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Integrable singularity in the exact exchange calculations in hybrid functionals is an old and well-known problem in plane-wave basis. Recently, we developed a hybrid functional named Gaussian-attenuating Perdew-Burke-Ernzerhof (Gau-PBE), which uses a Gaussian function as a modified Coulomb potential for the exact exchange. We found that the modified Coulomb potential of Gaussian function enables the exact exchange calculation in plane-wave basis to be singularity-free and, as a result, the Gau-PBE functional shows faster energy convergence on k and q grids for the exact exchange calculations. Also, a tight comparison (same k and q meshes) between Gau-PBE and two other hybrid functionals, i.e., PBE0 and HSE06, indicates Gau-PBE functional as the least computational time consuming. The Gau-PBE functional employed in conjunction with a plane wave basis provides bandgaps with higher accuracy than the PBE0 and HSE06 in agreement with bandgaps previously calculated using Gaussian-type-orbitals. [ABSTRACT FROM AUTHOR]

A new simple and conceptual theoretical scheme is proposed for estimating one‐electron excitation energies using Kohn–Sham (KS) solutions. One‐electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two‐step process, ionization, and electron attachment. KS with long‐range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one‐electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies. [ABSTRACT FROM AUTHOR]

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms. [ABSTRACT FROM AUTHOR]

We have calculated the nuclear volume term (ln Knv) of the isotope fractionation coefficient ([variant_greek_epsilon]) between 235U–238U isotope pairs by considering the effect of ligand coordination in a U(IV)–U(VI) reaction system. The reactants were modeled as [UO2Cl3]- and [UO2Cl4]2- for U(VI), and UCl4 for U(IV). We adopted the Dirac–Coulomb Hartree–Fock method with the Gaussian-type finite nucleus model. The result obtained was ln Knv=0.001 90 at 308 K, while the experimentally estimated value of ln Knv is 0.002 24. We also discuss how the ligand affects the value of ln Knv, especially for the various structures of different compounds, and different ligands within the halogen ion series (F, Cl, and Br). [ABSTRACT FROM AUTHOR]

A cusp correction scheme for the relativistic zeroth-order regular approximation (ZORA) quantum Monte Carlo method is proposed by extending the nonrelativistic cusp correction scheme of Ma et al. [J. Chem. Phys. 122, 224322 (2005)]. In this scheme, molecular orbitals that appear in Slater–Jastrow type wave functions are replaced with the exponential-type correction functions within a correction radius. Analysis of the behavior of the ZORA local energy in electron-nucleus collisions reveals that the Kato’s cusp condition is not applicable to the ZORA QMC method. The divergence of the electron-nucleus Coulomb potential term in the ZORA local energy is remedied by adding a new logarithmic correction term. This method is shown to be useful for improving the numerical stability of the ZORA-QMC calculations using both Gaussian and Slater basis functions. [ABSTRACT FROM AUTHOR]

This paper discusses the nuclear volume dependence of uranium isotope fractionations in the U3+–U4+ and U4+–UO22+ systems by reference to a series of ab initio molecular orbital calculations. Nuclear volume-dependent terms (≡ln Knv) in isotope fractionation coefficients (≡[variant_greek_epsilon]) are calculated from the energetic balance of the isotopomers involved in the systems. We used the Dirac–Coulomb Hartree–Fock (DCHF) method with the Gaussian-type finite-nucleus model. We employed three types of generally contracted Gaussian basis sets to check the basis set dependences. In the U3+–U4+ system, the present values of ln Knv for uranium, other than those with the smallest double-zeta basis set, are in good agreement with previous values of ln Knv obtained from a numerical atomic multiconfigurational DCHF method with the Fermi-type finite-nucleus model. The present calculations reasonably reproduce the experimental value of [variant_greek_epsilon] in the U3+–U4+ system, and the value of ln Knv in the U4+–UO22+ system, obtained empirically by temperature-dependent fitting of the experimental [variant_greek_epsilon] values. For instance, in the U4+–UO22+ system, the present ab initio ln Knv value for a 235U–238U isotope pair is 0.002 09 using the largest basis set, while the experimental value is 0.002 24. This paper also shows that nuclear volume effects are negligibly small on the U–O bond length and two force constants of UO22+. Hence, the molecular vibrational terms of the isotope fractionation coefficients mainly depend on the nuclear mass rather than the nuclear volume. [ABSTRACT FROM AUTHOR]

