Structures and Properties of the Products of the Reaction of

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Structures and Properties of the Products of the Reaction of Lanthanide Atoms with HO: Dominance of the +II Oxidation State 2

Tanya C. Mikulas, Mingyang Chen, Zongtang Fang, Kirk A. Peterson, Lester Andrews, and David A Dixon J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b11215 • Publication Date (Web): 07 Jan 2016 Downloaded from http://pubs.acs.org on January 12, 2016

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The Journal of Physical Chemistry

Structures and Properties of the Products of the Reaction of Lanthanide Atoms with H 2 O: Dominance of the +II Oxidation State Tanya C. Mikulas,a Mingyang Chen,a,d Zongtang Fang,a Kirk A. Peterson,b Lester Andrews,c and David A. Dixon,a,* a

Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, Alabama

35487-0336, USA b

Department of Chemistry, Washington State University, Pullman WA 99164-4630 USA

c

Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319 USA

d

National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge,

Tennessee, 37831, USA

1 ACS Paragon Plus Environment


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Abstract The reactions of lanthanides with H 2 O have been studied using density functional theory with the B3LYP functional. H 2 O forms an initial Lewis acid-base complex with the lanthanides exothermically with interaction energies from -2 to-20 kcal/mol. For most of the Ln, formation of HLnOH is more exothermic than H 2 LnO, HLnO + H and LnOH + H. The reactions to produce HLnOH are exothermic from -25 to -75 kcal/mol. The formation of LnO+H 2 for La and Ce is slightly more exothermic than formation of HLnOH and is less or equal exothermic for the rest of the lanthanides. The Ln in HLnOH and LnOH are in the formal +II and +I oxidation states, respectively. The Ln in H 2 LnO is mostly in the +III formal oxidation state with either LnO-/Ln-H- or Ln-(H 2 )-/Ln=O2- bonding interactions. A few of the H 2 LnO have the Ln in the +IV or mixed +III/+IV formal oxidation states with Ln=O2-/Ln-H- bonding interactions. The Ln in HLnO are generally in the +III oxidation state with the exception of Yb in the +II state. The orbital populations calculated within the Natural Bond Orbital (NBO) analysis are consistent with the oxidation states and reaction energies. The more exothermic reactions to produce HLnOH are always associated with more backbonding from the O(H) and H characterized by more population in the 6s and 5d in Ln and the formation of a stronger Ln-O(H) bond. Overall, the calculations are consistent with the experiments in terms of reaction energies and vibrational frequencies.

Keywords: Lanthanides; Density Functional Theory; Reaction Energies; Oxidation States; Vibrational Frequencies


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Introduction There is significant interest in studying small molecules containing lanthanide (Ln) atoms, which can be generated by the reaction of the metal with small reagents to better understand the role of lanthanide 6s, 6p, 5d and 4f electrons in bonds to the Ln as well as the oxidation state of the Ln. Although the 4f electrons do not typically contribute to the bonding due to the smaller size of the orbital and closer penetration to the nucleus, the filling of the 4f orbitals across the series causes characteristic trends in properties of lanthanides and the products of their reactions. 1,2 For example, the bond distances to the Ln usually undergo the well-known lanthanide contraction. We have previously used a combination of experimental matrix isolation infrared spectroscopy and electronic structure calculations to study the reactions of the lanthanides with CH 3 F, 3 CH 2 F 2 , 4 CHF 3, 5 CH 3 OH, 6 and OF 2 . 7 Additional studies for matrix isolated products of the reactions of lanthanides with O 2 ,8,9 H 2 , 10,11,12 N 2 ,13,14 NO, 15 CO,16,17,18 CO 2 ,19 and N 2 O 20,21 have been reported, as well as with H 2 O. 22,23

Furthermore, there is

substantial interest in the formation of novel oxidation states of the lanthanides, notably through the work of Evans and co-workers who have found complexes of Ln in the +II formal oxidation state in contrast to the usual +III oxidation state. 24,25,26 In our recent study of the reactions of OF 2 7 with Ln, OLnF and OLnF 2 were observed as the products. The bonding in the products was predicted to be highly ionic and largely determined by the oxidation state of the lanthanide. We also found that the correlation of the calculated Ln-O stretching frequency with the experimental value was a good measure of the quality of the electronic structure calculation and an important factor for assigning the formal oxidation state and the spin configuration on the Ln. For example, we showed the formation of a +IV oxidation state for Ce and a mixed III/IV oxidation state for Pr and Tb for the OLnF 2



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reaction products. The remaining OLnF 2 have the Ln in the +III oxidation state and the OLnF have the +III state as well for obvious reasons. This means that the O is O- for the +III Ln oxidation state in OLnF 2 . As a continuation of our studies of the bonding in these lanthanide compounds, we have now studied the potential products generated from the reaction of Ln with H 2 O and contrast these with the reaction of Ln with OF 2 . There are a number of potential differences to address as the O-F bond dissociation energy (BDE) in OF 2 is only 38 kcal/mol 27 in contrast to the OH BDE in H 2 O of 118 kcal/mol. 28 In addition, the electron affinity of H (0.75 eV) 29 is much less than that of F (3.40 eV) 30 so the formation of the hydride is less favorable than that of the fluoride.31 How does this affect the potential products and what is the bonding in the products? Xu et al.22,23 studied the reactions of the lanthanides Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb, with H 2 O using Ar matrix isolation infrared spectroscopy in Ar. They performed density functional theory calculations at the B3LYP level using the 6-311++G** basis sets for the H and O atoms and the scalar relativistic Stuttgart pseudopotential with associated basis sets for the lanthanides. These calculations did not include the 4f electrons in the valence electronic structure calculations for Ln = Gd, Tb, and Dy, instead including them in the effective core potential. Computational methods Electronic structure calculations for the products of reactions (1)-(6) given below, including geometry optimizations and predictions of vibrational frequencies, were done at the density functional theory level using the B3LYP hybrid functional 32,33 with the DZVP2 basis set 34 for H and O and the Stuttgart small core relativistic effective core potential (ECP) with its accompanying segmented basis set (ecp28mwb_seg) for the lanthanides 35,36 using Gaussian 09. 37 In a number of cases, calculations were also done with the BP86, PW91, and PBE functionals.


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For the latter two functionals, the frequencies were not in agreement with experimentally assigned values. The B3LYP functional was chosen as it was used in the previous work with the f electrons not included in the valence space in some cases,22,23 it gave reasonable agreement with experimental data except as described below, and because it gave good results for the products of the reaction of Ln + OF 2 .7 Orbital occupancies were determined using NBO6 38,39 for the natural bond orbital (NBO) 40,41,42,43 population analysis. A range of spin states was tested for each Ln and each complex. Results and Discussion Reaction (1): LnO. We first discuss the reaction energies relevant to the production of the potential products. The first reaction we consider is that of dehydrogenation together with oxidation of the Ln to form LnO as shown in reaction (1). This reaction is briefly discussed as Ln + H 2 O → LnO + H 2

(1)

the energetics for the reaction can be calculated from experimental data 44,45 and the experimental frequencies of the LnO are known. There is extensive literature on the electronic structures of the Ln atoms 46 and LnO, 47,48,49,50,51,52,53 which are complex with rich electronic structures. Here we want to use the experimental values to provide an assessment of our current computational results (Table 1). We do not expect exact agreement with experiment as most of the LnO may have substantial multireference character and we also ignore spin-orbit coupling as the present electronic structure calculations are probably not accurate enough for this to influence the conclusions of this work. It is not possible to perform detailed multireference calculations on all of the species in the current work and is not necessary to examine the experimental data and trends in the lanthanides. For most of the Ln except for Eu, Tm, and Yb, reaction (1) is



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Table 1. Experimental and Calculated Properties of LnO. (Frequencies in cm-1, Reaction Enthalpies in kcal/mol, Bond Lengths in Å, and Natural Populations).

