Toward accurate ab initio modeling of siliceous zeolite structures.

Structures of purely siliceous materials in the International Zeolite Association database were investigated with four different theoretical methods ranging from the empirical approaches, such as the distance least squares and force fields to the computationally demanding dispersion-corrected density functional theory method employing the generalized gradient approximation-type functional. The structural characteristics were first evaluated for dense silica polymorphs, for which reliable low-temperature experiments are available. Due to the significant errors in experimentally determined atomic positions of siliceous zeolites, lattice parameters and the cell volume were proposed as reliable descriptors for the structural assessment of zeolite frameworks. In this regard, the most consistently performing (systematically underestimating/overestimating) methods are the Sanders-Leslie-Catlow (SLC) force field and the PBEsol density functional. The best overall agreement with the experiment is observed for PBEsol-D2. However, it is a result of fortuitous error cancellations rather than improved description upon adding dispersion correction. We proposed two approaches to estimate accurate cell volumes of siliceous materials from theoretical data: (i) using the SLC and PBEsol volumes as lower and upper bounds and (ii) using a structural response to the dispersion correction along with the SLC compressibility as an additional criterion.

From double-four-ring germanosilicates to new zeolites: in silico investigation.

To date, the majority of zeolites have been prepared by the solvothermal route using organic structure directing agents. Two new zeolites with structural codes PCR and OKO were recently prepared from UTL germanosilicate by removal of the double-four ring (D4R) connecting the dense two-dimensional layers [Nature Chem. 2013, 5, 628]. The corresponding experimental protocol, Assembly-Disassembly-Organization-Reassembly (ADOR), is explored in this contribution with an in silico investigation. The structure and properties of hypothetical zeolites that could be obtained from zeolites with IWW, IWV, IWR, ITR, and ITH topologies using the ADOR protocol are reported based on a computational investigation. A total of 20 new structures are presented together with their characteristics.

Computational investigation of the Lewis acidity in three-dimensional and corresponding two-dimensional zeolites: UTL vs IPC-1P.

The adsorption and catalytic properties of three-dimensional zeolite UTL were investigated computationally along with properties of its two-dimensional analogue IPC-1P that can be obtained from UTL by a removal of D4R units. Adsorption properties and Lewis acidity of extra-framework Li(+) sites were investigated for both two- and three-dimensional forms of UTL using the carbon monoxide as a probe molecule. The CO adsorption enthalpies, calculated with various dispersion-corrected DFT methods, including DFT/CC, DFT-D2, and vdW-DF2, and the CO stretching frequencies obtained with the νCO/rCO correlation method are compared for corresponding Li(+) sites in 3D and 2D UTL zeolite. For the majority of framework Al positions the Li(+) cation is preferably located in one of the channel wall sites and such sites remains unchanged upon the 3D → 2D UTL transformation; consequently, the adsorption enthalpies become only slightly smaller in 2D UTL (less than 3 kJ mol(-1)) due to the missing part of dispersion interactions and νCO becomes also only up to 5 cm(-1) smaller in 2D UTL due to the missing repulsion with framework oxygen atoms from the opposite site of the zeolite channel (effect from the top). However, when Li(+) is located in the intersection site in 3D UTL (about 20% probability), its coordination with the framework is significantly increased in 2D UTL and that is accompanied by significant decrease of both νCO (about 20 cm(-1)) and adsorption enthalpy (about 20 kJ mol(-1)). Because the intersection sites in 3D UTL are the most active adsorption and catalytic Lewis sites, the results reported herein suggest that the 3D → 2D transformation of UTL zeolite is connected with partial decrease of zeolite activity in processes driven by Lewis acid sites.

Localised quantum states of atomic and molecular particles physisorbed on carbon-based nanoparticles.

The vibrational states of atomic and molecular particles adsorbed on long linear nanographenes are described using reliable theoretical potentials and appropriate vibrational (lateral) Hamiltonians. Although they rigorously obey the Bloch theorem only for infinite nanographenes, the energy patterns of the probed states closely resemble the usual Bloch bands and gaps. In addition, for any finite nanographene, these patterns are enriched by the presence of "solitary" energy levels and the "resonance" structure of the bands. While typical band states are profoundly delocalised due to a fast tunneling of the adsorbed particle, the "solitary" and "resonance" states exhibit strong localisation, similar to the behaviour of the states of the Wannier-Stark ladders in optical and semiconductor superlattices.

A novel correction scheme for DFT: a combined vdW-DF/CCSD(T) approach.

