complex. An accurate calcu~tiorl itlcludirlg correlation is very difficult because important correlating configurations are of different ionicity or orbital occupancy from the SCF configurations. and differential correlation effects for the ions embedded in the molecule complicate the caiculaticn. A qualitative description of the electronic structure and spectroscopy is still possible because the U3+(f3,41) sfdte is energetically separate from the other atomic ion states. The f3 doublets. for esample, are nearly 3 eV higher in enernv. =* The spin-orbit mising of the lowest energ)’ 42-. lIl. aa . 4+. “r. “H ,md 41 states has been studied perturbdtively using the AESOP operator [ 171. The lowest R states are still doxninsted by a sin&e tz function- The mixing coefikient of the ql function in the 52 = 912 ground state. for example, was calculated to be 0.94. Tr.msitions from the dominant 4I component will then provide a Lero-order description of absorption from the ground state. Smdll hlC SCF calculations were done to show thar the SCF elecrronic description was adequate for a qualitative ~lxtderst~l~ding of the ground state. The exited-state calculations were done by restricted valence configuration interxtion (VCI) using several sets of localized molecular orbitais. Since we are only interested in those states which are dipole radiatively coupled to the “11ground state. we will describe in this note the electronic structure of the low-Iying’l, AH and qK SI~IFS. These data will be used to quaIitativeiy describe the lluorescence pumping of cold UO’. These c~tlcul.nions are prrscnted to assist in the planning and interpretation of experiments designed to detect UOi, and IO present a preliminary analysis of the electronic stt ucturc of such heavy-metal oxides.
2.
Description
of the
olculations
double-zeta Slater function atomic basis was energy optimired using the AREP on the I._@+(6s26p66d5f3,5L). Ul+ (6s26p67s6d5f3,61_). and Ul+ (hsZGp67p6d5f3,6hl) states. SCF c&culations on the 3I. 4H, and 6~ molecutar states provided a set of molecular orbitais primarily locshzed on the o?+gen per and pn orbit&, and the uraA
41s
19
Aumt
1983
nium 6s. 6p, fu. 6. fs,f@, da-da, and 7s~ orbitals. In order IO determine the spin-orbit coupling among the lowest energy 4X-, 411,4A. 4& 4r, 4H, and 4I states that arise from all f3 couplings, it was necessary to calculate these states with a common orthogonal set. Using the SCF molecular orbitals from the 41 and 4H states. configuration interaction calculations were carried out using a base set of configurations for each state which arise from three-fold occupancy of the fu . fn, f6. or fQ orbitais and adding ail configurations arising from a single excitation from all valence orbitals in the base configurations into the virtual space. The spin-orbit interaction was calculated using the AESOP operator_ The energies of these fz coupled states are given in table I at one distance (3.625 au) relative to the energy of the unperturbed 41 state. The lowest-energy a states are still dominated by one A state. For example. the !2 = Q/r! ground state is represented by 419,z =0.9441-O_334
I-l -0.10~r+0.02%$
and the 4117,2 first excited state is given by =
4H7,2
0.83 “H - 0.48 4r - 0.25 4@ + O-OS 4A11.
The energy splitting of the 41 through 4C-state~ is ~0.3 eV, but after considering the spin-orbit coupling, the complex of a states is spread over 1 eV_ Since spin-orbit coupling to states outside the quartet f3 groups was neglected, only the description of the lowest-energy states has any validity_ Table 1 Ekcrronic
R
states at R = 3625 au
SL
E (cnt-t)
912
-4661
l/2
2074
712
-3342
912
2176
512
-2766
311
2553
3fl
-2567
512
2777
II/Z
-1098
712
2858
112
-1365
Is/L?
