Czakó Gábor, Furtenbacher Tibor, Barletta Paolo, Császár Attila G, Szalay Viktor, Sutcliffe Brian T
Laboratory of Molecular Spectroscopy, Institute of Chemistry, Eötvös University, P. O. Box 32, H-1518 Budapest 112, Hungary.
Phys Chem Chem Phys. 2007 Jul 14;9(26):3407-15. doi: 10.1039/b701911d. Epub 2007 May 24.
A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.
已开发出一种技术，原则上通过处理雅可比坐标和R(1)嵌入中给出的三原子旋转 - 振动动能算符中存在的重要奇点，能够确定三原子分子的完整旋转 - 振动态本征谱。与双原子型坐标R(1)相关的奇异项，被认为对光谱应用不重要，因此未给予特别关注。这项工作扩展了先前的[《化学物理杂志》，2005年，122卷，024101]仅振动方法，并采用了广义有限基表示（GFBR），得到了一个非对称哈密顿矩阵[《化学物理杂志》，2006年，124卷，014110]。所使用的基组是通过将与R(1)相关的一维离散变量表象（DVR）基与一个五维非直积基进行直积得到的，后者由依赖于导致奇点的距离型坐标的贝塞尔 - DVR函数、依赖于雅可比角的关联勒让德多项式以及依赖于三个欧拉角的旋转函数耦合而成。ARPACK软件包中的稳健隐式重启阿诺尔迪方法用于确定非对称哈密顿矩阵的多个本征值。通过确定略高于其线性化势垒的H(3)(+)基电子态的旋转 - 振动能级，证明了所提出方法的适用性。通过一种替代方法检查本征能量的收敛性，该方法采用以拉道坐标表示的哈密顿量、标准直积基且不处理奇点。
