Quantum mechanical calculation of the OH vibrational frequency in crystalline solids

Abstract

The OH vibrational frequency of four crystalline compounds ranging from ionic (brucite, Mg(OH) 2 , and portlandite, Ca(OH) 2 ) to semi-covalent (edingtonite, as representative of free surface OH groups in silica, and acid chabazite, as representative of acid zeolites) has been investigated at quantum mechanical level with the CRYSTAL program using the B3LYP hybrid functional. The OH vibration is calculated in two ways: (i) in the harmonic approximation, by diagonalizing the fully coupled dynamical matrix to yield the harmonic frequency ! h . (ii) at the anharmonic level, by decoupling the OH stretching mode from the bulk phonons and by numerically solving the one-dimensional Schro¨dinger equation associated with the OH potential energy to yield the fundamental ! 01 and the first overtone ! 02 frequencies. The harmonic and anharmonic frequencies differ by more than 150 cm À1 . In the cases where direct comparison is possible (brucite, portlandite and edingtonite), the experimental and calculated frequencies differ by less than 10 cm À1 ; the calculated anharmonicity constant, ! e x e ¼ (2! 01 À ! 02 )/2, is systematically smaller than the experimental value by about 10 cm À1 . The effect of the computational parameters on the computed frequencies is explored, with particular attention to the grid used for the construction of the DFT exchange and correlation contribution to the Hamiltonian and the accuracy in the geometry optimisation.

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

“…It contains a hybrid HF/DF exchange correlation term and is widely and successfully used in molecular quantum chemistry 13 as well as in solid state calculations, where it has been shown to reproduce equilibrium geometries and vibrational frequencies 4,5,[14][15][16] in excellent agreement with experimental data. 14,17 Computational conditions (tolerances for the truncation of the infinite Coulomb and exchange sums, SCF convergence criteria, grid size for integration of the DFT exchange and correlation contribution, and number of points in the reciprocal space) were set at the same values as in our previous studies of pyrope 4 and andradite, 5 where the effect of the basis set size on the calculated geometries and frequencies was documented. Here, basis set B (BSB) of ref.…”

Ab initio QM calculation of the electric field convergence versus atomic basis sets in periodic models of proton‐substituted zeolites

“…Hence, we performed partial optimization of the covalent OOH bond lengths, keeping the atomic positions of the other framework atoms fixed. This approximation corresponding to an "isolated" OOH vibration has been justified relative to precise computations with weighted Hessian matrix [25] when the vibration does not interact with other motions of close frequencies. The nearest OH groups in the periodic HCHA or HBRE models are spatially separated by nearly 6.689 and 8.098 Å, respectively, which allows the partition of the vibrations of the neighboring OH groups.…”

Performance of 12 DFT functionals in the study of crystal systems: Al2SiO5 orthosilicates and Al hydroxides as a case study

“…Details about the grid generation and its influence on the accuracy and cost of calculations can be found in Refs. [16,17,65]. Structure optimizations were performed by use of analytical energy gradients with respect to atomic coordinates and unit-cell parameters [66][67][68], within a quasi-Newton scheme combined with the BFGS scheme for Hessian updating [69][70][71][72].…”