Cost-effective composite methods for large-scale solid-state calculations.

Following the development in recent years of progressively more accurate approximations to the exchange-correlation functional, the use of density functional theory (DFT) methods to examine increasingly large and complex systems has grown, in particular for solids and other condensed matter systems. However the cost of these calculations is high, often requiring the use of specialist HPC facilities. As such, for the purpose of large-scale high-throughput screening of material properties, a hierarchy of simplified DFT methods has been proposed that allows rapid electronic structure calculation of large systems, and we have recently extended this scheme to the solid state (sol-3c). Here, we analyze the applicability and scaling of the new sol-3c DFT methods to molecules and crystals composed of light-elements, such as small proteins and model DNA-helices. Furthermore, the calculation of the electronic structure of large to very large porous systems, such as metal-organic frameworks and inorganic nanoparticles, is discussed. The new composite methods have been implemented in the CRYSTAL17 code, which efficiently implements hybrid functionals and enables routine application of the new methods to large-scale calculations of such materials with excellent performance, even with small-scale computing resources.

Extending and assessing composite electronic structure methods to the solid state.

A hierarchy of simplified Hartree-Fock (HF), density functional theory (DFT) methods, and their combinations has been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set global hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semiclassical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c, and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the CRYSTAL code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test bandgaps, vibrational frequencies, elastic constants, and dielectric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error for cohesive energies and unit cell volumes of molecular crystals of 1.5 kcal/mol and 2.8%, respectively. Lattice parameters of inorganic solids deviate by 3% from the references, and vibrational frequencies of α-quartz have standard deviations of 10 cm-1. Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with a substantial increase in computational efficiency.

Periodic density functional theory calculations for 3-dimensional polyacetylene with empirical dispersion terms.

We report periodic B3LYP density functional theory calculations for three-dimensional (3D) trans-polyacetylene (t-PA) fibers. Empirical dispersion terms, as proposed by Grimme, are included with an appropriate re-scaling to yield the B3LYP+D* method implemented in CRYSTAL06. The dispersion corrections are critical for obtaining correct unit cell parameters. In our calculations the out-of-phase P2(1)/n structure turns out to be a transition state for the interchain relative translational motion, which lies about 0.35 kcal mol(-1) above the two symmetrically located in-phase P2(1)/a minima. These results provide a possible new explanation for the observed XRD intensities. Our calculations should also be useful for comparison with more costly non-empirical treatments of 3D PA and other pi-conjugated polymers.

The vibrational spectrum of alpha-AlOOH diaspore: an ab initio study with the CRYSTAL code.

The vibrational spectrum of alpha-AlOOH diaspore has been calculated at the B3LYP level of theory with a double-zeta quality Gaussian-type basis set by using the periodic ab initio CRYSTAL code. Harmonic frequencies at the Gamma point and the corresponding 48 normal modes are analyzed and classified in terms of simple models (octahedra modes, hydrogen stretching, bending, rotations) by direct inspection of eigenvectors, graphical representation, and isotopic substitution. Hydrogen modes are fully separated from the octahedra modes appearing under 800 cm(-1); bending modes are located in the range of 1040-1290 cm(-1), whereas stretching modes appear at 3130-3170 cm(-1). The available experimental IR and Raman spectra are characterized by broad bands, in some cases as large as 800 cm(-1), and individual peaks are obtained by decomposing these bands in terms of Lorentz-Gauss product functions; such a fitting procedure is affected by a relatively large degree of arbitrariness. The comparison of our calculated data with the most complete sets of experimental data shows, nevertheless, a relatively good agreement for all but the H modes; the mean absolute differences for modes not involving H are 10.9 and 7.2 cm(-1) for the IR and the Raman spectra, respectively, the maximum differences being 15.5 and 18.2 cm(-1). For the H bending modes, differences increase to 30 and 37 cm(-1), and for the stretching modes, the calculated frequencies are about 200 cm(-1) higher than the experimental ones; this is not surprising, as anharmonicity is expected to red shift the OH stretching by about 150 cm(-1) in isolated OH groups and even more when the latter is involved in strong hydrogen bonds, as is the case here.

Ab initio investigation of structure and cohesive energy of crystalline urea.

The structure and cohesive energy of crystalline urea have been investigated at the ab initio level of calculation. The performance of different Hamiltonians in dealing with a hydrogen-bonded molecular crystal as crystalline urea is assessed. Detailed calculations carried out by adopting both HF and some of the most popular DFT methods in solid-state chemistry are reported. Local, gradient-corrected, and hybrid functionals have been adopted: SVWN, PW91, PBE, B3LYP, and PBE0. First, a 6-31G(d,p) basis set has been adopted, and then the basis set dependence of computed results has been investigated at the B3LYP level. All calculations were carried out by using a development version of the periodic ab initio code CRYSTAL06, which allows full optimization of lattice parameters and atomic coordinates. With the 6-31G(d,p) basis set, structural features are well reproduced by hybrid methods and GGA. LDA gives lattice parameters and hydrogen-bond distances that are too small relative to experiment, while at the HF level the opposite trend is observed. Results show that hybrid methods are more accurate than HF and both LDA and GGA functionals, with a trend in the computed properties similar to that of hydrogen-bonded molecular complexes. When BSSE and ZPE are taken into account, all methods, except LDA, give computed cohesive energies that are underestimated with respect to the experimental sublimation enthalpy. Dispersion energy, not properly taken into account by DFT methods, plays a crucial role. Such a deficiency also affects dramatically the computed crystalline structure, especially when large basis sets are adopted. We show that this is an artifact due to the BSSE. Indeed, with small basis sets the BSSE gives an extra-binding that compensates for the missing dispersion forces, thus yielding structures in fortuitous agreement with experiment.

