Vertical ionization potential benchmarks from Koopmans prediction of Kohn-Sham theory with long-range corrected (LC) functional.

The Kohn-Sham density functional theory (KS-DFT) with the long-range corrected (LC) functional is applied to the benchmark dataset of 401 valence ionization potentials (IPs) of 63 small molecules of Chong, Gritsenko and Baerends (the CGB set). The vertical IP of the CGB set are estimated as negative orbital energies within the context of the Koopmans' prediction using the LCgau-core range-separation scheme in combination with PW86-PW91 exchange-correlation functional. The range separation parameterµof the functional is tuned to minimize the error of the negative HOMO orbital energy from experimental IP. The results are compared with literature data, includingab initioIP variant of the equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD), the negative orbital energies calculated by KS-DFT with the statistical averaging of orbital potential, and those with the QTP family of functionals. The optimally tuned LC functional performs better than other functionals for the estimation of valence level IP. The mean absolute deviations (MAD) from experiment and from IP-EOM-CCSD are 0.31 eV (1.77%) and 0.25 eV (1.46%), respectively. LCgau-core performs quite well even with fixedµ(not system-dependent). Aµvalue around 0.36 bohr-1gives MAD of 0.40 eV (2.42%) and 0.33 eV (1.96%) relative to experiment and IP-EOM-CCSD, respectively. The LCgau-core-PW86-PW91 functional is an efficient alternative to IP-EOM-CCSD and it is reasonably accurate for outer valence orbitals. We have also examined its application to core ionization energies of C(1s), N(1s), O(1s) and F(1s). The C(1s) core ionization energies are reproduced reasonably [MAD of 46 cases is 0.76 eV (0.26%)] but N(1s), O(1s) and F(1s) core ionization energies are predicted less accurately.

Koopmans'-Type Theorem in Kohn-Sham Theory with Optimally Tuned Long-Range-Corrected (LC) Functionals.

In the present study, we have investigated the applicability of long-range-corrected (LC) functionals to a Kohn-Sham (KS) Koopmans'-type theorem. Specifically, we have examined the performance of optimally tuned LCgau-core functionals (in combination with BOP and PW86-PW91 exchange-correlation functionals) by calculating the ionization potential (IP) within the context of Koopmans' prediction. In the LC scheme, the electron repulsion operator, 1/r12, is divided into short-range and long-range components using a standard error function, with a range separation parameter µ determining the weight of the two ranges. For each system that we have examined (H2O, CO, benzene, N2, HF, H2CO, C2H4, and five-membered ring compounds cyclo-C4H4X, with X = CH2, NH, O, and S, and pyridine), the value of µ is optimized to minimize the deviation of the negative HOMO energy from the experimental IP. Our results demonstrate the utility of optimally tuned LC functionals in predicting the IP of outer valence levels. The accuracy is comparable to that of highly accurate ab initio theory. However, our Koopmans' method is less accurate for the inner valence and core levels. Overall, our results support the notion that orbitals in KS-DFT, when obtained with the LC functional, provide an accurate one-electron energy spectrum. This method represents a one-electron orbital theory that is attractive in its simple formulation and effective in its practical application.

Core-Level Excitation Energies of Nucleic Acid Bases Expressed as Orbital Energies of the Kohn-Sham Density Functional Theory with Long-Range Corrected Functionals.

The core electron binding energies (CEBEs) and core-level excitation energies of thymine, adenine, cytosine, and uracil are studied by the Kohn-Sham (KS) method with long-range corrected (LC) functionals. The CEBEs are estimated according to the Koopmans-type theorem for density functional theory. The excitation energies from the core to the valence π* and Rydberg states are calculated as the orbital energy differences between core-level orbitals of a neutral parent/cation and unoccupied π* or Rydberg orbitals of its cation. The model is intuitive, and the spectra can easily be assigned. Core excitation energies from oxygen 1s, nitrogen 1s, and carbon 1s to π* and Rydberg states, and the chemical shifts, agree well with previously reported theoretical and experimental data. The straightforward use of KS orbitals in this scheme carries the advantage that it can be applied efficiently to large systems such as biomolecules and nanomaterials.

Charge-Transfer Excitation Energies Expressed as Orbital Energies of Kohn-Sham Density Functional Theory with Long-Range Corrected Functionals.

Previously proposed theoretical schemes for estimating one-electron excitation energies using Kohn-Sham (KS) solutions with long-range corrected (LC) functionals are applied to the charge-transfer (CT) excitations of the ethylene···tetrafluoroethylene (C2H4-C2F4) system, and the CT complex between an aromatic donor (Ar = benzene, toluene, o-xylene, naphthalene, anthracene, and various meso-substituted anthracenes) and the tetracyanoethylene (TCNE) acceptor. The CT excited state is described well as a single-electron excitation between specific orbitals of donor and acceptor. Thus, CT excitation energies are well approximated by the orbital energies because of the satisfaction of the Koopmans-type theorem and the asymptotic behavior of the LC functional. We have examined three computational schemes: scheme 1 employs the orbital energies for the neutral and cationic systems, scheme 2 utilizes orbital energies of just the cation, and in scheme 3, because the electron affinity of a molecule is the ionization energy of its anion, a scale factor is applied to enforce this identity. The present schemes reproduce the correct asymptotic behavior of CT excitation energy of C2H4···C2F4 for the long intermolecular distances and give good agreement with accurate ab initio results. Calculated CT excitation energies for Ar-TCNE are compared with those of TD-DFT and ΔSCF methods. Scheme 1 with the optimal range-separation parameter µ accurately reproduces CT excitation energies for all Ar-TCNE systems and gives good agreement with the best TD-DFT calculations and experiment. Scheme 1, scheme 3, and TD-DFT show similar tendencies with respect to the variation in µ. Scheme 2 and ΔSCF approaches are rather insensitive to changes in µ, but both considerably underestimate the CT excitation energies for these systems. KS orbital energies are physically meaningful and they are practically useful; if the range-separation parameter is tuned, then good results can be obtained.