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.
Highlights
Growing interest in computational materials design[1,2,3,4,5] and quantum biology[6] has encouraged development of innovative methods for accurate electronic structure calculations of large systems.[7,8,9,10,11,12] Though quantum chemistry using atom-centred basis functions such as Gaussian basis sets shows unrivalled performance for small and medium size molecules in terms of computation costs, they face the limit of their capabilities in dealing with large systems
We investigated the features of KLI orbitals through comparison to HF orbitals and conventional KS orbitals obtained from local density approximation (LDA) and generalized gradient approximation (GGA).[29]
We found that the excitation energies from KS-configuration interaction singles (CIS) are relatively insensitive to the size of active space compared to HF-CIS
Summary
Growing interest in computational materials design[1,2,3,4,5] and quantum biology[6] has encouraged development of innovative methods for accurate electronic structure calculations of large systems.[7,8,9,10,11,12] Though quantum chemistry using atom-centred basis functions such as Gaussian basis sets shows unrivalled performance for small and medium size molecules in terms of computation costs, they face the limit of their capabilities in dealing with large systems. Most available codes using numerical grid basis sets adopt density functional theory (DFT) for ground state calculations and time-dependent DFT for excited state calculations.[7,8,9,10,16] Though (time-dependent) DFT offers a cost-effective way to describe large systems with reliable accuracy in many cases, it fails even qualitatively for strongly-correlated systems,[17,18] since it relies on a single-determinant approach. The so-called post-Hartree–Fock (post-HF) approaches may not be adequate for numerical grid basis sets, since the nonlocal HF exchange operator greatly reduces the sparsity of the Hamiltonian matrix and increases computational costs. The optimized effective potential (OEP) method which constructs a local potential from the nonlocal HF exchange energy can be employed to circumvent such a numerical burden. The Krieger–Li–Iafrate (KLI) approximation,[19,20,21,22,23] the localized HF method,[24,25,26] and the common energy denominator approximation[27,28] have been developed to implement EXX in a cost-effective manner
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