Laboratory of Molecular Spectroscopy, Institute of Chemistry, Eötvös University, H-1518 Budapest 112, P.O. Box 32, Hungary.
Phys Chem Chem Phys. 2012 Jan 21;14(3):1085-106. doi: 10.1039/c1cp21830a. Epub 2011 Oct 13.
Developments during the last two decades in nuclear motion theory made it possible to obtain variational solutions to the time-independent, nuclear-motion Schrödinger equation of polyatomic systems as "exact" as the potential energy surface (PES) is. Nuclear motion theory thus reached a level whereby this branch of quantum chemistry started to catch up with the well developed and widely applied other branch, electronic structure theory. It seems to be fair to declare that we are now in the fourth age of quantum chemistry, where the first three ages are principally defined by developments in electronic structure techniques (G. Richards, Nature, 1979, 278, 507). In the fourth age we are able to incorporate into our quantum chemical treatment the motion of nuclei in an exact fashion and, for example, go beyond equilibrium molecular properties and compute accurate, temperature-dependent, effective properties, thus closing the gap between measurements and electronic structure computations. In this Perspective three fundamental algorithms for the variational solution of the time-independent nuclear-motion Schrödinger equation employing exact kinetic energy operators are presented: one based on tailor-made Hamiltonians, one on the Eckart-Watson Hamiltonian, and one on a general internal-coordinate Hamiltonian. It is argued that the most useful and most widely applicable procedure is the third one, based on a Hamiltonian containing a kinetic energy operator written in terms of internal coordinates and an arbitrary embedding of the body-fixed frame of the molecule. This Hamiltonian makes it feasible to treat the nuclear motions of arbitrary quantum systems, irrespective of whether they exhibit a single well-defined minimum or not, and of arbitrary reduced-dimensional models. As a result, molecular spectroscopy, an important field for the application of nuclear motion theory, has almost black-box-type tools at its disposal. Variational nuclear motion computations, based on an exact kinetic energy operator and an arbitrary PES, can now be performed for about 9 active vibrational degrees of freedom relatively straightforwardly. Simulations of high-resolution spectra allow the understanding of complete rotational-vibrational spectra up to and beyond the first dissociation limits. Variational results obtained for H(2)O, H, NH(3), CH(4), and H(2)CCO are used to demonstrate the power of the variational techniques for the description of vibrational and rotational excitations. Some qualitative features of the results are also discussed.
在过去的二十年中，核运动理论的发展使得多原子体系的非时变、核运动薛定谔方程的变分解成为可能，其精确程度与势能面（PES）相当。核运动理论因此达到了一个水平，使得这个量子化学分支开始赶上发展完善且广泛应用的另一个分支，即电子结构理论。似乎可以公平地宣称，我们现在正处于量子化学的第四个时代，前三个时代主要由电子结构技术的发展所定义（G. Richards，《自然》，1979，278，507）。在第四个时代，我们能够以精确的方式将核运动纳入我们的量子化学处理中，例如超越平衡分子性质并计算准确的、温度依赖的有效性质，从而缩小测量和电子结构计算之间的差距。在这篇观点文章中，提出了三种用于变分求解非时变核运动薛定谔方程的基本算法，这些算法都使用了精确的动能算符：一种基于定制的哈密顿量，一种基于 Eckart-Watson 哈密顿量，还有一种基于通用的内坐标哈密顿量。本文认为，最有用和最广泛适用的程序是基于包含动能算符的哈密顿量的第三种程序，该动能算符由内坐标表示，分子的固定坐标系任意嵌入。这个哈密顿量使得处理任意量子体系的核运动成为可能，无论它们是否表现出一个明确的最小值，以及任意的简化模型。因此，核运动理论的一个重要应用领域，分子光谱学，几乎拥有了其可支配的黑盒式工具。基于精确的动能算符和任意 PES 的变分核运动计算现在可以相对直接地对大约 9 个活跃的振动自由度进行计算。高分辨率光谱的模拟允许对完整的旋转-振动光谱进行理解，直至并超过第一个离解极限。H(2)O、H、NH(3)、CH(4)和 H(2)CCO 的变分结果用于证明变分技术在描述振动和转动激发方面的强大功能。还讨论了结果的一些定性特征。
