General contraction of Gaussian atomic orbitals: Core, valence, polarization, and diffuse basis sets; Molecular integral evaluation

1973 ◽  
Vol 58 (10) ◽  
pp. 4452-4458 ◽  
Author(s):  
Richard C. Raffenetti
Keyword(s):  
Basis Sets ◽  
Molecular Integral ◽  
Integral Evaluation ◽  
Atomic Orbitals ◽  
General Contraction

Improvement of the long-range behavior of Gaussian basis sets using asymptotic constraints

1992 ◽  
Vol 70 (2) ◽  
pp. 362-365 ◽  
Author(s):  
Toshikatsu Koga ◽  
Ajit J. Thakkar
Keyword(s):  
Long Range ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Atomic Orbitals ◽  
Hartree Fock

It is suggested that atomic orbitals with improved long-range behavior can be obtained by using energy-optimized Gaussian basis sets to which Gaussians have been added to satisfy a subset of some recently derived constraints that must be satisfied by the exact Hartree–Fock orbitals. This procedure is demonstrated by illustrative calculations for helium. This method is found to be superior to the adhoc method of adding diffuse Gaussians in an even-tempered fashion. Keywords: Gaussian basis sets, long-range behavior, asymptotic constraints.

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 Quasi-Relativistic Calculation of EPR g-Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

2021 ◽  
Author(s):  
Yannick J. Franzke ◽  
Jason M. Yu
Keyword(s):  
Density Functional ◽  
Hyperfine Coupling Constant ◽  
Basis Set ◽  
Basis Sets ◽  
Generalized Gradient ◽  
Atomic Orbitals ◽  
Experimental Findings ◽  
The Impact ◽  
Derivatives Of ◽  
Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g-tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and "fully" relativistic ansätze for the g-tensor, this implementation results in a gauge-origin invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are considered to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU) and the (multipole-accelerated) resolution of the identity approximation. The X2C ansatz is compared to Douglas-Kroll-Hess theory and the zeroth-order regular approximation for 11 diatomic molecules. The impact of the relativistic Hamiltonian, the basis set, and the density functional approximation is subsequently assessed for a set of 17 transition-metal complexes to complement our previous work on the hyperfine coupling constant [DOI: 10.33774/chemrxiv-2021-wnz1v-v2]. In total, 24 basis sets and 22 density functional approximations are considered. The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent "fully" relativistic four-component theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. Generally, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations are needed to match the experimental findings. Here, hybrids based on the meta -generalized gradient approximation are not an a priori improvement. Compared to the other computational parameters, the impact of the GIAOs and the magnetic balance on the actual results in standard calculations is less pronounced. Routine calculations of large molecules are possible with widely available and comparably low- cost hardware as demonstrated for [Pt(C6Cl5)4]− with 3360 basis functions and three spin-(1/2) La(II) and Lu(II) compounds. Both approaches based on a common gauge origin and GIAOs using triple- ζ basis sets lead to a good agreement with the experimental findings. The best agreement is found with hybrid functionals such as PBE0 and ωB97X-D.

Pseudo-atomic orbitals as basis sets for the O(N) DFT code CONQUEST

2008 ◽  
Vol 20 (29) ◽  
pp. 294206 ◽  
Author(s):  
A S Torralba ◽  
M Todorović ◽  
V Brázdová ◽  
R Choudhury ◽  
T Miyazaki ◽  
...  
Keyword(s):  
Basis Sets ◽  
Atomic Orbitals

Relativistic AB Initio calculations of interaction energies: formulation and application to ionic solids

1986 ◽  
Vol 320 (1553) ◽  
pp. 71-105 ◽  
Keyword(s):  
Ab Initio ◽  
Inner Core ◽  
Basis Set ◽  
Basis Sets ◽  
Computational Techniques ◽  
Central Field ◽  
Atomic Orbitals ◽  
Molecule Formation ◽  
Ionic Solids ◽  
Free Atoms

The theory and computational techniques used in a computer program capable of performing fully relativistic ab initio electronic structure calculations for pairs of interacting atomic species are presented. If the species are ions in a crystal, a description of an ionic solid is obtained. If the two species are otherwise free, the program yields a wavefunction for a diatomic molecule. The molecular wavefunction is an antisymmetrized product of core and valence parts. The core is a Hartree product of the Dirac—Fock atomic orbitals of the free atoms. The largest contribution to the energy arises from the inner-core orbitals, each having negligible overlap with all other orbitals. The purely atomic inner-core energy does not contribute to the binding energy of the molecule, thus obviating the need to calculate the largest part of the molecular energy. The outer core consists of those remaining closed subshells of the isolated atoms that are not significantly affected on molecule formation. All the remaining orbitals, including at least the valence Dirac—Fock atomic orbitals of the free atoms plus further atomic functions needed to describe charge density changes upon molecule formation, are used to construct the valence wavefunction. This can be constructed to take account of correlation between the valence electrons. All atomic functions have central field form with the radial parts defined numerically. This method of constructing the molecular wavefunction avoids the need for large basis sets, ensures that the Dirac small components bear the correct relation to the large components and avoids basis set superposition errors. This program is used to initiate a non-empirical study of the properties of ionic solids. The results show that these properties cannot be reliably predicted by using free ion wavefunctions and that the Watson shell model for describing the non-negligible differences between free and in-crystal ion wavefunctions is not satisfactory. The results demonstrate the importance of inter-ionic dispersive attractions but show that it is not satisfactory to neglect the part quenching of the standard long-range form of these attractions arising from overlap of the ion wavefunctions.

AO integral evaluation using Cartesian exponential type orbitals (CETOs)

1992 ◽  
Vol 70 (2) ◽  
pp. 353-361 ◽  
Author(s):  
Ramon Carbó ◽  
Emili Besalú
Keyword(s):  
Exponential Type ◽  
Molecular Basis ◽  
Basis Sets ◽  
High Level Language ◽  
Integral Evaluation ◽  
Integral Forms ◽  
Exponential Type Orbitals ◽  
High Level ◽  
Integral Formulae ◽  
Nested Summation Symbols

CETO functions and their properties are defined and described, to provide a means of obtaining general expressions for many-center many-electron integral formulae. Compact integral expressions are written by means of nested summation symbols, a new concept developed in this paper. Integrals over CETO functions are computed by means of a set of several auxiliary integral forms. No transformations other than frame rotations are needed to compute the usual integral terms. The formulae obtained are immediately programmable in any high level language and the parallelizable terms are obtained with a simple rule. Results can be considered an encouraging alternative way to solve the STO integral problem. Keywords: many-center AO integrals, molecular basis sets, ETO, STO, CETO.

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