A system-specific but very accurate density functional theory (DFT) correction scheme is proposed for precise calculations of adsorbent-adsorbate interactions by combining the non-empirical van der Waals density functional (vdW-DF) method and the empirical DFT/CC correction scheme to reach accuracy of the coupled clusters method with single, double and perturbative triple excitations (CCSD(T)). The new approach is applied to small molecules (CH4, CO2, H2, H2O, N2) interacting with silica surfaces and purely siliceous microporous solids. The vdW-DF/CC results for a perfectly reconstructed α-quartz surface are consistent with other dispersion-corrected DFT methods. Corrected for ZPVE, the vdW-DF/CC enthalpies of adsorption in pure-silica zeolite LTA (ΔHads(0 K)) of 3.6 and 5.2 kcal/mol for methane and carbon dioxide, respectively, are in excellent agreement with experimental values of 3.6 and 5.0 kcal/mol. The very high accuracy of the new scheme and its relatively easy use and numerical stability as compared to the earlier DFT/CC scheme offer a straightforward solution for obtaining reliable predictions of adsorption energies.

Investigation of Brønsted acidity in zeolites through adsorbates with diverse proton affinities.

Understanding the adsorption behavior of base probes in aluminosilicates and its relationship to the intrinsic acidity of Brønsted acid sites (BAS) is essential for the catalytic applications of these materials. In this study, we investigated the adsorption properties of base probe molecules with varying proton affinities (acetonitrile, acetone, formamide, and ammonia) within six different aluminosilicate frameworks (FAU, CHA, IFR, MOR, FER, and TON). An important objective was to propose a robust criterion for evaluating the intrinsic BAS acidity (i.e., state of BAS deprotonation). Based on the bond order conservation principle, the changes in the covalent bond between the aluminum and oxygen carrying the proton provide a good description of the BAS deprotonation state. The ammonia and formamide adsorption cause BAS deprotonation and cannot be used to assess intrinsic BAS acidity. The transition from ion-pair formation, specifically conjugated acid/base interaction, in formamide to strong hydrogen bonding in acetone occurs within a narrow range of base proton affinities (812-822 kJ mol-1). The adsorption of acetonitrile results in the formation of hydrogen-bonded complexes, which exhibit a deprotonation state that follows a similar trend to the deprotonation induced by acetone. This allows for a semi-quantitative comparison of the acidity strengths of BAS within and between the different aluminosilicate frameworks.

Combined theoretical and experimental investigation of CO adsorption on coordinatively unsaturated sites in CuBTC MOF.

The adsorption of CO in metal-organic framework CuBTC material is investigated by a combination of theoretical and experimental approaches. The adsorption enthalpy of CO on CuBTC determined experimentally to be -29 kJ mol(-1) at the zero-coverage limit is in very good agreement with the adsorption enthalpy calculated at the combined DFT-ab initio level with the periodic model. Calculations show that polycarbonyl complexes cannot be formed on regular coordinatively unsaturated sites in CuBTC. Experimental IR spectra of the CO probe molecule adsorbed in CuBTC are interpreted based on calculated CO stretching frequencies. Calculations show that long-range interactions are insignificant for the CO/CuBTC system and that this system can be accurately modeled with just a Cu(2)(HCOO)(4) cluster model of the paddle wheel. The reliability of various methods for the description of CO interaction with the Cu(2+) site in CuBTC is discussed based on the experimental results and accurate coupled-cluster calculations. It is shown that standard exchange-correlation functionals do not provide a reliable description of CO interaction with coordinatively unsaturated Cu(2+) sites in CuBTC.

Brønsted acidity in zeolites measured by deprotonation energy.

Acid forms of zeolites have been used in industry for several decades but scaling the strength of their acid centers is still an unresolved and intensely debated issue. In this paper, the Brønsted acidity strength in aluminosilicates measured by their deprotonation energy (DPE) was investigated for FAU, CHA, IFR, MOR, FER, MFI, and TON zeolites by means of periodic and cluster calculations at the density functional theory (DFT) level. The main drawback of the periodic DFT is that it does not provide reliable absolute values due to spurious errors associated with the background charge introduced in anion energy calculations. To alleviate this problem, we employed a novel approach to cluster generation to obtain accurate values of DPE. The cluster models up to 150 T atoms for the most stable Brønsted acid sites were constructed on spheres of increasing diameter as an extension of Harrison's approach to calculating Madelung constants. The averaging of DPE for clusters generated this way provides a robust estimate of DPE for investigated zeolites despite slow convergence with the cluster size. The accuracy of the cluster approach was further improved by a scaled electrostatic embedding scheme proposed in this work. The electrostatic embedding model yields the most reliable values with the average deprotonation energy of about 1245 ± 9 kJ·mol-1 for investigated acidic zeolites. The cluster calculations strongly indicate a correlation between the deprotonation energy and the zeolite framework density. The DPE results obtained with our electrostatic embedding model are highly consistent with the previously reported QM/MM and periodic calculations.

