First‐principles calculations on thermodynamic properties of BaTiO3 rhombohedral phase

The calculations based on the linear combination of atomic orbitals have been performed for the low‐temperature phase of BaTiO₃ crystal. Structural and electronic properties, as well as phonon frequencies were obtained using hybrid PBE0 exchange–correlation functional. The calculated frequencies and total energies at different volumes have been used to determine the equation of state and thermal contribution to the Helmholtz free energy within the quasiharmonic approximation. For the first time, the bulk modulus, volume thermal expansion coefficient, heat capacity, and Grüneisen parameters in BaTiO₃ rhombohedral phase have been estimated at zero pressure and temperatures form 0 to 200 K, based on the results of first‐principles calculations. Empirical equation has been proposed to reproduce the temperature dependence of the calculated quantities. The agreement between the theoretical and experimental thermodynamic properties was found to be satisfactory. © 2012 Wiley Periodicals, Inc.     

First‐principles calculations on the four phases of BaTiO3

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO₃ crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange‐correlation density functional theory (DFT) functionals for four stable phases of BaTiO₃. A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO₃. The comparative phonon symmetry analysis in BaTiO₃ four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. © 2012 Wiley Periodicals, Inc.     

DFT study of the gas‐phase thermal decomposition kinetics of 2‐ethoxypyridine into 2‐pyridone

The mechanism of the gas‐phase elimination kinetics of 2‐ethoxypyridine has been studied through the electronic structure calculations using density functional methods: B3LYP/6‐31G(d,p), B3LYP/6‐31++G(d,p), B3PW91/6‐31G(d,p), B3PW91/6‐31++G(d,p), MPW1PW91/6‐31G(d,p), MPW1PW91/6‐31++G(d,p), PBEPBE/6‐31G(d,p), PBEPBE/6‐31++G(d,p), PBE1PBE1/6‐31G(d,p), and PBE1PBE1/6‐31++G(d,p). The elimination reaction of 2‐ethoxypyridine occurs through a six‐centered transition state geometry involving the pyridine nitrogen, the substituted carbon of the aromatic ring, the ethoxy oxygen, two carbons of the ethoxy group, and a hydrogen atom, which migrates from the ethoxy group to the nitrogen to give 2‐pyridone and ethylene. The reaction mechanism appears to occur with the participation of π‐electrons, similar to alkyl vinyl ether elimination reaction, with simultaneous ethylene formation and hydrogen migration to the pyridine nitrogen producing 2‐pyridone. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Influence of the exchange‐correlation functional in all‐electron calculations of the vibrational frequencies of corundum (α‐Al2O3)

The equilibrium structural parameters, high‐ and low‐frequency dielectric tensors, Born effective charges, and Γ‐point vibrational frequencies of bulk Al₂O₃ corundum are calculated by using the periodic, ab initio program CRYSTAL, which adopts an all‐electron Gaussian‐type basis set. The effect of basis set and the performance of three different functionals, i.e., LDA, PW91, and B3LYP, are discussed. The mean absolute deviation from the measured frequencies is as small as 7 cm^?1 for both the LDA and B3LYP functionals, indicating that these functionals perform extremely well in this case. The mean absolute deviation increases to 18 cm^?1 when the PW91 functional is used. All three functionals reproduce the equilibrium geometry of corundum to a high level of accuracy, with LDA and B3LYP outperforming PW91 slightly. The comparison of the current all‐electron calculations with previous plane‐wave, pseudo‐potential calculations shows an overall similar performance. The results of isotopic substitution for both Al and O are also presented. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical study of the vibrational frequencies of carbon disulfide

A benchmark comparison for different computational methods and basis sets has been presented. In this study, five computational methods (Hartree–Fock (HF), MP2, B3LYP, MPW1MP91, and PBE1PBE) along with 18 basis sets have been applied to optimize the geometry of carbon disulfide (CS₂), and further calculate the vibrational frequencies of the optimized geometries. The differences between the calculated frequencies and corresponding experimental data are used to evaluate the efficiency of each combination of computational method and basis set. The comparison of frequency difference indicates that B3LYP generally gives the best prediction of frequencies for CS₂, whereas the other two density functional theory (DFT) methods, i.e., MPW1PW91 and PBE1PBE, often give parallel results. Although MP2 predicts the frequencies with accuracy almost as good as those from DFT methods, in a particular case, HF calculation outperforms MP2 as well as MPW1PW91 and PBE1PBE for prediction of the frequency of asymmetrical stretching for CS₂. © 2013 Wiley Periodicals, Inc.     

