Abstract
General relations derived from the invariance of the electronic energy of molecules relative to the scaling of the electronic coordinates using the multiplier (R/Ro)ϰ, which depends on the internuclear distance, and relative to the translation of the nuclear core in the Hamiltonian were studied. “Universal” inequalities correct for the energy and its derivative over the internuclear distance R were obtained; the question of the allowed forms of the approximations for the adiabatic potentials of molecules was investigated; the problem of the determination of the optimal form of the electronic Hamiltonian for the calculation of the second derivative of the energy of molecules over R using the perturbation theory was formulated and solved. The use of the optimal Hamiltonian form makes it possible to decrease, by 6–9 times, the absolute value of the second-order relaxation contribution for light molecules (H2 + and H2). With increase in the nuclear charge and the number of electrons, this gain increases rapidly, and the optimal ϰ value approaches 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. Fock, Bemerkung zum Virialsatz, Z. Phys., 63, No. 11/12, 855–858 (1930).
V. Fock, Uber die Gültigkeit des Virialsatzes in der Fermi-Thomas'schen Theorie, Phys. Z. Sowjetunion, 1, No. 6, 747–755 (1932).
J. C. Slater, Electronic Structure of Molecules, McGraw-Hill, New York (1963).
T. K. Rebane, “Generalized convexity properties for energies of quantum-chemical systems,” Teor. Mat. Fiz., 56, No. 3, 432–438 (1983).
N. N. Penkina and T. K. Rebane, “A simple method for the determination of the energy limits of quantum-chemical systems,” Khim. Fiz., 5, No. 7, 867–874 (1986).
L. Salem, “Theoretical interpretation of force constants,” J. Chem. Phys., 38, No. 5, 1227–1236 (1963).
H. Narnhofer and W. Thirring, “Convexity properties for Coulomb systems,” Acta Phys. Austiaca, 41, No. 1, 281–297 (1975).
T. K. Rebane and N. N. Penkina, Scaling Transformation in the Quantum Theory of Atoms and Molecules [in Russian], Izd. Leningr. Univ., Leningrad (1985).
E. S. Kryachko and T. Koga, “Modern aspects of diatomic interaction theory,” Adv. Quantum Chem., 17, 97–223 (1935).
E. S. Kryachko, “On construction of diatomic potential energy functions,” Int. J. Quantum Chem., 25, No. 2, 277–291 (1984),
J. M. Peek, “Eigenparameters for 1sσg and 2pσu orbitals of H +2 ,” J. Chem. Phys., 43, No. 9, 3004–3006 (1965).
M. J. Stephen and J. P. Auffray, “Hyperfine interaction and quadrupole coupling constant in the hydrogen molecule ion,” J. Chem. Phys., 31, No. 2, 1329–1332 (1959).
D. M. Bishop and L. M. Cheung, “Moment functions (including static dipole polarizabilities; and radiative corrections for H +2 ,” J. Phys., B11, No. 18, 3133–3144 (1978).
W. Kolos and L. Wolniewicz, “Potential-energy curves for the X1Σ +g , b3Σ +u , and c1Πu states of the hydrogen molecule,” J. Chem. Phys., 43, No. 7, 2429–2441 (1965).
R. V. Reid and M. L. Vaida, “Electric field gradient and magnetic spin-spin interactions in isotopes of hydrogen molecule,” Phys. Rev., A7, No. 6, 1841–1849 (1973).
G. F. Newell, “The electric quadrupole moment of the deuteron,” Phys. Rev., 78, No. 6, 711–714 (1950).
T. K. Rebane and N. N. Penkina, “New applications of the scaling transformation in the theory of molecules,” Preprint of the Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kiev (1976).
T. K. Rebane, “Inclusion of translation invariance in the analysis of the contributions of perturbation theory in the tensor of molecular force constants,” Teor. Éksp. Khim., 21, No. 3, 280–287 (1985).
N. N. Penkina, and T. K. Rebane, “Refinement of the scaling method of the adiabatic potential functions of molecular ions,” Opt. Spektrosk., 61, No. 4, 751–755 (1986).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 3, pp. 257–267, May–June, 1987.
Rights and permissions
About this article
Cite this article
Rebane, T.K. Study of the general properties of the adiabatic potential energy of molecules using the scaling transformation. Theor Exp Chem 23, 239–248 (1987). https://doi.org/10.1007/BF00531374
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00531374