DFT calculations of atoms and molecules in Cartesian grids

Each of the exchange–correlation functionals in the density functional theory has been customized to particular systems or elements and has unique advantages and disadvantages. In one of the most recent research on exchange–correlation functionals, Chachiyo et al. present a relationship for exchange–correlation functional by assuming the simplest form of electron density. Their utilized electron density causes a systematic inaccuracy in the energy of the molecules since it does not fully account for the variation of the ionization energy for different atoms. We offer a novel relationship for exchange functional that improves the precision of the energy calculations for molecules by using the basic assumptions of the Chachiyo approach and correcting the electron density. Our density is directly related to the atom’s ionization energy. Our suggested functional was implemented for 56 molecules composed of atoms from the first, second, and third rows of the periodic table using Siam Quantum package. We discussed about the role of our functional on the reducing the computation error of dipole moment along with total, bonding and zero point energies. We also increased the portion of core electrons to improve the accuracy of the results.

In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.

Excited-state proton transfer (ESPT) processes of 2-(2'-hydroxyphenyl)benzimidazole (HBI) and its complexation with protic solvents (H2O, CH3OH, and NH3) have been investigated by both static calculations and dynamics simulations using density functional theory (DFT) at B3LYP/TZVP theoretical level for ground state (S0) and time-dependent (TD)-DFT at TD-B3LYP/TZVP for excited state (S1). For static calculations, absorption and emission spectra, infrared (IR) vibrational spectra of O-H mode, frontier molecular orbitals (MOs), and potential energy curves (PECs) of proton transfer coordinate were analyzed. Simulated absorption and emission spectra show an agreement with available experimental data. The hydrogen bond strengthening in the S1 state has been proved by the changes of IR vibrational spectra and bond parameters of the hydrogen moiety with those of the S0 state. The MOs provide the visual electron density redistribution confirming the hydrogen bond strengthening mechanism. The PECs show that the proton transfer (PT) process is easier to occur in the S1 state than the S0 state. Moreover, on-the-fly dynamics simulations of all systems were carried out to provide the detailed information on time revolution. The results revealed that the excited-state intermolecular proton transfer for HBI is fast, whereas the excited-state intermolecular proton transfer for HBI with protic solvents are slower than that of HBI because the competition between intra- and intermolecular hydrogen-bonds between HBI and protic solvent. These intermolecular hydrogen-bonds hinder the formation of tautomer, hence explaining the low quantum yield found in the protic solvent experiment. Especially for HBI complexing with methanol, only ESIntraPT occurs with small probability compared to HBI with water and ammonia.

Quantum chemical analysis of some Thiazole derivatives, namely (2-Chlorobenzothiazole; 5-acetyl-2,4dimethylthiazole; 2-Chlorobenzothiazole; Phthalylsulfathaizole; 2,4,5 Trimethyl thiazole) was performed by using Gaussian 9 software with semi-empirical calculation method such as density functional theory (DFT) and the basis sets used were the DFT/B3LYP methods using 6-311G (d, p). Various quantum chemical parameters such as electronic density, highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) energy levels, and the energy difference between highest and lowest unoccupied molecular orbitals (ELUMO-EHOMO), etc. were calculated. High EHOMO values suggests that the molecule can contribute the electrons towards bond formation; however, the lower values of ELUMO indicate that the molecule can easily accept the electrons. Besides that, the low value of the energy bandgap (ΔE) confirms the excellent inhibition efficiencies of the derivatives. Furthermore, by using these frontier orbital energies, different parameters like ionization energy, electron affinity, global hardness, electronegativity were also calculated. In this article, a theoretical study was performed only to determine the correlation between various parameters related to the electronic structure of Thiazole derivatives and their competence to mitigate the corrosion process.