LnO product 2

2

2

S /

∆H rxn (1) calc

υ(LnO)

υ(LnO)

r(Ln-O)

r(LnO)

r(Ln-O)

expta

υ(LnO) calc

calc

expt

calc

calc

expt

Ln occupancy

∆H rxn (1)

Ln NPA

LaO

0.75/0.75

-78.8

-74.6

804

800

813

1.833

1.828

1.826

s0.94f0.21d0.81

1.09

CeO

2.00/2.00

-77.9

-72.7

821

821

808

1.794

1.806

1.820

s0.94f1.23d0.82

1.04

4

PrO

3.76/3.75

-48.8

-60.8

830

826

817

1.802

1.797

s0.94f2.27d0.80

1.01

5

NdO

6.01/6.00

-35.9

-51.9

824

822

814

1.799

1.798

1.7991

s0.94f3.24d0.82

1.02

6

PmO

8.78/8.75

-24.8

-44.9b

766

790

c

1.813

1.804

c

s0.87f4.29d0.78

1.06

7

12.06/12.00

-8.7

-20.9

722

703

807

1.853

1.851

s0.64f5.50d0.72

1.14

8

EuO

15.80/15.75

3.4

3.0

702

689

668

1.884

1.884

1.89

s0.23f6.85d0.66

1.24

9

GdO

20.06/20.00

-44.0

-54.8

794

788

813

1.827

1.823

1.81251,52

s0.95f7.04d0.88

1.13

s

1.46 7.27 0.90

1.02

s

0.97 9.03 0.80

1.18

s

0.93 10.22 0.75

1.07

0.94 11.08 0.81

1.13

3

SmO

8

TbO

7

DyO

6

HoO

5

16.32/15.75 12.07/12.00 8.76/8.75

-68.7 -36.4 10.7

-49.8 -30.9 -28.7

841 777 835

842

824

769

829

839

828

1.779 1.834 1.791

1.772 1.834 1.792

f f

f

d

d

ErO

6.00/6.00

-6.5

-28.7

846

838

828

1.826

1.793

s

TmO

3.75/3.75

10.3

-6.7

834

831

832

1.800

1.800

s0.95f12.10d0.77

1.14

0.00/0.00

24.2

23.4

701

693

660

1.874

1.873

1.81

s0.36f13.82d0.46

1.32

0.75/0.75

-44.8

-43.8

845

841

829

1.794

1.791

1.790

s0.97f14d0.83

1.18

4

1

YbO

2

LuO

a

f

d

d

Calculated as the difference in the sum of the reactant and product bond dissociation energies (BDEs) from the heats of formation of H, O, and H 2 O form Ref. 45 at 0 K and the LnO BDEs from Ref. 44. b Estimated value of Pm-O BDE. c Radioactive element. 6 ACS Paragon Plus Environment

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exothermic. The calculated values differ from experiment by 4 to 16 kcal/mol for most of the Ln and we do not expect better agreement than that due to the complexities of getting both the Ln and LnO electronic structures exactly correct. For HoO, the difference is larger and this is due to the complexity of treating the significant number of low-lying electronic states of the later LnO diatomics. The calculated reaction energies decrease as the first half shell fills from LaO (-79 kcal/mol) to SmO (-6 kcal/mol). For Eu, the reaction is slightly endothermic, and our calculated value is consistent with the experimental value of 3 kcal/mol. The second half shell starts with GdO and the predicted reaction energy is quite exothermic consistent with experiment. As the second half shell fills, the reaction exothermicity decreases from GdO to ErO and our values follow the general trend, although with larger differences from experiment than for the first half shell. For TmO, we predict an endothermic reaction energy value of 5 kcal/mol for TmO in contrast to the exothermic experimental value of -7 kcal/mol. The reaction to form YbO is predicted to be endothermic in agreement with experiment and that to form LuO is predicted to be exothermic, again in agreement with experiment. The comparison of the calculated and experimental frequencies also provides insights into the quality of the calculations. For the early lanthanides up through Nd, the experimental and calculated Ln-O stretching frequencies are ~800-830 cm-1, and the calculations are in good agreement with experiment. For SmO, our calculated stretching frequency for the slightly higher energy (~ 10 kcal/mol) quintet SmO is 807 cm-1 in agreement with the experimental value of 808 cm-1 as opposed to the more stable septet with a value of 720 cm-1. For 5SmO, the Sm2+ has the approximate 4f46s2 electron configuration, as compared to the 4f6 (mixed with 4f56s1) Sm2+ electron configuration for 7SmO. From the NBO analysis, 7SmO has a lower Ln 6s population than other LnO except for EuO and YbO, which most likely leads to the longer bond distance



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and lower vibrational frequency. This suggests that the trend in the orbitals is changing at Sm. For EuO, there is a significant decrease in the Ln-O frequency which correlates with a decrease in the experimentally known BDE for this molecule. This decrease in frequency and bond energy is due to the stability of the filled half shell electronic configurations of f7 for this metal. The LnO from Gd to Tm all have stretches from experiment above 800 cm-1 and the calculated values are consistent with this. The frequency drops to about 700 cm-1 again for the closed shell YbO which has an ~ f14 occupancy. The lower frequencies for EuO and YbO are due to the 6s empty orbital on Ln2+, just as described for SmO. The stretch for LuO is again greater than 800 cm-1. Other calculated DFT values for the frequencies are consistent with our results. We can also compare our calculated values for some of the LnO with those reported by Cao et al. 54 at the multi-reference configuration interaction (MRCI) level who obtain 814 cm-1 for 2LaO, 734 cm-1 for 8EuO, 884 cm-1 for 9GdO, 736 cm-1 for 1YbO, and 857 cm-1 for 2LuO. Our DFT values are all closer to experiment than the MRCI values, with the MRCI values being too large. The calculated Ln-O bond distances are near 1.8 Å for the entire series except for EuO and YbO, which have longer bond lengths of ~1.9 Å, consistent with the differences in the vibrational frequencies. Experimental bond distances are available for LaO, PrO, EuO, GdO, and LuO and our calculations are within 0.015 Å of these values. For YbO, we predict a bond distance of 1.87 Å as compared to the experimental value of 1.81 Å; the latter distance is not consistent with the experimental vibrational frequency. The calculations by Wu et al. also predict a bond length of 1.87 Å for YbO. We assign the formal oxidation state of the O in LnO to be -2 leading to a formal +2 oxidation state for the lanthanides. The actual O populations are closer to s2p5 than to s2p6 showing substantial backbonding to the Ln. The spin densities show that most of the spin is on


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the Ln, consistent with the assignment of a -2 formal oxidation state to O. Up to Ln = Dy, there is some spin polarization with up to 0.20 e of β-spin on the O, with the largest amounts on Sm and Eu. For the latter part of the period past Dy, there is some spin delocalization of up to 0.1 αspin on the O. On the basis of the atomic ions, 55 we would expect the 6s electrons on the Ln to be the ones lost on oxidation to form the +II state. However, as shown in Table 1, the orbital occupancies of most of the LnO have a 6s14fx-15d1 configuration where the d1 is mostly spin paired with modest spin polarization and is occupied due to backbonding from the O. The 6s is singly occupied with very little spin polarization. There is a small amount of spin polarization on the 4f in some cases. The Ln have an NBO natural population analysis (NPA) charge just over +1 due predominantly to backbonding into the 5d. The exceptions are 1YbO with ~ 4f14 occupancy with the backbonding split between the s and d. In this case, there is higher positive charge on the Ln and a longer Ln-O bond. The other exception is EuO which has an approximately 4f7 configuration with less backbonding to the 5d and very little on the 6s. Again, the atom attains the f7 configuration leading to more positive charge on the Ln and a longer bond length. Reaction (2): HLnOH. For all of the lanthanide metals, the HLnOH configuration (Reaction 2) is predicted to be the ground state product for the Ln+H 2 O reaction (1) except for La and Ce Ln + H 2 O → HLnOH

(2)

(Figure 1 and Supporting Information). For these two Ln, the preferred reaction is (1), the dissociative formation of LnO and H 2 . There are a number of possible spin states for the Ln in the products of reaction (2), which depend on the oxidation state of the Ln(II) given that the OH is in the -1 oxidation state, and H is in the -1 oxidation state. As discussed in our previous work on Ln reactions, one has to be careful with spin polarization which can sometimes give a lower



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100 LnO+H2 (1) HLnOH (2)

80

H2LnO (3) LnOH+H (4)

60

HLnO+H (5) Ln(OH2) (6)

