Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron

2013 ◽  
Vol 138 (12) ◽  
pp. 124101 ◽  
Author(s):  
Wei-Cheng Tung ◽  
Michele Pavanello ◽  
Keeper L. Sharkey ◽  
Nikita Kirnosov ◽  
Ludwik Adamowicz
Keyword(s):  
Gaussian Functions ◽  
Energy Gradient ◽  
Explicitly Correlated

scholarly journals Progress in calculating the potential energy surface of H 3 +

2012 ◽  
Vol 370 (1978) ◽  
pp. 5001-5013 ◽  
Author(s):  
Ludwik Adamowicz ◽  
Michele Pavanello
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Molecular Geometry ◽  
Computational Procedure ◽  
Energy Functional ◽  
Basis Functions ◽  
Vibrational States ◽  
Energy Gradient ◽  
Explicitly Correlated

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh–Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H rovibrational spectrum is reproduced at the 0.1 cm −1 accuracy level up to 16 600 cm −1 above the ground state.

scholarly journals An algorithm for calculating atomic D states with explicitly correlated Gaussian functions

2011 ◽  
Vol 134 (4) ◽  
pp. 044120 ◽  
Author(s):  
Keeper L. Sharkey ◽  
Sergiy Bubin ◽  
Ludwik Adamowicz
Keyword(s):  
Gaussian Functions ◽  
Explicitly Correlated
Sign in / Sign up

Export Citation Format

Share Document