Variable-temperature IR spectroscopic and theoretical studies on CO2 adsorbed in zeolite K-FER.

Adsorption of CO(2) in K-FER zeolite is investigated by a combination of variable-temperature IR spectroscopy and periodic DFT calculations augmented for description of dispersion interactions. Calculated adsorption enthalpies for CO(2) adsorption complexes on single extra-framework K(+) sites and on dual-cation sites where CO(2) interacts simultaneously with two extra-framework K(+) cations (-40 and -44 kJ mol(-1), respectively) are in excellent agreement with experimental values. The analysis of effects on the frequency of the asymmetric CO(2) stretching mode ν(3) shows that polarization of CO(2) by the K(+) cation leads to an increase in ν(3), while the interaction of CO(2) with the zeolite framework leads to a decrease in ν(3). In the case of K-FER, the latter effect is slightly larger than the former, and thus a small redshift in ν(3) results (-3 cm(-1) with respect to free CO(2)). For adsorption complexes on dual K(+) sites, where CO(2) interacts with one K(+) cation on each end of the molecule, the polarization of CO(2) molecules on both sides results in a blueshift of ν(3). The origin of the redshift in ν(3) when CO(2) is adsorbed in purely siliceous FER is also investigated computationally. Calculations show that the dispersion interaction does not affect the vibrational frequency of adsorbed CO(2).

Accurate description of argon and water adsorption on surfaces of graphene-based carbon allotropes.

Accurate interaction energies of nonpolar (argon) and polar (water) adsorbates with graphene-based carbon allotropes were calculated by means of a combined density functional theory (DFT)-ab initio computational scheme. The calculated interaction energy of argon with graphite (-9.7 kJ mol(-1)) is in excellent agreement with the available experimental data. The calculated interaction energy of water with graphene and graphite is -12.8 and -14.6 kJ mol(-1), respectively. The accuracy of combined DFT-ab initio methods is discussed in detail based on a comparison with the highly precise interaction energies of argon and water with coronene obtained at the coupled-cluster CCSD(T) level extrapolated to the complete basis set (CBS) limit. A new strategy for a reliable estimate of the CBS limit is proposed for systems where numerical instabilities occur owing to basis-set near-linear dependence. The most accurate estimate of the argon and water interaction with coronene (-8.1 and -14.0 kJ mol(-1), respectively) is compared with the results of other methods used for the accurate description of weak intermolecular interactions.

DFT/CC investigation of physical adsorption on a graphite (0001) surface.

The physical adsorption of molecules (C(2)H(2), C(2)H(4), C(2)H(6), C(6)H(6), CH(4), H(2), H(2)O, N(2), NH(3), CO, CO(2), Ar) on a graphite substrate has been investigated at the DFT/CC level of theory. The calculated DFT/CC interaction energies were compared with the available experimental data at the zero coverage limit. The differences between the DFT/CC results and experiment are within a few tenths of kJ mol(-1) for the most accurate experimental estimates (Ar, H(2), N(2), CH(4)) and within 1-2 kJ mol(-1) for the other systems (C(2)H(2), C(2)H(4), C(2)H(6), C(6)H(6), CO, CO(2)). For water-graphite and ammonia-graphite complexes, DFT/CC predicts interaction energies of 13 kJ mol(-1) in good accord with the DF-DFT-SAPT and DFT-D calculations. The relevance of the results obtained with the coronene model for the description of the physisorption on graphite surface was also studied.

Experimental and theoretical determination of adsorption heats of CO(2) over alkali metal exchanged ferrierites with different Si/Al ratio.

The adsorption of CO(2) in Li-, Na-, and K-FER was investigated by a combination of volumetric adsorption experiments, FTIR spectroscopy, and density functional theory. Experimental isosteric heats of CO(2), Q(st), depend significantly on the cation size, cation concentration, and on the amount of adsorbed CO(2). The differences observed in experimentally determined isosteric heats were interpreted at the molecular level based on good agreement between experimental and calculated characteristics. The highest interaction energies were found for CO(2) adsorbed on so-called "dual cation sites" in which CO(2) is bridged between two alkali metal cations. The formation of CO(2) adsorption complexes on dual cation sites is particularly important on Na-FER and K-FER samples with higher cation concentration. On the contrary, the differences in Q(st) observed for Li-FER samples are due to the changes in the Li(+) coordination with the framework. The DFT/CC calculations show that the dispersion interactions between CO(2) and the zeolites framework are rather large (about -20 kJ mol(-1)).