40 20 0 -20 -40 -60 -80 -100 La

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Figure 1. B3LYP Reaction Energies for Reactions (1) to (6) in kcal/mol at 0 K. (Only the Ln Containing Reaction Products Listed.) On the singlet surface, dissociation to 1OYb+H 2 is much lower in energy than the bound triplet complex 3H 2 YbO, only 24.6 kcal/mol higher in energy than Yb + H 2 O .

energy state for lower spin due to spin polarization. In order to better assign the spin states, we resorted to comparison of the frequencies to experiment.22,23 For example, 4HHoOH is predicted to be lower in energy than 6HHoOH by ~5 kcal/mol. However, the Ho-OH stretch frequency for 4HHoOH is predicted to be 75 cm-1 below experiment and for 6HHoOH, the frequency is 10 ACS Paragon Plus Environment

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predicted to be only 12 cm-1 above experiment. The calculated frequency is a harmonic value while the experimental values also have anharmonic contributions and should be below the harmonic value. Thus we prefer the sextet over the quartet. A second example is found for Er, with 3HErOH predicted to be ~7 kcal/mol lower than 5HErOH, but, again the Er-O frequency is in better agreement with experiment for the latter higher spin state. In both cases, the high spin Ln-O frequencies are in better agreement with experiment than the low spin (spin polarized) result. The calculated reaction enthalpies at 0 K range from −23 kcal/mol for Yb and Er to −75 kcal/mol for La and Ce (Figure 1 and Supporting Information) for the production of HLnOH from reaction (2). The Ln-O bond lengths range from 2.12 Å for Sm to 1.95 Å for Lu and the LnH bond lengths range from 1.94 Å for Eu to 2.15 Å for Lu (Supporting Information). Thus, the Ln-OH and Ln-H bond distances do not follow the lanthanide contraction. For the HLnOH structures, there is very little difference between the Ln-OH and Ln-H bond lengths for a given molecule; at most they vary by 0.035 Å (Ln = Dy). This result is somewhat surprising given that both are assigned a formal oxidation state of -1. The OH bond distances (see the Supporting Information) are essentially all 0.96 Å. All of the LnOH bond angles are between 160° and 170° except for HYbOH which has an almost linear bond angle. The H-Ln-O(H) angles increase by about 7° from 109° to 116° for Ln = La to Ln = Eu. There is little change in the Ln-H and Ln-OH vibrations of HLnOH (Table 2) as the first half shell fills from 4f4 to 4f7 where we assign formal oxidation states of +2 to the Ln and -1 each to the H and OH. The variation in the frequencies correlates with the experimental observations for Ln = Nd, Sm, and Eu. The Ln-H vibrations for Nd, Sm, and Eu fall in a narrow range of 1139-1157 cm-1; a similar narrow range of 1225 to 1229 cm-1 is predicted. The difference of 75



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Table 2. Calculated Properties of HLnOH at the B3LYP Level. (Frequencies in cm-1, Energies in kcal/mol, Ln NBO Population Analysis). Ln La Ce Pr Nd Pm Sm Eu Gd

Tb Dy Ho Er Tm Yb Lu a

S2/

sym 2

0.75/0.75 2.00/2.00 3.76/3.75 6.01/6.00 8.76/8.75 12.01/ 12.00 15.76/ 15.75 20.06/ 20.00

A' 3 A" 4 A 5 A' 6 A" 7 A"

15.84/ 15.75 12.06/ 12.00 8.75/8.75 6.00/6.00 0.82/0.75 0 0.75/0.75

8

CASPT2.

b

υ(Ln – OH) calc 583.9 589.9 545.7 520.1 520.0 519.1

υ(Ln-OH) 22,23

expt

495.5

495.4

υ(Ln-H) calc 1344.6 1338.7 1282.6 1225.3 1237.5 1218.9

υ(Ln –H)

υ(O-H)

υ(O-H)

expt

calc 3910.7 3911.0 3915.2 3909.8 3924.5

expt

22,23

1139.0

1154.7

Ln-H BDE

Ln Occ

3925.7

62.7 61.2 57.4 52.3 55.3 51.3

6s0.854f0.095d0.82 6s0.884f1.135d0.78 6s0.694f2.545d0.48 6s0.494f3.775d0.39 6s0.474f4.805d0.36 6s0.354f5.955d0.29

Ln NPA 1.25 1.21 1.31 1.38 1.39 1.43

3924.0

50.1

6s0.314f6.985d0.27

1.46

3751.2

49.0

6s1.014f7.015d0.57

1.38

3755.8

49.9

6s1.054f7.965d0.39

1.50

48.0

6s1.044f9.015d0.37

1.52

50.8 50.3 52.3 53.1 47.0

6s0.964f10.035d0.64 6s0.984f11.035d0.61 6s0.444f12.885d0.22 6s0.364f13.965d0.18 6s1.044f14.005d0.56

1.32 1.33 1.45 1.50 1.34

22,23

8

A"

9

A" A"

7

A"

6

A" 5 A" 2 A" 1 A' 2 A'

523.0 565.8 610.5a 612.9b 543.8 606.7a 555.5 613.3a 623.1 628.8 529.5 539.3 639.9

494.4 602.4

609.3 619.3 611.6 623.4 514.0 511.8 629.0

1229.4 1302.2 1490.3a 1450.4b 1239.2 1480.7a 1286.8 1462.7a 1420.4 1431.8 1233.8 1270.7 1473.0

1157.0 1377.4

1388.0 1390.7 1401.3 1409.9 1237.1 1238.6 1423.1

3918.6 3893.8a 3923.6b 3924.5 3895.2a 3927.6 3903.1a 3950.4 3946.9 3943.6 3948.2 3963.1

CCSD(T).


3762.7 3764.9 3756.0

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to 100 cm-1 between the calculated and experimental values is due in part to the fact that anharmonic corrections due to the light mass of H are not included in the calculated values. We were able to perform some anharmonic calculations to verify this hypothesis. For HLaOH, and HYbOH, the anharmonic corrections are 67 and 44 cm-1, respectively. In addition, there are errors due to the use of density functional theory with the B3LYP functional to calculate the harmonic frequencies. The Ln-OH vibrations for the same metals are calculated to be in a narrow range of 520-523 cm-1, in agreement with a narrow range of 494-495 cm-1 from experiment. Again, the calculated harmonic frequencies are larger than the experimental values, which include anharmonicity. The experimental assignments for the Gd-H and Gd-OH stretching vibrations show respective frequency increases of 100 cm-1 and 200 cm-1 respectively, from the filled f-shell configuration for Eu (see Table 2). Our calculations at the B3LYP level predict harmonic values for these stretching vibrations of 566 cm-1 and 1302 cm-1, respectively, which are below the experimental values. The values were recalculated with the BP86 functional and the agreement with experiment did not improve. This difference from experiment is probably due to DFT giving a 4f75d1 configuration whereas the experimental state is probably based on the 4f76s1 state. Previous B3LYP calculations22 gave reasonable agreement with experiment but did not include the 4f electrons in the valence space, instead including them in the effective core potential. In order to investigate this difference further, CCSD(T) 56 and CASPT257,58 calculations were performed. The active space for the CASPT2 calculations included the 7 4f orbitals and the 6s orbital on the Ln. All other orbitals were optimized but constrained to be doubly occupied. In the PT2 part of the CASPT2 and in the CCSD(T) calculations, all electrons of the Ln were correlated through the 5s as well as the 2s and 2p electrons for O and the 1s