4128
912
-1062
1312
5027
712
-616
l/2
5117
3/2 5/z
-43s 136
1l/2
5799
912
5831
798
712
5991
107s
SlZ
6285
1627
313
6286
13/2
117 II/Z
$2
E (cm-‘)
CHEMICAL PHYSICS LETTERS
Volume 99, number 5.6
A Morse fit to the 4I SCF curve yields an equilibrium internuclear distance of 3.46 bohr and a vibrational constant of 949 cm-l for U160+. The 4Ig,2 groundstate energy curve is found to have the same R, and a vibrational constant that is only 10 cm-l smaller. A small multi-configuration SCF (MC SCF) calculation for the 41 state that includes the dominant back transfer correlation yields an R, of 3.48 bohr and an o, of 935 cm-l _Assuming the spin- orbit correction to the 41 CI function calculated above applies to the MC SCF result, the vibrational constant for the spin-orbit perturbed MC SCF energy curve is 935 cm-l _ A restricted valence confgnration interaction was performed on the 41, 4H, and 4K states to provide an estimate of the absorption spectrum. The U6s, U6p, and 02s orbitals were retained fully occupied and the f+r, dn, and d6 orbitals were obtained in the 6K SCF solution. This calculation does not allow for orbital relaxation, so the energy curves are not optimal. The R, calculated for the 4I state is -3.6 au in this calculation. This value is ~0.1 au larger than that obtained in the MC SCF calculation and is attributed to the use of orbitals that are intended to describe both the ground and excited states and are not optimal for either. The excitation wavelengths in the visible region from the 41 ground state are shown in fig. l_ All the curves are shifted so that the 4I R, agrees with the value calculated for the MC SCF curve while retaining their reAbsorption
s 1
Spectra
of
UO+
\
1
3.5
Table 2 Transition moments from the X41 state to the excited I. H, and K states (in e bohr) Ground state 1
41 4H
0.028
4K
0.30
lative positions.
Excited state 2
Excited state
0.31
0.092
0.31
0.61
3
The VCI total correlation
energy near states and results from two types of configuration interactionThe first is the double excitation between the slightly bonding (aU7s + 02p)4a valence orbital, which is doubly occupied in the SCF wavefunction and the slightly anti-bonding (U7s - cuO2p)50 correlating orbital (CY< 1). The second type of correlation mixing results from backbonding from the (02p)Zx valence orbital into n correlating orbitals. The dominant correlating orbital is primarily U6dn in character for 4I and a mixture of U5 fir and U6ds for 4H. The same correlating configurations were included in the MC SCF calculation of the 41 ground state. Transition moments from the ground 41 state to excited 4I states and all the 4H and 4K states are given in table 2 for R = 3.625 bohr. The four strongest transitions which range from 0.75 D to over 1 D are all atomic f to d transitions. These electronic transitions range from the far red around 750 cm to the green at 455 nm. The electronic transition between the ground “1 and 4H states has a relatively weak transition moment of 0.07 D.
R, is ~1 eV for both the 41 and 4H ground
341
305
nn
34H
455
run
3. Discussion The ground-state electronic structure and spectroscopic constants are based on SCF and MC SCF calculations using the AREP with inclusion of the spin-orbit coupling as a perturbation. The MC SCF calculation shows little change in the orbitals from the SCF results with only a modest shift in the dipole moment (==0.2 au) as a result of the 71back-bonding. However, at least two major correlation effects have been neglected because of the inability to handle the calculation at this time. The differential atomic-like correlation between states of different ionic&y and d or f occupancy and
14K
625
nm
2k
655
nm
z41
755
Inn
141 *30
19 August 1983
45
5.0
R (hk) Fig. 1. Energy curves calculated at the valence configration interaction level with a common molecular orbital basis. The vertical transition wavelengths from the 1 41 state are shown on the right.