Ab initio vibrational dynamics of molecular hydrogen on graphene: An effective interaction potential.

The interaction potential confining the stretching and translational motions of a molecular hydrogen physisorbed on the graphene surface has been calculated by means of the DFT/CC approach. Using a simple adiabatic separation of the stretching and translational motions, a set of effective stretching potentials is generated by performing a "finite box" integrating over the translational degrees of freedom. The resulting potentials, forming energetically narrow bands, are used to evaluate the corresponding average stretching energies, which are in turn compared to their experimental counterparts. The mass-dependent "translational" corrections of the purely stretching potential significantly improve the theory versus experiment agreement, thus evidencing their importance in the physisorption processes. Although not fully quantitative, the DFT/CC stretching potentials seem to exhibit physically correct shapes, as their morphing by only a few parameters allows for a quantitative fitting of the observed vibrational energies in terms of the effective (mass-dependent) interaction potentials.

DFT/CCSD(T) investigation of the interaction of molecular hydrogen with carbon nanostructures.

The interaction of molecular hydrogen with carbon nanostructures is investigated within the DFT/CC correction scheme. The DFT/CC results are compared with the benchmark calculations at the CCSD(T) level of theory for benzene and naphthalene, and at the MP2 level for the more extended systems. The DFT/CC method offers a reliable alternative to the highly correlated ab initio calculations at a cost comparable to the standard DFT method. The results for H(2) adsorbed on graphene as well as single-wall carbon nanotubes (SWCNT) are presented. The DFT/CC binding energy on graphene of 5.4 kJ mol(-1) is in good agreement with experiment (5.00+/-0.05 kJ mol(-1)). For (10,10)-SWCNT, the H(2) molecule is mostly stabilized inside the tube with an estimated binding energy of 7.2 kJ mol(-1).

Investigation of the benzene-naphthalene and naphthalene-naphthalene potential energy surfaces: DFT/CCSD(T) correction scheme.

The potential energy surfaces of the naphthalene dimer and benzene-naphthalene complexes are investigated using the recently developed DFT/CCSD(T) correction scheme [J. Chem. Phys. 2008, 128, 114 102]. One and three minima are located on the PES of the benzene-naphthalene and the naphthalene dimer complexes, respectively, all of which are of the parallel-displaced type. The stabilities of benzene-naphthalene and the naphthalene dimer are -4.2 and -6.2 kcal mol(-1), respectively. Unlike the benzene dimer, where the T-shaped complex is the global minimum, the lowest-energy T-shaped structure is about 0.2 and 1.6 kcal mol(-1) above the global minimum on the benzene-naphthalene and the naphthalene dimer potential energy surfaces, respectively.

Theoretical investigation of CO interaction with copper sites in zeolites: periodic DFT and hybrid quantum mechanical/interatomic potential function study.

Periodic DFT and combined quantum mechanics/interatomic potential function (QM-pot) models were used to describe the interaction of CO with the Cu+ sites in FER. The CO stretching frequencies were calculated using omega(CO)(CCSD(T))/r(CO)(DFT) scaling method relating frequencies determined using a high-level quantum-chemical (coupled clusters) method for simple model carbonyls to CO bond lengths calculated using periodic DFT and QM-pot methods for the Cu+-zeolite system. Both periodic DFT and QM-pot models together with omega(CO)/r(CO) scaling describe the CO stretching dynamics with the "near spectroscopic accuracy", giving nu(CO) = 2156 cm(-1) in excellent agreement with experimental data. Calculations for various Cu+ sites in FER show that both types of Cu+ sites in FER (channel-wall sites and intersection sites) have the same CO stretching frequencies. Thus, the CO stretching frequencies are not site-specific in the CO/Cu+/FER system. The convergence of the results with respect to the model size was analyzed. When the same exchange-correlation functional is used the adsorption energies from periodic DFT and QM-pot are in good agreement (about 2 kcal/mol difference) but substantially larger than those of the experiment. The adsorption energy calculated with the B3LYP functional agrees with available experimental data. The overestimation of the adsorption energy in DFT calculations (periodic or QM-pot) is related to a red-shift of the CO stretching mode, both result from an underestimation of the HOMO(5sigma)-LUMO(2pi) gap of CO and the consequent overestimation of the Cu(+)(d)-CO(2pi*) back-donation. For the adsorption energy, this can be overcome by the use of hybrid B3LYP exchange-correlation functional. For the frequency calculations, the DFT problem can be overcome by the use of the omega(CO)(CCSD(T))/r(CO)(DFT) correlation.

