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.

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.

Au@UiO-66: a base free oxidation catalyst

We present the in situ synthesis of Au nanoparticles within the Zr based Metal Organic Framework, UiO-66.

Correction: Au@UiO-66: a base free oxidation catalyst

Correction for ‘Au@UiO-66: a base free oxidation catalyst’ by K. Leus et al., RSC Adv., 2015, 5, 22334–22342.

Base catalytic activity of alkaline earth MOFs: a (micro)spectroscopic study of active site formation by the controlled transformation of structural anions

The selective decomposition of structural nitrate anions in alkaline earth MOFs generates highly dispersed base sites with catalytic applications.

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.

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.

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.

Spin-Polarized Conceptual Density Functional Theory Study of the Regioselectivity in Ring Closures of Radicals

The regioselectivity of ring-forming radical reactions is investigated within the framework of the so-called spin-polarized conceptual density functional theory. Two different types of cyclizations were studied. First, a series of model reactions of alkyl- and acyl-substituted radicals were investigated. Next, attention was focused on the radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals (a three-step mechanism). In both of these reactions, the approaching radical (carbon or nitrogen centered) adds to a carbon-carbon double bond within the same molecule to form a radical ring compound. In this process, the number of electrons is changing from a local point of view (a charge transfer occurs from one part of the molecule to another one) at constant global spin number Ns (both the reactant and the product ring compound are in the doublet state). It is shown that the experimentally observed regioselectivities for these ring-closure steps can be predicted using the spin-polarized Fukui functions for radical attack, f0NN(r).

X- (X = O, S) Ions in Alkali Halide Lattices through Density Functional Calculations. 1. Substitutional Defect Models

Monoatomic X- (X = O, S) chalcogen centers in MZ (M = Na, K, Rb and Z = Cl, Br, I) alkali halide lattices are investigated within the framework of density functional theory with the principal aim to establish defect models. In electron paramagnetic resonance (EPR) experiments, X- defects with tetragonal, orthorhombic, and monoclinic g-tensor symmetry have been observed. In this paper, models in which X- replaces a single halide ion, with a next nearest neighbor and a nearest neighbor halide vacancy, are validated for the X- centers with tetragonal and orthorhombic symmetry, respectively. As such defect models are extended, the ability to reproduce experimental data is a stringent test for various computational approaches. Cluster in vacuo and embedded cluster schemes are used to calculate energy and EPR parameters for the two vacancy configurations. The final assignment of a defect structure is based on the qualitative and quantitative reproduction of experimental g and (super)hyperfine tensors.

X- (X = O, S, Se) Ions in Alkali Halide Lattices through Density Functional Calculations. 2. Interstitial Defect Models

Density functional theory techniques are used to investigate the defect structure of X- (X = O, S, Se) ions in MZ (M = Na, K, Rb and Z = Cl, Br) alkali halides which exhibit monoclinic-I g-tensor symmetry, using cluster in vacuo, embedded cluster, and periodic embedding schemes. Although a perturbed interstitial defect model was suggested from electron paramagnetic resonance experiments (EPR), the nature of the perturbation is still unknown. An appropriate defect model is developed theoretically by comparing structural and energetical properties of various defect configurations. Further validation is achieved by cross referencing experimental and computed EPR data. On the basis of the computational results, the following defect model is proposed: the X- ion is located interstitially with a charge compensating halide vacancy in its first coordination shell.

Density Functional Investigation of High-Spin XY (X = Cr, Mo, W and Y = C, N, O) Molecules

The performance of a density functional theory approach in calculating the equilibrium bond length, dipole moment, and harmonic vibrational frequency in a series of group 6 (Cr, Mo, W) transition metal-containing diatomic molecules is evaluated. Using flexible basis sets comprised of Slater type functions, a wide range of exchange-correlation functionals is investigated. Comparing with known experimental values and published results from high-level theoretical calculations, the most suitable functional form is selected. The importance of relativistic effects is checked, and predictions are made for several unknown dipole moments. The best agreement with experimental parameters is obtained when using a general gradient approximation, while special and hybrid functional forms give less accurate results.

