Frequencies Of Normal Vibrations Research Articles

Gas phase H+, H3O+ and NH4+ affinities of oxygen-bearing volatile organic compounds; DFT calculations for soft chemical ionisation mass spectrometry.

Quantum chemistry calculations were performed using the density functional theory, DFT, to understand the structures and energetics of organic ions relevant to gas phase ion chemistry in soft chemical ionisation mass spectrometry analytical methods. Geometries of a range of neutral volatile organic compound molecules and ions resulting from protonation, the addition of H3O+ and the addition of NH4+ were optimised using the B3LYP hybrid DFT method. Then, the total energies and the normal mode vibrational frequencies were determined, and the total enthalpies of the neutral molecules and ions were calculated for the standard temperature and pressure. The calculations were performed for several feasible structures of each of the ions. The proton affinities of several benchmark molecules agree with the accepted values within ±4 kJ mol-1, indicating that B3LYP/6-311++G(d,p) provides chemical accuracy for oxygen-containing volatile organic compounds. It was also found that the binding energies of H3O+ and NH4+ to molecules correlate with their proton affinities. The results contribute to the understanding of ligand switching ion-molecule reactions important for secondary electrospray ionisation, SESI, and selected ion flow tube, SIFT, mass spectrometries.

МОДЕЛИРОВАНИЕ РАЗОГРЕВА ЭНЕРГЕТИЧЕСКИХ МАТЕРИАЛОВ

An analysis of the known approximations for describing the dependence of the heat capacity at a constant volume of energetic materials (molecular crystals) on the crystal temperature has shown that there are reliable approximations of the dependence of the heat capacity at a constant volume that do not require complex quantum mechanical calculations to determine the frequencies of normal vibrations, both intermolecular and inside the molecule. To obtain the dependence of the thermal part of the internal energy of a molecular crystal, which is responsible for heating the material, it is required to integrate the heat capacity expression at constant volume over temperature. In this work, calculations have been made for the dependence of the thermal part of the internal energy of a molecular crystal in case when it is calculated through the frequencies of normal vibrations, and in case when it is calculated by integrating the heat capacity at a constant volume with respect to temperature using approximation formulas. When solving the spectral problem of determining the frequencies of normal vibrations within the molecule, the PM3 and DFT quantum chemical methods have been used. The paper presents the dependences of the thermal part of the internal energy of molecular crystals on temperature, calculated for different methods of determination, and a comparative analysis, which has shown that the difference has equaled less than 1 %.

Quantum chemical calculation of normal vibration frequencies of polyatomic molecules

Quantum calculation of molecular vibrational frequency is important in investigating infrared spectrum and Raman spectrum. In this work, a low computational cost method of calculating the quantum chemistry of vibrational frequencies for large molecules is proposed. Usually, the calculation of vibrational frequency of a molecule containing <i>N</i> atoms needs to deal with the Hessian matrix, which consists of second derivatives of the 3<i>N</i>-dimensional potential hypersurface, and then solve secular equations of the matrix to obtain normal vibration modes and the corresponding frequencies. Larger <i>N</i> implies higher computational cost. Therefore, for a limited computational hardware condition, higher-level computations for large <i>N</i> atomic molecule’s vibrational frequencies cannot be implemented in practice. Here we solve this problem by calculating the vibrational frequency for only one vibrational mode each time instead of calculating the Hessian matrix to obtain all vibrational frequencies. When only one vibrational mode is taken into consideration, the molecular potential hypersurface can be transformed into one-dimensional curve. Hence, we can calculate the curve with high-level computational method, then deduce the expression of one-dimensional curve by using harmonic oscillating approximation and obtain the vibrational frequency by using the expression to fit the curve. It should be noted that this method is applied to vibrational modes whose vibrational coordinates can be completely determined by equilibrium geometry and the molecular symmetry and be independent of the molecular force constants. It requires that there exists no other vibrational mode with the same symmetry but with different frequencies. The lower computational cost for a one-dimensional potential curve than that for 3<i>N</i>-dimensional potential hypersurface’s second derivatives permits us to use higher-level method and larger basis set for a given computational hardware condition to achieve more accurate results. In this paper we take the calculation of<i> B</i><sub>2</sub> vibrational frequency of water molecule for example to illustrate the feasibility of this method. Furthermore, we use this method to deal with the SF<sub>6</sub> molecule. It has 7 atoms and 70 electrons, hence there exists a large amount of electronic correlation energy to be calculated. The MRCI is an effective method to calculate the correlation energy. But by now no MRCI result of SF<sub>6</sub> vibrational frequencies has been reported. So here we use MRCI/6-311G* to calculate the potential curves of A<sub>1g</sub>, E<sub>g</sub>, T<sub>2g</sub> and T<sub>2u</sub> vibrational modes separately, deduce their expressions, then use the expressions to fit the curves, and finally obtain the vibrational frequencies. The results are then compared with those obtained by other theoretical methods including HF, MP2, CISD, CCSD(T) and B3LYP methods through using the same 6-311G* basis set. It is shown that the relative error to experimental result of the MRCI method is the least in the results from all these methods.

