Zeo-1, a computational data set of zeolite structures.

Fast, empirical potentials are gaining increased popularity in the computational fields of materials science, physics and chemistry. With it, there is a rising demand for high-quality reference data for the training and validation of such models. In contrast to research that is mainly focused on small organic molecules, this work presents a data set of geometry-optimized bulk phase zeolite structures. Covering a majority of framework types from the Database of Zeolite Structures, this set includes over thirty thousand geometries. Calculated properties include system energies, nuclear gradients and stress tensors at each point, making the data suitable for model development, validation or referencing applications focused on periodic silica systems.

Background & Summary

Atomistic models are an essential tool for the prediction of thermodynamic, mechanical or biochemical properties of a substance. More recently, the use of pre-trained models has become increasingly popular due to their comparably low complexity and high accuracy on modern hardware[1-6]. In order for such models to perform well, their empirical parameters require fitting to high-quality reference data. Depending on the application, reference data are either experimental, or come from computationally more expensive ab initio calculations. Although there are already a handful of large computational data sets covering small organic molecules[7-9], such data is still scarce for larger periodic systems (cf. Materials Cloud Archive[10,11] or the NOMAD database[12,13]). Motivated by this fact, we present a quantum-chemical data set for zeolites. Zeolites are porous materials comprised of interconnected SiO4 or AlO4 tetrahedra. Their properties can be fine-tuned through synthesis of materials with specific pore size, or the inclusion of additional metal cation sites[14-17]. Because of their topology and synthetic flexibility, zeolites have various applications as adsorbents[18-20] and catalysts[17,21-23]. To this day, a myriad of different zeolite framework types is available experimentally, and many more hypothetical structures can be derived[24-26]. The documentation of fundamental zeolite framework types and derived materials has led to the publication of the well-known Atlas of Zeolite Structures[27] in several editions. The atlas lists each unique framework type by its three-letter-code, as assigned by the by the Structure Commission of the International Zeolite Association (IZA). Today, its contents are available online at the Database of Zeolite Structures[28], which we use as a source of initial structures for our data set. In this first installment, we include properties for 204 out of the currently available 256 zeolite framework types in the database (a total of 226 unique geometries when also considering derived materials). Our descriptor provides the complete optimization trajectories for each system with atomic positions, lattice vectors, atomic gradients and stress tensors at each step. We envision future extensions of the data set to focus on derived geometries, covering structural defects and host-guest interactions.

Methods

Initial zeolite structures are collected from the public Database of Zeolite Structures[28] in the Crystallographic Information File (CIF) format, before conversion to the XYZ format with the Atomic Simulation Environment[29] (ASE) package. After selection of all systems with less than 301 atoms, each is manually filtered by removing redundant atom positions in case of fractional occupancies and adding missing hydrogen atoms where needed. Each structure’s coordinates and cell parameters are energy-minimized with the periodic density functional code BAND[30], as implemented in the Amsterdam Modeling Suite[31] (AMS). The calculations are performed with the revPBE functional[32,33], a ‘Small’ frozen core and the double-ζ polarized (DZP) basis set. Grimme’s D3(BJ) dispersion correction[34] is applied to all calculations. Previous research has shown that the selected level of theory can accurately reproduce zeolite geometries, albeit slightly overestimating the Si-O bond length (in the range of 2 pm) and smaller Si-O-X angles (in the range of 5 degrees) when compared to experimental results[35,36]. At the same time, dispersion-corrected functionals are generally more accurate when describing adsorption processes[37-39]. For the optimization of the initial structures, geometry convergence criteria are left at their default values, namely 0.001 Hartree/Å, 0.00001 Hartree/Atom and 0.1 Å for atomic gradients, energy and atomic displacements respectively. We use a Quasi-Newton optimizer[40] in the delocalized coordinates space for the initial optimizations. Cases of problematic convergence are restarted with the FIRE[41] optimizer.

