The performance of density functional theory for the description of ground

and excited state properties of inorganic and organometallic uranium

compounds

Daniel Reta,1 Fabrizio Ortu,1 Simon Randall,1 David P. Mills,1 Nicholas F. Chilton,1

Richard E. P. Winpenny,1 Louise Natrajan,1 Bryan Edwards2 and Nikolas

Kaltsoyannis1,*

1 School of Chemistry, The University of Manchester, Oxford Road, Manchester M13

9PL, UK

2 Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell

Oxford, Didcot OX11 0QX, UK

1

Abstract

Molecular uranium complexes are the most widely studied in actinide chemistry, and

make a significant and growing contribution to inorganic and organometallic chemistry.

However, reliable computational procedures to accurately describe the properties of

such systems are not yet available. In this contribution, 18 experimentally characterized

molecular uranium compounds, in oxidation states ranging from III to VI and with a

variety of ligand environments, are studied computationally using density functional

theory. The computed geometries and vibrational frequencies are compared with X-ray

crystallographic, and infra-red and Raman spectroscopic data to establish which

computational approach yields the closest agreement with experiment. NMR parameters

and UV-vis spectra are studied for three and five closed-shell U(VI) compounds

respectively. Overall, the most robust methodology for obtaining accurate geometries is

the PBE functional with Grimme’s D3 dispersion corrections. For IR spectra, different

approaches yield almost identical results, which makes the PBE functional with

Grimme’s D3 dispersion corrections the best choice. However, for Raman spectra the

dependence on functional is more pronounced and no such clear recommendation can

be made. Similarly, for 1H, 13C NMR chemical shifts, no unequivocal recommendation

emerges as to the best choice of density functional, although for spin-spin couplings, the

LC-ωPBE functional with solvent corrections is the best approach. No form of

time-dependent density functional theory can be recommended for the simulation of the

electronic absorption spectra of uranyl (VI) compounds; the orbitals involved in the

transitions are not calculated correctly, and the energies are also typically unreliable.

Two main approaches are adopted for the description of relativistic effects on the

uranium centres: either a relativistic pseudopotential and associated valence basis set, or

an all-electron basis set with the ZORA Hamiltonian. The former provides equal, if not

better, agreement with experiment vs all-electron basis set calculations, for all properties

investigated.

2

1. Introduction

Computational quantum chemistry has matured rapidly in recent years, to the point

that it is now central to many areas of research. It has benefitted from complementary

developments in theoretical understanding and the availability of high performance

computer systems. Many methods are well developed and understood for the treatment

of systems containing only atoms with low to intermediate atomic numbers, and in

favourable cases it is now possible to calculate structural, spectroscopic and

thermodynamic properties that accurately rivals experiment. By contrast, the

computational chemistry of systems containing atoms with large atomic numbers

(especially the actinides) remains challenging. The two principal reasons for this are (i)

relativistic effects[1,2] (the modification of energies and spatial extent of atomic orbital

vs non-relativistic analogues, and spin-orbit coupling) have a significant effect on 5f

element chemistry, and must be explicitly included in calculations, and (ii) the near

degeneracy of several sets of valence atomic orbitals (5f, 6d, 7s and 7p) can lead to a

plethora of closely-spaced electronic states which pose formidable electron correlation

challenges.

The principal workhorse of molecular computational chemistry in the 5f series is

density functional theory (DFT).[3–6] However, there is by no means a standard

approach to DFT calculations for molecular actinide species. For example, among the

leading players, Liddle et al. favour the generalised gradient approximation (GGA)

functional BP86[7,8] and Gagliardi et al. also often use GGAs.[9,10] By contrast, the

Los Alamos team routinely employs hybrid DFT (primarily B3LYP),[11,12] an

approach also adopted by Maron et al.[13] who exclusively use B3PW91. Research in

our group has employed both GGA[14,15] and hybrid[16] functionals. Meta variants of

both GGAs and hybrids are gaining popularity, such as in the recent TPSS/TPSSh work

of Kerridge et al.[17] and Pandey,[18] and the M06 calculations of Steele et al.[19] It is

therefore not uncommon that a random selection of three different papers on molecular

actinide chemistry will report the results of DFT calculations from three different rungs

of Perdew’s “Jacob’s ladder”,[20] yet there is little evidence that conclusions

concerning molecular actinide chemistry are functional independent.

With this in mind, we were keen to establish the best DFT methodology for

studying molecular uranium inorganic and organometallic complexes, and here report

3

the results of a wide-ranging investigation. We have conducted extensive calculations

on 18 uranium compounds, featuring the metal in a variety of oxidation states and

ligand environments, for which there is a range of high quality experimental data

available with which we can compare our results. The properties we have studied

include molecular geometries and vibrational frequencies (XRD, IR and Raman data)

and, for closed shell U(VI) species, NMR parameters and electronic excitations (UV-vis

data). All of these types of data are routinely acquired by experimental molecular

actinide chemists, and are often reported in conjunction with supporting DFT results.

We shall see that for some properties there are clear-cut recommendations as to the best

DFT approach to adopt, whereas for others the picture is either much less clear, or just

depressing. We expect that the actinide, and wider, community will find our work, and

conclusions, highly valuable.

4

2. Target compounds

Figure 1 introduces the compounds investigated in this work, and indicates the

references from which we draw experimental data. The list contains representative

examples of the rich variety of molecular uranium complexes, and the compounds

considered display a wide range of physical properties. The structural and spectroscopic

of all of these complexes have been experimentally well characterized. Our

classification of the different compounds is done on the basis of the oxidation state of

the uranium centre, which also provides the framework for the discussion throughout

this work. Compounds 1 – 3, 4 – 8, 9 and 10 – 16 feature a U(III), U(IV), U(V) and

U(VI) centre with three, two, one and zero unpaired electrons in the 5f orbitals,

respectively. Compounds 17 – 18, by contrast to the other compounds, are dimeric

species with formally one unpaired electron on each of the two paramagnetic U(V)

centres. An additional feature that varies throughout the list of compounds is the charge.

Most of them are neutral, apart from compound 10 which has a -1 charge, compounds 9

and 17 which are dianions and compound 13 which carries a -4 charge.

5

Figure 1. Schematic representation of the 18 uranium compounds investigated. The numbering scheme is used throughout the work, and superscripts indicate the sources of the experimental data. Each column

features a different oxidation state of the uranium centre, including monomeric U(III), U(IV), U(V), U(VI) and dimeric U(V)–U(V). The circles indicate the system of colours that has been used throughout

this work to refer to each group of molecules.

6

3. Methodology

One of the aims of this work is to determine which quantum chemistry

approach(es) offer(s) the most reliable description of molecular uranium compounds.

Several programs exist with which this evaluation could be performed, with differing

performance in terms of functionality, computational cost and accuracy of the results,

and we have selected two of the key players to study the different properties;

Gaussian09 version D.01[40] and ADF 2016[41]. These codes allow us to compare i)

Gaussian-type orbitals (Gaussian09) with Slater-type orbitals (ADF) and ii) the effect of

the differing treatments of relativistic effects on the predicted NMR and UV-vis spectra;

relativistic pseudopotentials (Gaussian09), all electron basis sets and the ZORA[42–45]

Hamiltonian and/or inclusion of SOC (ADF). Template inputs for both programs can be

found in section 10 of the SI.

Density functional based-methods[46,47] have been used to reproduce the

experimentally available crystal structures, infra-red, Raman, NMR and UV-vis spectra.

The chosen functionals range across generalized gradient approximation (GGA), meta-

GGA, hybrid and range-corrected approaches. Specifically, we have selected the

PBE[48,49] and TPSS[50] pure exchange-correlation functionals, the PBE0,[51]

B3LYP[52] and TPSSh[50] hybrid functionals and the LC-ωPBE[53–55] long range-

corrected functional. Additionally, for each functional empirical dispersion corrections

as proposed by Grimme[56–58] have been included when available (hereafter referred

to as “-D3”). Finally, UV-vis spectra were studied by means of time dependent DFT

(TD-DFT) for those closed-shell molecules with available experimental data. In this

case, in addition to the previously mentioned functionals, we also considered the

popular CAMB3LYP.[59] Note that all these functionals were investigated when using

Gaussian09; initial attempts to use functionals other than the pure-exchange PBE with

ADF resulted in persistent Self-Consistent Field (SCF) convergence problems and slow

performance. Thus, throughout the text when referring to ADF results, only data from

the PBE functional are discussed.