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electrons for H. The CASPT2 and CCSD(T) calculations were done with the aug-cc-pVDZ basis set 59 for O and H and the ecp28mwb_ano basis set and ECP for Gd. 60,61 These correlated molecular orbital theory calculations were carried out with MOLPRO. 62 The CCSD(T) values are 613 cm-1 for the Gd-OH stretch and 1450 cm-1 for the Gd-H stretch; the corresponding CASPT2 values are 610 cm-1 and 1490 cm-1. Both sets of Gd-OH and Gd-H stretches are above experiment as they should be. The CASPT2 and CCSD(T) Gd-OH stretch are essentially the same. The CCSD(T) value for the Gd-H stretch is closer to experiment than the CASPT2 value. The molecules HTbOH and HDyOH exhibit similar issues to HGdOH in terms of the DFT frequencies. Again, the CASPT2 results are in better agreement with and larger than experiment as compared to the DFT results. The CASPT2 calculations were done as described above for Gd except that two states in the symmetry of the ground electronic state were stateaveraged to obtain well-defined solutions. From Tb to Er, the NBO analysis of the optimized structures (Table 2) predicts orbital occupancies corresponding to electronic configurations of 6s14fn-1 or (6s5d)14fn-1. Experimental spectra for the series from Tb to Er show the stretching frequencies are 609 to 623 cm-1 for the Ln-OH and 1388 to 1410 cm-1 for Ln-H. The B3LYP stretching frequencies for 6HHoOH and 5HErOH are in the same frequency ranges as the experimental results, ~600 cm-1 for Ln-OH and ~1400 cm-1 for Ln-H. As discussed above, 4HHoOH (6s04f11) is predicted to be more stable energetically by ~5 kcal/mol than 6HHoOH (6s14f10), but the Ho-O stretching frequency predicted for the s0f11 configuration is 536 cm-1, about 70 cm-1 lower than the observed frequency of 612 cm-1. This issue with the quartet state arises due to mixing of the β electrons in the 6s and 4f orbitals. The Ho-O stretching frequency for the (6s5d)14f10 electronic state is predicted to be 623 cm-1, in much better agreement with experiment. A similar situation exists for 3HErOH


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and 5HErOH, with the triplet having a lower energy, but it is the high spin quintet predicted frequencies which correlate with the experimental spectra just as in the Ho case. The predicted Tm-O frequency of 530 cm-1 for 2HTmOH with an electronic state of 6s04f13 agrees with the experimentally observed absorption at 514 cm-1. The isotopic shifts are all consistent with expected shifts with the 16O/18O ratios for the Ln-O(H) bond being ~ 1.05, the 1H/2H for the LnH bond being ~1.41 and the 1H/2H for the O-H bond being ~1.37. The NPA population analysis is given in Table 2 and the Supporting Information. The Ln in HLnOH are in the formal +II oxidation state but the actual charges on the Ln show substantial backbonding. Table 2 shows that the 6s and 5d mix in HLaOH and in HCeOH so that there is approximately a singly occupied (6s5d) orbital on La giving a (6s5d)1 configuration and a (6s5d)14f1 configuration for the Ce. For these 2 elements, reaction (2) is slightly less exothermic than reaction (1). For Pr, reactions (1) and (2) have essentially the same exothermicity and there is one electron in a mixed 6s5d4f orbital and two electrons in the 4f orbitals giving a (6s5d4f)14f2 configuration. For Nd, reaction (2) is slightly more exothermic than reaction (1) and the Nd occupancy is ~ 4f4 with ~0.25 e spin on the 6s and 5d. The amount of unpaired density and total density in the 6s and 5d orbitals decrease from Nd to Eu. Pm, Sm, and Eu have almost pure 4f5, 4f6, and 4f7 configurations. The Gd atom has the 6s14f7 electron configuration with the 6s component having some 5d character as well. In this case, the mixing of the 5d orbital and the corresponding spin polarization is enough to make the calculated frequencies fall below the experiment. For Ln = Tb and Dy, the populations show that the Ln configurations are approximately 6s14f8 and 6s14f9 with only a small amount of spin polarization on the 6s and some 5d population. For Ln = Ho and Er, the spin polarization issues are worse in the 6s and 5d and there is more mixing of the 6s and 5d orbitals; again, the electron configurations are best



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described as (6s5d)14f10 and (6s5d)14f11. Tm and Yb have less backbonding and are almost pure 4f13 and 4f14 configurations, respectively. Lu, as might be expected, has a (6s5d)14f14 configuration. The O atoms are closer to the 2s22p6 formal -2 oxidation state for the OH than for the LnO described above with a slightly smaller 2s population and ~0.4 more electrons in the 2p. The proton on the OH group has a charge of ~+0.5 e. The hydridic hydrogen in the Ln-H bond has an excess population of -0.5 to -0.7 e, consistent with the simplest oxidation state arguments. For the HLnOH, if the sum of the 6s + 5d population on the Ln is < 1, then ν(Ln-OH) is ~ 520 to 540 cm-1; this happens for Ln = Nd, Pm, Sm, Eu, Tm, and Yb. If the sum of the 6s + 5d population on the Ln is > 1.5 (significant d population), then ν(Ln-OH) is larger, ranging from ~ 590 to 640 cm-1; this is found for Ln = La, Ce, Gd, Ho, Er, and Lu. We note that HTbOH and HDyOH fall in the latter case at the CCSD(T) level and that HPrOH represents an intermediate case. Reaction (3): H 2 LnO. The calculated reaction enthalpies at 0 K for the formation of the OLnH 2 product (Reaction 3, Figure 1 and Supporting Information) are exothermic only for La, Ce, Tb, Dy, and Lu. Ln + H 2 O → H 2 LnO

(3)

A simple bond energy analysis provides an explanation of the results (Table 3). For a reaction to be exothermic, the sum of bond energies for the products must be greater than the sum of bond energies of the reactants. Assuming that the Ln-O BDEs in H 2 LnO are comparable to those in the diatomic, for reaction (3) to be exothermic, we can use Hess’ Law to show that the sum of the two calculated Ln-H BDEs must be greater than the difference between 219.3 kcal/mol and the Ln-O BDE for reaction 3 to be exothermic. As an example, consider H 2 YbO, with a known


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value of 44 kcal/mol for the BDE of Yb-H.44 The minimum Yb-H value calculated for this reaction to be exothermic is 63 kcal/mol, so the reaction will be endothermic, as predicted. Using these same values for H 2 O and the Ln-O BDE in conjunction with the ∆H rxn values from Figure 1 for reaction 3, we can estimate the Ln-H BDE (Table 3). When the difference between the calculated Ln-H BDE and the minimum Ln-H BDE is positive, we find an exothermic reaction.

Table 3. Ln-H Diatomic BDE’s Estimated from Reaction (3) in kcal/mol.a Ln-H calc -

Ln

Ln=O BDE

BDE H2O BDE LnO

Ln-H min

Ln-H calc

La

190.7

28.6

14

36.1

22

Ce

188.8

30.5

15

48.3

33

Pr

176.9

42.4

21

27.7

7

Nd

51.3

26

24.5

-1

Pm

168 161±13

58.3

29

21.8

-29

Sm

137

82.3

41

22.8

-18

Eu

113.1

106.3

53

23.6

-29

Gd

170.9

48.4

24

11.6

-13

Tb

165.9

53.4

27

43.5

17

Dy

147.0

72.3

36

42.2

6

Ho

144.8

74.5

37

16.5

-21

Er

144.8

74.5

37

21.2

-16

Tm

122.8

96.5

48

26.4

-22

Yb

92.7±2.4

126.6

63

50.9

-12

Ln-H min

Lu

59.4 30 38.4 9 159.9 The total bond dissociation energy (BDE) of BDE H2O = 219.3 kcal/mol at 298 K which is the sum of the reactant bond energies. a

The early lanthanides through Sm are all planar and have similar occupancies which are best described as (6s5d4f)14fx-1 similar to that for the LnO, indicating some backbonding from 17 ACS Paragon Plus Environment


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the O. The stretching vibrations for the Ln-O and Ln-H are all similar for the early Ln. At Eu, the frequencies all decrease and the bond lengths all increase. The occupancy in the 4f orbitals is increasing and in the 5d orbitals is decreasing, because Eu attains the 4f7 configuration. The Gd attains the more stable 4f7 configuration, so the occupancy increases for both the 6s and 5d orbitals. The changes from Eu to Gd continue for Tb, where the occupancy in the 4f shell is still ~ 4f7, and the 6s and 5d increase to maintain the 4f7. Starting with Tb, the symmetry changes from planar C 2v to non-planar C s and the Ln-H frequencies increase to the 1300 cm-1 range with a corresponding decrease in the Ln-H bond lengths. For these later lanthanides, there is more electron density on the Ln in the 6s, 4f, or 5d orbitals which helps to make the molecule nonplanar. The Ln-O bond lengths decrease as well. At Tb, the occupancy of the 2p orbitals on the O begins to decrease, and the charge on the Ln is more positive. As a consequence, the hydrogens gain negative charge to become more hydridic. As the second half of the 4f shell is filling, the frequencies are all much higher than for the early part of the lanthanide series. As the H-Ln-H angle becomes much smaller, the H atoms become closer together, and the H atoms become more negative. The occupancies on the 2p orbitals of the O slightly decrease suggesting slightly more backbonding into the metal 4f orbitals. Two types of Ln‒H bonds and two types of Ln‒O bonds can be identified in H 2 LnO. The first type of Ln‒H bond is (H 2 )-‒Ln, for which the bond distances range from 2.27 to 2.17 Å and the corresponding υ(Ln‒H) frequencies range from 870 to 990 cm-1 (Table 4 and Supporting Information). The two H’s share a unpaired electron and thus are bonded to Ln effectively as (H 2 )- with a combined net spin density close to 1. The (H 2 )-‒Ln bond is found in H 2 LnO for Ln = La and Pr‒Gd. The second type of Ln‒H bond is H-‒Ln, with the bond distances ranging from 2.03 to 1.96 Å and the υ(Ln‒H) frequencies ranging from 1240 to 1520 cm-1. The H has a formal


