Ayako Nakata

Time-dependent density functional theory calculations for core-excited states: Assessment of standard exchange-correlation functionals and development of a novel hybrid functional

A new hybrid functional for accurate descriptions of core and valence excitations, the core-valence Beckes three-parameter exchange (B3)+Lee-Yang-Paar (LYP) correlation functional (CV-B3LYP), is proposed. The construction of the new hybrid functional is based on the assessment that B3LYP performs well for properties concerning valence electrons and Beckes half-and-half exchange+LYP functional (BHHLYP), which includes 50% portion of Hartree-Fock exchange, performs well for core excitations. By using the appropriate portions of Hartree-Fock exchange for core and valence regions separately, CV-B3LYP overcomes the disadvantages of BHHLYP and B3LYP, which give inferior descriptions of valence and core excitations, respectively. Density functional theory (DFT) calculations with the CV-B3LYP functional reproduce core- and valence-orbital energies close to those of BHHLYP and B3LYP, respectively. Time-dependent DFT calculations with the CV-B3LYP functional yield both core- and valence-excitation energies with reasonable accuracy.

Hybrid exchange-correlation functional for core, valence, and Rydberg excitations: core-valence-Rydberg B3LYP.

The core-valence-Rydberg Beckes three-parameter exchange (B3)+Lee-Yang-Parr (LYP) correlation functional (CVR-B3LYP) is proposed as a means to improve descriptions of Rydberg excitations of core-valence B3LYP (CV-B3LYP). CV-B3LYP describes excitations from both core and occupied valence orbitals to unoccupied valence orbitals with high accuracy but fails to describe those to Rydberg orbitals. CVR-B3LYP, which adopts the appropriate portions of Hartree-Fock exchange for unoccupied valence and Rydberg regions separately, overcomes the disadvantage of CV-B3LYP. Numerical assessment confirms that time-dependent density functional theory calculations with CVR-B3LYP succeed in describing not only core excitations but also Rydberg excitations with reasonable accuracy.

Core-excitation energy calculations with a long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP)

We report the calculations of core-excitation energies of first-row atoms using the time-dependent density functional theory (DFT) and the long-range correction (LC) scheme for exchange-correlation functionals, including LC-BOP, Coulomb-attenuated method BLYP, and our recently developed LCgau-BOP method, which includes a flexible portion of short-range Hartree-Fock (HF) exchange through the inclusion of a Gaussian function in the LC scheme. We show that the LC scheme completely fails to improve the poor accuracy of conventional generalized gradient approximation functionals, while the LCgau scheme gives an accuracy which is an order of magnitude better than BLYP and significantly better than B3LYP. A reoptimization of the two parameters controlling the inclusion of short-range HF exchange in the LCgau method enables the errors to be reduced to the order of 0.1 eV which is competitive with the best DFT methods we are aware of. This reparametrization does not affect the LC scheme and therefore maintains the high accuracy of predicted reaction barrier heights. Moreover, while there is some loss in accuracy in thermochemical predictions compared to the previously optimized LCgau-BOP, rms errors in the atomization energies over the G2 test set are found to be comparable to B3LYP. Finally, we attempt to rationalize the success of the LC and LCgau schemes in terms of the well-known self-interaction error (SIE) of conventional functionals. To estimate the role of the SIE, we examine the total energy calculations for systems with a fractional number of electrons, not only in the highest occupied molecular orbital but also in the 1s-characterized core orbital. Our conclusion is that the inclusion of short-range HF exchange in LC-type functionals can significantly alleviate the problems of the SIE in the core region. In particular, we confirm that the absence of the SIE diagnostics in the core orbital energies correlates with the accurate prediction of core-excitation energies using the newly optimized LCgau approach.

Extension of the Core-Valence-Rydberg B3LYP Functional to Core-Excited-State Calculations of Third-Row Atoms

A modified core-valence-Rydberg Beckes three-parameter exchange (B3) + Lee-Yang-Parr (LYP) correlation (CVR-B3LYP) functional is proposed in order to calculate core-excitation energies of third-row atoms with reasonable accuracy. The assessment of conventional exchange-correlation functionals shows that the appropriate portions of Hartree-Fock (HF) exchange for core-excited-state calculations depend on shells:  70% and 50% for K-shell and L-shell excitations, respectively. Therefore, the modified CVR-B3LYP functional is designed to use the appropriate portions of HF exchange, 70%, 50%, and 20%, for K-shell, L-shell, and valence regions separately. Time-dependent density functional theory calculations with the modified CVR-B3LYP functional yield both K-shell and L-shell excitation energies with reasonable accuracy. The modified CVR-B3LYP also provides valence-excitation energies and standard enthalpies of formation accurately. Thus, the modified CVR-B3LYP describes all of the K-shell, L-shell, and valence electrons appropriately.