An underlying feature common to all our systems is the need to include relativistic

effects due to the uranium centre; these have been accounted for by means of either

relativistic pseudopotentials[60] or the scalar relativistic ZORA Hamiltonian.[42–45]

Spin-orbit coupling (SOC) calculations are indicated whenever they are performed. The

7

description of the uranium centres depends on the program used: in Gaussian09, the

inner uranium electrons were described with the ECP60MWB[61–63] relativistic

pseudopotential, and the valence electrons with the associated segmented basis set,[62]

while in ADF, the internal ZORA/QZ4P/U basis set was used. The choice was guided

by extensive previous works on the use and effect of pseudopotentials.[64–66] The

lighter atoms (H, C, N, O, F, Na, Si, P, S, Cl) were described with the Dunning-type cc-

pVDZ[67] basis in Gaussian09, and the iodine atoms in compounds 5 and 6 with the

ECP46MWB[68] relativistic pseudopotential and the associated

(14s10p3d1f)/[3s3p2d1f] VTZ basis set.[69] Using an ECP28MDF[70] and the same

VTZ basis set provides nearly identical molecular structures. In ADF the internal

ZORA/DZP basis set with the keyword “core small” was used for the lighter atoms, and

the ZORA/TZP/I basis set for iodine.

All optimized geometries have been obtained using the default convergence

criteria. The crystal structure was always used as input for geometry optimizations and

geometries converged with a different functional were never used as starting point for

problematic cases, in order to facilitate a clean comparison of the different methods. For

a given functional, geometries optimized with dispersion corrections did use those

structures converged without corrections as a starting point; test calculations showed,

however, that using either the non-D3 structures or crystal structures as starting points

yielded the same -D3 geometries. No symmetry was imposed for any calculations, i.e.

the C1 point group was always employed. Solvent effects were included, where

required, by means of the Polarizable Continuum Model (PCM) using the default

parameters as implemented in Gaussian09, specifying in each case the appropriate

solvent.

Explicit calculations of the Hessian to characterize the stationary points on the

Potential Energy Surfaces (PES) and model the IR spectra were performed using the

default convergence criteria. However, more often than not we needed to carry out a

vibrational frequency calculation at an intermediate point and use these forces in

subsequent calculations to achieve full convergence for the geometries. In some cases

(particularly the U(III) and U(V)-U(V) compounds) this had to be repeated several

times. Raman intensities were also computed using the default criteria using the same

functionals and basis sets used for geometry optimizations.

8

The performance of standard DFT methods to reproduce NMR parameters of

closed-shell uranium compounds has been investigated in a subset of our molecules; the

chemical shifts and spin-spin coupling constants of compounds 11 – 13 were modelled

using the default criteria and approaches.[71–73] The same set of functionals and basis

sets as used for the calculation of vibrational and Raman intensities, were employed to

calculate the NMR properties as well as the specialized IGLOII[74] and jcpl[75,76]

basis sets in Gaussian09 and ADF, respectively. Within Gaussian09, the effect of triple-

and quadrupole-ζ polarized (cc-pVTZ[67] and cc-pVQZ,[67] respectively) quality basis

sets on hydrogen and carbon atoms was studied for PBE functional. We also investigate

the effect of including relativistic effect via scalar ZORA[77] or ZORA + SOC[78] in

ADF2016.

Time dependent DFT was employed to model UV-vis spectra of compounds 10, 11

and 13 – 15, using the default criteria. Given that they are all closed-shell molecules,

only singlet-singlet excitations were computed. In addition to the standard functionals,

CAMB3LYP was also investigated, in all cases using the same basis sets as for the

geometry optimizations. For [UO2Cl4]2- and compound 14, the effect of diffuse

functions was also investigated by using aug-cc-pVDZ[79] for light atoms.

Table 1 presents the approaches that have been followed to model each of the

experimentally available data types, depending on whether or not the uranium centre

has any unpaired electrons, i.e. the closed-shell U(VI) complexes (10 – 16) and the

(open-shell) molecules (1 – 9, 17, 18).

Compounds 10 – 16 Compounds 1 – 9, 17, 18XRD – IR –

Raman NMR UV-vis XRD – IR – Raman

Prog

ram

/ M

etho

d / B

asis

set Gaussian /

DFT /Dunning-

ECP

Gaussian /DFT /

Dunning-ECPGaussian /TD-DFT /Dunning-

ECP

Gaussian /DFT /

Dunning-ECPGaussian /DFT /

IGLOII-ECP

ADF /DFT /

Slater-scalar ZORA

ADF /DFT /Slater-scalar

ZORAADF /

TD-DFT /Slater- scalar

ZORA

ADF /DFT /

Slater-scalar ZORAADF /DFT /Slater-spin orbit

ZORA

9

Table 1. Summary of employed computational approaches depending on the experimental data being modelled.

The Computational Shared Facility of The University of Manchester was employed

to carry out all of the calculations here discussed. Matplotlib[80] and Python2.7 were

used to display the data. The graphical program Inkscape was used to compile the

figures.

10

4. Results and discussion

4.1. Molecular geometries

All the compounds shown in Figure 1 have a well-established molecular geometry

obtained from X-ray diffraction (XRD) experiments. The agreement between these data

and the predicted geometries obtained computationally has been addressed using the

Root-Mean-Square Deviation (RMSD) between the two sets of atomic positions

(excluding hydrogen atoms). This value (in Å) measures the average distance between

corresponding pairs of atoms in the optimized and experimental structures. In order to

ensure that the rotation applied to superimpose the two structures yields the lowest

possible RMSD value, we follow the algorithm proposed by Kabsch[81,82] and

implemented by Kroman and Bratholm.[83] Thus, the smaller the RMSD value, the

more similar are the optimized and experimental structures.

Geometry optimizations using a pseudopotential for the uranium centres were

carried out using the PBE, PBE0, TPSS, TPSSh, B3LYP and LCωPBE functionals

within the Gaussian09 program. PBE calculations were also carried out using Slater all-

electron basis sets and scalar ZORA relativistic corrections within the ADF2016 code.

Additionally, each calculation was carried out including Grimme’s D3 dispersion

corrections (indicated by the suffix -D3). For all cases, we explicitly calculated the

Hessian to ensure that all frequencies are real and that the forces are zero, to ensure that

we located a stationary minimum. For each compound, this results in 11 optimized

structures obtained using a pseudopotential (note that Grimme parameters are not

defined for the TPSSh functional in Gaussian09) and 2 optimized structures obtained

using Slater basis sets and the ZORA Hamiltonian. This yields a maximum of 234

possible optimized structures considering both approaches. Detailed information on the

performance of both approaches, indicating whether they converged properly or not

(and the reason) depending on the functional used and compound studied can be found

in Table SI 1 and Table SI 2 of section 1 of the SI. Summarising, with Gaussian09 we

were able to obtain 148 correctly converged results out of the 198 possible structures

(75%). For ADF, of the possible 36 optimized structures, 29 (80%) structures converged

correctly. Therefore, a total of 177 out of 234 structures (76%) were characterized as

stationary points on their potential energy surfaces.

11

Figure 2 presents the RMSD values for the 18 compounds as determined by

Gaussian09; the closer the data point lies to the middle of the figure, the better the

agreement between theory and experiment. Note that not all compounds have data for

all functionals, compound 10 being the most extreme case as no structure was

converged. It is worth noting that this is not the case for compound 9, despite the

similarity between them. Only for half of the compounds (4 – 6 and 11 – 16) did all

functionals provide a converged structure. For the rest of them, the most common

behaviour is a generally good convergence with PBE and TPSSh, a less efficient

performance for PBE0, TPSS and B3LYP and a persistent failure of LC-ωPBE. This

reveals that the computational description of the structural features in these compounds

is sensitive to characteristics such as oxidation state and charge. A similar plot to Figure

2 obtained using Slater basis set and ZORA Hamiltonian, can be found in Figure SI 1 of

section 2 of the SI. A comparison between the two figures indicates that the use of

pseudopotentials for the uranium atoms provides very similar results to those obtained

with all electron basis sets.

