Abstract
Moments of the molecular electron density can be related directly to several experimental observables, but formerly they have only been accurately calculated through methods which lack consistency with standard quantum chemical methods. Here we report analytical solutions to the basic molecular integrals required to compute the moments of the molecular electron charge density over Gaussian basis functions. These are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of the molecular electronic structure. Illustrative calculations for the hydrogen molecule, at both the Hartree–Fock and the full configuration interaction levels of theory, are shown and discussed in connection with observables linked directly to some of the calculated moments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Dupuis, D. Spangler and J.J. Wendoloski, NRCC software catalog, Program QG01, University of California, Berkeley, CA (1980).
S. Fraga and G. Malli, Many-Electron System: Properties and Interactions (W.B. Saunders Co., Philadelphia, PA, 1968).
M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzales, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, Gaussian '92/DFT, Revision F.4 (Gaussian, Inc., Pittsburgh, PA, 1992).
S.R. Gadre and S.J. Chakravorty, J. Chem. Phys. 84 (1986) 7051.
F.W. King, Phys. Rev. A 35 (1988) 6017.
W. Kolos and C.C.J. Roothaan, Rev. Mod. Phys. 32 (1960) 219.
W. Kolos and L. Wolniewicz, J. Chem. Phys. 43 (1965) 2429.
R.K. Pattak, B.S. Sharma and A.J. Thakkar, J. Chem. Phys. 85 (1986) 958.
R. Pucci and N.H. March, J. Chem. Phys. 76 (1982) 4089.
P. Pyykkö and Y. Zhao, Report HUKI 1-89, University of Helsinki (1989).
N.F. Ramsey, Molecular Beams (Oxford University Press, Oxford, 1956).
V.R. Saunders, in: Computational Techniques in Quantum Chemistry and Molecular Physics (Reidel, Dordrecht, 1975).
M.W. Schmidt, K.K. Baldridge, J.A. Boatz, J.H. Jensen, S. Koseki, M.S. Gordon, K.A. Nguyen, T.L. Windus and S.T. Elbert, QCPE Bull. 10 (1990) 42.
P.E.M. Siegbahn and B. Liu, J. Chem. Phys. 68 (1978) 2457.
J.M. Ugalde, C. Sarasola, L. Dominguez and R.J. Boyd, J. Math. Chem. 6 (1991) 51.
J. Wang and V.H. Smith, Jr., J. Phys. B 27 (1994) 5159.
J.S. Wright and V.J. Barclay, J. Chem. Phys. 86 (1987) 3054.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sarasola, C., Elorza, J. & Ugalde, J. Closed‐form analytical solutions for the calculation of the moments of the molecular electron density. Journal of Mathematical Chemistry 23, 405–414 (1998). https://doi.org/10.1023/A:1019145913874
Issue Date:
DOI: https://doi.org/10.1023/A:1019145913874