Simplifications in the generation and transformation of two‐electron integrals in molecular calculations

@article{Beebe1977SimplificationsIT,
  title={Simplifications in the generation and transformation of two‐electron integrals in molecular calculations},
  author={Nelson H. F. Beebe and J. Linderberg},
  journal={International Journal of Quantum Chemistry},
  year={1977},
  volume={12},
  pages={683-705}
}
Approximate numerical linear dependence among the columns of the two-electron integral matrix and the positiveness of the Coulomb operator are exploited in order to reduce the number of integrals that need to be calculated when a numerical accuracy is given by the machine in use or by the choice of the investigator. Numerical results presented indicate that the method leads to an algorithm for carrying out the two-electron integral four-index transformation which in practice can be achieved in… 
Analytic derivatives for the Cholesky representation of the two-electron integrals.
TLDR
An implementation of gradients at the nonhybrid density functional theory level is presented, and sample calculations demonstrate that the errors in equilibrium geometries due to the Cholesky representation of the integrals can be controlled by adjusting the decomposition threshold.
COUPLED-CLUSTER THEORY EMPLOYING APPROXIMATE INTEGRALS : AN APPROACH TO AVOID THE INPUT/OUTPUT AND STORAGE BOTTLENECKS
By representing orbital products in an expansion basis, certain classes of two‐electron integrals are approximated for use in CCSD(T) calculations (singles and doubles coupled‐cluster plus a
Four-Index Transformations
Atomic and molecular electronic structure calculations are most frequently performed by employing basis set expansion techniques; that is, by invoking the algebraic approximation (for recent reviews
Integral approximations in ab initio, electron propagator calculations.
TLDR
Treatments of interelectronic repulsion that avoid four-center integrals have been incorporated in ab initio, electron-propagator calculations with diagonal self-energy matrices, reducing storage requirements and lowering the scaling of integral transformations to the molecular orbital base.
Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals.
TLDR
A generalized dual space strategy is presented that sheds a new light on variants over the standard density and Coulomb-fitting schemes, including the possibility of introducing minimization constraints.
Conventional and unconventional techniques in quantum chemistry
The computational cost of ab initio molecular electronic structure calculations is dominated by the generation of electron–electron repulsion integrals, of which there are O(N4), where N is the
Direct calculation of the Coulomb matrix: Slater-type orbitals
It is proved that the evaluation of the Coulomb potential and the calculation of its matrix elements can be carried out in separate steps whose costs formally increase as the square of the number of
Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods.
TLDR
It is shown that RI methods lead to insignificant errors only, which are partly comparable to or even better than that of CD treatments; but RI procedures are superior in speed.
Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals.
TLDR
A recurrence relation is derived that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and a near-optimal algorithm for its use is proposed.
On the use of spatial symmetry in atomic‐integral calculations: An efficient permutational approach
TLDR
It is proved that lobe orbitals are always more efficient than the familiar Cartesian Gaussians, in the sense that GLOS provide the shortest integral lists.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
Multicenter Integrals in Quantum Mechanics. II. Evaluation of Electron‐Repulsion Integrals for Slater‐Type Orbitals
A unified method for the evaluation of electron‐repulsion integrals for Slater‐type orbitals is described. This method applies to every electron‐repulsion integral needed for polyatomic molecule
Molecular Orbital Studies of Diatomic Molecules. I. Method of Computation for Single Configurations of Heteronuclear Systems
This paper describes a method of molecular orbital calculation for heteronuclear diatomic molecules, in the approximation of a single spatial configuration which is a product of one‐electron
Charge‐conserving integral approximations for ab initio quantum chemistry
Three charge‐conserving integral approximations are presented that either zero or economically calculate the less important integrals that arise in quantum chemical calculations on molecular systems
GROUP ALGEBRA, CONVOLUTION ALGEBRA, AND APPLICATIONS TO QUANTUM MECHANICS.
The symmetry group of the Hamiltonian plays a fundamental role in quantum theory in the classification of stationary states and in studying transition probabilities and selection rules. It is here
On methods for converging open-shell Hartree-Fock wave-functions
The ‘level-shifting’ technique of Saunders and Hillier is extended so as to allow guaranteed convergence of the restricted Hartree-Fock energy for many commonly found open-shell configurations. The
Lower Bounds for Eigenvalues with Displacement of Essential Spectra
New constructions of comparison operators for rigorous lower bounds to eigenvalues of a class of self-adjoint operators are presented. The formulation uses noncompact finite perturbations to displace
Optimized transformation of four center integrals
The n5-order algorithm for the transformation of the quantummechanical four center integrals is analyzed. An optimum implementation of this algorithm for computers with a reasonable amount of
The two-electron integral transformation and two-body density matrix transformation
Ann5 algorithm for the transformation of quantum-mechanical four centre functions is presented in a form best suited for computers having a virtual memory capability.
...
1
2
...