12

Figure 2. Polar plot of structural differences (RMSD values in Å) between the XRD and DFT-computed structures for the 18 investigated compounds, as obtained with the chosen functionals using Gaussian09.

The suffix “-D3” after the employed functional indicates the use of Grimme dispersion corrections for the optimization of the geometries.

A general conclusion from Figure 2 is that the performance across all the different

compounds with the six density functionals is in reasonable agreement with experiment,

rarely exceeding an RMSD of 0.6 Å. In fact, the mean and standard deviation for all 177

results is 0.3 ± 0.2 Å. Also, for a given compound, the converged structures generally lie

in a narrow range of RMSD values. This is not the case for compounds 2 and 5, for

which the RMSD values are considerably dispersed. Apart from compound 10,

compounds 1 – 3 were the most difficult to converge, especially compound 3 for which

only the TPSSh functional provided a true minimum. Of similar difficulty is compound

13

18; attempts to locate a stationary point were unsuccessful with any functional other

than the pure exchange PBE, in either singlet or triplet multiplicities. As already noted,

compound 10 is the most problematic case, as no converged structure was obtained

using a pseudopotential. However, all-electron basis set calculations did provide

converged structures with RMSD values around 0.25 Å (see Figure SI 1 of section 2 of

the SI). In general it seems that there is no pattern to the performance of the various

methods that can be associated with a particular oxidation state or molecular charge.

Figure 3a and b present the RMSD values (in Å) as a function of the employed

functional rather than as a function of the compound investigated, aiming to highlight

the different performance of each functional. In Figure 3a the order of the compounds

and the colour assignment for the oxidation states are the same as in Figure 1 and Figure

2. In Figure 3b the numbers appearing beneath the functional indicate the number of

stationary points located with it. These complementary plots reveal that: i) the inclusion

of dispersion corrections systematically reduces the range of RMSD values, as found in

previous works[18,84,85] ii) that the PBE functional provides the most robust (larger

number of converged structures) and consistent approach (narrower range of RMSD

values centred on ~0.3 Å) for describing the molecular structures, iii) the B3LYP results

are similar to those obtained with PBE, but the number of converged structures is

smaller, iv) PBE0 and LC-ωPBE have the smallest number of converged structures (and

those obtained with PBE0 have a much smaller spread than the ones associated with

LC-ωPBE), and v) TPSS, TPSSh and LC-ωPBE yield the most widely distributed sets

of results.

Finally, solvent effects were included for the PBE functional within Gaussian09, as

presented in Table SI 3 in section 1 of the SI. The generally small RMSD values

between gas-phase and solution geometries across the series of compounds allows us to

conclude that the inclusion of a solvent model for structural optimization does not

greatly impact the comparison with XRD data, for the investigated compounds. Thus,

implicit solvent effects will not be discussed any further. However, it should be noted

that for aqueous uranyl(VI), the combination of explicit water molecules in the first

coordination sphere with PCM solvation has previously produced results in better

agreement with experiment.[86–89]

14

Figure 3. RMSD values (Å) between XRD and DFT-computed structures, as given by the different functionals used. Note that PBE was used in both the Gaussian09 and ADF programs a) Bar plot of

RMSD values at the optimized geometries obtained without (o, ˂) or with (˃, *) dispersion corrections, respectively. b) Polar plot of RMSD values for each functional employed. Beneath each functional the number of converged structures is indicated. Note that the maximum possible number is 18, except for

PBE for which it is 36.

In summary, our recommendation is that the most robust approach to obtain reliable

geometries is to employ the PBE functional with dispersion corrections, and to use a

pseudopotential to account for scalar relativistic effects (as such calculations are

typically less computationally demanding than all-electron calculations with a

relativistic Hamiltonian, provided that all other parameters (system size, code, machine

etc) are similar.

4.2. Infra-red and Raman spectra

For each of the geometries obtained, calculation of analytical Hessians and hence

vibrational frequencies was performed at the stationary point. Figure 4 presents the IR

spectra obtained for compound 1 and exemplifies the very similar plots produced for the

15

rest of the compounds, to be found in section 3 of the SI (Figures SI 2-15). These plots

consist of three subplots, presenting the same data in different ways so as to facilitate

their interpretation. The upper left subplot introduces all the IR spectra overlapped,

while the upper right subplot splits those and presents them in two groups; the ones

obtained without the inclusion of dispersion corrections and the ones with them. It also

includes the most relevant signals obtained experimentally. Finally, the lower subplots

present the separated IR spectra according to the functional used. Obviously, the

functionals that failed to provide a converged geometry do not have IR spectra.

Figure 4. Comparison of IR spectra obtained with the investigated functionals using Gaussian09 for compound 1. Similar plots can be found in section 3 of the SI for the rest of the molecules. Upper left plot

shows all obtained IR overlapped. Upper right plot is split in two to see the influence of including dispersion corrections (suffix “-D3”) and presents the experimental signals (and corresponding height) (weak, medium, strong and very strong) as vertical lines. Lower figure compares each functional; blank

boxes highlight for which functionals it proved impossible to obtain converged geometries.

The IR spectra do not depend strongly on the choice of functional, which agrees

with previous studies on model actinide compounds,[65] and extends the conclusion to

long-range corrected functionals. Note, however, that for those model compounds, other

studies conclude that GGA functionals provide better geometries and IR frequencies

than hybrid counterparts.[66,89–91] For our results, differences in the principal features

16

are barely distinguishable between the different functionals. This is not unexpected

given the similarities of the geometries obtained from the different functionals; the

RMSD values between the computed structures rarely exceed 0.2 Å, although in the

worst case scenarios such as TPSS vs PBE for compound 2 and TPSSh vs B3LYP for

compound 5, the corresponding RMSD values are rather larger, 1.06 and 0.61 Å,

respectively. If one checks the influence on the predicted IR spectra, it is very minor.

When comparing predicted and computed spectra, a general observation is that for

all functionals investigated, the lower energy region (from 0 to ~750 cm -1) is described

more poorly vs experiment than other energetic regions. As a specific example, let us

consider compound 1 (Figure 4) to further discuss specific features. The most

significant vibrational modes associated with the U-N-Si2 stretching are well captured

by all functionals, although the most energetic experimental vibrational modes have

intensities which are underestimated by all functionals. Above ~3000 cm-1, the lack of

experimental data prevents addressing how meaningful the predicted features are, by

contrast to compound 2 (Figure SI 3). Compound 5 (Figure SI 5) displays the most

significant differences between computed spectra; notably, PBE functional predicts an

intense peak at ~1500 cm-1, which matches very well with the experimental value.

Finally, for compounds 11 and 13, the computed frequencies are generally

overestimated (in wavenumber) with respect to experiment.

We conclude that as different approaches provide very similar IR spectra, the PBE

functional appears the best choice because of its reliability in obtaining molecular

structures. This supports earlier studies on U(VI) complexes which concluded that

relativistic DFT is a robust approach for geometries and IR spectra,[92–94] and extends

the conclusions to open-shell uranium systems.

In the same manner as for the IR spectra, calculation of third derivatives was

performed to obtain Raman spectra. The experimental Raman spectra for compounds 6

and 16 are presented in section 7 of the SI. At variance with the previous results,

analytical solutions could not be calculated by all functionals in the Gaussian09 code. In

fact, for TPSS and TPSSh, the numerical approach had to be taken by making use of the

freq=NRaman keyword. For the LC-ωPBE functional, Raman spectra could not be

obtained. Figure 5 introduces the calculated Raman spectra for compound 6, presented in

a similar manner to the IR results. The rest of the calculated Raman spectra can be

17

found in section 4 of the SI (Figures SI 16 – 21). By contrast with the IR spectra, for the

Raman spectra the choice of the functional has a larger impact on the relative positions

of the signals. Additionally, the overall agreement with experiment is much poorer, with

calculation predicting important features where experiment is silent. This is particularly

true for the higher energy regions.