419
Volume 99, number 5.6
CHEMKAL
PHYSICS LETTERS
charge transfer plus polarization configurations must be considered at some future date. As a result it is impossible to gauge the XCUmCy of the calculations without recourse to comparison with experimentAn estimate of the ground-state vibrational frequency can be obtained by comparing the spectroscopic constants between the SCF curves for the 41 state of UO* and the s 1 state of UO. The VCI curve is not sufficiently reliable because the correlation is not optimized as a function of the distance. The best Morse fits to the SCF curves yield an equilibrium internuclear distance of 3-46 boht and a vibrational constant of 949 cm-l for U160+ compared to 3.56 bohr and S63 cm-l for U160_ A band at WZO cm-l has been assigned to U160 in the Ar-matrix-isolated spectrum [S], but this value may be appreciably red-shifted from the gasphase value. For the Kr matrix the 810 cm-1 band is split and red-shifted to SI9 and 815 ~m-~. These shifts are smaller tflan analogous shifts observed in the lithium halides [ 13-151. Linevsky [ 131 has shown that the dominant interaction causing the shift is the dipofeinduced-dipole coupling of nearest neighbors with the difference in the square of the dipole moments in the u = 0 and I let& determining the magnitude of tfie shift. Both UO and the alkali halides have large dipole moment derivatives which we find are of comparable magnitudes. But the calculated value of the anhamionic constant for UO is ~2 cm-l or about half the value for LiCl [ 16]_ The variation of the dipote moment as a functiori of rhe vibrdtionaf state in UO is then much less than that in the alkali halides. However. it must be recognized that the w,*, is obtained from a Morse fit to an energy curve that is not represented well by a hlorse curve. Tilt UO MC SCF calculations yield an R, of 357 bohr ,md an o, of ==S45 cm-l or =3% larger than the nlatris-isolatiorl-obsc~ed frequency_ The spin -orbit coupling will be more complicated in UO than UOc hut the additional states that mix would tend to lower the frequency. We thus feel that the accuracy is \\ithin the 3% range for the UOf oe of 925 cm_1 determined from the spin-orbit perturbed hlC SCF energy curve. The vibrational infrared transition for the 41,,, state is very strong with an oscillator strength of ~5 X io-s for the IJ = 0 to u = 1 transition. This compares with an electronic oscillator strength of %!.2 X loss for the “1 9/2--Q infrared transition. The vibrational and electronic infrared transitions will interleave. The pres-
19 Argnust 1983
ent calculation predicts, for example, the lowest energy transition to be a vibrational transition at =933 cm-1 followed by an electronic transition at ~131.5 cm-l. The visible electronic transitions will be split by the spin-orbit interaction into a range over 1 eV wide roughly centered around the transitions given in fig. 1, The spin-orbit interaction for the excited states is too complicated to be treated by the present methods, but the prediction of strong radiative transitions in the visible will not be affected. The quartet states that couple to the lowest 42, 4~Y 4A, 4#, 4E’, and 4H states are also predominantly fzd systems and have the same transition moment behavior as the 4H, 41, and 4K excited states. Calculations on the sextet states indicate a dominant configuration with ionicity U2+01- that will not couple strongly to the radiatively importmt quartets with ionicity U3*02-. The f3 doublets are in this energy region but again the spin-orbit coupling is weak because the f and d orbitaIs, though polarized, do retain considerable atomic character. Strong radiative transitions are expected in the red part of the visible. The fluorescence will pump the excited vibrational levels of the lower complex of states (which have similar vibrational structure) because the excited states are shifted in frequency and R,. Under low-pressure excitation conditions the strong visible and IR transitions at =925 cm-l would be expected. Detailed modeling is not possible because of the true complexity of this system.
Acknowledgement Research supported in part by the Air Force Office of Scientific Research under Contract No. AFOSR ISSA-St-00017.
References [I] W.L.
Fiite and P- Irving, 3. Chem, Phys. 56 (1977) 4227. [2] W-L. Fite, H.H. Lo and P. Irving, 3. Chem. Phys. 60 (1974) 1136. [3] D.H.W. Carstens, DM_ Cruen and J.F. Kozlowski, High Temp. Sci. 4 (1972) 436. [4] S.D. Gabetick, G.T. Reedy and h1.G. Chasanov, Chem. Phys. Letters 19 (1973) 90; 3. Chem. Phys. 58 (1973) 4468.
Volume 99, number 5,6
CHEMICAL PHYSICS LETTERS
[S] S. Abramowitz and N. Aquista, J- Res. NBS 78A (1974) 421. 161 D.W. Green, S.D. Gab&&k and G-T_ Reedy, J. Chem. Phys. 64 (1976) 1697. [7] PA Christiansen.YS. Lee and KS. Pitzer, 3. Chem. Phys. 71(1979) 444s. 18J W-I. Stevens and M. Krauss, Appl. Phys. Letters 41(1982) 301. 19) Y.S. Lee, WC. Ermler and KS. Pitter, J. Chem. Phys. 67 (1977) 5861. [ 101 J_P_Desclaur, Computer Phys. Commun. 9 (19753 31.
19 August 1983
[ 1 I] WC. Ermler, Y.S. Lee, P-A. Christiansenand KS. Pitzer, Chem. Phys. Letters Sl(1981) 70. [ 121 W3. Stevens and M. Krauss.Chem. Phys. Letters 86 (1982) 320; J. Cbem. Phys. 76 (1982) 3834. 1131 MJ. Linevsky, J. Chem. Phys. 34 (1961) 587: 38 (1963) 658. 1141 S. S&lick and 0. Schnepp. J- C&em. Phys. 41(1964) 463_ {IS] K.P. Huber and G. Heaberg, Molecular spectra and molecular structure. Constants of diatomic molecules (Van Nostrand, Princeton, 1979). [ 161 R.L. Matcha, J. Chem. Phys. 47 (1967) 4595.
