Molecular electronic-structure theory part 1
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For both hierarchies, solid improvements are obtained with each increment in X. To estimate the complete basis set limit, an exponential form was used. Among the various approaches considered here, a three-parameter exponential extrapolation applied to the TZP, QZP, and 5ZP results yields the most accurate basis set limits. In addition, 5ZP highest occupied molecular orbital HF energies of some diatomic molecules are evaluated and compared with the corresponding ones obtained with the cc-pV5Z and numerical HF results. Keywords: ab initio, calculations, diatomic molecules, Gaussian basis set, total and orbital HF energies.
6.1: Theoretical Treatment of Electronic Structure
Para estimar o limite do conjunto de base completo, uma forma exponencial foi usada. The use of finite expansions in analytic basis functions lies at the heart of computational molecular electronic structure theory. The growth of central processing power, in uniprocessor and multiprocessor environments, and memory in high-performance computers facilitates the use of increasingly large flexible basis sets in molecular electronic structure calculations which in turn allows calculations of increasing accuracy by reducing the error associated with basis set truncation.
We recall that these sets were constructed from the general contraction scheme of Raffenetti. At the Hartree-Fock HF and Mfller-Plesset secondorder levels, these sets were applied with success in calculations of energies, dissociation energy, harmonic vibrational frequency, and electric dipole moment of a set of diatomic molecules containing atoms of the first- and second-row and second-row diatomic hydrides.
Basis set convergence and extrapolations are among the most important issues of contemporary molecular ab initio theory. This suggests that, when studying the basis set convergence of the energy, one should treat the HF and correlation parts separately. When examining basis set convergence, it is mandatory to have a hierarchical sequence of basis sets with systematic improvements from level to level. The cc-pVXZ basis sets 4,5 constitute such a hierarchy and have been extensively used in previous works on basis set convergence studies.
Thus, the main purpose of this short report is to compare the performance of the two hierarchical sequences of basis sets when used to achieve the CBS limit.
Extrapolation to the complete basis set. In a previous study, Halkier et al. In this equation E R L is the total energy computed at the inter-nuclear distance R and L denotes the highest angular functions of the basis sets used in extrapolation. The quantities A and B are fitting parameters without physical significance. Halkier et al. Thus, we consider in this work only the 3,4,5 collection. Results and Discussion. The NHF energies are also shown.
Modern Electronic Structure Theory, Part 1
A brief look at Table 1 offers some general trends. In all cases enlargement of the basis set causes improvement of E HF. For the HF calculations, the convergence towards the basis set limit is monotonic, smooth, and fast. Email or Customer ID. Forgot password?
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Forgot your username? In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions. This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics.
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Electronic Structure Methods
Table of contents Second Quantization. Spin in Second Quantization.
Orbital Rotations. Exact and Approximate Wave Functions. The Standard Models.
Atomic Basis Functions. Short-Range Interactions and Orbital Expansions.