Search

The vibrational spectrum of [alpha]-AlOOH diaspore calculated at the B3LYP level of theory with a double-(symbol) quality Gaussian-type basis set by using the periodic ab initio CRYSTAL code is reported.

A study was conducted to analyze the interaction of water molecules with titanium sites in titanium-containing zeolites. The ab initio periodic Hartree-Fock program CRYSTAL was utilized to carry out the analysis. The zeolitic portion of the system was characterized by a perfect crystalline chabazite framework. Results indicated that the stability and electronic structure of the hydrated sites were dependent on the framework flexibility.

The electronic structure, relative stability and equilibrium geometry of titanozeolites were investigated at an ab initio level of theory using the periodic quantum mechanical program called CRYSTAL. Nine periodic crystalline models of composition (TiO2)(sub x) (SiO2)(sub 1-x) with different framework type structures were examined for this purpose. The geometry of these models was completely optimized with the aid of a split valence double-zeta basis set. The influence of more extended basis sets on the electronic properties and relative stabilities of titanozeolites at the optimized geometry was also analyzed.

The vibrational spectrum of the Si-free katoite hydrogarnet is calculated at the periodic ab initio quantum mechanical level with the CRYSTAL program, using a Gaussian type basis set and the hybrid B3LYP Hamiltonian. The parameters controlling the numerical differentiation, as well as the numerical integration of the exchange-correlation functional for the self-consistent filed calculation shows to affect the obtained frequencies by less than 3 cm(super -1).

A study is conducted to show that it is possible to perform the calculations of the full vibrational spectrum of a large unit cell system containing heavy atoms such as Fe and Ca, with an open-shell configuration by using ab initio quantum mechanical methods and all-electron basis sets. The results confirm that vibrational frequencies in good agreement with experiment can be computed for garnets with a large basis set and B3LYP Hamiltonian (mean absolute differences of 6-8 cm(super -1)).

The linear and nonlinear optical (NLO) properties of fullerene and fullerene-like structures, including crystallogen and pnictogen elements, are computed quantum mechanically. The tensors of optical polarizability, α, and second hyperpolarizability, γ, for a series of buckyball fullerene analogues, namely, Si 60 , Ge 60 , Sn 60 , Pb 60 , P 60 , As 60 , Sb 60 , and Bi 60 , are reported and analyzed. The eight considered nanocages are here classified into four categories: nanocages stabilized in the X 60 form, including C 60 , As 60 , Sb 60 , and Bi 60 ; nanocages that are not stabilized in the X 60 form but are found to be stable in a distorted buckled b-X 60 form, with X = Si and Ge; nanocages stabilized only in an exohedral decorated X 60 -Y 60 form, X = Sn, Y = H or F; and finally nanocages that are not stable in either distorted or decorated form; however, their corresponding tabular nanotubes are found to be stable; such group includes P and Pb elements. A suggested nomenclature for the above-mentioned fullerenes is given for the first time, where many geometrical, energetic, and optical parameters are discussed extensively. These systems are energetically stable. The cohesive energies of Bi 60 and Sn 60 -F 60 range from -1.2 to -4.8 eV/atom and can be compared to -2.4 and -3.3 eV/atom from the corresponding 2D bismuthene and stanene monolayers, respectively. While bismuthellene, Bi 60 , shows vigorous optical responses compared to standard fullerene, the (9, 0) phosphorus nanotube gives not only enhanced polarizability and second hyperpolarizability but also an inducing first hyperpolarizability, β, which was null by symmetry in the case of spherical fullerenes. The proposed models are expected to be promising materials for optoelectronic and NLO applications.

The local structure and composition of the diamond paramagnetic defects labelled N3 and OK1 in which two heteroatoms (one of them is nitrogen) occupy vicinal substitutional positions are still a matter of debate. The electron paramagnetic resonance (EPR) is the technique adopted experimentally to characterize these defects, whose ground state is a doublet. In the present study, two models suggested in literature that contain N and O impurities are investigated at the quantum mechanical level by using the supercell model, a local Gaussian-type basis set, and the hybrid B3LYP functional as implemented in the CRYSTAL code. The computed EPR results (the Fermi contact and the available elements of the hyperfine coupling and electric field gradient tensors) are in good agreement (much better than in all previous, in some cases recently, studies) with an experiment. The two defects are further characterized in terms of local geometry, charge and spin density distributions, and IR and Raman spectra.

