B3LYP Hamiltonian Research Articles

Ab Initio Calculations of the Main Crystal Surfaces of Baryte (BaSO4)

In this work, we revisited the theoretical morphology of baryte for determining the character (flat, stepped, and kinked) and the different profiles (or terminations) of the crystal faces, and presented an accurate ab initio study of the structures and surface energies at 0 K of the low-index (001), (011), (210), (101), (100), (010), (201), (012), and (211) baryte faces, by using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian. According to the surface energy values, the stability order of the baryte faces was found to be (210) ≅ (001) < (211) < (101) < (010) < (011) < (201) ≅ (100) < (012). Then, the equilibrium shape of baryte was drawn and compared with the previous ones obtained at an empirical level. This is a preliminary work, which is necessary to successively evaluate the influence of water and/or impurities adsorption on the most important baryte surfaces, both at equilibrium and during growth. Indeed, to evaluate these adsorption effects on the crystal morphology, it is fundamental ...

Analysis of the Configurations of a Crystal Surface. Pyrope (Mg3Al2Si3O12) as a Case Study

This paper presents a working methodology to determine all the possible surface configurations of a hkl crystal face. As a case study, we have applied our strategy to individuate the surface configurations of the {100}, {110}, and {112} forms of pyrope (Mg3Al2Si3O12). To identify the most stable surface termination, we have performed an accurate ab initio study of the surface structures and energies at 0 K of the pyrope {100} configurations, by using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian and a localized all-electron Gaussian-type basis set. Even if we are mainly interested in obtaining informations about the habit and genesis of natural garnets included in diamond (and pyrope is the main component of garnets trapped in diamonds), our results could be extremely useful to any researcher involved in the study of the surfaces of whatever crystalline phase.

Ab Initio Calculations of the Main Crystal Surfaces of Forsterite (Mg2SiO4): A Preliminary Study to Understand the Nature of Geochemical Processes at the Olivine Interface

We present an accurate ab initio study of the structure and surface energy at 0 K of the (010), (101), (111), (001), (110), (120), and (021) faces of forsterite (Mg2SiO4) using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian and a localized all-electron Gaussian-type basis set. According to the surface energy values, the stability order of the forsterite faces was found to be (010) < (120) < (001) < (101) < (111) < (021) < (110). Then, the equilibrium shape of forsterite was drawn and compared with the previous ones obtained at an empirical level. Our results were combined with experimental evidence to develop some considerations about the shape and genesis of olivine included in diamond. They provide crucial information on the diamond formation mechanism with respect to its guest inclusions, a topic that is still under strong debate in the scientific community. In particular, we discuss the peculiar crystal morphology of olivine included in diamond, and we demonstrate that it cannot be consi...

A comparative DFT study on the differences between normal modes of polyethylene and polyethylene glycol via B3LYP Hamiltonian and the Hartree–Fock method in multiple bases

The vibrations of polyethylene and polyethylene glycol molecule using Gaussian 03W software via density functional theory and Hartree–Fock method have been studied numerically. Infrared spectra of polyethylene in room temperature is used, reported by Kholodkov et al. [Vacuum, 70, 505 (2003)] and comparing obtained numerical results with this spectra. The aim of this paper is to investigate various numerical methods in calculating frequency of vibrations of polyethylene. This manuscript represents a technical study where well established methodologies are used to calculate the vibrational properties of a molecular system. Crystal vibrations of polyethylene are calculated via density functional theory by Srinivasan et al. [Canadian J. Chem., 47, 3877 (1969)] and Hartree–Fock method by Kholodkov et al. [Vacuum, 70, 505 (2003)]. The effects of applying ether's groups on the vibrations of the obtained results for polyethylene glycol are studied in different bases. The calculations are done on basis sets of 6-31G(2d), 6-311G(d,p), 6-311G(2d), 6-311G(2d,2p). Various functionals were evaluated considering the agreement of the calculated modes with the corresponding experimental data. From these evaluations we obtained that the B3LYP functional gives the closest agreement between calculated and experimental values.

The (100), (111) and (110) surfaces of diamond: an ab initio B3LYP study

We present an accurate ab initio study of the structure and surface energy of the low-index (100), (111) and (110) diamond faces, by using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian and a localised all-electron Gaussian-type basis set. A two-dimensional periodic slab model has been adopted, for which convergence on both structural and energetic parameters has been thoroughly investigated. For all the three surfaces, possible relaxations and reconstructions have been considered; a detailed geometrical characterisation is provided for the most stable structure of each orientation. Surface energy is discussed for all the investigated faces.

