The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

The spectroscopic characterization of interstitial oxygen in bulk silicon: A quantum mechanical simulation.

The vibrational Infrared and Raman spectra of six interstitial oxygen defects in silicon containing a Si-O-Si bridge between adjacent Si atoms are obtained from all-electron B3LYP calculations within a supercell scheme, as embodied in the CRYSTAL code. Two series of defects have been considered, starting from the single interstitial defect, O1. The first consists of four defects, O1,n, in which two O1 defects are separated by (n - 1) Si atoms, up to n = 4. The second consists of four defects, On, in which nO1 defects surround a single Si atom, with n = 1-4, where O4 has the same local nearest neighbor structure as α-quartz. For both series of defects, the equilibrium geometries, charge distributions, and band structures are reported and analyzed. The addition of 1-4 oxygen atoms to the perfect lattice generates 3-12 new vibrational modes, which, as a result of the lighter atomic mass of O with respect to Si, are expected to occur at wavenumbers higher than 521 cm-1, the highest frequency of pristine silicon, thereby generating a unique new Raman spectrum. However, only a small subset of these new modes is found in the spectrum. They appear at 1153 cm-1 (O1), at 1049 cm-1 and 1100 cm-1 (O1,2), at 1108 cm-1 (O1,3), at 1130 cm-1 and 1138 cm-1 (O1,4), and 773 cm-1, 1057 cm-1, and 1086 cm-1 (O4), and can be considered "fingerprints" of the respective defects, as they are sufficiently well separated from each other. Graphical animations indicate the nature and intensity of each of the observed modes which are not overtones or combinations.

On the Models for the Investigation of Charged Defects in Solids: The Case of the VN- Defect in Diamond.

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-.

Low energy excitations in NiO based on a direct Δ-SCF approach.

This paper reports calculated energies and electronic structures of nineteen excited states in NiO based on a Δ-SCF approach reported previously for the [Formula: see text] transitions in NiO and Sr2CuO2Cl2. They are the spin-flip: [Formula: see text]; eight [Formula: see text]: (one electron) 3A2g → 3 T 2g , (two electron) 3A2g → 3 T 1g , 3A2g → a 1 E g , 3A2g → 1 T 2g , 3A2g → 1 T 1g , 3A2g → b1 E g , 3A2g → b1 T 2g ; two O(2p) → Ni(3d); seven Ni(3d) → O(2p) (including two spin-flip) and the O(2s) → Ni(3d) charge transfer excitations, which span an energy range from 0.25 eV to 17.53 eV, and include the fundamental band gap associated with an excitonic O(2p) → Ni(3d) transition at 4.23 eV. These are compared to absorption and emission spectra, and previous calculations. In the case of the O(2p) → Ni(3d) excitations, comparisons are given for gap and Γ-point energies derived from HF, PBE0, HSE06, B3LYP, B1WC, GGA and LDA one-electron approximations. Finally, the directly calculated Stokes shifts and associated luminescence energies for the two O(2p) → Ni(3d) transitions are reported, where the excitonic value is found to be in good agreement with the recently reported experimental value.

Interstitial nitrogen atoms in diamond. A quantum mechanical investigation of its electronic and vibrational properties.

The electronic and vibrational features of the single- (I1N) and double- (I2N) nitrogen interstitial defects in diamond are investigated at the quantum mechanical level using a periodic supercell approach based on hybrid functionals constructed from all electron Gaussian basis sets within the Crystal code. The results are compared with those of the well characterized 100 split self-interstitial defect (I2C). The effect of defect concentration has been investigated using supercells with different size, containing 64 and 216 atoms. Band structure, formation energy, charge and spin density distributions of each defect are analyzed. Irrespective of the defect concentration, these defects show important features for both IR and Raman spectroscopies. Stretching modes of the two atoms involved in the defect are calculated to be around 1837, 1761 and 1897 cm-1 for the I1N, I2N and I2C case, respectively. Since they are well removed from the one-phonon mode of pristine diamond (1332 cm-1), they are, in principle, detectable from the experimental point of view.

Vibrational spectroscopy of hydrogens in diamond: a quantum mechanical treatment.

The electronic and vibrational features of the VHn (n = 1 to 4) family of defects in diamond (hydrogen atoms saturating the dangling bonds of the atoms surrounding a vacancy) are investigated at the quantum mechanical level by using the periodic supercell approach, an all electron Gaussian type basis set, hybrid functionals, and the Crystal code. Most of the results have been collected for supercells containing 64 atoms; however, in order to explore the effect of the defect concentration on both the IR and Raman spectra, supercells containing 216, 512 and 1000 atoms have also been considered in the VH4 case. For each system, all the possible spin states are considered; their relative stability, band structure, charge and spin density distributions are thoroughly described. All the investigated systems present specific IR and Raman spectra, with vibrational spectroscopic features that can in principle be used as fingerprints for their characterization. This is particularly true for the C-H stretching, that ranges between 2500 and 4400 cm-1. The stretching modes are strongly affected by anharmonicity that has been evaluated in this work; it turns out to be extremely sensitive to the H load and spin state of the system, and ranges from -335 cm-1 for VH1 to +85 cm-1 for VH4. All of the investigated defects have very low C-H stretching IR intensity, so that they essentially appear as silent, the exception being VH1. The situation is different for the Raman spectra: the stretching modes of all defects do have similar large intensity; unfortunately here it is the experimental evidence that is lacking.

Characterization of the B-Center Defect in Diamond through the Vibrational Spectrum: A Quantum-Mechanical Approach.

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.

The VN3H defect in diamond: a quantum-mechanical characterization.

The VN3H defect in diamond (a vacancy surrounded by three nitrogen and one carbon atoms, the latter being saturated by a hydrogen atom) is investigated quantum-mechanically by use of a periodic supercell approach, an all-electron Gaussian-type basis set, "hybrid" functionals of density functional theory, and the Crystal program. Three fully optimized structural models (supercells containing 32, 64, and 128 atoms) are considered to investigate the effect of defect concentration. The electronic configuration of the defect is reported along with a description of its structural features. In particular, the influence of the lone-pair electrons of the three nitrogen atoms on the C-H bond is discussed. A thorough characterization of the vibrational spectroscopic features of the VN3H defect is also presented, where the anharmonicity of the most relevant normal modes is discussed. The infrared and Raman spectra show specific peaks, which allow for the identification of this particular defect among the many defects that are commonly present in both natural and irradiation-damaged diamonds. In particular, the main feature of the spectral fingerprint of the defect (i.e. the C-H stretching mode), experimentally observed at 3107 cm-1, is here computed at 3094 cm-1 with the B3LYP "hybrid" functional (with an anharmonic redshift of 157 cm-1 with respect to its harmonic value). The role played by the three nitrogen atoms on the spectral features of the defect is clearly identified through the redshift due to the 14N → 15N isotopic substitution.

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.

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.