The A-center defect in diamond: quantum mechanical characterization through the infrared spectrum.

The A-center in diamond, which consists of two nitrogen atoms substituting two neighboring carbon atoms, has been investigated at the quantum mechanical level using an all-electron Gaussian type basis set, hybrid functionals and the periodic supercell approach. In order to simulate different defect concentrations, four supercells have been considered containing 32, 64, 128 and 216 atoms, respectively. The ground state is a closed shell system where the two neighboring nitrogen atoms are separated, as a consequence of the strong repulsive interaction between the lone pairs, by 2.22 Å. The calculated band gap of a perfect diamond is 5.75 eV, which is in very good agreement with the experimental value of 5.80 eV (at 0 °K); the vertical electronic transition energy from the defective band to the conduction band is 4.75 and 4.46 eV for the cells containing 128 and 216 atoms, respectively. The presence of the A-center does not affect the Raman spectrum of diamond. Several intense peaks appear on the contrary in the IR spectrum, which permit (or should permit) the identification of this defect. The four peaks proposed by Sutherland et al. (Nature, 1954, 174, 901-904) and widely accepted as fingerprints of the A-center (at 480, 1093, 1203, 1282 cm-1), and the most important features of the spectrum published by Davies 22 years later (J. Phys. C: Solid State Phys., 1976, 9, 537-542) are very well reproduced by our simulated spectrum with the largest supercell. The modes in which the nitrogen atoms are more involved are identified by the frequency shift due to the 14N → 15N isotopic substitution; the two modes corresponding to the experimental ones at 480 and 1282 cm-1 show the largest isotopic shift. The graphical animation of the modes (available at ) not only confirms this attribution, but permits also the investigation of the nature of the full set of modes.

Infrared and Raman spectroscopic features of the self-interstitial defect in diamond from exact-exchange hybrid DFT calculations.

Quantum-mechanical calculations are performed to investigate the structural, electronic, and infrared (IR) and Raman spectroscopic features of one of the most common radiation-induced defects in diamond: the "dumb-bell" 〈100〉 split self-interstitial. A periodic super-cell approach is used in combination with all-electron basis sets and hybrid functionals of density-functional-theory (DFT), which include a fraction of exact non-local exchange and are known to provide a correct description of the electronic spin localization at the defect, at variance with simpler formulations of the DFT. The effects of both defect concentration and spin state are explicitly addressed. Geometrical constraints are found to prevent the formation of a double bond between the two three-fold coordinated carbon atoms. In contrast, two unpaired electrons are fully localized on each of the carbon atoms involved in the defect. The open-shell singlet state is slightly more stable than the triplet (the energy difference being just 30 meV, as the unpaired electrons occupy orthogonal orbitals) while the closed-shell solution is less stable by about 1.55 eV. The formation energy of the defect from pristine diamond is about 12 eV. The Raman spectrum presents only two peaks of low intensity at wave-numbers higher than the pristine diamond peak (characterized by normal modes extremely localized on the defect), whose positions strongly depend on defect concentration as they blue shift up to 1550 and 1927 cm(-1) at infinite defect dilution. The first of these peaks, also IR active, is characterized by a very high IR intensity, and might then be related to the strong experimental feature of the IR spectrum occurring at 1570 cm(-1). A second very intense IR peak appears at about 500 cm(-1), which, despite being originated from a "wagging" motion of the self-interstitial defect, exhibits a more collective, less localized character.

Chemical interaction of water molecules with framework Al in acid zeolites: a periodic ab initio study on H-clinoptilolite.

Periodic quantum-chemistry methods as implemented in the CRYSTAL14 code were considered to analyse the interaction of acid clinoptilolite with water. Initially adsorbed molecules hydrolyse the Al-O bonds, giving rise to defective dealuminated materials. A suitable and representative periodic model of the partially disordered hydrated H-zeolite is the primitive cell (18 T sites) of a decahydrated trialuminated structure of HEU topology. The water distribution inside the material cavities was initially investigated. The model considered for further dealumination was the most stable one from those generated through a combined force field Monte Carlo and ab initio optimization strategy. Optimizations and energy estimations were made at the hybrid DFT level of theory (PBE0 functional) with an atomic basis set of VDZP quality. The energetics of the different pathways involved in the dealumination process was addressed by considering the Gibbs free energy with thermal and zero-point corrections through phonon analysis. It arises that hydrated models exhibit protonated water clusters stabilized by different kinds of H-bonds. The first Al extraction is slightly more energetically favourable from T3 than T2 sites, but at the same time the latter is more probable owing to its larger Al population. However, concerning the second dealumination step, it is more favourable removing the Al atom from both remaining sites after a starting abstraction from T2 rather than T3. These facts determine that the most probable overall pathways go through a first Al removal from T2. The agreement with experimental results is discussed.

