Ab Initio Quantum Mechanical Level Research Articles

The V + I defects in diamond: An ab initio investigation of the electronic structure, of the Raman and IR spectra, and of their possible recombination.

The double defect in diamond, vacancy (V) plus 〈100〉 self-split-interstitial (V+I), is investigated at the ab initio quantum mechanical level, by considering the vicinal case VI1 (V is one of the first neighbors of one of the two C atoms constituting the I defect) and the two possible "second neighbors" cases, VI2D, VI2S, in which a carbon atom is a first neighbor of both V and I. The case in which the two defects are at a larger distance is simulated by considering the two isolated defects separately (VI∞). A 6-21G local Gaussian-type basis set and the B3LYP hybrid functional are used for most of the calculations; richer basis sets and other functionals (a global hybrid as PBE0, a range-separated hybrid as HSE06, LDA, PBE, and Hartree-Fock) have also been used for comparison. With this computational approach we evaluate the energy difference between the various spin states, the location of the corresponding bands in the energy gap of pristine diamond, as well as the defect formation energy of the four defects. The path for the recombination of V and I is explored for the vicinal case, by using the distinguished reaction coordinate strategy. A barrier as high as 0.75 eV is found with B3LYP between VI1 and the perfect diamond recombined structure; when other hybrids are used, as PBE0 or HSE06, the barrier increases up to 1.01 eV (pure density functional theory produces lower barriers: 0.62 and 0.67 for PBE and LDA, respectively). Such a barrier is lower than the one estimated in a very indirect way through experimental data, ranging from 1.3 to 1.7 eV. It confirms however the evidence of the extremely low recombination rate also at high temperature. The Raman (and IR) spectra of the various defects are generated, which permit one to unambiguously attribute to these defects (thanks also to the graphical animation of the modes) many of the peaks observed in damaged diamond above the dominant peak of perfect bulk. For the residual non-attributed peaks, more complicated aggregations of defects should be explored.

A Hybrid statistical mechanics—quantum chemical model for proton transfer in 5‐azauracil and 6‐azauracil in water solution

A hybrid statistical physics—quantum‐chemical methodology was implemented to study the water‐assisted intramolecular proton‐transfer processes in 5‐ and 6‐azauracils in aqueous solutions. The solvent effects were included in the model by explicit inclusion of two pairs of water molecules, which model the relevant part of the first hydration shell around the solute. The position of these water molecules was initially estimated by carrying out a classical Metropolis of dilute water solutions of the title compounds and subsequently analyzing solute–solvent intermolecular interactions in the Monte Carlo‐generated configurations. Sequentially to the statistical physics simulation, ab initio quantum mechanical (QM) level of theory was implemented. The effects of the water as solvent (at ab initio QM level) were introduced at two different levels—using solute–solvent clusters (four‐water molecules) and using the same clusters embedded in an external continuum. Full geometry optimizations of these complexes were carried out at MP2/6–31 + G(d, p) and conductor‐polarizable continuum model (C‐PCM)/MP2/6–31 + G(d, p). Single point calculations were performed at CCSD(T)/6–31 + G(d, p)//MP2/6–31 + G(d, p) computational level to obtain more accurate energies. According to our calculations hydrated azauracils should exist in three forms: mainly dioxo form and two hydroxy forms. The calculated proton transfer activation energies for tautomeric reactions of 5‐azauracil and 6‐azauracil show different pictures for these two compounds. According to C‐PCM/MP2/6–31 +G(d, p) data, water‐assisted proton transfer in 5‐azauracil realizes through two parallel reactions: 1,3,5‐triazine‐2,4(1H,3H)‐dione → 6‐hydroxy‐1,3,5‐triazin‐2(1H)‐one and 1,3,5‐triazine‐2,4(1H,3H)‐dione → 4‐hydroxy‐1,3,5‐triazin‐2(1H)‐one. Tautomeric equilibrium in 6‐azauracil in water could occur by two contiguous reactions: 1,2,4‐triazine‐3,5(2H,4H)‐dione → 5‐hydroxy‐1,2,4‐triazin‐3(2H)‐one and 5‐hydroxy‐1,2,4‐triazin‐3(2H)‐one → 3‐hydroxy‐1,2,4‐triazin‐5(2H)‐one. The proton transfer investigated reactions in 5‐ and 6‐azauracils involve concerted atomic movement. © 2015 Wiley Periodicals, Inc.

