Configuration interaction singles based on the real-space numerical grid method: Kohn–Sham versus Hartree–Fock orbitals

Abstract

We developed a program code of configuration interaction singles (CIS) based on a numerical grid method. We used Kohn-Sham (KS) as well as Hartree-Fock (HF) orbitals as a reference configuration and Lagrange-sinc functions as a basis set. Our calculations show that KS-CIS is more cost-effective and more accurate than HF-CIS. The former is due to the fact that the non-local HF exchange potential greatly reduces the sparsity of the Hamiltonian matrix in grid-based methods. The latter is because the energy gaps between KS occupied and virtual orbitals are already closer to vertical excitation energies and thus KS-CIS needs small corrections, whereas HF results in much larger energy gaps and more diffuse virtual orbitals. KS-CIS using the Lagrange-sinc basis set also shows a better or a similar accuracy to smaller orbital space compared to the standard HF-CIS using Gaussian basis sets. In particular, KS orbitals from an exact exchange potential by the Krieger-Li-Iafrate approximation lead to more accurate excitation energies than those from conventional (semi-) local exchange-correlation potentials.

Approximations to the exact exchange potential: KLI versus semilocal

“…The KLI approximation to OEP, which has also been used for functionals other than EXX (e.g., self-interaction corrected [18][19][20][21] or MGGA [22][23][24] functionals) is an interesting alternative to the OEP since it avoids the numerical difficulties of EXX-OEP (very recent works are Refs. [25][26][27][28][29][30][31][32][33] in the case of EXX and Refs. 23 and 24 for MGGAs).…”

Update to ACE‐molecule: Projector augmented wave method on lagrange‐sinc basis set

“…[7][8][9] It provides the pseudopotential [7] and the PAW methods, various exchange-correlation functionals, and the exact exchange under the Krieger-Li-Iafrate approximation. [8] Other features, such as the geometry optimization, configuration interaction singles [9] and doubles, hybrid functionals, and linear response time-dependent DFT have been implemented; at present they are under performance tests. We will report the test results in near future.…”

“…Its details can be found in Refs. [7][8][9]. We carried out benchmark calculations for atoms and molecules in the AE6 test set, [19,20] and compared the results to those from a pseudopotential method.…”

“…Moreover, the type of basis sets and the parameters should be carefully chosen to obtain reliable computational results. [7][8][9] Grid-based methods are able to accurately span orbital spaces without predefined parameters; the error is determined only by the grid spacing. However, the grid-based methods need a large number of grid points, especially due to the rapidly varying electron density near nuclei.…”

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms

“…Recently, an implementation of random phase approximation (RPA) 12 appeared that uses an efficient imaginary time grid to yield temperature-independent RPA energy. The above mentioned methods are just a few examples of using efficient quadrature, a more extensive literature on the subject can be found in refs [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Thus, it is fair to say that extensive knowledge exist on representing temperature-independent quantities on a grid when ground state methods are used.…”