Katoite under pressure: an ab initio investigation of its structural, elastic and vibrational properties sheds light on the phase transition.

The evolution under pressures up to 65 GPa of structural, elastic and vibrational properties of the katoite hydrogarnet, Ca3Al2(OH)12, is investigated with an ab initio simulation performed at the B3LYP level of theory, by using all-electron basis sets with the Crystal periodic program. The high-symmetry Ia3d phase of katoite, stable under ambient conditions, is shown to be destabilized, as pressure increases, by interactions involving hydrogen atoms and their neighbors which weaken the hydrogen bonding network of the structure. The corresponding thermodynamical instability is revealed by anomalous deviations from regularity of its elastic constants and by numerous imaginary phonon frequencies, up to 50 GPa. Interestingly, as pressure is further increased above 50 GPa, the Ia3d structure is shown to become stable again (all positive phonon frequencies and regular elastic constants). However, present calculations suggest that, above about 15 GPa and up to at least 65 GPa, a phase of I4[combining macron]3d symmetry (a non-centrosymmetric subgroup of Ia3d) becomes more stable than the Ia3d one, being characterized by strengthened hydrogen bonds. At low-pressures (between about 5 GPa and 15 GPa), both phases show some instabilities (more so for I4[combining macron]3d than for Ia3d), thus suggesting either the existence of a third phase or a possible phase transition of second order.

Structural, electronic and energetic properties of giant icosahedral fullerenes up to C6000: insights from an ab initio hybrid DFT study.

The properties of the (n,n) icosahedral family of carbon fullerenes up to n = 10 (6000 atoms) have been investigated through ab initio quantum-mechanical simulation by using a Gaussian type basis set of double zeta quality with polarization functions (84,000 atomic orbitals for the largest case), the hybrid B3LYP functional and the CRYSTAL14 code featuring generalization of symmetry treatment. The geometry of giant fullerenes shows hybrid features, between a polyhedron and a sphere; as n increases, it approaches the former. Hexagon rings at face centres take a planar, graphene-like configuration; the 12 pentagon rings at vertices impose, however, a severe structural constraint to which hexagon rings at the edges must adapt smoothly, adopting a bent (rather than sharp) transversal profile and an inward longitudinal curvature. The HOMO and LUMO electronic levels, as well as the band gap, are well described using power laws. The gap is predicted to become zero for n ≥ 34 (69,360 atoms). The atomic excess energy with respect to the ideal graphene sheet goes to zero following the log(Nat)/Nat law, which is well described through the continuum elastic theory applied to graphene; the limits for the adopted model are briefly outlined. Compared to larger fullerenes of the series, C60 shows unique features with respect to all the considered properties; C240 presents minor structural and energetic peculiarities, too.

Periodic quantum chemical studies on anhydrous and hydrated acid clinoptilolite.

Periodic quantum chemistry methods as implemented in the crystal09 code were considered to study acid clinoptilolite (HEU framework type), both anhydrous and hydrated. The most probable location of acid sites and water molecules together with other structural details has been the object of particular attention. Calculations were performed at hybrid and pristine DFT levels of theory with a VDZP quality basis set in order to compare performances. It arises that PBE0 provides the best agreement with experimental data as concerns structural features and the most stable Al distribution in the framework. The role of the water molecule distribution in the stability of the systems, the most probable structure that they induce in the material, and their eventual influence on further chemical modification processes, such as dealumination, are discussed in detail. Results show that, apart from the usually considered interactions of water molecules with the zeolite framework, that is, a H-bond with Brönsted acid sites and coordination with framework Al as Lewis ones, it is necessary to consider cooperation of other weaker effects so as to fully understand the hydration effect in this kind of materials.

On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations.

