This paper is part of the 2012 Quantum Chemistry thematic issue.

A very accurate ground-state potential energy curve (PEC) of the He(2)(+) molecule is calculated with 1200 explicitly correlated Gaussian functions with shifted centers in the range between 0.9 and 100 a(0). The calculations include the adiabatic corrections determined for the (3)He(4)He(+), (3)He(2)(+), and (4)He(2)(+) isotopologues. The absolute accuracy of the PEC is better than 0.05 cm(-1) and that of the adiabatic corrections is around 0.01 cm(-1). The depths of the PECs augmented with the adiabatic corrections for the three isotopologues are: 19 956.708 cm(-1) for (4)He(2)(+), 19 957.054 cm(-1) for (3)He(4)He(+), and 19 957.401 cm(-1) for (3)He(2)(+). The rovibrational energies are also determined. For (3)He(4)He(+) the computed rovibrational transitions corresponding to the ν = 1-0 band differ from the experiment by less than 0.005 cm(-1). For the rovibrational transitions corresponding to the ν = 23-22 band the difference is around 0.012 cm(-1). Presently, this represents the best agreement between theory and experiment for He(2)(+).

We present very accurate calculations of the ground-state potential energy curve (PEC) of the LiH molecule performed with all-electron explicitly correlated Gaussian functions with shifted centers. The PEC is generated with the variational method involving simultaneous optimization of all Gaussians with an approach employing the analytical first derivatives of the energy with respect to the Gaussian nonlinear parameters (i.e., the exponents and the coordinates of the shifts). The LiH internuclear distance is varied between 1.8 and 40 bohrs. The absolute accuracy of the generated PEC is estimated as not exceeding 0.3 cm(-1). The adiabatic corrections for the four LiH isotopologues, i.e., (7)LiH, (6)LiH, (7)LiD, and (6)LiD, are also calculated and added to the LiH PEC. The aforementioned PECs are then used to calculate the vibrational energies for these systems. The maximum difference between the computed and the experimental vibrational transitions is smaller than 0.9 cm(-1). The contribution of the adiabatic correction to the dissociation energy of (7)LiH molecule is 10.7 cm(-1). The magnitude of this correction shows its importance in calculating the LiH spectroscopic constants. As the estimated contribution of the nonadiabatic and relativistic effects to the ground state dissociation energy is around 0.3 cm(-1), their inclusion in the LiH PEC calculation seems to be the next most important contribution to evaluate in order to improve the accuracy achieved in this work.

Explicitly correlated Gaussian functions with floating centers have been employed to recalculate the ground state potential energy surface (PES) of the H(3) (+) ion with much higher accuracy than it was done before. The nonlinear parameters of the Gaussians (i.e., the exponents and the centers) have been variationally optimized with a procedure employing the analytical gradient of the energy with respect to these parameters. The basis sets for calculating new PES points were guessed from the points already calculated. This allowed us to considerably speed up the calculations and achieve very high accuracy of the results.

Efficient optimization of the basis set is key to achieving a very high accuracy in variational calculations of molecular systems employing basis functions that are explicitly dependent on the interelectron distances. In this work we present a method for a systematic enlargement of basis sets of explicitly correlated functions based on the iterative-complement-interaction approach developed by Nakatsuji [Phys. Rev. Lett. 93, 030403 (2004)]. We illustrate the performance of the method in the variational calculations of H(3) where we use explicitly correlated Gaussian functions with shifted centers. The total variational energy (-1.674 547 421 Hartree) and the binding energy (-15.74 cm(-1)) obtained in the calculation with 1000 Gaussians are the most accurate results to date.