An extended hindered-rotor model with incorporation of Coriolis and vibrational-rotational coupling for calculating partition functions and derived quantities

Large-amplitude motions, particularly internal rotations, are known to affect substantially thermodynamic functions and rate constants of reactions in which flexible molecules are involved. Up to now all methods for computing the partition functions of these motions rely on the Pitzer approximation of more than 50 years ago, in which the large-amplitude motion is treated in complete independence of the other (vibrational) degrees of freedom. In this paper an extended hindered-rotor model (EHR) is developed in which the vibrational modes, treated harmonically, are correctly separated from the large-amplitude motion and in which relaxation effects (the changes in the kinetic-energy matrix and potential curvature) are taken into account as one moves along the large-amplitude path. The model also relies on a specific coordinate system in which the Coriolis terms vanish at all times in the Hamiltonian. In this way an increased level of consistency between the various internal modes is achieved, as compared with the more usual hindered-rotor (HR) description. The method is illustrated by calculating the entropies and heat capacities on 1,3-butadiene and 1-butene (with, respectively, one and two internal rotors) and the rate constant for the addition reaction of a vinyl radical to ethene. We also discuss various variants of the one-dimensional hindered-rotor scheme existing in the literature and its relation with the EHR model. It is argued why in most cases the HR approach is already quite successful.

Rules for Generating Conformers and Their Relative Energies in n-Alkanes with a Heteroelement O or S: Ethers and Alcohols, or Sulfides and Thiols

With the aid of density functional theory calculations, all conformers of several single-chain alcohols, thiols, ethers, and sulfides are investigated. Starting from earlier computational works on n-alkanes, we construct an extended set of general rules for predicting the number and occurrence of conformers in these oxygen- or sulfur-containing compounds. In alcohols and thiols, it is found that only the conformers generated by internal rotations in the HXCH(2)CH(2)CH(2) (X = O or S) top are distinctive from those in n-alkanes. In ethers and sulfides, the primary influence of the heteroelement also extends up to three internal rotations, but many more conformers are possible. However, a number of double gauche sequences are forbidden, and therefore, several conformers can be eliminated. These exclusions in particular make up a set of rules for eventually deducing all possible conformers. Furthermore, on the basis of only an exact calculation of these gg conformations in addition to single gauche conformers, it is possible to make an accurate estimate of the relative energy. This two-dimensional approximation scheme constitutes an effective tool for adequately describing the relative energies of all possible conformers at a minimal computational cost.

N-Alkenyl-2-aziridinylmethyl Radicals and N-Alkenylaminyl Radicals in Cascade Cyclizations to Pyrrolizidines and Indolizidines

[reaction: see text] The radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals to pyrrolizidines and indolizidines were examined using density functional theory (DFT) calculations. A large preference for cyclization to pyrrolizidines was found. These predictions corroborated very well with experimental results, leading to an efficient synthesis of pyrrolizidines. No radical cascade cyclization to indolizidines could be performed in practice as only ring opening of N-alkenyl-2-aziridinylmethyl radicals to N-allyl-N-alkenylamines occurred.

Ab Initio Study of Free-Radical Polymerizations: Cost-Effective Methods to Determine the Reaction Rates

The addition of carbon-centered radicals to ethene, which are important in free-radical polymerization processes, are studied from a theoretical point of view. Experimental data for the rate constants are only available for the addition of methyl, ethyl, propyl and butyl radicals. The latter reactions are taken as model systems to derive a cost-effective method for the addition of alkyl radicals to ethene. The proposed model must be accurate and computationally feasible for additions in which larger radicals are involved. Accuracy is validated by direct comparison of theoretical and experimental rate constants in the temperature range from 300 to 600 K. A variety of electronic-structure methods were tested ranging from Hartree-Fock and post-Hartree-Fock methods to pure and hybrid density functional theory methods. Molecular partition functions were refined by treating large amplitude vibrations beyond the harmonic oscillator approximation.

Density functional theory as a tool for the structure determination of radiation-induced bioradicals

The use of density functional methods for the elucidation of the structure of radiation-induced bio-radicals by comparison of computed and experimental EPR properties is discussed. Three case studies, radiation induced radicals of the amino acid alanine, steroid hormones and beta-D-fructose, with increasing degree of uncertainty about the proposed radical structures, are investigated. Next to the analysis of the isotropic and anisotropic components of the hyperfine tensor, also the direction cosines of the principal axes of this tensor were investigated in greater detail in the case of the beta-D-fructose radicals. Since all radicals considered in this contribution are formed in a solid matrix, also the question as to how to incorporate the effect of the molecular environment is addressed. It is concluded that the methodology outlined represents a powerful tool to aid experimentalists in the assignment of the contributions of various radicals contributing to the observed EPR spectra.

Saturation of nuclear matter and short-range correlations

A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pionic contributions to ring diagrams in nuclear matter leads to higher saturation densities than empirically observed. A possible resolution of the nuclear matter saturation problem is suggested.