Effects of chemical composition on the structural stability, elastic, vibrational, and electronic properties of Cs2NaLnX6 (Ln = La…Lu, X = F, Cl, Br, I) elpasolites

AbstractElpasolite crystals are very important materials, both from the applied and fundamental points of view. Those elpasolites, which contain rare earth ions with a high atomic number Z, are very much suitable for the low‐cost high‐performance gamma‐ray detection, applications in medicine, food industry, nuclear energy production, processing, and detection of nuclear proliferation. The thermal and structural stabilities are important parameters required for detecting applications, because the performance conditions for such devices are usually very harsh. Since it is widely believed that elpasolites may have even better detection properties, the lack of systematic studies on the elpasolites and thus the unavailability of reliable data on their physical properties and trends in their variation caused by chemical composition considerably hinders search for more efficient new materials. Therefore, to fill in this gap and provide with all essential information about a large number of elpasolites crystals, for the first time, the structural stability, elastic, vibrational, and electronic properties of 60 cubic elpasolite Cs2NaLnX6 (Ln = La, …, Lu, X = F, Cl, Br, I) crystals were consistently calculated in the framework of the same computational approach based on the density functional theory (DFT). Variation of all calculated parameters (such as the lattice constants, elastic constants, Debye temperature, normal vibrational modes frequencies, Mulliken effective charges, bond populations, and band gaps) across the considered groups of crystals was analyzed and several trends, which are important for the search and preparation of new stable materials with improved performance, were identified.

INFLUENCE OF PRESSURE ON STRUCTURAL, ELECTRONIC, AND OPTICAL PROPERTIES OF CHOLINE IODIDE

The influence of pressure on structural, electronic, and optical properties of choline iodide is studied within the density functional theory approach using the РВЕ gradient functional, the D3(BJ) dispersion correction, and a basis set of localized orbitals. Elastic constants, parameters of the Birch–Murnaghan equation of state, density of electronic states, and frequencies of normal longwave vibrations are calculated. It is shown that the immediate environment of the iodine atom contains 12 carbon atoms with the shortest O–H⋯I distance equal to 2.486 A. The О–H distance increases slightly together with pressure, and the I–H distance decreases while its linear modulus is an order of magnitude smaller than the bulk modulus under 97 GPa. In contrast to intramolecular vibrations, the pressure shifts of lattice vibrations exceed 10 cm–1/GPa, and their modal Gruneisen parameters are an order of magnitude larger.

Теоретическое исследование силового поля дифтораминотринитрометана в координатах Xδ0