The calculation of active Raman modes of α-quartz crystal via density functional theory based on B3LYP Hamiltonian in 6–311+G(2d) basis set†

We obtained an approximation of the force field of α-quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals18, 231 (1991)] in 6−311+G(2d) basis set for H16Si7O6 cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.

Ab initio Quantum Mechanical Study of Crystalline Nitric Acid Hydrates: Structures and Vibrational Spectra

The vibrational spectra of crystalline nitric acid hydrates have been investigated at the periodic ab initio quantum level by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian with CRYSTAL06 code. Using as input the X-ray structures of crystalline nitric acid monohydrate NAM, dihydrate α-NAD and trihydrate β-NAT, the inner coordinates within each unit cell have been optimized. The calculated structures of these atmospherically relevant systems are used in the evaluation of their vibrational normal modes. The obtained theoretical results show in general a good agreement compared to the observed spectra in the range 4000- 600 cm-1 and 200-20 cm-1 for infrared and Low-Frequency Raman spectra, respectively.

First-principles computational studies of the torsional potential energy surface of the sec-butyl radical

First-principles calculations were carried out to investigate the torsional potential energy surface (PES) of the sec-butyl radical. All the wave function methods employed predict a cis-like stable conformation with a dihedral angle of about 47° in addition to the trans-like global minimum conformation and a gauche conformation. However, most of the popular density functional approaches predict only the latter two local minima and lack the cis conformation that was experimentally observed. On the other hand, some density functional methods that incorporate the exact exchange and asymptotically corrected correlation functionals can locate the cis conformation successfully. The basis-set effect was also measured using popular B3LYP and MP2 Hamiltonians: only moderate shape changes were found for PES profiles upon basis-set variations. The stationary structures and their Hessians were obtained at both MP2 and B3LYP levels, with or without incorporating the zero-point energies. Opposite to the relative stability within the Born–Oppenheimer approximation, the cis conformation is more stable than the gauche conformation upon the zero-point correction, consistent with the experiment observations.

First-principles modelling of lithium iron oxides as battery cathode materials

Starting from published charge/discharge curves and X-ray data on Pmmn-LiFeO 2 and LiFe 5O 8 as cathode materials vs. Li anode, a scheme of electrochemical reactions is proposed to explain the unclear electrode functionality of the ‘corrugated layer’ LiFeO 2 phase. The scheme was validated by quantum-mechanical calculations (CRYSTAL09 code, hybrid B3LYP Hamiltonian) on a number of structural models for Li 1− x FeO 2, LiFe 5O 8, and Li 3Fe 5O 8. Magnetic interactions were taken into account, finding antiferromagnetic (Li 1− x FeO 2) and ferrimagnetic (LiFe 5O 8 and Li 3Fe 5O 8) orderings as stable states. At variance with spinel-like LiFe 5O 8, Li 3Fe 5O 8 displays a rocksalt-type superstructure. The computed energies for reactions (I) 4LiFeO 2 → 4Li 0.75FeO 2 + Li, (II) 4Li 0.75FeO 2 + Li → 4/5LiFe 5O 8 + 8/5Li 2O, and (III) 1/2LiFe 5O 8 + Li ↔ 1/2Li 3Fe 5O 8 are 4.44, −3.62, and −2.10 eV, respectively. Such values compare satisfactorily with the average charge/discharge voltages observed for positive electrodes made up of Pmmn-LiFeO 2 and of LiFe 5O 8.

Ab initio quantum-mechanical calculation of CaCO3 aragonite at high pressure: thermodynamic properties and comparison with experimental data

Structure and vibrational frequencies (at the Γ point) of CaCO 3 aragonite have been calculated from first principles, by using the hybrid Hartree-Fock/DFT B3LYP Hamiltonian, at different unit-cell volumes in the 185–242 A 3 range. By using the frequencies evaluated at such different volumes, the mode- γ Gruneisen’s parameters were estimated for each vibrational mode, and the zero point and thermal pressure contributions to the total pressure, at each volume and temperature, have then been determined by means of standard thermodynamic formulas, within the limits of the quasi-harmonic approximation. This allowed for the determination of ( i ) the equation of state at different temperatures; ( ii ) the thermal expansion as a function of pressure and temperature, and ( iii ) the evaluation of some thermodynamic properties (entropy and specific heat) together with their temperature dependences. Results were directly compared with relevant experimental data. The agreement of the calculated frequencies with the experimental data, at variable pressure, shows that the ab initio simulation can reproduce, at a relatively low computational cost, the full vibrational spectra of crystalline compounds of mineralogical interest. Moreover, the elastic properties (bulk modulus in particular), thermal expansion and thermodynamic properties, which play an important role in the characterization and in the understanding of the stability relations between carbonate phases, at high-pressure and high-temperature conditions, can be satisfactorily estimated. Precisely, at room temperature and pressure conditions, the calculated bulk modulus was 64.7 GPa, to be compared with an experimental value of 65(1) GPa (mean of three different experimental determinations); the estimated thermal expansion was about 6.1 · 10 −5 K −1 , which is only slightly underestimated with respect to the experimental datum [6.3(2) · 10 −5 K −1 ]; the calculated entropy ( S ) and the constant-pressure specific heat ( C P ) were 87.5 and 83.1 J mol −1 K −1 respectively, which are in close agreement with the experimental data [84(6) and 82.6 J mol −1 K −1 , for S and C P respectively].

