Comparison of Siliceous Zeolite Potentials from the Perspective of

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A Comparison of Siliceous Zeolite Potentials from the Perspective of Infrared Spectroscopy Jiasen Guo, and Karl D. Hammond J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12491 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 1, 2018

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The Journal of Physical Chemistry

A Comparison of Siliceous Zeolite Potentials from the Perspective of Infrared Spectroscopy Jiasen Guo†,¶ and Karl D. Hammond∗,†,‡ †Department of Chemical Engineering, University of Missouri, Columbia, Missouri, 65211, USA ‡Nuclear Engineering Program, University of Missouri, Columbia, Missouri, 65211, USA ¶Present Address: Department of Physics and Astronomy, University of Missouri, Columbia, Missouri, 65211, USA E-mail: [email protected]

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Abstract Zeolites—microporous crystalline aluminosilicate materials—are the basis of many physical and chemical processes. Computational modeling of these processes requires an accurate description of the zeolite structure and the potential energy surface. In this work, two published force fields, the MZHB potential [Sahoo and Nair, J. Comput. Chem. 2015, 36, 1562–1567], and the core–shell model [Schröder and Sauer, J. Phys. Chem. 1996, 100, 11043–11049] are tested in terms of their abilities to predict the structural and dynamical properties, including infrared spectra, of five silica polymorphs (three siliceous zeolites: zeolite Y, sodalite, and silicalite-1; as well as α-quartz and α-cristobalite) via classical molecular dynamics simulations. Normal Mode Analysis at the Γ point and quantum mechanical cluster calculations are carried out on periodic crystals and a finite-size representative cluster model, respectively in order to assist in the assignment of infrared bands. We observe that the core–shell model predicts a broader distribution of bond angles because of its omission of three-body interactions for the Si−O−Si angles. The MZHB potential, in contrast, consistently shifts angle-bending modes to higher wavenumbers relative to experiments.

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Introduction

Zeolites are crystalline aluminosilicate materials with micropores comparable in size to small molecules. Zeolites have been widely used in the petrochemical industry as catalysts, since their micropores affect the diffusion of reacting species based on molecular size and shape. A shining example is the production of p-xylene via toluene reacted with methanol. 1 Zeolites are also widely used in environmental protection, including water softening via ion exchange 2,3 and adsorption of organic pollutants such as phenol by natural zeolites; 4 as well as separation of gases such as CO2 and CH4 by adsorption in zeolite pores. 5 Diffusion and separation in zeolites are governed in part by the structure of the pores and by vibrations of the framework atoms. Therefore, a fundamental understanding of zeolites and their vibrations is important to the study of the dynamical and thermal properties of catalytic reactions and adsorption processes that occur in zeolites. 2


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Computational modeling of zeolite infrared spectra (IR) has been a powerful way to interpret and augment experimental observations. Computed infrared spectra are characteristic of the zeolite’s structure and bonding. While quantum mechanical calculations are generally more accurate than classical calculations, quantum mechanical calculations are often intractable because of the size of the system and the resulting simulation time and memory requirements. Nevertheless, for insulating materials with localized electronic structures such as silica polymorphs, quantum mechanical cluster calculations can be used to investigate the material properties from the properties of their characteristic building units. 6 On the other hand, all-atom classical mechanical simulations using interatomic potentials are often used for computational studies of bulk materials, such as zeolites, due to their relatively low computational expense. Such studies require an accurate, computationally inexpensive model of the zeolite potential energy surface. Several potentials that predict siliceous zeolites’ properties and infrared spectra to different levels of accuracy have been developed by other researchers. For example, Ermoshin et al. 7 developed the Generalized Valence Force Field (GVFF) based on quantum mechanical calculations on a cluster consisting of two SiO4 tetrahedra terminated by hydrogen atoms, and defined the potential energy as a function of internal coordinates. Smirnov and Bougeard 8 compared the performance of a harmonic potential (DHFF) 9 to their previous Simplified Generalized Valence Force Field (SGVFF). 10 Their comparison of infrared spectra for siliceous FAU showed that the SGVFF did a better job in predicting zeolite infrared spectra than the DHFF. One possible reason is that the DHFF does not have three-body angle interactions, indicating that simple models may not be able to reproduce zeolites’ properties accurately. Nicholas et al. 11 developed a more accurate valence potential for siliceous zeolites that included higher-order energy corrections for three-body interactions, and a good reproduction of the silicalite-1 infrared spectrum was achieved using this potential. Liang et al. 12 adopted a polarized potential parameterized by ab initio calculations; their model showed good reproductions of the infrared spectra for α-quartz, α-cristobalite, and other silica polymorphs. Studies have also been undertaken to evaluate the transferability of existing potentials to other