Application of the Sakurai-Sugiura projection method to core-excited-state calculation by time-dependent density functional theory

The Sakurai‐Sugiura projection (SS) method was implemented and numerically assessed for diagonalization of the Hamiltonian in time‐dependent density functional theory (TDDFT). Since the SS method can be used to specify the range in which the eigenvalues are computed, it may be an efficient tool for use with eigenvalues in a particular range. In this article, the SS method is applied to core excited calculations for which the eigenvalues are located within a particular range, since the eigenvalues are unique to atomic species in molecules. The numerical assessment of formaldehyde molecule by TDDFT with core‐valence Beckes three‐parameter exchange (B3) plus Lee‐Yang‐Parr (LYP) correlation (CV‐B3LYP) functional demonstrates that the SS method can be used to selectively obtain highly accurate eigenvalues and eigenvectors. Thus, the SS method is a new and powerful alternative for calculating core‐excitation energies without high computation costs.

Density functional theory for comprehensive orbital energy calculations

This study reveals the reason core 1s orbital energies and the highest occupied molecular orbital (HOMO) energies of hydrogen and rare gas atoms are underestimated by long-range corrected (LC) density functional theory (DFT), which quantitatively reproduces the HOMO energies of other systems and the lowest unoccupied molecular orbital (LUMO) energies. Applying the pseudospectral regional (PR) self-interaction correction (SIC) drastically improved the underestimated orbital energies in LC-DFT calculations, while maintaining or improving the accuracies in the calculated valence HOMO and LUMO energies. This indicates that the self-interaction error in exchange functionals causes the underestimations of core 1s orbital energies and the HOMO energies of hydrogen and rare gas atoms in LC-DFT calculations. To clarify the reason for the improvement, the fractional occupation dependences of total electronic energies and orbital energies were examined. The calculated results clearly showed that the LC-PR functional gives almost linear dependences of total electronic energies for a slight decrease in the occupation number of core 1s orbitals, although this linear dependence disappears for significant decrease due to the shrinking of exchange self-interaction regions. It was also clarified that the PRSIC hardly affects the occupation number dependences of the total electronic energies and orbital energies for the fractional occupations of HOMOs and LUMOs. As a result, it was concluded that core orbital energies are obtained accurately by combining LC-DFT with PRSIC.

Ab initio molecular dynamics study on the excitation dynamics of psoralen compounds

Ab initio molecular dynamics (AIMD) simulations are performed for studying the S0→T1 excitation dynamics of psoralen compounds; namely, nonsubstituted psoralen, 5-methoxypsoralen (5-MOP), and 8-methoxypsoralen (8-MOP). The density functional theory calculations at the B3LYP/D95V level are used for evaluating the atomic forces in every AIMD step. The specific behavior of 8-MOP in the T1 state, which has been reported by the experimental study, is found to be due to a unique open-ring structure, which leads to a different spin distribution in comparison with the cases of psoralen and 5-MOP and further to a crossing between the S0 and T1 states.

Efficient Calculations with Multisite Local Orbitals in a Large-Scale DFT Code CONQUEST.

Multisite local orbitals, which are formed from linear combinations of pseudoatomic orbitals from a target atom and its neighbor atoms, have been introduced in the large-scale density functional theory calculation code CONQUEST. Multisite local orbitals correspond to local molecular orbitals so that the number of required local orbitals can be minimal. The multisite support functions are determined by using the localized filter diagonalization (LFD) method [ Phys. Rev. B 2009 , 80 , 205104 ]. Two new methods, the double cutoff method and the smoothing method, are introduced to the LFD method to improve efficiency and stability. The Hamiltonian and overlap matrices with multisite local orbitals are constructed by efficient sparse-matrix multiplications in CONQUEST. The investigation of the calculated energetic and geometrical properties and band structures of bulk Si, Al, and DNA systems demonstrate the accuracy and the computational efficiency of the present method. The representability of both occupied and unoccupied band structures with the present method has been also confirmed.

Modified regional self-interaction correction method based on the pseudospectral method.

A modification of the regional self-interaction correction (RSIC) scheme (Tsuneda et al., J. Comput. Chem. 2003, 24, 1592), pseudospectral RSIC (PSRSIC), is proposed to eliminate the self-interaction errors (SIEs) especially in core regions. PSRSIC reduces the SIEs by substituting the HF exchange energy density calculated with the use of the pseudospectral technique for the exchange energy in the SI-domain region. PSRSIC is combined with the long-range correction (LC) scheme. TDDFT calculations with LC-PSRSIC yield all of the core-, valence-, Rydberg-, and charge-transfer-excitation energies with reasonable accuracy. Core-ionization energies are also well-reproduced by LC-PSRSIC.

On low-lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the CC bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values.