Actual problem of modern chemists-researchers is studying the properties of molecules of compounds. The latest achievements in the field of computer engineering and quantum chemistry make it possible to research various physicochemical parameters of studying compounds using theoretical calculations. Calculation methods can greatly simplify the task, as they are safer and more economical than experiment. It is noted that methane derivatives are also currently of interest for research in connection with their widespread use. This paper is devoted to the study of the force fields of molecule of (difluoro-amino)trinitromethane using quantum chemical calculations. The Becke-Lee-Yang-Parr method of density functional theory (DFT) B3LYP with a hybrid potential of 6-311++G(3df, 3pd) was chosen as the main approximation for the work performed, since when using it, the best quality of the result is noted. Also, in the present work, as an alternative to chemical (natural) coordinates, new coordinates Xδ0 were chosen, which allows one to take into account torsional vibrations. The calculations presented in this work were performed using the Gaussian and GaussView programs, designed to calculate a large number of properties and characteristics of chemical reactions. In this paper, using the proposed approach, the geometry of the molecule of (difluoroamino)tri-notromethane has been optimized, the geometric parameters of these compound were considered, in particular, the valence angles, dihedral angles, and long bonds were calculated, corresponding to the minimum energy of this molecule. For the first time, generalized force coefficients for F2NC(NO2)3 were calculated, and the "stiffness" of the chemical compounds of the molecule under study was evaluated. The frequencies of normal vibrations (wave numbers) for the studied compound in the harmonic approximation were calculated and analyzed. A comparison of the obtained wave numbers with experimental data is given. The results obtained indicate a satisfactory agreement between theory and experiment. A general view of the vibrational spectrum of (difluoroamino)trinotromethane obtained as a result of quantum chemical calculations is presented. The conclusion is drawn about the possibilities of applying the B3LYP 6-311++G(3df, 3pd) approach for calculating the frequencies of normal vibrations and force coefficients.

Теоретическое исследование силового поля тринитрохлорметана в координатах Xδ0

At present, nitro compounds are widely used in industry and medicine. This necessitates a more thorough study of their specific properties and the construction of theoretical models for their prediction. A special role in this process is given to IR and Raman spectroscopy. However, model calculations are needed to interpret vibrational spectra. This work is devoted to quantum-chemical studies of the force field of the ClC(NO2)3 molecule and the solution of the direct spectral problem for the selected object. The Becke-Lee-Yang-Parr B3LYP method with a hybrid potential of 6-311++G(3df, 3pd), as the most promising, was used as the main approach for the study. In addition, in this paper, as an alternative to chemical (natural) coordinates, new coordinates Xδ0 were chosen, it lets talk about the correctness of the calculations. The calculations presented in this article were implemented using Gaussian and GaussView computer programs designed to calculate a number of molecular properties and characteristics of chemical reactions. Using the chosen method, in this work, the geometry of the trinitrochloromethane molecule was optimized, the geometric parameters of the compound under study were examined, in particular, were calculated the values of valence angles, dihedral angles, and bond lengths characteristic of the equilibrium configuration of the compound under study. For the first time, generalized force coefficients were obtained for the ClC(NO2)3 molecule in the Xδ0 coordinates, which were proposed by L.S. Mayants and G.B. Shaltuper, as universal coordinates in which it is possible to correctly solve the spectral problem. An assessment of the "rigidity" of the chemical bonds of the test compound was carried out. The wave numbers (frequencies of normal vibrations) for the studied molecule in the harmonic approximation are calculated and analyzed. A comparison of the obtained wave numbers with experimental data is given. The results obtained demonstrate a satisfactory agreement between theory and experiment. A general view of the vibrational spectrum of trinitrochloromethane obtained by calculation is presented.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T).

Previous studies have shown that the weakly bonded H2S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H2S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H2S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H2S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H2S dimer.

Spectral Diagnostics of the Dynamics of the Formation of a Homoconjugated Complex [HCN.H.NCH

A quantum-mechanical analysis of the manifestations of the NHN hydrogen bond in the vibrational spectra of the [HCN.H.NCH]+ linear complex along the profile of the proton transition reaction path is given, and the laws governing the diagnostic parameters, that is, potential descriptors of the dynamics of this process, are determined. We calculated the surface of the potential energy and harmonic frequencies of normal vibrations along the profile of the reaction path of the proton transition in the system under study. When the fragments [HCNH]+ and NCH approach each other, a noticeable distortion of the forms of their skeletal vibrations occurs, up to complete mixing into the symmetric and antisymmetric forms. The frequency of the longitudinal vibration of the central proton ν(NH) varies along the reaction path from ~3600 to ~500 cm–1. An abrupt frequency change is observed in the region of intersection of the terms ν(NH) and ν(CN).