Volume 99, number 5,6
19 Aqyst 1983
THE ELECTRONIC STRUCTURE AND SPECTRA OF UO* M_ KRAUSS
and W_J_ STEVENS
Molecular Spectroscopy
Division, National Bureau of Standards, Washington. DC 20234, USA
Received 25 April 1983; in final foti
13 June 1983
Relativistic effective potentials are used to calculate the electronic structure and spectroscopic properties of UO+_ The lowest-energy states are very ionic and the molecular orbitals substantially localized so that the molecule is described by the ionic fmgments. U 3+ (f 3 , 41) and 02-(1S). TheR, and we of theground n = 9/2 state have been determined to be 3-48 bohr and 925 cm-‘_ The vibrational and electronic states are interleaved with the lowest excited electronic state, Q = 7/2, at 13 15 cm-’ _ The excitation energies of the excited states of UOi were calculated using a restricted valence configuration interaction. Strong radiative transitions are predicted in the red part of the visible.
1. Introduction The study of the positive ions oflzanium oxide dates from the observation of UO” and UOZ from the interaction of U + 0, in a molecular beam experiment [ 1,2]. Althougb the infrared spectra of matrix-isolated neutral uranium oxide species from UO to UO, [3-51 and the spectra of UO: have been assigned [6], there is no reported spectrum of UO*. In order to assist in the search for the IR and visible spectra of this ion, we have cafculated the electronic stmcture and energies of the lowest 41 and 4H states of the ion and selected excited states which can couple radiatively with the 41 ground state. The use of relativistic effective potentials (REPS) makes these calculations possible. Recent work on low2 molecules with non-relativistic effective potentials has shown that the energy curves compare well with all-electron ab initio curves [7,8]. Lee et al. [9] have described the method for calculating the j-dependent REPS based on pseudospinors. The 6s1/2,6p1/2,6~31~, 5fsjz, 5f~~~,6d3/~, and 6dsi2 spinors were obtained from a Dirac-Fock solution [IO] of a degeneracyweighted energy average of the (core)6s26p65f36d open-shell configuration of U2+ and the 6g spinors were obtained from the (core)6sz6p66g ionic configurations. The spin-orbit interaction is very large for uranium, but the large components of the 6d and 5f spinors with differentj values are not SubstantiaIly dif0 009-2614/83/0000-0000/S
03.00 0 1983 North-Iiolland
ferent. The positions of the peaks of the outermost maxima of the 5fsj2 and 5f7iz orbitals differ by 0.020 bohr and the 6d312 and 6ds11 differ by 0.092 bohr. The calculation of the electronic structures of the ground states of the actinide metal oxides are more readily done initially with neglect of the spin-orbit interaction using Z-dependent relativistic effective potentials, and subsequently introducing the spin-orbit interaction through configuration mixing. The spin-orbit components, or j dependence, of the REPS is eliminated by taking a weighted average [ 1 I] of thej=Z+ l/2 andj=Z - l/2 potentials: UlAREp = I
21+ 1
The average potential has been designated AREP. Using the ALCHEMY system of codes *, modified to use the AREP, we performed preliminary self-consistent-field (SCF) calculations which determined that the electronic structure of the lowest-energy states is very ionic, and the molecular orbitals are substantially localized. AlI of the lowest-energy states arise from the maximum projection of the angular momentum of the ionic fragments, U3’(f3,41) 02-(IS), on the molecular axis. The * ALCHEMY is a system of programs for the calculation of molecular wavefunctions developed by P-S. Bagus, B. Liu, A.D. McLean and hl. Yoshimine at IBM-San Jose, California.