The anharmonic vibrational frequencies of FHF- were computed by the vibrational self-consistent-field, configuration-interaction, and second-order perturbation methods with a multiresolution composite potential energy surface generated by the electronic coupled-cluster method with various basis sets. Anharmonic vibrational averaging was performed for the bond length and nuclear magnetic resonance indirect spin-spin coupling constants, where the latter computed by the equation-of-motion coupled-cluster method. The calculations placed the vibrational frequencies at 580 (ν1), 1292 (ν2), 1313 (ν3), 1837 (ν1+ν3), and 1864 cm-1 (ν1+ν2), the zero-point H–F bond length (r0) at 1.1539 Å, the zero-point one-bond spin-spin coupling constant [1J0(HF)] at 124 Hz, and the bond dissociation energy (D0) at 43.3 kcal/mol. They agreed excellently with the corresponding experimental values: ν1=583 cm-1, ν2=1286 cm-1, ν3=1331 cm-1, ν1+ν3=1849 cm-1, ν1+ν2=1858 cm-1, r0=1.1522 Å, 1J0(HF)=124±3 Hz, and D0=44.4±1.6 kcal/mol. The vibrationally averaged bond lengths matched closely the experimental values of five excited vibrational states, furnishing a highly dependable basis for correct band assignments. An adiabatic separation of high- (ν3) and low-frequency (ν1) stretching modes was examined and found to explain semiquantitatively the appearance of a ν1 progression on ν3. Our calculations predicted a value of 186 Hz for experimentally inaccessible 2J0(FF). [ABSTRACT FROM AUTHOR]

An efficient approximate scheme for density-functional theory (DFT) calculations, which eliminates the time-consuming self-consistent-field (SCF) procedure, is proposed using a dual-level DFT approach. In this approach, dual levels of basis sets and exchange-correlation functionals are adopted. The dual-level DFT approach is based on the idea that the total electron density in the ground state can be represented in terms of the density evaluated using the low-quality basis set and the low-cost exchange-correlation functional. Since the SCF procedure is avoided in the total energy evaluation, the dual-level DFT approach drastically reduces the computational cost. The applications of several dual-level DFT calculations to molecular systems show that our approach is more efficient than the self-consistent DFT approach with a moderate accuracy. [ABSTRACT FROM AUTHOR]

Using orthogonal localized occupied orbitals we have developed and implemented a parallelized local second-order Møller–Plesset (MP2) method based on the idea developed by Head-Gordon and co-workers. A subset of nonorthogonal correlation functions (the orbital domain) was assigned to each of the localized occupied orbitals using a distance criterion and excitations from localized occupied orbitals that were arranged into subsets. The correlation energy was estimated using a partial diagonalization and an iterative efficient method for solving large-scale linear equations. Some illustrative calculations are provided for molecules with up to 1484 Cartesian basis sets. The orbital domain sizes were found to be independent of the molecular size, and the present local MP2 method covered about 98%–99% of the correlation energy of the conventional canonical MP2 method. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report on the performance of the third-order Douglas-Kroll ab initio model potential (DK3-AIMP) method-based electron-correlated spin-orbit calculations. Our treatment assumes that the problem can be separated into a spin-free correlation treatment and a spin-orbit calculation. The correlation effects were calculated using the multistate complete active space second-order perturbation method, and the spin-orbit effects were treated by means of the restricted active space state interaction spin-orbit method, where the spin-orbit effects were approximated by the Douglas-Kroll type of atomic mean-field spin-orbit method. We used our method for illustrative calculations on the ground and low-lying electronic states of thorium monoxide. For a proper description of the inner core region in the spin-orbit calculations, an auxiliary spin-orbit basis set was introduced. The DK3-AIMP-based electron-correlated spin-orbit calculations on ThO yield good agreement with corresponding all-electron results and with the available experimental data. This confirms that the DK3-AIMP method can be easily combined with highly accurate correlation treatments and relativistic effects, both of which are vital for studying the actinides. To our knowledge, the literature contains no references to AIMP calculations on the low-lying states of ThO. [ABSTRACT FROM AUTHOR]

Recently, we proposed a simple yet efficient method for the computation of a long‐range corrected (LC) hybrid scheme [LC‐DFT(2Gau)], which uses a modified two‐Gaussian attenuating operator instead of the error function for the long‐range HF exchange integral. This method dramatically reduced the computational time while maintaining the improved features of the LC density functional theory (DFT). Here, we combined an LC hybrid scheme using a two‐Gaussian attenuating operator with one‐parameter progressive correlation functional and Becke88 exchange functional with varying range‐separation parameter values [LC‐BOP(2Gau) with various μ values of 0.16, 0.2, 0.25, 0.3, 0.35, 0.4, and 0.42] and demonstrated that LC‐BOP(2Gau) reproduces well the thermochemical and frontier orbital energies of LC‐BOP. Additionally, we revised the scaling factors of the Gaussian multipole screening scheme for LC‐DFT(2Gau) to correspond to the angular momentum of orbitals, which decreased the energy deviations from the energy with the no‐screening scheme. © 2018 Wiley Periodicals, Inc. The authors proposed a simple yet efficient method for the computation of a long‐range corrected (LC) hybrid scheme [LC‐DFT(2Gau)], which uses a modified two‐Gaussian attenuating operator instead of the error function for the long‐range HF exchange integral. This method dramatically reduced the computational time while maintaining the improved features of the LC density functional theory. The authors combined an LC scheme using a two‐Gaussian attenuating operator with OP correlation functional and Becke88 exchange functional with varying range‐separation parameter values [LC‐BOP(2Gau) with μ = 0.16–0.42] and demonstrated that LC‐BOP(2Gau) reproduces well the thermochemical and frontier orbital energies of LC‐BOP. [ABSTRACT FROM AUTHOR]

Studies a complete active space self-consistent field wave function transformed into a valence bond type representation built for nonorthogonal orbitals. Construction of the orbitals using Ruedenberg's projected localization procedure; Valence bond structures; Orbitals constituting the wave functions closest to the concept of the oldest valence bond method.