An extension of the CRYSTAL program is presented allowing for calculations of anharmonic infrared (IR) intensities and Raman activities for periodic systems. This work is a follow-up of two papers devoted to the computation of anharmonic vibrational states of solids from DFT (density functional theory) calculations (Erba et al. J. Chem. Theory Comput. 2019, 15, 3755-3765 and Erba et al. J. Chem. Theory Comput. 2019, 15, 3766-3777). The approach presented here relies on the evaluation of integrals of the dipole moment and polarizability operators over anharmonic wave functions obtained from either VSCF (vibrational self-consistent field) or VCI (vibrational configuration interaction) calculations. With this extension, the program now allows for a more complete characterization of the vibrational spectroscopic features of solids within the density functional theory. In particular, it is able (i) to provide reliable positions and intensities for the most intense spectral features and (ii) to check whether a first overtone or a combination band has a nonvanishing IR intensity or Raman activity. Therefore, it becomes possible to assign the transition(s) corresponding to satellite peak(s) around a fundamental transition or the overtones or combination bands that may be as intense as their corresponding fundamental transitions through the strongest mode-mode couplings, as in so-called Fermi resonances. The present method is assessed on two molecular systems, H 2 O and H 2 CO, as well as on two solid state cases, boron hydrides BH 4 and their deuterated species BD 4 in a crystalline environment of alkali metals (M = Na, K). The solid state cases are particularly insightful as, in the B-H (or B-D) stretching region here considered, they exhibit many spectral features entirely due to anharmonic effects: two out of three in the IR spectrum and four out of six in the Raman spectrum. All IR and Raman active overtones and combination bands experimentally observed are correctly predicted with our approach. The effect of the adopted quantum-chemical model (DFT exchange-correlation functional/basis set) for the electronic structure calculations on the computed spectra is discussed and found to be significant, which suggests some special care is needed for the analysis of subtle spectral features.

Two methods are implemented in the Crystal program for the calculation of anharmonic vibrational states of solids: the vibrational self-consistent field (VSCF) and the vibrational configuration-interaction (VCI). While the former is a mean-field approach, where each vibrational mode interacts with the average potential of the others, the latter allows for an explicit and complete account of mode-mode correlation. Both schemes are based on the representation of the adiabatic potential energy surface (PES) discussed in Part I, where the PES is expanded in a Taylor's series so as to include up to cubic and quartic terms. The VSCF and VCI methods are formally presented and their numerical parameters discussed. In particular, the convergence of computed anharmonic vibrational states, within the VCI method, is investigated as a function of the truncation of the expansion of the nuclear wave function. The correctness and effectiveness of the implementation is discussed by comparing with available theoretical and experimental data on both molecular and periodic systems. The effect of the adopted basis set and exchange-correlation functional in the description of the PES on computed anharmonic vibrational states is also addressed.

A computational approach is presented to compute anharmonic vibrational states of solids from quantum-mechanical DFT calculations by taking into explicit account phonon-phonon couplings via the vibrational configuration interaction (VCI) method. The Born-Oppenheimer potential energy surface (PES) is expanded in a Taylor's series in terms of harmonic normal coordinates, centered at the equilibrium nuclear configuration, is truncated to quartic order, and contains one-mode, two-mode, and three-mode interatomic force constants. The description of the anharmonic terms of the PES involves the numerical evaluation of high-order energy derivatives (cubic and quartic in our case) with respect to nuclear displacements and constitutes the most computationally demanding step in the characterization of anharmonic vibrational states of materials. Part I is devoted to the description of the PES. Four different numerical approaches are presented for the description of the potential, all based on a grid representation of the PES in the basis of the normal coordinates, that require different ingredients (energy and/or forces) to be evaluated at each point (i.e., nuclear configuration) of the grid. The numerical stability and relative computational efficiency of the various schemes for the description of the PES are discussed on two molecular systems (water and methane) and two extended solids (Ice-XI and MgH 2 ). All the presented algorithms are implemented into a developmental version of the Crystal program.

Local charged defects in periodic systems are usually investigated by adopting the supercell charge compensated (CC) model, which consists of two main ingredients: (i) the periodic supercell, hopefully large enough to reduce to negligible values the interaction among defects belonging to different cells; (ii) a background of uniform compensating charge that restores the neutrality of the supercell and then avoids the "Coulomb catastrophe". Here, an alternative approach is proposed and compared to CC, the double defect (DD) model, in which another point defect is introduced in the supercell that provides (or accept) the electron to be transferred (subtracted) to the defect of interest. The DD model requires obviously a (much) larger supercell than CC, and the effect of the relative position of the two defects must be explored. A third possible option, the cluster approach, is not discussed here. The two models have been compared with reference to the VN - defect; for DD, the positive compensating charge is provided by a P atom. Three cubic supercells of increasing size (containing 216, 512, and 1000 atoms) and up to eight relative VN - -P + defect-defect positions have been considered. The comparison extends to the equilibrium geometry around the defect, band structure, charge and spin distribution, IR and Raman vibrational spectra, and electron paramagnetic resonance constants. It turns out that the CC and DD models provide very similar results for all of these properties, in particular when the P + compensating defect is not too close to VN - .