Calculations of solid‐state 43Ca NMR parameters: A comparison of periodic and cluster approaches and an evaluation of DFT functionals

We present a computational study of magnetic‐shielding and quadrupolar‐coupling tensors of ⁴³Ca sites in crystalline solids. A comparison between periodic and cluster‐based approaches for modeling solid‐state interactions demonstrates that cluster‐based approaches are suitable for predicting ⁴³Ca NMR parameters. Several model chemistries, including Hartree–Fock theory and 17 DFT approximations (SVWN, CA‐PZ, PBE, PBE0, PW91, B3PW91, rPBE, PBEsol, WC, PKZB, BMK, M06‐L, M06, M06‐2X, M06‐HF, TPSS, and TPSSh), are evaluated for the prediction of ⁴³Ca NMR parameters. Convergence of NMR parameters with respect to basis sets of the form cc‐pVXZ (X = D, T, Q) is also evaluated. All DFT methods lead to substantial, and frequently systematic, overestimations of experimental chemical shifts. Hartree–Fock calculations outperform all DFT methods for the prediction of ⁴³Ca chemical‐shift tensors. © 2017 Wiley Periodicals, Inc.     

Theoretical study of the mechanism for the gas‐phase pyrolysis kinetics of 2‐methylbenzyl chloride

The study of the kinetics and mechanism of dehydrochlorination reaction of 2‐methyl benzyl chloride in the gas phase was carried out by means of electronic structure calculations using ab initio Móller‐Plesset MP2/6‐31G(d,p), and Density Functional Theory (DFT) methods: B3LYP/6‐31G(d,p), B3LYP/6‐31++G(d,p), MPW1PW91/6‐31G(d,p), MPW1PW91/6‐31++G(d,p)], PBE/6‐31G(d,p), PBE/6‐31++G(d,p). Investigated reaction pathways comprise: Mechanism I, a concerted reaction through a six‐centered cyclic transition state (TS) geometry; Mechanism II, a 1,3‐chlorine shift followed by beta‐elimination and Mechanism III, a single‐step elimination with simultaneous HCl and benzocyclobutene formation through a bicyclic type of TS. Calculated parameters ruled out Mechanism III and suggest the elimination reaction may occur by either unimolecular Mechanism I or Mechanism II. However, the TS of the former is 20 kJ/mole more stable than the TS of the latter. Consequently, the Mechanism I seem to be more probable to occur. The rate‐determining process is the breaking of C‐Cl bond. The involvement of π‐electrons of the aromatic system was demonstrated by NBO charges and bond order calculations. The reaction is moderately polar in nature. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 537–546, 2011     

Theoretical calculations on the mechanisms of the gas‐phase elimination kinetics of 2‐chloro‐1‐phenylethane, 3‐chloro‐1‐phenylpropane, 4‐chloro‐1‐phenylbutane, 5‐chloro‐1‐phenylpentane,and their corresponding chloroalkanes: The effect of the phenyl ring

The kinetics and mechanisms of the dehydrochlorination of 2‐chloro‐1‐ phenylethane, 3‐chloro‐1‐phenylpropane, 4‐chloro‐1‐phenylbutane, 5‐chloro‐1‐phenylpentane, and their corresponding chloroalkanes were examined by means of electronic structure calculation using density functional theory methods B3LYP/6–31G(d,p), B3LYP/6–31++G(d,p), MPW1PW91/6–31G(d,p), MPW1PW91/6–31++G(d,p), PBEPBE/6–31G(d,p), and PBEPBE/6–31++G(d,p). The potential energy surface was investigated for the minimum energy path. Calculated enthalpies and energies of activation are in good agreement with experimental values using the MPW1PW91 and B3LYP methods. The transition state of these reactions is a four‐centered cyclic structure. The reported experimental results proposing neighboring group participation by the phenyl group was not supported by theoretical calculations. The rate‐determining process in these reactions is the breaking of Cl? C bond. The reactions are described as concerted moderately polar and nonsynchronous. © 2011 Wiley Peiodicals, Inc. Int J Chem Kinet 43: 292–302, 2011     

