The application of an optimization technique to the development of universal basis sets

1992 ◽  
Vol 70 (2) ◽  
pp. 580-588 ◽  
Author(s):  
R. Custodio ◽  
J. D. Goddard ◽  
M. Giordan ◽  
N. H. Morgon
Keyword(s):  
Total Energy ◽  
Energy Criterion ◽  
Basis Set ◽  
Basis Sets ◽  
Weight Functions ◽  
Statistical Criterion ◽  
Minimum Total Energy ◽  
Discretization Technique ◽  
Universal Bases ◽  
Molecular Calculations

The Simplex method was used to define atomic and universal meshes using the integral discretization technique for the Griffin–Hill–Wheeler-Hartree–Fock equations. This technique represents a basis set as an exponential set of the form:[Formula: see text]For atoms, the minimum total energy criterion was employed. For the universal basis, three different procedures were tested: (a) defining the universal basis using information on the isolated atoms, (b) determining the universal Ω0(k) through atomic calculations and reoptimizing the ΔΩ(k) for different symmetries employing simultaneously a single atomic calculation as a reference point, and (c) optimizing the universal mesh using a statistical criterion such as the squares of the deviations of the total energy. The meshes obtained by the minimum total energy criterion or the squares of deviations of the total energy for the universal basis are accurate for the total energy but the weight functions are deficient in the valence region. Shifting the optimized Ω0(k) to [Formula: see text], fixing [Formula: see text], and reoptimizing ΔΩ(k) for each symmetry species produces a better description of weight functions at the expense of a less accurate total energy. In general, no significant statistical difference was observed for the various universal bases generated by procedures (a) and (b) or by (c) provided the shift correction was made to the latter. Application of these bases to diatomic molecules (N2, CO, P2, CS) showed that the universal bases are as accurate as those optimized for atomic systems. If the bases are transferred from atoms to molecules, the shift corrections to the weight functions of the atoms are not useful in molecular calculations. The almost equivalent molecular properties and the good total energies show that the best basis for molecular calculations is that optimized by procedure (c). Keywords: universal basis sets, integral discretization technique.

The Effects of Split Valence Basis Sets on Muon Hyperfine Interaction in Guanine Nucleobase and Nucleotide Structures

2019 ◽  
Vol 966 ◽  
pp. 222-228 ◽  
Author(s):  
Wan Nurfadhilah Zaharim ◽  
Shukri Sulaiman ◽  
Siti Nuramira Abu Bakar ◽  
Nur Eliana Ismail ◽  
Harison Rozak ◽  
...  
Keyword(s):  
Total Energy ◽  
Hyperfine Interactions ◽  
Phosphate Group ◽  
Basis Set ◽  
Basis Sets ◽  
Cluster Method ◽  
Sugar Phosphate ◽  
Atomic Orbitals ◽  
Fermi Contact ◽  
Triple Zeta

The DFT cluster method was employed to investigate the electronic structures and muonium hyperfine interactions in guanine nucleobase and nucleotide using three different basis sets. The total energy and Fermi contact values were calculated for muon trapped at carbon '8'. The three basis sets, 6-31G, 6-311G and 6-311G(d,p), were used in tandem with the B3LYP functional. There are significant quantitative differences in the calculated total energy. 6-311G(d,p) produced the lowest total energy as compared to the other basis sets. The lowering of the total energy is due to the increase in the number of basis functions to describe the atomic orbitals, which is consistent with the postulate on basis set completeness. The 6-31G basis set produced the muon Fermi contact value that is the closest to the experimental value. The calculated Fermi contact values for the nucleobase and nucleotide are significantly lowered in going from the double-zeta to the triple-zeta basis set by 5% and 4% respectively. The lowering of the Fermi contact value can be attributed to the extension of the triple-zeta basis set in describing the valence atomic orbitals. The presence of the sugar phosphate group in the nucleotide instead of the methyl group tends to lower the Fermi contact value. Thus, the sugar phosphate group should be taken into consideration when designing a calculation model.

scholarly journals Quantum Mechanical Study of YTiO3 to the Investigation of Piezoelectricity

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Raimundo Dirceu de Paula Ferreira ◽  
Marcos Antonio Barros dos Santos ◽  
Maycon da Silva Lobato ◽  
Jardel Pinto Barbosa ◽  
Marcio de Souza Farias ◽  
...  
Keyword(s):  
Total Energy ◽  
Piezoelectric Properties ◽  
Piezoelectric Effect ◽  
Basis Set ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate ◽  
Mechanical Study ◽  
Quantum Mechanical Study

