×

H2SOLV: Fortran solver for diatomic molecules in explicitly correlated exponential basis. (English) Zbl 1380.65482

Summary: We present the Fortran package H2SOLV for an efficient computation of the nonrelativistic energy levels and the wave functions of diatomic two-electron molecules within the Born-Oppenheimer approximation. The wave function is obtained as a linear combination of the explicitly correlated exponential (Kołos-Wolniewicz) functions. The computations of H2SOLV are performed within the arbitrary-precision arithmetics, where the number of working digits can be adjusted by the user. The key part of H2SOLV is the implementation of the algorithm of an efficient computation of the two-center two-electron integrals for arbitrary values of internuclear distances developed by one of us [the first author, “Efficient approach to two-center exponential integrals with applications to excited states of molecular hydrogen”, Phys. Rev. A 88, No. 2, Article ID 022507, 8 p. (2013; doi:10.1103/physreva.88.022507)]. This have been one of the long-standing problems of quantum chemistry. The code is parallelized, suitable for large-scale computations limited only by the computer resources available and can produce highly accurate results. As an example, we report several benchmark results obtained with H2SOLV, including the energy value accurate to 18 decimal digits.

MSC:

65Z05 Applications to the sciences
81V55 Molecular physics
35Q40 PDEs in connection with quantum mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Software:

gmp; H2SOLV; MPFR
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Liu, J., J. Chem. Phys., 130, Article 174306 pp. (2009)
[2] Liu, J., J. Chem. Phys., 132, Article 154301 pp. (2010)
[3] Dickenson, G. D., Phys. Rev. Lett., 110, Article 193601 pp. (2013)
[4] Piszczatowski, K.; Łach, G.; Przybytek, M.; Komasa, J.; Pachucki, K.; Jeziorski, B., J. Chem. Theor. Comput., 5, 3039 (2009)
[5] Komasa, J.; Piszczatowski, K.; Łach, G.; Przybytek, M.; Jeziorski, B.; Pachucki, K., J. Chem. Theor. Comput., 7, 3105 (2011)
[6] Pachucki, K.; Komasa, J., J. Chem. Phys., 130, Article 164113 pp. (2009)
[7] Heitler, W.; London, F., Z. Phys., 44, 455 (1927)
[8] James, H. M.; Coolidge, A. S., J. Chem. Phys., 1, 825 (1933)
[9] Kołos, W.; Wolniewicz, L., Phys. Rev. Lett., 20, 243 (1968)
[10] Kołos, W.; Wolniewicz, L., J. Chem. Phys., 49, 404 (1968)
[11] Harris, F. E., Int. J. Quantum Chem., 88, 701 (2002)
[12] Pachucki, K., Phys. Rev. A, 88, Article 022507 pp. (2013)
[14] Pachucki, K., Phys. Rev. A, 82, Article 032509 pp. (2010)
[15] Pachucki, K., Phys. Rev. A, 85, Article 042511 pp. (2012)
[18] Herring, C.; Flicker, M., Phys. Rev., 134, A362 (1964)
[19] Burrows, B. L.; Dalgarno, A.; Cohen, M., Phys. Rev. A, 86, Article 052525 pp. (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.