Norm-Conserving Pseudopotentials and Basis Sets Optimized

doi.org/10.26434/chemrxiv.8246498.v2

Norm-Conserving Pseudopotentials and Basis Sets Optimized forLanthanide Molecules and Solid-State CompoundsJunbo Lu, David Cantu, Manh-Thuong Nguyen, Jun Li, Vassiliki-Alexandra Glezakou, Roger Rousseau

Submitted date: 21/09/2019 • Posted date: 26/09/2019Licence: CC BY-NC-ND 4.0Citation information: Lu, Junbo; Cantu, David; Nguyen, Manh-Thuong; Li, Jun; Glezakou, Vassiliki-Alexandra;Rousseau, Roger (2019): Norm-Conserving Pseudopotentials and Basis Sets Optimized for LanthanideMolecules and Solid-State Compounds. ChemRxiv. Preprint.

A complete set of pseudopotentials and corresponding basis sets for all lanthanide elements are presentedbased on the relativistic, norm-conserving, Gaussian-type pseudo potential protocol of Goedecker, Teter, andHutter (GTH) within the generalized gradient approximation and exchange-correlation functional of Perdew,Burke, and Ernzerhof. The accuracy and reliability of our GTH pseudopotentials and companion basis setsoptimized for lanthanides is illustrated by a series of test calculations on lanthanide-containing molecules andsolid-state systems.

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1

Norm-conserving pseudopotentials and

basis sets optimized for lanthanide

molecules and solid-state compounds

Jun-Bo Lua, c, David C. Cantub, Manh-Thuong Nguyenc, Jun Lia*, Vassiliki-Alexandra Glezakouc*, Roger Rousseauc*

aDepartment of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China; bChemical and Materials Engineering, University of Nevada, Reno, Reno, Nevada 89557, USA; cBasic and Applied Molecular Foundations, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA *Corresponding authors: [email protected], [email protected], [email protected]

ABSTRACT

A complete set of pseudopotentials and accompanying basis sets for all lanthanide elements are

presented based on the relativistic, norm-conserving, separable, dual-space Gaussian-type

pseudopotential protocol of Goedecker, Teter and Hutter (GTH) within the generalized gradient

approximation (GGA) and the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE).

The corresponding basis sets have been molecularly optimized (MOLOPT) using a contracted form

with a single set of Gaussian exponents for s, p and d states. The f states are uncontracted explicitly

with Gaussian exponents. Moreover, the Hubbard U values for each lanthanide element, to be used in

DFT+U calculations, are also tabulated, allowing for the proper treatment of the strong on-site Coulomb

interactions of localized 4f electrons. The accuracy and reliability of our GTH pseudopotentials and

companion basis sets optimized for lanthanides is illustrated by a series of test calculations on

lanthanide-centered molecules, and solid-state systems, with the most common oxidation states. We

anticipate that these pseudopotentials and basis sets will enable larger-scale density functional theory

calculations and ab initio molecular dynamics simulations of lanthanide molecules in either gas or

condensed phases, as well as of solid state lanthanide-containing materials, allowing to further explore

the chemical and physical properties of lanthanide systems.

2

1. INTRODUCTION

Research on lanthanide chemistry, physics, and materials is an active area due to the unique

properties lanthanides that primarily arise from their extremely localized 4f electrons.1-3 The presence of

lanthanides in materials results in interesting optical, luminescent, magnetic, or superconducting

properties, as well as medical contrast agents, and catalysts.4-14 The rapid development of computational

technology and electronic structure theory has enabled the modeling of the physical and chemical

properties of lanthanide-based systems. Density functional theory (DFT) in particular, when

supplemented with the appropriate pseudopotentials, can be a highly effective method for modeling

lanthanide-containing systems with reduced computational costs.15-16 Furthermore, the relativistic effects

in heavy elements can be built into the pseudopotential parameterization. For condensed phase codes,

pseudopotentials are a requisite, often accompanied by large plane wave basis sets required to model core

electrons.

Several quantum chemistry groups have developed lanthanide pseudopotentials that are reported in

the literature. Examples include: (i) Dolg et al., derived energy-consistent small-core and f-in-core

pseudopotentials for lanthanides.15-18 (ii) Ross et al., developed norm-conserving pseudopotentials with

54 core electrons.19 (iii) Cundari et al., proposed that 46-electron core pseudopotentials provide the best

compromise between computational savings and chemical accuracy.20 (iv) Hay and Wadt report a 54-

core electron pseudopotential for lanthanum.21 Although the mentioned pseudopotentials have been

widely used by the quantum chemical community, most electronic structure calculations with lanthanides

include less than ~100 atoms.22-23 Besides gas phase calculations, lanthanides in solution have been

modeled with the first solvent shell explicitly24-27, and solid-state calculations with lanthanides28 and

actinides29 have been performed as well. Modeling lanthanides in the solid or condensed phases requires

plane waves and pseudopotentials that, in principle, enable large scale calculations (i.e., 102-103 atoms

with periodic boundary conditions, with full explicit solvent boxes and/or in the condensed phase), and

molecular sampling from ab initio molecular dynamics (AIMD), which can be used to determine physical

and chemical properties of lanthanide-containing systems.13, 30 Bachelet, Hamann, and Schüler were the

first to publish a set of norm-conserving pseudopotentials for all elements up to Pu,31 later followed by

Harwigsen, Goedecker and Hutter.32-33

3

In the late 90s, Goedecker, Teter and Hutter (GTH) proposed a dual-space Gaussian-type

pseudopotential that is separable and satisfies a quadratic scaling with respect to system size.32-33 The

employment of GTH pseudopotentials in a mixed Gaussian-planewave scheme has proven to be an

effective and efficient way to perform AIMD simulations.34 Accurate GTH pseudopotentials are available

for most elements,32-33, 35 except for lanthanides and actinides due to the way that their f states were

included into the fitting procedure of the potentials, which in effect removed their variational flexibility.

This problem becomes most acute when dealing with multiple oxidation states, since a change in redox

state will induce a change in the electronic structure of the f orbitals. This compromises the transferability

of the pseudopotentials and limits their use in many chemical applications.

Recently, cerium pseudopotentials and basis sets were optimized to study the surface properties of

ceria.36-37 It was demonstrated that a full inclusion of f states into the fitting procedure can result in highly

transferable, though computationally expensive, potentials.37 However, accurate GTH pseudopotentials

and basis sets for the remaining lanthanides are still lacking, preventing larger-scale DFT calculations

and AIMD simulations of lanthanide-containing systems in the condensed phase or solid state.

The objective of this work is to fill this critical gap by producing a full set of well benchmarked

pseudopotentials for the entire lanthanide series along with the corresponding Gaussian basis sets.

Although these same potentials could be used as a starting point for higher levels of approximation to the

electronic structure, our goal is to provide a reliable tool for simulating condensed phase systems

including bulk solids, surfaces, and molecular species in gas and solution at a gradient corrected DFT

level of theory. Hence, we report our optimized GTH pseudopotentials and corresponding basis sets with

uncontracted valence 4f states with Gaussian exponents. For the late lanthanides (Tb to Lu), the 4d10

configuration is treated as a semi-core state. Also, as the on-site Coulomb interactions are particularly

strong for localized 2p, 3d and 4f electrons due to the quantum primogenic effect,38 we determined the

corresponding Hubbard term (+U) values based on the third ionization potential. The accuracy of our

lanthanide GTH pseudopotentials and basis sets with uncontracted f states is illustrated by a series of

benchmarks on lanthanide molecules in the gas phase and solid-state.

2. THEORETICAL AND COMPUTATIONAL METHODOLOGY

2.1 GTH pseudopotentials and MOLOPT basis sets

The norm-conserving, separable, dual-space GTH pseudopotentials comprises of two parts.32, 35 A

4

local part given by:

𝑉"#$%%(𝑟) = −+,-.

/erf(a33𝑟) + ∑ 𝐶7

%%87 9√2a33𝑟<

=7>=´exp[−(a33𝑟)=] (Eq. 1)

where,

a33 = D√=/E-F

GG (Eq. 2)

where 𝑟"#$%% is the range of the Gaussian ionic charge distribution.

A non-local part given by:

𝑉H"%%(𝒓, 𝒓K) = ∑ ∑ < 𝒓|𝑝7"O > ℎ7R" < 𝑝R"O|𝒓′ >7R"O (Eq. 3)

in which Gaussian-type projectors are:

< 𝒓|𝑝7"O >= 𝑁7"𝑌"O(𝑟)𝑟"V=7>=𝑒𝑥𝑝 Y−D=(//E)=Z. (Eq. 4)

where 𝑁7"is a normalization constant, and 𝑌"O is a Laplace’s spherical harmonic.

These pseudopotentials have optimal decay properties in both real space and Fourier space,

which can be calculated analytically, and are critical for condensed phase calculations.32 VandeVondele

and Hutter39 proposed molecularly optimized (MOLOPT) Gaussian basis sets with analytical dual-

space GTH pseudopotentials, where all angular-momentum functions share the same exponents in

MOLOPT basis sets.

We followed the general procedure shown in Figure 1 to optimize the lanthanide GTH

pseudopotentials and corresponding MOLOPT basis sets. Our derivation of lanthanide GTH

pseudopotentials closely follows the scheme by Goedecker et al.32-33 First, we fitted the pseudopotential

parameters to obtain the best representation of orbital eigenvalues and charge density of the atomic

ground states. The f states were handled by explicitly fitting the non-local projectors in each step of the

pseudopotential optimization. The GTH pseudopotential parameters, for the ubiquitously used PBE

functional, were optimized with respect to atomic all-electron wavefunctions, obtained from fully

relativistic density functional calculations specificly modified to directly fit the f states, as originally

proposed.33 For the fitting process, we used a weighted average of Kohn-Sham eigenvalues, radial

densities, and location of the radial nodes. The weights of these factors were heaviest on the semi-core

states (5s, 5p, 4d), one order of magnitude lower than the valence states (6s, 6d, 5d, 4f), and a further

reduction of one order of magnitude for the virtual states. Typical differences between the optimized

orbital enegies of pseudo-wavefunctions and all-electron wavefunctions in the valence region were ~10-

5

4-10-5 Hartree, and ~10-3 Hartree for unoccupied orbitals. Given the large impact of the rloc parameter

on the fitting procedure with respect to all other parameters, we fitted the potentials by first fixing rloc

and relaxing all other parameters, then choosing the best fit from the resulting series of potentials. We

uncontracted the f states with additional Gaussian exponents. We previously followed this scheme to

produce accurate calculations for cerium.37 The contraction coefficients of the s, p, and d states were

optimized to minimize the objective function, which consists of energies and condition numbers of the

overlap matrix of training molecules. The resulting pseudopotentials and basis sets appear in the

Supporting Information (SI), as well as a more detailed discussion about the optimization procedures

in Part A of the SI, Tables S1-S3.

Figure 1. Our general procedure to generate, optimize and benchmark the GTH pseudopotentials and

companion basis sets.

2.2 Computational methodology

6

We used CP2K (version 4.1) and CPMD (version 4.1) for benchmarking the optimized

pseudopotentials and basis sets.40-43 To assess pseudopotential transferability, we calculated two redox

reaction energies, and compared results with all-electron calculations performed with the standard

quantum chemistry software ADF (version 2016.106) that uses Slater-type basis functions.44 Noting

that the most stringent test of the transferability of a pseudopotential is its ability to reproduce the energy

of redox chemistry, we focused on two prototypical reactions, chosen to represent the most common

spin and oxidation states that dominate lanthanide chemistry:

LnCl +12Cl= = LnCl=(𝑅1)

LnCl= +12Cl= = LnCla(𝑅2)

An ionic model of LnCl, LnCl2, LnCl3 is assumed where chlorine atoms are treated as closed-shell

anions, and the lanthanide including all the spin density with electrons occupying the same orbitals as

a lanthanide cation.45 The electron configurations of lanthanide ions followed Peterson’s work.46 The

electron configurations of LnCl, LnCl2 and LnCl3 are depicted in Table S4 of the SI. LnCln (n = 1 – 3)

and Cl2 structures were optimized using Gaussian47 (version Gaussian09 D.01) at the PBE48 level. We

use the same geometries (calculated with Gaussian) to compare the redox reaction energy for ADF and

CP2K for consistency. After we get optimized pseudopotential and basis sets, we use the optimized

geometries and computed the reaction energetics (Table S11). Relativistic effects were included using

the ECP28MWB Ln effective core potentials (ECP).16 We used the ECP28MWB_SEG basis sets for Ln

atoms and cc-pVTZ basis sets for Cl.16, 49 Minima were confirmed by vibrational analysis that resulted

in all positive normal modes of the optimized geometries.

Using these optimized geometries, we performed PBE single-point calculations with the ZORA

relativistic correction and TZ2P all-electron basis sets for Ln and Cl.50-55 Three different schemes were

tested to compute the reaction energetics of lanthanides, with reactions R1 and R2 as reference points

using ADF, see detailed discussion in Part B of the SI, Table S5. Scheme 3 (Fermi-Dirac), which is

closer to the smearing algorithm in CP2K, was also used to calculate R2 reaction energetics and bond

energies of 3d transition metals, see Tables S6 and S7 in the SI. In both cases, mean average deviations

are quite small, 0.9 kcal/mol for reaction energies and 3.8 kcal/mol for bond energies.

