# Calculation of the molecular integrals with the range-separated correlation factor.

@article{Sikowski2014CalculationOT, title={Calculation of the molecular integrals with the range-separated correlation factor.}, author={Michał Siłkowski and Michał Lesiuk and Robert Moszynski}, journal={The Journal of chemical physics}, year={2014}, volume={142 12}, pages={ 124102 } }

Explicitly correlated quantum chemical calculations require calculations of five types of two-electron integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called "range-separated" correlation factor is used. This correlation factor combines the well-known short range behaviour resulting from the electronic cusp condition, with the exact long-range…

## 5 Citations

### Monte Carlo explicitly correlated second-order many-body perturbation theory.

- ChemistryThe Journal of chemical physics
- 2016

A stochastic algorithm proposed and implemented that computes a basis-set-incompleteness (F12) correction to an ab initio second-order many-body perturbation energy as a short sum of 6- to 15-dimensional integrals of Gaussian-type orbitals, confirming the best overall performance of the Slater-type geminal among 6 forms satisfying the same cusp conditions.

### Dispersion Energy of Symmetry-Adapted Perturbation Theory from the Explicitly Correlated F12 Approach.

- ChemistryJournal of chemical theory and computation
- 2018

Methods of the explicitly correlated F12 approach are applied to the problem of calculating the uncoupled second-order dispersion energy in symmetry-adapted perturbation theory and clearly outperforms regular orbital calculations in the basis set of quintuple-ζ quality.

### Combining Slater-type orbitals and effective core potentials

- Chemistry
- 2017

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation…

### Perspective: Explicitly correlated electronic structure theory for complex systems.

- MathematicsThe Journal of chemical physics
- 2017

This perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids.

## References

SHOWING 1-10 OF 85 REFERENCES

### Evaluation of molecular integrals over Gaussian basis functions

- Computer Science
- 1976

This method is computationally simple and numerically well behaved, and has been incorporated into a new molecular SCF program HONDO, and preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.

### Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1950

This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and…

### Linear R12 Terms in Coupled Cluster Theory

- Chemistry
- 2003

Highly accurate molecular electronic energies and properties can be obtained computationally when the molecular electronic trial wave function depends explicitly on the inter-electronic distances r…

### Evaluation of two-electron integrals for explicit r12 theories

- Computer Science
- 2000

We present a practical scheme for the evaluation of nonstandard two-electron molecular integrals that appear in ab initio theories employing explicitly correlated wave functions with linear r12 terms…

### Explicitly-correlated Gaussian geminals in electronic structure calculations

- Computer Science
- 2010

The capability of explicitly correlated Gaussian (ECG) functions to accurately describe many-electron atoms and molecules was demonstrated only in the early 1980s when Monkhorst, Zabolitzky and the present authors cast the many-body perturbation theory (MBPT) and coupled cluster (CC) equations as a system of integro-differential equations and developed techniques of solving these equations with two-Electron ECG functions (Gaussian-type geminals, GTG).

### Weak intermolecular interactions calculated with diffusion Monte Carlo.

- ChemistryThe Journal of chemical physics
- 2005

The performance of fixed node diffusion Monte Carlo (FNDMC) for weakly interacting molecules is investigated and it is found that accurate reference binding energies of the water, the ammonia, and the T-shaped as well as the parallel-displaced benzene dimer are correctly reproduced by FNDMC.

### Gaussian Geminals in Coupled Cluster and Many-Body Perturbation Theories

- Physics, Chemistry
- 2003

The capability of modern electronic structure theory to quantitatively predict properties of atomic and molecular systems strongly depends on how accurately the electron correlation effects can be…

### Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study.

- PhysicsThe Journal of chemical physics
- 2008

A quantum Monte Carlo study of the hydrogen-benzene system where binding is very weak is presented, demonstrating that the binding is well described by a Jastrow correlated single determinant geminal wave function with an optimized compact basis set that includes diffuse orbitals.