Therefore, there is no clear recommendation as to which functional to use when

seeking accurate Raman spectra, although PBE generally performs a little better than

the other functionals tested.

18

Figure 5. Comparison of Raman spectra as obtained with the investigated functionals using Gaussian09 for compound 6. Similar plots can be found in section 4 of the SI for the rest of the molecules. Upper left

plot shows all obtained spectra overlapped. Upper right plot is split in two to see the influence of including dispersion corrections (suffix “-D3”) and presents the reported experimental signals (and

corresponding heights, counts relative to the signal with the largest amount of counts) as vertical lines. Lower figure compares each functional; blank boxes highlight for which functionals it proved impossible

to obtain converged geometries .

4.3. NMR spectra

DFT-based calculations have proved capable of correctly reproducing chemical

shifts of diamagnetic uranium compounds,[95,96] although particular difficulties for 19F

chemical shifts have been reported,[65] raising some contradictions.[97,98] On the

other hand, paramagnetic systems remain an issue due to the inherent deficiencies of

DFT to treat systems with pronounced multireference character and important

relativistic contributions. Recent theoretical and computational efforts provide

appropriate descriptions for such complex problems,[99,100] but they rely on

wavefunction-based methods and they are therefore out the scope of this work. We now

present the 1H and 13C NMR results on the closed shell target molecules for which

19

experimental data are available, i.e. compounds 11 – 13. The approaches employed are

given in Table 1.

All calculations have been performed with the same functional used to optimize the

geometry. Thus, when discussing the results obtained with B3LYP, for example, it is

implicit that the geometry used is the one obtained with B3LYP functional. For both

Gaussian09 and ADF, each calculation has been carried out with two basis sets; the

same basis set used to optimize the structures and additionally the IGLOII basis sets for

hydrogen and carbon atoms in the case of Gaussian09 and jcpl in the case of ADF2016,

which have been explicitly developed for NMR properties. The interest of comparing

the results from Gaussian09 and ADF2016 is that it allows us to address the effect of

including relativistic effects either with a pseudopotential (Gaussian09) or by means of

scalar ZORA Hamiltonian alone or together with spin-orbit coupling (ADF2016) on the

chemical shifts and spin-spin couplings.

The deviation from experiment is calculated as the difference between the

experimental and calculated isotropic shifts, all referenced to the tetramethlysilane

(TMS) standard. The TMS molecule has been treated at the same level of theory (code,

functional, basis set) as the one used to treat the uranium complex in each case. Section

5 of the SI presents a detailed explanation of how the different absolute and relative

errors were calculated. As a large amount of data is involved, only the mean and

standard deviation of those differences together with the corresponding relative errors

are presented. Note that these means have been calculated using the absolute values of

the differences between experiment and theory, to avoid error cancellation. In order to

avoid oversimplification of the discussion arising from consideration of only

comparative averages, and to help discern which approach behaves best for the series of

investigated compounds, Tables SI 4 – 7 in section 5 of the SI provide the smallest and

largest relative errors for each experimental signal together with the associated method.

Solvent effects have been included by the PCM; note that these are single point

calculations in which the PCM is used at the geometry of the gas-phase calculation. We

concluded in section 4.1 that the inclusion of solvent effects makes virtually no

difference to the geometry but, as a test case, have calculated the deviations from

experiment of the 1H chemical shifts of compound 11 (vide infra) at the geometries

optimized without and with inclusion of the solvent. At the PBE (cc-pVDZ basis set)

20

PCM level, these are 0.40 and 0.40 for the 1.73 ppm signal and 0.24 and 0.20 for the

5.81 ppm signal, i.e. the minor differences in the underlying geometry have similarly

minimal effect on the computed NMR data.

4.3.1. Compound 11

Compound 11[28] has a 1H NMR spectrum in C6D6 with two distinct signals, a

singlet at 1.73 ppm, assigned to the methyl groups of the tBu moiety, and another at 5.81

ppm, associated with the γ-carbon of the ketoiminate ring. The 13C NMR spectrum

measured in CD2Cl2 shows four distinct signals at 33.6, 102.9, 171.8 and 173.4 ppm.

Table 2 presents the deviations of the calculated chemical shifts. Examining first the 1H

shifts obtained with Gaussian09, we can see that the average absolute error from

experiment and the corresponding standard deviation, considering all 22 calculations, is

0.42 ± 0.03 and 0.17 ± 0.09 ppm for the 1.73 and 5.81 ppm experimental signals,

respectively. These values correspond to relative errors of 24 and 3%, respectively. The

same set of calculations was carried out using the IGLOII basis set, obtaining for the

same experimental signals the following mean and standard deviations, 0.13 ± 0.05 and

0.28 ± 0.09. The change of basis set thus results in a much smaller relative error of 8%

for the hydrogens of the methyl groups of the tBu moiety and a similar relative error

(5%) for the γ-carbon hydrogens, i.e. the IGLOII basis sets are superior for calculation

of these 1H chemical shifts. For the pVDZ basis set, the methods that yield the smallest

absolute error from the two experimental signals are PBE0 with solvent at the geometry

optimized without dispersion corrections (i.e. PBE0-PCM, 0.37 ppm, δx = 21.4 %) and

PBE0 without solvent at the optimized geometry with dispersion corrections (i.e. PBE0-

D3, 0.01 ppm, δx = 0.2 %). Similarly, the largest absolute errors arise from LC-ωPBE

without solvent at the optimized geometry with dispersion corrections (i.e. LC-ωPBE-

D3, 0.50 ppm, δx = 29.0 %) and B3LYP with no solvent and no dispersion corrections

(i.e. B3LYP, 0.31 ppm, δx = 5.3 %). For the IGLOII basis set, B3LYP and TPSS with

no solvent and no dispersion corrections yield the smallest deviations (0.09 and -0.14

ppm for both signals, respectively) while the largest absolute errors are found when

using LC-ωPBE without solvent at the geometry optimized with dispersion corrections

(i.e. LC-ωPBE-D3, 0.26 ppm) and PBE0 with solvent and dispersion corrections (i.e.

PBE0-D3-PCM, 0.47 ppm). This data can be found in Table SI 4 in section 5.1 of the

SI.

21

For similar discussion of the 13C values, the reader is referred to Table SI 4, where a

more explicit description of the averaged relative error and the methods that provide the

smallest and largest relative errors for each signal can be found. However, it is worth

mentioning that the differential effect of considering different basis sets seems to dilute

when averaging over all experimental signals, even making the results from the IGLOII

basis set slightly worse, at variance with the 1H case.

Hence a clear recommendation as to which method is best suited is not so

straightforward. That said, we can safely say that for the 13C chemical shifts, PBE0 and

TPSS often perform the worst.

Gaussian 09a) ADFb)

Exp. δ (ppm) ∆x µ ± σ δx (%) ∆x δx (%)

1H

1.73 0.42 ± 0.03 24.2 0.34 19.90.13 ± 0.05 7.8 0.17 9.9

5.81 0.17 ± 0.09 3.1 0.18 3.00.28 ± 0.09 4.8 0.27 4.6

µ ± σof δx (%)

13.6 ± 10.6 11.4 ± 11.96.3 ± 1.5 7.3 ± 3.7

13C

33.6 4.38 ± 2.51 13.0 1.81 5.45.12 ± 1.72 15.2 3.06 9.1

102.9 6.46 ± 3.53 6.3 3.04 3.03.24 ± 2.68 3.1 4.23 4.1

171.8 2.39 ± 2.18 1.4 3.19 1.97.65 ± 4.34 4.5 5.23 3.0

173.4 2.50 ± 1.90 1.4 9.30 5.48.51 ± 4.06 4.9 8.81 5.1

µ ± σof δx (%)

5.5 ± 4.8 3.9 ± 1.86.9 ± 4.8 5.3 ± 2.6

a) 1H results are averaged over the 22 calculations: 6 functionals, 2 geometries each (except TPSSh), with/without solvent each. For 13C solvent was not considered.

b) Results at PBE geometry only.