Use of symmetry can dramatically reduce the computational cost (running time and memory allocation) of self-consistent-field ab initio calculations for molecular and crystalline systems. Crucial for running time is symmetry exploitation in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock, and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the symmetry adapted crystalline orbital basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. Quantitative examples, referring to the implementation in the CRYSTAL code, are given for high symmetry families of compounds such as carbon fullerenes and nanotubes.

Boronate ligands in materials: determining their local environment by using a combination of IR/solid-state NMR spectroscopies and DFT calculations.

Boronic acids (R-B(OH)(2)) are a family of molecules that have found a large number of applications in materials science. In contrast, boronate anions (R-B(OH)(3)(-)) have hardly been used so far for the preparation of novel materials. Here, a new crystalline phase involving a boronate ligand is described, Ca[C(4)H(9)-B(OH)(3)](2), which is then used as a basis for the establishment of the spectroscopic signatures of boronates in the solid state. The phase was characterized by IR and multinuclear solid-state NMR spectroscopy ((1)H, (13)C, (11)B and (43)Ca), and then modeled by periodic DFT calculations. Anharmonic OH vibration frequencies were calculated as well as NMR parameters (by using the Gauge Including Projector Augmented Wave--GIPAW--method). These data allow relationships between the geometry around the OH groups in boronates and the IR and (1)H NMR spectroscopic data to be established, which will be key to the future interpretation of the spectra of more complex organic-inorganic materials containing boronate building blocks.

The electronic structure of MgO nanotubes. An ab initio quantum mechanical investigation.

The structural, vibrational and response properties of the (n,0) and (m,m) MgO nanotubes are computed by using a Gaussian type basis set, a hybrid functional (B3LYP) and the CRYSTAL09 code. Tubes in the range 6 ≤ n ≤ 140 and 3 ≤ m ≤ 70 were considered, being n = 2 × m the number of MgO units in the unit cell (so, the maximum number of atoms is 280). Tubes are built by rolling up the fully relaxed 2-D conventional cell (2 MgO units, with oxygen atoms protruding from the Mg plane alternately up and down by 0.38 Å). The relative stability of the (n,0) with respect to the (m,m) family, the relaxation energy and equilibrium geometry, the band gap, the IR vibrational frequencies and intensities, and the electronic and ionic contributions to the polarizability are reported. All these properties are shown to converge smoothly to the monolayer values. Absence of negative vibrational frequencies confirms that the tubes have a stable structure. The parallel component of the polarizability α(∥) converges very rapidly to the monolayer value, whereas α(⊥) is still changing at n = 140; however, when extrapolated to very large n values, it coincides with the monolayer value to within 1%. The electronic contribution to α is in all cases (α(∥) and α(⊥); 6 ≤ n ≤ 140) smaller than the vibrational contribution by about a factor of three, at variance with respect to more covalent tubes such as the BN ones, for which the ratio between the two contributions is reversed.

Raman spectrum of pyrope garnet. A quantum mechanical simulation of frequencies, intensities, and isotope shifts.

The Raman spectrum of pyrope garnet is simulated in ab initio quantum mechanical calculations, using an all-electron Gaussian-type basis set and the hybrid B3LYP functional. Frequencies calculated for the 25 Raman-active modes are in excellent agreement with the several sets of experimental data, with the mean absolute difference ranging from 4 to 8 cm(-1). Comparison of the computed and experimental spectrum shows excellent agreement for most of the intensities as well. Modes missing from experiment are shown to be characterized by low (computed) intensity. Spurious peaks in the experimental spectra are also identified. The isotopic effect has been simulated for (24)Mg → (26)Mg substitution and shows excellent agreement with shifts reported in one of the experiments. Agreement is excellent for all but one mode, which turns out to be attributed to the wrong symmetry in the experiment.

Zeolite synthesis in fluoride media: structure direction toward ITW by small methylimidazolium cations.