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zeolite frameworks and to develop potentials that can be used for a wide range of zeolite frameworks. Bueno-Pérez et al. 13 tested the performance of three published potentials in predicting infrared spectra and found out that none of the potentials was good enough to enable the assignment of experimental spectra. Gabrieli et al. 14 developed a new potential which reproduced infrared spectra of silicalite-1, NaA, CaA, NaX, and NaY well; however, in their potential, different sets of atomic partial charges for the zeolite framework atoms were used for each zeolite framework. Atomic partial charges generate electrostatic interactions between the zeolite framework and guest molecules, which strongly affect the behavior of guest molecules inside zeolites. Consequently, it is still necessary to develop a potential that uses a single parameter set for a wide range of zeolites. The first step in developing potentials for zeolites is to generate an accurate and robust potential for siliceous materials. This work aims to find possible candidates for the further development of zeolite potential energy models by testing the performance of some published siliceous zeolite potentials. In the present work, two published potentials for siliceous zeolites, namely the MZHB potential developed by Sahoo and Nair 15 and the core–shell model developed by Schröder and Sauer, 16 were tested in terms of their abilities to predict the infrared spectra of five silica polymorphs (αquartz and α-cristobalite, as well as three siliceous zeolites: zeolite Y, sodalite, and silicalite-1). Equilibrium bond lengths and angles, bulk moduli, and lattice constants were also calculated. We find that the core–shell model predicts broad distributions and large average values for the Si−O−Si angles, probably due to its omission of three-body interactions defined for the Si−O−Si angles. The MZHB potential, in contrast, consistently shifts angle-bending modes to higher wavenumbers based on the results of normal mode analysis and quantum mechanical cluster calculations.

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2 Theory and Methodology 2.1

Force Fields

2.1.1 The MZHB Potential The first model we will discuss is the MZHB potential of Sahoo and Nair. 15 In this model, the Lennard-Jones parameters and partial atomic charges were taken from the prior work of Zimmerman, Head-Gordon, and Bell 17 (ZHB); as such, Sahoo and Nair’s modification was named the Modified ZHB potential (MZHB). The bond length and angle force parameters were determined in Sahoo and Nair’s work via fitting to the experimental zeolite Y bulk modulus. Tests of the potential’s performance were based on the prediction of the FAU infrared spectrum, as well as bond length and angle distributions and lattice parameters for six silica polymorphs (FAU, LTA, SOD, MFI, α-quartz, and α-cristobalite). The functional forms of this potential are as follows: X 1 kR (R − R0 )2 , 2 bonds X 1 kθ (θ − θ0 )2 , Vangle = 2 angles X 1 qi q j Vel = , 4πε0 ri, j i< j r 6  X  rm 12 m  , VvdW =  −2 r r i, j i, j i< j Vbond =

(1) (2) (3) (4)

where R0 , θ0 , kR , and kθ are the equilibrium bond length and bond angle and the corresponding force constants; R and θ are the instantaneous bond length and angle, respectively; qi and ri, j are the atomic partial charge and interatomic distance; and rm are the Lennard-Jones energy parameter and minimum energy internuclear distance parameter. Arithmetic mean and geometric

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mean combination rules are used for rm and , viz., rm,i + rm, j , 2 √ = i j .

rm =

(5) (6)

Ewald summation 18 is applied to calculate the electrostatic energy [Eq. (3)] among the fixed point charges with a cutoff of 12 Å. The cutoff of the Lennard-Jones interactions is also 12 Å. Note that in the MZHB potential, the non-valence interactions [Eqs. (3) and (4)] are included even between bonded atom pairs separated by one, two, and three bonds, typically known as 1–2, 1–3, and 1–4 interactions, respectively. These non-valence interactions between neighboring atoms are typically excluded in CHARMM-style potentials 19 because the interactions between 1–2 and 1–3 atom pairs have already been covered by bond length and bond angle terms, respectively, and the interactions between 1–4 atom pairs have been partially covered by torsional interaction terms (dihedral, improper, etc.). Table 1 lists the model parameters of the MZHB potential. Table 1: The MZHB potential parameters from Sahoo and Nair. 15 bond potential Si–O

kR (eV/Å2 ) 23.3000

angle potential O–Si–O Si–O–Si

kθ (eV/rad2 ) θ0 (◦ ) 6.8000 109.470 2.2200 149.800

Lennard-Jones Si O

(eV) 0.00864 0.00324

charge Si O

q (e) 0.700 −0.350

R0 (Å) 1.620

rm (Å) 2.200 1.770

2.1.2 The Core–Shell Model The core–shell model of Schröder and Sauer 16 is a type of ion pair potential, meaning it treats ions as pairs of nuclei and electron shells under the constraints of charge conservation and mass 6


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conservation. Oxygen atoms are separated into cores and shells, while silicon atoms are treated as ordinary atoms. Besides the electrostatic and angle-bending interactions given in Equations (2) and (3), a short-range interaction and a harmonic potential between the cores and shells are included: Vshort-range =

