scholarly journals Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions

2011 ◽  
Vol 7 (10) ◽  
pp. 3027-3034 ◽  
Author(s):  
Ewa Papajak ◽  
Jingjing Zheng ◽  
Xuefei Xu ◽  
Hannah R. Leverentz ◽  
Donald G. Truhlar
Keyword(s):  
Basis Functions ◽  
Basis Sets

Basis sets in the LCAO Xα method. On the use of bond-centered basis functions in second-row homonuclear diatomics

1985 ◽  
Vol 114 (5-6) ◽  
pp. 529-535 ◽  
Author(s):  
H. Jörg ◽  
N. Rösch ◽  
J.R. Sabin ◽  
B.I. Dunlap
Keyword(s):  
Basis Functions ◽  
Basis Sets

scholarly journals Performance of polarization-consistent vs. correlation-consistent basis sets for CCSD(T) prediction of water dimer interaction energy

2019 ◽  
Vol 25 (10) ◽  
Author(s):  
Teobald Kupka ◽  
Aneta Buczek ◽  
Małgorzata A. Broda ◽  
Adrianna Mnich ◽  
Tapas Kar
Keyword(s):  
Interaction Energy ◽  
Cardinal Number ◽  
Reference Value ◽  
Basis Functions ◽  
Water Dimer ◽  
Basis Set ◽  
Basis Sets ◽  
Complete Basis Set ◽  
Correlation Consistent ◽  
Consistent Basis

Abstract Detailed study of Jensen’s polarization-consistent vs. Dunning’s correlation-consistent basis set families performance on the extrapolation of raw and counterpoise-corrected interaction energies of water dimer using coupled cluster with single, double, and perturbative correction for connected triple excitations (CCSD(T)) in the complete basis set (CBS) limit are reported. Both 3-parameter exponential and 2-parameter inverse-power fits vs. the cardinal number of basis set, as well as the number of basis functions were analyzed and compared with one of the most extensive CCSD(T) results reported recently. The obtained results for both Jensen- and Dunning-type basis sets underestimate raw interaction energy by less than 0.136 kcal/mol with respect to the reference value of − 4.98065 kcal/mol. The use of counterpoise correction further improves (closer to the reference value) interaction energy. Asymptotic convergence of 3-parameter fitted interaction energy with respect to both cardinal number of basis set and the number of basis functions are closer to the reference value at the CBS limit than other fitting approaches considered here. Separate fits of Hartree-Fock and correlation interaction energy with 3-parameter formula additionally improved the results, and the smallest CBS deviation from the reference value is about 0.001 kcal/mol (underestimated) for CCSD(T)/aug-cc-pVXZ calculations. However, Jensen’s basis set underestimates such value to 0.012 kcal/mol. No improvement was observed for using the number of basis functions instead of cardinal number for fitting.

Development of new auxiliary basis functions of the Karlsruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD, def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations

2015 ◽  
Vol 17 (2) ◽  
pp. 1010-1017 ◽  
Author(s):  
Arnim Hellweg ◽  
Dmitrij Rappoport
Keyword(s):  
Basis Functions ◽  
Basis Sets ◽  
Scf Calculations

Optimized auxiliary basis sets RI-post-SCF calculations are reported for the moderately diffuse def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets.

scholarly journals Model Reduction of Systems With Localized Nonlinearities

2007 ◽  
Vol 2 (3) ◽  
pp. 249-266 ◽  
Author(s):  
Daniel J. Segalman
Keyword(s):  
Linear System ◽  
Structural Dynamics ◽  
Small Amplitude ◽  
Basis Functions ◽  
Basis Sets ◽  
Reduced Order Models ◽  
Linear Combinations ◽  
Reduced Order ◽  
Galerkin Solution ◽  
Good Agreement

An approach to development of reduced order models for systems with local nonlinearities is presented. The key of this approach is the augmentation of conventional basis functions with others having appropriate discontinuities at the locations of nonlinearity. A Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system very efficiently—employing small basis sets. This method is particularly useful for problems of structural dynamics, but may have application in other fields as well. For problems involving small amplitude dynamics, when one employs as a basis the eigenmodes of a reference linear system plus the discontinuous (joint) modes, the resulting predictions, though still nonlinear, are approximated well as linear combinations of the eigenmodes. This is in good agreement with the experimental observation that jointed structures, though demonstrably nonlinear, manifest kinematics that are well described using eigenmodes of a corresponding system where the joints are replaced by linear springs.

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