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Table 4. B3LYP Properties of H 2 LnO Molecules. Frequencies in cm-1 and Ln NBO Population Analysis. H 2 LnO 2

H 2 LaO

1

H 2 CeO

S2/

υ(Ln-O)

0.77/0.75

722.0

0/0

848.9

υ(Ln-H) asym υ(Ln-H) sym 885.0 1314.4

927.4 1370.0

Ln Natural Charge

Ln occ 6s0.214f0.215d1.00

1.67

6s

0.29

0.84

1.27

1.72

0.25

2.31

0.95

1.56

4f

5d

4

H 2 PrO

3.77/3.75

771.0

890.1

934.9

6s

5

H 2 NdO

6.02/6.00

766.0

936.3

977.5

6s0.254f3.245d1.01

1.56

6

H 2 PmO

8.78/8.75

774.8

968.3

1015.2

6s0.264f4.225d1.02

1.56

7

12.06/12.00

758.9

985.8

1013.8

6s0.274f5.255d0.97

1.55

8

H 2 EuO

15.95/15.75

716.2

953.9

979.0

6s0.294f6.375d0.85

1.54

9

H 2 GdO

20.20/20.00

746.0

871.0

1049.2

6s0.504f6.985d0.94

1.54

8

H 2 TbO

16.32/15.75

836.7

1331.5

1330.4

6s0.854f7.155d1.37

1.60

7

H 2 DyO

12.50/12.00

851.3

1372.1

1371.5

6s0.834f8.235d1.33

1.59

6

H 2 HoO

8.77/8.75

687.6

1239.4

1254.0

6s0.354f10.165d0.73

1.78

5

H 2 ErO

6.01/6.00

528.3

1456.1

1495.8

6s0.474f11.045d0.63

1.84

H 2 TmO

3.75/3.75

665.6

1448.6

1508.9

6s0.464f12.075d0.56

1.89

H 2 SmO

4

3

H 2 YbO

2

H 2 LuO

2.01/2.00 0.76/0.75

394.9 464.8

1363.4 1479.3

1377.7 1519.5

6s

4f

0.42

6s

5d

13.08

4f

0.47

0.67

5d

14

4f 5d

0.68

1.82 1.84

oxidation state of –1 in the H-‒Ln bond type, and there is zero or a small net spin density on the H. The H-‒Ln bond exists in H 2 LnO for Ln = Ce and Tb‒Lu. For Tb, and Dy, and Ho there is a net spin density of ~ 0.5 (β for Tb and Dy and α for Ho) on the two hydrogens, showing that the bonding between Ln and the two hydrogens is a combination of both bond types; the vibrational frequencies suggest they are more like H-‒Ln. Similarly, the bond between Ln and O can be either a Ln‒O- or a Ln=O2- bond. The Ln‒O- bond has an unpaired electron on O, characterized by the net spin density of ~1 on O. In contrast, there is zero or a very low spin density on O in the Ln=O2- bond. The Ln‒O- bond is found in H 2 LnO for Ln = Er to Lu, with r(Ln‒O) in the 19 ACS Paragon Plus Environment


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range of 1.95‒2.08 Å and υ(Ln‒O) in the range of 400‒670 cm-1. The Ln=O2- bond is found in H 2 LnO, Ln = La to Dy, where the r(Ln‒O) range from 1.86 to 1.77 Å and υ(Ln‒O) range from 850 to 690 cm-1. H 2 HoO has a net spin density of 0.6 on O, and the bond between Ho and O is a mix of both bond types. For each type of the Ln-H and Ln-O bonds, the bond lengths follow the lanthanide contraction in general. The formal oxidation state of the Ln can be determined with the identification of the Ln‒ O and Ln‒H bond types in H 2 LnO, as the Ln oxidation state is the negative of the oxidation state sum of the O and the two hydrogens. H 2 LnO for Ln = La and Pr to Gd has the Ln=O2- and Ln‒ (H 2 )- bond types, so the Ln oxidation state is +III. The Ln oxidation state for H 2 LnO, Ln = Er‒ Lu, is also +III, and this is due to the combination of Ln‒O- and Ln‒H- bond types. Ce forms an oxidation state of +IV, with Ln=O2- and Ln‒H- bond types, consistent with the fact that Ce has 4 valence electrons (6s25d14f1). Tb and Dy form the +III/+IV state, with more +IV character. The Tb4+ and Dy4+ have approximate 4f7 and 4f76s1 configurations, respectively, both of which are relatively stable half full shell configurations. The Ce and Tb results are consistent with the electronic structures of F 2 LnO. There is spin density on both the H 2 and O of 6H 2 HoO, and the natural charges on H 2 and O are in between the typical values of the (H 2 -)Ln3+(O2-) and (H) 2 Ln3+(O-), showing both H 2 and O are in the mixed -I/-II oxidation state. Thus the state for 6H 2 HoO obtained at the DFT level is very likely a mixture of (H 2 -)Ho3+(O2-) and (H) 2 Ho3+(O-), leading to the oxidation state of +III for Ho. As described above, reaction (3) is endothermic for all Ln except for Ln = La, Ce, Tb, Dy, and Lu, which can be used to understand our prediction of the Ln oxidation state in H 2 LnO. On the basis of our predictions, the Lnn+ in H 2 LnO has the electron configuration of [Xe], [Xe], [Xe]4f7, [Xe]4f7s1, and [Xe]4f14 for Lnn+ =


Page 21 of 42

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La3+, Ce4+, Tb4+, Dy4+, and Lu3+, respectively. The valence shells are either fully occupied or half occupied in these Ln cations, which leads to the higher stabilities of the compounds. In our previous work with lanthanides and OF 2 , we found the Ln in the OLnF 2 configuration to have formal oxidation state of +III except for Ce(IV) and the mixed III/IV oxidation state for Pr, and Tb. Although H 2 LnO shows basically the same Ln formal oxidation state as OLnF 2 has for each Ln, the electronic configurations of early-Ln H 2 LnO (Ln = La, and Pr to Gd) are different than their OLnF 2 counterparts. H 2 LnO (Ln = La, and Pr to Gd) is more like (H 2 )-Ln3+O2- as compared to the (F-) 2 Ln3+O- configuration for OLnF 2 . The vibrational frequency calculations and the NBO analysis (Table 4) indicate that the two hydrogens are more like (H 2 )- for Ln = La, and Pr to Gd, and are more like (H-) 2 for Ln = Ce, and Tb‒Lu. Thus the H 2 LnO for Ln = Er to Lu have the same basic electronic structure as F 2 LnO with O in the -1 oxidation state. Reaction (4): LnOH. We previously studied the properties of LnOH as part of our study of the potential energy surfaces for the reaction of CH 3 OH with Ln. Except for Ln = La, Ce, and Pr, LnOH formation is favored over HLnO formation, i.e., the +I oxidation state for Ln is favored over higher oxidation states (Figure 1 and Supporting Information). For Ln = La, Ce, Gd, Tb, Dy, and Lu, reaction (4) is exothermic (Figure 1). However, HLaO and HCeO will be generated preferentially over Ln + H 2 O → LnOH + H

(4)

LaOH and CeOH. The Ln-OH bond lengths vary from 1.93 Å for LuOH to 2.11 Å for SmOH. Most of the Ln-OH bond lengths are just larger than 2.0 Å and tend to be slightly shorter than the Ln-OH bond lengths in HLnOH. (Supporting Information) The Ln-OH stretches are in the region of 520 to 600 cm-1 for most of the lanthanides (Table 5) and follow similar patterns to the Ln-OH



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Page 22 of 42

stretch in HLnOH. These bands are predicted to be of moderate intensity in the infrared. The spin densities show that most of the spin is localized on the Ln. These results suggest that the H in HLnOH is not really impacting the Ln-OH interaction. The H-Ln BDEs for HLnOH are given in Table 2 and range from 47 to 62 kcal/mol.