Data Records

The data is made available at the Materials Cloud Archive[42]. Each system’s trajectory is stored in an individual NumPy[43]. npz file. We describe the data types held in each file in Table 1, storing the complete geometry optimization trajectory, including atomic coordinates, system energies, nuclear gradients, lattice vectors and stress tensors for each geometry optimization step. Entries at the first position correspond to the input structure; the last position holds the data for the final, optimized structure. Hirshfeld partial charges[44] are provided for the final (optimized) geometries. Atomic coordinates and lattice vectors are stored in ångström, all other properties are stored in atomic units.

Table 1

Overview of the data structures stored in a .npz file.

Data	Unit	Key	Array Shape
Atomic Numbers	—	numbers	(R,)
Atomic Coordinates	Å	xyz	(N, R, 3)
x-, y- and, z-Components of the Lattice Vectors	Å	lattice	(N, 3, 3)
Energy	hartree	energy	(N,)
Nuclear Gradients	hartree/bohr	gradients	(N, R, 3)
Stress Tensors	atomic units	stress	(N, 3, 3)
Hirshfeld Charges	atomic units	charges	(R,)

Each array can be accessed through the respective key. The variables N and R denote the number of geometry optimization steps and the system size respectively. Partial charges are only computed for the last geometry.

Technical Validation

The complete data set includes geometry optimizations of 226 systems, resulting in a total of 32550 geometries. System sizes range between 15 and 334 atoms (mean: 126). We illustrate the convergence of all reference calculations in Fig. 1, showing that all optimized systems are well within the defined convergence criteria. Elemental occurrences in the data set are listed in Table 2. Si-O, Si-Si distances as well as Si-O-Si angles are presented in Fig. 2 as the most prominent geometrical descriptors. As most of the initial structures from the IZA database are idealized geometries[45], a sharp mean for the Si-O bond distance can be observed at roughly 161 pm (Fig. 2a, blue histogram). Long tails in the distribution vanish and the mean is shifted towards approximately 164 pm when considering geometry-optimized structures (Fig. 2a, orange histogram). Considering the Si-O-Si angles, a slight shift towards smaller values is observed (mean of 149 vs. 142 degrees, Fig. 2c). Both effects have been previously reported by Fischer et al.[35,36] and are inherent to the selected level of theory. Distributions of the Si-Si distances in the second coordination sphere do not shift significantly when comparing initial and optimized geometries (Fig. 2b). Relative changes in the cell volumes are presented in Fig. 3 as the ratio of each system’s optimized-to-initial volume. Values below 1 translate to a shrinking unit cell as the optimization progresses. Overall, the geometrical descriptors are in good agreement with experimental data[46-51]. Additional averages for bond distances and angles are summarized in Tables 3, 4 respectively. Distributions of energies, atomic gradients, cell volumes and stress tensors are depicted in Fig. 4. As expected from geometry optimization trajectories, all properties have – with the exception of relative cell volumes – a distinct mean close to zero. Structures close to the initial input geometries contribute to the relatively high standard deviations. Evaluation of the relative cell volumes shows a shifted distribution, with roughly 76% of all structures having a larger volume than their respective optimized geometry. A detailed overview of all calculated structures, sorted by their IZA three-letter-code, the system size and number of iterations is provided in Online Table 1.

Fig. 1

Distribution of convergence criteria at the last optimization step for all calculated systems in the data set. Showing (a) the highest absolute component of all nuclear gradients, (b) change in system energy and (c) highest relative atomic displacement.

Table 2

Elemental occurrences in the complete data set.

Element	Occurrence
Si	226
O	226
H	21
Al	12
N	4
Ca	4
Ge	3
Li	2
Na	2
K	2
C	2
F	1
Be	1
Cs	1
Ba	1

Counting all structures containing at least one atom of the listed element. Each element’s isolated atomic energy is listed in hartree.

