libgrpp

A library for the evaluation of molecular integrals of the generalized relativistic pseudopotential operator (GRPP) over Gaussian functions.

Features

basis functions:
- Cartesian contracted GTOs
- max angular momentum of basis functions $l_{max} = 10$ (up to $n$-functions, can be increased by hands)
RPP integrals:
- scalar-relativistic part: integrals over the local potential (type 1 integrals)
- scalar-relativistic part: integrals with angular projectors (type 2 integrals)
- integrals over the effective spin-orbit (SO) interaction operator
- integrals over GRPP-specific non-local terms (with projectors onto subvalence shells)
- analytic gradients of GRPP integrals
other one-electron integrals:
- overlap integrals
- nuclear attraction integrals
C and Fortran 90 interfaces
no dependence on external libraries
thread safety

What is a generalized pseudopotential?

Generalized relativistic pseudopotentials (GRPPs) of atomic cores imply the use of different potentials for atomic electronic shells with different principal quantum numbers. GRPPs give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters and solids. GRPPs readily incorporate the effects of Breit electron–electron interactions and one-loop quantum electrodynamics effects. GRPPs are one of the most precise relativistic Hamiltonians at the moment, allowing one to completely bypass any complicated four-component calculations.

Library of generalized pseudopotentials: http://qchem.pnpi.spb.ru/recp

How to compile examples and run tests

mkdir build
cd build
CC=icc FC=ifort cmake ..
make
make test

Citation

A. V. Oleynichenko, A. Zaitsevskii, N. S. Mosyagin, A. N. Petrov, E. Eliav, A. V. Titov.

LIBGRPP: A Library for the Evaluation of Molecular Integrals of the Generalized Relativistic Pseudopotential Operator over Gaussian Functions.

Symmetry, 15(1), 197 (2023)

doi: 10.3390/sym15010197

@article{Oleynichenko2023,
  title = {{LIBGRPP}: A library for the evaluation of molecular integrals of the generalized relativistic pseudopotential operator over {G}aussian functions},
  author = {A. V. Oleynichenko and A. Zaitsevskii and N. S. Mosyagin and A. N. Petrov and E. Eliav and A. V. Titov},
  year = {2022},
  journal = {Symmetry},
  volume = {15},
  year = {2023},
  number = {1},
  article-number = {197},
  url = {https://www.mdpi.com/2073-8994/15/1/197},
  doi = {10.3390/sym15010197}
}

Bug report

Alexander Oleynichenko, alexvoleynichenko@gmail.com

References: more on algorithms used

type 1 integrals (local part):
- L. E. McMurchie, E. R. Davidson. One- and two-electron integrals over Cartesian Gaussian functions. J. Comput. Phys. 26, 218 (1978)
- J. O. Jensen, A. H. Carrieri, C. P. Vlahacos, D. Zeroka, H. F. Hameka, C. N. Merrow. Evaluation of one-electron integrals for arbitrary operators $V(r)$ over Cartesian Gaussians: Application to inverse-square distance and Yukawa operators. J. Comput. Chem. 14, 986 (1993)
- B. Gao, A. J. Thorvaldsen, K. Ruud. GEN1INT: A unified procedure for the evaluation of one-electron integrals over Gaussian basis functions and their geometric derivatives. Int. J. Quantum Chem. 111, 858 (2011)
type 2 integrals (semilocal part):
- L. E. McMurchie, E. R. Davidson. Calculation of integrals over ab initio pseudopotentials. J. Comput. Phys. 44, 289 (1981)
- C. K. Skylaris, L. Gagliardi, N. C. Handy, A. G. Ioannou, S. Spencer, A. Willetts, A. M. Simper. An efficient method for calculating effective core potential integrals which involve projection operators. Chem. Phys. Lett. 296, 445 (1998)
- R. Flores-Moreno, R. J. Alvarez-Mendez, A. Vela, A. M. Köster. Half-numerical evaluation of pseudopotential integrals. J. Comput. Chem. 27, 1009 (2006)
- C. van Wüllen. Numerical instabilities in the computation of pseudopotential matrix elements. J. Comput. Chem. 27, 135 (2006)
- R. A. Shaw, J. G. Hill. Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials. J. Chem. Phys. 147, 074108 (2017)
spin-orbit integrals:
- R. M. Pitzer, N. W. Winter. Spin-orbit (core) and core potential integrals. Int. J. Quantum Chem. 40, 773 (1991)
integrals non-local terms (with projectors onto subvalence shells):
- A. V. Oleynichenko, A. Zaitsevskii, N. S. Mosyagin, A. N. Petrov, E. Eliav, A. V. Titov. LIBGRPP: A library for the evaluation of molecular integrals of the generalized relativistic pseudopotential operator over Gaussian functions. Symmetry, 15(1), 197 (2023).

Libgrpp

Install / Use

README