In this work, we theoretically investigate the properties of excited state process for a novel salicylidene sal-3,4-benzophen (Sal-3,4-B) system, which contains two intramolecular hydrogen bonds (O1-H2[Formula: see text]N3 and O4-H5[Formula: see text]N6). Based on the density functional theory (DFT) and time-dependent DFT (TDDFT) methods, we find these two hydrogen bonds should be strengthened in the S1 state, while the O4-H5[Formula: see text]N6 one could be largely affected upon the excitation process. Analyses about infrared (IR) vibrational spectra about hydrogen bond moieties also confirm this viewpoint. Frontier molecular orbitals (MOs) depict the nature of electronic excited state and support the excited state intramolecular proton transfer (ESIPT) reaction.Two kinds of stepwise potential energy curves of Sal-3,4-B in the S1 state demonstrate that only one proton could be transferred. Also based on constructing potential energy curves, the synergetic situation could be eliminated. Due to the specific ESIPT mechanism for Sal-3,4-B, we successfully explain the previous experiment and provide a reasonable attribution to the second emission peak of experiment.

Finite difference method and a spurious reflection of waves in a layer of fluid

SIMULATION OF NATURAL CONVECTION IN A SQUARE CAVITY BY TAYLOR SERIES EXPANSION- AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD

The first-principles approach is applied to study the electronic, vibrational, and superconducting properties of B1-NbC. We used a variety of density functional theory methods that involve local density approximation (PW), generalized gradient approximation; PBE, PBEsol, and GGA functionals corrected with nonlocal correlation functionals (rVV10, vdW-DF2, vdW-DF3). Although the electronic band structures from different methods show an overwhelming agreement, the phonon dispersion curves display significant differences at certain points. The optical phonons make an appreciable part of the electron-phonon coupling constant, λ (up to 23%). This contribution is found to be the largest for PW and the smallest for PBE whereas the nonlocal functionals give intermediate values. This behavior is in perfect analogy with the interaction energies for the three types of methods. The nonlocal functionals, rVV10 and vdW-DF3, fine tuned λ to obtain a value in close agreement with a recently reported experimental value of λ = 0.848 Yan et al. Despite the fact that variations in λ due to nonlocal functionals are not very large, the effects on the superconducting transition temperatures are significant. In addition, the Coulomb screening potential, μ * = 0.1525 gives superconducting transition temperature in the best agreement with the experiment.

Preserving the beneficial properties of the second-order screened exchange (SOSEX) method, such as its freedom from one-body self-correlation error, and its seamless treatment of long-range dispersion interaction, we construct new nonlocal functionals by down-scaling the higher-order terms in the SOSEX series to reduce the many-body self-correlation error in molecular systems. Our down-scaled SOSEX (dsSOSEX) and scaled equation SOSEX (seSOSEX) approaches deliver considerably more accurate noncovalent interaction energies, reaction energies, and barrier heights than the original SOSEX method. The dsSOSEX approach improves on the description of medium- and long-range correlation, for example, in isogyric processes, while the seSOSEX approach improves on the description of processes with short- and medium-range rearrangement in the electronic structure, such as atomization. The He2+ potential energy curve shows that the many-body self-correlation error is slightly smaller in the dsSOSEX method than in the seSOSEX approach. Furthermore, the H2 potential energy curve reveals that the static correlation error can also be reduced at medium range by the dsSOSEX and seSOSEX schemes. As our dsSOSEX method provides a better description of medium- and long-range correlation, it generally leads to more accurate energetics than the seSOSEX method; hence it should be preferred over the latter. We compare our results to other empirical and nonempirical direct random phase approximation (dRPA) and beyond-dRPA methods and also discuss the possibilities for further development.

The study involves the application of quantum mechanical calculations using density function theory (DFT) with B3LYP/6-31G on ibuprofen for the purpose of calculation the equilibrium geometries , energies of HOMO , LUMO orbital , ionization energies , electronic densities , the vibrational modes . The thermodynamic functions ( E0 , H0 , A0 ,S0 ,CV ) was calculated of compounds studied and also some physical properties (EHOMO , ELUMO , , IP ) was also calculated . This study is considered important of ibuprofen to reach information about ibuprofen in order to compare it with information about derivatives in order to reach the substance with the least side effects on the body. Keywords:; Ibuprofen , Theoretical Study , density function theory

159. Industrial mass spectrometer for gas analysis: L N Ozerov and A E Rafalson,Priborostroenie, (8), 1965, 14, (in Russian)

Heteroatom substitution effect on electronic structures, photophysical properties, and excited-state intramolecular proton transfer processes of 3-hydroxyflavone and its analogues: A TD-DFT study

Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.

