Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals.

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta)stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible.

Exploring the Flexibility of MIL-47(V)-Type Materials Using Force Field Molecular Dynamics Simulations.

The flexibility of three MIL-47(V)-type materials (MIL-47, COMOC-2, and COMOC-3) has been explored by constructing the pressure versus volume and free energy versus volume profiles at various temperatures ranging from 100 to 400 K. This is done with first-principles-based force fields using the recently proposed QuickFF parametrization protocol. Specific terms were added for the materials at hand to describe the asymmetry of the one-dimensional vanadium-oxide chain and to account for the flexibility of the organic linkers. The force fields are used in a series of molecular dynamics simulations at fixed volumes but varying unit cell shapes. The three materials show a distinct pressure-volume behavior, which underlines the ability to tune the mechanical properties by varying the linkers toward different applications such as nanosprings, dampers, and shock absorbers.

A Comparison of Barostats for the Mechanical Characterization of Metal-Organic Frameworks.

In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterize the rigid MOF-5 and flexible MIL-53(Al) metal-organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna-Tuckerman-Tobias-Klein (MTTK), and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behavior in isothermal-isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well-reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well-reproduced by any of the coupling schemes.

Determining the storage, availability and reactivity of NH3 within Cu-Chabazite-based Ammonia Selective Catalytic Reduction systems.

Three different types of NH3 species can be simultaneously present on Cu(2+)-exchanged CHA-type zeolites, commonly used in Ammonia Selective Catalytic Reduction (NH3-SCR) systems. These include ammonium ions (NH4(+)), formed on the Brønsted acid sites, [Cu(NH3)4](2+) complexes, resulting from NH3 coordination with the Cu(2+) Lewis sites, and NH3 adsorbed on extra-framework Al (EFAl) species, in contrast to the only two reacting NH3 species recently reported on Cu-SSZ-13 zeolite. The NH4(+) ions react very slowly in comparison to NH3 coordinated to Cu(2+) ions and are likely to contribute little to the standard NH3-SCR process, with the Brønsted groups acting primarily as NH3 storage sites. The availability/reactivity of NH4(+) ions can be however, notably improved by submitting the zeolite to repeated exchanges with Cu(2+), accompanied by a remarkable enhancement in the low temperature activity. Moreover, the presence of EFAl species could also have a positive influence on the reaction rate of the available NH4(+) ions. These results have important implications for NH3 storage and availability in Cu-Chabazite-based NH3-SCR systems.

ACKS2: atom-condensed Kohn-Sham DFT approximated to second order.

A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)] in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.

Hirshfeld-E Partitioning: AIM Charges with an Improved Trade-off between Robustness and Accurate Electrostatics.

For the development of ab initio derived force fields, atomic charges must be computed from electronic structure computations, such that (i) they accurately describe the molecular electrostatic potential (ESP) and (ii) they are transferable to the force-field application of interest. The Iterative Hirshfeld (Hirshfeld-I or HI) scheme meets both requirements for organic molecules. For inorganic oxide clusters, however, Hirshfeld-I becomes ambiguous because electron densities of nonexistent isolated anions are needed as input. Herein, we propose a simple Extended Hirshfeld (Hirshfeld-E or HE) scheme to overcome this limitation. The performance of the new HE scheme is compared to four popular atoms-in-molecules schemes, using two tests involving a set of 248 silica clusters. These tests show that the new HE scheme provides an improved trade-off between the ESP accuracy and the transferability of the charges. The new scheme is a generalization of the Hirshfeld-I scheme, and it is expected that its improvements are to a large extent applicable to molecular systems containing elements from the entire periodic table.

Accurate spin-orbit and spin-other-orbit contributions to the g-tensor for transition metal containing systems.