In CP2K, reaction energies were calculated with molecules placed in cubic boxes with cell lengths

7

of 20 Å, which allows modeling isolated molecules in a periodic code. A cutoff distance of 800 Ry was

chosen, based testing with Ce and Tb (Tables S8 – S9 in the SI). The energetics of the two reactions

were also calculated in CPMD42-43, with a wavefunction cutoff of 250 Ry.

Additional benchmark calculations were performed with CP2K to test the new GTH

pseudopotentials and basis sets with uncontracted f states for molecules and solids. We used a cutoff of

800 Ry owing to the very tight cores of the resulting potentials which necessitate a large number of

plane waves to represent their core densities. Non-periodic conditions were used with molecular tests,

except for enthalpies of formation where all calculations were done with uncharged boxes in periodic

conditions. Periodic conditions were also used for solid state calculations. Results were compared to

relativistic, all-electron reference calculations performed with ADF or to published all-electron

calculations, as well as to experimental data when available.

3. RESULTS AND DISCUSSION

3.1 Pseudopotential transferability and reaction energies

The lanthanide series starts (La) with the ground states of the 4f orbitals empty, and ends (Lu) with

them fully filled. The 6s orbital is fully occupied in the ground state configuration for all lanthanides.

The 5d orbitals are occupied by one electron for La, Ce, Gd, and Lu. The 4f orbitals lie energetically

above the 5s and 5p orbitals, and are partially occupied for nearly all lanthanides. Because of increased

effective nuclear charge, the 4f orbitals become more and more contracted from La to Lu as shown in

Figure 2b. Generally, for lanthanides, the 4f, 5d and 6s orbitals are treated as valence orbitals, and the

semi-core 5s and 5p orbitals expand into valence region too, as shown in Figure 2a. Therefore, the 5s

and 5p orbitals are treated as semi-core states in the “large-core” pseudopotential scheme.

Hartwigsen and co-workers published the first relativistic GTH pseudopotentials for lanthanides,33

and their large-core GTH pseudopotentials and MOLOPT basis sets are included in CP2K data library

(LnPP0 hereafter). However, the existing LnPP0 pseudopotentials and basis sets do not replicate redox

reaction energies, which motivated our work.

8

Figure 2. (a) Radial densities D(r) = r2R(r)2 for 4d, 5s, 5p, 4f, 5d and 6s orbitals of atomic ions Sm3+.

(b) Radial densities r2R(r)2 of 4f orbitals from La3+ to Lu3+.

To test the transferability of the pseudopotentials and basis sets, we calculated the R1 and R2

reaction energies with lanthanide ions in the +1, +2 and +3 oxidation states. Table 1 compares reaction

energies obtained with the LnPP0 GTH pseudopotentials with their corresponding ADF results that

serve as a comparison point. Reaction energies do not match those computed with ADF when using the

basis sets with contracted s, p, d and f states, since results underestimate reaction energies with early

lanthanides and overestimate them for the late lanthanides. We uncontracted the f states by using the

Gaussian exponents from the CRENBL ECP basis set,19 as previously done for cerium by our group.37

By using the uncontracted f states, we reduced the error significantly for the early lanthanides (La to

Gd). However, the reaction energetics of late lanthanides (Tb to Yb) are still overestimated compared

to the ADF reaction energies (Table 1). Therefore, uncontracting the f states in the LnPP0 basis sets

improves their reaction energy accuracy for early lanthanides, but significant errors remain for late

lanthanides.

9

Table 1. Reaction energies (kcal/mol) with previously existing LnPP0 lanthanide pseudopotentials and

basis sets at the PBE level. Error calculated with respect to the reaction energies computed with ADF.

f contracteda f uncontractedb Contracted errorc Uncontracted errorc R1 R2 R1 R2 R1 R2 R1 R2

La -90.3 -89.3 -90.3 -89.3 3.9 0.8 3.9 0.8 Ce -89.8 -70.5 -91.3 -81.2 1.6 14.0 0.1 3.3 Pr -83.9 -56.2 -85.9 -73.3 3.0 20.4 0.9 3.2 Nd -80.4 -43.0 -80.3 -61.0 -0.8 26.8 -0.6 8.7 Pm -79.6 -59.4 -82.9 -66.8 0.2 4.0 -3.0 -3.4 Sm -82.6 -28.9 -81.3 -37.0 -5.2 19.5 -3.8 11.3 Eu -76.7 -13.4 -76.6 -20.3 -1.7 19.9 -1.5 13.1 Gd -89.8 -83.4 -88.1 -81.9 3.8 0.4 5.3 1.9 Tb -73.1 -95.7 -73.7 -93.1 -3.0 -13.2 -3.6 -10.6 Dy -78.6 -95.6 -76.7 -95.5 -4.4 -29.5 -2.5 -29.4 Ho -77.4 -93.2 -76.9 -91.8 -4.4 -28.3 -3.9 -26.9 Er -72.2 -94.5 -71.0 -93.8 -2.1 -27.6 -0.9 -26.9 Tm -75.6 -75.0 -74.5 -81.8 -3.3 -22.9 -2.2 -29.8 Yb -77.6 -58.2 -72.8 -72.2 -3.7 -18.8 1.1 -32.7 Lu -72.0 -89.9 -70.3 -88.3 0.5 -4.8 2.2 -3.2

MADd

2.7 kcal/mol

16.7 kcal/mol

2.4 kcal/mol

13.7 kcal/mol

a f states contracted using the same Gaussian exponents with s, p and d states. b f states uncontracted using different Gaussian exponents with s, p and d states. c Error = (ECP2K – EADF). Contracted error means the error using contracted basis set. Uncontracted error means error using f

state uncontracted basis set. d Mean absolute deviation. MAD = ∑ |Ei|/N7 where Ei is the error for each lanthanide element, and N is number of

lanthanide elements.

As demonstrated by Goedecker and Maschke, pseudopotential transferability is related to the

existence of a region around the nuclei where its charge density is practically independent of the

chemical environment.56 The ideal choice of the cutoff radius (rc) is one that distinguishes these two

regions. Core electrons should reside exclusively within an inert region,56 where charge density does

not change in different chemical environments. The significant errors in Table 1 are likely due to the

fact that an inert region was not identified in the LnPP0 large-core pseudopotentials. Noticeably,

uncontracting the f states did not improve results for dysprosium. Therefore, we generated tighter norm-

conserving GTH pseudopotentials, especially for the late lanthanides where the LnPP0 pseudopotentials

are less accurate.

The semi-core state is also important for lanthanide pseudopotentials. Dolg and co-workers found

10

that the most accurate pseudopotentials include all orbitals with the same main quantum number as the

conventional valence orbitals (e.g., 4s, 4p, 4d, 4f in valence).15-17, 57 Transferable pseudopotentials have

clearly delimited core and valence regions, making it possible to replace the core electrons with a norm-

conserving potential. This is a challenge for the lanthanides, since the f states are close to the core but

should be considered as part of the valence, as shown by the spatial overlap between the 4d orbitals and

4f orbitals (Figure 2a). This effect is even more pronounced for the late lanthanides due to contraction

(Figure 2b).

Figure 3. The Rmax of 4s, 4p, 4d and 4f orbitals derived from numerical Dirac-Fock calculations. For

(a), j = l + D=; for (b), j = l - D

=.

To compare the orbital properties of 4s, 4p, 4d, and 4f orbitals quantitatively, we obtained the

radius of maximum radial densities (Rmax) of these orbitals (Figure 3) with numerical relativistic Dirac-

Fock calculations.58 We found no significant boundary between the 4f and 4d orbitals for Tb to Lu.

Therefore, the spatial correlation between the 4d and 4f orbitals is highly relevant due to the

compactness of 4f orbitals, as has been discussed by Gomes and co-workers.59 The high correlation

between 4d and 4f orbitals likely explains the reaction energy results with the LnPP0 large-core

lanthanide pseudopotentials (Table 1).

For increased accuracy, the 4s, 4p and 4d orbitals are usually treated as semi-core states near the

valence space. Since pseudopotentials with semi-core wave functions are computationally more

expensive, a balance between chemical accuracy and computational cost has to be met. Therefore, we

included the more relevant 4d10 configuration as a semi-core state, while keeping the 4s and 4p states

11

in the core, as there is significant boundary between 4d and 4s, 4p orbitals (Figure 3). We tested different

rloc values with Tb to define our pseudopotentials, details in Table S10 of the SI. To facilitate discussion,

we classified pseudopotentials by their cores (Table 2). As example for Ce, detailed definitions of three

different core-region pseudopotentials are depicted in Table 2.

Table 2. The electronic configurations of core, semi-core and valence region for small-core, medium-core and large-core pseudopotentials for Ce.

Core type Corea Semi-core Valence Small-core [Ar]3d10 4s24p64d105s25p6 4f15d16s2

Medium-core [Kr] 4d105s25p6 4f15d16s2 Large-core [Kr]4d10 5s25p6 4f15d16s2

a [Ar] and [Kr] mean the electronic configurations of Ar and Kr atoms.

We adopted a large-core pseudopotential scheme for the early lanthanides (La to Gd), and a

medium-core scheme for the late lanthanides (Tb to Lu). Our new GTH pseudopotentials, and

corresponding MOLOPT basis sets with uncontracted f states, are displayed in Part F of the SI.

The energies of the two redox reaction (R1 and R2), computed using our new GTH

pseudopotentials and basis sets in both CP2K and CPMD, are listed in Table 3. Errors with respect to

ADF all-electron calculations are considerably smaller: less than 5% for all lanthanides except Nd and

Dy. Notably, reaction energies for late lanthanides are not being significantly overestimated, a result

that is consistent with our discussion about the overlap between the 4d and 4f orbitals (Figure 3). Based

on this, we suspect that results for Nd and Dy could be further improved with medium-core and small-

core pseudopotentials, respectively.

Our new GTH pseudopotentials and MOLOPT basis sets with uncontracted f states (LnPP1

hereafter) show accuracy of 2-3 kcal/mol (mean absolute deviation) when using CP2K. As a comparison,

we also include results with CPMD (Table 3), using planewave basis sets. In principle, results should

be converging to the same values at the limit of complete Gaussian or planewave basis sets. However,

the ability to control the final electronic state during the initial guess and self-consistent field procedure

differs between the two codes, and this control is critical for the electronic structure of the f-block

elements. Compared with Gaussian basis sets, very large planewave basis sets have difficulty

converging to the same states with tightly contracted 4f orbitals, as shown in Table 3.

12

Table 3. Reaction energies (kcal/mol) with our new LnPP1 GTH lanthanide pseudopotentials and

MOLOPT basis sets with uncontracted f states, at the PBE level. Mean absolute deviations (MAD) are

calculated with respect to the reaction energies calculated with ADF.

CP2K CPMD CP2K error CPMD error R1 R2 R1 R2 R1 R2 R1 R2

La -89.7 -88.6 -85.7 -50.9 4.4 1.5 8.4 39.3 Ce -88.5 -85.4 -76.9 -63.8 2.9 -0.9 14.5 20.7 Pr -85.7 -73.8 -76.9 -46.3 1.1 2.8 9.9 30.3 Nd -77.6 -62.3 -72.9 -43.0 2.1 7.4 6.7 26.7 Pm -80.6 -61.9 -77.1 -53.5 -0.8 1.5 2.7 9.9 Sm -78.9 -48.4 -72.7 -29.2 -1.4 -0.0 4.7 19.1 Eu -75.9 -32.3 -72.0 -8.1 -0.9 1.0 3.0 25.2 Gd -89.3 -81.3 -87.4 -80.8 4.2 2.5 6.1 3.0 Tb -68.4 -83.6 -69.9 -92.6 1.7 -1.0 0.2 -10.0 Dy -76.4 -60.9 -70.7 -24.7 -2.1 5.3 3.5 41.5 Ho -71.8 -65.3 -72.3 -74.1 1.3 -0.4 0.8 -9.1 Er -67.6 -68.6 -78.0 -82.7 2.5 -1.7 -7.9 -15.8 Tm -74.0 -50.1 -68.7 -62.9 -1.7 2.0 3.6 -10.8 Yb -71.6 -41.0 -67.7 -45.8 2.2 -1.6 6.1 -6.4 Lu -67.7 -87.2 -72.5 -83.3 4.8 -2.1 -0.1 1.8

MAD

2.3 kcal/mo

l

2.1 kcal/mo

l

5.2 kcal/mo

l

18.0 kcal/mo

l

3.2 Molecular tests

We performed tests on molecules in the gas phase to check the accuracy of our new LnPP1 GTH

pseudopotentials and companion MOLOPT basis sets. These include lanthanide aqua-ions [Ln(H2O)n]3+,

lanthanide chloride geometries, Ln-Cl bond energies, as well as enthalpies of formation of lanthanide

chlorides, fluorides and LnO. Results show small errors compared to experiment and all-electron

methods.