Table 2. Summary of calculated 1H and 13C NMR shifts (ppm) for compound 11. ∆x (Hz) and δx represents the absolute and relative error, respectively. µ ± σ stands for the mean and standard deviation of the absolute errors. The order of the signals is as reported in ref[28] for that paper’s compound 1. For the Gaussian09 results for each signal, the first row gives the results obtained with the pVDZ basis set,

while the second row collects those for the IGLOII basis set. For the ADF results for each signal, the first row presents the results obtained with scalar ZORA, while the second row gives ZORA+SOC data, using the internal jcpl (for C and H) basis set. The relative error is calculated with respect to the averaged value

of the absolute error (deviation). µ ± σ in the last row refers to the mean and standard deviation for all relative errors.

22

Let us now discuss the effect of all-electron basis sets and relativistic effects (i.e.

ZORA Hamiltonian, at either the scalar only or scalar + SOC levels) on the calculated

chemical shifts. This has been probed using the ADF programme with the PBE

functional, at the unique PBE optimized geometry and therefore geometry effects are

not considered here. These results can be found in the rightmost part of Table 2 from

which the differential effect of considering scalar ZORA or ZORA + SOC is not that

large. Note, however, that the inclusion of SOC effects reduces the standard deviation of

the relative errors, particularly for 1H chemical shifts. A comparison of the mean and

standard deviation of the relative errors µ ± σ of δx (%) results from Gaussian09 and

ADF2016 in Table 2 indicates that the use of a pseudopotential on the metal centre

provides similar results to those obtained with all electron basis sets. The effect of

different basis sets on the calculation of chemical shifts considering relativistic effects

via ZORA or ZORA+SOC can be seen by comparing these data with Table SI 5 in

section 5.1 the SI. One can see that for 1H chemical shifts, the use of jcpl improves

agreement markedly, but for 13C it is practically negligible. It is worth noting that the

largest deviation, no matter the approach taken, is associated with the 1H of the tert-

butyl groups.

4.3.2. Compound 12

Compound 12[30] has 10 and 16 distinct signals for 1H and 13C chemical shifts

respectively, in addition to different spin-spin couplings. These can be found in the

supplementary information of reference [30] (compound 3). From this, we chose the

J HH=7.6, J HH=9.2, J PH=35.64 and J PC=135.87 (Hz) signals to compare with our

computed results. The first two couplings are associated with 4H from p-Ph-CH and 8H

from m-Ph-CH; the third coupling corresponds to the doublet PH and the last one to

CHP2. First, let us discuss the chemical shifts. Table 3 presents the deviations from

experiment of the calculated chemical shifts and the relative error of their averaged

value as calculated with Gaussian09. We start by discussing the effect of the two basis

sets employed by considering the mean and standard deviation of the relative errors (µ ±

σ of δx (%) at the bottom of Table 3). As was observed for compound 11, 1H chemical

shifts are better described with IGLOII, although here the difference with respect to

pVDZ is less pronounced (10.6 ± 6.7 vs 9.2 ± 9.0 for pVDZ and IGLOII, respectively). 13C chemical shifts are better described with the pVDZ basis set. Overall, the agreement

with experiment is reasonable, within a ~12% error, although it is worth mentioning that

23

the smallest signals suffer from a large deviation. In order to gain further insight the

reader is referred to Table SI 5 in section 5.2 of the SI, where a more detailed

description of the methods that perform the best and worst for each signal is presented.

Overall, for compound 12, the recommendation of which approach to take to

properly describe chemical shifts using Gaussian09 is as unclear as for compound 11.

The inclusion of relativistic effects via ZORA or ZORA+SOC was also

investigated, both for the chemical shifts and spin-spin couplings, using PBE within

ADF. The results are similar to those obtained with Gaussian09, and hence are

presented in Table SI 8 in section 5 of the SI. The inclusion of relativistic effects by

means of scalar or spin-orbit ZORA affects much more the description of 13C than 1H

chemical shifts; thus, ZORA + SOC reduces the mean and standard deviation of the

relative errors (1H and 13C together) from 12.1 ± 22.5 to 8.7 ± 8.5 (when using jcpl basis

set), as can be observed from the µ ± σ of δx (%) values of Table 5; more details can be

found in Table SI 8. Comparison of the µ ± σ of δx (%) values obtained with

Gaussian09 and ADF2016 permits addressing the effect of using a relativistic

pseudopotential or relativistic Hamiltonian plus all electron basis set, respectively.

These are very similar, with an almost identical value for the 1H chemical shifts and a

noticeably better agreement with experiment of the ZORA + SOC jcpl basis set results

for the 13C shifts.

Exp. δ (ppm) ∆x µ ± σ δx (%) Exp. δ

(ppm) ∆x µ ± σ δx (%)1H 13C

1.48 0.15 ± 0.05 9.9 7.09 5.6 ± 3.4 78.80.47 ± 0.05 31.5 6.9 ± 4.2 97.0

2.39 0.23 ± 0.03 9.8 20.37 2.2 ± 0.3 10.70.13 ± 0.04 5.4 3.9 ± 0.6 19.4

2.46 0.40 ± 0.06 16.0 20.68 1.8 ± 0.3 8.90.06 ± 0.05 2.3 3.6 ± 0.6 18.0

2.81 0.79 ± 0.06 28.0 21.06 2.2 ± 0.3 10.60.52 ± 0.06 18.5 4.1 ± 0.5 19.4

4.53 0.35 ± 0.13 7.7 21.45 3.2 ± 0.5 15.10.13 ± 0.11 2.9 5.2 ± 0.7 24.3

6.90 0.62 ± 0.11 9.0 25.59 3.4 ± 1.4 13.30.90 ± 0.09 13.1 5.6 ± 1.3 22.1

7.00 0.19 ± 0.17 2.8 75.42 1.8 ± 1.1 2.40.58 ± 0.15 8.3 5.6 ±2.4 7.5

7.13 0.33 ± 0.14 4.6 127.8 2.8 ± 2.0 2.20.10 ± 0.08 1.5 6.0 ± 3.5 4.7

7.28 0.57 ± 0.14 7.9 129.1 3.1 ± 2.2 2.40.18 ± 0.10 2.5 7.7 ± 4.1 5.9

7.82 0.80 ± 0.14 10.2 129.6 3.1 ± 2.2 2.40.45 ± 0.12 5.7 7.4 ± 4.1 5.7

24

130.9 3.0 ± 1.9 2.38.7 ± 4.0 6.7

132.4 4.0 ± 2.2 2.96.0 ± 4.1 4.5

134.4 2.4 ± 1.6 1.86.6 ± 3.4 4.9

135.3 2.5 ± 1.5 1.88.4 ± 3.2 6.2

136.6 5.3 ± 3.0 3.93.1 ± 2.1 2.3

144.6 1.5 ± 1.0 1.010.3 ± 1.7 7.2

µ ± σof δx (%)

10.6 ± 6.7 10.0 ± 18.39.2 ± 9.0 15.9 ± 22.1

Table 3. Summary of calculated 1H and 13C NMR shifts (ppm) for compound 12 as calculated using Gaussian09. ∆x (ppm) and δx represents the absolute and relative error, respectively. µ ± σ stand for the

mean and standard deviation of the absolute errors. The order of the signals is the same as the one reported in the SI for compound 3 in[30]. The leftmost values correspond to 1H NMR and the rightmost values to 13C NMR. For each signal, the first row presents the results obtained with the pVDZ basis set,

while the second row is for IGLOII basis set. The relative error is calculated with respect to the averaged value of the absolute error (deviation). µ ± σ in the last row refers to the mean and standard deviation for

all relative errors for 1H and 13C, using the pVDZ and IGLOII basis sets, respectively.

