Environmental Effects on Vibrational Proton Dynamics in H₅O₂⁺: DFT Study on Crystalline H₅O₂⁺ClO₄^‐

Abstract

For Abstract see ChemInform Abstract in Full Text.

Revisiting the Aqueous Solutions of Dimethyl Sulfoxide by Spectroscopy in the Mid- and Near-Infrared: Experiments and Car–Parrinello Simulations

“…There are at least two different approaches for calculating the vibrational spectrum: (1) The normal modes can be obtained by diagonalization of the Hessian matrix evaluated by computing the second derivative of the potential surface. (2) A more systematic approach is calculating the vibrational density of the states from a molecular dynamics (MD) simulation by Fourier transformation of the dipole moment autocorrelation function. − With the neglect of dipole moment variations with positions, e.g., bond lengths, the IR absorption can be further simplified as Fourier transformation of the velocity autocorrelation function (VAF): where ⟨ ⟩ is the equilibrium ensemble average. We have two remarks: First, since dipole fluctuations of the system relevant to IR absorption are approximated as position (and thus velocity) fluctuations of individual atoms in eq , its predictions for peak intensities are not as accurate as those for peak positions.…”

“…(2) A more systematic approach is calculating the vibrational density of the states from a molecular dynamics (MD) simulation by Fourier transformation of the dipole moment autocorrelation function. 27−29 With the neglect of dipole moment variations with positions, e.g., bond lengths, the IR absorption can be further simplified as Fourier transformation of the velocity autocorrelation function 30 (VAF):…”

Combined X-ray Crystallographic, IR/Raman Spectroscopic, and Periodic DFT Investigations of New Multicomponent Crystalline Forms of Anthelmintic Drugs: A Case Study of Carbendazim Maleate

“…Periodic DFT computations of molecular crystals sometimes lead to the appearance of imaginary frequencies [6,72,73]. We encountered this problem when calculating the IR/Raman spectra of [CRB + MLE] (1:1) using the PBE-D3/PW (FullOpt) approximation (see Table S5, Supplementary Materials).…”

“…Unlike calculations of non-periodic systems, there is no universal recipe for solving the problem of imaginary frequencies appearing in periodic calculations. This problem is usually solved by reducing the space symmetry of a crystal [72,74]. Other methods include (i) the use of extended basis sets [73], (ii) variation of the cell parameters [74], and (iii) increasing the atomic displacement value in numerical second derivative calculations [41].…”

Development and Validation of Quantum Mechanically Derived Force-Fields: Thermodynamic, Structural, and Vibrational Properties of Aromatic Heterocycles

“…Finally, the vibrational frequencies were recovered, over the 1 ns NVE runs, from the classical dipole moment correlation function according to where μ̅( t ) is computed according to eq and the function Q (ν) is a QM correction. Among the many different equations proposed to account for such correction, − following the suggestions of ref , the function here employed reads with β = 1/ k B T , where T is the simulation temperature and k B the Boltzmann constant.…”