High-pressure thermo-elastic properties of beryl (Al4Be6Si12O36) from ab initio calculations, and observations about the source of thermal expansion

Ab initio calculations of thermo-elastic properties of beryl (Al4Be6Si12O36) have been carried out at the hybrid HF/DFT level by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume to get static pressure and mode-γ Gruneisen’s parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V, T) curves were fitted by appropriate EoS’, to get bulk modulus (K 0) and its derivative (K′), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K 0 and K′ values of 180.2 Gpa and 4.0, respectively) and the low values observed for the thermal expansion coefficient. A zone-centre soft mode $$ P6/mcc \to P\bar{1} $$ phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low-frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model; Dove et al. in Miner Mag 59:629–639, 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.

Ab initio quantum‐mechanical prediction of the IR and Raman spectra of Ca3Cr2Si3O12 Uvarovite garnet

AbstractThe IR and Raman spectra of uvarovite (Ca3Cr2Si3O12) garnet were simulated with the periodic ab initio CRYSTAL code by adopting an all‐electron Gaussian‐type basis set and the B3LYP Hamiltonian. The two sets of 17 F1u Transverse‐Optical (TO) and Longitudinal‐Optical (LO) frequencies are generated, together with their intensities. As regards the IR experimental spectrum, only five peaks are available, that are in excellent agreement with the calculated data (mean absolute difference $\vert\overline\Delta\vert$ smaller than 5.2 cm−1). The analysis of the TO‐LO eigenvalue overlaps permits to establish a correspondence between LO and TO modes. The set of experimental Raman peaks is much reacher (23 out of 25) and the agreement with our calculations excellent ($\vert\overline\Delta\vert$ smaller than 6 cm−1). Isotopic substitution is used to identify the zones of the spectrum where Cr and Ca contributions are relevant. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Quantum-mechanical ab initio simulation of the Raman and IR spectra of Mn3Al2Si3O12 spessartine

The IR and Raman spectra of spessartine garnet Mn3Al2Si3O12, are simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The frequencies of the 25 Raman active modes (3 of A1g, 8 of Eg and 14 of F2g symmetry) and of the two sets of 17 F1u transverse-optical and longitudinal-optical frequencies are generated, as well as the IR oscillator strength. The agreement between calculated and experimental data is excellent: for the IR and Raman sets, the mean absolute difference \( \overline{|\Updelta|}\) is 4.0 and 6.8 cm−1, respectively. Isotopic substitution permits to highlight the Mn, Al and Si participation to the various zones of the spectrum. Graphical animation, available on the authors’ web-site (http://www.crystal.unito.it/vibs/garnets/spessartine/), provides a very readable description of the movement of atoms and groups in each vibrational mode.

Ab initio quantum‐mechanical simulation of the Raman spectrum of grossular

AbstractThe Raman spectrum of the grossular garnet Ca3Al2Si3O12 has been simulated with the periodic ab initio CRYSTAL code by adopting an all‐electron Gaussian‐type basis set and the B3LYP Hamiltonian. The wavenumbers of the 25 Raman active modes (3 of A1g, 8 of Eg and 14 of F2g symmetry) are in excellent agreement with two sets of accurate experimental data. Isotopic substitution is used to measure the participation of Ca and Si (Al is constrained in a centro‐symmetric position) to the various modes. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Structure and stability of aluminium trihydroxides bayerite and gibbsite: A quantum mechanical ab initio study with the C rystal06 code

The structure and energetics of bayerite and gibbsite have been investigated at the periodic ab-initio quantum-mechanical level by using a Gaussian type basis set and the B3LYP Hamiltonian. Both systems have layered structure, with intra-layer and inter-layer hydrogen bonds (HBs). In gibbsite the latter are stronger than in bayerite: 23.15 and 17.59 kJ/mol, respectively. The formation Gibbs free energy has been calculated, including entropic and enthalpic contributions: at 298 K gibbsite is more stable than bayerite by 7.74 kJ/mol.