Iodate Sensing Electrodes Based on Phosphotungstate‐ Doped‐Glutaraldehyde‐Cross‐Linked Poly‐L‐lysine Coatings

Glassy carbon electrode modified with phosphotungstate‐doped‐glutaraldehyde‐cross‐linked poly‐L ‐lysine (PLL‐GA‐PW) film was employed for iodate determination. The PLL‐GA‐PW film electrode shows excellent electrocatalytic activity towards iodate reduction with significant reduction of overpotential. Under optimized experimental conditions, a linear range from 5×10^?8 to 2.27×10^?2 M with a sensitivity of 61.75 μA mM^?1 was obtained. Possible interfering species, in iodate determination, were evaluated and the applicability of proposed sensor for iodate estimation in table salt was also demonstrated. The PLL‐GA‐PW film electrode shows fast response, wider linear range, and good selectivity and stability.     

Benchmark calculations of 29Si–1H spin–spin coupling constants across double bond

Benchmark calculations of geminal and vicinal ²⁹Si–¹H spin–spin coupling constants across double bond in three reference alkenylsilanes have been carried out at both DFT and SOPPA levels in comparison with experiment. At the former, four density functionals, B3LYP, B3PW91, PBE0 and KT3, were tested in combination with five representative basis sets. At the latter, three main SOPPA‐based methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), were examined in combination with the same series of basis sets. On the whole, the wavefunction methods showed much better results as compared to DFT, with the most efficient combination of SOPPA/cc‐pVTZ‐su2 characterized by a mean absolute error of only 0.4 Hz calculated for a set of nine coupling constants in three compounds with a sample span of around 40 Hz. Copyright © 2012 John Wiley & Sons, Ltd.     

Calculation of the vibration frequencies of alpha-quartz: the effect of Hamiltonian and basis set

The central-zone vibrational spectrum of alpha-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree-Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm(-1), respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm(-1).     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

First‐principles modeling of hafnia‐based nanotubes

Hybrid density functional theory calculations were performed for the first time on structure, stability, phonon frequencies, and thermodynamic functions of hafnia‐based single‐wall nanotubes. The nanotubes were rolled up from the thin free layers of cubic and tetragonal phases of HfO₂. It was shown that the most stable HfO₂ single‐wall nanotubes can be obtained from hexagonal (111) layer of the cubic phase. Phonon frequencies have been calculated for different HfO₂ nanolayers and nanotubes to prove the local stability and to find the thermal contributions to their thermodynamic functions. The role of phonons in stability of nanotubes seems to be negligible for the internal energy and noticeable for the Helmholtz free energy. Zone folding approach has been applied to estimate the connection between phonon modes of the layer and nanotubes and to approximate the nanotube thermodynamic properties. It is found that the zone‐folding approximation is sufficiently accurate for heat capacity, but less accurate for entropy. The comparison has been done between the properties of TiO₂, ZrO₂, and HfO₂. © 2017 Wiley Periodicals, Inc.     

Comparative study of unscreened and screened molecular static linear polarizability in the Hartree–Fock,hybrid‐density functional,and density functional models

The sum‐over‐states (SOS) polarizabilities are calculated within approximate mean‐field electron theories such as the Hartree–Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self‐consistent solution of the single‐particle equations. The SOS polarizabilities are then compared with those calculated using the finite‐field (FF) method. Three widely used mean‐field models are as follows: (1) the Hartree–Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (GGA) (B3LYP), and (3) the parameter‐free generalized gradient approximation due to Perdew–Burke–Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6‐311++G(d,p) basis set at the geometries optimized at the B3LYP/6‐311G** level. The results show that the SOS method almost always overestimates the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method. A few exceptions to these trends are found. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78, 1.87, and 3.44 ų for the HF, B3LYP, and PBE‐GGA methods, respectively. Finally, a simple scheme is devised to obtain FF quality polarizability from the SOS polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.