The static response function in Kohn-Sham theory: An appropriate basis for its matrix representation in case of finite AO basis sets

2014 ◽  
Vol 141 (13) ◽  
pp. 134106 ◽  
Author(s):  
Christian Kollmar ◽  
Frank Neese
Keyword(s):  
Response Function ◽  
Matrix Representation ◽  
Basis Sets ◽  
Static Response ◽  
Static Response Function

Static response function in superfluid4He

1992 ◽  
Vol 89 (1-2) ◽  
pp. 325-333 ◽  
Author(s):  
F. Dalfovo ◽  
S. Stringari
Keyword(s):  
Response Function ◽  
Static Response ◽  
Static Response Function

Response Function Basis Sets:  Application to Density Functional Calculations

1996 ◽  
Vol 100 (15) ◽  
pp. 6231-6235 ◽  
Author(s):  
Gerald Lippert ◽  
Jürg Hutter ◽  
Pietro Ballone ◽  
Michele Parrinello
Keyword(s):  
Response Function ◽  
Density Functional Calculations ◽  
Density Functional ◽  
Basis Sets

Matrix Approximations

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Matrix Representation ◽  
Finite Basis ◽  
Basis Set ◽  
Basis Sets ◽  
Dirac Matrix ◽  
The Matrix ◽  
Proper Account ◽  
Matrix Approximations

In quantum chemistry, regardless of which operators we choose for the Hamiltonian, we almost invariably implement our chosen method in a finite basis set. The Douglas– Kroll and Barysz–Sadlej–Snijders methods in the end required a matrix representation of the momentum-dependent operators in the implementation, and the regular methods usually end up with a basis set, even if the potentials are tabulated on a grid. Why not start with a matrix representation of the Dirac equation and perform transformations on the Dirac matrix rather than doing operator transformations, for which the matrix elements are difficult to evaluate analytically? It is almost always much easier to do manipulations with matrices of operators than with the operators themselves. Provided proper account is taken in the basis sets of the correct relationships between the range and the domain of the operators (Dyall et al. 1984), matrix manipulations can be performed with little or no approximation beyond the matrix representation itself. In this chapter, we explore the use of matrix approximations.

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