Table 5. Properties of LnOH. Frequencies in cm-1. S2/

ν(Ln-OH)

ν(O-H)

ν(Ln-O-H) bend

Ln occ

Ln NBO charge

LaOH

0

638

3903

310π

6s1.854f0.075d0.38

0.71

CeOH

0.95/0.75

589

3909

294π

6s1.734f1.235d0.34

0.71

5

PrOH

6.00/6.00

539

3911

333π

6s0.954f2.875d0.37

0.81

6

NdOH

8.75/8.75

538

3917

311π

6s0.974f3.965d0.27

0.81

5

PmOH

6.86/6.00

521

3924

304π

6s1.184f4.795d0.22

0.81

3933

221π

3924

326π

3915

254π

LnOH 1 2

8

SmOH 15.76/15.75

9

EuOH 20.01/20.00

8

GdOH 16.08/15.75

532 530 602

6s

0.96

5.98

0.22

0.84

6s

0.96

6.99

0.19

0.85

6s

1.74

7.01

0.31

0.77

1.58

8.01

0.23

0.81

TbOH 12.00/12.00

575

3921

326π

6s

DyOH

7

4f 4f 4f 4f

5d 5d 5d 5d

6

9.29/8.75

578

3923

312π

6s1.624f9.015d0.23

0.81

5

HoOH

6.01/6.00

535

3949

287

6s1.264f10.705d0.20

0.82

4

ErOH

3.76/3.75

596

3956

195

6s1.874f11.035d0.32

0.75

TmOH

2.00/2.00

537

3951

301π

6s1.084f12.875d0.16

0.86

0.75/0.75

537

3948

330π

6s0.994f13.975d0.14

0.88

0

657

3950

281π

6s1.894f14.005d0.32

0.77

3

2

YbOH

1

LuOH

Reaction (5): HLnO. For La, Ce, and Tb, reaction (5) is also exothermic. Ln + H 2 O → HLnO + H

(5)

The endothermic reaction enthalpies at 0 K for the formation of the HLnO molecules (Reaction 5) range from 1 to 80 kcal/mol. It is interesting that there is spectroscopic evidence for the HLnO


Page 23 of 42

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molecules for Ln = Nd, Gd, Tb, Dy, Ho, Er, and Tm.22,23 Again, using the assumption that the Ln-O bond is like the LnO diatomic, we can make an estimate to see if the product will be exothermic using Hess’ Law. For the reaction to be exothermic, BDE Ln-H + BDE Ln-O (Table 3) must be greater than 161 kcal/mol. The Ln-O BDEs for Ln = La, Ce, Pr, Gd, and Tb are near to or exceed this value. It is important to recall that laser ablation can impart kinetic and electronic energy to the ablated metal atoms so that endothermic reactions can be observed experimentally. The overall trend in bond lengths for the HLnO with increasing atomic number for the Ln is decreasing in general, consistent with lanthanide contraction. The Ln-O and Ln-H bonds increase or decrease together from one metal to the next through the lanthanide series (Supporting Information). The Ln-H bond lengths range from 2.14 Å for Ce to 1.94 Å for Lu, and the Ln-O bond lengths for O-Ln-H are calculated to be within a few hundredths of an Å of 1.8 Å. The calculated frequencies follow this trend too, with decreases in frequency for Ln-O and Ln-H correlating with increases in bond length, and frequency increases with bond length contractions. The first half-filled 4f shell occurs for Gd, and the Tb-O bond is shorter than the Gd-O bond by 0.02 Å. For 7HTbO, which has a lower reaction energy than 9HTbO by ~7 kcal, the predicted M-H bond length of 2.02 Å is comparable to the value of 2.03 Å for Gd. All bond angles are between 108° to 118° except for OYbH which has a calculated bond angle of 154°. The Ln-H frequencies range from 1245 cm-1 for Gd to 1482 cm-1 for Lu. The same occupancy trend (Table 6) in the middle of the series for Eu to Tb is predicted as discussed above, with the occupancy on the metal attaining the ~ 4f7 configuration. At Eu, the Ln-O vibration has a large decrease to 704 cm-1 as compared to Sm which is 791 cm-1. The Gd-O stretch increases to 768 cm-1. The predicted Ln-H stretch is decreased from Eu by about 80 cm-1, and the population on the H decreases and the O population increases. For Tb the H and O occupancies both increase,



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and the occupancy on Tb increases more in the 6s and 5d than the 4f, again to maintain the 4f7 configuration. Our frequency calculations, which include all f electrons in the electronic structure calculations for Gd

Table 6. Calculated B3LYP Properties for HLnO. Frequencies in cm-1.

HLnO

S2/

ν(Ln-O) ν(Ln-O) exp/calc ν(Ln-H) ,

1

HLaO HCeO 3 HPrO

0 0.75/0.75 2.01/2.00

782.5 793.1 805.1

4

3.78/3.75

809.2

2

HNdO

5

HPmO 6.02/6.00 HSmO 8.81/8.75 7 HEuO 12.21/12.00

803.4 790.9 703.5

8

768.1

6

HGdO 16.05/15.75

7

HTbO

6

HDyO

5

HHoO

4

12.77/12.00 9.29/8.75 6.01/6.00

835.7 737.4 820.5

1275.2 1308.2 1316.0 777.5/ 821.0

1302.1

782.7/ 785.4 793.4/ 846.6 798.2/ 790.6 800.2/ 836.8 801.3/ 837.4 806.4/ 820.3

1244.9 1337.5 1243.2 1362.7

3.75/3.75

831.7

HTmO

2.00/2.00

814.2

0.76/0.75

683.7

1334.1

0

839.9

1481.9

2

HYbO

1

HLuO

1220.2/ 1264.6

1327.0 1325.5 1322.8

HErO

3

ν(Ln-H) exp/calc,

1375.8 1380.6

1300.6/ 1346.4 1310.1/ 1349.4 1316.1/ 1370.1 1337.6/ 1392.1 1363.2/ 1402.7 1376.3/ 1363.3

Ln occ

Ln Charge

6s0.214f0.225d0.97 6s0.224f1.245d0.98 6s0.244f2.285d0.95 6s0.264f3.345d0.88

1.68 1.62 1.59 1.57

6s0.254f4.225d0.97 6s0.264f5.285d0.90 6s0.294f6.395d0.78 6s0.594f7.015d0.90

1.60 1.59 1.58 1.50

6s0.844f7.415d1.04

1.64

6s1.004f8.265d1.14

1.56

6s0.334f 10.215d0.