Ab initio quantum mechanical study of γ-AlOOH boehmite: structure and vibrational spectrum

The structure and vibrational spectrum of boehmite have been investigated at the quantum-mechanical level with the CRYSTAL code, using a Gaussian-type basis set and the B3LYP Hamiltonian. Three space groups are considered in this study: Cmcm, Cmc21, P21/c. Cmcm turns out to correspond to a transition state, whereas Cmc21 and P21/c are minimum energy structures. The difference among them is the position of H atoms only, the Al-O frame being essentially the same. Harmonic frequencies at the Γ point have been computed. The comparison between calculated and experimental frequencies shows a good agreement for the Al-O part of the spectrum (under 790 cm−1). For the Al-OH bending modes (800–1,300 cm−1) an absolute differences of 50–100 cm−1 is observed; for the OH stretching modes (3,200–3,500 cm−1) it increases to 120–200 cm−1: anharmonicity is large because OH groups are involved in strong hydrogen bonds.

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

IR spectra of pyrope Mg(3)Al(2)Si(3)O(12), grossular Ca(3)Al(2)Si(3)O(12) and andradite Ca(3)Fe(2)Si(3)O(12) 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 F(1u) 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 epsilon(infinity) 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 epsilon(0) 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.

Ab-initio quantum mechanical study of akdalaite (5Al2O3· H2O): structure and vibrational spectrum

The structure and the vibrational spectrum of akdalaite (5Al2O3·H2O, also known as tohdite) have been investigated at the periodic ab-initio quantum-mechanical level by using a high quality Gaussian type basis set and the hybrid B3LYP Hamiltonian with the CRYSTAL06 code. Three space groups proposed in the literature, namely P63mc and its two P31c and Cmc21 subgroups, have been considered, obtaining essentially the same energy (the largest total energy difference is 0.2 kJ/mol per cell) and geometry.The harmonic frequencies at the τ point have been computed. Isotopic substitution and graphical representation permit a complete classification of normal modes in terms of simple models (octahedra and tetrahedra modes, hydrogen stretching and bending). The Al-O octahedra and tetrahedra modes appear below 880 cm−1, Al-OH bending modes are located in the range 870-900 cm−1, and OH stretching modes are at 3330-3400 cm-1.

Ab initio vibrational spectra and dielectric properties of carbonates: magnesite, calcite and dolomite

The equilibrium geometry, the Raman and IR vibrational spectra at the Γ point, TO–LO splitting, IR intensities, Born and dielectric tensors of magnesite MgCO3, dolomite MgCa(CO3)2 and calcite CaCO3 have been calculated with the periodic ab initio program CRYSTAL, by using an all-electron gaussian type basis set and the B3LYP hamiltonian. LO (longitudinal-optical) modes are computed by correcting the dynamical matrix through Born charges and high frequency dielectric tensors obtained from well localized Wannier functions and a saw-tooth computational scheme. The mean absolute difference between calculated and experimental frequencies (IR TO and LO and RAMAN) is as small as 6.9 cm−1 for magnesite, 7.7 cm−1 for dolomite and 8.5 cm−1 for calcite. Calculated IR intensities are in semiquantitative agreement with experiment. The modes of the three compounds are compared through graphical animation available on the CRYSTAL web-site.

The vibrational frequencies of forsterite Mg2SiO4: an all-electron ab initio study with the CRYSTAL code

The vibrational spectrum of Mg2SiO4 olivine was calculated at the Γ point by using the periodic ab initio CRYSTAL program. An all electron localized Gaussian-type basis set and the B3LYP Hamiltonian were employed. The full set of frequencies (35 IR active, 36 Raman active, 10 “silent” modes) was computed and compared to experimental data from different sources (four for IR and four for Raman). A generally good agreement is observed with experiment (the mean absolute difference ranging from 7 to 10 cm−1 for the various sets), when some of the experimental frequencies, whose attribution is uncertain or appears to be affected by large errors, are not taken into account. A small number of observed peaks are not consistent with calculated frequencies, and a few theoretical peaks do not correspond to measured values. The implications are discussed in detail. The full set of modes are characterized using different tools, namely isotopic substitution, direct inspection of the eigenvectors and graphical representation, so as to obtain a consistent mode assignment.