Fig. 2

Distributions of (a) Si-O bond lengths, (b) Si-Si distances in the second coordination sphere and (b) Si-O-Si angles as calculated from all geometries in the data set. Blue and orange bars denote data from initial and optimized geometries, respectively. Mean μ and standard deviation σ printed in the same color as the underlying data. N denotes the total sample size.

Fig. 3

Distribution of relative cell volumes per system as the quotient of optimized-to-initial cell volumes. Values below 1 describe a shrinking cell as the optimization progresses. Black line marks V/V0  =  1. Sample size is 226.

Table 3

Mean atomic bond length distributions and their standard deviations (std. dev.) in in ångström.

Bond	Mean	Std. Dev.	Number of points
Si-O	1.638	0.0085	30439
H-O	0.999	0.1174	266
Al-O	1.763	0.0133	234
Ge-O	1.795	0.0239	202
Na-O	2.473	0.0841	104
C-C	1.540	0.0049	100
C-H	1.100	0.0027	98
K-O	3.175	0.4809	61
Ca-O	2.469	0.0925	57
N-H	1.055	0.0913	50
Si-K	3.945	0.3196	41
Cs-O	3.429	0.2820	28
Li-O	1.970	0.0263	21
Be-O	1.669	0.0152	16
Al-K	3.625	0.1650	14
C-N	1.472	0.0037	10
Ba-O	2.903	0.1261	10

Averaged over all geometry-optimized structures.

Table 4

Mean Si-O-R angle distributions and their standard deviations (std. dev.) in degrees.

Angle	Mean	Std. Dev.	Number of points
Si-O-Si	148.7	11.2	12548
Si-O-Al	140.6	8.9	170
Si-O-K	106.8	8.8	81
Si-O-Na	112.8	15.1	64
Si-O-Ge	143.2	12.0	52
Si-O-H	110.7	7.9	40
Si-O-Cs	101.6	6.9	36
Si-O-Ca	118.5	16.6	19
Si-O-Be	129.9	0.2	16
Si-O-Li	112.7	4.2	8
Si-O-Ba	112.6	14.1	5

Averaged over all geometry-optimized structures.

Fig. 4

Distributions of physical quantities in the data set. Showing (a) energy differences per atom, relative to the respective energy of the optimized system; (b) atomic gradient components; (c) unit cell volumes, relative to the optimized system’s volume; (d) stress tensor components. Data is printed on a logarithmic y-scale for a clear display of the distribution. Mean μ and standard deviation σ printed in the same units as the underlying data. N denotes the total sample size.

Online Table 1

Summary of all calculated systems, sorted by their IZA code. Showing the chemical formula, system size R and number of iterations N.