Pure silica ITW zeolite can be synthesized using 1,2,3-trimethylimidazolium and 1,3-dimethylimidazolium cations and fluoride anions as structure-directing agents (SDAs). Similarly to the previously reported 1,3,4-trimethylimidazolium, the dimethyl cation can also produce the zeolite TON, but this higher framework density phase finally transforms in situ into ITW. The structures of the as-made and calcined phases prepared with the new cations show a unit cell doubling along z, and the refined structures are reported. Periodic Density Functional Theory calculations provide the energies of the six SDA-ITW and SDA-TON zeolites, and their relative stabilities fully agree with the experimental observations. Structure-direction in this system is discussed from experimental and theoretical results that give strong support to the idea that strained silica frameworks are made possible in fluoride media by decreasing the covalent character of the Si-O bond. This decreased covalency is enhanced with the 1,2,3-trimethyl isomer, which is shown to be the strongest SDA for ITW and, at the same time, is the more hydrophilic of the three SDAs tested. Our observations with the three SDAs agree with the so-called Villaescusa's rule, i.e., the low framework density phase is favored at higher concentrations, but at the same time question the supersaturation hypothesis that has been proposed to explain this rule, since here the low-density phase is the most stable one.

Exceptionally low shear modulus in a prototypical imidazole-based metal-organic framework.

Using Brillouin scattering, we measured the single-crystal elastic constants (C(ij)'s) of a prototypical metal-organic framework (MOF): zeolitic imidazolate framework (ZIF)-8 [Zn(2-methylimidazolate)(2)], which adopts a zeolitic sodalite topology and exhibits large porosity. Its C(ij)'s under ambient conditions are (in GPa) C(11)=9.522(7), C(12)=6.865(14), and C(44)=0.967(4). Tensorial analysis of the C(ij)'s reveals the complete picture of the anisotropic elasticity in cubic ZIF-8. We show that ZIF-8 has a remarkably low shear modulus G(min) < or approximately 1 GPa, which is the lowest yet reported for a single-crystalline extended solid. Using ab initio calculations, we demonstrate that ZIF-8's C(ij)'s can be reliably predicted, and its elastic deformation mechanism is linked to the pliant ZnN(4) tetrahedra. Our results shed new light on the role of elastic constants in establishing the structural stability of MOF materials and thus their suitability for practical applications.

In situ transformation of TON silica zeolite into the less dense ITW: structure-direction overcoming framework instability in the synthesis of SiO2 zeolites.

Under specific synthesis conditions the crystallization of a dense silica zeolite (TON) is followed by its in situ transformation into a less dense and, in the absence of occluded species, less stable zeolite (ITW). Periodic ab initio calculations including energy corrections for van der Waals interactions as well as zero-point and thermal effects are used first to assess the relative stability of both SiO(2) (calcined) phases and then to investigate host-guest interactions in the as-made zeolites, as well as their relative stability. The less dense SiO(2)-ITW is less stable than SiO(2)-TON, with an energy difference that is significantly larger than expected from their difference in molar volume. This extra destabilization is ascribed to the strained double 4-ring units of silica tetrahedra (D4R). Regarding the as-made materials, the organic cation fills in more efficiently the zeolitic voids in ITW than in TON, bringing about a larger stabilization in the former owing to the extension of the long-range addition of dispersion force contributions. On the other hand, fluoride induces a polarization of the silica framework that is highly localized in TON (showing pentacoordinated [SiO(4/2)F](-) units) but has a large global character in ITW (where fluoride is encapsulated into D4R units). We argue that the structure-directing role toward D4R materials that has been proposed for fluoride consists fundamentally in the ability to induce a global polarization of the silica framework that allows relaxation of the strain associated with these units. In this sense, fluoride stabilizes the otherwise strained D4R-SiO(2) frameworks making them reachable for crystallization. This work documents a case in which the structure directing agents "choose" a structure not kinetically but through stabilization.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented.

Catalytic reaction mechanism of Mn-doped nanoporous aluminophosphates for the aerobic oxidation of hydrocarbons.

In this work we apply state-of-the-art electronic-structure-based computational methods based on hybrid-exchange density functional theory to study the mechanism of the aerobic oxidation of hydrocarbons catalysed by Mn-doped nanoporous aluminophosphates (Mn-AlPOs). We compare our results with available experimental data. We show that the catalytic efficiency of Mn-AlPOs in oxidation reactions is intrinsically linked to 1) the Mn redox activity, in particular between 2+ and 3+ oxidation states, and 2) the coordinative insaturation of tetrahedral Mn embedded in AlPO frameworks, which facilitates the reaction by stabilising oxo-type radicals through the formation of Mn complexes. Our mechanism demonstrates the crucial role of both Mn(III) and Mn(II) in the reaction mechanism: Mn(III) sites undergo an initial reaction cycle that leads to the production of the alkyl hydroperoxide intermediate, which can only be transformed into the oxidative products (alcohol, aldehyde and acid) by Mn(II). A preactivation step is required to yield the reduced Mn(II) sites able to decompose the hydroperoxide intermediates; this step takes place through a transformation of the hydrocarbon into the corresponding peroxo-derivative, stabilised by forming a complex with Mn(III) and yielding at the same time reduced Mn(II) sites. Both species enter a subsequent propagation cycle in which Mn(II) catalyses the dissociation of the hydroperoxide that proceeds until the formation of the oxidative products by two parallel pathways, through alkoxy- or hydroxy-radical-like intermediates, whilst the Mn(III)-peroxo complex enables further production of the hydroperoxide intermediate.