Large-Scale Density Functional Theory Transition State Searching in Enzymes.

Linear-scaling quantum mechanical density functional theory calculations have been applied to study the rearrangement of chorismate to prephenate in large-scale models of the Bacillus subtilis chorismate mutase enzyme. By treating up to 2000 atoms at a consistent quantum mechanical level of theory, we obtain an unbiased, almost parameter-free description of the transition state geometry and energetics. The activation energy barrier is calculated to be lowered by 10.5 kcal mol(-1) in the enzyme, compared with the equivalent reaction in water, which is in good agreement with experiment. Natural bond orbital analysis identifies a number of active site residues that are important for transition state stabilization in chorismate mutase. This benchmark study demonstrates that linear-scaling density functional theory techniques are capable of simulating entire enzymes at the ab initio quantum mechanical level of accuracy.

Infrared spectra of inorganic aerosols: ab initio study of (NH4)2SO4, NH4NO3, and NaNO3

The structures and vibrational spectra of inorganic aerosols, including ammonium sulfate (NH4)2SO4, ammonium nitrate NH4NO3, and sodium nitrate NaNO3 are investigated at the periodic ab initio quantum mechanical level with the CRYSTAL code, which is based on Gaussian basis sets. Local density (LDA), gradient-corrected (PW91), and hybrid (B3LYP) density functionals have been used and the results are compared with experiment. All three functionals reproduce the equilibrium geometry of these aerosols to a high level of accuracy. The calculations of the frequencies gave a mean absolute deviation from experiment of 3% for B3LYP, clearly showing that this functional performs extremely well in this case. The mean absolute deviation is about 7% and 6% for PW91 and LDA, respectively.

Anomalous birefringence in andradite–grossular solid solutions: a quantum-mechanical approach

The static linear optical properties (refractive indices, birefringence and axial angle) of andradite–grossular (Ca3Fe2Si3O12–Ca3Al2Si3O12) solid solutions have been computed at the ab initio quantum-mechanical level through the Coupled Perturbed Kohn–Sham scheme, using an all-electron Gaussian-type basis set. Geometry relaxation after substitution of 1–8 Al for Fe atoms in the primitive cell of andradite yields 23 non-equivalent configurations ranging from cubic to triclinic symmetry. Refractive indices vary quite regularly between the andradite (1.860) and grossular (1.671) end-members; the birefringence δ and the axial angle 2V at intermediate compositions can be as large as 0.02° and 89°, respectively. Comparison with experiments suffers from inhomogeneities and impurities of natural samples; however, semi-quantitative agreement is observed.

Electronic structure, dielectric properties and infrared vibrational spectrum of fayalite: An ab initio simulation with an all‐electron Gaussian basis set and the B3LYP functional

AbstractThe electronic structure, the static and high frequency dielectric tensors, and the infrared (IR) spectrum of fayalite Fe2SiO4, the Fe‐rich end‐member of olivine solid solutions, are explored at an ab initio quantum mechanical level, by using an all‐electron Gaussian type basis set, the B3LYP hybrid DFT functional, and the CRYSTAL09 code. Mulliken population analysis and spin density maps illustrate the electronic structure, characterized by a nearly pure d6, high‐spin configuration of the transition metal atom. The full set of IR wavenumbers and intensities is computed. The availability of highly accurate synchrotron radiation data (Suto et al., Astron Astrophys 2002, 389, 568) permits a very accurate comparison between simulated and measured quantities, in primis wavenumbers (ν) and oscillator strengths (f). The mean absolute difference ${\overline{\vert\Delta\nu\vert}}$ is as small as 4 cm−1, and the maximum absolute difference |Δνmax| never exceeds 12 cm−1, whereas the summed absolute difference ΔF between fexp and fcalc is around 10%. Modes not detected in the experiment turn out to be (i) characterized by low computed intensity, or (ii) very close to a large intense peak. Computed and experimental IR reflectance curves are in striking agreement also. The nature of the vibrational modes is investigated by means of isotopic substitutions, which clarify the participation of the various atomic species to each mode. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Andradite−Uvarovite Solid Solutions. An ab Initio All-Electron Quantum Mechanical Simulation with the CRYSTAL06 Code

