Przybytek Michał, Jeziorski Bogumil
Faculty of Chemistry, Warsaw University, Pasteura 1, 02-093 Warsaw, Poland.
J Chem Phys. 2005 Oct 1;123(13):134315. doi: 10.1063/1.2042453.
We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 3S state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C6 through C14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 3S helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest 5Sigmag+ state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower VL(R) and upper VU(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C6 through C12 (including C11). We found that the complete-basis-set BO potential has a well depth De=1048.24+/-0.36 cm-1. The highest rotationless vibrational level is bound by D14=90.2+/-4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for De and D14 were obtained using the VL(R) and VU(R) potentials. The S-wave scattering length computed using the VL(R), V(R), and VU(R) potentials (assuming atomic masses) is aL=7.41 nm, a=7.54 nm, and aU=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D14 and of a (both computed assuming nuclear masses) are 87.4+/-6.7 MHz and 7.64+/-0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.
我们开发了一系列相关性一致的极化多ζ基组，这些基组是专门针对氦原子的2 3S态能量进行优化的。随后，这些基组通过针对范德华常数C6至C14进行优化的弥散函数进行了扩充，这些常数决定了在大原子间距R下2 3S氦原子之间二阶色散相互作用的渐近行为。所得基组被用于计算氦二聚体最低5Sigmag+态的玻恩-奥本海默（BO）势能。采用耦合簇和全组态相互作用技术来考虑电子相关效应。使用基数外推技术获得相互作用势的完全基组极限V(R)，并找到其下限VL(R)和上限VU(R)。所得势能被拟合为一个包含精确范德华常数C6至C12（包括C11）的解析函数。我们发现完全基组BO势能的阱深De = 1048.24±0.36 cm-1。最高的无转动振动能级由D14 = 90.2±4.7 MHz束缚，比之前最精确的估计值15.2 MHz要强得多。De和D14的误差范围是使用VL(R)和VU(R)势能获得的。使用VL(R)、V(R)和VU(R)势能（假设原子质量）计算的S波散射长度分别为aL = 7.41 nm、a = 7.54 nm和aU = 7.69 nm。我们还计算了对BO势能的绝热、相对论和量子电动力学（QED）修正。当考虑这些修正时，D14和a（均假设核质量计算）的值分别为87.4±6.7 MHz和7.64±0.20 nm；误差范围现在也反映了所包含的绝热、相对论和QED修正的不确定性。我们研究得出的散射长度值超出了基于自旋极化氦原子玻色-爱因斯坦凝聚体性质的所有实验测定的误差范围。