The geometry optimization results of lanthanide aqua-ions [Ln(H2O)n]3+, (Ln = La – Lu, n = 8, 9)

are presented in Table 4 and Figure 4. The coordination number (CN) represents the number of water

molecules in the first coordination sphere of the lanthanide ion (Table 4). A CN of nine was observed

for La to Sm, and a CN of eight for Eu to Lu, in agreement with the reported values for La and Lu.24

Average Ln-O bond lengths calculated with our new pseudopotentials and basis sets are consistent with

previous findings24, 26-27, 60, except for slightly larger bond lengths (~1% for the early lanthanides and

13

~2% for the late lanthanides, Table 4, Figure 4). The lanthanide contraction quantified as the difference

between the average Ln-O bond lengths of La(H2O)93+ and Lu(H2O)8

3+, is 0.210 Å. This result is in

excellent agreement with published electronic structure calculations using four-component relativistic

Hartree-Fock (0.210 Å), MP2 (0.210 Å), and small-core pseudopotential (0.207 Å).24, 61

Table 4. Average Ln-O bond lengths (Å) and binding energies (kcal/mol) of lanthanide aqua-ions

(Ln(H2O)n3+, Ln = La – Lu, n = 8, 9).

CN

Bond Length Binding Energy Error ADF CP2K ADF CP2K Bond Lengtha Binding Energyb

La 9 2.59 2.62 -57.2 -58.2 0.03 -1.0 Ce 9 2.57 2.59 -59.3 -59.7 0.02 -0.4 Pr 9 2.54 2.57 -61.3 -61.1 0.03 0.2 Nd 9 2.53 2.55 -63.2 -62.4 0.02 0.8 Pm 9 2.52 2.54 -64.0 -62.8 0.02 1.2 Sm 9 2.51 2.53 -63.5 -63.4 0.02 0.1 Eu 8 2.45 2.50 -67.8 -68.5 0.05 -0.7 Gd 8 2.43 2.46 -67.4 -67.6 0.03 -0.2 Tb 8 2.42 2.47 -69.4 -68.1 0.05 1.3 Dy 8 2.41 2.46 -71.4 -68.0 0.05 3.4 Ho 8 2.39 2.44 -73.4 -68.2 0.05 5.2 Er 8 2.38 2.44 -74.4 -69.2 0.06 5.2 Tm 8 2.38 2.43 -73.4 -69.4 0.05 4.0 Yb 8 2.37 2.43 -73.1 -70.3 0.06 2.8 Lu 8 2.35 2.41 -72.7 -71.1 0.06 1.6

MAD 0.04 Å 1.9 kcal/mol a. Error of bond length is calculated by LCP2K - LADF, where L is bond length. b. Error of binding energy is calculated by ECP2K - EADF, where E is binding energy.

14

Figure 4. Average Ln-O bond lengths in Ln(H2O)n3+ (Ln = La – Lu, n = 8, 9).

Our new LnPP1 pseudopotentials and basis sets also reproduce the structure of lanthanide chloride

compounds (LnCln, n = 1 – 3), within 0.04 Å for bond lengths and within 2 degrees for bond angles

compared to optimized geometries using with all-electron calculations. Tables S12 and S13 in the SI

show the average bond lengths and angles of the optimized structures obtained with ADF using all-

electron methods and our LnPP1 pseudopotentials and basis sets with CP2K.

From the optimized structures we also calculated the homolytic bond Ln-Cl dissociation energies

in LnCl3 (Ln = La – Lu) using reaction reaction 3:

LnCla = LnCl= + Cl(𝑅3)

Reactions 2 and 3 differ by a constant amount representing half the atomization energy of

dichlorine (61.6 kcal/mol, close to the well-known Cl-Cl bond energy of ~58.0 kcal/mol) and the

relative errors (both reactions with respect to ADF values) is ~4.0 kcal/mol. The M-Cl bond

dissocitation energy errors with lanthanides are similar to those computed for 3d transition metal

chlorides, see Part B of the SI.

15

Table 5. Ln-Cl bond energies (kcal/mol) in LnCl3 (Ln = La – Lu) calculated with our LnPP1

pseudopotentials and basis sets (CP2K) and all-electron (ADF), both with the PBE functional.

ADF CP2K Error La -125.0 -119.4 5.6 Ce -119.3 -116.2 3.1 Pr -111.4 -104.6 6.8 Nd -104.6 -93.1 11.5 Pm -98.2 -92.7 5.5 Sm -83.1 -79.2 3.9 Eu -68.1 -63.1 5.0 Gd -118.6 -112.1 6.5 Tb -117.4 -114.4 3.0 Dy -101.0 -91.7 9.3 Ho -99.8 -96.1 3.7 Er -101.7 -99.4 2.3 Tm -86.9 -80.9 6.0 Yb -74.3 -71.8 2.5 Lu -120.0 -118.0 2.0

MAD 5.1 kcal/mol

We calculated the formation enthalpies of LnCln (n = 2, 3), LnFn (n=1, 2, 3), and LnO, which are

part of the LnHF54 data set compiled in 2016 by Grimmel et al., where they performed all-electron

calculations on the enthalpies of formations with many functionals, including PBE.45 Results show that

the MADs of our LnPP1 pseudopotentials and basis sets with respect to experiment are very similar to

those reported by Grimmel et al., using the PBE functional. Only the lanthanide molecules with known

experimental enthalpies of formation were calculated. Except for the Ln oxidation state of +1 (LnF),

our calculated results have similar accuracy to all-electron methods. It should be noted that the all-

electron calculations performed by Grimmel et al., are based on single molecules as a gas phase

reference, and our CP2K calculations were performed under periodic conditions with uncharged boxes

and include an empirical fit to experiment, with predictive value throughout the lanthanide series, see

Part D of the SI for details, where Tables (S14 to S19) with all the computed enthalpies of formation

are reported as well.

16

Table 6. Computed MAD values for enthalpies of formation using CP2K with our LnPP1

pseudopotentials and basis sets with respect to experiment, and previously done with all-electron45 with

respect to experiment. Both methods used the PBE functional.

CP2K – Experiment MAD (kcal/mol)

All-electron – Experiment MAD (kcal/mol)

LnCl3 7.8 9.6 LnCl2 18.6 8.0 LnF3 28.1 34.4 LnF2 3.6 11.9 LnF 33.8 4.7 LnO 6.1 23.0

3.3 Solid state tests

Considering the importance of lanthanides in materials science, we tested our LnPP1

pseudopotentials and basis sets in the solid state with lanthanide bulk metals. As calculating solid metals

is computationally expensive, we limited our tests to La, Eu, Gd and Er for which there are experimental

data. The calculated lanthanide metal crystal lattice constants are listed in Table 7, and the work

functions and surface energies of the (001) surface, computed using slabs made up with of 5 x 5 x 3

layers in periodic conditions, are reported in Table 8. We calculated work functions as VH - εF, where

VH is the one-particle Hartree potential away from the surface and εF is Fermi level of the lanthanide

surface. The surface energies were computed as:

𝜎 = hiEjk>lmhknEo=p

(Eq. 5)

in which 𝐸r"st is is the energy of the slab, 𝛿𝐸tv"w is the enegy of each atom in the bulk, N is the

number of atoms in the slab, and 2A is the total surface area on both sides of the slab.

Fortunately, theoretical and experimental data on lanthanide surface energies and work functions

are known.62-69 The calculated crystal lattice constants are within ~0.12 Å of experiment (Table 7). The

work functions calculated with our pseudopotentials and basis sets have a mean absolute deviation of

0.12 eV (2.77 kcal/mol) with respect to experimental values, and the surface energies calculated have a

mean absolute deviation of 0.21 J/m2 from experiment, as shown in Table 8. The values calculated with

our LnPP1 GTH pseudopotential and basis sets are also comparable to published theoretical results, see

17

Table 8.

Table 7. Crystal lattice constants (Å) calculated with our LnPP1 GTH pseudopotentials and basis sets

with uncontracted f states, at the PBE level.

Crystal Structure

Geometry (CP2K) Geometry (Expt.)a Errorb a0 c0 a0 c0 a0 c0

La Hcp 3.89 6.05 3.75 6.07 0.14 0.02 Eu Bcc 4.37 4.48 4.61 4.61 -0.24 -0.13 Gd Hcp 3.74 5.99 3.63 5.78 0.11 0.21 Er Hcp 3.59 5.66 3.56 5.59 0.03 0.07

MAD 0.13 Å 0.11 Å a Experiment data reference70 b. Error of crystal lattice constant is calculated by dCP2K – dExpt where d is crystal lattice constant.

Table 8. Work functions (eV) and surface energies (J/m2) calculated with our new GTH

pseudopotentials and basis sets with uncontracted f states, at the PBE level.

Surface

Work function Surface energy CP2K Expt. Theor. Errora CP2K Expt. Theor. Errorb

La hcp (001) 3.19 3.50c 3.21d -0.31 0.75 1.02g 0.57h -0.27 Eu bcc (001) 2.52 2.50c 2.42d 0.02 0.31 0.45g 0.34h -0.14 Gd hcp (001) 3.07 3.10e 3.30f 0.03 0.91 - - - Er hcp (001) 3.29 - - - 1.07 - - -

MAD

0.12 eV

0.21 J/m2

a Error of work function is calculated by WCP2K – WExpt, where W is work function. b Error of surface energy is calculated by ECP2K – EExpt, where E is surface energy. c The experimental data of work function for La, Eu is from reference64 d The previous theoretical data of La, Eu work functions are from reference68, where the bcc(110) surface of Eu is computed. e The experimental data of work function for Gd is from reference63 f The previous theoretical data of work function for Gd is from reference66 g The experimental data of surface energy for La, Eu is from reference67 h The previous theoretical data of surface energy for La, Eu is from reference68

3.4 DFT +U correction

We performed DFT+U calculations with our LnPP1 pseudopotentials and basis sets based on third

ionization potentials, whose values for lanthanides are known from experiment.71 We varied the +U

18

values to best match experiment (Table 9), details for Ce are shown in Table S20 in the SI. We

previously found that, for lanthanides, U values have a larger effect on energies of reaction that involve

a change in population of the 4f electrons.37 Therefore, no values were calculated for Gd and Lu. Results

show that larger U values are required for the early than for the late lanthanides to accurately reproduce

ionization potentials. Finally, it is noted that U values will vary for different properties and need to be

fitted accordingly, but this set may serve as a starting point for additional studies, see SI Table S21.

Table 9. The U value (eV) and third ionization potential (kcal/mol) calculated by DFT and DFT+U,

using our LnPP1 GTH pseudopotentials and basis sets with uncontracted f states in CP2K.

U DFT DFT+U Expt. Error (DFT)a Error (DFT+U)b La 3.27 449.7 442.4 442.2 7.5 0.2 Ce 4.08 504.1 466.3 465.8 38.3 0.5 Pr 4.63 528.8 498.4 498.7 30.1 -0.3 Nd 3.54 552.5 510.6 510.6 41.9 0 Pm 5.44 552.3 514.7 514.0 38.3 0.7 Sm 3.54 570.0 540.9 540.3 29.7 0.6 Eu 4.08 604.6 575.0 574.7 29.9 0.3 Tb 2.45 527.3 506.1 505.3 22 0.8 Dy 1.90 551.0 529.5 528.8 22.2 0.7 Ho 0.54 532.0 525.8 526.7 5.3 -0.9 Er 1.63 541.7 525.0 524.4 17.3 0.6 Tm 2.18 565.5 546.0 546.1 19.4 -0.1 Yb 0.54 582.0 577.2 577.7 4.3 -0.5

MAD 23.6 kcal/mol 0.5 kcal/mol a. Error (DFT) is calculated by IPDFT – IPExpt, where IP is ionization potential. b. Error (DFT+U) is calculated by IPDFT+U – IPExpt, where IP is ionization potential

4. CONCLUSIONS

We have constructed new sets of GTH pseudopotentials and companion basis sets for the whole

lanthanide series. We adopted large-core pseudopotentials for lanthanum to gadolinium, and medium-

core pseudopotentials for terbium to lutetium. This scheme provides a good compromise between

computational cost and chemical accuracy. The corresponding MOLOPT basis sets were optimized

with the f states uncontracted in the valence orbitals. Our LnPP1 GTH pseudopotentials and basis sets

performed comparably to all-electron calculations in a variety of molecular and solid-state benchmarks

19

that included structural, electronic, and thermodynamic quantities. Additionally, DFT+U parameters,

based on the ionization potentials from experiment, were determined. These new pseudopotentials and

basis sets will facilitate larger-scale DFT calculations and AIMD simulations of lanthanide-containing

systems in the condensed phase and/or the solid state, where reliable potentials accounting for the

chemistry were largely absent. Although this set is based on the PBE functional, it can serve as a starting

point for additional parametrization suitable for other functionals, including meta-GGA and hybrid

functionals.

SUPPORTING INFORMATION

The SI is divided into parts corresponding to sections of the main text. Part A has the supporting

information on how the pseudopotentials and basis sets were optimized (Section 2.1), along with Tables

S1 – S3. Part B has the supporting information on the computational methodology (Section 2.2) with

additional detail on the ADF calculations along with Tables S4 to S9. Part C has the supporting

information regarding our results with pseudopotential transferability and reaction energies (Section

3.1) with Table S10 and S11. Part D has the supporting information for our molecule test results (Section

3.2) with lanthanide chloride geometries (Figure S1, Tables S12 and S13) and a discussion on the

calculation of enthalpies of formation with CP2K (Figure S1, Tables S14-S19). Part E has the

supporting information on the DFT +U calculations (Table S20-S21). Most importantly, Part F includes

our LnPP1 pseudopotentials and basis sets in CP2K format, so that the scientific community can readily

use them.