Andradite−uvarovite (Ca3Fe2Si3O12−Ca3Cr2Si3O12) solid solutions have been investigated at an ab initio quantum-mechanical level by using an all-electron Gaussian-type basis set and the hybrid B3LYP functional in its unrestricted formulation. Only ferromagnetic phases have been considered. All possible nonequivalent geometrical configurations resulting from the substitution of Cr atoms for x = 1−8 Fe atoms in the 16a site in the garnet primitive cell have been fully optimized (cell parameters and fractional coordinates of 80 atoms). As the lattice parameters of the two end-members are very similar (11.99 and 12.05 A for uvarovite and andradite, respectively), geometry rearrangements at the various x are extremely small, the largest excess volume being 0.15 A3 and the largest excess energy 3.68 kJ/mol. Thermodynamic functions are calculated from the configurational contribution to entropy and disregarding the vibrational contribution, which is expected to be negligible. Almost ideal miscibility is predicted.

Structure and Stability of the Al(OH)3 Polymorphs Doyleite and Nordstrandite: A Quantum Mechanical ab Initio Study with the CRYSTAL06 Code

The crystal structures and relative energies of doyleite and nordstrandite, two of the four aluminum trihydroxide polymorphs, were investigated at the periodic ab initio quantum-mechanical level wi...

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 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.

Vibrational Spectrum of Katoite Ca3Al2[(OH)4]3: A Periodic ab Initio Study

The vibrational spectrum of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been calculated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian. The harmonic frequencies at the Gamma point have been obtained by diagonalizing the mass-weighted Hessian matrix, that is evaluated by numerical differentiation of the analytical first derivatives of the energy with respect to the atomic Cartesian coordinates. The parameters controlling the numerical differentiation, as well as the numerical integration of the exchange-correlation functional for the self-consistent field (SCF) calculation, are shown to affect the obtained frequencies by less than 3 cm-1. Before diagonalization, the dynamical matrix is transformed to a block diagonal form according to the irreducible representations of the point group, so that the 345 vibrational modes are automatically classified by symmetry. Various tools are adopted (graphical representation, isotopic substitution, "freezing" part of the unit cell) that permit a complete classification of normal modes and, in particular, an analysis of the modes in terms of simple models (octahedra modes, Ca modes, H stretching, bending, rotations). The harmonic OH stretching band (48 modes) is quite narrow (20 cm-1), indicating that the interaction among OH groups is very weak. As the OH stretching modes are known to be totally separable from the other modes and strongly anharmonic, the one-dimensional Schroedinger equation for the anharmonic oscillator is solved numerically for the two extreme situations, corresponding to the vibration of one decoupled OH and of all 48 OH groups moving in phase. The anharmonic frequencies are 3682 and 3673 cm-1, respectively, in good agreement with IR experiments (a single band at 3661 cm-1 with a width at half band height of 33 cm-1) and confirming that the interaction between OH groups is extremely weak.

Boric acid, “carbonic” acid, and N-containing oxyacids in aqueous solution: Ab initio studies of structure, p Ka, NMR shifts, and isotopic fractionations