417
CHEMICAL PHYSICS LETTERS
Volume 99, number 5.6
lowest energy state at the SCF level is the 41. All of the SCF quartet states from S- to 1 are found to be similar in electronic structure with the f orbitals being highly iocalized. Radiative transitions from the 41 state will be assumed to be representative of the complex. An accurate calcu~tiorl itlcludirlg correlation is very difficult because important correlating configurations are of different ionicity or orbital occupancy from the SCF configurations. and differential correlation effects for the ions embedded in the molecule complicate the caiculaticn. A qualitative description of the electronic structure and spectroscopy is still possible because the U3+(f3,41) sfdte is energetically separate from the other atomic ion states. The f3 doublets. for esample, are nearly 3 eV higher in enernv. =* The spin-orbit mising of the lowest energ)’ 42-. lIl. aa . 4+. “r. “H ,md 41 states has been studied perturbdtively using the AESOP operator [ 171. The lowest R states are still doxninsted by a sin&e tz function- The mixing coefikient of the ql function in the 52 = 912 ground state. for example, was calculated to be 0.94. Tr.msitions from the dominant 4I component will then provide a Lero-order description of absorption from the ground state. Smdll hlC SCF calculations were done to show thar the SCF elecrronic description was adequate for a qualitative ~lxtderst~l~ding of the ground state. The exited-state calculations were done by restricted valence configuration interxtion (VCI) using several sets of localized molecular orbitais. Since we are only interested in those states which are dipole radiatively coupled to the “11ground state. we will describe in this note the electronic structure of the low-Iying’l, AH and qK SI~IFS. These data will be used to quaIitativeiy describe the lluorescence pumping of cold UO’. These c~tlcul.nions are prrscnted to assist in the planning and interpretation of experiments designed to detect UOi, and IO present a preliminary analysis of the electronic stt ucturc of such heavy-metal oxides.
2.
Description
of the
olculations
double-zeta Slater function atomic basis was energy optimired using the AREP on the I._@+(6s26p66d5f3,5L). Ul+ (6s26p67s6d5f3,61_). and Ul+ (hsZGp67p6d5f3,6hl) states. SCF c&culations on the 3I. 4H, and 6~ molecutar states provided a set of molecular orbitais primarily locshzed on the o?+gen per and pn orbit&, and the uraA
41s
19
Aumt
1983
nium 6s. 6p, fu. 6. fs,f@, da-da, and 7s~ orbitals. In order IO determine the spin-orbit coupling among the lowest energy 4X-, 411,4A. 4& 4r, 4H, and 4I states that arise from all f3 couplings, it was necessary to calculate these states with a common orthogonal set. Using the SCF molecular orbitals from the 41 and 4H states. configuration interaction calculations were carried out using a base set of configurations for each state which arise from three-fold occupancy of the fu . fn, f6. or fQ orbitais and adding ail configurations arising from a single excitation from all valence orbitals in the base configurations into the virtual space. The spin-orbit interaction was calculated using the AESOP operator_ The energies of these fz coupled states are given in table I at one distance (3.625 au) relative to the energy of the unperturbed 41 state. The lowest-energy a states are still dominated by one A state. For example. the !2 = Q/r! ground state is represented by 419,z =0.9441-O_334
I-l -0.10~r+0.02%$
and the 4117,2 first excited state is given by =
4H7,2
0.83 “H - 0.48 4r - 0.25 4@ + O-OS 4A11.
The energy splitting of the 41 through 4C-state~ is ~0.3 eV, but after considering the spin-orbit coupling, the complex of a states is spread over 1 eV_ Since spin-orbit coupling to states outside the quartet f3 groups was neglected, only the description of the lowest-energy states has any validity_ Table 1 Ekcrronic
R
states at R = 3625 au
SL
E (cnt-t)
912
-4661
l/2
2074
712
-3342
912
2176
512
-2766
311
2553
3fl
-2567
512
2777
II/Z
-1098
712
2858
112
-1365
Is/L?