X

Ai, j e−ri, j /ρi, j ,

(7)

i, j

Vcore–shell =

X

k s ri2 ,

(8)

i

where Ai, j and ρi, j are the Born–Mayer potential parameters of the two involved atoms i and j. Equation (7) effectively replaces Equations (1) and (4) in the MZHB potential, though the summation runs over all particle pairs regardless of the distance between the two involved particles. Compared with the Lennard-Jones interactions given by Eq. (4), this short-range interaction only accounts for repulsions between particles i and j. The summation of the self-polarization potential, given by Equation (8), runs over all core–shell pairs, where k s and ri are the force constant and separation distance of the specific core–shell pair, respectively. Electrostatic interactions are computed between all particles using Ewald summation with a cutoff of 10 Å, except for the core and shell of the same core–shell pair. Note that the short-range interactions, together with the three-body interactions [Equation (2)] in the core-shell model, are only defined between silicon atoms and oxygen shells and are only defined for O−Si−O angles in the core–shell model. Model parameters are listed in Table 2.

2.2 Silica Polymorph Models The initial structures of silica polymorphs for energy minimization were built from crystallographic coordinates, available from the International Zeolite Association. 20 The supercells of the five silica polymorphs used in this work and the references used for their crystal structures are listed in Table 3.

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Table 2: The core–shell model parameters from Schröder and Sauer. 16 charge

qcore

qshell

Si O

4 1.062370

−3.062370

short-range

A (eV)

ρ (Å)

Si−O

1550.950

0.30017

core–shell

k s (eV/Å2 )

O

112.7629

angle potential

k (eV/rad2 )

θ0 (◦ )

O−Si−O

0.18397

109.47

Table 3: Silica polymorphs studied in this work. framework

supercell

ref.

α-Cristobalite 6 × 6 × 6 (tetragonal standard cell, 2592 atoms) α-Quartz 6 × 6 × 6 (monoclinic standard cell, 1944 atoms) FAU 3 × 3 × 2 (triclinic primitive cell, 2592 atoms) SOD 4 × 4 × 4 (cubic standard cell, 2304 atoms) MFI 2 × 2 × 2 (orthorhombic standard cell, 2304 atoms)

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21 22 23 24 25

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2.3

Methodology

For each calculation, geometry optimization was first performed to minimize the total energy with respect to both internal and external degrees of freedom via relaxing atomic positions and the simulation box size at the same time using GULP. 18 The energy-minimized structures were then taken as initial configurations for molecular dynamics (MD) simulations using LAMMPS 26 with the parameters listed in Table 4. A 100 ps molecular dynamics simulation was first carried out at 300 K with a Nosé–Hoover thermostat in place, followed by a 200 ps simulation without a thermostat in place for trajectory sampling. Note that the time step (0.1 fs; see Table 4) is unnecessarily small; a time step of 1 fs is probably small enough for this particular set of simulations. From the perspective of the simulation of infrared spectra, time steps of 1 fs 11,15 or even 2 fs 8 have been used in literature for zeolites. Trajectories for infrared spectra calculations were sampled every 100 time steps (10 fs); trajectories for the calculation of average bond lengths and angles were sampled every 4000 time steps (400 fs). Infrared spectra at 300 K were computed with the Fourier transform of the dipole moment autocorrelation function using TRAVIS. 27–29 In order to assign the computed Table 4: The MD simulation parameters adopted in this work. parameter

value

time step 0.1 fs (unnecessarily small) sampling frequency every 100 steps (10 fs) equilibration time 100 ps simulation length 200 ps a shell/core mass ratio 0.01 a The shell/core mass ratio applies only to the core–shell model infrared peaks to specific crystal vibrations, a combination of the Normal Mode Analysis (NMA) and quantum mechanical cluster calculations were carried out. Normal Mode Analysis calculates the vibrational frequencies and the corresponding eigenvectors of the studied material at the center of the reciprocal lattice, also called the Γ point (k = 0); the resulting eigenvectors are proportional to the displacements of each atom during a vibration, and are extremely useful in visualizing the normal modes to assist with peak assignments (see Figure 5). In this work, the NMA was carried 9



Figure 1: The cluster model used for peak assignments consisting of a double six-membered ring (D6R) surrounded by four layers of silicon and oxygen atoms, terminated by hydrogen atoms. out using GULP. 18 The cluster calculation was performed using GAUSSIAN 09 30 on the cluster shown in Figure 1. This cluster consists of a double six-membered ring (D6R) unit surrounded by four layers of silicon and oxygen atoms, then terminated by hydrogen atoms; the initial coordinates of this structure were drawn from the FAU supercell optimized using GULP 18 with the MZHB potential. Since silica polymorphs are electronic insulators with localized electron density, edge effects will not significantly change the properties near the center of the cluster, so the properties of the center D6R of the cluster model will approach the properties of the bulk structure as the cluster gets bigger and bigger. We show in the Supporting Information that this cluster is large enough to reproduce the relative infrared peak positions of the characteristic vibrational modes of the periodic FAU structure.