B(OH) 3 and CO 2 are acidic species of considerable geochemical importance, yet the microscopic nature of the acid dissociation reactions for these B and C species is not well understood. Quantum mechanical methods have recently been applied to the direct ab initio calculation of p K a values for many organic and inorganic weak acids, but the B and C acids have not yet been considered in detail. In the present study, p K a values are calculated quantum mechanically for the oxyacids B(OH) 3, H 2CO 3 and HNO 3, which have experimental first p K a values of 9.2, 6.4 and −1.3, respectively. We calculate the gas-phase reaction free energies at the highly accurate CBS-QB3 ab initio quantum mechanical level and reaction free energies of hydration using a polarizable continuum method. Using a thermodynamic cycle corresponding to the simple dissociation process HA A − + H +, in aqueous solution, we calculate p K a values of 21.6, 3.8 to 2.2 and −0.8 for the three oxyacids mentioned above, closely matching experiment only for HNO 3. The discrepancies with experiment arise from the more complex nature of the acid dissociation process for B(OH) 3, which involves the addition of H 2O to B(OH) 3 and formation of the B(OH) 4 − anion, and from the instability of hypothetical H 2CO 3 compared to the proper hydrated reactant complex CO 2. . . H 2O. When the proper microscopic description of the reactants and products is used the calculated p K a values for the three acids become 11.1, 7.2 and −0.8, in considerably better agreement with experiment for B(OH) 3 and CO 2. . . H 2O. Thus p K a calculations using this approach are accurate enough to give information on the actual acid species present in solution and the details of their acid dissociation processes at the microscopic level. 11B and 13C-NMR chemical shifts are also calculated for the various species and compared to experiment. By comparison of our calculations with experiment it is apparent that the 13C-NMR chemical shift has never been measured for an actual H 2CO 3 molecule in solution, consistent with its thermodynamic and kinetic instability with respect to CO 2 + H 2O. By contrast, the good agreement of calculated and experimental NMR shifts for the species B(OH) 3 and B(OH) 4 − support their existence in solution. Calculations of the IR spectra of H 2CO 3 and its H-bonded dimer support the idea that spectra previously assigned to condensed phase or surface H 2CO 3 are better interpreted as arising from some type of H-bonded H 2CO 3 oligomer, rather than the monomer. Calculations of the relative free energy for different isotopomers of the B and C oxyacids establish that the partitioning of 13C and 12C between CO 2(aq) and HCO 3 − is considerably different from the fractionation between hypothetical H 2CO 3 and HCO 3 −. We find a much better match to the experimental CO 2(g) vs. HCO 3 −(aq) 13,12C fractionation if the bicarbonate cluster model includes a counter ion, such as Na +. The 11,10B fractionation between B(OH) 3 and the van der Waals complex B(OH) 3. . . H 2O is quite small, while that between gas-phase B(OH) 3 and B(OH) 4 − is on the order of 30‰, in qualitative agreement with more rigorous values recently obtained from supermolecule or “water-droplet” calculations.

The vibrational spectrum of calcite (CaCO3): an ab initio quantum-mechanical calculation

The vibrational spectrum of calcite (CaCO3) is evaluated at an ab initio periodic quantum-mechanical level by using the CRYSTAL package. A localized basis set of Gaussian-type functions and the B3LYP hybrid Hamiltonian are adopted. The dynamical matrix is obtained by differentiating numerically the analytical first derivatives of the energy. The accuracy with respect to all computational parameters is documented. The calculated frequencies are compared with available IR and RAMAN data (16 and 5 peaks, respectively), the mean absolute error being less than 12 cm−1 (frequencies range from 100 to 1600 cm−1). Overall, the agreement with experiment is very satisfactory, and shows that simulation can produce at a relatively low cost the full spectra of crystalline compounds of mineralogical interest.

The katoite hydrogarnet Si-free Ca3Al2([OH]4)3: a periodic Hartree-Fock and B3-LYP study.

The structure of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been investigated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and both the HF and the hybrid B3-LYP Hamiltonians. The structure has been fully optimized at various pressures in the 0-46 GPa range; the modifications of the structure, and in particular of the (OH)4 group, as a function of pressure are analyzed. At the B3-LYP level and P greater than 15 GPa, a O-H...O interaction of increasing strength appears, with important modifications in the local geometry of the tetrahedral site. The calculated omega01(O-H) fundamental vibrational frequency at zero pressure is in excellent agreement with experiment (3674 and 3663 cm(-1), respectively); the omega01(O-H) stretching frequency remains essentially constant in the 0-15 GPa interval, whereas it dramatically decreases at higher pressures with a corresponding anharmonicity increase, as a consequence of the formation of a strong hydrogen bond. The hydration energy of grossular and the formation energy of Si-free katoite have also been computed, and the B3-LYP results are in quite good agreement with experiment.

QM/MM Molecular Dynamics Simulation of the Structure of Hydrated Fe(II) and Fe(III) Ions

The hydration shell structure of Fe(II) and Fe(III) ions in their high spin state has been studied by combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, in which the ion and its first hydration sphere were treated at the Hartree−Fock ab initio quantum mechanical level, whereas ab initio generated pair plus three-body potentials were employed for the remaining system. The coordination number in the first hydration shell is 6 for both Fe(II) and Fe(III) ions. The second hydration shell contains 12.4 and 13.4 water molecules for Fe(II) and Fe(III) ions, respectively, in good agreement with the experimental values. The residence time of a water molecule in the second hydration shells of Fe(II) and Fe(III) is 24 and 48 ps, respectively. The complex configuration and ligand orientations observed in this study prove that many-body effects play an important role in the hydration of both Fe(II) and Fe(III) ions. The hydration energies computed from the simulation are...