4128
912
-1062
1312
5027
712
-616
l/2
5117
3/2 5/z
-43s 136
1l/2
5799
912
5831
798
712
5991
107s
SlZ
6285
1627
313
6286
13/2
117 II/Z
$2
E (cm-‘)
CHEMICAL PHYSICS LETTERS
Volume 99, number 5.6
A Morse fit to the 4I SCF curve yields an equilibrium internuclear distance of 3.46 bohr and a vibrational constant of 949 cm-l for U160+. The 4Ig,2 groundstate energy curve is found to have the same R, and a vibrational constant that is only 10 cm-l smaller. A small multi-configuration SCF (MC SCF) calculation for the 41 state that includes the dominant back transfer correlation yields an R, of 3.48 bohr and an o, of 935 cm-l _Assuming the spin- orbit correction to the 41 CI function calculated above applies to the MC SCF result, the vibrational constant for the spin-orbit perturbed MC SCF energy curve is 935 cm-l _ A restricted valence confgnration interaction was performed on the 41, 4H, and 4K states to provide an estimate of the absorption spectrum. The U6s, U6p, and 02s orbitals were retained fully occupied and the f+r, dn, and d6 orbitals were obtained in the 6K SCF solution. This calculation does not allow for orbital relaxation, so the energy curves are not optimal. The R, calculated for the 4I state is -3.6 au in this calculation. This value is ~0.1 au larger than that obtained in the MC SCF calculation and is attributed to the use of orbitals that are intended to describe both the ground and excited states and are not optimal for either. The excitation wavelengths in the visible region from the 41 ground state are shown in fig. l_ All the curves are shifted so that the 4I R, agrees with the value calculated for the MC SCF curve while retaining their reAbsorption
s 1
Spectra
of
UO+
\
1
3.5
Table 2 Transition moments from the X41 state to the excited I. H, and K states (in e bohr) Ground state 1
41 4H
0.028
4K
0.30
lative positions.
Excited state 2
Excited state
0.31
0.092
0.31
0.61
3
The VCI total correlation
energy near states and results from two types of configuration interactionThe first is the double excitation between the slightly bonding (aU7s + 02p)4a valence orbital, which is doubly occupied in the SCF wavefunction and the slightly anti-bonding (U7s - cuO2p)50 correlating orbital (CY< 1). The second type of correlation mixing results from backbonding from the (02p)Zx valence orbital into n correlating orbitals. The dominant correlating orbital is primarily U6dn in character for 4I and a mixture of U5 fir and U6ds for 4H. The same correlating configurations were included in the MC SCF calculation of the 41 ground state. Transition moments from the ground 41 state to excited 4I states and all the 4H and 4K states are given in table 2 for R = 3.625 bohr. The four strongest transitions which range from 0.75 D to over 1 D are all atomic f to d transitions. These electronic transitions range from the far red around 750 cm to the green at 455 nm. The electronic transition between the ground “1 and 4H states has a relatively weak transition moment of 0.07 D.
R, is ~1 eV for both the 41 and 4H ground
341
305
nn
34H
455
run
3. Discussion The ground-state electronic structure and spectroscopic constants are based on SCF and MC SCF calculations using the AREP with inclusion of the spin-orbit coupling as a perturbation. The MC SCF calculation shows little change in the orbitals from the SCF results with only a modest shift in the dipole moment (==0.2 au) as a result of the 71back-bonding. However, at least two major correlation effects have been neglected because of the inability to handle the calculation at this time. The differential atomic-like correlation between states of different ionic&y and d or f occupancy and
14K
625
nm
2k
655
nm
z41
755
Inn
141 *30
19 August 1983
45
5.0
R (hk) Fig. 1. Energy curves calculated at the valence configration interaction level with a common molecular orbital basis. The vertical transition wavelengths from the 1 41 state are shown on the right.
419
Volume 99, number 5.6
CHEMKAL
PHYSICS LETTERS
charge transfer plus polarization configurations must be considered at some future date. As a result it is impossible to gauge the XCUmCy of the calculations without recourse to comparison with experimentAn estimate of the ground-state vibrational frequency can be obtained by comparing the spectroscopic constants between the SCF curves for the 41 state of UO* and the s 1 state of UO. The VCI curve is not sufficiently reliable because the correlation is not optimized as a function of the distance. The best Morse fits to the SCF curves yield an equilibrium internuclear distance of 3-46 boht and a vibrational constant of 949 cm-l for U160+ compared to 3.56 bohr and S63 cm-l for U160_ A band at WZO cm-l has been assigned to U160 in the Ar-matrix-isolated spectrum [S], but this