In this paper an overview is presented of several approximations within Density Functional Theory (DFT) to calculate g-tensors in transition metal containing systems and a new accurate description of the spin-other-orbit contribution for high spin systems is suggested. Various implementations in a broad variety of software packages (ORCA, ADF, Gaussian, CP2K, GIPAW and BAND) are critically assessed on various aspects including (i) non-relativistic versus relativistic Hamiltonians, (ii) spin-orbit coupling contributions and (iii) the gauge. Particular attention is given to the level of accuracy that can be achieved for codes that allow g-tensor calculations under periodic boundary conditions, as these are ideally suited to efficiently describe extended condensed-phase systems containing transition metals. In periodic codes like CP2K and GIPAW, the g-tensor calculation schemes currently suffer from an incorrect treatment of the exchange spin-orbit interaction and a deficient description of the spin-other-orbit term. In this paper a protocol is proposed, making the predictions of the exchange part to the g-tensor shift more plausible. Focus is also put on the influence of the spin-other-orbit interaction which becomes of higher importance for high-spin systems. In a revisited derivation of the various terms arising from the two-electron spin-orbit and spin-other-orbit interaction (SOO), new insight has been obtained revealing amongst other issues new terms for the SOO contribution. The periodic CP2K code has been adapted in view of this new development. One of the objectives of this study is indeed a serious enhancement of the performance of periodic codes in predicting g-tensors in transition metal containing systems at the same level of accuracy as the most advanced but time consuming spin-orbit mean-field approach. The methods are first applied on rhodium carbide but afterwards extended to a broad test set of molecules containing transition metals from the fourth, fifth and sixth row of the periodic table. The set contains doublets as well as high-spin molecules.

Ab Initio Parametrized Force Field for the Flexible Metal-Organic Framework MIL-53(Al).

A force field is proposed for the flexible metal-organic framework MIL-53(Al), which is calibrated using density functional theory calculations on nonperiodic clusters. The force field has three main contributions: an electrostatic term based on atomic charges derived with a modified Hirshfeld-I method, a van der Waals (vdW) term with parameters taken from the MM3 model, and a valence force field whose parameters were estimated with a new methodology that uses the gradients and Hessian matrix elements retrieved from nonperiodic cluster calculations. The new force field predicts geometries and cell parameters that compare well with the experimental values both for the large and narrow pore phases. The energy profile along the breathing mode of the empty material reveals the existence of two minima, which confirms the intrinsic bistable behavior of the MIL-53. Even without the stimulus of external guest molecules, the material may transform from the large pore (lp) to the narrow pore (np) phase [Liu et al. J. Am. Chem. Soc.2008, 120, 11813]. The relative stability of the two phases critically depends on the vdW parameters, and the MM3 dispersion interaction has the tendency to overstabilize the np phase.

Assessment of periodic and cluster-in-vacuo models for first principles calculation of EPR parameters of paramagnetic defects in crystals: Rh2+ defects in NaCl as case study.

In order to find a reliable and efficient calculation scheme for electron paramagnetic resonance (EPR) spectroscopic parameters for transition metal complexes in ionic solids from first principles, periodic and finite cluster-in-vacuo density functional theory (DFT) simulations are performed for g tensors, ligand hyperfine tensors (A), and quadrupole tensors (Q) for Rh(2+)-related centers in NaCl. EPR experiments on NaCl:Rh single crystals identified three Rh(2+) monomer centers, only differing in the number of charge compensating vacancies in their local environment, and one dimer center. Periodic and cluster calculations, both based on periodically optimized structures, are able to reproduce experimentally observed trends in the ligand A and Q tensors and render very satisfactory numerical agreement with experiment. Taking also computation time into account as a criterion, a full periodic approach emerges as most appropriate for these parameters.The g tensor calculations, on the other hand, prove to be insufficiently accurate for model assessment. The calculations also reveal parameters of the complexes which are not directly accessible through experiments, in particular related to their geometry.

The Significance of Parameters in Charge Equilibration Models.

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach.