In previous articles we reported through theoretical studies the piezoelectric effect in BaTiO3, SmTiO3, and YFeO3. In this paper, we used the Douglas-Kroll-Hess (DKH) second-order scalar relativistic method to investigate the piezoelectricity in YTiO3. In the calculations we used the [6s4p] and [10s5p4d] Gaussian basis sets for the O (3P) and Ti (5S) atoms, respectively, from the literature in combination with the (30s21p16d)/[15s9p6d] basis set for the Y (3D) atom, obtained by generator coordinate Hartree-Fock (GCHF) method, and they had their quality evaluated using calculations of total energy and orbital energies (HOMO and HOMO-1) of the 2TiO+1 and 1YO+1 fragments. The dipole moment, the total energy, and the total atomic charges in YTiO3 in Cs space group were calculated. When we analyze those properties we verify that it is reasonable to believe that YTiO3 does not present piezoelectric properties.

Basis Set Effects in Density Functional Theory Calculation of Muoniated Cytosine Nucleobase

2020 ◽  
Vol 860 ◽  
pp. 282-287
Author(s):  
Wan Nurfadhilah Zaharim ◽  
Shukri Sulaiman ◽  
Saidah Sakinah Mohd Tajudin ◽  
Siti Nuramira Abu Bakar ◽  
Nur Eliana Ismail ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Total Energy ◽  
Density Functional ◽  
Density Functional Theory Calculation ◽  
Geometry Optimization ◽  
Density Functional Theory Method ◽  
Basis Set ◽  
Basis Sets ◽  
Functional Theory ◽  
Muonium Hyperfine

The Density Functional Theory method was employed to investigate the electronic structure and muonium hyperfine interaction of muonium trapped near carbon atom labelled as '5' in cytosine nucleobase. Eighteen different basis sets in combination with B3LYP functional were examined in geometry optimization calculations on the muoniated radical. There are significant quantitative differences in the calculated total energy. The employment of basis set that does not include polarization function produces an optimized structure with high total energy. The 6-311++G(d,p) basis set yielded the lowest total energy as compared to other basis sets. The bond order of muonium trapped at C5 atom is in the range of 0.841 to 0.862. The 6-31G basis set produced the muonium Fermi contact coupling constant that is the closest to the experimental value.

scholarly journals Adapted Gaussian basis sets for atoms from Li through Xe generated with the generator coordinate Hartree-Fock method

2001 ◽  
Vol 73 (4) ◽  
pp. 511-517 ◽  
Author(s):  
EUSTÁQUIO V. R. DE CASTRO ◽  
FRANCISCO E. JORGE
Keyword(s):  
Total Energy ◽  
Wave Functions ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate ◽  
Discretization Technique

The generator coordinate Hartree-Fock method is used to generate adapted Gaussian basis sets for the atoms from Li (Z=3) through Xe (Z=54). In this method the Griffin-Hill-Wheeler-Hartree-Fock equations are integrated through the integral discretization technique. The wave functions generated in this work are compared with the widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti (1974), and with other basis sets reported in the literature. For all atoms studied, the errors in our total energy values relatively to the numerical Hartree-Fock limits are always less than 7.426 mhartree.

Small Gaussian basis sets for molecular calculations. II. Effect of basis set size on the calculated wavefunction and a useful GTO basis set

1973 ◽  
Vol 26 (7) ◽  
pp. 1381 ◽  
Author(s):  
FR Burden ◽  
BT Hart
Keyword(s):  
Wave Functions ◽  
Basis Set ◽  
Basis Sets ◽  
Confidence Limits ◽  
Optimum Size ◽  
Minimal Basis ◽  
Gaussian Basis Sets ◽  
Large Molecules ◽  
Set Size ◽  
Molecular Calculations

A quantitative assessment of the importance of basis set variation at the minimal basis level of accuracy has been carried out. A number of basis sets, using Gaussian lobe functions, were tested by calculating the energy and one-electron properties for a number of molecules and the results used to select an optimum sized accurate basis set. This basis set consisted of a five-component 1s-Gaussian type orbital (GTO), a three-component 2s-GTO and a three-component 2p-GTO for each first row atom, and a three-component 1s-GTO for hydrogen. The accuracy of wave functions calculated with the minimal basis sets was very sensitive to changes in the 2p-GTO. ��� A Gaussian lobe basis set of optimum size for use with large molecules is given. The results of testing this set by calculating several one-electron properties for ten molecules, together with confidence limits, are also presented.