IZA Code	Chemical Formula	R	N
ABW	Si8O16	24	102
ABW_0	Si4Al4O20Li4H8	40	30
ACO	Si16O32	48	4
AEI	Si48O96	144	16
AEL	Si40O80	120	16
AEN	Si48O96	144	137
AET	Si72O144	216	188
AFG	Si48O96	144	248
AFI	Si24O48	72	369
AFN	Si32O64	96	72
AFO	Si40O80	120	19
AFR	Si32O64	96	283
AFS	Si56O112	168	20
AFT	Si72O144	216	471
AFV	Si30O60	90	14
AFX	Si48O96	144	29
AFY	Si16O32	48	42
AHT	Si24O48	72	263
ANA	Si48O96	144	7
APC	Si32O64	96	245
APD	Si32O64	96	408
AST	Si40O80	120	178
ASV	Si20O40	60	22
ATN	Si16O32	48	168
ATO	Si36O72	108	100
ATS	Si24O48	72	299
ATT	Si12O24	36	63
ATV	Si24O48	72	401
AVL	Si42O84	126	54
AWO	Si48O96	144	21
AWW	Si24O48	72	11
BCT	Si8O16	24	5
BEA	Si64O128	192	61
BEC	Si32O64	96	395
BIK	Si12O24	36	106
BIK_0	Si4Al2O14Li2H4	26	54
BOF	Si24O48	72	18
BOG	Si96O192	288	21
BOZ	Si92O184	276	14
BPH	Si28O56	84	143
BRE	Si16O32	48	23
BSV	Si96O192	288	9
CAN	Si12O24	36	14
CAS	Si24O48	72	316
CAS_0	Cs4Si20Al4O48	76	325
CDO	Si36O72	108	987
CFI	Si32O64	96	339
CGF	Si36O72	108	30
CGS	Si32O64	96	307
CHA	Si36O72	108	20
CHI	Si28O60H8	96	25
CON	Si56O112	168	37
CSV	Si20O40	60	342
CZP	Si24O48	72	14
DAC	Si24O48	72	293
DFT	Si8O16	24	10
DOH	Si34O68	102	359
DON	Si64O128	192	30
EAB	Si36O72	108	55
EDI	Si5O10	15	5
EDI_0	Ba2Si6Al4O28H16	56	198
EMT	Si96O192	288	11
EPI	Si24O48	72	398
ERI	Si36O72	108	20
ESV	Si48O96	144	20
ETL_0	Si72O144	216	11
ETR	Si48O96	144	10
ETV	Si14O28	42	25
EWO	Si24O48	72	21
EWS	Si96O192	288	19
EZT	Si48O96	144	12
FAR	Si84O168	252	39
FER	Si36O72	108	25
FRA	Si60O120	180	264
GIS	Si16O32	48	7
GIU	Si96O192	288	37
GME	Si24O48	72	12
GON	Si32O64	96	16
GOO	Si32O64	96	1627
GOO_0	Ca2Si12Al4O42H20	80	195
HEU	Si36O72	108	46
IFO	Si32O64	96	179
IFR	Si32O64	96	15
IFW	Si64O128	192	138
IFY	Si48O96	144	13
IRN	Si92O184	276	417
IRR	Si52O104	156	14
IRR_0	Ge12Si40O104	156	29
IRY	Si76O154H4	234	241
ISV	Si64O128	192	40
ITE	Si64O128	192	27
ITG	Si56O112	168	29
ITH	Si56O112	168	65
ITN	Si54O109H2	165	518
ITT	Si46O92	138	43
ITW	Si24O48	72	259
IWR	Si56O112	168	47
JBW	Si6O12	18	12
JNT	Si32O64	96	33
JRY	Si24O48	72	232
JSN	Si16O32	48	16
JSR	Si96O192	288	11
JST	Si48O96	144	8
JSW	Si48O96	144	19
KFI	Si96O192	288	170
LAU	Si24O48	72	15
LAU_0	Ca4Si16Al8O64H32	124	306
LEV	Si54O108	162	16
LEV_1	Si54O108N8C60H104	334	14
LIO	Si36O72	108	660
LIT	Si24O52H8	84	24
LOS	Si24O48	72	393
LOV	Si18O36	54	468
LTA	Si24O48	72	41
LTJ	Si16O32	48	11
LTJ_0	Si8Al8O36N8H40	100	172
LTL	Si36O72	108	14
MAR	Si72O144	216	561
MAZ	Si36O72	108	42
MEI	Si34O68	102	307
MEL	Si96O192	288	47
MEP	Si46O92	138	379
MER	Si32O64	96	131
MFI	Si96O192	288	175
MFS	Si36O72	108	1351
MON	Si16O32	48	86
MOR	Si48O96	144	43
MRE	Si48O96	144	11
MRT	Si24O48	72	80
MSO	Si90O180	270	71
MTF	Si44O88	132	15
MTT_0	Si24F2O48N2H8	84	298
MTW	Si28O56	84	386
MVY	Si12O24	36	122
MWW	Si72O144	216	16
NAB	Si10O20	30	455
NAB_0	Si16Na8O56Be4H32	116	72