In a previous paper [Ghysels et al., J. Chem. Phys. 126, 224102 (2007)] the mobile block Hessian (MBH) approach was presented. The method was designed to accurately compute vibrational modes of partially optimized molecular structures. The key concept was the introduction of several blocks of atoms, which can move as rigid bodies with respect to a local, fully optimized subsystem. The choice of the blocks was restricted in the sense that none of them could be connected, and also linear blocks were not taken into consideration. In this paper an extended version of the MBH method is presented that is generally applicable and allows blocks to be adjoined by one or two common atoms. This extension to all possible block partitions of the molecule provides a structural flexibility varying from very rigid to extremely relaxed. The general MBH method is very well suited to study selected normal modes of large macromolecules (such as proteins and polymers) because the number of degrees of freedom can be greatly reduced while still keeping the essential motions of the molecular system. The reduction in the number of degrees of freedom due to the block linkages is imposed here directly using a constraint method, in contrast to restraint methods where stiff harmonic couplings are introduced to restrain the relative motion of the blocks. The computational cost of this constraint method is less than that of an implementation using a restraint method. This is illustrated for the alpha-helix conformation of an alanine-20-polypeptide.

Mobile Block Hessian Approach with Adjoined Blocks: An Efficient Approach for the Calculation of Frequencies in Macromolecules.

In an earlier work, the authors developed a new method, the mobile block Hessian (MBH) approach, to accurately calculate vibrational modes for partially optimized molecular structures [ J. Chem. Phys. 2007 , 126 ( 22 ), 224102. ]. It is based on the introduction of blocks, consisting of groups of atoms, that can move as rigid bodies. The internal geometry of the blocks need not correspond to an overall optimization state of the total molecular structure. The standard MBH approach considers free blocks with six degrees of freedom. In the extended MBH approach introduced herein, the blocks can be connected by one or two adjoining atoms, which further reduces the number of degrees of freedom. The new approach paves the way for the normal-mode analysis of biomolecules such as proteins. It rests on the hypothesis that low-frequency modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino acid residues. The method is validated for a series of small molecules and further applied to alanine dipeptide as a prototype to describe vibrational interactions between two peptide units; to crambin, a small protein with 46 amino acid residues; and to ICE/caspase-1, which contains 518 amino acid residues.

Schonland ambiguity in the electron nuclear double resonance analysis of hyperfine interactions: principles and practice.

For the analysis of the angular dependence of electron paramagnetic resonance (EPR) spectra of low-symmetry centres with S=1/2 in three independent planes, it is well-established-but often overlooked-that an ambiguity may arise in the best-fit g<--> tensor result. We investigate here whether a corresponding ambiguity also arises when determining the hyperfine coupling (HFC) A<--> tensor for nuclei with I=1/2 from angular dependent electron nuclear double resonance (ENDOR) measurements. It is shown via a perturbation treatment that for each set of M(S) ENDOR branches two best-fit A<--> tensors can be derived, but in general only one unique solution simultaneously fits both. The ambiguity thus only arises when experimental data of only one M(S) multiplet are used in analysis or in certain limiting cases. It is important to realise that the ambiguity occurs in the ENDOR frequencies and therefore the other best-fit result for an ENDOR determined A<--> tensor depends on various details of the ENDOR experiment: the M(S) state of the fitted transitions, the microwave frequency (or static magnetic field) in the ENDOR measurements and the rotation planes in which data have been collected. The results are of particular importance in the identification of radicals based on comparison of theoretical predictions of HFCs with published literature data. A procedure for obtaining the other best-fit result for an ENDOR determined A<--> tensor is outlined.

ZEOBUILDER: A GUI toolkit for the construction of complex molecular structures on the nanoscale with building blocks.

In this paper, a new graphical toolkit, ZEOBUILDER, is presented for the construction of the most complex zeolite structures based on building blocks. Molecular simulations starting from these model structures give novel insights in the synthesis mechanisms of micro- and mesoporous materials. ZEOBUILDER is presented as an open-source code with easy plug-in facilities. This architecture offers an ideal platform for further development of new features. Another specific aspect in the architecture of ZEOBUILDER is the data structure with multiple reference frames in which molecules and molecular building blocks are placed and which are hierarchically ordered. The main properties of ZEOBUILDER are the feasibility for constructing complex structures, extensibility, and transferability. The application field of ZEOBUILDER is not limited to zeolite science but easily extended to the construction of other complex (bio)molecular systems. ZEOBUILDER is a unique user-friendly GUI toolkit with advanced plug-ins allowing the construction of the most complex molecular structures, which can be used as input for all ab initio and molecular mechanics program packages.