Now let us discuss the spin-spin coupling constants presented in Table 4. Technical

details can be found in section 10 of the SI. There is a clear dependence of the

agreement on the experimental signal considered, and the consistency of results between

Gaussian09 and ADF for the chemical shifts is not maintained for the spin-spin

coupling constants. For instance, the results for J PC obtained with Gaussian09 show a

very good agreement with experiment along the series, while ADF2016 predicts values

with relative errors three times larger. Also, J PH has a systematic relative error larger

than 80 %, for all methods and both programs. The effect of the basis set employed is

much more pronounced here than for chemical shifts[76]; there is a significant

improvement when going to IGLOII in Gaussian09 and to jcpl in ADF2016. However,

the effect of geometry (PBE vs PBE+D3) and the inclusion of relativistic corrections is

not significant (see ADF2016 part of Table 4). Table SI 7 in section 5.2 of the SI

summarizes which functionals at which geometries provide the best and worst

agreement for Gaussian09 results; we conclude that LC-ωPBE with solvent corrections

is the best choice for describing spin-spin coupling constants.

a) Gaussian09J HH J PH J PC

Exp (Hz) 7.6 9.2 35.64 135.87

∆x µ ± σ 2.7 ± 0.4 3.8 ± 0.5 29.9 ± 3.1 13.3 ± 7.20.4 ± 0.3 1.3 ± 0.4 29.6 ± 2.7 11.6 ± 10.1

25

δx (%) 35.5 41.1 83.8 9.85.3 14.1 83.2 8.5

b) ADF2016PBE PBE-D3

Exp (Hz) ZORA ZORA + SOC ZORA ZORA +

SOC

J HH

7.6 ∆x / δx(%) 1.6 / 21.5 - 1.6 / 21.7 1.6 / 20.70.4 / 4.7 0.3 / 3.8 0.4 / 4.8 0.3 / 3.9

9.2 ∆x / δx(%) 2.8 / 30.7 - 2.8 / 30.5 2.7 / 29.81.6 / 17.2 1.5 / 16.5 1.6 / 17.7 1.6 / 17.0

J PH 35.64 ∆x / δx(%) 28.5 / 80.0 - 26.5 / 74.3 26.6 / 74.731.7 / 88.9 31.7 / 89.0 30.0 / 84.3 30.1 / 84.7

J PC 135.87 ∆x / δx(%) 53.3 / 39.2 - 48.7 / 35.8 47.4 / 34.936.1 / 26.6 34.7 / 25.5 30.7 / 22.6 29.2 / 21.5

Table 4. Summary of calculated 1H NMR spin-spin coupling constants (Hz) for compound 12. ∆x (Hz) and δx are the absolute and relative error, respectively. The relative error is calculated with respect to the averaged value of the absolute error (deviation). a) presents the values from Gaussian09. µ ± σ stand for the mean and standard deviation of the absolute errors. For each signal, the first row provides the results

obtained with the pVDZ basis set, while the second row gives those from the IGLOII basis set. b) introduces the values from ADF2016 calculations at the PBE level (without and with dispersion

corrections) and highlights the effect of explicitly including relativistic effects. For each signal, the first row presents the results obtained with the pVDZ basis set, while the second row gives the jcpl basis set

data.

4.3.3. Compound 13

Compound 13 displays a single 13C NMR experimental signal at 168.2 ppm vs

TMS. The mean and standard deviation of the differences vs experiment of the

calculated chemical shifts using the pVDZ basis set is -1.30 ± 2.61, which corresponds

to a relative error of 1%. LC-ωPBE without considering the solvent yields the poorest

result (-6.48 ppm) while TPSSh without solvent performs the best (-0.04 ppm).

Following the trend observed for compounds 11 and 12, the IGLOII basis set performs

more poorly for the 13C NMR signals, as the mean and standard deviation is 12.61 ±

3.12, which translates to an 8 % relative error. In this case, LC-ωPBE without inclusion

of solvent again yields the least accurate results (-18.35 ppm), while TPPS with solvent

is the closest to experiment (-9.12 ppm). Calculation of the chemicals shifts including

relativistic effects via scalar ZORA or ZORA + SOC at the PBE optimized geometries

are reported in Table 5. As observed, the effect of both basis sets and spin orbit coupling

appear to be negligible, since the relative errors vary between 7.0 and 7.6 %.

4.3.4. Effect of exchange-correlation functional and inclusion of relativity.

An interesting effect to evaluate over the three compounds studied is the role of the

exchange-correlation functional, which has caused debate for 19F chemical shifts in

UF6-nCln compounds.[95,97,98] By looking at Tables SI 4, 6 and 7 in section 5 of the SI,

26

one can draw some conclusions. For compound 11, for 1H chemical shifts hybrid

functionals perform better for both basis sets investigated, while for 13C with IGLOII,

GGA (PBE) is the most appropriate. For compound 12, for 1H chemical shifts, the best

and worst performing functionals are hybrid and LC-ωPBE, respectively. For the 13C

with the IGLOII basis set, there is a further dependency on which atoms are described.

Thus, for the furthest located from the uranium centre (the tert-butyl ones), LC-ωPBE

performs best whereas the GGA TPSS functional correctly predicts the chemical shifts

of the closest carbon atom to uranium centre. For compound 13, the best option is TPSS

and the worst LC-ωPBE. Finally, for the spin-spin coupling constants of compound 12,

the best performing is the long-range corrected LC-ωPBE functional and the worst the

hybrid PBE0. In model systems the clear separation seen between GGA, hybrid and

long-range corrected functionals for the description of chemical shifts[95,97,98] may

arise due to the similar chemical environment of all centres. However, for the bigger,

more realistic compounds investigated here, this appears to be not feasible.

We now compare on a one-to-one basis the effect of using pseudopotentials or

ZORA and ZORA+SOC to treat relativistic effects, together with the quality of the

basis sets. Table 5 presents the mean and standard deviation of the relative errors (in

absolute values) associated with each 1H and 13C chemical shift for the three compounds

11 – 13. Those are calculated using the PBE functional, at the corresponding geometry,

with Gaussian09 and ADF2016. Table 5 is complementary to the more detailed Table SI

8 in section 5 of the SI. Supporting previous discussion, the experimental chemical 1H

shifts of compound 11 show a more pronounced variation through the different

methods, as compared to 13C. If one uses pseudopotentials for the uranium centre, the

IGLOII basis set performs the best, whereas including relativistic effects through

ZORA+SOC with the jcpl basis set results in a better agreement and a less dispersed set

of data. Nevertheless, the overall agreement with the different experimental values is

very good. Compound 12 shows a more pronounced variation for the 13C chemical shifts

depending on the approach used, and a worse performance when the IGLOII basis set is

employed. Interestingly, all investigated methods predict a chemical shift for the first 13C signal (7.09 ppm) that is persistently off the experimental value by more than 100%,

except for ZORA+SOC with the jcpl basis set that shows a 35% relative error (see

Table SI 8 in section 5 of the SI and Table 3). Interestingly, this carbon atom is the

closest to the uranium centre (~2.9 Å) and sits between the two phosphorus atoms. This

27

suggests that even if the rest of the chemical shifts are similarly reproduced by the

different methods, only ZORA+SOC with jcpl ensures a good description of the

chemical shifts of all atoms, no matter their surroundings. For compound 13 the

agreement is independent on method and basis sets, at ~7% of relative error.

Surprisingly, the smallest basis set performs noticeably better than larger counterparts.

For all three compounds, including triple- and quadrupole-ζ polarized quality basis sets

(cc-pVTZ and cc-pVQZ, respectively) does not introduce any further improvement.

