Basis set correlation energy

A survey of these tables reveals that NOF values are more like CCSD(T) calculations, which are very accurate results for the basis-set correlation energies on... 

Basis set Correlation energy included by Errors in predicted geometries Representative references... 

Hamiltonian operator includes only one- and two-electron terms, only singly and doubly substituted configurations can interact directly with the reference, and they typically account for about 95% of the basis set correlation energy of small molecules at their equilibrium geometries,38 where q) provides a good zeroth-order description. Truncation of the Cl space according to excitation class is discussed more fully in section 2.4.1. 

Few studies have employed configuration interaction with all singles, doubles, triples, and quadruples (CISDTQ) because the number of triple and quadruple substitutions grows very rapidly with the number of electrons and basis functions (cf. Table 3). CISDTQ results are most commonly reported in benchmark full Cl studies to indicate the fraction of the basis set correlation energy recovered by triples and quadruples.17,22,39,801234,241,264 Nevertheless, the CISDTQ method has occasionally been used for benchmarking in cases where the full Cl was not technically feasible, because the CISDTQ results are expected to be very close to full Cl for small molecules. For systems with eight electrons or less at their equilibrium geometries, the CISDTQ method recovers more... 

As with Cl calculations, MP calculations with small basis sets are of little practical value, and MP calculations should use a 6-31G or larger basis set for useful results. For DZP basis sets, MP2 calculations on closed-shell molecules typically yield 85% to 95% of the basis-set correlation energy [R. J. Bartlett, Ann. Rev. Phys. Chem., 32, 359 (1981)] and substantially improve the accuracy of equilibrium-geometry and vibrational-frequency predictions. 

Let y be the fraction of the basis-set correlation energy obtained by a CI-SD calculation on a molecule with n electrons. Sasaki showed that an approximate equation satisfied by y is y — 1 = pyn — p, where is a quantity whose value is typically 0.015 to 0.03 for molecules consisting of first-row atoms. For such molecules, use this equation to estimate the percent of the basis-set correlation energy obtained by CI-SD calculations for n = 20,50,100, and 200. 

Exercise 4.13 Consider the exact basis set correlation energy of minimal basis H2 given in Eq. (4.23). Assuming that 1 show that... 

The correlation energies of H2O obtained via a variety of many-election theories within the same one-electron basis are shown in Table 5.3. These results must be compared with the exact basis set correlation energy ( 0.296 a.u.), which is different from the exact correlation energy (—0.37 a.u.) because the one-electron basis is incomplete. Otherwise one would obtain the erroneous conclusion that of all the methods, the lEPA works the best. It is, in fact, the worst it overestimates the correlation energy by 13%. We note that the correlation energies obtained via the L-CCA and CCA are close to each other and to the exact result. Both are superior to SDCI. The closeness of the L-CCA and CCA is somewhat surprizing because the L-CCA involved an apparently drastic approximation to CCA. 

Nyden MR, Petersson GA. Complete basis set correlation energies. 1. The asymptotic convergence of pair natural orbital expansions. J Chem Phys. 1981 75 1843 2. 

When the Hartree-Fock reference determinant offers a very good zero-order description of the system, and no individual determinants or group of determinants make large contributions to the correlated many-body wave-function, the molecule is said to be dominated by dynamical correlation. In such a scenario, the cluster expansion of the wavefunction converges rapidly, and a gold standard correlation method like CCSD(T) [1] truly comes very close to the exact (i.e., full Cl) basis set correlation energy. 

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