NAT	Si20O40	60	303
NAT_0	Si24Al16Na16O96H32	184	103
NAT_3	Ca4Si12Al8O52H24	100	251
NON	Si88O176	264	7
NPO	Si6O12	18	19
NPT	Si36O72	108	9
NSI	Si12O24	36	73
OBW	Si76O152	228	11
OFF	Si18O36	54	37
OKO	Si68O136	204	35
OSI	Si32O64	96	11
OSO	Si9O18	27	8
OWE	Si16O32	48	39
PAR	Si32O68H8	108	24
PCR	Si60O120	180	40
PCR_0	Si60O120	180	38
PCS	Si64O128	192	32
PHI	Si32O64	96	882
PON	Si24O48	72	33
POR	Si64O128	192	288
POS	Si64O128	192	21
PTT	Si24O48	72	355
PTY	Si10O20	30	20
PUN	Si36O72	108	30
PWO	Si20O40	60	307
PWW	Si40O80	120	30
RHO	Si48O96	144	7
RRO	Si18O36	54	35
RSN	Si36O72	108	17
RTE	Si24O48	72	22
RTH	Si32O64	96	205
RUT	Si36O72	108	49
RWY	Si48O96	144	19
SAF	Si64O128	192	16
SAO	Si56O112	168	121
SAS	Si32O64	96	338
SAT	Si72O144	216	23
SAV	Si48O96	144	730
SBN	Si10O20	30	14
SBS	Si96O192	288	51
SEW	Si66O132	198	32
SFE	Si14O28	42	178
SFF	Si32O64	96	256
SFG	Si74O148	222	212
SFH	Si64O128	192	26
SFN	Si32O64	96	313
SFO	Si32O64	96	19
SFS	Si56O112	168	26
SIV	Si64O128	192	49
SOD	Si12O24	36	5
SOF	Si40O80	120	372
SOR	Si48O96	144	18
SOS	Si24O48	72	323
SSF	Si54O108	162	145
SSY	Si28O56	84	335
STF	Si32O64	96	22
STF_0	Si16O32	48	48
STI	Si72O144	216	13
STT	Si64O128	192	21
STW	Si60O120	180	40
SVR	Si92O192H16	300	27
SVV	Si56O112	168	61
SWY	Si72O144	216	21
SZR	Si36O72	108	12
SZR_0	K4Si32Al4O72	112	32
TER	Si80O160	240	114
THO	Si10O20	30	225
TOL	Si72O144	216	217
TON	Si24O48	72	334
TON_0	Si24O48N1C4H11	88	389
UEI	Si48O96	144	40
UFI	Si64O128	192	30
UFI_0	K8Si56Al8O128	200	243
UOE	Si12O24	36	13
UOS	Si24O48	72	11
UOZ	Si40O80	120	19
USI	Si40O80	120	31
UTL	Si76O152	228	70
UTL_0	Ge16Si60O152	228	216
UWY	Si60O120	180	26
UWY_0	Ge36Si24O142H44	246	512
VET	Si17O34	51	384
VFI	Si36O72	108	288
VSV	Si36O72	108	27
WEI	Si20O40	60	17
WEN	Si20O41H2	63	357
YUG	Si16O32	48	22
YUG_0	Ca2Si12Al4O40H16	74	372
ZON	Si32O64	96	307

Usage Notes

No data points were filtered as outliers with regards to the distributions of chemical properties (see. Figure 4). Consecutive structures from the same optimization trajectory will be autocorrelated. The data repository provides an interactive plotting script, displaying the system energy, maximum absolute component of the nuclear gradients and the cell volume at every iteration step for each structure. This requires the Bokeh[52] (v. 2.3.1) package for Python to be installed. SHA-1 hash sums are provided for each file to guarantee data integrity, as well as an example input script for a calculation with BAND. Naming conventions: Derived materials are referred to by their IZA three-letter-code, e.g. H-EU-12 is tabulated as ETL_0. Leading non-alphabetical characters have been removed, e.g. *-ITN is tabulated as ITN.

Measurement(s)	potential energy
Technology Type(s)	Computational Chemistry
Factor Type(s)	Crystal structure, composition and topology