1.64

83

6s0.334f11.075d0.9

1.68

3

6s0.334f12.165d0.8

1.69

2

6s0.254f13.455d0.5

1.77

2

6s0.404f145d0.94

1.67

and Dy, are significantly lower than the experimental values.22,23 The prior electronic structure calculations22,23 for HGdO, HTbO, and HDyO include some of the valence f electrons in the effective core potential. For HGdO and HDyO, the prior results are in better agreement with experiment than our lower values for the frequencies; however, our frequency calculations for 24 ACS Paragon Plus Environment

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HTbO are in better agreement with experiment. From Ho through the rest of the series, as well as for Nd which also has an experimental value, our calculations are in good agreement with experiment. The spin densities for HLnO (Supporting Information) show that most of the spin is localized on the Ln. Thus it is appropriate to assign the Ln to the +III oxidation state. There is excess β spin on the O and H for the Ln from Ce to Tb. Up to Eu, most of the excess β spin is on the O. For the Ln before Eu, the excess β spin is < 0.15 e. For HEuO, there is 0.34 e of β spin on the O, which suggests a +II/+III oxidation state for Eu. For HGdO, there is almost 0.5 e of β spin on the O and H, with the H having more β spin density than the O at the B3LYP/ecp28mwb_seg level, leading to a +II/+III oxidation state. A B3LYP calculation with the larger ecp28mwb_ano basis sets on Gd, however, predicted a +III oxidation state for Gd in 8HGdO, with basically zero spin densities on O and H. The calculated vibrational frequencies with the ecp28mwb_ano basis set are in excellent agreement with experiment. For Ln heavier than Tb, there is excess α spin on the O and for HYbO, there is more than 0.4 e of α spin on the O and H. Similar to the Eu case, the excess spin densities on O and H suggest a +II/+III oxidation state for HGdO and HYbO. For HEuO and HYbO, the calculated ν(Ln-O) is ~100 cm-1 lower than those for ν(Ln+III-O), showing that the oxidation state of Eu and Yb have significant amounts of the +II state. Reaction (6): Ln(OH 2 ) All of the Ln can form a Ln-H 2 O complex (reaction (6)), Ln + H 2 O → Ln(OH 2 )

(6)

with complexation energies ranging from -2 kcal/mol for Gd(H 2 O) to -20 kcal/mol for Ce(H 2 O) (Table 7). In order to test the ability of the B3LYP functional to predict the binding energies correctly because of the possible role of missing weak dispersion forces, we also calculated the binding energies at the B3LYP-D3 63,64 and ωB97xD65 functionals. The results (Supporting



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Information) show that for the cases where the correct atomic states are calculated, there is good agreement within about 2 kcal/mol for the binding energies for the three functionals except for Gd where the B3LYP complex is not bound enough. For Gd, the binding energy is -8.8 kcal/mol at the B3LYP-D3 level as compared to -1.7 kcal/mol at the B3LYP level. We thus use the B3LYP-D3 values for the Gd complex in our discussion. The Ln-OH 2 bond distance is 2.48 Å

Table 7. Calculated B3LYP Properties for Ln(OH 2 ) Complexes. Frequencies in cm-1. Ln(H 2 O)

υ(Ln-O)

H2O

υ(O-H) sym

υ(O-H) asym

υ(H-O-H) bend

3833.0

3951.9

1630.5

2

270.4

3555.0

3668.7

1545.4

3

242.2

3601.6

3723.6

1574.7

4

215.0

3643.1

3758.3

1589.7

5

212.2

3656.3

3773.3

1593.1

6

208.8

3657.8

3776.6

1593.8

7

201.1

3662.8

3781.7

1596.3

8

197.4

3665.5

3784.9

1597.3

9

181.7

3669.5

3798.1

1603.6

8

180.2

3685.9

3806.3

1602.5

5

170.4

3662.4

3794.1

1587.2

7

182.7

3627.7

3738.5

1570.7

4

188.3

3667.7

3787.4

1599.7

3

187.7

3673.4

3794.5

1600.5

2

184.7

3672.4

3793.0

1600.8

1

186.5

3671.2

3791.7

1601.0

2

200.3

3705.5

3784.3

1610.2

La(OH 2 ) Ce(OH 2 ) Pr(OH 2 ) Nd(OH 2 ) Pm(OH 2 ) Sm(OH 2 ) Eu(OH 2 ) Gd(OH 2 )a Tb(OH 2 ) Dy(OH 2 ) Dy(OH 2 ) Ho(OH 2 ) Er(OH 2 ) Tm(OH 2 ) Yb(OH 2 ) Lu(OH 2 )

At the B3LYP-D3 level. At the B3LYP level, the values in cm-1 for the complex are: υ(Ln-O) = 161.4, υ(O-H) sym = 3739.5, υ(O-H) asym = 3841.9, and υ(H-O-H) bend = 1615.7. The corresponding values at the B3LYP-D3 level in cm-1 for H 2 O are: υ(O-H) sym = 3832.4, υ(O-H) asym = 3951.8, and υ(H-O-H) bend = 1629.9. a


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for La and those for Ce to Eu are in the range of 2.55 to 2.58 Å. The bond distance for Gd is also about 2.58 Å and the distances decrease for the remainder of the period. The O-H bond distances are slightly longer than the O-H bond distance of 0.97 Å for H 2 O calculated at the same level of theory. The ∠HOH bond angles are all larger by 2° to 3° for the lanthanide complexes than the bond angle of 105.5° for H 2 O obtained at the same level of theory. The complexes are

approximately planar except for Ln = La, Ce, Pr, and Gd, which have values of the non-planarity parameter ∆θ (∆θ = 360-∑(HOLn bond angles)) of 16.6°, 16.5°, 6.0°, and 28.4° respectively. The O-H asymmetric and symmetric stretches of the complex are lower by between 100 to 300 cm-1 as compared to the calculated values for H 2 O (Table 7). The H-O-H bend decreases by 25 to 85 cm-1 for the complexes as compared to the calculated values for H 2 O. The Ln-O stretching vibrations range from 270 cm-1 for La to 180 cm-1 for Gd. For the first half of the series, there are significant decreases of ~30 cm-1 between La, Ce, and Pr. La has a 6s25d1 electron configuration and Ce has a 6s25d14f1 configuration, so these lanthanides have many vacant orbitals and few electrons and can form a strong complex with water, consistent with higher Ln-O vibrational frequencies and more exothermic reaction energies than most of the rest of the series. For Nd to Eu there are slight decreases in the Ln-O vibrations but these frequencies are all within ~20 cm-1 and the complexation energies are -10 to -11 kcal/mol, with the exception of Nd, which follows the Ln-O vibration trend but is notably more exothermic. Eu(H 2 O) is 2.4 kcal/mol less exothermic than Sm(H 2 O), with little change in frequencies or bond distance. From Tb to Lu, the stretching frequencies for the late lanthanides are within 20 cm-1 of each other and reaction energies also do not change much for this group. Discussion



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An initial Lewis acid-base complex between the Ln and H 2 O is expected to form for all Ln with a maximum Lewis acid-base complexation energy of -20 kcal/mol for Ce with most values around -10 kcal/mol with the exception of Gd having a value of only -2 kcal/mol. This small value for Gd is likely due to the high spin atomic configuration of 6s25d14f7 leading to more repulsion with the H 2 O lone pair. The dominant product channel for the reactions of Ln + H 2 O is formation of HLnOH for all of the lanthanides except for La and Ce. For these 2 lanthanides, the preferred reaction product is LnO+H 2 . The channel producing H 2 and LnO is only 3 kcal/mol more exothermic than the HLnOH channel, so HLnOH is expected to be observed for all Ln under matrix reaction conditions. The reaction to produce HLnOH is exothermic for all of the lanthanides. The magnitude of the reaction exothermicity reaches a minimum for Eu, increases to Tb and Dy, and decreases to ~ -25 kcal/mol for the remaining Ln except for Lu where the value is large like the two early Ln. The reaction to produce LnO + H 2 is exothermic for all Ln except for Eu and Tm where it is slightly endothermic and for Yb where it is substantially endothermic. On the basis of the accuracy of the calculations as compared to experiment for the LnO + H 2 channel, only the Yb reaction can definitely be predicted to be endothermic. Thus in these cases, there is a preference for the +II oxidation state for the Ln. Three other possible reaction product channels are formation of H 2 LnO, production of LnOH + H, and HLnO + H. Most of these reactions are endothermic except for those Ln where the reactions to form HLnOH are highly exothermic, La, Ce, Tb, Dy (reactions (3) and (4)) and Lu. The reaction to form H 2 LnO is more exothermic than that for the production of HLnO + H or LnOH + H for La, Ce, and Tb. So the compounds that can form the +IV or +III/+IV oxidation states do so and form H 2 LnO. For Dy, the +I oxidation state is preferred leading to DyOH as it is for Lu as well.


