Bartolomeo Civalleri

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.

Hartree-Fock geometry optimisation of periodic systems with the CRYSTAL code

Abstract Results are reported on the geometry optimisation of periodic systems with the Hartree–Fock analytical gradients recently implemented in the C rystal code. Application to the structure optimisation of molecules, polymers, slabs and crystals is presented.

Ab-initio prediction of materials properties with CRYSTAL: MOF-5 as a case study

MOF-5 is by far the most relevant member of the new class of metal–organic framework materials and has been adopted as a case study to show that reliable ab initio prediction of materials properties of complex systems can be obtained by means of a solid state computational tool like the CRYSTAL code. Structure, electronic properties and vibrational frequencies of MOF-5 computed at the B3LYP level of theory are reported and discussed. Animations representing MOF-5 vibrations are available at the web site: http://www.crystal.unito.it/vibs/mof5

Intermolecular interaction energies in molecular crystals: comparison and agreement of localized Møller-Plesset 2, dispersion-corrected density functional, and classical empirical two-body calculations.

A comparative analysis of the intermolecular energy for a data set including 60 molecular crystals with a large variety of functional groups has been carried out using three different computational approaches: (i) a method based on a physically meaningful empirical partition of the interaction energy (PIXEL), (ii) density functional methods with a posteriori empirical correction for the dispersion interactions (DFT-D), and (iii) a full periodic ab initio quantum mechanical method based on Møller-Plesset perturbation theory for the electron correlation using localized crystal orbitals (LMP2). Due to the large computational cost, LMP2 calculations have been restricted to a subset of seven molecular crystal comprising benzene, formic acid, formamide, succinic anhydride, urea, oxalic acid, and nitroguanidine, and the results compared with PIXEL and DFT-D data as well as with the experimental data show excellent agreement among all adopted methods. This shows that both DFT-D and PIXEL approaches are robust predictive tools for studying molecular crystals. A detailed analysis shows a very similar dispersion contribution of the two methods across the 60 considered molecular crystals. The study also confirms that pure DFT shows serious deficiencies in properly handling molecular crystals in which the dispersive contribution is large. Due to the negligible requested computational resources, PIXEL is the method of choice in screening of a large number of molecular crystals, an essential step to predict crystal polymorphism or to study crystal growth processes. DFT-D can then be used to refine the ranking emerged from PIXEL calculations due to its general applicability and robustness in properly handling short-range interactions.

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 calculation of elastic constants of crystalline systems with the CRYSTAL code

An automated procedure for calculating second-order elastic constants for crystalline systems of any symmetry using the CRYSTAL program is described. Second derivatives with respect to strain are evaluated numerically from analytical gradients. The internal co-ordinates are re-optimized with each applied strain. Point group symmetry is exploited to reduce the number of needed deformations according to Laue classes. A set of test cases covering many of the crystal classes is used to document the numerical accuracy of the scheme, and to define default values of the computational parameters so as to reduce the input file to a single keyword.

Geometrical Correction for the Inter- and Intramolecular Basis Set Superposition Error in Periodic Density Functional Theory Calculations

We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys-Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 Å and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.

Normal vibrational analysis of the syndiotactic polystyrene s(2/1)2 helix.

The full vibrational spectra of the gamma, delta, and epsilon crystalline phases of syndiotactic polystyrene (sPS), i.e., phases presenting the s(2/1)2 helical conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite helix. The assignment of the different modes was highly facilitated and validated by the experimental evaluation of the direction of the transition moment vector of most IR peaks, which was made possible for the first time by measurements on sPS films with different uniplanar orientations of the crystalline phase. The normal vibration analysis of most representative modes of the periodic model allowed for a general description of each one to be obtained, which was further confirmed by the direct inspection of mode animations.