Correlation consistent polarized basis set

The structure of the cyclic water trimer was optimized also using correlation-consistent polarized basis sets, augmented with additional diffuse functions . Whereas the three R(0"0) distances are all different at the SCF level, MP2 correlation brings them within 0.002 A of being equal to one another. The three H-bonds are all nonlinear by about 30°, that is, e(OH--O) 150°. 

Correlation-consistent polarized basis sets are another popular choice, so called because they have been optimized using correlated (CISD) wavefunctions. These basis sets are labeled with the prefix cc-p before the valence zeta notation. They can then be augmented with diffuse functions, to give aug-cc-pVDZ, for... 

Electron correlation studies demand basis sets that are capable of very high accuracy, and the 6-31IG set I used for the examples above is not truly adequate. A number of basis sets have been carefully designed for correlation studies, for example the correlation consistent basis sets of Dunning. These go by the acronyms cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z and cc-pV6Z (double, triple, quadruple, quintuple and sextuple-zeta respectively). They include polarization functions by definition, and (for example) the cc-pV6Z set consists of 8. 6p, 4d, 3f, 2g and Ih basis functions. 

G(d,p), both intermediate and TS geometries become more reliable, at least as judged from a comparison with the corresponding geometries achieved using the augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) basis sets.32... 

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

The quality of quantum-chemical calculations depends not only on the chosen n-electron model but also critically on the flexibility of the one-electron basis set in terms of which the MOs are expanded. Obviously, it is possible to choose basis sets in many different ways. For highly accurate, systematic studies of molecular systems, it becomes important to have a well-defined procedure for generating a sequence of basis sets of increasing flexibility. A popular hierarchy of basis functions are the correlation-consistent basis sets of Dunning and coworkers [15-17], We shall use two varieties of these sets the cc-pVXZ (correlation-consistent polarized-valence X-tuple-zeta) and cc-pCVXZ (correlation-consistent polarized core-valence X-tuple-zeta) basis sets see Table 1.1. 

In the present work, correlation consistent basis sets have been developed for the transition metal atoms Y and Hg using small-core quasirelativistic PPs, i.e., the ns and (nA)d valence electrons as well as the outer-core (nA)sp electrons are explicitly included in the calculations. This can greatly reduce the errors due to the PP approximation, and in particular the pseudo-orbitals in the valence region retain some nodal structure. Series of basis sets from double-through quintuple-zeta have been developed and are denoted as cc-pVwZ-PP (correlation consistent polarized valence with pseudopotentials). The methodology used in this work is described in Sec. II, while molecular benchmark calculations on YC, HgH, and Hg2 are given in Sec. III. Lastly, the results are summarized in Sec. IV. 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

All methods employ a correlation-consistent polarized double-zeta basis set. 

A complementary paper was reported soon after by Adam, Bach and coworkers where eight transition structures for the epoxidation of the chiral allylic alcohol (Z)-3-methyl-3-penten-2-ol with peroxyformic acid were computed by the B3LYP density functional method with 6-31G(d) and 6-31G(d,p) basis sets. The four lowest-energy transition structures and their respective prereaction clusters were fuUy re-optimized by employing 6-31H-G(d,p) and correlation-consistent polarized valence triple- cc-pZTV basis sets. 

Examining the results given in these two tables, it is seen that, for this small molecule, very advanced calculations can be carried out. In the tables, all the methods employed have been introduced in the previous sections. For the basis sets, aug-cc-pVnZ stands for augmented correlation consistent polarized valence n zeta, with n = 2-5 referring to double, triple, quadruple, and quintuple, respectively. Clearly, these basis functions are specially designed for... 

The basis sets used in the reactions including F and Cl are the augmented correlation consistent polarized valence double zeta (aug-cc-pVDZ) sets [16]. In the reactions including Br and I, the relativistic effective core potential (ECP) due to Stevens et al. [17,18] and their associated basis sets were used for Br and I, and the cc-pVDZ set for H. The basis sets of Br and I were augmented by adding a d polarization function with an exponent of 0.389 (Br) / 0.266 (I) and sp diffuse functions with an exponent 0.03574 (Br) / 0.03007 (I). The diffuse p polarization function of the aug-cc-pVDZ set of H was omitted for consis-... 

FCI energies of the ground state and several excited states (3 12+, 2 ll, and 2 2A states) were obtained by Olsen et al. [66] in 1989 using a DZP basis set augmented with diffuse functions. These data have been used as tests for a wide variety of EOM/FR-CC methods, including CCSD [20, 24], CCSDT-la [44], CC3 [45], CCSDT-3 [46], and CCSDt [52], Later Hirata et al. [49] obtained FCI results with the 6-31G basis set. Shiozaki et al. [57] have obtained FCI results with the augmented correlation-consistent polarized valence double-zeta (cc-pVDZ) and valence triple-zeta (aug-cc-pVTZ) sets. 

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