ACKNOWLEDGMENTS

The manuscript was partially authored by battelle Memorial Institute under contract No. DE-

AC05-76RL01830 with the U.S. Department of Energy, The United States Government retains and the

publisher, by accepting the article for publication, acknowledges that the United States Government

retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published

form of this manuscript, or allow others to do so, for United States Government purposes. V.-A.G. was

supported by the U.S. Department of Energy, Basic Energy Sciences, Chemistry, Geochemistry and

Biological Sciences Separations Program, and R.R. and M.-T.N. were supported by PNNL Laboratory

Directed Research and Development CheMSR Agile Investment. J.-B.L. and J.L. were supported by

20

the National Natural Science Foundation of China (Nos. 21433005, 91645203, and 21590792). D.C.C.

was supported by Research and Innovation at the University of Nevada, Reno. Calculations were

performed at PNNL Research Computing, Tsinghua National Laboratory for Information Science and

Technology and the Computational Chemistry Laboratory under Tsinghua Xuetang Talents Program,

and University of Nevada, Reno High Performance Computing. J.-B. L. and J. L. acknowledge

discussions with Dr. Yang-Gang Wang (Southern University of Science and Technology).

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1

Supporting Information

Norm-conserving pseudopotentials and basis sets optimized for

lanthanide molecules and solid-state compounds

Jun-Bo Lua, c, David C. Cantub, Manh-Thuong Nguyenc, Jun Lia*, Vassiliki-Alexandra Glezakouc*, Roger Rousseauc*

a Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China

b Chemical and Materials Engineering, University of Nevada, Reno, Reno, Nevada 89557, USA

c Basic and Applied Molecular Foundations, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA *Corresponding authors: [email protected], [email protected], [email protected]

Table of Contents

Part A: SI for Section 2.1 “GTH pseudopotentials and MOLOPT basis sets” 2 Part B: SI for Section 2.2 “Computational methodology” 5 Part C: SI for Section 3.1 “Pseudopotential transferability and reaction energies” 9 Part D: SI for Section 3.2 “Molecular tests” 10 Part E: SI for Section 3.4 “DFT +U correction” 17 Part F: Our LnPP1 pseudopotentials and basis sets optimized for lanthanides 18

2

Part A: SI for Section 2.1 “GTH pseudopotentials and MOLOPT basis sets”

GTH pseudopotentials contain local and non-local parts. The local part includes one or two coefficients. The non-local part has three scattering coefficients for s and p angular momentum, one scattering coefficient for d and f angular momentum. There is no standard way to optimize pseudopotential parameters. For this purpose, we minimized a user defined penalty function. In order to evaluate the penalty function for a given set of pseudopotential parameters, calculations on the radial Schrodinger equation of the pseudo-atom must be performed at each step of the fitting cycle. The penalty function consists of a weighted sum of square deviations to the reference data, which is derived from all-electron calculations of atom:

S = ∑ 𝑤%,',() (𝑝%,',- − 𝑝%,'/0)%,' (Eq. S1) Several important atomic properties were chosen for the penalty function: (1) Atomic eigenvalue εn, l (2) Charge density within a sphere of radius rloc (3) Nodeless of atomic orbitals. The weights of each property were chosen carefully. In the present work, we gave the highest weight to the eigenvalue and the next highest weight to charge density. It is believed that the eigenvalues of valence orbitals are right if eigenvalues of lower core orbitals are correct. Therefore, we decreased the weight by one order of magnitude with increasing principle quantum number n.

After getting the pseudopotential parameters, we optimized the Gaussian exponents for the s, p, d and f orbitals. We tested the Gaussian exponents of f orbitals chosen from different existing basis set:

(1) f_crenbl_n: the Gaussian exponents of f orbitals are chosen from the Gaussian exponents of

CRENBL ECP basis set, where n is the number of exponents of f orbitals. (2) f_stg_n: the Gaussian exponents of f orbitals chosen from the Gaussian exponents of Stuttgart RSC

ANO/ECP basis set. n is the number of exponents of f orbitals. (3) f_spd_n: the Gaussian exponents of f orbitals are chosen from the Gaussian exponents of s, p and d

states generated by ATOM code. n means the number of exponents of f orbitals. The Gaussian exponents of s, p and d orbitals were optimized by the ATOM code in the CP2K package. The confinement parameters of GTH pseudopotentials are modulated to get different Gaussian exponents for the s, p and d orbitals.

The number of Gaussian exponents of s, p and d orbitals, the value of Gaussian exponents of s, p and d orbitals, and f orbitals are three key basis set factors. Tables S1 – S3 show the results of testing the three factors with Ce. Calculations are based on uncontracted basis sets. We tested the three key factors for all lanthanides. Here we take the testing of Ce as example: For the testing of number of Gaussian exponents of s, p and d orbitals, the Gaussian exponents of s, p and d orbitals are:

3

Gau_num = 6: 0.04091750, 0.12993444, 0.34483678, 0.77787686, 1.72233946, 3.96902350 Gau_num = 7: 0.04053284, 0.11467513, 0.30691395, 0.71562304, 1.51652533, 2.36809432, 4.15237224 Gau_num = 8: 0.04024110, 0.08851298, 0.19917888, 0.44370691, 0.93200530, 1.75066160, 2.51467732, 4.22060316 The Gaussian exponents of f orbitals which are grasped from CRENBL ECP basis set are: 6.9560000, 2.7930000, 1.0680000, 0.3499000.

For the testing of value of Gaussian exponents of s, p and d orbitals, we choose the following Gaussian exponents for s, p and d orbitals:

BS_1: 0.08775575, 0.16447973, 0.38040355, 0.83282172, 1.65665417, 2.58067085, 4.22245063 BS_2: 0.08104942, 0.14873630, 0.36148785, 0.80493102, 1.61437811, 2.51363675, 4.20565015 BS_3: 0.08019980, 0.12570707, 0.33070112, 0.75330363, 1.52928534, 2.37168605, 4.16775673 BS_4: 0.07073186, 0.13538834, 0.34409140, 0.77774428, 1.57616853, 2.45410483, 4.18880700 BS_5: 0.07055351, 0.11069368, 0.30792855, 0.71255837, 1.45299554, 2.25060217, 4.13501187 BS_6: 0.06073284, 0.12805253, 0.33396022, 0.76185311, 1.55595368, 2.42392346, 4.17935077 BS_7: 0.06091388, 0.10832212, 0.30262724, 0.70317879, 1.43381466, 2.22341926, 4.12774705 BS_8: 0.05648421, 0.09698038, 0.28029298, 0.65661696, 1.31944838, 2.08377973, 4.09031932 BS_9: 0.05097481, 0.12786786, 0.32763789, 0.75072837, 1.57226158, 2.47592859, 4.18237524 BS_10: 0.04053284, 0.11467513, 0.30691395, 0.71562304, 1.51652533, 2.36809432, 4.15237224 BS_11: 0.03787913, 0.10855637, 0.29403882, 0.69185398, 1.47593046, 2.28939079, 4.13019283 The f states are: 6.9560000, 2.7930000, 1.0680000, 0.3499000

For testing of value of Gaussian exponents for f states, we choose the following Gaussian exponents for f orbitals:

f_stg_4: 8.6013000, 3.8049000, 1.6176000, 0.6364000 f_stg_5: 19.4518000, 8.6013000, 3.8049000, 1.6176000, 0.6364000 f_stg_6: 43.9881000, 19.4518000, 8.6013000, 3.8049000, 1.6176000, 0.6364000 f_stg_7: 43.9881000, 19.4518000, 8.6013000, 3.8049000, 1.6176000, 0.6364000, 0.2164000 f_crenbl_4: 6.9560000, 2.7930000, 1.0680000, 0.3499000 f_crenbl_5: 18.2400000, 6.9560000, 2.7930000, 1.0680000, 0.3499000 f_spd_4: 0.65661696, 1.31944838, 2.08377973, 4.09031932 f_spd_5: 0.28029298, 0.65661696, 1.31944838, 2.08377973, 4.09031932 f_spd_6: 0.09698038, 0.28029298, 0.65661696, 1.31944838, 2.08377973, 4.09031932 f_spd_7: 0.05648421, 0.09698038, 0.28029298, 0.65661696, 1.31944838, 2.08377973, 4.09031932 The s, p and d states are: 0.05648421, 0.09698038, 0.28029298, 0.65661696, 1.31944838, 2.08377973, 4.09031932

Finally, the contract coefficients of s, p and d orbitals are optimized, and f orbitals are uncontracted. The training molecules of each lanthanide element consisted of lanthanide oxide, nitride, fluoride, hydride and chloride complexes. The lanthanide oxidation states in these complexes range from I to III, due to the fact that lanthanide chemistry is dominated by low oxidation states.

To double check our approach, we used the ATOM code in the CP2K package to verify that the same potentials can be generated.

4

Table S1. The number of Gaussian exponent of s, p and d orbitals tests for CeCln (n = 1 - 3). The unit of energy is Hartree.

Gau_num E(CeCl) E(CeCl2) E(CeCl3) R1 R2 6 -53.66561 -68.77244 -83.87044 -0.13801 -0.12918 7 -53.66742 -68.77428 -83.87752 -0.13804 -0.13442 8 -53.66767 -68.77475 -83.87797 -0.13826 -0.13440

ADF_ref -0.14564 -0.13469

Table S2. The f states tests for CeCln (n = 1 - 3). The unit of energy is Hartree.

f state E(CeCl) E(CeCl2) E(CeCl3) R1 R2 f_ano_4 -53.71134 -68.81445 -83.90328 -0.13429 -0.12001 f_ano_5 -53.7097 -68.81458 -83.90334 -0.13606 -0.11994 f_ano_6 -53.70975 -68.81548 -83.90332 -0.13691 -0.11902 f_ano_7 -53.73602 -68.83488 -83.91793 -0.13004 -0.11423

f_crenbl_4 -53.66742 -68.77428 -83.87752 -0.13804 -0.13442 f_crenbl_5 -53.6875 -68.79152 -83.88961 -0.1352 -0.12927

f_spd_4 -53.70416 -68.81033 -83.90097 -0.13735 -0.12182 f_spd_5 -53.73329 -68.83375 -83.91185 -0.13164 -0.10928 f_spd_6 -53.73739 -68.83592 -83.91869 -0.12971 -0.11395 f_spd_7 -53.73754 -68.83606 -83.91276 -0.1297 -0.10788 ADF_ref -0.14564 -0.13469

Table S3. The s, p and d states tests for CeCln (n = 1 - 3). The unit of energy is Hartree.

spd state E(CeCl) E(CeCl2) E(CeCl3) R1 R2 BS_1 -53.64651 -68.76884 -83.87752 -0.15351 -0.13986 BS_2 -53.65155 -68.77003 -83.8774 -0.14966 -0.13855 BS_3 -53.65447 -68.77074 -83.87742 -0.14745 -0.13786 BS_4 -53.6574 -68.77155 -83.87749 -0.14533 -0.13712 BS_5 -53.65942 -68.77206 -83.87743 -0.14382 -0.13655 BS_6 -53.6618 -68.77274 -83.8775 -0.14212 -0.13594 BS_7 -53.66253 -68.77291 -83.87745 -0.14156 -0.13572 BS_8 -53.66412 -68.77335 -83.87743 -0.14041 -0.13526 BS_9 -53.66511 -68.77371 -83.87761 -0.13978 -0.13508

BS_10 -53.66721 -68.77422 -83.87744 -0.13819 -0.1344 BS_11 -53.66742 -68.77428 -83.87752 -0.13804 -0.13442

ADF_ref -0.14564 -0.13469

5

Part B: SI for Section 2.2 “Computational methodology”

Table S4. The electronic configuration of LnCl, LnCl2 and LnCl3.

Complex LnCl LnCl2 LnCl3 La 5d2 5d1 5s25p6 Ce 4f15d2 4f16s1 4f1 Pr 4f36s1 4f3 4f2 Nd 4f46s1 4f4 4f3 Pm 4f56s1 4f5 4f4 Sm 4f66s1 4f6 4f5 Eu 4f76s1 4f7 4f6 Gd 4f76s2 4f76s1 4f7 Tb 4f96s1 4f9 4f8 Dy 4f106s1 4f10 4f9 Ho 4f116s1 4f11 4f10 Er 4f126s1 4f12 4f11 Tm 4f136s1 4f13 4f12 Yb 4f146s1 4f14 4f13 Lu 4f146s2 4f146s1 4f14

Discussion on ADF calculations

It is difficult to determine the occupation of f orbitals in lanthanide complexes using ADF. Here we calculate the energetics of the two redox reactions (R1 and R2, see main text) by three schemes:

(1) Scheme 1: Defining the occupation pattern. As the DFT wavefunction is a single-reference slater

determinant, we must find an occupation pattern for f orbital electronic configuration. Here our standard is that Mz is largest.

(2) Scheme 2: Fully fragment occupation for f orbitals. As energy levels of f orbitals are very close, all f orbitals can occupy electrons. We divided electrons into every f orbitals in equal footing, e. g., the occupation number is 1/7 if we have the electronic configuration f1.

(3) Scheme 3: Dirac-Fermi smearing. Based on scheme 2, Dirac-Fermi smearing made electrons occupy different f orbitals fragmentally, but not with a fully fragmented occupation. Here, the smearing value is 0.01 Hartree. The occupation of f orbitals in most solid state packages follows scheme 3. In order to check scheme

3’s feasibility, we tested it for 3d-transition metal. As shown in Tables S5 and S6, the agreement between our new GTH pseudopotential results and ADF all-electron results are satisfactory. The error is relatively small.