We present a perspective on the use of diffuse basis functions for electronic structure calculations by density functional theory and wave function theory. We especially emphasize minimally augmented basis sets and calendar basis sets. We base our conclusions on our previous experience with commonly computed quantities, such as bond energies, barrier heights, electron affinities, noncovalent (van der Waals and hydrogen bond) interaction energies, and ionization potentials, on Stephens et al.'s results for optical rotation and on our own new calculations (presented here) of polarizabilities and of potential energy curves of van der Waals complexes. We emphasize the benefits of partial augmentation of the higher-zeta basis sets in preference to full augmentation at a lower ζ level. Benefits and limitations of the use of fully, partially, and minimally augmented basis sets are reviewed for different electronic structure methods and molecular properties. We have found that minimal augmentation is almost always enough for density functional theory (DFT) when applied to ionization potentials, electron affinities, atomization energies, barrier heights, and hydrogen-bond energies. For electric dipole polarizabilities, we find that augmentation beyond minimal has an average effect of 8% at the polarized triple-ζ level and 5% at the polarized quadruple-ζ level. The effects are larger for potential energy curves of van der Waals complexes. The effects are also larger for wave function theory (WFT). Even for WFT though, full augmentation is not needed for most purposes, and a level of augmentation between minimal and full is optimal for most problems. The calendar basis sets named after the months provide a convergent sequence of partially augmented basis sets that can be used for such calculations. The jun-cc-pV(T+d)Z basis set is very useful for MP2-F12 calculations of barrier heights and hydrogen bond strengths.

This thesis primarily consists of two parts. In the first one, we benchmarked the performance of the functionals in density functional theory which have the asymptotically correct behavior. We compare the performance of the two different asymptotically corrected schemes, the long-range corrected (LC) hybrid scheme and the asymptotically corrected (AC) model potential scheme, in a wide range of applications. These schemes aim at producing the correct asymptotic behavior, which is known to be important to the Rydberg excitations and the frontier orbital energies of molecules. Based on our investigation, we found that the LC hybrid scheme outperforms the AC model potential scheme almost on all the properties studied, and we conclude that the LC hybrid scheme provides a promising direction for the future development of new exchange-correlation functionals. Besides, in the process of the benchmark, I established a molecular database ``IP131 full set', which consists of 131 experimental geometries of atoms and molecules, and their reference values of 131 experimental vertical ionization energies, 131 CCSD(T) calculated vertical electron affinities, 131 CCSD(T) calculated fundamental gaps and 113 CCSD(T) calculated atomization energies. The IP131 full set can be used in the benchmarks for other Ab Initio calculation methods, or in the parameter fitting in the development of density functionals in the future. In the second part, we adopted the Schrodinger equation numerical solutions to improve the applicability of the normal mode analysis in the case of TMA-H+-H2O, for the motivation that the theoretical simulated infrared spectrum of TMA-H+-H2O given by the normal mode analysis is far from the experiment results. Normal mode analysis is a convenient and widely adopted method that people usually use it to analyse the vibrational motions of multi-body mechanical systems, both classical and quantum. However, normal mode analysis is a approximate method and its assumptions, which make the analysis procedures simple and systematically solvable, also make the normal mode analysis not applicable to some vibrational motions in some mechanical systems. Our main modification method in this work is to regard the vibrational normal modes as some low dimensional quantum systems and adopt the Schrodinger equation numerical solutions in these quantum systems to replace the results from the normal mode analysis. By doing so, we can not only get a closer result to the experimental infrared spectrum, but also have a deeper understanding of the capability and applicability of normal mode analysis. Once in the future we encounter same problems when using the normal mode analysis in different systems, we may again adopt the procedures developed here to make it better.