Identification and conformational study of stable radiation-induced defects in sucrose single crystals using density functional theory calculations of electron magnetic resonance parameters.

One of the major stable radiation-induced radicals in sucrose single crystals (radical T2) has been identified by means of density functional theory (DFT) calculations of electron magnetic resonance parameters. The radical is formed by a net glycosidic bond cleavage, giving rise to a glucose-centered radical with the major part of the spin density residing at the C 1 carbon atom. A concerted formation of a carbonyl group at the C 2 carbon accounts for the relatively small spin density at C 1 and the enhanced g factor anisotropy of the radical, both well-known properties of this radical from several previous experimental investigations. The experimentally determined and DFT calculated proton hyperfine coupling tensors agree very well on all accounts. The influence of the exact geometrical configuration of the radical and its environment on the tensors is explored in an attempt to explain the occurrence and characteristics of radical T3, another major species that is most likely another conformation of T2. No definitive conclusions with regard to the actual structure of T3 could be arrived at from this study. However, the results indicate that, most likely, T3 is identical in chemical structure to T2 and that changes in the orientation of neighboring hydroxy groups or changes in the configuration of the neighboring fructose ring can probably not account for the type and size of the discrepancies between T2 and T3.

Molecular environment and temperature dependence of hyperfine interactions in sugar crystal radicals from first principles.

The effect of the molecular environment and the temperature dependence of hyperfine parameters in first principles calculations in alpha-d-glucose and beta-d-fructose crystal radicals have been investigated. More specifically, we show how static (0 K) cluster in vacuo hyperfine calculations, commonly used today, deviate from more advanced molecular dynamics calculations at the experimental temperature using periodic boundary conditions. From the latter approach, more useful information can be extracted, allowing us to ascertain the validity of proposed molecular models.

Calculating Reaction Rates with Partial Hessians: Validation of the Mobile Block Hessian Approach.

In an earlier paper, the authors have developed a new method, the mobile block Hessian (MBH), to accurately calculate vibrational modes for partially optimized molecular structures [J. Chem. Phys. 2007, 126 (22), 224102]. The proposed procedure remedies the artifact of imaginary frequencies, occurring in standard frequency calculations, when parts of the molecular system are optimized at different levels of theory. Frequencies are an essential ingredient in predicting reaction rate coefficients due to their input in the vibrational partition functions. The question arises whether the MBH method is able to describe the chemical reaction kinetics in an accurate way in large molecular systems where a full quantum chemical treatment at a reasonably high level of theory is unfeasible due to computational constraints. In this work, such a validation is tested in depth. The MBH method opens a lot of perspectives in predicting accurate kinetic parameters in chemical reactions where the standard full Hessian procedure fails.

Radiation-induced defects in sucrose single crystals, revisited: a combined electron magnetic resonance and density functional theory study.

The results are presented of an electron magnetic resonance analysis at 110 K of radiation-induced defects in sucrose single crystals X-irradiated at room temperature, yielding a total of nine (1)H hyperfine coupling tensors assigned to three different radical species. Comparisons are made with results previously reported in the literature. By means of electron paramagnetic resonance and electron nuclear double resonance temperature variation scans, most of the discrepancies between the present 110 K study and a previous 295 K study by Sagstuen and co-workers are shown to originate from the temperature dependence of proton relaxation times and hyperfine coupling constants. Finally, radical models previously suggested in the literature are convincingly refuted by means of quantum chemical density functional theory calculations.

Cartesian formulation of the mobile block Hessian approach to vibrational analysis in partially optimized systems.

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.

Vibrational modes in partially optimized molecular systems.

In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem. 65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di-n-octyl-ether.