Explicitly correlated Gaussian functions basis sets

The symmetry requirements and the need to very effectively describe the correlation effects have been the main motivations that have turned our attention to explicitly correlated Gaussian functions as the choice for the basis set in the atomic and molecular non-BO calculations. These functions have been used previously in Born-Oppenheimer calculations to describe the electron correlation in molecular systems using the perturbation theory approach [35 2], While in those calculations, Gaussian pair functions (geminals), each dependent only on a single interelectron distance in the exponential factor, exp( pr ), were used, in the non-BO calculations each basis function needs to depend on distances between aU pairs of particles forming the system. 

It can be shown that the basis of spherical explicitly correlated Gaussian functions with floating centers (FSECG) form a complete set. These functions... 

The results for the non-BO diagonal polarizability are shown in Table XIII. Our best—and, as it seems, well-converged—value of a, 29.57 a.u., calculated with a 244-term wave function, is slightly larger than the previously obtained corrected electronic values, 28.93 and 28.26 a.u. [88,91]. It is believed that the non-BO correction to the polarizability will be positive and on the order of less than 1 a.u. [92], but it is not possible to say if the difference between the value obtained in this work and the previous values for polarizability are due to this effect or to other effects, such as the basis set incompleteness in the BO calculations. An effective way of testing this would be to perform BO calculations of the electronic and vibrational components of polarizability using an extended, well-optimized set of explicitly correlated Gaussian functions. This type of calculation is outside of our current research interests and is quite expensive. It may become a possibility in the future. As such, we would like the polarizability value of 29.57 a.u. obtained in this work to serve as a standard for non-BO polarizability of LiH. 

All explicitly correlated calculations were performed at the CCSD(F12) level of theory, as implemented in the TurbomOLE program [58, 69]. The Slater-type correlation factor was used with the exponent 7 = 1.0 aQ. It was approximated by a linear combination of six Gaussian functions with linear and nonlinear coefficients taken from Ref. [44]. The CCSD(F12) electronic energies were computed in an all-electron calculation with the d-aug-cc-pwCV5Z basis set [97]. For all cases we used full CCSD(F12) model (see Subsection 4.9 for the discussion about models implemented in Turbomole), the open-shell species were computed with a UHF reference wave function. The explicitly correlated contributions to the relative quantities are collected in Tables 10 and 11 under the label F12 . 

---