High-accuracy calculations

A second issue is the practice of using the same set of exponents for several sets of functions, such as the 2s and 2p. These are also referred to as general contraction or more often split valence basis sets and are still in widespread use. The acronyms denoting these basis sets sometimes include the letters SP to indicate the use of the same exponents for s andp orbitals. The disadvantage of this is that the basis set may suffer in the accuracy of its description of the wave function needed for high-accuracy calculations. The advantage of this scheme is that integral evaluation can be completed more quickly. This is partly responsible for the popularity of the Pople basis sets described below. 

Several basis schemes are used for very-high-accuracy calculations. The highest-accuracy HF calculations use numerical basis sets, usually a cubic spline method. For high-accuracy correlated calculations with an optimal amount of computing effort, correlation-consistent basis sets have mostly replaced ANO... 

Ahlrichs VDZ, pVDZ, VTZ Available for Li(4.v) to (Ihv) through Kr(14.vl0/ 5d) to (17.vl3/ 6d). These have been used for many high-accuracy calculations. 

Some of the basis sets discussed here are used more often than others. The STO—3G set is the most widely used minimal basis set. The Pople sets, particularly, 3—21G, 6—31G, and 6—311G, with the extra functions described previously are widely used for quantitative results, particularly for organic molecules. The correlation consistent sets have been most widely used in recent years for high-accuracy calculations. The CBS and G2 methods are becoming popular for very-high-accuracy results. The Wachters and Hay sets are popular for transition metals. The core potential sets, particularly Hay-Wadt, LANL2DZ, Dolg, and SBKJC, are used for heavy elements, Rb and heavier. 

The results of this study are somewhat atypical in the sense that the inferred re and tq structures of Sis are nearly the same. This is a somewhat fortuitous circumstance, which cannot be attributed entirely to the fact that Sis appears to be only weakly anharmonic (see cubic constants in Table I), since it has a relatively low-frequency bending mode that is potentially problematic. Nonetheless, it can be stated with some certainty that the structure obtained in the present research is accurate to within 0.002A and 0.2 . Hence, this structure can be used as a reference for benchmarking quantum chemical methods intended for high accuracy calculations on silicon clusters, as well as for comparison with structures of other silicon-containing molecules. 

High-Accuracy Calculations for Heavy and Super-Heavy Elements... 

For this reason, modern Cl calculations are really limited to high accuracy calculations on small molecules. With this limitation both excited and ground states may be treated with uniform accuracy provided the same procedure is followed for each state. This requires a separate SCF calculation, integral transformation, and Cl calculation for each desired state. 

Within the last few years, there has been a resurgence of interest in high-accuracy calculations of simple atomic and molecular systems. For helium, such calculations have reached an extraordinary degree of precision. These achievements are only partially based on the availability of increased computational power. We review the present state of developments for such accurate calculations, with an emphasis on variational methods. Because of the central place occupied by the helium atom and its ground state, much of the discussion centers on methods developed for helium. Some of these methods have also been applied to more complex systems, and calculations on such systems now approach or even surpass a level of precision once only associated with calculations on helium. Hence, other atoms and molecules amenable to high-precision methods are also discussed. 

The recent developments in generalized Valence Bond (GVB) theory have been reviewed by Goddard and co-workers,13 and also the use of natural orbitals in theoretical chemistry,14 15 and the accuracy of computed one-electron properties.18 The Xa method has been reviewed by Johnson,17 and Hurley has discussed high-accuracy calculations on small molecules.18 Several other reviews of interest have appeared in Advances in Quantum Chemistry.17 Localized orbital theory has been reviewed by England, Salmon, and Ruedenberg,19 and the bonding in transition-metal complexes discussed by Brown et a/.20 Finally, the recent developments in computational quantum chemistry have been reviewed by Hall.21... 

Kowalksi K, Piecuch P (2004) New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states. J Chem Phys 120 1715-1738. 

A new field of research opened with the experimental work of Madden and Codling (1963), who proved the existence of autoionizing states embedded in the continuum. High accuracy calculations of resonances were subsequently reported by many researchers. We mention, e.g., the work by Ho (1981), Bhatia and Temkin (1984), Lindroth (1994), Muller et al. (1994), and Burgers (1995). 

High-accuracy calculations clearly require very flexible basis sets extended in a number of ways such as with multiple polarization sets, with diffuse basis function augmentation, and with other than atom-centered functions. Use of smaller bases goes along with less reliability however, with bases smaller than double-zeta in the valence plus one well-chosen set of polarization functions on all centers, including hydrogens, the reliability is so limited that results are not likely to be meaningful for most contemporary problems of weak interaction. 

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