scholarly journals Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions

2010 ◽  
Vol 132 (18) ◽  
pp. 184106 ◽  
Author(s):  
Keeper L. Sharkey ◽  
Sergiy Bubin ◽  
Ludwik Adamowicz
Keyword(s):  
Carbon Atom ◽  
Basis Functions ◽  
Energy Gradient ◽  
Variational Calculations ◽  
Explicitly Correlated ◽  
Gaussian Basis Functions

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.

Matrix Elements of One Dimensional Explicitly Correlated Gaussian Basis Functions

2019 ◽  
Vol 61 (1) ◽  
Author(s):  
Timothy Zaklama ◽  
David Zhang ◽  
Keefer Rowan ◽  
Louis Schatzki ◽  
Yasuyuki Suzuki ◽  
...  
Keyword(s):  
Basis Functions ◽  
Matrix Elements ◽  
One Dimensional ◽  
Explicitly Correlated ◽  
Gaussian Basis Functions
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