We present the implementation of an implicit solvation model in the CRYSTAL code. The solvation energy is separated into two components: the electrostatic contribution arising from a self-consistent reaction field treatment obtained within a generalized finite-difference Poisson model, augmented by a nonelectrostatic contribution proportional to the solvent-accessible surface area of the solute. A discontinuous dielectric boundary is used, along with a solvent-excluded surface built from interlocking atom-centered spheres on which apparent surface point charges are mapped. The procedure is general and can be performed at both the Hartree-Fock and density functional theory levels, with pure or hybrid functionals, for systems periodic in 0, 1, and 2 directions, that is, for isolated molecules and extended polymers and surfaces. The Poisson equation resolution and apparent surface charge formalism is first validated on model analytical test cases. The good agreement obtained on solvation free energies is further confirmed by calculations performed on a large test set of 501 neutral molecules, for which a mean unsigned error of 1.3 kcal/mol is obtained when compared to the available experimental data. Importantly, the self-consistent reaction field procedure converges well for all molecules tested. This is further verified for all polymers and surfaces considered. In particular, for periodic systems, results obtained on an infinite glycine chain and on the wettability parameters of SiO 2 surfaces are in good agreement with previously published data. The size extensivity of the energetic terms involved in the electrostatic contribution to the solvation energy is also well verified. These encouraging results constitute a first step to take into account complex environments in the CRYSTAL code, potentially allowing for a more accurate modeling of complex processes for both periodic and nonperiodic systems.

The B-center in diamond, which consists of a vacancy whose four first nearest-neighbors are nitrogen atoms, has been investigated at the quantum-mechanical level with an all-electron Gaussian-type basis set, hybrid functionals, and the periodic supercell approach. To simulate various defect concentrations, four cubic supercells have been considered, containing (before the creation of the vacancy) 64, 216, 512, and 1000 atoms, respectively. Whereas the B-center does not affect the Raman spectrum of diamond, several intense peaks appear in the IR spectrum, which should permit us to identify this defect. It turns out that of the seven peaks proposed by Sutherland in 1954, located at 328, 780, 1003, 1171, 1332, 1372, and 1426 cm -1 , and frequently mentioned as fingerprints of the B center, the first one and the last three do not appear in the simulated spectrum at any concentration. The graphical animation of the modes confirms the attribution of the remaining three and also permits investigation of the nature of the full set of modes.

An enhancement of the piezoelectric properties of lead-free materials, which allow conversion of mechanical energy into electricity, is a task of great importance and interest. Results of first-principles calculations of piezoelectric/electromechanical properties of the Ba (1-x) Sr x TiO 3 (BSTO) ferroelectric solid solution with a perovskite structure are presented and discussed. Calculations are performed within the linear combination of atomic orbitals (LCAO) approximation and periodic-boundary conditions, using the advanced hybrid functionals of density functional theory (DFT). A supercell model allows the investigation of multiple chemical compositions x. In particular, three BSTO solid solutions with x = 0, 0.125, 0.25 are considered within the experimental stability domain of the ferroelectric tetragonal phase of the solid solution (x < 0.3). The configurational disorder with x = 0.25 composition is also investigated explicitly considering the seven possible atomic configurations corresponding to this composition. It is predicted that Sr-doping of BaTiO 3 makes it mechanically harder and enhances its electromechanical/piezoelectric properties, which are important for relevant applications.

Nowadays, the efficient exploitation of high-performance computing resources is crucial to extend the applicability of first-principles theoretical methods to the description of large, progressively more realistic molecular and condensed matter systems. This can be achieved only by devising effective parallelization strategies for the most time-consuming steps of a calculation, which requires some effort given the usual complexity of quantum-mechanical algorithms, particularly so if parallelization is to be extended to all properties and not just to the basic functionalities of the code. In this Article, the performance and capabilities of the massively parallel version of the Crystal17 package for first-principles calculations on solids are discussed. In particular, we present: (i) recent developments allowing for a further improvement of the code scalability (up to 32 768 cores); (ii) a quantitative analysis of the scaling and memory requirements of the code when running calculations with several thousands (up to about 14 000) of atoms per cell; (iii) a documentation of the high numerical size consistency of the code; and (iv) an overview of recent ab initio studies of several physical properties (structural, energetic, electronic, vibrational, spectroscopic, thermodynamic, elastic, piezoelectric, topological) of large systems investigated with the code.

The electronic second harmonic generation (SHG) tensor, d, of crystalline urea and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBE0, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases. The hybrid functionals turn out to provide results that agree well with experiment. For urea and KDP the percentage of exact exchange determined by the inverse dielectric constant is too large. At 1064 nm the vibrational contribution for urea is found to be less than 5% of the total value. To the authors' knowledge, this is the first coupled (self-consistent) calculation of SHG for any periodic system.

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.

The coupled perturbed Kohn-Sham (CPKS) computational scheme for the evaluation of electric susceptibility tensors in periodic systems, recently implemented in the CRYSTAL code, has been extended to third-order. It is, then, used to obtain static electronic hyperpolarizabilities of zigzag BN nanotubes for the first time. This procedure, which is fully analytic in all key steps, requires a double self-consistent treatment for taking into account the first- and second-order response of the system to the applied field. The performance of different functionals is compared and the B3LYP hybrid is ultimately chosen for calculations on nanotubes having radii as large as R = 20 Å (6-200 atoms in the unit cell). Such large radii are sufficient to give the pure longitudinal component of the (hyper)polarizability tensors to within 1% of the "exact" hexagonal BN monolayer limit. Other tensor components involving the transverse direction converge more slowly. They can, however, be extrapolated to the monolayer limit to within 4% accuracy except for the pure transverse second hyperpolarizability, which has an error of 13% in that limit.

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.