scholarly journals EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

2009 ◽  
Vol 08 (04) ◽  
pp. 597-602 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Charge Densities ◽  
Hartree Fock ◽  
Expansion Formulae ◽  
Multicenter Multielectron Integrals ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
Exponential Type Orbitals ◽  
The One

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

EVALUATION OF ONE- AND TWO-ELECTRON MULTICENTER INTEGRALS OF YUKAWA-LIKE SCREENED CENTRAL AND NONCENTRAL INTERACTION POTENTIALS OVER SLATER ORBITALS USING ADDITION THEOREMS

2005 ◽  
Vol 16 (06) ◽  
pp. 837-842 ◽  
Author(s):  
I. I. GUSEINOV ◽  
B. A. MAMEDOV
Keyword(s):  
Numerical Stability ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Interaction Potentials ◽  
Multicenter Integrals ◽  
Expansion Formulae ◽  
Slater Orbitals ◽  
Exponential Type Orbitals ◽  
The One

By the use of complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETOs, where α =1, 0, -1, -2, …), the series expansion formulae are established for the one- and two-electron multicenter integrals of arbitrary Yukawa-like screened central and noncentral interaction potentials (YSCPs and YSNCPs) in terms of two- and three-center overlap integrals of three Slater type orbitals (STOs). The convergence of the series is tested by the concrete cases of parameters. The formulae given in this study for the evaluation of one- and two-electron multicenter integrals of YSCPs and YSNCPs show good rate of convergence and numerical stability.

COMPUTATION OF THREE-CENTER OVERLAP INTEGRALS OVER NONINTEGER n SLATER TYPE ORBITALS USING Ψα-ETO

2007 ◽  
Vol 06 (03) ◽  
pp. 641-646 ◽  
Author(s):  
I. I. GUSEINOV ◽  
B. A. MAMEDOV
Keyword(s):  
Exponential Type ◽  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Interaction Potentials ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using complete orthonormal sets of Ψα-exponential type orbitals (Ψα- ETO , α = 1, 0, -1, -2,…), the three-center overlap integrals over noninteger n STO (NISTO) appearing in the evaluation of multicenter–multielectron integrals of central and noncentral interaction potentials are calculated. The final results are expressed in terms of one- or two-center overlap integrals between NISTO and integer n STO (ISTO). The formulas obtained are valid for arbitrary noninteger principal quantum numbers, screening parameters, and location of NSTO.

scholarly journals The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit

2018 ◽  
Vol 71 (4) ◽  
pp. 238 ◽  
Author(s):  
Manoj K. Kesharwani ◽  
Amir Karton ◽  
Nitai Sylvetsky ◽  
Jan M. L. Martin
Keyword(s):  
Computational Cost ◽  
The Other ◽  
Basis Set ◽  
Basis Sets ◽  
Explicitly Correlated ◽  
Non Covalent Interactions ◽  
Explicitly Correlated Methods ◽  
The One ◽  
High Level ◽  
Covalent Interactions

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.

scholarly journals UNSYMMETRICAL AND SYMMETRICAL ONE-RANGE ADDITION THEOREMS FOR SLATER TYPE ORBITALS AND COULOMB–YUKAWA-LIKE CORRELATED INTERACTION POTENTIALS OF INTEGER AND NONINTEGER INDICES

2008 ◽  
Vol 07 (02) ◽  
pp. 257-262 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Basis Functions ◽  
Slater Type Orbitals ◽  
Addition Theorems ◽  
Slater Type ◽  
Interaction Potentials ◽  
Hartree Fock ◽  
Quantum Numbers ◽  
Noninteger Principal Quantum Numbers ◽  
Multicenter Multielectron Integrals ◽  
Exponential Type Orbitals

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of ψa-exponential type orbitals (ψa-ETOs, a = 1, 0, -1, -2,…), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb–Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree–Fock–Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.

Molecular overlap integrals with exponential‐type orbitals

1986 ◽  
Vol 84 (3) ◽  
pp. 1598-1605 ◽  
Author(s):  
A. K. Bhattacharya ◽  
S. C. Dhabal
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Exponential Type Orbitals

Comparison of Experimental and Theoretical Structure Amplitudes and Valence Charge Densities of GaAs

1998 ◽  
Vol 54 (3) ◽  
pp. 231-239 ◽  
Author(s):  
J. Stahn ◽  
M. Möhle ◽  
U. Pietsch
Keyword(s):  
Ab Initio ◽  
Density Functional ◽  
Theoretical Data ◽  
Charge Densities ◽  
Hartree Fock ◽  
Structure Factors ◽  
Nearest Neighbours ◽  
Kinematic Limit ◽  
Order Of Magnitude ◽  
The One

The current best sets of X-ray structure amplitudes for GaAs, gallium arsenide, are completed by highly precise data recorded at 0.50 < sin θ/λ < 1.35 Å−1. For the strong reflections the required accuracy of ΔF/F ≤ 1% was realized by the use of Pendellösung measurements at λ = 0.30 Å, recording the integral intensities as a function of the effective thickness from ∼500 µm thick GaAs wafers. Additionally, several weak reflections were determined from their integral intensities within the kinematic limit at wavelengths λ = 0.3, 0.56 and 0.71 Å. From these data individual Debye–Waller factors for gallium and arsenic were determined using the model of independent spherical atoms [B Ga = 0.666 (4) and B As = 0.566 (4) Å2]. The extended set of experimental structure factors now available is compared with those obtained by ab initio solid-state Hartree–Fock (HF) and density functional (DF) calculations. Therefore, the theoretical data were adapted to room temperature using the experimentally evaluated Debye–Waller factors and the model mentioned above. The valence and difference charge densities obtained from experimental and theoretical data show the expected charge accumulation between nearest neighbours slightly shifted towards the arsenic site. The disagreement remaining between the experimental and theoretical data, on the one hand, and between those of both ab initio methods, on the other hand, are of the same order of magnitude.

scholarly journals The S66 noncovalent interactions benchmark reconsidered using explicitly correlated methods near the basis set limit

2017 ◽  
Author(s):  
Manoj Kumar Kesharwani ◽  
Amir Karton ◽  
Nitai Sylvetsky ◽  
Jan M. L. Martin
Keyword(s):  
Noncovalent Interactions ◽  
Computational Cost ◽  
The Other ◽  
Basis Set ◽  
Basis Sets ◽  
Other Hand ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
The One ◽  
High Level

<p>The S66 benchmark for noncovalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 “high-level corrections” are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66x8 problem set in particular, and for accurate calculations on noncovalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, while half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.</p>

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