Role of dispersive interactions in the CO adsorption on MgO(001): periodic B3LYP calculations augmented with an empirical dispersion term.

Empirically dispersion corrected B3LYP method (i.e. B3LYP-D) is demonstrated to give excellent results for structure, adsorption energy and vibrational frequency shift for the CO molecule adsorbed on the MgO(001) surface, a system considered a challenge for current density functional methods. A periodic approach was adopted to model the interaction using a three-layer slab model. For the B3LYP-D* method an interaction energy of -13.1 kJ mol(-1) is computed at low-coverage in very good agreement with experimental evidence (-12.6 kJ mol(-1)) as well as a positive CO vibrational shift of 10 cm(-1) to be compared with the experimental value of 14 cm(-1).

Vibration Frequencies of Mg3Al2Si3O12 Pyrope. An ab initio study with the CRYSTAL code.

The vibrational spectrum of Mg(3)Al(2)Si(3)O(12) pyrope is calculated at the Gamma point by using the periodic ab initio CRYSTAL program that adopts an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The full set of frequencies (17 IR active, 25 RAMAN active, 55 silent modes) is calculated. The effect of the basis set and of the computational parameters on the calculated frequencies is discussed. It is shown that the mean absolute difference with respect to the experimental IR and RAMAN data is as small as 6 and 8 cm(-1), respectively. The IR and RAMAN modes are fully characterized by various tools such as isotopic substitution, direct inspection of the eigenvectors, and graphical representation. The present calculation permits to clarify some of the assignment and interpretation problems raised by experiment and previous simulations with force fields.

Electronic charge density analysis of Li-doped polyacetylene: molecular vs periodic descriptions and nature of Li-to-chain bonding.

A detailed analysis of the electronic structure and charge distribution around the trigonal site of Li-doped polyacetylene is reported using finite chain and periodic descriptions of the polymer. Atoms-in-molecules (AIM) analysis is done to characterize the nature of the bond between Li and the polymer backbone through the location of the bond critical points and computation of the total charge on the atomic basins around the doping site. We find that the Li atom donates practically one electron to the π-system, in accordance with the classical Su-Schriffer-Heeger model. However, despite that the Li atom is equidistant from the three closest C atoms in the geometric soliton, a single Li-C bond critical point is found. The AIM quantitative analysis of the electronic density reveals that the Li(+) ion is immersed into the polymer π-cloud in a way that resembles a metallic bonding interaction.

Comparative Study on the Performance of Hybrid DFT Functionals in Highly Correlated Oxides: The Case of CeO2 and Ce2O3.

The outstanding catalytic properties of cerium oxides rely on the easy Ce(3+) ↔ Ce(4+) redox conversion, which however constitutes a challenge in density functional based theoretical chemistry due to the strongly correlated nature of the 4f electrons present in the reduced materials. In this work, we report an analysis of the performance of five exchange-correlation functionals (HH, HHLYP, PBE0, B3LYP, and B1-WC) implemented in the CRYSTAL06 code to describe three properties of ceria: crystal structure, band gaps, and reaction energies of the CeO2 → Ce2O3 process. All five functionals give values for cell parameters that are in fairly good agreement with experiment, although the PBE0 hybrid functional is found to be the most accurate. Band gaps, 2p-4f-5d in the case of CeO2 and 4f-5d in the case of Ce2O3, are found to be, in general, overestimated and drop off when the amount of Hartree-Fock exchange in the exchange-correlation functional decreases. In contrast, the reaction energies are found to be underestimated, and increase when the amount of HF exchange lowers. Overall, at its standard formulation, the B1-WC functional seems to be the best choice as it provides good band gaps and reaction energies, and very reasonable crystal parameters.