An ab initio periodic study of acidic chabazite as a candidate for dihydrogen storage.

A theoretical B3LYP study, adopting a polarized double-zeta quality Gaussian basis set, was performed to characterize acidic chabazite by using the periodic CRYSTAL03 program. Different Si/Al loadings (1/1, 3/1, 5/1, and 11/1) were considered, and for each of them the most stable aluminum distribution and location of the acidic proton, needed as charge balancer, were identified. With the optimal structures, the energy of formation and the anharmonic O-H stretching frequency were calculated with the latter being in good agreement with the experimental data. The B3LYP optimal position of H2 physisorbed at the acidic Brönsted sites of chabazite (Si/Al = 11/1 and 5/1) brings about an interaction energy definitely smaller than that derived from infrared spectroscopy, because of the known deficiencies of this functional to cope with dispersive interactions. The latter was included by means of an ONIOM-like procedure that combines periodic B3LYP energy with results at the MP2 level on selected clusters cut out of the chabazite framework. Adsorption of two H2 molecules for Si/Al = 5/1 chabazite showed a complete independence of each Brönsted site, and neither through-space nor intrastructure polarization effects are present. Within the periodic B3LYP approach shifts in both O-H and H-H anharmonic frequencies were also computed and compared with unperturbed values and with the available experimental results.

The katoite hydrogarnet Si-free Ca3Al2([OH]4)3: a periodic Hartree-Fock and B3-LYP study.

The structure of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been investigated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and both the HF and the hybrid B3-LYP Hamiltonians. The structure has been fully optimized at various pressures in the 0-46 GPa range; the modifications of the structure, and in particular of the (OH)4 group, as a function of pressure are analyzed. At the B3-LYP level and P greater than 15 GPa, a O-H...O interaction of increasing strength appears, with important modifications in the local geometry of the tetrahedral site. The calculated omega01(O-H) fundamental vibrational frequency at zero pressure is in excellent agreement with experiment (3674 and 3663 cm(-1), respectively); the omega01(O-H) stretching frequency remains essentially constant in the 0-15 GPa interval, whereas it dramatically decreases at higher pressures with a corresponding anharmonicity increase, as a consequence of the formation of a strong hydrogen bond. The hydration energy of grossular and the formation energy of Si-free katoite have also been computed, and the B3-LYP results are in quite good agreement with experiment.

The calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code.

The problem of numerical accuracy in the calculation of vibrational frequencies of crystalline compounds from the hessian matrix is discussed with reference to alpha-quartz (SiO(2)) as a case study and to the specific implementation in the CRYSTAL code. The Hessian matrix is obtained by numerical differentiation of the analytical gradient of the energy with respect to the atomic positions. The process of calculating vibrational frequencies involves two steps: the determination of the equilibrium geometry, and the calculation of the frequencies themselves. The parameters controlling the truncation of the Coulomb and exchange series in Hartree-Fock, the quality of the grid used for the numerical integration of the Exchange-correlation potential in Density Functional Theory, the SCF convergence criteria, the parameters controlling the convergence of the optimization process as well as those controlling the accuracy of the numerical calculation of the Hessian matrix can influence the obtained vibrational frequencies to some extent. The effect of all these parameters is discussed and documented. It is concluded that with relatively economical computational conditions the uncertainty related to these parameters is smaller than 2-4 cm(-1). In the case of the Local Density Approximation scheme, comparison is possible with recent calculations performed with a Density Functional Perturbation Theory method and a plane-wave basis set.

Entrapping molecules in zeolites nanocavities: a thermodynamic and ab-initio study.

Adsorption enthalpies of Ar, N2, CO, H2O, CH3CN and NH3 on H-BEA and H-MFI zeolites and on Silicalite, have been measured calorimetrically at 303K in order to assess the energetic features of dispersive forces interactions (confinement effects), H-bonding interactions with surface silanols and specific interactions with Lewis and Brønsted acidic sites. The adsorption of the molecular probes with model clusters mimicking surface silanols, Lewis and Brønsted sites has been simulated at ab-initio level. The combined use of the two different approaches allowed to discriminate among the different processes contributing to the measured (-deltaadsH). Whereas CO and N2 single out contributions from Lewis and Brønsted acidic sites, Ar is only sensitive to confinement effects. For H2O, CH3CN and NH3 the adsorption on Brønsted sites is competitive with the adsorption on Lewis sites. The energy of interaction of H2O with all considered zeolites is surprisingly higher than expected on the basis of -deltaadsH vs PA correlation.