value may be appreciably red-shifted from the gasphase value. For the Kr matrix the 810 cm-1 band is split and red-shifted to SI9 and 815 ~m-~. These shifts are smaller tflan analogous shifts observed in the lithium halides [ 13-151. Linevsky [ 131 has shown that the dominant interaction causing the shift is the dipofeinduced-dipole coupling of nearest neighbors with the difference in the square of the dipole moments in the u = 0 and I let& determining the magnitude of tfie shift. Both UO and the alkali halides have large dipole moment derivatives which we find are of comparable magnitudes. But the calculated value of the anhamionic constant for UO is ~2 cm-l or about half the value for LiCl [ 16]_ The variation of the dipote moment as a functiori of rhe vibrdtionaf state in UO is then much less than that in the alkali halides. However. it must be recognized that the w,*, is obtained from a Morse fit to an energy curve that is not represented well by a hlorse curve. Tilt UO MC SCF calculations yield an R, of 357 bohr ,md an o, of ==S45 cm-l or =3% larger than the nlatris-isolatiorl-obsc~ed frequency_ The spin -orbit coupling will be more complicated in UO than UOc hut the additional states that mix would tend to lower the frequency. We thus feel that the accuracy is \\ithin the 3% range for the UOf oe of 925 cm_1 determined from the spin-orbit perturbed hlC SCF energy curve. The vibrational infrared transition for the 41,,, state is very strong with an oscillator strength of ~5 X io-s for the IJ = 0 to u = 1 transition. This compares with an electronic oscillator strength of %!.2 X loss for the “1 9/2--Q infrared transition. The vibrational and electronic infrared transitions will interleave. The pres-
19 Argnust 1983
ent calculation predicts, for example, the lowest energy transition to be a vibrational transition at =933 cm-1 followed by an electronic transition at ~131.5 cm-l. The visible electronic transitions will be split by the spin-orbit interaction into a range over 1 eV wide roughly centered around the transitions given in fig. 1, The spin-orbit interaction for the excited states is too complicated to be treated by the present methods, but the prediction of strong radiative transitions in the visible will not be affected. The quartet states that couple to the lowest 42, 4~Y 4A, 4#, 4E’, and 4H states are also predominantly fzd systems and have the same transition moment behavior as the 4H, 41, and 4K excited states. Calculations on the sextet states indicate a dominant configuration with ionicity U2+01- that will not couple strongly to the radiatively importmt quartets with ionicity U3*02-. The f3 doublets are in this energy region but again the spin-orbit coupling is weak because the f and d orbitaIs, though polarized, do retain considerable atomic character. Strong radiative transitions are expected in the red part of the visible. The fluorescence will pump the excited vibrational levels of the lower complex of states (which have similar vibrational structure) because the excited states are shifted in frequency and R,. Under low-pressure excitation conditions the strong visible and IR transitions at =925 cm-l would be expected. Detailed modeling is not possible because of the true complexity of this system.
Acknowledgement Research supported in part by the Air Force Office of Scientific Research under Contract No. AFOSR ISSA-St-00017.
References [I] W.L.
Fiite and P- Irving, 3. Chem, Phys. 56 (1977) 4227. [2] W-L. Fite, H.H. Lo and P. Irving, 3. Chem. Phys. 60 (1974) 1136. [3] D.H.W. Carstens, DM_ Cruen and J.F. Kozlowski, High Temp. Sci. 4 (1972) 436. [4] S.D. Gabetick, G.T. Reedy and h1.G. Chasanov, Chem. Phys. Letters 19 (1973) 90; 3. Chem. Phys. 58 (1973) 4468.
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CHEMICAL PHYSICS LETTERS
[S] S. Abramowitz and N. Aquista, J- Res. NBS 78A (1974) 421. 161 D.W. Green, S.D. Gab&&k and G-T_ Reedy, J. Chem. Phys. 64 (1976) 1697. [7] PA Christiansen.YS. Lee and KS. Pitzer, 3. Chem. Phys. 71(1979) 444s. 18J W-I. Stevens and M. Krauss, Appl. Phys. Letters 41(1982) 301. 19) Y.S. Lee, WC. Ermler and KS. Pitter, J. Chem. Phys. 67 (1977) 5861. [ 101 J_P_Desclaur, Computer Phys. Commun. 9 (19753 31.
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[ 1 I] WC. Ermler, Y.S. Lee, P-A. Christiansenand KS. Pitzer, Chem. Phys. Letters Sl(1981) 70. [ 121 W3. Stevens and M. Krauss.Chem. Phys. Letters 86 (1982) 320; J. Cbem. Phys. 76 (1982) 3834. 1131 MJ. Linevsky, J. Chem. Phys. 34 (1961) 587: 38 (1963) 658. 1141 S. S&lick and 0. Schnepp. J- C&em. Phys. 41(1964) 463_ {IS] K.P. Huber and G. Heaberg, Molecular spectra and molecular structure. Constants of diatomic molecules (Van Nostrand, Princeton, 1979). [ 161 R.L. Matcha, J. Chem. Phys. 47 (1967) 4595.