6

Table S5. The energetics (kcal/mol) of two redox reactions by ADF through three schemes.

Element Scheme_1 Scheme_2 Scheme_3

R1 R2 R1 R2 R1 R2 La -91.0 -90.2 -94.2 -106.6 -94.1 -90.2 Ce -90.5 -85.6 -89.9 -86.9 -91.4 -84.5 Pr -79.8 -88.5 -78.7 -87.1 -86.8 -76.6 Nd -79.4 -68.0 -80.1 -70.0 -79.7 -69.8 Pm -82.4 -62.3 -79.6 -54.2 -79.8 -63.4 Sm -72.3 -52.4 -76.9 -41.5 -77.4 -48.3 Eu -75.0 -26.8 -75.0 -28.5 -75.0 -33.3 Gd -78.7 -83.8 -78.7 -83.8 -93.5 -83.8 Tb -83.1 -81.6 -83.1 -89.1 -70.1 -82.6 Dy -73.1 -64.1 -74.9 -73.3 -74.2 -66.1 Ho -75.1 -69.1 -74.9 -63.2 -73.0 -65.0 Er -68.8 -52.2 -70.2 -58.1 -70.1 -66.0 Tm -74.8 -42.5 -74.1 -44.2 -72.3 -52.1 Yb -73.8 -35.0 -73.8 -34.7 -73.8 -39.5 Lu -72.5 -85.2 -72.5 -85.2 -72.5 -85.2

Table S6. The reaction energies (kcal/mol) of MCl2 + ½ Cl2 = MCl3 (M = Sc-Cu) by CP2K and ADF at PBE level.

Element CP2K ADF Errora Sc -88.1 -87.3 -0.8 Ti -79.1 -80.0 0.9 V -58.2 -59.5 1.3 Cr -50.5 -50.7 0.2 Mn -20.5 -20.5 0.0 Fe -36.6 -36.1 -0.5 Co -31.1 -30.0 -1.1 Ni -12.5 -11.5 -0.9 Cu -1.5 -2.9 1.4 Zn 15.8 17.8 -2.0

MAD 0.9 kcal/mol a Error is calculated by E(CP2K) – E(ADF)

7

Table S7. The bond energies (kcal/mol) of M-Cl in MCl3 (M = Sc-Cu) by CP2K and ADF at PBE level.

Element CP2K ADF Errora Sc -122.1 -118.9 -3.2 Ti -114.8 -109.9 -4.9 V -94.3 -89.0 -5.3 Cr -85.5 -81.3 -4.1 Mn -55.3 -51.4 -4.0 Fe -70.9 -67.4 -3.4 Co -64.8 -61.9 -2.9 Ni -46.3 -43.3 -3.1 Cu -37.7 -32.3 -5.4 Zn -17.0 -15.0 -2.0

MAD 3.8 kcal/mol

a Error is calculated by E(CP2K) – E(ADF)

Table S8. The cutoff (Ry) tests of density in CP2K for CeCln (n = 1 - 3). The unit of energy is Hartree.

cutoff E(CeCl) E(CeCl2) E(CeCl3) R1 R2 100 -53.72723 -68.83262 -83.92163 -0.13767 -0.12129 200 -53.66146 -68.76988 -83.87110 -0.14070 -0.13350 300 -53.65818 -68.76592 -83.86964 -0.14002 -0.13600 400 -53.65741 -68.76613 -83.86966 -0.14100 -0.13581 500 -53.65726 -68.76531 -83.86926 -0.14033 -0.13623 600 -53.65696 -68.76587 -83.86962 -0.14119 -0.13603 700 -53.65702 -68.76588 -83.86957 -0.14114 -0.13597 800 -53.65690 -68.76572 -83.86954 -0.14110 -0.13610 900 -53.65687 -68.76578 -83.86945 -0.14119 -0.13595

1000 -53.65687 -68.76582 -83.86959 -0.14123 -0.13605

8

Table S9. The cutoff (Ry) tests of density in CP2K for TbCln (n = 1 – 3). The unit of energy is Hartree.

cut-off E(TbCl) E(TbCl2) E(TbCl3) R1 R2 100 -429.21729 -445.46461 -459.97638 -1.27960 0.45595 200 -425.11815 -440.33827 -455.34466 -0.25240 -0.03867 300 -425.003 -440.08789 -455.17276 -0.11717 -0.11715 400 -424.95845 -440.04016 -455.13251 -0.11399 -0.12463 500 -424.9385 -440.01561 -455.11595 -0.10939 -0.13262 600 -424.92801 -440.00461 -455.10617 -0.10888 -0.13384 700 -424.92576 -440.00214 -455.10312 -0.10866 -0.13326 800 -424.92401 -440.00071 -455.10162 -0.10898 -0.13319 900 -424.92372 -440.00034 -455.10128 -0.10890 -0.13322

1000 -424.92383 -440.00077 -455.10133 -0.10922 -0.13284

9

Part C: SI for Section 3.1 “Pseudopotential transferability and reaction energies”

Table S10. The rloc in medium-core pseudopotential tests for Tb. The unit energy is Hartree.

rloc E(TbCl) E(TbCl2) E(TbCl3) E(R1) E(R2) 0.48 -425.37674 -440.45817 -455.56388 -0.11261 -0.13689 0.49 -424.84606 -439.92731 -455.0342 -0.11243 -0.13807 0.5 -424.94475 -440.02427 -455.12763 -0.11070 -0.13454

0.51 -424.55303 -439.63273 -454.73568 -0.11088 -0.13413 ADF_ref -0.11173 -0.13161

Table S11. The redox reaction energy (kcal/mol) by using CP2K optimized structure and Gaussian optimized structure in CP2K.

Element CP2K optimized

structure Gaussian optimized

structure Reac_1 Reac_2 Reac_1 Reac_2

La -89.9 -88.5 -89.7 -88.6 Ce -88.4 -84.9 -88.5 -85.4 Pr -86.2 -73.3 -85.7 -73.8 Nd -80.5 -59.3 -77.6 -62.3 Pm -79.7 -61.9 -80.6 -61.9 Sm -78.8 -48.5 -78.9 -48.3 Eu -75.9 -32.3 -75.9 -32.3 Gd -90.0 -81.3 -89.3 -81.3 Tb -74.2 -77.7 -68.4 -83.6 Dy -76.9 -61.3 -76.4 -60.9 Ho -71.8 -65.9 -71.7 -65.3 Er -70.8 -66.0 -67.6 -68.6 Tm -74.3 -50.4 -74.0 -50.1 Yb -71.6 -41.5 -71.6 -41.0 Lu -67.8 -87.5 -67.7 -87.2

10

Part D: SI for Section 3.2 “Molecular tests”

Table S12. Ln-Cl distance (Å) in LnCln (Ln = La – Lu, n = 1 – 3) optimized by ADF and CP2K.

Element Molecule ADF/PBE CP2K/PBE Errora

La

LaCl 2.52 2.55 0.03 LaCl2 2.55 2.55 0.01 LaCl3 2.62 2.59 -0.03

Ce

CeCl 2.54 2.56 0.02 CeCl2 2.54 2.58 0.04 CeCl3 2.56 2.56 0.00

Pr

PrCl 2.55 2.60 0.05 PrCl2 2.54 2.59 0.05 PrCl3 2.54 2.54 0.00

Nd

NdCl 2.55 2.59 0.03 NdCl2 2.54 2.59 0.04 NdCl3 2.52 2.53 0.01

Pm

PmCl 2.56 2.58 0.03 PmCl2 2.56 2.58 0.02 PmCl3 2.51 2.52 0.01

Sm

SmCl 2.55 2.59 0.04 SmCl2 2.56 2.58 0.02 SmCl3 2.51 2.52 0.01

Eu

EuCl 2.54 2.58 0.04 EuCl2 2.55 2.58 0.03 EuCl3 2.53 2.56 0.03

Gd

GdCl 2.44 2.49 0.04 GdCl2 2.45 2.47 0.02 GdCl3 2.47 2.48 0.01

Tb

TbCl 2.45 2.47 0.02 TbCl2 2.47 2.51 0.05 TbCl3 2.46 2.49 0.03

Dy

DyCl 2.45 2.54 0.09 DyCl2 2.47 2.54 0.08 DyCl3 2.45 2.51 0.06

Ho

HoCl 2.46 2.51 0.05 HoCl2 2.47 2.51 0.04 HoCl3 2.44 2.48 0.04

Er

ErCl 2.46 2.50 0.05 ErCl2 2.45 2.52 0.07 ErCl3 2.43 2.48 0.05

TmCl 2.46 2.56 0.10

11

Tm

TmCl2 2.46 2.53 0.07 TmCl3 2.43 2.51 0.07

Yb

YbCl 2.45 2.53 0.07 YbCl2 2.45 2.50 0.05 YbCl3 2.44 2.50 0.06

Lu

LuCl 2.37 2.41 0.05 LuCl2 2.38 2.46 0.08 LuCl3 2.39 2.43 0.04

MAD 0.04 Å

a Error of bond length is calculated by dCP2K – dADF.

Table S13. Cl-Ln-Cl angle (º) in LnCln (Ln = La – Lu, n = 2, 3) optimized by ADF and CP2K.

Element Molecule ADF/PBE CP2K/PBE Errora

La LaCl2 115 113 -2 LaCl3 120 120 0

Ce CeCl2 115 117 2 CeCl3 120 120 0

Pr PrCl2 114 119 5 PrCl3 120 120 0

Nd NdCl2 115 120 5 NdCl3 120 121 1

Pm PmCl2 120 120 0 PmCl3 120 120 0

Sm SmCl2 121 122 1 SmCl3 120 120 0

Eu EuCl2 120 123 3 EuCl3 120 120 0

Gd GdCl2 119 120 1 GdCl3 118 116 -2

Tb TbCl2 119 126 7 TbCl3 120 120 0

Dy DyCl2 118 129 11 DyCl3 120 120 0

Ho HoCl2 121 123 2 HoCl3 120 120 0

Er ErCl2 119 132 13 ErCl3 120 120 0

Tm TmCl2 123 124 1 TmCl3 120 120 0

Yb YbCl2 123 125 2 YbCl3 120 120 0

12

Lu LuCl2 123 180 57 LuCl3 120 120 0

MAD 4º

a Error of angle is calculated by aCP2K – aADF.

Figure S1. Comparison of the bond length for Ln-Cl (Ln = La - Lu) calculated with CP2K using the GTH pseudopotentials optimized for PBE and the bond length for Ln-Cl (Ln = La - Lu) obtained by ADF all-electron calculations with the TZ2P basis set.

Discussion on the calculation of enthalpies of formation with CP2K

Enthalpies of formation of LnCln (n = 2, 3), LnFn (n=1, 2, 3), and LnO were calculated using our LnPP1 GTH pseudopotentials and basis sets with uncontracted f states in the gas-phase under periodic conditions, based on varying the optimized structures and comparing with experiment. First, each structure was optimized in CP2K, yielded the “formed” structure (see Figure S1 below). Then, keeping the optimized angles, the optimized Ln-Cl, Ln-F, or Ln-O bond lengths were increased by a factor of x, to give the “non-formed” structure.

13

Figure S2. Structure of formed and non-formed structures, example with CeCl3, with Ce3+ (black) and Cl- (green).

The enthalpy of formation is simply calculated as:

𝐻3 ≅ 𝐸36789: − 𝐸%6%;36789: (Eq. S2)

There is one empirical parameter, x, which is varied to match experiment. The fitting is performed in one early lanthanide, a middle lanthanide, and a late lanthanide, while retaining predictive values for the rest of the series. Tables S14 – S19 include all the calculated enthalpies of formation, with reported optimized ropt values, as well as x values.

Although our procedure is not based on pure gas-phase reference molecules, it is a simple and fast procedure to calculate enthalpies of formation at acceptable with accuracy with respect to experiment. Calculations based on pure gas-phase reference molecules would include charged boxes (e.g., Ln3+, Cl-). CP2K is not as well suited as quantum chemistry codes to perform calculations with charged boxes. Our approach avoids the use of charged boxes. Also, the Cl, F, and O MOLOPT basis sets are parametrized for short-range interactions.

Table S14. LnCl3 enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.

Ln-Cl average optimized

bond length (Å)

x Hf with our pseudopotentials

and basis sets

Hf with all-

electrona

Hf from experimentb

Error between our calculations and experiment

Error between all-electron

and experiment

La 2.59 1.50 -193.2 -175.4 -177.0 -16.2 1.6 Ce 2.55 1.50 -169.8 -178.2 -171.4 1.6 -6.8 Pr 2.53 1.50 -173.9 -155.4 -174.5 0.6 19.1 Nd 2.51 1.50 -158.9 -152.4 -172.4 13.5 19.7 Gd 2.48 1.45 -172.2 -152.7 -164.9 -7.3 -0.6

MAD 7.8 kcal/mol 9.6 kcal/mol a S. Grimmel, G. Schoendorff, and Angela K. Wilson (2016), J. Chem. Theory Comput., 12, 1259−1266. b Experimental data from various sources compiled in S. Grimmel, G. Schoendorff, and Angela K. Wilson (2016), J. Chem. Theory Comput., 12, 1259−1266.