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3 Results and Discussion 3.1

Bond Length and Angle Distributions

The calculated bond length and angle distributions of five silica polymorphs are listed in Table 5. Good agreement between model-computed data and experimental data is achieved, especially for the average Si−O bond lengths and O−Si−O angles, though a larger variance of the Si−O−Si angles is predicted by the core–shell model. Figure 2 shows the SOD O−Si−O and Si−O−Si angle distributions for both models at 300 K. The average value of the Si−O−Si angles predicted by the core–shell model matches with the experimental value better than that predicted by the MZHB potential. The broad Si−O−Si angle distribution predicted by the core–shell model ranges from 140◦ to 180◦ ; we think this might be because of the absence of three-body interactions that constrain the Si−O−Si angles, which leads to a larger variance in Si−O−Si angle. This large variance was also observed in the work of Smirnov and Bougeard. 8 In general, although the two potentials have similar performance in predicting geometric observables, we think the MZHB potential is preferable in the sense that it predicts narrower distributions of the Si−O−Si angles (see Table 5 and Figure 2) and costs less in terms of simulation time (data not shown); the computational cost difference is expected in light of the extra degree of freedom (the shell position) in the implementation of the core–shell model.

3.2 Infrared Spectra Zeolite infrared peak assignments have been studied empirically by Flanigen et al. 32 ; a typical wavenumber range of infrared peaks associated with zeolite framework vibrations is between 400 cm−1 and 1200 cm−1 . Some peaks originate from the vibration of individual SiO4 tetrahedra; these “internal tetrahedral” vibrations are insensitive to the topology of the framework and have been assigned approximately to the same wavenumbers among various frameworks. On the other hand, “external-linkage” peaks are sensitive to the topology of the framework and some secondary building units, and therefore vary among different zeolite frameworks. 32 Typical zeolite 11



O-Si-O (MZHB) Si-O-Si (MZHB) O-Si-O (Core-shell) Si-O-Si (Core-shell)

Expt. = 109.0° Probability

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Expt. = 159.7°

100

120

140 160 Angle /degrees

180

200

Figure 2: The SOD angle distributions at 300 K as modeled by the MZHB potential 15 and the core–shell model 16 via molecular dynamics. The average values for the O−Si−O angle and the Si−O−Si angle are predicted to be 109.43◦ and 155.031◦ with the MZHB potential and 109.43◦ and 159.24◦ with the core–shell model; although a broader Si−O−Si angle distribution is predicted by the core–shell model, probably because of its omission of three-body interactions that constrain the Si−O−Si angles, the experimental value is better-reproduced by the core–shell model.

Table 5: Silica polymorphs’ bond and angle distributions predicted by the MZHB potential and the core–shell model at 300 K. Standard deviations are included in parentheses. RSi−O (Å)

θO−Si−O (◦ )

θSi−O−Si (◦ )

SOD

MZHB shell expt.

1.62 (0.04) 1.61 (0.03) 1.587a

109 (3) 109 (4) 109.0a

155 (5) 159 (7) 159.7a

α-quartz

MZHB Shell expt.

1.60 (0.04) 1.62 (0.04) 1.609b

109 (3) 109 (4) 109.375b

150 (5) 148 (6) 143.73b

FAU

MZHB shell expt.

1.60 (0.04) 1.62 (0.03) 1.605c

109 (4) 109 (5) 109.5c

146 (6) 147 (8) 143.7c

α-cristobalite

MZHB shell expt.

1.60 (0.04) 1.61 (0.04) 1.603d

109 (4) 109 (5) 109.73d

150 (5) 158 (9) 146.49d

MFI

MZHB shell expt.

1.60 (0.04) 1.61 (0.04) 1.584–1.591e

109 (4) 109 (5) 109.5e

150 (7) 156 (10) 150–162.8e

a

Ref. 31. b Ref. 22. c Ref. 23. d Ref. 21. e Ref. 25.

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infrared peak assignments as assigned by Flanigen et al. 32 are listed in Table 6. In the following discussion about the model predictions of silica polymorphs’ infrared spectra, peak assignments are based on Table 6; specifically for the angle-bending modes of FAU, additional assignments are performed via comparing the mode visualizations predicted by both the cluster calculations and the MZHB potential. Such comparisons help demonstrate the consistent peak shifts predicted by the MZHB potential. Table 6: Zeolite infrared peak assignments from Flanigen et al. 32 vibration

wavenumber (cm−1 )

internal tetrahedral

asymmetric stretch symmetric stretch angle bend

950–1250 650–720 420–500

externallinkages

double ring pore opening symmetric stretch asymmetric stretch

500–650 300–420 750–820 1050–1150 (∗ )

*: Weak shoulder

3.2.1 FAU (Siliceous Zeolite Y) The cluster calculations were performed using GAUSSIAN 09 30 at HF/6-31G∗ , as many classical mechanical potentials are parameterized at this level; 33 also, HF/6-31G∗ has been observed to be one of the best levels of theory that minimizes the objective function when fitting computed infrared frequencies once scaling factors are applied. 34 Details for the cluster calculations are available in the Supporting Information. The computed infrared spectrum for the cluster is presented in Figure 3; peak assignments are based on vibration visualizations with GaussView. 35 Note that the experimentally-observed major peak in the angle-bending region at around 462 cm−1 is assigned to the six-membered ring (6R) deformation, and two infrared modes associated with the four-membered ring (4R) breathing motion are observed on both sides of this major peak (see the Supporting Information); these findings serve as the foundation of the rest of the discussion. 13



+

*: 4R breathing +: 6R deformation

* Intensity (a. u.)