Quantum Chemical Determination of the Molecular Structure of 1,2,4-Triazole and the Calculation of its Infrared Spectrum

The molecular structure of 1,2,4-triazole is calculated by the density functional theory method in the B3LYP/6–31G approximation using the Gaussian program package. The calculated bond lengths and bond angles are well consistent with their experimental values. The results of the calculation show that triazole has a planar structure. Normal vibrational frequencies of triazole are calculated and these normal vibrations are assigned. Absorption band intensities are calculated and the IR spectrum of triazole is constructed. When compared, the theoretical spectrum qualitatively reproduces the experimental one.

Спектральная диагностика динамики образования гомосопряженного комплекса [HCN.H.NCH]-=SUP=-+-=/SUP=-

A quantum-mechanical analysis of the manifestations of the NHN hydrogen bond in the vibrational spectra of the [HCN.H.NCH] + linear complex along the proton transfer reaction profile is given, and the laws governing the diagnostic parameters — potential descriptors of the dynamics of this process — are established. The surface of the potential energy and harmonic frequencies of normal vibrations along the profile of the proton transfer reaction path in the system studied are calculated. It has been shown that when the [HCNH] + and NCH fragments come closer together, a noticeable distortion of the forms of their skeletal vibrations occurs, up to complete mixing into the symmetric and antisymmetric forms. The frequency of the longitudinal vibration of the central proton ν (NH) varies along the reaction path from ~ 3600 to ~ 500 cm-1. In the region of intersection of the terms ν (NH) and ν (CN) an abrupt nature of frequency change is detected.

Calculation and Comparative Analysis of Ir Spectra of Homobrassinolide and (22S,23S)-24-Epibrassinolide

Normal vibrational frequencies and absolute IR band intensities of the biologically active steroid phytohormones homobrassinolide and (22S,23S)-homobrassinolide were calculated in the framework of an original approach that combined classical analysis of normal modes using molecular mechanics with quantum-chemical estimation of the absolute intensities. IR absorption bands were interpreted based on a comparison of the experimental and theoretical absorption spectra. The impact of structural differences in the side chains of these molecules on the formation of their IR spectra in the region 1500–950 cm −1 was estimated.

GEOMETRICAL AND ELECTRONIC STRUCTURE OF PROPYL-, TETRAMETHYL-, DIMETHYLETHYL- AND BUTYLADAMANTANES AND THEIR THERMODYNAMIC CHARACTERISTIC ACCORDING TO DFT

Propyladamantanes were synthesized by alkylation of adamantane with isopropyl alcohol in the temperature range from 5 to 40 °C in the presence of 96% sulfuric acid. Tetramethyl- and dimethylethyladamantanes were synthesized by isomerization of perhydroanthracene in the presence of aluminium oxide catalyst on the setup of the flow type. Isomers of butyladamantanes were obtained by the reaction of alkylation of the adamantane with isooctane. For each molecule, the optimization of the geometric parameters of atoms was carried out using analytical calculation methods. By calculating the frequencies of normal vibrations using the second derivatives, it was confirmed that the stationary points determined by optimizing the geometry correspond to the minima of the potential energy surface. The structure of 1-n-propyladamantane (I), 1-isopropyl-adamantane (II), 2-n-propyladamantane (III), 1,2-di-n-propyladamantane (IV), 1,3-dimethyl-5-ethyladamantane (V), 1,3,5,6-tetramethyladamantane (VI), 1,3,5,7-tetramethyladamantane (VII), perhydroanthracene (VIII), 1-n-butyladamantane (IX), 1-isobutyladamantane (X), 1-sec-butyladamantane (XI) has been studied using the DFT method with the Becke–Lee–Yang–Parr hybrid energy functional of electron density with the 6-31G* basis set. The geometric and electronic characteristics of the compounds and their total energy, normal vibration frequencies have been calculated. It has been shown that the calculated Gibbs free energies of formation for the perhydroanthracene isomerization products are in qualitative agreement with the experimental product composition of the isomerate and alkylation of adamantane with isopropyl alcohol are in qualitative agreement with the experimental composition of the products. A good agreement of calculated and experimental data on the composition of equilibrium mixtures was obtained. The theoretical geometry of the synthesized alkyladamantanes with Td symmetry very well agrees with the results of electron diffraction. Closest to the results obtained experimentally, the geometry was predicted by B3LYP, in which the lengths of C-C and C-H bonds are close to 1.544 and 1,100Ả, respectively, and the C-Csec-C and C-Cter-C angles are 109°. The results of the calculation using the B3LYP method are in good agreement with the experimental data. There is no definite relationship between the size of the molecules and the convergence of the calculated and experimental data. A practically important conclusion arising from the results of this and previous studies is that the use of the calculation method leads to “chemically accurate” data.