Formed: Gas phase optimization, periodic boundary conditions, zero box charge

ropt: optimized bond length

r=x*ropt

Non-formed: Gas phase single point energy calculation, all angles as optimized geometry, r changes

14

Table S15. LnCl2 enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.

Ln-Cl average optimized

bond length (Å)


and basis sets

Hf with all-

electrona

Hf from experimentb

Error between our

calculations and experiment


and experiment

La 2.55 1.33 -75.2 -84.3 -85.0 9.8 0.7 Ce 2.52 1.33 -69.9 -93.1 -70.0 0.1 -23.1 Pr 2.51 1.33 -74.7 -83.8 -82.0 7.3 -1.8 Nd 2.54 1.33 -66.2 -91.4 -85.0 18.8 -6.4 Sm 2.53 1.33 -34.7 -104.4 -119.6 84.9 15.2 Eu 2.52 1.33 -66.7 -107.0 -109.1 42.4 2.1 Gd 2.44 1.33 -77.0 -81.1 -73.0 -4.0 -8.1 Tb 2.51 1.33 -73.8 -55.3 -73.0 -0.8 17.7 Ho 2.50 1.33 -78.0 -81.8 -85.0 7.0 3.2 Er 2.52 1.33 -72.7 -85.7 -84.0 11.3 -1.7


Table S16. LnF3 enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.

Ln-F average optimized

bond length (Å)

X Hf with our pseudopotentials

and basis sets

Hf with all-

electrona

Hf from experimentb



and experiment

La 2.12 2.00 -344.0 -309.0 -306.9 -37.1 -2.1 Ce 2.10 2.00 -313.5 -311.3 -315.1 1.6 3.8 Pr 2.09 2.00 -315.5 -287.5 -409.2 93.7 121.7 Nd 2.08 2.00 -300.9 -287.2 -315.3 14.4 28.1 Gd 2.03 1.75 -297.7 -295.9 -299.9 2.2 4.0 Tb 2.07 1.75 -293.6 -264.7 -298.7 5.1 34.0 Dy 2.07 2.30 -316.5 -255.6 -296.6 -19.9 41.0 Ho 2.05 2.30 -330.1 -251.5 -300.5 -29.6 49.0 Er 2.04 2.30 -292.5 -254.0 -301.2 8.7 47.2 Lu 2.02 2.30 -367.1 -285.2 -298.7 -68.4 13.5


15

Table S17. LnF2 enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.


bond length (Å)

X Hf with our pseudopotentials

and basis sets

Hf with all-

electrona

Hf from experimentb

Error between our



and experiment

La 2.09 1.55 -149.0 -176.7 -147.0 -2.0 -29.7 Sm 2.05 1.80 -179.8 -185.0 -182.0 2.2 -3.0 Eu 2.04 1.80 -180.4 -184.0 -187.0 6.6 3.0


Table S18. LnF enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.


bond length (Å)


and basis sets

Hf with all-

electrona

Hf from experimentb



and experiment

La 2.05 1.20 -21.5 -39.0 -21.0 -0.5 -18.0 Ho 2.05 1.85 -80.0 -40.1 -40.0 -40.0 -0.1 Yb 2.03 1.85 -75.8 -80.1 -80.0 4.2 -0.1 Lu 1.96 1.85 -104.3 -14.5 -14.0 -90.3 -0.5


16

Table S19. LnO enthalpies of formation (kcal/mol). Our calculations and the publisheda all-electron calculations both used the PBE functional.

Ln-O average optimized

bond length (Å)


and basis sets

Hf with all-

electrona

Hf from experimentb

Error between our



and experiment

La 1.87 1.18 -30.0 -39 -28.4 -1.6 -10.6 Ce 1.84 1.18 -29.3 -47.7 -31.5 2.2 -16.2 Pr 1.83 1.18 -30.4 -21.9 -34.7 4.3 12.8 Nd 1.82 1.18 -31.4 -17.2 -28.7 -2.7 11.5 Sm 1.81 1.10 -11.0 -19.3 -25.1 14.1 5.8 Eu 1.83 1.10 -11.1 -23.6 -13.5 2.4 -10.1 Gd 1.85 1.10 -11.5 -26.4 -16.3 4.8 -10.1 Tb 1.88 1.10 -23.8 46.5 -20.2 -3.6 66.7 Dy 1.90 1.10 -17.3 88.7 -17 -0.3 105.7 Ho 1.88 1.10 -15.3 27.6 -13.8 -1.5 41.4 Er 1.92 1.10 -22.9 17.4 -7.9 -15.0 25.3 Yb 1.92 1.10 -16.8 -4.9 -3.3 -13.5 -1.6 Lu 1.84 1.10 -11.6 -8.1 -3.8 -7.8 -4.3


17

Part E: SI for Section 3.4 “DFT +U correction”

Table S20. The energies (Hartree) of Ce2+ and Ce3+ and the third ionization potential (IP) (kcal/mol) for Ce in different U (eV) value.

U E(Ce2+) E(Ce3+) IP 0.05 -37.94316 -37.16058 491.1 0.1 -37.90733 -37.14571 477.9

0.15 -37.87412 -37.13098 466.3 0.2 -37.82359 -37.11635 443.8

Expt. 465.8

Table S21. The DFT and DFT+U results (kcal/mol) of fourth ionization potential for Ce and Tb by using the U value (eV) determined by the third ionization potential.

Element U value Exp. DFT DFT+U Error(DFT) Error(DFT+U)

Ce 4.08 848.0 937.2 909.1 89.2 61.1

Tb 2.45 908.3 1012.4 922.8 104.1 14.5

18

Part F: Our LnPP1 pseudopotentials and basis sets optimized for lanthanides (CP2K format)

The GTH pseudopotentials from La to Lu are:

La GTH-PBE-q11 4 6 1 0 0.536621886 2 20.187083390 -1.461153313 4 0.541927081 2 1.342431782 0.450502384 -1.181781197 0.478778498 3 0.979802043 0.376291820 0.008876396 -0.824267358 -0.021005386 0.029857280 0.626441601 1 0.328796868 0.300352697 1 -18.352319697 Ce GTH-PBE-q12 4 6 0 2 0.539004680 2 18.85114190 -0.77960224 4 0.498081460 2 1.19529290 0.62204575 -1.62871685 0.47069322 2 1.18088300 0.55487102 -1.53066452 0.65606409 1 0.07990999 0.30705426 1 -17.32458585 Pr GTH-PBE-q13 4 6 0 3 0.532486240 2 18.514048206 -0.582682182 4 0.524682347 2 1.598493376 0.440830770 -1.719989118 0.461080992 2 0.890293235 0.917885701 -1.989243896 0.571698543 1 0.017967543 0.301480737 1 -17.898484476

19

Nd GTH-PBE-q14 4 6 0 4 0.531351369 2 18.007481210 -0.707850932 4 0.494947486 2 1.730672873 0.811897086 -2.169289264 0.483476215 2 0.754160538 0.658311314 -1.583172072 0.380970008 1 0.043574337 0.294938171 1 -18.499650577 Pm GTH-PBE-q15 4 6 0 5 0.528636435 2 18.245839784 -0.486314424 4 0.484664155 2 1.282682334 0.959291011 -2.495974035 0.472066166 2 0.193983187 0.667699003 -1.597663074 0.473753437 1 -0.430483026 0.291785846 1 -19.326738513 Sm GTH-PBE-q16 4 6 0 6 0.525294147 2 17.251599705 -0.531859084 4 0.479541125 2 1.730666754 1.009862710 -2.661213312 0.489714555 2 -0.091063341 0.465485746 -1.109941887 0.470798767 1 -0.410255744 0.284444333 1 -19.973327048 Eu GTH-PBE-q17 4 6 0 7 0.522100054 2 17.359358474 -0.648460166 4 0.468993404 2 1.776114604 1.117935246 -2.917719665 0.445886269 2 0.500415952 0.890257661 -2.117280466 0.489972387 1 -0.425678559 0.278525768 1 -20.949306600

20

Gd GTH-PBE-q18 4 6 0 8 0.517500043 2 17.556643024 -0.667762780 4 0.462629406 2 1.481423675 1.139411985 -2.993835804 0.457796465 2 -0.173373434 0.619844494 -1.515130079 0.484114514 1 -0.566029370 0.273335071 1 -21.965466277 Tb GTH-PBE-q29 4 6 10 9 0.500000000 1 -7.272801776 4 0.259166302 2 229.865072125 -254.613943211 295.196064370 0.270251357 2 398.718952272 -233.124922698 168.561767849 0.245407837 1 -13.288686713 0.180455163 1 -33.908357345 Dy GTH-PBE-q30 4 6 10 10 0.500000000 1 -7.465003311 4 0.252286021 2 233.922888625 -255.562057179 292.904849233 0.266723795 2 390.748247766 -235.364530025 169.923036441 0.252493399 1 -13.041564434 0.180670438 1 -34.118812490 Ho GTH-PBE-q31 4 6 10 11 0.500000000 1 -7.070002029 4 0.242339356 2 237.963483100 -257.518622800 293.321138600 0.261022150 2 434.742743633 -250.778942067 168.922458067 0.259084819 1 -13.212357286 0.183863195 1 -33.334176813

21

Er GTH-PBE-q32 4 6 10 12 0.500000000 1 -8.440641881 4 0.240632456 2 229.192874000 -251.217461600 288.569581400 0.262955148 2 452.933664300 -246.816963067 158.044670000 0.251742832 1 -14.143079042 0.175943441 1 -37.369242337 Tm GTH-PBE-q33 4 6 10 13 0.500000000 1 -7.820984622 4 0.229824520 2 237.571048959 -252.425857659 284.841129864 0.245648958 2 439.356463332 -234.946254129 160.668667820 0.268822896 1 -13.225193664 0.180076023 1 -35.800235126 Yb GTH-PBE-q34 4 6 10 14 0.500000000 1 -7.857588330 4 0.217536443 2 261.367665552 -258.017370096 284.373264272 0.278341463 2 452.078741970 -249.539240792 147.629693880 0.269939733 1 -13.844248648 0.185203058 1 -33.857938124 Lu GTH-PBE-q35 4 6 11 14 0.490000000 1 -8.165545656 4 0.220945258 2 317.613963120 -245.012664370 227.382408876 0.252847006 2 515.381490011 -256.956789586 148.927676699 0.222838425 1 -20.524328427

22

The corresponding MOLOPT basis sets are:

La DZV-MOLOPT-GTH 1 2 0 3 7 3 2 2 1 2.23164410000000 6.36920883417662E-01 1.03388584239346E-01 -2.06422567585900E-01 -3.81942784914523E-01 5.20906412067701E-01 4.73211491187013E-01 1.15889907098170E-01 6.93296946031992E-01 2.16099087000000 -6.75418466404104E-01 -8.42664751856035E-02 2.59875568312406E-01 4.37373559309912E-01 -5.93937877136375E-01 -5.49741748678359E-01 -1.46277969697783E-01 -7.17876496123734E-01 1.41317457000000 -9.66147249143188E-03 -6.64158779908996E-02 -1.95672298632518E-02 -3.45694579474865E-02 4.93015199101241E-02 7.82129620957820E-02 -4.59601495753897E-02 5.97219634971428E-02 0.50086179000000 -8.68264727109291E-02 1.43122704225202E-02 -4.91563714156940E-01 -8.83582552959101E-03 1.94125027653746E-01 1.64040718482716E-01 5.59472052518504E-01 1.02116139497366E-02 0.21269094000000 1.20385193656121E-01 -2.59245000182893E-01 9.30792964823556E-02 -4.37185110575576E-02 8.28677725547327E-02 3.63493703937926E-01 4.13305278955870E-01 1.77787925070400E-02 0.08321277000000 2.55759093405274E-01 4.04459579776489E-01 7.53245521359801E-01 -6.07374755222125E-01 -4.25188404683415E-01 5.25530276796041E-01 -5.82889025583462E-01 2.19592403155021E-03 0.03171828000000 -2.24953760541049E-01 8.64175057544492E-01 -2.67944173556757E-01 -5.39198996607485E-01 -3.84872569218779E-01 1.80328935494740E-01 -3.73456961853954E-01 8.85102846811129E-04 Ce DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 4.18237524000000 -2.55709413226539E-02 7.36576300368870E-03 -8.32438573926917E-03 2.04333917053169E-02 2.29293502559452E-02 4.66384465884811E-03 -8.97726446250939E-03 2.47592859000000 -2.61623852719931E-02 -9.37132186661999E-03 -9.37683158753043E-02 -8.00136921826957E-02 -8.65367299268815E-02 -1.86416546876456E-02 3.42415058191077E-02 1.57226158000000 4.66464565930329E-01 3.87198316643733E-02 4.44948388737540E-01 -2.48812113210110E-01 -2.75619313069053E-02 -8.97742761765502E-02 -8.58222366695025E-02 0.75072837000000 -4.20528848168514E-01 -3.47952702110125E-01 -1.49275170519501E-01 6.39627584982445E-01 4.43127743588676E-02 3.29281054212053E-01 1.74049133412445E-01 0.32763789000000 -5.33826251578161E-01 -1.26830422964948E-01 -2.34686468638884E-01 6.24649527433705E-01 3.92774887661322E-01 8.23168217192468E-01 2.23887188040902E-01

