Claudio M. Zicovich-Wilson

CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals

Abstract CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations. CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography. The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4, 5].

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 α‐quartz (SiO2) 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.

B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals

The B3LYP method augmented with a damped empirical dispersion term (−f(R)C6/R6) is shown to yield structures and cohesive energies, for a representative set of molecular crystals, in excellent agreement with experimental data. Vibrational lattice modes of crystalline urea are also reported to be very close to experiment. The role of the damping function in scaling the dispersion contribution has been analyzed as well as the relevance of the BSSE in the prediction of structure and cohesive energy.

Calculation of the vibration frequencies of α-quartz: The effect of Hamiltonian and basis set

The central‐zone vibrational spectrum of α‐quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high‐frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree–Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm−1, respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane‐wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm−1.

A general method to obtain well localized Wannier functions for composite energy bands in linear combination of atomic orbital periodic calculations

A method for obtaining spatially localized crystalline orbitals starting from delocalized Bloch functions is proposed. The method, that has been implemented in the LCAO CRYSTAL code, is intrinsic and general for nonconducting systems, and provides a set of well localized Wannier functions that can be used for applications that take advantage of their localized character. Examples are given that illustrate the performances and efficiency of the proposed scheme.

Local-MP2 electron correlation method for nonconducting crystals.

Rigorous methods for the post-HF (HF-Hartree-Fock) determination of correlation corrections for crystalline solids are currently being developed following different strategies. The CRYSTAL program developed in Torino and Daresbury provides accurate HF solutions for periodic systems in a basis set of Gaussian type functions; for insulators, the occupied HF manifold can be represented as an antisymmetrized product of well localized Wannier functions. This makes possible the extension to nonconducting crystals of local correlation linear scaling On techniques as successfully and efficiently implemented in Stuttgarts MOLPRO program. These methods exploit the fact that dynamic electron correlation effects between remote parts of a molecule (manifesting as dispersive interactions in intermolecular perturbation theory) decay as an inverse sixth power of the distance R between these fragments, that is, much more quickly than the Coulomb interactions that are treated already at the HF level. Translational symmetry then permits the crystalline problem to be reduced to one concerning a cluster around the reference zero cell. A periodic local correlation program (CRYSCOR) has been prepared along these lines, limited for the moment to the solution of second-order Moller-Plesset equations. Exploitation of point group symmetry is shown to be more important and useful than in the molecular case. The computational strategy adopted and preliminary results concerning five semiconductors with tetrahedral structure (C, Si, SiC, BN, and BeS) are presented and discussed.

Flexibility in a Metal–Organic Framework Material Controlled by Weak Dispersion Forces: The Bistability of MIL‐53(Al)

Breathtaking MOFs: DFT calculations reveal that the exceptional, thermally induced density change of the metal-organic framework MIL53(Al) is controlled by a competition between shortand long-range interactions and entropic factors. As shown in the picture (C green, Al cyan, O red, H white), dispersive interactions between the phenyl rings are responsible for stabilizing a narrow-pore form at low temperature. At 325-375 K, vibrational entropy causes the structure to expand markedly, permitting large volumes of light gases to be adsorbed.

Ab initio study of the vibrational spectrum and related properties of crystalline compounds; the case of CaCO3 calcite

Abstract The static and high frequency dielectric tensors, Born effective charges, vibrational spectrum at the Γ point, TO-LO splitting and IR intensities of calcite CaCO3 have been calculated with the periodic ab initio CRYSTAL program, with five different basis sets of increasing size and four different Hamiltonians (HF, LDA, PBE, B3LYP). B3LYP is shown to perform better than the other options, in particular of LDA and PBE that are often used for the calculation of the vibrational spectrum of crystalline solids. When comparing B3LYP and experimental frequencies, the mean absolute difference is as small as 8.5 cm-1; this number reduces to 4.8 cm-1 if the two lowest experimental frequencies, that we suspect to be affected by a relatively large error, are excluded from statistics. Static and high frequency dielectric tensors, as well as IR intensities computed with the same hybrid scheme (B3LYP) compare quite favourably with experiment. The full set of modes is characterized by various tools including isotopic substitution, “freezing” one of the two subunits (Ca2+ or CO32-) and graphical representations. A general tool has been implemented, that permits the automatic generation of the animation of the full set of modes starting from the CRYSTAL output (available at www.crystal.unito.it/vibs/calcite).

Ab Initio Modeling of Protein/Biomaterial Interactions : Glycine Adsorption at Hydroxyapatite Surfaces

How does glycine adsorb at hydroxyapatite surfaces? Ab initio simulations based on periodic B3LYP GTO calculations reveal the detailed mechanism of binding to the (001) and (010) surfaces by shedding light on how acid and basic amino acid residues of proteins interact with hydroxyapatite based biomaterials.

Ab initio simulation of the IR spectra of pyrope, grossular, and andradite

IR spectra of pyrope Mg3Al2Si3O12, grossular Ca3Al2Si3O12 and andradite Ca3Fe2Si3O12 garnets were simulated with the periodic ab initio CRYSTAL code by adopting an all‐electron Gaussian‐type basis set and the B3LYP Hamiltonian. Two sets of 17 F1u Transverse Optical (TO) and Longitudinal Optical (LO) frequencies were generated, together with their intensities. Because the generation of LO modes requires knowledge of the high frequency dielectric constant ε∞ and Born effective charges, they were preliminary evaluated by using a finite field saw‐tooth model and well localized Wannier functions, respectively. As a by‐product, the static dielectric constant ε0 was also obtained. The agreement of the present calculated wavenumbers (i.e. peak positions) with the available experimental data is excellent, in that the mean absolute difference for the full set of data smaller than 8 cm−1. Missing peaks in experimental spectra were found to correspond to modes with low calculated intensities. Correspondence between TO and LO modes was established on the basis of the overlap between the eigenvectors of the two sets and similarity of isotopic shifts; as result, the so called LO‐TO splitting could be determined. Animation of the normal modes was employed to support the proposed pairing.