Gaussian09 a) ADF2016 b)

µ ± σ of |δx| ZORA ZORA-SOC

cc-pVDZ

IGLO-II cc-pVTZ cc-pVQZ DZP jcpl DZP jcpl

11

1H 13.7 ± 13.5

5.4 ±2.6 6.1 ±2.0 6.0 ±4.2 14.3 ±

15.711.4

±11.918.3

±23.7 7.3 ±3.7

13C 3.0 ± 2.3

4.8 ±4.6 5.1 ±4.0 7.2 ±5.2 4.5 ±3.7 3.9 ±

1.8 3.4 ±3.9 5.3 ±2.6

Total 6.5 ± 8.4

5.0 ± 3.8 5.4 ± 3.3 6.8 ± 4.5 7.8 ± 9.1 6.4 ±

6.78.4 ± 13.5 6.0 ± 2.8

12

1H 10.0 ± 6.8

8.4 ± 9.0

9.9 ± 10.4

10.5 ± 10.8 8.7 ± 8.1 9.0 ±

7.9 9.8 ± 8.0 9.5 ± 8.0

13C 15.0 ± 35.7

21.7 ± 43.4

19.8 ± 35.4

23.7 ± 38.3

17.5 ± 46.7

14.1 ± 28.2

13.1 ± 28.3 8.2 ± 9.0

Total 13.1 ± 28.1

16.6 ± 34.6

16.0 ± 28.5

18.7 ± 31.1

14.1 ± 36.8

12.1 ± 22.5

11.8 ± 22.5 8.7 ± 8.5

13 13C 0.2 6.6 7.6 8.8 7.3 7.6 7.0 7.4

Table 5. Average and standard deviation (µ ± σ) of the relative errors (δx, in absolute value) calculated for 1H and 13C chemical shifts with PBE functional, for compounds 11 – 13. a) presents the data

calculated for different basis sets within Gaussian09. b) presents the results obtained when relativistic effects are included either scalar ZORA or spin-orbit ZORA, with DZP and jcpl basis sets.

To sum up, there is no clear recommendation as to which DFT-based approach

provides consistently better results for 1H and 13C chemical shifts, and spin-spin

couplings. However, there are some conclusions that hold for the three compounds

investigated. First, the geometry used does not introduce large deviations for the 1H and 13C chemical shifts, for both Gaussian09 and ADF2016. This is expected since the

different functionals predict very similar geometries, but it contrasts with early results

on the dependence on geometries.[95] Compound 12 has the largest deviations from

experiment, but even so the disagreement rarely exceeds 15%. The relative errors

calculated for compounds 11 and 13 are persistently small. For 1H chemical shifts

calculated with Gaussian09, the IGLOII basis set provides better results than pVDZ

while the opposite holds for 13C shifts. Triple- and quadrupole-ζ polarized quality basis

28

sets perform substantially worse than IGLOII for either case, at least for the PBE

functional. The effect of including relativistic effects via scalar ZORA or ZORA + SOC

in ADF2016 results in a smaller standard deviation of the relative errors for the latter;

however, this effect is not large vs Gaussian09. The use of a relativistic pseudopotential

for describing the inner electrons of uranium performs as well as a description of

relativistic effects via scalar ZORA or ZORA + SOC plus all electron basis sets for

chemical shifts. Therefore, the comparative ease of use and speed of SCF convergence

using the pseudopotential approach with Gaussian09 makes this the best approach for

calculating chemical shifts in these types of closed shell compounds. However, it is

found that the correct description of 13C NMR chemical shifts of carbon atoms close to

the uranium centre requires the use of ZORA+SOC with the jcpl basis set. Our range of

relative errors for 13C chemical shifts agrees with the PBE results from similar studies,

where the role of exchange-correlation is investigated.[101] For spin-spin couplings,

LC-ωPBE with solvent corrections at the geometry optimized with LC-ωPBE appears

the best choice. However, due to the difficulty of obtaining converged structures, the

most appropriate approach would be to use the LC-ωPBE functional at the PBE-D3

optimized geometries.

29

4.4. UV-vis spectra

The UV-vis spectra of compounds 10, 11 and 13 – 15 were simulated using time-

dependent DFT (TD-DFT) within the Gaussian09 and ADF2016 programs, using the

same functionals and basis sets discussed in section 3 and used for the previously

presented results. The geometries are those from our previous optimisations, unless

otherwise indicated. We have also included solvent effects in Gaussian09 for each

geometry through single point calculations with the PCM. Additionally, the

CAMB3LYP functional[59] was employed at the PBE optimized geometries, as it is a

widely used functional for studying optical properties, and has previously been

recommended.[102–106] Therefore, per functional per compound there are four

different UV-vis spectra. The agreement with experiment has been quantified by

calculating the relative error (in %) in the energy position of the experimental maximum

absorbance peak with respect to the transition with the largest oscillator strength for

each functional.

In general, similar conclusions hold for each of the closed-shell compounds 10, 11

and 13 – 15, so we will discuss in detail only the results for compound 14, as a

representative example. Computed data for the other compounds can be found in section

6 of the SI, and the experimental UV-vis spectrum of compound 10 is given in section 7

of the SI. Figure 6 compares the experimental UV-vis spectrum of compound 14 with

those simulated by TD-DFT. An overlapped graphical representation of all spectra

obtained can be found in Figure SI 28 in section 6 of the SI. The geometries used are

from the same functional as for the TD-DFT calculations, except for CAMB3LYP

results which are obtained at the PBE optimized geometry. For each subplot, the

experimental absorbance is compared with the absorbance calculated with the excitation

energies and oscillator strengths predicted by a particular functional, with and without

solvent.

There are two main conclusions that one can derive from Figure 6, and from the rest

of compounds presented in section 6 of the SI. Firstly, using the optimised geometry

with or without dispersion corrections does not modify the curves and the inclusion of

the solvent only modifies the peaks height. Secondly, and more importantly, pure

exchange functionals consistently provide more accurate results (14 % of averaged

relative errors for PBE) while long-range corrected functionals are off by 40 – 50 %.

30

Hybrid functionals lie within these two extremes. This seemingly better performance of

the pure exchange functionals stems from their predicting transitions in the lower

energy regions, whereas long-range corrected functionals largely overestimate these

energies. This is summarized in Table 6 where the relative errors of all the investigated

compounds are presented. Hyphen-containing rows of compounds 10, 11, 13 – 15

denote that the calculation did not converge properly and stopped due to “Excessive

mixing of frozen core and valence orbitals.” Interestingly, these results appear to be in

sharp contrast to the recommendations made for other U(VI) molecules,[102–106] for

which CAMB3LYP functional is favoured.

Figure 6. Predicted UV-vis spectra for compound 14 using Gaussian09. The left y-axis in each subplot presents the calculated absorbance whereas the right y-axis refers to the predicted oscillator strength,

denoted here by vertical lines; x-axis shows the wavelength values in nm. A half-field value of 0.4 eV has been used. The experimental absorbance is shown as black vertical lines, to which an arbitrary shift factor

of 4000 has been applied to facilitate comparison between computed and measured data. The list of relative errors for each functional in the same order as the subplots is [(9,18,14,15),(40,40,41,37),

(22,22,19,20),(32,30),(32,32,34,29),(49,52,50,50),(39,39,40,41)].

31

In order to explore these discrepancies further, we performed TD-DFT calculations

on [UO2Cl4]2-, using pure-exchange (PBE, TPSS) and long-range corrected (LC-ωPBE,

CAMB3LYP) functionals. [UO2Cl4]2- features the UO22+ unit at the heart of all of our

other target systems, and has been previously studied both experimentally and

computationally. The geometry we employ has D4h point group symmetry with U-O and

U-Cl distances of 1.783 Å and 2.712 Å, respectively; these are the same as those

reported by Pierloot et al. in their CASPT2[107] calculations, for which results match

experiment.[108–113] The experimental values that we use as a reference are in Table 2

of reference [111].