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* FAU Expt. +

*

* D6R+4layer 300

400

600 700 500 -1 Wavenumber cm

800

900

Figure 3: Infrared spectra of the cluster model (Figure 1). We assign the experimentally-observed major peak in the angle-bending region at around 462 cm−1 (+) to the 6R deformation. Two infrared modes (*) associated with the 4R breathing motion are observed in both sides of this major peak. The measured FAU spectrum is for zeolite Y with Si/Al = 33 from the work of Jacobs and coworkers. 36 Figure 4 compares the FAU infrared spectrum predicted by the MZHB potential with a measured spectrum from Jacobs et al. 36 Peak assignments in the angle-bending region are labeled in Figure 4. In order to support these peak assignments, visualizations of the angle-bending infrared peaks that we believe should correspond to the same vibration, as predicted by both the MZHB potential via NMA and the cluster calculation are presented in Figure 5. All of these visualizations focus on the D6R unit in Figure 1. Figure 5a depicts the molecular motion associated with the infrared peak at around 453 cm−1 in the MZHB-computed infrared spectrum. Apparently, as is indicated by the arrows, this molecular motion is the 4R breathing motion originating mainly from the movements of oxygen atoms, in which three of the four oxygen atoms in each 4R move, causing the expansion or contraction of the corresponding 4R. In the work of Sahoo and Nair, 15 this vibration was assigned to the major peak in the angle-bending region at around 462 cm−1 (“+” in Figure 4). However, by comparing the molecular motion of the cluster corresponding to the infrared peak at around 414 cm−1 , presented in Figure 5b, we think this MZHB-predicted peak should be assigned as a 4R breathing mode (leftmost “*” in Figure 4); in other words, to the band at around 400 cm−1 in the measured infrared spectrum. Note that pure ring-breathing modes are not infrared-active, since the vibrations do 14


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*: 4R breathing +: 6R deformation Intensity (a. u.)

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+ * * Expt. MZHB

0

200

* +* 400

600 800 1000 -1 Wavenumber /cm

1200

1400

Figure 4: FAU infrared spectra predicted by the MZHB potential at 300 K. We believe that the measured and computed peaks labeled with the same symbol (“*” and “+”) correspond to the same underlying vibrations, based on a comparison between mode visualizations predicted by both the cluster calculation and the MZHB potential via NMA (see text). Although two infrared peaks associated with 4R breathing motion are predicted by the MZHB potential on both sides of the 6R deformation peak, apparent peak shifts to higher wavenumbers are observed in the angle-bending region, indicating that the angle-bending force constants of the MZHB potential are too large. The measured infrared spectrum is for zeolite Y with an Si/Al ratio of 33, from the work of Jacobs et al. 36 not change the dipole moment. The breathing modes we observe here, however, are asymmetric, characterized by the motions of three of the oxygen atoms in the 4R, with the remaining oxygen atom almost stationary (see Figure 5a). Thus, in this case, the ring-breathing mode is infraredactive. Another such 4R breathing infrared mode is also predicted by the MZHB potential at around 564 cm−1 (right-most “*” in Figure 4), shown in Figure 5c, which corresponds to the cluster infrared peak at around 460 cm−1 , shown in Figure 5d. As suggested by Figure 3, a 6R deformation mode exists in between the two 4R breathing modes; this 6R deformation mode is also reproduced by the MZHB potential at around 528 cm−1 (see Figure 5e), which matches with the cluster infrared mode at around 446 cm−1 (Figure 5f). The above discussion about the peak assignments of the angle-bending peaks indicates consistency between the MZHB-predicted FAU infrared spectrum and the cluster-calculated infrared spectrum in the sense that two 4R breathing modes are predicted on both sides of the major peak in the angle-bending region. Therefore, according to the match between cluster infrared modes

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(a) 453 cm−1 (453 cm−1 )

(b) 414 cm−1

(c) 564 cm−1 (562 cm−1 )

(d) 460 cm−1

(e) 528 cm−1 (527 cm−1 )