AB Initio Approach to the Ferroelectric Properties of ABO 3 Perovskites: The Case of KNbO 3

The ferroelectric perovskite KNbO 3 is investigated at the ab initio quantum mechanical level, by using the CRYSTAL program and a gaussian type basis set. A set of well localized Wannier functions (LWF) is obtained by applying a unitary transformation to the delocalized crystalline orbitals describing the ground state. The spontaneous polarization, the Born effective charges and the piezo-electric constants obtained from the LWF with various hamiltonians are compared. The calculations are performed at the Hartree-Fock (HF), density functional (DFT) and hybrid (B3LYP) level of theory. As regards DFT, the local density (LDA) and generalized gradient (GGA) approximations are used.

Polarization properties of ZnO and BeO: Anab initiostudy through the Berry phase and Wannier functions approaches

The spontaneous polarization and the piezoelectric constants of ZnO and BeO are calculated at an ab initio quantum-mechanical level by using two alternative strategies, namely, through the Berry phase scheme applied to delocalized crystalline orbitals, and through the definition of well-localized Wannier functions. The two sets of results, obtained in the same computational conditions (both schemes are implemented in the CRYSTAL code) compare extremely well, and are in good agreement with available experimental data.

Structural and vibrational properties of solid Mg(OH) 2 and Ca(OH) 2 – performances of various hamiltonians

The layered minerals brucite Mg(OH) 2 and portlandite Ca(OH) 2 are investigated at the ab initio quantum mechanical level, by using the periodic C rystal 98 program and an all-electron Gaussian-type basis set. The equilibrium lattice parameters, lattice formation and hydration energies (with respect to the MO+ H 2 O → M( OH) 2 reaction, where M=Mg, Ca) and the Raman O–H vibrational frequencies have been evaluated. The calculations have been performed at the Hartree–Fock (HF), density functional theory (DFT) and hybrid (B3LYP) levels. As regards DFT, the local density (LDA) and generalized gradient (GGA) approximations have been used. Excellent agreement between calculated and experimental lattice and hydration energies and Raman frequencies has been found with the B3LYP approximation.

Investigation of Cu2+ Hydration and the Jahn−Teller Effect in Solution by QM/MM Monte Carlo Simulations

The Cu2+ hydration shell structure has been studied by a combined ab initio quantum mechanical/molecular mechanical (QM/MM) Monte Carlo simulation, in which the ion and its first hydration sphere are treated at the Born−Oppenheimer ab initio quantum mechanical level, while classical pair and three-body potentials are employed for the remaining system. Whereas traditional simulations based on MM potentials are not able to predict higher-body effects such as the Jahn−Teller (JT) distorted octahedral structure of the first hydration shell of Cu2+, the combined QM/MM approach reproduces correctly this experimentally confirmed property and delivers more accurate hydration energy values as well.

Energy and energy derivatives for molecular solutes: Perspectives of application to hybrid quantum and molecular methods

We examine the state of the art of the solvation procedure called the polarizable continuum model (PCM), focusing our attention on the basic properties: energy of the solute, solvation energy, and their derivatives with respect to nuclear coordinates. The PCM method is based on the use of an effective solute Hamiltonian, where the solute-solvent potential is described in terms of continuous response functions with boundary conditions given in terms of the solute cavity surface. This exposition is mainly based on recent progress, a large part of which is still in press. The new procedures are quite effective, at the ab initio quantum mechanical level, but cannot be applied to very large solutes for the limitations of computer hardware. We introduce then other methods, presented here for the first time, which make possible the classical calculation of the solvation energy also for very large solutes (a few thousand atoms). The strategy outlined here regards a new method to define cavity surfaces (supplemented with analytical definitions of its partition in tesserae) and of their derivatives, combined with a fast noniterative method to compute solvation energy. Finally, we discuss the introduction of this procedure in hybrid quantum mechanical/molecular mechanics descriptions of large solutes (enzymes), where the quantum description is limited to the reacting portion of the enzyme. © 1996 John Wiley & Sons, Inc.