Systematic sequences of well-balanced Gaussian basis sets

1994 ◽  
Vol 72 (7) ◽  
pp. 1741-1752 ◽  
Author(s):  
Mariusz Klobukowski
Keyword(s):  
Molecular Structure ◽  
Ab Initio ◽  
Basis Set ◽  
Basis Sets ◽  
Structure And Properties ◽  
Gaussian Basis Sets ◽  
Molecular Calculations

Systematic sequences of Gaussian basis sets with controlled energy errors for the studies of convergence of the basis set effects on the computed results of molecular calculations are presented. The basis sets were prepared for atoms H–Ne and Al–Ar and may be used in systematic ab initio ad limitem studies of molecular structure and properties.

A Systematic DFT Study of Two Elementary Steps Involving Hydrogen Peroxide and the Hydroxyl Radical in the Fenton Reaction

2018 ◽  
Author(s):  
Danilo Carmona ◽  
David Contreras ◽  
Oscar A. Douglas-Gallardo ◽  
Stefan Vogt-Geisse ◽  
Pablo Jaque ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Hydroxyl Radical ◽  
Ab Initio ◽  
Fenton Reaction ◽  
Basis Set ◽  
Basis Sets ◽  
Dft Methods ◽  
Elementary Steps ◽  
Oxygen Oxygen ◽  
Complete Basis Set

The Fenton reaction plays a central role in many chemical and biological processes and has various applications as e.g. water remediation. The reaction consists of the iron-catalyzed homolytic cleavage of the oxygen-oxygen bond in the hydrogen peroxide molecule and the reduction of the hydroxyl radical. Here, we study these two elementary steps with high-level ab-initio calculations at the complete basis set limit and address the performance of different DFT methods following a specific classification based on the Jacob´s ladder in combination with various Pople's basis sets. Ab-initio calculations at the complete basis set limit are in agreement to experimental reference data and identified a significant contribution of the electron correlation energy to the bond dissociation energy (BDE) of the oxygen-oxygen bond in hydrogen peroxide and the electron affinity (EA) of the hydroxyl radical. The studied DFT methods were able to reproduce the ab-initio reference values, although no functional was particularly better for both reactions. The inclusion of HF exchange in the DFT functionals lead in most cases to larger deviations, which might be related to the poor description of the two reactions by the HF method. Considering the computational cost, DFT methods provide better BDE and EA values than HF and post--HF methods with an almost MP2 or CCSD level of accuracy. However, no systematic general prediction of the error based on the employed functional could be established and no systematic improvement with increasing the size in the Pople's basis set was found, although for BDE values certain systematic basis set dependence was observed. Moreover, the quality of the hydrogen peroxide, hydroxyl radical and hydroxyl anion structures obtained from these functionals was compared to experimental reference data. In general, bond lengths were well reproduced and the error in the angles were between one and two degrees with some systematic trend with the basis sets. From our results we conclude that DFT methods present a computationally less expensive alternative to describe the two elementary steps of the Fenton reaction. However, choice of approximated functionals and basis sets must be carefully done and the provided benchmark allows a systematic validation of the electronic structure method to be employed

DFT Benchmark Study of the O--O Bond Dissociation Energy in Peroxides Validated with High-Level Ab-Initio Calculations

2019 ◽  
Author(s):  
Danilo Carmona ◽  
Pablo Jaque ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Reference Value ◽  
Basis Set ◽  
Basis Sets ◽  
Mean Deviation ◽  
Bond Dissociation ◽  
Dissociation Energies ◽  
The Mean ◽  
Experimental Values ◽  
High Level ◽  
Almost All

<div><div><div><p>Peroxides play a central role in many chemical and biological pro- cesses such as the Fenton reaction. The relevance of these compounds lies in the low stability of the O–O bond which upon dissociation results in radical species able to initiate various chemical or biological processes. In this work, a set of 64 DFT functional-basis set combinations has been validated in terms of their capability to describe bond dissociation energies (BDE) for the O–O bond in a database of 14 ROOH peroxides for which experimental values ofBDE are available. Moreover, the electronic contributions to the BDE were obtained for four of the peroxides and the anion H2O2− at the CBS limit at CCSD(T) level with Dunning’s basis sets up to triple–ζ quality provid- ing a reference value for the hydrogen peroxide anion as a model. Almost all the functionals considered here yielded mean absolute deviations around 5.0 kcal mol−1. The smallest values were observed for the ωB97 family and the Minnesota M11 functional with a marked basis set dependence. Despite the mean deviation, order relations among BDE experimental values of peroxides were also considered. The ωB97 family was able to reproduce the relations correctly whereas other functionals presented a marked dependence on the chemical nature of the R group. Interestingly, M11 functional did not show a very good agreement with the established order despite its good performance in the mean error. The obtained results support the use of similar validation strategies for proper prediction of BDE or other molecular properties by DF Tmethods in subsequent related studies.</p></div></div></div>

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