All-electron basis sets

Table 11.16 H2O MP2 harmonic frequencies (cm function of basis set (all electrons) " ) as a...

Table 2. The Cauchy moments S(k) for Ne calculated at various levels of the CC hierarchy using the d-aug-cc-pV6Z basis-set (all electrons correlated). All numbers in a.u.

Accounting for electron correlation in a second step, via the mixing of a limited number of Slater determinants in the total wave function. Electron correlation is very important for correct treatment of interelectronic interactions and for a quantitative description of covalence effects and of the structure of multielec-tronic states. Accounting completely for the total electronic correlation is computationally extremely difficult, and is only possible for very small molecules, within a limited basis set. Formally, electron correlation can be divided into static, when all Slater determinants corresponding to all possible electron populations of frontier orbitals are considered, and dynamic correlation, which takes into account the effects of dynamical screening of interelectron interaction. 

Since these earlier papers, Laws et a/.575 have computed a large number of one-electron properties, using a near-HF wavefunction, and investigated their dependence on the basis set. All computed properties were within 5 % of experiment for the largest near-HF basis set. Pulay and Meyer576 have calculated the force constants of NHa with a variety of GTO basis sets, all of which yield excellent agreement with experiment. 

With a given basis set and electronic structure method, if all possible excitations (corresponding to physically meaningful transitions, or generated as artifacts from using an incomplete basis and an approximate functional) are included in the SOS for... 

An LCAO description of the electronic structure requires at least the minimal basis set (all orbitals that may be occupied in the ground state of the atom) of five d states per atom and the s state. Consideration of the bands from F ig. 20-1 indicates that in fact the highest-cnergy slates shown (for examples, H,s and X4) have p-like symmetry, and we shall not reproduce this with our minimal set, but the bands at this energy arc unoccupied in any case and it will be of little consequence. For constructing bands in solids, the angular forms for the d states in terms of cartesian coordinates, shown in Eq. (1-21), arc most convenient. Here we shall carry out the calculation explicitly for chromium, in the body-centered cubic structure it is carried out for the face-centered cubic structure in Problem... 

Table 24 The calculated rate constants for the electron-transfer reaction for three different systems in comparison with experimental values. The two different calculated values correspond to two different basis sets. All energies are from ref 82... 

Figure 1 shows the structure of all-trans-polymethineimine and Table 1 lists the optimized geometries for both HF and MBPT(2) methods with three basis sets, STO-3G, 6-31G, and 6-31G [68], We can see that both the size of the basis sets and electron correlation have a strong influence on the stable structure, especially on the difference between the two bond lengths, Tn=c and Yc-n-Table 2 presents the HF and MBPT (2) fundamental vibrational frequencies for all-trans-polymethineimine [68], The vibrational frequencies listed in each... 

Elxcept for the calculations made using the 3-21G basis set, all correlation energies were larger in magnitude for the syn -conformer, i.e. the electron correlation energy favours the syn -conformer for all basis sets besides 3-21G, where the correlation energy is very small, but favours the anti-conformer. 

The three-dimensional potential energy function was determined from the electronic energies of 150 selected conformations. Calculations were performed at the RHF/MP2 level with the 6-31lG(d,p) basis set. All the structures were fully optimized taking into account in some way the interactions with the remaining vibration modes. 

Table 11.9 Total energy (+76 au) as a function of basis set and electron correlation (all electrons)...

It has not been possible within the space available to give a completely comprehensive account of all of the developments which have recently been made in the field of basis set construction, a field that forms the foundation upon which the vast majority of contemporary atomic and molecular electronic structure studies are based. This review has necessarily been selective but should provide the reader with an up-to-date account of the most important aspects of current thinking on the algebraic approximation. It has concentrated on the construction of basis sets for electron correlation energy calculations, for calculations of atomic and molecular properties (other than the energy), for the study of small interaction energies such as van der Waals interactions, for the determination of relativistic effects and for studies of extended molecular systems. 

A special Cl calculation, called full configuration interaction (FCI), is the most accurate, and most expensive, for a given basis set. All possible electron configurations are included. This is equivalent to complete-order coupled-cluster theory. For an A-electron molecule, the FCI result is attained when Ath excitations are included in the Cl or CC calculation. Unlike truncated Cl, such as CISD, FCI is size-consistent. Continuing the... 

Lastly, we mention the basis sets. All ab initio ECP computations after 1984 described in this chapter were done using valence Gaussian basis sets in conjugation with effective core potentials. Typically, valence Gaussian basis sets for the heavy metal are of (3s 3p 3d) quality where the numbers in front of s, p and d specify the numbers of contracted Gaussian functions. For lanthanides and actinides, obviously 4f-type Gaussian functions are included in the basis set. We will describe in individual sections the basis sets used prior-to describing the calculational results. We will also describe the valence space of electrons when ECPs are included. 

Karamanis, R, Maroulis, G., 8c Pouchan, C. (2006a). Basis set and electron correlation effects in all-electron ab initio calculations of the static dipole polarizability of small cadmium selenide clusters, (CdSe) , n = 1,2,3,4. Chemical Physics, 331(1), 19-25. 

The LMP2 and GVB-LMP2 methods can also be u.sed to study thermochemistry. As in all ab initio correlation methods which are applicable to molecules of reasonable size, it is not possible to converge the basis set and electron correlation sufficiently to achieve chemical accuracy without the use of... 

Table 2 CCSD basis set error statistics for sample test sets of reaction energies and atomization energies computed with different CCSD-F12 models and cc-pVXZ-F12 basis sets. All values in kJ/mol per valence electron. Reproduced with permission in modified form from Ref. 55. Copyright 2010 American Institute of Physics.

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). 

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