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The reaction energetics can be explained in terms of the bond dissociation energies (BDEs) of the reactants and products. The average H-O BDE in H 2 O is 111 kcal/mol, so twice that much energy must be released by the product bond formation for the formation of H 2 LnO or HLnO. Thus, the strong LnO BDEs are driving the formation of the LnO product and when these decrease, as they do towards the center and end of the Ln series, the reaction exothermicity drops. The Ln-H BDEs can be estimated and they are expected to be quite small, approximately 30 to 40 kcal/mol in most cases for these compounds. Thus, the only H 2 LnO or HLnO products that form must have strong LnO BDEs. The HLnOH forms more readily because only ~ 100 kcal/mol is needed to break an OH bond in H 2 O and a strong Ln-(OH) bond with potentially significant ionic character can be formed. For HLnOH with the Ln in the +II oxidation state, the Ln-H BDEs are ~ 50 to 60 kcal/mol. Furthermore, in HLnOH, the oxidation state of the Ln is only +II and this is easier to reach in the gas phase than the higher oxidation states unless the ligands are highly electronegative such as F, O and OH. The +II oxidation state and the different effective electronegativities of the H and OH produce the interesting trend in the bond distances that the Ln-H and Ln-(OH) bond distances are approximately equal as the H is much less electronegative than the OH. Although the electronegativity of the OH is not defined as precisely as the atomic values, we note that the ability of the OH to bind an electron (The electron affinity of OH of ~ 1.6 eV is much larger than that for H of ~ 0.75 eV.) means that the OH will have a larger ionic bonding component leading to a stronger and shorter bond. Thus the Ln-H and Ln-O(H) bonds can be of similar length even though this is not what one would expect from the covalent radii. The HLnOH are all quite bent, near 110º to 120º (up to 15º larger than the bond angle in H 2 O) and the Ln-O-H bond is almost linear as would be expected for a fully ionic M-O(H) bond.



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We can contrast the reactions of Ln and H 2 O with those for OF 2 . In the latter reaction, the possible product F 2 bond is very weak, 38 kcal/mol, and the O-F bond is also weak, ~ 46 kcal/mol, in OF 2 . In contrast, the Ln-F bonds are strong (Supporting Information). The reactions will be much more exothermic as strong Ln-F and Ln-O bonds are formed in the products which are OLnF 2 and OLnF. The weak O-F bond precludes the formation of FLnOF which can either eliminate the F or rearrange to form OLnF 2 . Such is also the case for the Group 3 and 4 metals. 66,67 As in the Ln + OF 2 reactions, the LnO stretch serves as a diagnostic of the quality of the wavefunction. Although spin polarization solutions were found with slightly lower energies than a higher spin solution, the stretching frequencies did not match the experiments. We find that the Ln-(OH) stretches are larger from Gd to Er and for Lu in excellent agreement with experiment. The low Ln-OH values found for Nd, Sm, Eu, Tm, and Yb are also in good agreement with experiment confirming our states and the calculations. The HLnOH with low Ln-OH stretches are also formed in the least exothermic reactions for the HLnOH formation, consistent with a weaker Ln-O(H) bond, and the converse is true for those compounds with high reaction exothermicities and Ln-O(H) bonds with higher frequencies. The orbital populations calculated using NBO are consistent with these results. The products generated by the more exothermic reactions forming HLnOH have more population in the 6s and 5d than do the HLnOH generated by reactions with lower exothermicity. This suggests that there is more backbonding from the O(H) and H into these Ln orbitals than for the products generated in the more highly exothermic reactions which strengthens their bonds. The NPA atomic charges are also consistent with this as the O and H become less negative for the compounds formed with high exothermicity and higher Ln-OH frequencies.


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Conclusions The reaction of lanthanides with H 2 O has been studied with density functional theory using the B3LYP exchange-correlation functional. The vibrational frequencies predicted by the B3LYP functional generally agree well with experiment except for a couple of cases where CASPT2 and CCSD(T) are required to deal with spin polarization issues to match the experimental measurements. The initial formation of a Lewis acid-base complex between H 2 O and a lanthanide is an exothermic process in the range of -7 to-20 kcal/mol for most cases except for Gd where the exothermicity is only -2 kcal/mol. Formation of HLnOH is the most exothermic process for all Ln except La and Ce where formation of LnO+H 2 is slightly more exothermic in comparison to formation of H 2 LnO, HLnO + H and LnOH + H. All the exothermic reaction energies to produce HLaOH range from -25 to -75 kcal/mol. The higher exothermicities are associated with the formation of a strong Ln-O(H) bond. The Ln in HLnOH are in the formal +II oxidation state with substantial backbonding from H and OH. The results clearly show that the +II oxidation state plays the dominant role in determining the most stable products of these reactions in contrast to the role played by the +III and +IV Ln oxidation states in the reactions of Ln with OF 2 . The difference in the role that the various Ln oxidation states play is due to the differences in the bond energies of the reactants and the specific negative charges that the ligands can support. When the bond energies are weak in the reactants and the ligands can strongly support the additional electrons as anions, the products are in the +III and +IV oxidation states as found for OLnF and OLnF 2 in contrast to the strong bonds in the reactants and the lower ability of H to support a negative charge as a ligand leading to the importance of the +II oxidation state in HLnOH. Evans and coworkers24,25,26 have been able to generate complexes of Ln in the +II oxidation state with the Ln(II) complexed to three trimethysilylcyclopentadienyl ligands to



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generate an anionic complex interacting with a K+-18-crown-6 cation. The Evans work focused on the reduction of Ln(III) complexes by potassium and shows that there are other chemical ways to stabilize the +II oxidation state in the presence of the +III oxidation state. The reaction channels to form H 2 LnO, HLnO + H and LnOH + H are generally endothermic with exceptions such as La and Ce, which have high Ln-O bond energies and other Ln with fully or half occupied valence shells. The Ln in H 2 LnO for most lanthanides is in the +III formal oxidation state with either Ln-O-/Ln-H- or Ln-(H 2 )-/Ln=O2- bonding interactions. The Ln in H 2 LnO for Ce, Tb, and Dy is in the +IV or mixed +III/+IV formal oxidation state with Ln=O2-/Ln-H- bonding interactions, similar to the results for OLnF 2 . The OH group in LnOH always behaves as OH-, so the Ln is in the +I formal oxidation state. In most cases, the Ln in HLnO is in the +III formal oxidation state with the exception of Yb which is in the +II oxidation state and the O is in the -1 oxidation state. The NBO orbital population analyses are consistent with the assigned formal oxidation states and the reaction energies. More backbonding from the O(H) and H to the Ln 6s and 5d is predicted for the more exothermic reactions forming HLnOH.

Acknowledgment. DAD acknowledges the Department of Energy, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences, Heavy Element Program for support via a subcontract from Argonne National Laboratory. DAD also thanks the Robert Ramsay Chair Endowment, University of Alabama, for support. LA gratefully acknowledges financial support from U.S. Department of Energy Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry Program through Grant No. DESC0001034. KAP acknowledges the support of U.S. Department of Energy Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry Program through


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Grant No. DE-FG02-12ER16329. This research used resources of and was partially supported by (MC) the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the DOE Office of Advanced Scientific Computing Research under Contract No. DE-AC05–00OR22725 with UT-Battelle, LLC.

Supporting Information Complete references for 37 and 62. Tables: B3LYP reaction energies for reactions (2) to (6); B3LYP NBO population analysis and spin densities for ground state LnO, HLnOH, H 2 LnO, LnOH and HLnO; Optimized geometries for ground state HLnOH, H 2 LnO, LnOH, HLnO and Ln(OH 2 ) with the B3LYP; Frequencies and IR intensities for ground state LnOH and HLnO calculated with the B3LYP; H 2 O Binding Energies in Ln(OH 2 ) complexes with the B3LYP, B3LYP-D3 and ωB97xD Functionals. Selected NBO population analysis for the molecules on low-spin states with unpaired beta spin; Ln-F and Ln-O BDEs at 298 K; LnOF 2 and OLnF natural charges from Ref 7. Figures: Spin densities for ground state HLnOH calculated with the B3LYP.

References (1) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd Ed.; ButterworthHeinemann: Oxford, 1997. (2) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th Ed.; Wiley, New York, 1988. (3) Chen, M.; Dixon, D. A.; Wang, X.; Cho, H.-G.; Andrews, L. Matrix Infrared Spectroscopic and Electronic Structure Investigations of the Lanthanide Metal Atom-Methyl Fluoride Reaction Products CH3-LnF and CH2-LnHF: The Formation of Single Carbon-Lanthanide Metal Bonds. J. Phys. Chem. A 2011, 115, 5609−5624.



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TOC Figure Ln + H2O Potential Energy

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(+III, +IV) H2LnO

(+II) HLnOH Reaction Coordinate


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Structures and Properties of the Products of the Reaction of

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