Accurate ab initio description of adsorption on coordinatively unsaturated Cu(2+) and Fe(3+) sites in MOFs.

The performance of different exchange-correlation functionals was evaluated for the description of the interaction of small molecules with (i) cluster models containing Cu(2+) and Fe(3+) coordinatively unsaturated metal sites and (ii) HKUST-1 metal organic framework (MOF). Adsorbates forming dispersion-bound complexes (CH4), complexes with important dispersion and electrostatic contributions (H2, N2, CO2), and complexes stabilized also by a partial dative bond (CO, H2O, and NH3) were considered. The interaction with coordinatively unsaturated sites was evaluated with respect to the coupled-cluster calculations for Cu(2+) and Fe(3+) centers represented by cluster models. The adsorption on dispersion-stabilized sites was examined for the cage-window and the cage-center sites in HKUST-1 with respect to the experimental and DFT/CC results. None of the functionals considered can accurately describe the interaction of all seven adsorbates with Cu(2+) and Fe(3+) sites and with dispersion-dominated adsorption sites. The interaction with coordinatively unsaturated sites was frequently underestimated, for adsorbates forming a partial dative bond in particular, while the adsorption at dispersion-stabilized sites was overestimated. Consequently, interaction energies calculated for different adsorption sites were often in qualitatively incorrect order. The optimal exchange-correlation functional for a particular adsorbate/MOF can thus be found by comparing the performance of various functionals with respect to highly accurate calculations on smaller cluster models as a good representative of MOF structural building blocks.

Intermolecular pi-pi interactions in solids.

A parameter-free DFT/CCSD(T) correction scheme is proposed for precise calculations (close to CCSD(T) accuracy) of weakly bound molecular solids. The correction scheme has been tested for solid benzene and graphite. The CCSD(T)/CBS correction to planewave DFT calculations reproduces the experimentally determined lattice constants for solid benzene. The calculated cohesive energy of benzene (457 meV per molecule) compares well with the experimental values of the heat of sublimation (460-560 meV per molecule). For graphite, the correction yields structural parameters (a = 2.46 A, c = 6.60 A) in good agreement with experiment (a = 2.46 A, c = 6.67 A). The calculated exfoliation energy of 54 meV per atom agrees fairly well with the most recent experimental value of 52 +/- 5 meV per atom.

Investigation of the benzene-dimer potential energy surface: DFT/CCSD(T) correction scheme.

A novel method, designated as the density functional theory/coupled-cluster with single and double and perturbative triple excitation [DFT/CCSD(T)] correction scheme, was developed for precise calculations of weakly interacting sp(2) hydrocarbon molecules and applied to the benzene dimer. The DFT/CCSD(T) interaction energies are in excellent agreement with the estimated CCSD(T)/complete basis set interaction energies. The tilted T-shaped structure having C(s) symmetry was determined to be a global minimum on the benzene-dimer potential energy surface (PES), approximately 0.1 kcal/mol more stable than the parallel-displaced structure. A fully optimized set of ten stationary points on the benzene-dimer PES is proposed for the evaluation of the reliability of methods for the description of weakly interacting systems.

On the site-specificity of polycarbonyl complexes in Cu/zeolites: combined experimental and DFT study.

The preferred Cu(+) sites and formation of mono-, di-, and tricarbonyl complexes in the Cu-FER were investigated at the periodic density functional theory level and by means of FTIR spectroscopy. The site-specificity of adsorption enthalpies of CO on Cu-FER and of vibrational frequencies of polycarbonyl complexes were investigated for various Cu(+) sites in Cu-FER. Large changes in the Cu(+) interaction with the zeolite framework were observed upon the formation of carbonyl complexes. The dicarbonyl complexes formed on Cu(+) in the main channel or on the intersection of the main and perpendicular channels are stable and both, adsorption enthalpies and CO stretching frequencies are not site-specific. The fraction of Cu(+) ions in the FER cage, that cannot form dicarbonyl can be determined from IR spectra (about 7% for the Cu-FER with Si/Al = 27.5 investigated here). The tricarbonyl complexes can be formed at the Cu(+) ions located at the 8-member ring window at the intersection of main and perpendicular channel. The stability of tricarbonyl complexes is very low (DeltaH degrees (0 K)>or=-4 kJ mol(-1)).