23

0.12786786000000 2.96715777665402E-01 4.92379406450713E-01 -7.68362738102677E-01 3.88855309298648E-02 3.67189162504830E-01 4.52912034209198E-01 -5.82760423497633E-01 0.05097481000000 -4.80850531409368E-01 7.86615649161499E-01 3.54142664048518E-01 -3.61178977485272E-01 8.36757051839597E-01 -2.02504175300237E-02 -7.55879082055740E-01 2 3 3 1 1 6.95600000000000 1.00000000000000 2 3 3 1 1 2.79300000000000 1.00000000000000 2 3 3 1 1 1.06800000000000 1.00000000000000 2 3 3 1 1 0.34990000000000 1.00000000000000 Pr DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 4.39591796000000 -8.31398562719043E-03 2.48341744528545E-02 -1.05972247582625E-02 8.58418269268012E-03 5.07646221667311E-02 1.06767902584073E-02 -2.78422614696601E-02 2.56776794000000 -4.00895549063873E-02 -1.64983644699875E-02 -8.21043904821067E-02 -7.00378391774263E-02 -1.65003425642652E-01 -3.74162025200424E-02 7.94712225353780E-02 1.57060627000000 4.19900087764128E-01 -1.19913081586626E-01 5.08085579909234E-01 -2.50298914949444E-01 3.92597332654944E-02 -6.33497448055813E-02 -1.31375996370367E-01 0.78494829000000 -4.11629409226868E-01 -2.13669589456472E-01 -3.19766212239041E-01 6.31410227527661E-01 3.59110194577983E-02 3.00047271985428E-01 2.07285766973044E-01 0.34094115000000 -5.37128529423651E-01 -7.73284440975443E-02 -2.03032949162405E-01 6.21327598603499E-01 4.23614239083528E-01 8.12607734494970E-01 1.66127500478465E-01 0.13034558000000 4.62826527141755E-01 5.12750571651612E-01 -6.64754606346762E-01 1.43895101247268E-01 1.60039642730230E-01 4.93094570446624E-01 -3.54360969191497E-01 0.06078830000000 -3.87109028102813E-01 8.18647903655388E-01 3.86812765798592E-01 -3.56284725591908E-01 8.73100328649776E-01 3.11591524425493E-02 -8.82899795419343E-01 2 3 3 1 1 7.22300000000000 1.00000000000000 2 3 3 1 1 2.82900000000000 1.00000000000000 2 3 3 1 1

24

1.05000000000000 1.00000000000000 2 3 3 1 1 0.33900000000000 1.00000000000000 Nd DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 4.67686881000000 -1.84635523839561E-02 -9.41436411029488E-03 9.48423388053217E-03 1.81766590529120E-02 1.40050086242962E-02 5.53525329419063E-03 5.56890457881671E-03 2.94144388000000 1.01926178672860E-03 6.82301673560527E-02 -1.39775590815099E-01 -4.50888096035157E-02 -4.28783480100715E-03 -1.56539638362687E-02 -1.82796944740753E-02 1.71549407000000 3.54281925073881E-01 -1.33505211062628E-01 5.56087176114545E-01 -2.79326785460719E-01 -1.12804459149377E-01 -7.60155188722356E-02 2.61790755541406E-03 0.82158105000000 -4.19471586499703E-01 -1.01795034100547E-01 -2.77163650823389E-01 5.87707373866578E-01 6.44180068537356E-02 2.79449538875024E-01 3.75493084850524E-02 0.35689793000000 -5.34441025251133E-01 -2.26726231314072E-01 -2.66709969039673E-01 7.22249475705701E-01 9.89946373806572E-02 8.06719400515469E-01 3.72451471686853E-01 0.13970930000000 4.80328814451032E-01 4.87706533380857E-01 -6.24869521097830E-01 8.95239761610916E-02 4.68417975184734E-01 5.14754612271509E-01 -5.91500265323160E-01 0.04267857000000 -4.26430515513051E-01 8.23290773053057E-01 3.64313149311161E-01 -2.11079014770283E-01 8.68156443786987E-01 9.24167070790305E-03 -7.13880503603356E-01 2 3 3 1 1 7.82500000000000 1.00000000000000 2 3 3 1 1 3.06200000000000 1.00000000000000 2 3 3 1 1 1.14300000000000 1.00000000000000 2 3 3 1 1 0.37110000000000 1.00000000000000 Pm DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 4.81656463000000 -8.44045237337290E-02 -7.20582698324575E-03 9.35411888630469E-02 1.12531818046019E-02 4.01984167766320E-02 2.34560596362279E-03 -3.70164731710461E-02

25

3.01992424000000 1.65468640015913E-01 6.02490312219872E-02 -3.15683735249028E-01 -4.93109777090491E-02 -4.68500836801754E-02 -7.74261033322132E-03 9.13208096639175E-02 1.70203691000000 3.24279923539893E-01 -9.26069834332587E-02 5.90566444993444E-01 -2.29964246796829E-01 -1.03377395525530E-01 -6.97801846876570E-02 -1.28203327972035E-01 0.80884291000000 -5.21039727425882E-01 -8.81250330722742E-02 -2.45708085096556E-01 6.32870724812486E-01 7.45952924969446E-02 3.40680528075547E-01 1.86335061049843E-01 0.34454172000000 -5.84429805020692E-01 -2.60319099057729E-01 -1.05500973055877E-01 7.04779397263568E-01 1.19311339943585E-01 8.18304397046495E-01 2.81203925014031E-01 0.13230951000000 3.42175004945482E-01 3.95063277048839E-01 -6.13637771395787E-01 3.54229131136986E-02 5.35757309214463E-01 4.57576773823515E-01 -6.62078753574052E-01 0.04044278000000 -3.60852058566285E-01 8.69560250501888E-01 3.07848772048831E-01 -2.14625493980741E-01 8.23812310640968E-01 -1.86106546082244E-03 -6.49391652840782E-01 2 3 3 1 1 9.19600000000000 1.00000000000000 2 3 3 1 1 3.64100000000000 1.00000000000000 2 3 3 1 1 1.40200000000000 1.00000000000000 2 3 3 1 1 0.47480000000000 1.00000000000000 Sm DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 5.14254447000000 -1.75691630797067E-02 6.88448709667556E-03 2.64406530493253E-03 1.27601492233223E-02 1.22259234557231E-02 2.48227490115885E-03 -3.89035740349234E-03 3.24872886000000 1.61140068846953E-02 9.95758193327239E-03 -8.13721665631279E-02 -3.79293152582252E-02 -2.70323214814880E-03 -9.04265838870334E-03 9.99838622349882E-03 1.73741769000000 4.34358694121963E-01 -9.32786458763034E-02 4.22598620911098E-01 -2.14150370856299E-01 -1.19678269071057E-01 -5.94645929148260E-02 -3.57105257243345E-02 0.80945305000000 -6.75730471699104E-01 -9.96399131690378E-02 -4.46786201674431E-02 6.44953302809119E-01 1.28181264720146E-01 3.71291486166409E-01 1.34362126196976E-01

26

0.34005735000000 -4.07389323001301E-01 -1.02589168771824E-01 -3.51262287446826E-01 6.99237232026099E-01 9.46907752651636E-02 8.49626757416796E-01 2.90715740298455E-01 0.12681129000000 3.65140632089842E-01 3.91848727038729E-01 -7.61919176440182E-01 -2.66419900330171E-02 6.58296122067300E-01 3.69659537814207E-01 -8.05646702579844E-01 0.03914979000000 -2.34219503992175E-01 9.03965967221909E-01 3.29969362095629E-01 -2.16635406176179E-01 7.25789065341539E-01 2.20506571353798E-03 -4.96965012604975E-01 2 3 3 1 1 9.38550000000000 1.00000000000000 2 3 3 1 1 4.27900000000000 1.00000000000000 2 3 3 1 1 1.88830000000000 1.00000000000000 2 3 3 1 1 0.77480000000000 1.00000000000000 Eu DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 5.34652456000000 -2.30514587773043E-02 1.97109917409011E-03 7.65388089517225E-03 1.79127928238801E-02 1.20910455595489E-02 3.15865034443402E-03 -1.20089921571522E-04 3.31221973000000 5.65857145370741E-02 1.48139364756093E-02 -1.10077430163909E-01 -7.56109875194690E-02 -7.26551238711004E-03 -1.08781591014321E-02 -4.39078342094372E-04 1.80858834000000 3.14760419467496E-01 -2.42194637852433E-02 5.39638657898657E-01 -1.93297982388296E-01 -1.27914269745379E-01 -5.35186229333161E-02 -2.57654687557505E-02 0.85719456000000 -5.80792172328951E-01 -1.53483337910867E-01 -2.32486179370011E-01 6.23754797394118E-01 1.68111784667483E-01 3.26834702065335E-01 1.29445726707913E-01 0.35821506000000 -4.09137777535115E-01 -1.76814321555905E-01 -3.20829100639841E-01 7.09575935204607E-01 9.74337317661253E-02 8.08824650762631E-01 4.16961656850869E-01 0.13357636000000 5.13372537647854E-01 3.36415594349455E-01 -7.12766226532001E-01 1.66530558728500E-03 5.64155610279647E-01 4.81286580073895E-01 -7.17118799104300E-01 0.04023003000000 -3.59065362628116E-01 9.11698518252094E-01 1.77757326929121E-01 -2.53035910668474E-01 7.92093745526737E-01 6.59729889214731E-02 -5.42644765876224E-01 2 3 3 1 1 9.44790000000000 1.00000000000000

27

2 3 3 1 1 4.31490000000000 1.00000000000000 2 3 3 1 1 1.91210000000000 1.00000000000000 2 3 3 1 1 0.78970000000000 1.00000000000000 Gd DZV-MOLOPT-SR-GTH 5 2 0 2 7 3 2 2 5.59677090000000 -1.35878826330605E-02 6.72095162666337E-04 1.28533946067190E-02 8.85750972497280E-03 1.75484692016863E-02 3.12812909049960E-03 -2.12036726871308E-03 3.50230035000000 5.91186819277078E-03 2.02410127252069E-02 -1.15129279080133E-01 -3.77008387521725E-02 -1.02465087973366E-02 -1.11420421226726E-02 5.47631500541752E-03 1.89721105000000 4.70003822920645E-01 -1.10331786006664E-01 3.96861575545720E-01 -2.03550364664786E-01 -1.42685632578040E-01 -5.12878754602592E-02 -2.79764089883626E-02 0.91341748000000 -6.55628449474706E-01 -5.14502449345743E-02 1.67966445478583E-02 6.37811214261053E-01 1.40238291412014E-01 3.42640447025973E-01 1.09841840429153E-01 0.38939153000000 -4.94687687723429E-01 -8.43818737817532E-02 -2.22733172437647E-01 6.84442075224601E-01 1.79556488628826E-01 8.39165265433382E-01 3.37788624190813E-01 0.14481943000000 3.01933944230836E-01 2.81384869857912E-01 -8.37666389976923E-01 -2.97743830042233E-02 5.45815691374363E-01 4.18792162468975E-01 -7.48983095760161E-01 0.05080032000000 -1.14665369120110E-01 9.47877562439806E-01 2.78394962116352E-01 -2.84458831934409E-01 7.93350988279841E-01 1.57457785779562E-02 -5.58606097604262E-01 2 3 3 1 1 9.52330000000000 1.00000000000000 2 3 3 1 1 4.34760000000000 1.00000000000000 2 3 3 1 1 1.92410000000000 1.00000000000000 2 3 3 1 1 0.79260000000000 1.00000000000000 Tb DZV-MOLOPT-SR-GTH 6 2 0 2 7 3 2 3

28

12.62165193000000 2.63150313397855E-01 2.75920747568875E-01 -2.29534159641915E-01 3.23339286916022E-03 4.42554560140806E-02 3.66201960419660E-03 2.45332089696323E-02 5.58475121303479E-04 6.72437222000000 1.12100175379467E-01 3.30092032872405E-01 -5.42442558532860E-01 2.10462052221002E-01 -1.16624848593508E-01 -3.08486266065285E-01 -3.44853285345094E-01 -6.06346654165208E-01 3.41699150000000 3.00217068620189E-01 -5.87552929899234E-02 5.17949773393714E-01 -4.85442534528900E-01 2.88189417112265E-01 -2.97287705027119E-01 3.55693485753689E-01 -6.17295238061172E-01 1.58752341000000 -2.07461573961026E-01 -2.35011210559256E-01 3.27973544983787E-01 7.92373070753704E-02 -5.47909128510165E-01 9.32072675152942E-02 6.26385825767554E-01 -2.31015730704829E-01 0.65525611000000 -5.96201511927088E-01 -5.15564402503859E-01 -3.70688898005795E-01 7.56159063449380E-01 9.54644339323703E-02 3.22225314789337E-01 -5.57532338519373E-01 -3.35364771268595E-01 0.24700792000000 7.57032345089346E-02 7.15323211326409E-02 -2.72623762736979E-01 3.69657224072585E-01 4.84757097453906E-01 8.06993522602640E-01 1.85663574943541E-01 -2.61362721260212E-01 0.05016424000000 -6.51020466450908E-01 6.96635493824822E-01 2.55924893608170E-01 7.30703225488018E-02 -5.97561414739346E-01 2.29537665688777E-01 -1.27608789503469E-01 -1.30926477266939E-01 2 3 3 1 1 27.76000000000000 1.00000000000000 2 3 3 1 1 10.98000000000000 1.00000000000000 2 3 3 1 1 4.27900000000000 1.00000000000000 2 3 3 1 1 1.59200000000000 1.00000000000000 2 3 3 1 1 0.50630000000000 1.00000000000000 Dy DZV-MOLOPT-SR-GTH 6 2 0 2 7 3 2 3 12.56351020000000 1.01946219877616E-02 5.30482693003410E-03 -3.76876660244758E-02 8.48062946355694E-03 8.85392342837320E-03 1.49696948253197E-03 2.13887030494234E-03 2.68641670216845E-03 6.70570037000000 2.43612524808085E-01 -3.04390742530620E-02 -2.96034516351133E-01 1.78436344905181E-01 7.93368397957354E-02 9.49883082377906E-02 1.20455701847814E-01 -4.90817398295040E-01 3.49925238000000 -4.53996389328329E-01 5.09401495444984E-02 5.23194485404674E-01 -4.13540069787687E-01 -1.88544862045712E-01 8.42174340487461E-02 2.45503456954647E-01 -7.40788288552856E-01