DFT Simulations of the Vibrational Spectrum and Hydrogen Bonds of Ice XIV

It is always a difficult task to assign the peaks recorded from a vibrational spectrum. Herein, we explored a new pathway of density functional theory (DFT) simulation to present three kinds of spectra of ice XIV that can be referenced as inelastic neutron scattering (INS), infrared (IR), and Raman experimental spectrum. The INS spectrum is proportional to the phonon density of states (PDOS) while the photon scattering signals reflect the normal vibration frequencies near the Brillouin zone (BZ) center. Based on good agreements with the experimental data, we identified the relative frequency and made scientific assignments through normal vibration modes analysis. The two hydrogen bond (H-bond) peaks among the ice phases from INS were discussed and the dynamic process of the H-bond vibrations was found to be classified into two basic modes. We deduced that two H-bond modes are a general rule among the ice family and more studies are ongoing to investigate this subject.

Crystallography, vibrational, electronic and optical analysis of 4-Bromo-2-(2,5-dichloro-phenylimino)-phenol

This work reports synthesis and characterization of a novel compound, 4-Bromo-2-(2,5-dichloro-phenylimino)-phenol (BDP). The crystal structure of this Schiff base is determined and compared with DFT calculations. Density functional theory (DFT) and time dependent density functional theory (TD-DFT) is applied to study the optical, electronic properties, vibrational frequencies and optimized structure of 4-Bromo-2-(2,5-dichloro-phenylimino)-phenol by B3LYP, M06–2X, and ab initio (HF) methods and 6–311++G (d,p) basis set. The geometry and electronic properties, thermodynamic functions and atomic charges of the title compound are reported too. Finally, the calculated normal mode vibrational frequencies provide thermodynamic properties through the principle of statistical mechanics. A natural bond orbital (NBO) analysis was carried out to explain the charge transfer or delocalization of charge due to intra-molecular interactions.

Syntheses, Geometrical and Electronic Structure of Alkyladamantanes and Their Thermodynamic Characteristic According to the Density Functional Theory

Propyladamantanes synthesized by of alkylation adamantane with isopropyl alcohol temperature range from 5 to 40°C in the presence of 96% sulfuric acid. Tetramethyl- and Dimethylethyladamantanes synthesized by of isomerization of Perhydroanthracene in the presence of aluminium oxide catalyst on the setting of the flow type. Isomers Butyladamantanes was obtained by the reaction of alkylation of the adamantane with n-butane and isobutane. Adamantane and its derivatives have been the subject of many experimental and theoretical studies. The molecular structure of adamantane was studied by gasphase electron diffraction, Penning ionization electron spectroscopy, photoelectron spectroscopy, electron spin resonance, and quantum calculations of ionization potentials (IP) and electron affinity (SE). The structure 1-n-propyladamantane (1), 1-isopropyladamantane (2), 2-n-propyladamantane (3), 1,2-di-n-propyladamantane (4), 1,3-dimethyl-5-ethyladamantane (5), 1,3,5,6-tetramethyladamantane (6), 1,3,5,7-tetramethyladamantane (7), perhydroanthracene (8), 1-n-butyladamantane (9), 1-isobutyladamantane (10), 1-sec-butyladamantane (11) has been studied using the Becke–Lee–Yang–Parr (B3LYP) hybrid energy functional of electron density with the 6-31G* basis set. The geometric and electronic characteristics of the compounds and their total energy, normal vibration frequencies have been calculated. It has been shown that the calculated Gibb free energies of formation for the perhydroanthracene isomerization products are in qualitative agreement with the experimental product composition of the isomerate and alkylation of adamantane with isopropyl alcohol are in qualitative agreement with the experimental composition of the products. Obtained good agreement of calculated and experimental data on the composition of equilibrium mixtures.