(f) 446 cm−1

Figure 5: A graphical comparison between the MZHB-predicted infrared modes via NMA and cluster infrared modes. (a), (c), and (e) present the MZHB-predicted FAU infrared modes via NMA at around 453, 564 and 528 cm−1 , respectively; MD-derived wavenumbers are given in parenthesis. (b), (d), and (f) present the cluster infrared modes at around 414, 460, and 446 cm−1 , respectively. Arrows denote atomic displacements, indicate that identical molecular motions are predicted by both the MZHB potential and the cluster calculation. (a) and (b) depict a 4R breathing motion characterized by the motions of the three highlighted oxygen atoms in (b); similar motions are observed in (c) and (d); (e) and (f) depict a 6R deformation motion, where the atoms move along the circumference of the 6R. and experimentally measured infrared modes in Figure 3, it is clear that the MZHB potential shifts these three angle-bending modes to higher wavenumbers. These peak shifts in the angle-bending region are observed in the MZHB-predicted spectra for all five silica polymorphs studied in this work. We believe that these shifts are due to too-large angle-bending force constants. In the companion paper, 37 we show how the predictions of these angle-bending peaks can be improved via reparameterizing and extending the MZHB potential. Figure 6 compares the FAU infrared spectrum predicted by the core–shell model to a measured infrared spectrum of zeolite Y from Jacobs et al. 36 Although all the experimentally-observed in16


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frared peaks in the angle-bending region are reproduced, it is difficult to tell how well the core–shell model predicts the FAU infrared spectrum. For instance, according to Figure 3, one would expect the computed peak at around 370 cm−1 to be a 4R breathing mode. However, when visualized (data not shown), the molecular motion of this mode is different from the 4R breathing motion. The molecular motion of another computed infrared peak at around 547 cm−1 is also inconsistent with the cluster calculation. We think that one possible explanation for these observations is that the core–shell model lacks three-body interactions for the Si−O−Si angles. As is evident in Figure 2, the lack of three-body interactions to constrain the deformation of Si−O−Si angles results in a broader angle distribution. For this reason, peak assignments are carried out empirically based on Table 6. Note that the measured infrared peak at around 1210 cm−1 is reproduced by the core–shell model, though it is missing in the infrared spectrum predicted by the MZHB potential. This peak, according to Table 6, should be assigned as an external asymmetric stretching mode; however, the measured peak at 1210 cm−1 may originate from aluminum, since enhancement of this peak with increasing aluminum concentration had been observed experimentally. 36 It is also possible that this shoulder near 1210 cm−1 is also an internal asymmetric stretching mode splitting from the principal peak near 1090 cm−1 . In the work of Van Santen and Vogel, 38 performed on siliceous SOD, the broad internal asymmetric stretching infrared peak near 1100 cm−1 was deconvoluted into three components; the appearance of these components was then attributed to the breaking of the cubic symmetry of silica sodalite lattice by comparing to 29 Si nuclear magnetic resonance (NMR) results (see Figure 18 in Ref. 38). Such breaking of symmetry was attributed to the non-equivalence of silica tetrahedra in the all-silica SOD. 39 Recall that the core–shell model predicts broad Si−O−Si angle distributions for silica polymorphs due to its omission of three-body interactions defined for the Si−O−Si angle (see Figure 2 and Table 5); such wide distributions of the Si−O−Si angle will give dispersive

29

Si chemical shifts according to published empirical correlation relations, 40

indicating the existence of wide distributions of non-equivalent silica tetrahedra during molecular dynamics simulations with the core–shell model. Therefore, following the reasoning used by Van Santen and Vogel, 38 it is not surprising that the core–shell model predicts shoulders, which split

17



*: 4R breathing +: 6R deformation Intensity (a. u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 30

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Expt. Core-shell

0

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Figure 6: FAU infrared spectra predicted by the core–shell model at 300 K. Although the measured infrared spectrum 36 is roughly reproduced, the molecular motions associated with computed infrared peaks in the angle-bending region are not consistent with predictions from the cluster calculation. One possible reason is that the core–shell model lacks three–body interactions defined for the Si−O−Si angles, which leads to normal modes that give rise to large Si−O−Si angle deviations. from the principal peak at 1090 cm−1 in Figure 6. The visualization of the vibration associated with the shoulder near 1210 cm−1 (data not shown) shows that the vibration of this shoulder largely resembles that of the principal internal asymmetric stretching mode, which helps convince us that this shoulder is an internal asymmetric stretching mode. As such, in the remainder of this work, this shoulder, which appears in the infrared spectra of other silica polymorphs, is assigned as an internal asymmetric stretching mode, regardless of the assignment in Table 6. Full peak assignments for the predictions from both models are listed in Table 7.