29

1.61426607000000 1.09913768476936E-01 -3.11635564438197E-02 1.04967358280927E-01 5.41768248520402E-02 1.62197229205481E-02 7.98472407187404E-02 5.32084121930716E-02 -3.39305549873108E-01 0.64232855000000 -3.38884634569258E-01 -7.32588443193683E-02 -7.85010704959878E-01 7.44567651957788E-01 2.32011470829891E-01 6.54211023933368E-01 -6.59968502658633E-02 6.21098379814215E-02 0.22899342000000 7.40793097792432E-01 -2.98301199419964E-01 6.77717437482374E-02 3.52006590293371E-01 1.52285365706923E-01 6.50127816446322E-01 -4.52268365211918E-01 -1.84175346371598E-02 0.07047220000000 2.42359320289416E-01 9.49278037056382E-01 -7.31968096556035E-02 -3.40365104142343E-01 9.38506725746041E-01 -3.56158083972736E-01 -8.44677754060626E-01 -3.01659878850734E-01 2 3 3 1 1 27.76000000000000 1.00000000000000 2 3 3 1 1 10.98000000000000 1.00000000000000 2 3 3 1 1 4.27900000000000 1.00000000000000 2 3 3 1 1 1.59200000000000 1.00000000000000 2 3 3 1 1 0.50630000000000 1.00000000000000 Ho DZV-MOLOPT-SR-GTH 6 2 0 2 7 3 2 3 12.30521213000000 -1.09498800559440E-02 -6.73056881188356E-03 -5.73216470190983E-02 1.20748030014911E-02 3.89315123139363E-03 2.89861562096413E-03 7.00110635542719E-03 7.70333920625418E-03 6.89265331000000 9.04473460907019E-02 -1.63214032728612E-02 -3.50974648148776E-01 1.35767925014780E-01 1.28924983132233E-01 1.44050961927728E-02 -4.62773533071611E-02 -4.25684611516166E-01 3.74514009000000 -1.76834465914595E-01 2.56788971158107E-02 6.63538933842279E-01 -3.21056401626826E-01 -2.87964852316636E-01 -4.91771078981686E-03 2.56508278332187E-02 -8.19487178211919E-01 1.73557208000000 2.29124216333128E-01 8.10209457811409E-02 6.57130385447420E-02 -3.41922315822506E-03 6.05679671746153E-02 -4.16969980457300E-02 -8.64145527850708E-02 -3.81161909915498E-01 0.70494403000000 -6.56905573137469E-01 -3.09163255173879E-01 -5.03533091094195E-01 7.10509992228838E-01 3.44697363965317E-01 6.42333275737345E-01 3.81350731707496E-02 -3.01507808256395E-02 0.26191801000000 6.56261520761308E-01 -2.01810548823772E-02 -3.66680107547675E-01 2.25659292495078E-01 4.02921559040170E-01 6.11281004260719E-01 -6.26033177283207E-01 2.41189582625750E-02

30

0.04869946000000 -2.13838554090060E-01 9.46823805414948E-01 -2.02309243195857E-01 -5.67966372429461E-01 7.84607482641121E-01 -4.60179056907483E-01 -7.72212489094851E-01 1.99709671065952E-02 2 3 3 1 1 34.38000000000000 1.00000000000000 2 3 3 1 1 12.94000000000000 1.00000000000000 2 3 3 1 1 5.04100000000000 1.00000000000000 2 3 3 1 1 1.87500000000000 1.00000000000000 2 3 3 1 1 0.58960000000000 1.00000000000000 Er DZV-MOLOPT-SR-GTH 7 2 0 2 7 3 2 3 13.29786362000000 -1.88258997114713E-02 -1.12923622850546E-02 -3.59985774371780E-02 2.91511147970692E-03 -2.85616974662119E-03 4.46317596728246E-03 5.55068354904846E-03 6.09241047822173E-03 7.20153202000000 2.69801972656753E-02 -3.14201631140619E-02 -3.91538351118871E-01 1.55734983485313E-01 1.16291132649830E-01 -6.65793505476507E-02 -5.72197683089214E-02 -4.33672919878100E-01 3.89149849000000 -7.45325639894567E-02 3.91965351360620E-02 6.79857949307220E-01 -3.36553888837010E-01 -2.43485178180600E-01 -1.44060017335282E-01 1.10111833987007E-02 -7.99137864521800E-01 1.82211428000000 2.41658115702460E-01 1.20026388872551E-01 3.05374279128731E-02 -3.15752575901760E-02 5.16366934175329E-02 -1.14364636559818E-01 -8.40688648901724E-02 -3.66104555330849E-01 0.74199544000000 -6.87232115788379E-01 -4.34879554084935E-01 -3.48116489314522E-01 7.53344784053229E-01 2.40969421567430E-01 6.15851897059552E-01 -1.19652008766815E-01 -1.36134886731089E-01 0.27368575000000 5.48780601953728E-01 6.00335122120518E-02 -4.75675470753964E-01 2.84899449743213E-01 3.87598221257440E-01 4.36960349456210E-01 -7.60521407772502E-01 -3.30104134632282E-02 0.04998959000000 -4.01890254204036E-01 8.88942239046961E-01 -1.86574951899199E-01 -4.61277075017281E-01 8.46296751387000E-01 -6.25705046601108E-01 -6.29918131935292E-01 1.40051470432146E-01 2 3 3 1 1 22.27540000000000 1.00000000000000 2 3 3 1 1 10.21230000000000 1.00000000000000 2 3 3 1 1 4.65890000000000 1.00000000000000

31

2 3 3 1 1 2.05510000000000 1.00000000000000 2 3 3 1 1 0.84060000000000 1.00000000000000 2 3 3 1 1 0.29960000000000 1.00000000000000 Tm DZV-MOLOPT-SR-GTH 6 2 0 2 7 3 2 3 13.07159832000000 4.82640863819318E-01 5.30962714586083E-01 4.81035344739481E-01 1.54527161195963E-02 2.73918158063254E-02 1.94326800952731E-02 1.26343666206368E-01 2.20430204249432E-02 7.69124664000000 -1.40423485625341E-01 7.94492570837716E-02 2.69608993815981E-01 1.60976620751110E-01 -1.29694839216536E-01 -1.45524359039653E-01 -4.30024180852938E-01 -2.43106400772169E-01 4.14640499000000 3.46080701857410E-01 -7.55963373952662E-02 -4.55438266261998E-01 -3.88879276828200E-01 2.57769097415642E-01 -4.56195408905127E-01 -8.46920750804919E-02 -7.68665681565586E-01 1.90595415000000 -2.04332883476302E-01 -1.67129705586130E-01 -3.84395783723523E-01 -3.48504723505320E-02 -3.08933145344357E-01 -1.29944762570536E-01 7.36416808121053E-01 -3.11042111935698E-01 0.77641959000000 -4.25703349727655E-01 -4.05224581951437E-01 5.22087096462240E-01 8.01263862408963E-01 3.72438344330715E-01 2.34823968919336E-01 -4.71414933279035E-01 -2.32789244687416E-01 0.28494144000000 -1.84170524385739E-01 -5.25601562277349E-02 1.42354998125132E-01 4.19977595100555E-01 -5.31270827649495E-01 7.85476150749333E-01 1.53381690023162E-01 -4.13625079522189E-01 0.05144299000000 -6.08829317433754E-01 7.14947364993345E-01 -2.18842347047294E-01 5.47826266039235E-02 6.32127620495588E-01 2.85184255648461E-01 -6.22578258038006E-02 -1.65959991829858E-01 2 3 3 1 1 35.69000000000000 1.00000000000000 2 3 3 1 1 13.54000000000000 1.00000000000000 2 3 3 1 1 5.29900000000000 1.00000000000000 2 3 3 1 1 1.97000000000000 1.00000000000000 2 3 3 1 1 0.61620000000000 1.00000000000000

32

Yb DZV-MOLOPT-SR-GTH 6 2 0 2 7 3 2 3 12.17373040000000 2.07362348970018E-04 1.47446619839764E-01 -1.09022057680819E-01 -2.26197536087966E-02 -2.50123759552461E-03 -8.13330415547623E-01 2.03729589600744E-01 -4.64591114630638E-01 6.86323383000000 -1.82670457585053E-01 1.24214794565837E-02 -2.48388016900023E-03 1.00691019419771E-01 1.31104615382825E-01 1.33501650894867E-01 5.72399632057193E-02 -3.34757394645174E-01 3.87428635000000 4.42159476178132E-01 -3.35744116700326E-01 2.45970619601946E-01 -2.03661757828175E-01 -3.20891816087186E-01 4.69782601167514E-01 1.83487196328873E-01 -6.94605645824650E-01 1.84256942000000 -2.76505025141618E-01 -1.68171598954976E-01 2.02033253141520E-01 2.38589211197316E-01 3.34519917406246E-02 2.18894837608890E-01 8.61239507450086E-02 -2.83153705299204E-01 0.75839072000000 -5.19918580936243E-01 2.05718231618124E-01 -5.75119844827363E-01 -1.69853029653692E-01 8.45138662995554E-01 -2.23656386738234E-01 -2.84209442147208E-01 -2.51781588606154E-01 0.27877809000000 6.12342350285100E-01 5.88020817282881E-01 -3.33304631992987E-01 3.92808504188513E-01 3.89175896956264E-01 2.60451585081994E-02 -8.55689597000181E-01 -1.89187697633446E-01 0.05199452000000 -2.22245235873348E-01 6.70082778598187E-01 6.67033902117279E-01 -8.41307416708132E-01 1.14006542755405E-01 -3.68750925614999E-02 -3.18046005170323E-01 -1.01260088897879E-01 2 3 3 1 1 40.55000000000000 1.00000000000000 2 3 3 1 1 14.98000000000000 1.00000000000000 2 3 3 1 1 5.86000000000000 1.00000000000000 2 3 3 1 1 2.16900000000000 1.00000000000000 2 3 3 1 1 0.67220000000000 1.00000000000000 Lu DZV-MOLOPT-SR-GTH 7 2 0 2 7 3 2 3 12.64717647000000 -7.46473450415586E-02 -1.25017022698197E-02 -8.45216706360905E-02 1.43102338976610E-02 1.26295142205977E-02 9.65694842306751E-03 7.80936697122167E-03 -5.45048154100064E-02 7.31232980000000 -4.70383438631707E-02 -5.44258989060867E-03 -1.36821300357875E-01 7.64829732394098E-02 6.51444846689639E-02 6.26840514242059E-02 1.98598556769331E-02 -7.27964859722694E-01

33

3.50738970000000 3.67222823169333E-01 7.63693693465873E-02 6.20098730302488E-01 -3.38372487389196E-01 -2.81597037450698E-01 -2.92463179712271E-02 5.51097975893657E-02 -6.52038066927356E-01 1.57826189000000 -4.72308055533134E-02 3.91918956568624E-02 -2.72035695698600E-01 1.91838648929557E-01 1.87980237143454E-01 1.10822507645460E-01 -4.78959753056949E-02 -1.94475956844904E-01 0.64515220000000 -6.20042694984947E-01 -5.75136636811166E-01 -7.95333334332790E-02 7.73251787600272E-01 2.82041547226272E-01 7.82074534398664E-01 2.24413920041415E-01 4.65196306045735E-02 0.23243020000000 2.69750411342863E-01 3.22639300949557E-01 -6.89246132356973E-01 8.86174748654325E-02 3.99227488185820E-01 5.82338001287281E-01 -5.40148023467217E-01 7.64656887296803E-03 0.05975385000000 -6.30803922951773E-01 7.46704446803679E-01 1.84998329203890E-01 -4.86699271302765E-01 8.01269747803634E-01 -1.79115472894852E-01 -8.07522130294446E-01 -4.35809998258455E-02 1 3 3 1 1 28.36240000000000 1.00000000000000 1 3 3 1 1 13.24780000000000 1.00000000000000 1 3 3 1 1 6.14400000000000 1.00000000000000 1 3 3 1 1 2.76230000000000 1.00000000000000 1 3 3 1 1 1.15740000000000 1.00000000000000 1 3 3 1 1 0.42440000000000 1.00000000000000

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Norm-Conserving Pseudopotentials and Basis Sets Optimized