Variational estimates of quantities in perturbation theory second approximations

Static dipole polarizability for the 1sσ electronic state of the H+2molecular ion

“…If nonrelativistic energy values of H + 2 (0, 0) are required to 10 −15 au accuracy, then the wavefunctions must be accurate, at least, to this same level. The wavefunctions, 5 .283 2.202 [22] 5 .173 1.847 [21] 5 .084 1.767 [20] 5 .06 1.76 [18] 5 .199 1.829 [14] 5 .077 65 1.757 65 This work 5.077 6490 1.757 6486 however, are typically accurate to less than half as many significant figures as the energy. From table 3, the precision nonrelativistic energy value E 0 at bond length R = 2.0 au can easily reach 15 significant digits for the basic function number N = 60 and the unperturbed wavefunction 0 has 10 significant digits using the same number of terms.…”

“…Bishop and Cheung [14] had calculated variationally the first accurate mean electronic polarizability over a wide range of internuclear separations. Rahman [19] and Adamov et al [22] had performed 5.061 1.758 [23] 5.283 2.202 [22] 5.173 1.847 [21] 5.084 1.767 [20] 5.06 1.76 [18] 5.199 1.829 [14] 5.077 65 1.757 65 this work 5.077 6490 1.757 6486 accurate first order variational calculations near the equilibrium distance R = 2.0 a.u..…”

“…Static dipole polarizability of the 1Sσ(v = 0, J = 0) electronic state of the the H + 2 molecular ion had been calculated theoretically many times in the Born-Oppeheimer approximation [18,19,20,21,22,23]. Furthermore, several laser spectroscopy experiments have been proposed [24,25,26] for high precision measurements of the rovibrational spectrum of hydrogen molecular ions H + 2 and HD + .…”

“…The static dipole polarizability of the 1Sσ (v = 0, J = 0) electronic state of the H + 2 molecular ion has been calculated theoretically many times in the Born-Oppenheimer approximation [18][19][20][21][22][23].…”

Theoretical Studies on the M′‐Centre in Alkali Halide Crystals

“…I n this case it was necessary t o derive the three cent,rv integrals with respect t o the coordinates of the third centre. We have expressed these integrals by some auxiliary functions (see [19]), and the derivat,ives ~( T c~ calculated in elliptical coordinates. I n detail we considered the calculations of this kind in [20].…”