3.2.2 SOD (Siliceous Sodalite) Figure 7 compares the computed SOD infrared spectra predicted by both the MZHB potential and the core–shell model with a measured infrared spectrum from Van Santen and Vogel. 38 All of the measured bands are qualitatively reproduced by both potentials. Two major differences between the two model-predicted infrared spectra are observed. The first difference occurs in the anglebending region, where a measured infrared peak with medium intensity is observed at around 460 cm−1 . This peak was predicted by the MZHB potential at around 530 cm−1 , which is consis18


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Table 7: A comparison of the calculated and measured infrared wavenumbers for siliceous zeolite Y (FAU), siliceous sodalite (SOD), α-quartz and α-cristobalite. Values are in cm−1 . MZHBa

core–shella

expt.b

assignmentc

453

370

400

pore opening (4R breathing)

527 562

445 547

462 482 529

angle bending (6R deformation) Angle bending (4R breathing) angle bending

605

632

612

D6R

837

857 892

794 834

external symmetric stretching

1091

1072 1205

1090 1210

internal asymmetric stretching

530

438

460

angle bending

740 795

850

788


1090

1090

1126

internal asymmetric stretch

394 458 515 563

349 388 431 476

363 388 459 498

angle bending

754

690

Internal symmetric stretching

714 793

840 886

764 786


1095

1087 1161

1071 1147

internal asymmetric stretching

555 586

438 443

472

angle bending

609

angle bending

787


FAU

SOD

α-quartz

α-cristobalite

615 771

849

1089 1110 1086 internal asymmetric stretching b Calculated wavenumbers at 300 K; Sources of experimental spectra: FAU, 36 SOD, 38 α-quartz, 41 α-cristobalite; 42 c Peak assignments were carried out based on Table 6, and additional assignments for FAU (in parenthesis) for the angle-bending modes were performed via comparing mode visualizations of these modes between MZHB potential predictions and cluster calculation predictions.

a

19


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Intensity (a. u.)


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Figure 7: SOD infrared spectra predicted by both the MZHB potential and the core–shell model at 300 K. The MZHB potential predicts the angle-bending mode at a high wavenumber, probably because of a too large O−Si−O force constant; while the core–shell model predicts angle-bending modes to a lower wavenumber, probably due to the lack of three-body interactions for the Si−O−Si angles. The measured infrared spectrum is from Van Santen and Vogel. 38 tent with the finding in the MZHB-predicted FAU spectrum (see Figure 4): infrared peaks in the angle-bending region are shifted to higher wavenumbers. On the other hand, the core–shell model predicted this peak at a lower wavenumber at around 438 cm−1 ; this peak shift is also consistent with Figure 6: the core–shell model shifts angle-bending modes to lower wavenumbers. Another major difference occurs in the external-linkage symmetric stretching band from 750–820 cm−1 . A measured infrared peak with low intensity is observed at around 788 cm−1 . The core–shell model shifts this peak to approximately 850 cm−1 , while the MZHB potential predicts two peaks with low intensities in this region at around 740 and 790 cm−1 , which has been seen experimentally (see Figure 18 in Reference 38). A visualization of the peak at around 740 cm−1 in Figure 7 (data not shown) shows large displacements of silicon atoms, while oxygen atoms are almost stationary, causing a symmetric stretching motion of Si−O−Si bonds. This observation indicates that this mode originates from the relative movements of silicon atoms, and can be assigned as an external symmetric stretching mode. The internal asymmetric stretching mode measured at around 1126 cm−1 in the measured spectrum is predicted by both potentials to be at around 1090 cm−1 . Peak assignments are given in Table 7.

20


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Intensity (a. u.)

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Figure 8: Quartz infrared spectra predicted by both the MZHB potential and the core–shell model at 300 K. The MZHB potential shifts infrared peaks to higher wavenumbers to different extent, while the core–shell model predicts angle-bending modes at lower wavenumbers and externallinkage symmetric stretching modes at higher wavernumbers; a weak shoulder is predicted at around 1161 cm−1 by the core–shell model, which we speculate to be an internal asymmetric stretching mode splitting from the principal peak due to the breaking of symmetry. The measured infrared spectrum is from Ocaña et al. 41 3.2.3

α-Quartz

Figure 8 compares the α-quartz infrared spectra predicted by both models with a measured infrared spectrum from Ocaña et al. 41 All the measured infrared peaks are qualitatively reproduced by both models, with peaks shifted to different extents. Again, all the MZHB-predicted infrared peaks are shifted to higher wavenumbers, especially for peaks in the angle-bending region; the core– shell model, on the other hand, predicts angle-bending modes shifted to lower wavenumbers and external-linkage symmetric stretching modes shifted to higher wavenumbers. These observations are consistent with the findings for both FAU and SOD (see Figures 4, 6, and 7). Indeed, these observations are common to all five silica polymorphs studied in this work. As has been observed in the MZHB-predicted SOD infrared spectrum in Figure 7, two externallinkage symmetric stretching modes originating from the motions of silicon atoms are also observed in the infrared spectra for α-quartz, in the 700–800 cm−1 range as predicted by the MZHB potential. The molecular motions associated with these two modes are both Si−O−Si symmetric stretching motions; the difference between the two modes is in the directions of the atomic dis-

21



placements of silicon atoms. These observations in molecular motions are also true for the two peaks predicted by the core–shell model in the range 840–900 cm−1 . Note that a weak shoulder at around 1161 cm−1 is predicted by the core–shell model, which matches with the measured shoulder at around 1147 cm−1 . This shoulder is also observed in the measured infrared spectra of other silica polymorphs, such as FAU. The appearance of this shoulder in the measured infrared spectrum of α-quartz actually helps confirm our attribution of this shoulder to the existence of non-equivalent silica tetrahedra instead of the effects of aluminum content in the case of FAU: quartz does not contain aluminum, so the existence of non-equivalent silica tetrahedra is the only option here. Full peak assignments are presented in Table 7.