Prior to commenting on our results, it is instructive to highlight some

well-understood features of the [UO2Cl4]2- electronic spectrum. It is experimentally

known[108,113] and theoretically supported[107,114] that the lowest energy excitations

(below ~30000 cm-1 = 333 nm) are effectively confined to the orbitals of the uranyl unit,

originating from the σ u HOMO. The more energetic region (~33000 cm-1 = 303 nm) is

assigned to chloride-to-uranyl charge transfers, on the basis of CASSCF data[115] in a

crystalline environment and gas-phase CASPT2[116] calculations. This agrees with

what has been observed for uranyl(VI) aquo ions showing ligand-to-metal charge

transfer (LMCT) at around 272 – 219 nm.[117] However, no clear experimental

information on these LMCT transitions in [UO2Cl4]2- is available. The comparison

between our calculated and the experimental UV-vis spectrum for [UO2Cl4]2- can be

found in Figure SI 31 in section 6 of the SI, and reveals the same behaviour as for

compounds 10, 11 and 13 – 15 (see last row of Table 6). Figure 7a summarizes the

[UO2Cl4]2- results, highlighting the energy range spanned by the orbitals that participate

in electronic transitions with an oscillator strength larger than 0.01. It is clear that:

i) for both pure-exchange and long-range corrected functionals, the predicted

excitation spectra are governed largely by transitions originating from

orbitals centred on the chlorine atoms, as noted previously from DFT

calculations.[106,112–114]

ii) the long-range corrected functionals yield a spectrum with a single

dominant absorption at ~40485 cm-1 = 247 nm and ~35714 cm-1 = 280 nm,

giving an error relative to experiment of 50 and 43% for LCωPBE and

CAMB3LYP, respectively. These excitations are dominated by chloride-to-

uranyl charge transfers, but also feature the πg orbitals of the uranyl unit.

32

iii) pure exchange functionals yield two features involving chloride-to-uranyl

orbitals only: a main one centred at ~23255 cm-1 = 430 nm and ~24096 cm-1

= 415 nm for PBE and TPSS, respectively (relative errors to experiment of

13 and 16%), and a second transition occurring at more-or-less the same

energy as those for long-range corrected functionals, matching the chloride-

to-uranyl charge transfers predicted by CASPT2 results.[116]

iv) the orbitals implicated by the pure exchange functionals span a much

narrower energy range than the long-range corrected functionals, the latter

predicting the πg orbitals of the uranyl to be ~11 eV lower in energy than the

empty f-orbitals. This explains why the excitations predicted by long-range

corrected functionals are much more energetic than the pure functionals (see

Figure SI 31 in section 6 of SI).

Note that we also performed analogous studies on [UO2Cl4]2- at the various

different reported geometries,[103] and found similar results to those summarised

above.

In order to examine the potential role of diffuse functions, we repeated our study of

[UO2Cl4]2- using the aug-cc-pVDZ basis sets for oxygen and chlorine, retaining the

same uranium ECP and basis. The results are almost identical to those obtained without

diffuse functions. Thus, PBE with (and without) diffuse functions predicts two main

electronic excitations at 434 and 305 nm (430 and 301 nm) with the largest oscillator

strengths. On the other hand CAMB3LYP predicts a single electronic excitation at 291

nm (281 nm).

We now turn our attention to our target compounds. The above observations (i)-(iv)

are equally applicable to compound 14, as shown in Figure 7 b), as well as the rest of

U(VI) molecules investigated (see Figure SI 32 for an explicit comparison with

compound 10). An additional feature present in compound 14 is that the spectra

predicted by LC-ωPBE and CAMB3LYP also contain contributions from excitations to

virtual orbitals located entirely on the ligands; this is not found using the pure-exchange

functionals. As in the case of uranyl, we investigate the effect of diffuse functions for

compound 14 and find essentially the same conclusions, except for an electronic

excitation at 252 nm for which the use of diffuse functions reduces its oscillator strength

by one order of magnitude.

33

We therefore conclude that all the forms of TD-DFT we have explored perform

poorly. While the long-range corrected functionals do at least capture some of the

anticipated uranyl character of the transitions, they predict the wrong orbital to be

involved (g as opposed to u) and predict the energy of the transition very poorly. By

contrast, the pure functionals give much better agreement with experiment in terms of

energies, but the character of the predicted transitions is incorrect. We therefore do not

recommend any form of TD-DFT for the simulation of uranyl (VI) electronic absorption

spectra.

Finally, we briefly discuss the results obtained when all-electron basis sets and

scalar relativistic effects are included via the ZORA Hamiltonian. As in Table 6, Table

SI 8 presents the relative error between the energy position of the experimental

maximum absorbance and the largest calculated oscillator strength, using the PBE

functional. These results indicate that, for these compounds, including scalar relativistic

corrections not only does not improve the results obtained with respect to

pseudopotentials but in some cases leads to poorer agreement with experimental

energies.

Relative error (%)Pure exchange Hybrid Long-range correctedPBE TPSS PBE0 TPSSh B3LYP LC-ωPBE CAMB3LYP

compound10 -4 -1 23 10 17 39 3211 - - 4 - - - -13 11 15 36 26 28 - -14 9 22 40 32 32 49 3915 12 - 42 25 28 51 -

[UO2Cl4]2- 13 16 50 43

Table 6. Summary of relative errors in % for the UV-vis spectra of all closed-shell compounds, as predicted by the employed functionals using a pseudopotential in Gaussian09. Note that these results are obtained at the geometries consistent with the TD-DFT method, except for compound 10 and [UO2Cl4]2-

for which we used the experimental structures.

34

Figure 7. Energies and associated orbitals involved in key transitions (oscillator strengths ¿ 0.01) as predicted by the pure exchange PBE and long-range corrected CAMB3LYP functionals. a) [UO2Cl4]2- and b) compound 14 (hydrogen atoms have been omitted for clarity). The energy of the π-type uranyl orbitals

has been set to zero as reference for both cases. Vertical dashed lines separate occupied and virtual orbitals. Red bars indicate the energetic range involved in the orbitals taking part in the most relevant

excitations.

35

5. Conclusions

In this contribution, we have performed a detailed investigation of the performance

of a range of DFT methodologies for the description of the ground and excited state

properties of a series of representative uranium-based molecules, comparing our results

with experimental data throughout. The molecules investigated cover a wide variety of

oxidation states and ligand types, ensuring the generality of the conclusions, the

principal ones of which are:

The most robust approach to obtain accurate geometries is to employ the PBE

functional with dispersion corrections.

The principal factor guiding the choice of functional for calculating IR spectra is

the functional which consistently predicts the most accurate molecular

structures, i.e. PBE. By contrast, there is no clear recommendation as to which

functional to use when seeking accurate Raman spectra, although PBE also

generally performs a little better than the other functionals tested.

For NMR parameters of closed shell U(VI) species, no DFT based approach

provides consistently reliable results for 1H and 13C chemical shifts and spin-spin

couplings, although we can make some general observations: i) Among the

investigated approaches, the disagreement with experiment of the averaged 1H

and 13C chemical shifts rarely exceeds 15% for the three compounds ii) the

geometry employed has relatively little effect on the 1H and 13C chemical shifts

iii) The NMR-specific IGLOII and jcpl basis sets provide the best results

overall; increasing the quality of the basis set to include triple- and quadrupole-ζ

polarization does not bring any improvement iv) for the 13C chemical shifts,

PBE0 and TPSS often perform worse than other functionals v) for spin-spin

couplings, LC-ωPBE with solvent corrections at the geometry optimized with

LC-ωPBE works best (albeit based on a small data set) vi) the inclusion of

relativistic effects via scalar ZORA + SOC results in a less dispersed set of

results for 13C NMR signals vs scalar ZORA vii) ZORA + SOC with jcpl basis

sets is required for a balanced description of the chemical shifts of all NMR

active atoms in the molecule.

No form of TD-DFT performs acceptably in predicting both the character and

energies of the electronic excitations of uranyl (VI) compounds.

36

The use of a pseudopotential on the uranium centres provides equal, if not better,

agreement with experiment vs all-electron basis set calculations, for all

properties investigated.

We are now extending our study to the calculation of the electronic excitation

energies and magnetic properties of both our closed- and open-shell targets using

wavefunction-based approaches, and these results will be reported in a forthcoming

paper.

6. Acknowledgements.

We thank the STFC for funding (DR and FO) and the University of Manchester’s

Computational Shared Facility for computational resources. We also thank Henry

Storms La Pierre for ideas, help and advice with the synthesis of compounds 9, 10 and

17 and Karsten Meyer for providing a studentship placement for SR. We are grateful to

the EPSRC for funding a Career Acceleration Fellowship (LSN) and a studentship (SR)

(grant number EP/G004846/1). We also thank the Leverhulme Trust for additional

postdoctoral funding (FO) (RL-2012-072) and a research Leadership award (LSN). This

work was also part funded by the EPSRC (grant number EP/K039547/1)

37

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