Accurate determination of both fundamental and optical gap is necessary for designing molecules relevant for organic photovoltaics. Here, we study how range-separated density functionals reproduce frontier orbital energies, HOMO (highest occupied molecular orbital)–LUMO (lowest unoccupied molecular orbital) gaps, and optical gaps for molecules relevant for organic photovoltaics. In this study, we consider 12 different range-separated density functional for computing HOMO energy, HOMO–LUMO gap, and optical gap which are compared with available experimental and reported GW values. We found that the reproduction of desired photovoltaic properties primarily depend on range separation parameter. Moreover, the tested functionals are comparable with OT-BNL functional. [ABSTRACT FROM AUTHOR]

In this article, we show that the long-range-corrected (LC) density functionals LC-BOP and LCgau-BOP reproduce frontier orbital energies and highest-occupied molecular orbital (HOMO)-lowest-unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6-311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO-LUMO gaps of LC-BOP and LCgau-BOP are better than those of recently proposed ωM05-D (Lin et al., J. Chem. Phys. 2012, 136, 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree-Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr−1 for the above test set molecules with LC-BOP functional and found our parameter value, 0.47 bohr−1, is usefully applicable to our tested systems. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

A density functional theory method using partially fixed molecular orbitals (PFMOs) is presented. The PFMOs, which have some fixed molecular orbital coefficients and are non-orthogonal, are a generalization of the extreme localized orbitals (ELMOs) of Couty, Bayse, and Hall (1997) Theor Chem Acc 97:96. A non-orthogonal Kohn-Sham method with these PFMOs is derived, and is applied to molecular calculations on the ionization potential of pyridine, the energy difference between cis- and trans-butadiene, the reaction barrier height of the cyclobutene-cis-butadiene interconversion, and the potential energy curve of the hydrogen shift reaction of hydroxycarbene to formaldehyde. The PFMO Kohn-Sham method reproduces well the results of the full Kohn-Sham method without having a restriction on the molecular orbital coefficients. The difference is less than 0.1 eV in the ionization potential and about 0.1 kcal/mol in the barrier height and in the potential energy calculations. [ABSTRACT FROM AUTHOR]

A highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) calculations over generally contracted spherical harmonic Gaussian-type spinors (GTSs) is presented. Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M[sub 2] (M=Cu, Ag, and Au), by the Dirac-Hartree-Fock (DHF) method were performed with a new four-component relativistic ab initio MO program package oriented toward contracted GTSs. The relativistic electron repulsion integrals (ERIs), the major bottleneck in routine DHF calculations, are calculated efficiently employing the fast ERI routine SPHERICA, exploiting the general contraction scheme, and the accompanying coordinate expansion method developed by Ishida. Illustrative calculations clearly show the efficiency of our computational scheme. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The anharmonic vibrational frequencies of FHF- were computed by the vibrational self-consistent-field, configuration-interaction, and second-order perturbation methods with a multiresolution composite potential energy surface generated by the electronic coupled-cluster method with various basis sets. Anharmonic vibrational averaging was performed for the bond length and nuclear magnetic resonance indirect spin-spin coupling constants, where the latter computed by the equation-of-motion coupled-cluster method. The calculations placed the vibrational frequencies at 580 (ν1), 1292 (ν2), 1313 (ν3), 1837 (ν1+ν3), and 1864 cm-1 (ν1+ν2), the zero-point H–F bond length (r0) at 1.1539 Å, the zero-point one-bond spin-spin coupling constant [1J0(HF)] at 124 Hz, and the bond dissociation energy (D0) at 43.3 kcal/mol. They agreed excellently with the corresponding experimental values: ν1=583 cm-1, ν2=1286 cm-1, ν3=1331 cm-1, ν1+ν3=1849 cm-1, ν1+ν2=1858 cm-1, r0=1.1522 Å, 1J0(HF)=124±3 Hz, and D0=44.4±1.6 kcal/mol. The vibrationally averaged bond lengths matched closely the experimental values of five excited vibrational states, furnishing a highly dependable basis for correct band assignments. An adiabatic separation of high- (ν3) and low-frequency (ν1) stretching modes was examined and found to explain semiquantitatively the appearance of a ν1 progression on ν3. Our calculations predicted a value of 186 Hz for experimentally inaccessible 2J0(FF). [ABSTRACT FROM AUTHOR]