Composition and structure of hydrates of CH3COOH molecules and CH3CO2− anions in aqueous solutions

The optimal configurations, energy parameters, and normal vibrational frequencies of hydrates of the acetic acid molecule and anion (CH3COOH·(H2O) n (n = 1-10) and CH3CO2−⋅(H2O) n (n = 1-8, 16)) are calculated by density functional theory (B3LYP/6-31++G(d,p)). The comparison of the calculation results with the known experimental data (Raman, NMR, and so on) gives arguments in favor of the existence of two stable heteroassociates (HAs) in СН3СООН–H2O solutions: previously found CH3COOH·(H2O)2 heterotrimer and CH3COOH·(H2O)8, and three complexes (CH3CO2−⋅(H2O)2, CH3CO2−⋅(H2O)6, and CH3CO2−⋅(H2O)16) in NaCH3CO2−–H2O solutions. Each of them is most stable in a series of isomers, contains unstrained H bonds, and is characterized by the maximum molecular packing density among HAs with similar n values. The structure of the subsequent complex formed in solution uniquely follows the structure of the preceding complex and is based on it.

An ab initio study of the vibrational properties of alkaline-earth metal nitrates and their crystallohydrates

The vibrational frequencies and corresponding intensities have been calculated ab initio for the center of the Brillouin zone of crystalline magnesium, calcium, strontium, and barium nitrates; magnesium nitrate hexahydrate; and calcium nitrate tetrahydrate. The calculation has been performed within the electron- density functional theory using the PBE exchange-correlation functional in the basis of localized atomic orbitals with the aid of the CRYSTAL14 software. The calculated values and the experimental IR and Raman spectral data on strontium and barium nitrates are shown to be in satisfactory agreement. The frequencies of normal long-wavelength vibrations in the nitrates become red-shifted with an increase in the cation atomic mass. The occurrence of several peaks due to the vibrations of hydrogen atoms in water molecules with different dynamic charges is predicted in the IR spectrum of hexahydrate magnesium in the frequency range above 3430 cm–1.

Theoretical basis of 2,4-methyl migration, an intramolecular rearrangement, during isomerization of alkyladamantyl cations

Quantum-chemical calculations of dimethyl-, trimethyl-, and methylethyladamantyl cations have been performed using the density functional theory method DFT B3LYP/6-31G* with full optimization of energy and computation of normal vibration frequencies and changes in these parameters during the course of their mutual isomeric transformations. The geometric parameters of the compounds, electronic characteristics, electron density distribution, the total energy, transformation energies, transformation entropies, activation energies, and normal vibration frequencies have been calculated. The calculation results confirm earlier experimental data on the occurrence of the direct 2,4-migration of the methyl group during the isomerization of methyladamantyl cations and the preference of this rearrangement to the well-known 1,2-methyl shift in alicyclic carbocations.

Oxide films state analysis by IR spectroscopy based on the simple oscillator approximation

Stabilization of structure-phase state in a wide temperature range is one of the most important problems of improving properties of oxide compounds. As such, the search of new effective methods for obtaining metal oxides with desired physic-chemical, electro-physical and thermal properties and their control is important and relevant. The aim of this work is identification features state of the oxide films of some metals Be, Al, Fe, Cu, Zr on the metal surface of the polycrystalline samples by infrared spectroscopy. To identify the resonance emission bands the algorithm of IR-spectra processing was developed and realized on the basis of table processor EXCEL-2010, which allow revealing characteristic resonance bands successfully and identification of inorganic chemical compounds. In the frame of simple oscillator model, resonance frequencies of normal vibrations of water and some inorganic compounds: metal oxides – Be, Al, Fe, Cu, Zr were calculated and characteristic frequencies for different states (aggregate, deformation, phase) were specified. By means of IR-spectroscopy fundamental possibility of revealing oxides films on metal substrate features state is shown, that allow development and optimization of the technology for production of the oxide films with desired properties.