Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure

Ground state of Li and Be+^+ using explicitly correlated functions

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be$^+$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground state energies $-7.478 060 323 910 10(32)$, $-14.324 763 176 790 43(22)$ of Li and Be$^+$ correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128 functions we obtained about $10^{-9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.Comment: 15 page

Excited states of beryllium atom from explicitly correlated wave functions

A study of the first excited states of beryllium atom starting from explicitly correlated wave functions is carried out. Several properties are obtained and discussed focusing on the analysis of the Hund's rules in terms of the single--particle and electron pair intracule and extracule densities. A systematic study of the differences on the electronic distributions of the singlet and triplet states is carried out. The trial wave function used to describe the different bound states consists of a generalized Jastrow-type correlation factor times a configuration interaction model wave function. This model wave function has been fixed by using a generalization of the optimized effective potential method to deal with multiconfiguration wave functions. The optimization of the wave function and the calculation of the different quantities is carried out by means of the Variational Monte Carlo method.Comment: 28 pages, 6 figure

Explicitly correlated intermolecular distances and interaction energies of hydrogen bonded complexes

We have optimized the lowest energy structures and calculated interaction energies for the H2O–H2O, H2O–H2S, H2O–NH3, and H2O–PH3 dimers with the recently developed explicitly correlated CCSD(T)-F12 methods and the associated VXZ-F12 (where X=D,T,Q) basis sets. For a given cardinal number, we find that the results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. In general we find that CCSD(T)-F12 results obtained with the VTZ-F12 basis set are better than the conventional CCSD(T) results obtained with an aug-cc-pV5Z basis set. We also investigate two ways to reduce the effects of basis set superposition error with conventional CCSD(T), namely, the popular counterpoise correction and limiting diffuse basis functions to the heavy atoms only. We find that for a given cardinal number, these selectively augmented correlation consistent basis sets yield results that are closer to the complete basis set limit than the corresponding fully augmented basis sets. Furthermore, we find that the difference between standard and counterpoise corrected interaction energies and intermolecular distances is reduced with the selectively augmented basis sets

XH-stretching overtone transitions calculated using explicitly correlated coupled cluster methods

We have calculated XH-stretching (where X=O, C, F, Cl) fundamental and overtone transitions for three diatomics and a few small molecules using a local mode model. The potential energy curves and dipole moment functions are calculated using the recently developed explicitly correlated coupled cluster with single doubles and perturbative triples theory [CCSD_T_-F12] with the associated VXZ-F12 (where X=D, T, Q) basis sets. We find that the basis set convergence of calculated frequencies and oscillator strengths obtained with the explicitly correlated method is much more rapid than with conventional CCSD(T) and the Dunning type correlation consistent basis sets. Furthermore, CCSD(T)-F12 frequencies and oscillator strengths obtained with the VTZ-F12 and VQZ-F12 basis sets are found to be in excellent agreement with the CCSD(T) complete basis set limit. We find that comparison of CCSD(T)-F12 frequencies with experiment is less good. The inclusion of explicit correlation exposes the inherent error of the CCSD(T) method to overestimate vibrational frequencies, which is normally compensated by basis set incompleteness error. As a consequence, we suggest that conventional CCSD(T) in combination with the aug-cc-pVTZ or aug-cc-pVQZ basis sets is likely to yield calculated XH-stretching frequencies in closest agreement with experiment