3.2.4

α-Cristobalite

Figure 9 compares the computed α-cristobalite infrared spectra predicted by both models with a measured infrared spectrum from Finnie et al. 42 The MZHB potential predicts angle-bending modes shifted to higher wavenumbers in the range 400–600 cm−1 , while the peak predicted by the core–shell model shifts to a lower wavenumber at around 438 cm−1 . Note that while the internal asymmetric stretching mode is well-reproduced by both models, the core–shell model fails to predict the external-linkage symmetric stretching mode at around 787 cm−1 and the peak at around 609 cm−1 . Peak assignments are given in Table 7.

3.2.5 MFI (Silicalite-1) Figure 10 compares the computed infrared spectra of silicalite-1 as predicted by both models with a measured infrared spectrum from Serrano et al. 43 Consistent shifts of angle-bending modes to higher wavenumbers are predicted by the MZHB potential, leaving only one broad band in the 400–600 cm−1 range. In the work of Flanigen et al., 32 infrared bands in the range from 500 to 650 cm−1 of frameworks that do not contain double-ring blocks are also assigned as double-ring peaks; following their assignments, we assign the two experimentally-observed bands in the 400– 500 cm−1 and 500–600 cm−1 ranges in Figure 10 to an angle-bending mode and a double-ring

22


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Intensity (a. u.)

Page 23 of 30

Expt.

Core-shell MZHB 0

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1200

1400

Figure 9: Cristobalite infrared spectra predicted by both the MZHB potential and the core–shell model at 300 K. Apparent peak shifts in the angle-bending region predicted by both the two models are observed; the core–shell model fails to predict the external-linkage symmetric stretching band at around 787 cm−1 and the peak at around 609 cm−1 . The measured spectrum is from Finnie et al. 42 mode, respectively. The merging of these two experimentally-observed peaks might be because of the fact that the positions of these two peaks have different sensitivities to the angle-bending force constants; consequently, these two peaks merge into one when predicted by the MZHB potential, for which the three-body interaction force constants are probably too large, as is discussed in the case of FAU and α-cristobalite. However, the internal asymmetric stretching mode at around 1096 cm−1 and the external symmetric stretching mode at around 799 cm−1 are well-reproduced by the MZHB potential. On the other hand, two broad bands slightly shifted to lower wavenumbers are predicted by the core–shell model at around 400 and 550 cm−1 , which is consistent with the measured spectrum. The external linkage symmetric stretching mode is predicted by the core–shell model at a higher wavenumber than that seen experimentally.

4

Conclusion

In this work, two published potentials are tested in terms of their abilities to predict silica polymorphs’ bond length and angle distributions as well as infrared spectra. We observe that the MZHB potential in general has slightly better performance in predicting silica polymorphs’ geometric ob23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Intensity (a. u.)


Page 24 of 30

Expt.

Core-shell MZHB 0

200

400


1200

1400

Figure 10: Silicalite-1 (MFI) infrared spectra predicted by both the MZHB potential and the core– shell model at 300 K. While the core–shell model clearly predicts two broad infrared bands at around 400 and 550 cm−1 , respectively, the MZHB potential predicts only one broad band in the region ranging from 400 to 600 cm−1 ; however, the external-linkage symmetric stretching mode predicted by the MZHB potential matches better with the measured peak at around 800 cm−1 . The measured infrared spectrum is from Serrano et al. 43 servables, especially for bond angles, while the core–shell model predicts broader Si−O−Si angle distributions. We attribute the broader angle distribution predicted by the core-shell model to its omission of three-body interactions that constrain the deformation of the Si−O−Si angles. This observed broader angle distribution predicted by the core-shell model is consistent with our findings for the core–shell–predicted infrared spectra, in the sense that a consistent shift of the anglebending modes towards lower wavenumbers is observed in all five silica polymorphs studied in this work (zeolite Y, sodalite, silicalite-1, α-quartz, and α-cristobalite). On the other hand, although the MZHB potential shows its ability to predict the silica polymorphs’ average bond lengths and bond angles, it also consistently shifts angle-bending modes to higher wavenumbers for all five silica polymorphs studied in this work. This has been confirmed by a combination of normal mode analysis and quantum cluster calculations. The consistent peak shifts to higher wavenumbers (i.e., larger force constants) indicate that the angle-bending force constants of the MZHB potential are likely too large.

24


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Supporting Information Available The full citations of References 19 and 30, cluster models and corresponding infrared spectra used to investigate the FAU characteristic infrared modes, and the methodology of the cluster calculations are available as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Comparison of Siliceous Zeolite Potentials from the Perspective of

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